Answer:
Options B and E.
Step-by-step explanation:
We want to see for which systems the point (-3, 2) is a solution (a solution of a system means that both equations intersect in that point).
The point (-3, 2) is a solution of the system only if this point belongs to both linear equations in the system.
Then for each system, we need to replace x by -3 and y by 2 in both equations and see if the equality is true or not.
A)
6x - y = 15
-3x + 4y = -18
In the first equation we have:
6*(-3) - (2) = 15
-18 - 2 = 15
-20 = 15
This is false, so we can discard option A.
B)
2x + y = -4
3x + 2y = -5
In the first equation we have:
2*(-3) + 2 = -4
-6 + 2 = -4
-4 = - 4
This is true, now let's look at the other equation.
3*(-3) + 2*(2) = -5
-9 + 4 = -5
-5 = - 5
This is also true, then the point (-3, 2) is a solution for both equations, then the point (-3, 2) is a solution for the system.
C)
x + 8y = 19
4x - 5y = 2
In the first equation we have:
(-3) + 8*(2) = 19
-3 + 16 = 19
13 = 19
This is false, then we can discard option C.
D)
8x + y = 22
-2x - 5y=4
In the first option we have:
8*(-3) + 2 = 22
-24 + 2 = 22
-22 = 22
This is false, so we can discard option D.
E)
5x - y = -17
x + 4y = 5
In the first option we have:
5*(-3) - (2) = -17
-15 - 2 = -17
-17 = -17
This is true, now let's look at the other equation:
(-3) + 4*(2) = 5
-3 + 8 = 5
5 = 5
This is also true, then the point (-3, 2) is a solution for both equations in the system, which means that the point (-3, 2) is a solution for the system.
Then the correct options are B and E.
What number is ten more than 21?
The number that is 10 more than 21 is 31, using the concept of addition.
Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").
Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.
Here, what we can do is use addition to find the number 10 more than 21.
= 21 + 10
= 31
Hence, the number 10 more than 21 is 31.
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what is the product of -8x^7 and -2xy^3
Answer:
16x^8y^3
Step-by-step explanation:
Simplify the expression.
Answer:
[tex]-8x^7(-2xy^3) = 16x^8y^3[/tex]
Step-by-step explanation:
⭐Multiplication rules
negative * negative = positivenegative * positive = negativepositive * positive = positive⭐ Exponent multiplication rule
[tex]a^n * a^m = a^{n+m}[/tex]⭐ Multiplying two terms with variables
multiply the coefficients (the numbers next to the variables) and the variablesWe need to utilize these 3 key points (⭐) when multiplying to terms with variables.
First, let's multiply the coefficients:
-8 * -2 = 16
negative * negative = positiveNext, let's multiply the variables:
[tex]x^7 * xy^3[/tex]
These two variables have the same base (x), so we will add their exponents up.
* remember: if you see a variable without an exponent, it has an exponent of 1 *
[tex]x^7 * x = x^8[/tex]
[tex]a^n * a^m = a^{n+m}[/tex]The variable [tex]y^3[/tex] will stay the same because there is no other y variable.
= [tex]x^8y^3[/tex]
Now, "attach" the variables to the product of the coefficients:
= [tex]16x^8y^3[/tex]
How do you find the degree of a polynomial step by step?
Put the polynomial in conventional form. Count the number of terms in the polynomial. The degree of the polynomial is one more than the number of terms.
Begin by writing the polynomial in standard form. This means that the terms should be written in descending order of degree, with the coefficient of the leading term being positive. Make sure that each term is separated by a plus or minus sign.Count the number of terms in the polynomial. Include the constant term, even if it is equal to zero.The degree of the polynomial is one more than the number of terms. For example, if the polynomial has two terms, its degree is three. If the polynomial has three terms, its degree is four.If the polynomial has an exponent that is not a whole number, it is called a rational polynomial. The degree of a rational polynomial is equal to the degree of the numerator of the rational expression. If the polynomial has a negative exponent, it is called an inverse polynomial. The degree of an inverse polynomial is equal to the negative of the exponent. If the polynomial is a combination of rational and inverse polynomials, the degree is equal to the highest
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Jonas knows the following information about the
19
1919 members in his travel group:
5
55 members have been to both the United States and Australia.
11
1111 members in total have been to the United States.
12
1212 members in total have been to Australia.
Can you help Jonas organize the results into a two-way frequency table?
Have been to the United States Have not been to the United States
Have been to Australia
Have not been to Australia
The complete two-way frequency table is shown below.
what is frequency table?
a table that displays the distribution of a characteristic's occurrence frequency in accordance with a specific set of class intervals.
explanation:
Denote the events as follows:
U = a member have been to the United States
NU = a member have not been to the United States
A = a member have been to Australia
NA = a member have not been to Australia
The information provided is:
A NA Total
U 5 __ 11
NU __ __ __
Total 12 __ 19
Complete the table as follows:
n (U ∩ NA) = n (U) - n (U ∩ A)
= 11 - 5
= 6
n (NU) = N - n (U)
= 19 - 11
= 8
n (NU ∩ A) = n (A) - n (U ∩ A)
= 12 - 5
= 7
n (NA) = N - n (A)
= 19 - 12
= 7
n (NU ∩ NA) = n (NA) + n (U ∩ NA)
= 7 - 6
= 1
Therefore, the complete 2-way Frequency table is:
A NA Total
U 5 6 11
NU 7 1 8
Total 12 7 19
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Select all the true statements.if vertical angles are congruent, then two lines cut by a transversal are parallel. if two parallel lines are cut by a transversal, then corresponding angles are congruent. if two parallel lines are cut by a transversal, then alternate interior angles are congruent. points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints. points on a perpendicular bisector of a line segment are never equidistant from the segment’s endpoints.
By the property of alternate interior angles, Option (1) is the correct statement.
∠XWY ≅ ∠ZYW
Property of the alternate angles states, if two parallel lines are cut by a transversal, then the alternate angles are congruent.
By this property,
Lines XW and YZ are the parallel lines intersected by a transversal WY.
Here, ∠XWY and ∠ZYW represent the interior angles between the parallel lines and the transversal.
Therefore, interior alternate angles ∠XWY and ∠ZYW will be congruent.
Hence, Option (1) will be the correct option.
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What is the function of rational root theorem?
A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.
A polynomial expression is given and after solving them we get the two values known as the roots of the function.
These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .
We should use the rational root theorem only when the value of coefficients are small.
The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,
p is an integer factor of the constant term a0, and
q is an integer factor of the leading coefficient an.
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he cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810.
What is the administration fee?
$50
$54
$55
$60
The one-time administration fee is (d) $60
How to determine the administration fee?From the question, we have the following parameters that can be used in our computation:
12 months costs $660.
15 months costs $810.
This means that
(x, y) = (12, 660) and (15, 810)
For the one-time administration fee, we have
(x, y) = (0, y)
So, we calculate the slope using
slope = (y₂ - y₁)/(x₂ - x₁)
So, we have
(y - 660)/(0 - 12) = (810 - 660)/(15 - 12)
This gives
(660 - y)/12 = 50
So, we have
660 - y=600
This gives
y = 60
Hence, the administration fee is $60
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Chen rode his skateboard 3 3/4 miles in 3/4 of an hour. What was his average speed in miles per hour?
A 2 13/16
B 4
C 4 1/2
D 5
The average speed of Chen when skating is 5 miles per hour
How to determine the average speed of Chen ?From the question, we have the following parameters that can be used in our computation:
Time = 3/4 of an hour
Distance covered = 3 3/4 miles
The average speed can be calculated using the following equation
Average speed = Distance covered/Time
Substitute the known values in the above equation, so, we have the following representation
Average speed = (3 3/4)/(3/4)
Evaluate the quotient
Average speed = 5
Hence, the average speed is 5 miles per hour
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Find the solution to the following system by substitution.
y=-2x-3
y = 3x + 12
O A. (-1/2, 3/)
O B. (3,21)
O
C. (-3,3)
о
D. (-3,-9)
I need help with this
The value of function (f + g)(x) is 7x² + x - 4.
What is the function?A function is an expression, rule, or law in mathematics that defines a relationship between a single variable (the independent variable) and then another variable (the dependent variable).Here the functions provided are,
f(x) = 4x² - 5x
g(x) = 3x² + 6x - 4
The p addition property of functions (f + g)(x) allows them to be written as,
(f + g)(x) = f(x) + g(x)
In the above equation, we can substitute the values of each function.
(f + g)(x) = 4x² - 5x + 3x² + 6x - 4
We have to combine the similar terms,
(f + g)(x) = 4x² - 5x + 3x² + 6x - 4
= 7x² + x - 4
So (f + g)(x) = 7x² + x - 4
Therefore the correct answer is option B.
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How do you explain what a function is?
A function is a mathematical relationship between the domain and the range, two sets of values. The range is the set of output values that the function produces, and the domain is the set of input values for which it is defined.
What is a function, exactly?
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
Consider the function f(x) = x^2 as an illustration. This function generates the value f from the supplied value x. (x). This function will return the value 9 if the given value is 3, since 3^2 = 9.
Generally speaking, a function describes the relationship between two sets of values (the domain) (the range). For instance, the relationship between the input value x and the output value f(x) is described by the function f(x) = x^2.
A formula, which is a guide that explains how to calculate the output value for a specific input value, is typically used to express a function. For instance, the function f(x) = x^2 has the formula f(x) = x^2. We just enter the input value into the formula and simplify to determine the output value for a particular input value.
A fundamental idea in mathematics, functions are used to model and describe a wide variety of real-world occurrences. For instance, the quadratic function f(x) = x^2 + 2x + 1 can be used to simulate how an item would move in the presence of gravity. A population's expansion over time can be predicted using the exponential function f(x) = 3^x.
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How do you write a geometric function?
A geometric sequence is an exponential function. Instead of y=ax, we write an=crn where r is the common ratio and c is a constant (not the first term of the sequence, however). A recursive definition, since each term is found by multiplying the previous term by the common ratio, ak+1=ak * r.
Geometric function theory is the study of geometric properties of analytic functions. A fundamental result in the theory is the Riemann mapping theorem.
There are many shapes in geometry based on their dimensions. Circle, Triangle, Square, Rectangle, Kite, Trapezium, Parallelogram, Rhombus and different types of polygons are the 2-d shapes. Cube, Cuboid, Sphere, Cone and Cylinder are the basic three-dimensional shapes.
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How do you find the height of a pyramid if you know the length and slant height?
The height of pyramid if the length and slant height is known is . h² = S² - (x/2)².
Define the term height of a pyramid?The perpendicular distance between a pyramid's base and apex determines the pyramid's height. The altitude of the pyramid is the length of the line that extends from the base to the apex and is perpendicular to the base.We can employ the Pythagoras theorem to accomplish this as the triangle is right-angled and is created by the slant height (s), its altitude (h), and 1⁄2 of side length of a base (x/2).
As a result, (x/2)² + h² = s².
We can utilize this while figuring out how to find the pyramid's volume given the slant height.
h² = S² - (x/2)²
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A tailor cuts 234 yards from a roll of fabric to make one curtain. She has 1812 yards of fabric available to make curtains. Use the drop-down menus to answer each question.
The symbol that should be used is the division symbol. On the other hand, in the result the whole number represents the number of curtains, while the fraction represents a fraction of the next curtain.
Given :
The numerator: Number above.
The denominator: Number below.
A whole number: Optional element.
The number of curtains the tailor can make is equal to the total fabric divided by the fabric required for one curtain. Based on this, the symbol should be ÷.
= 18 1/2 ÷ 2 3/4
The whole number represents the number of curtains. The division of the total fabric and the total fabric required for one curtain will include a whole number and a fraction. In this situation, the whole number represents the number of curtains that can be made from the total fabric.
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how to cross multiply fractions with whole numbers
If you simply multiply the numerator, which is the top number on the bar, you can multiply a fraction by a full number.
What are fractions and whole numbers?A number that is not negative and doesn't have any fractional or decimal components. Anything that isn't a whole number is a fraction. most often expressed with a numerator (top) and denominator (bottom). All fractions should ideally be "correct" fractions, that is, less than 1.
You can multiply a fraction by a whole number by only multiplying the numerator which is the top number on the bar. for example:
E = 2 x 3/4
E = 6/4
E = 1²/₄
Hence, If you simply multiply the numerator, which is the top number on the bar, you can multiply a fraction by a full number.
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Graph the line. 2x+y=8
Answer:
Step-by-step explanation:
put it into the y=mx+c equation
y=-2x+8
therefore th y intercept is at (0,8)
and the gradient in -2
What is the median of 25 and 29?
The median of the set of numbers 25 and 29 is 27. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.
The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 25 and 29. When we order this set from least to greatest, we get 25, 29. There are two numbers in this set, so the median is the average of the two middle numbers, which is the only number in the set. The only number in this set is 27, so the median is 27.
To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are two numbers in the set, so the median is the average of the two middle numbers.
In summary, the median of the set of numbers 25 and 29 is 27. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.
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What are the factors of x³ 4x² x 6?
The factors of x³ 4x² x 6 are (1) x³, (2) 4x², (3) x and (4) 6. These factors are the numbers that can be multiplied together to give x³ 4x² x 6 as the product.
To find the factors of x³ 4x² x 6, we must first expand the expression. x³ 4x² x 6 can be expanded to x³ x x 4x² x 6, which can be further simplified to x³ + 4x² + 6. The factors of this expression are the numbers that can be multiplied together to give x³ 4x² x 6 as the product. In this case, the factors are (1) x³, (2) 4x², (3) x, and (4) 6. In other words, x³ 4x² x 6 can be written as (x³)(4x²)(x)(6). Understanding the factors of an expression is an important skill in algebra, as it can help you simplify and solve equations.
The factors of x³ 4x² x 6 can be calculated by factoring the expression:
x³ 4x² x 6 = (x³)(4x²)(x)(6)
This can be further simplified to:
x³ 4x² x 6 = x⁴ (4x²)(6)
Therefore, the factors of
x³ 4x² x 6 are (1) x³, (2) 4x², (3) x, and (4) 6.
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What is the slope of 3x y =- 12?
The slope of the given straight line equation 3x+y=-12 is m=-3.
How slope can be find on graph?Finding the change in values divided by the change in values will reveal the slope between two places. As long as the line is linear, you can really use any two locations along the line to get the slope (straight line). An easy approach to do it is to use the end points since they are provided.
What are four types of slope?Negative, positive, zero and undefined are four types of slope.
The equation is given as:
3x+y= -12
Separate y we get:
y= -3x-12
This is a straight line equation and we can compare it with y=mx+c where m is the slope.
Upon comparison with general equation slope m=-3.
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in how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major?
There probability two ways to pick two representatives with one majoring in mathematics and the other majoring in computer science.
In order to pick two representatives with one majoring in mathematics and the other majoring in computer science, there are two approaches that can be taken. The first approach is to pick one representative who majors in mathematics first, then the second representative who majors in computer science. The second approach is to pick one representative who majors in computer science first, then the second representative who majors in mathematics. Both of these approaches would yield two representatives, one with a mathematics major and the other with a computer science major. It is important to note that whichever approach is taken, both representatives must be chosen from the same pool of potential representatives. Thus, the pool of potential representatives should be large enough to encompass both mathematics and computer science majors in order to successfully pick two representatives with one majoring in mathematics and the other majoring in computer science.
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What is the difference between a figure also called a pre-image and an image?
The image is the final appearance of a figure after a transformation operation. The pre-image is the original appearance of a figure in a transformation operation.
What is transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.
Preimages are the original, unaltered shapes, and images are the new (transformed) shapes. To put it another way, a transformation is a process that maps a preimage onto an image.
Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.
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At a supermarket, shopping trolleys are 1 meter long. Your friend works by collecting them and stacking them into an area. Each shopping trolley in the stack adds on 0.25 m. How many trolleys could be stacked in a single line of 10 metres?
Answer:
If each shopping trolley is 1 meter long, and each trolley in the stack adds 0.25 meters, then the total length of the stack will be equal to the length of each trolley plus the length added by each additional trolley in the stack. This means that the total length of the stack will be equal to 1 + 0.25 = 1.25 meters per trolley.
If the stack has a total length of 10 meters, and each trolley adds 1.25 meters to the stack, we can divide the total length by the length added by each trolley to find the number of trolleys that can be stacked in a single line of 10 meters:
10 / 1.25 = <<10/1.25=8>>8 trolleys
Therefore, if each shopping trolley is 1 meter long and each trolley in the stack adds 0.25 meters, a single line of 10 meters could hold a stack of 8 trolleys.
Step-by-step explanation:
Please help !!!!!!!!
Answer: 64.5 hours
Step-by-step explanation:
2580 divided by 40
A windowpane is 63 inches tall and the diagonal distance from one corner to the other is 65 inches. How wide is the windowpane?
Answer:
16 inches
Step-by-step explanation:
Using the Pythagorean theorem, the distance is [tex]\sqrt{65^2-63^2}=16[/tex].
HELP ME PLEASE : Math is a bit different at the North Pole. Can you solve this math with Christmas symbols problem?
The sum of the two Santa models is 24.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is math is a bit different at the north pole and a problem is shown in the image.
We can assume the three variables as : [x], [y] and [z]. So, we can write the equations as -
3x = 21 ........ Eq[1]
y + z = 16 ........ Eq[2]
x + y - z = - 1 ........ Eq[3]
Now, it is given that -
3x = 21
x = 21/3
x = 7
and
y + z = 16
y = 16 - z
So, we can write the equation as -
x + y - z = - 1
7 + 16 - z - z = - 1
23 - 2z = - 1
2z = 24
z = 12
So, we can write -
[z] + [z] = 12 + 12 = 24
Therefore, the sum of the two Santa models is 24.
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Two brothers, Leo and William, are racing their bikes around
a 9.5-mile loop. Since Leo is younger, he is given a 1.5-mile
head start. The graph to the right shows Leo's progress.
The expression 19x can be used to determine y, the distance
in miles that William has traveled after x hours have passed.
Which statement about this situation is not true?
A. William is traveling at a faster speed than Leo.
B. The difference between their speeds is exactly
1.5 miles per hour.
C. Leo traveled only 8 miles during the race.
D. Both brothers will finish the race in 1/2 hour.
The incorrect answer is b) The difference between their speeds is exactly 1.5 miles per hour.
What is distance?
The distance between two sites is the length of the route. The metre is the SI unit for distance.
What is speed?
The speed at which an object’s location changes in any direction. The distance travelled divided by the time it took to travel that distance is how fast something is moving.
What is time?
The amount of time that something happens, goes through a process, or remains the same.
Let distance be Y and time be X.
Distance (Y) travelled by William after X hours;
Y= 19X
Speed of Leo = [tex]\frac{distance}{time}[/tex]
= [tex]\frac{8}{0.5}[/tex]= 16 m/hr
Difference in speed= 19-16= 3m/hr
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Enter the correct answer in the box.
This graph represents a transformation of the parent cube root function.
Graph shows a radical function plotted on a coordinate plane. A curve enters quadrant 3 at (minus 10, minus 3.2), goes through (minus 4, minus 3), (0, minus 2.5), data point (3, minus 1), (5, 0), and exits quadrant 1.
Replace the values of h and k to create the equation of the transformed function.
Replacing the values of h and k to create the equation of the transformed function gives us; y = [∛(x - 4)] - k
What function does the graph represent?The graph represents a transformation of the parent cube root function.
The parent cube root function is; y = ∛x
In this parent function, we see that the value of h and k are equal to 0. Where;
h = 0, k = 0 in parent function
Then the graph changes direction at the coordinate (0,0) in parent function.
From the given graph, we can see that it changes direction at the coordinate (4,-1)
This tells us that the graph is shifted by 4 units to the right and then by 1 unit downwards.
Thus, it means that the value of h = 4 and the value of k = 1.
Thus, the equation of the transformed function will be written as;
y = [∛(x - 4)] - k
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The tables show functions representing the growth of two types of bacteria on certain days within an experiment that lasted a total of 10 days. How do the functions in the table compare? since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria b than bacteria a at the start. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria b than bacteria a at the start. Since the maximum value in the table for bacteria a is greater than the maximum value in the table for bacteria b, bacteria a has a faster growth rate than bacteria b. Since the minimum value in the table for bacteria a is less than the minimum value in the table for bacteria b, bacteria a has a slower growth rate than bacteria b.
False , the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
Given :
A. Since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
False, it is the y-intercept of the function that indicates the amount at the start of the experiment.
B. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
True, the y-intercept is given when x = 0, indicating the initial value of the function.
C. Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.
False, because the maximum value of each table is given in different times, and also the initial value of each table is different.
D. Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.
False, the growth rate is not given by the inicial value. If we model both tables with an exponential function, the count of bacteria A quadruped in two days, and the count of bacteria B doubled in one day, so they have the same growth rate.
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Full question :
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The Abubakar family household uses 850 kWh of electricity per month (kWh stands for Kilowatt hour, a measure of electricity usage). They want to decrease their electricity usage, so they begin to decrease their usage by 25 kWh per month. The equation y = –25x + 850 can be used to model this scenario.
How many kWh of electricity will they be using 12 months after they've started doing this?
Answer:
550 kWh
Step-by-step explanation:
To find the number of kilowatt hours of electricity the Abubakar family will be using 12 months after they've started decreasing their usage, we can substitute 12 for x in the equation y = –25x + 850. This gives us y = –25 * 12 + 850 = –300 + 850 = 550.
Therefore, the Abubakar family will be using 550 kilowatt hours of electricity 12 months after they've started decreasing their usage.
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