The roots of the quadratic equation 4x² + 4√3x - 3 = 0 are two distinct imaginary roots.
To find the roots of a quadratic equation, we have to use the quadratic formula. The formula is x = [-b ± √(b² - 4ac)]/2a. In this case, a = 4, b = 4√3, and c = -3. Plugging in the values, we get x = [-4√3 ± √(4√3² - 4*4*(-3))]/8. Simplifying and solving, we get x = [-2i ± √12]/4. Since both solutions contain an imaginary component, this means that the roots of the equation are two distinct imaginary roots.
x = [-4√3 ± √(4√3² - 4*4*(-3))]/8
x = [-4√3 ± √(48)]/8
x = [-2i ± √12]/4
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help please!!!
Find the value of x.
13
13
X!
24
Answer:
x = 5 units
Step-by-step explanation:
since it is an isosceles triangle, the perpendicular "x" bisects the base (24) into two units of 12.
using the Pythagorean theorem:
x² = 13² - 12² = 169 - 144 = 25
x = √25 = 5
The measure of ∠ABD is (0.18x+56)° and the measure of ∠CBD is (0.07x+46)°. Find the value of x.
Answer:
x = 312
Step-by-step explanation:
We know that ∠ABD and ∠CBD are supplementary, meaning their measures add up to 180°. We can use this knowledge to put both measures into an equation.
[tex](0.18x+56) + (0.07x+46)= 180[/tex]
Simplify.
[tex]0.18x+56 + 0.07x+46= 180[/tex]
Simplify.
[tex]0.25x + 102 = 180[/tex]
Subtract 102.
[tex]0.25x = 180 - 102[/tex]
Simplify.
[tex]0.25x = 78[/tex]
Divide by 0.25
[tex]x = \frac{78}{0.25}[/tex]
Simplify.
[tex]x = 312[/tex]
A 23.7-foot tall flagpole casts a 42-foot shadow. What is the angle that the sun hits the flagpole? Express your answer in DMS
Answer:
60.6°
Step-by-step explanation:
Using trigonometry :
Opposite = Height of shadow = 42 feets
Adjacent = height of flagpole = 23.7 feets
Tan θ = opposite / Adjacent
Tan θ = height of shadow / height of flagpole
Tan θ = 42 / 23.7
Tan θ = 1.7721518
θ = tan^-1(1.7721518)
θ = 60.56
θ = 60.6°
Describe the translation below using words and then write a rule for it.
PLEASEPLEASE ANSWER
and if i get any more bots answering with links im gonna cry ive put this question 5 times
Answer:
x = 7
Step-by-step explanation:
A triangle's total interior angle measurement will equal 180°.
Set all measurements equal to 180:
(82) + (9x - 6) + (6x - 1) = 180
Simplify. Combine like terms:
(82 - 6 - 1) + (9x + 6x) = 180
(82 - 7) + (15x) = 180
(75) + 15x = 180
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, Subtract 75 from both sides of the equation:
15x + 75 = 180
15x + 75 (-75) = 180 (-75)
15x = 180 - 75
15x = 105
Next, divide 15 from both sides of the equation:
(15x)/15 = (105)/15
x = 105/15
x = 7
7 is your value for x.
~
Complete the proof.
Given:
AB∙BP=CB∙BM
Prove: ∆CBA~∆PBM
Answer:
Step-by-step explanation:
5. Give in the question.
6. AB/CB = BM/BP (Not sure about the rule, you can find it on textbook I guess)
7. CBA = PBM
8. Conclusion
A city has a population of 340, 000 people. Suppose that each year the population grows by 3.75%. What will the population be after 10 years ? Use the calculator provided and round your answer to the nearest whole number.
Answer:
491,315.
Step-by-step explanation:
Population in 10 years = 340000(1.0375)^10
= 491,315.
Solve the system.
2x + y = 3
-2g = 14 – 6x
Write each equation in slope-intercept form.
Answer:
x = 2, y = -1
Step-by-step explanation:
Assuming it should be y not g
y = -2x + 3
-2y = -6x + 14
y = 3x - 7
-2x + 3 = 3x - 7
10 = 5x
x = 2
y = -1
find the quotient 12/15÷6/11
Answer:
.8
Step-by-step explanation:
A box contains four equal-sized cards labeled 1 , 3, 5, and 7. Tim will select one card from the box. What is the probability that Tim will select a card labeled 3?
Answer: 1/4
Step-by-step explanation:
Since the box box contains four equal-sized cards labeled 1 , 3, 5, and 7. The probability of selecting any number out of the four numbers will be 1/4 if they are selected once.
If Tim selects one card from the box, the probability that Tim will select a card labeled 3 will be: = 1/4
This is because 3 only occurs once and there are 4 numbers in total.
Hey can someone tell me what -3x^2(14x^2-2x-8) equals
Answer:
-42x^4 + 6x^3 + 24x^2
Step-by-step explanation:
Help Please I put 70 pts on this
The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, sold by the company:
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x = 1 to x = 4, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
Answer: A) intercepts: zero profit; maximum: maximum profit. increasing: x < 4; decreasing x > 4
B) average slope: ≈50, about $50 increased profit for each $1 increase in price.
Step-by-step explanation:
A) The vertical axis of the graph represents profit, so the x-intercepts represent prices that produce zero profit. The maximum value of the graph is the maximum profit that can be obtained for any price.
The function is increasing for all prices below the one producing maximum profit (x < 4). The function is decreasing for all prices above the one producing maximum profit (x > 4). Obviously profit is increasing with price for x < 4, and is decreasing with price for x > 4.
__
B) We read the value of f(1) from the graph to be about 120, so the average rate of change is about ...
(f(4) -f(1))/(4 -1) = (270 -120)/(3) = 50
The average rate of change from x=1 to x=4 is about 50.* This means profit will increase on average $50 for each $1 increase in price in that interval.
_____
* If we take the peak profit to be $270, we can write f(x) as ...
f(x) = 16.875x(x -8)
Then f(1) = 118.125 and the average rate of change is 50.625. For the purpose here, we judge the extra precision to be pointless.
Step-by-step explanation:
A) Intercepts zero profit; maximum: maximum profit. increasing: x < 4; decreasing x > 4
B) average slope: ≈50, about $50 increased profit for each $1 increase in price.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
A) The vertical axis of the graph represents profit, so the x-intercepts represent prices that produce zero profit. The maximum value of the graph is the maximum profit that can be obtained for any price.
The function is increasing for all prices below the one producing maximum profit (x < 4). The function is decreasing for all prices above the one producing maximum profit (x > 4). Profit is increasing with price for x < 4, and is decreasing with price for x > 4.
B) The value of f(1) from the graph to be about 120, so the average rate of change is about.
(f(4) -f(1))/(4 -1) = (270 -120)/(3) = 50
The average rate of change from x=1 to x=4 is about 50.* This means profit will increase on average $50 for each $1 increase in price in that interval.
If we take the peak profit to be $270, we can write f(x) as:
f(x) = 16.875x(x -8)
Then f(1) = 118.125 and the average rate of change are 50.625. For the purpose here, we judge the extra precision to be pointless.
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what is the slope of the graph in the picture?
Answer:
slope is 2
Step-by-step explanation:
Pick any two points
say point (0,0) and point (2, 4)
to find slope, subtract the x and y coordinates as a fraction.
y on the top, x on the bottom
y/x = (4 -0)/ (2-0) = 4/2 = 2
Which expression can be used to find measure angle R
Answer:
cos-1(-4/14)
Step-by-step explanation:
If
4.5=r
3.5=s
2=t
By law of cosines:
[tex]r^{2}=s^{2}+t^{2} -2st cosR\\\\CosR= \frac{r^{2} -s^{2} -t^{2} }{-2st} \\\\R=cos^{-1} (\frac{(4.5)^{2}-3.5^{2} -2^{2} }{-2(3.5)(2)} )\\R= cos^{-1} (-\frac{4}{14} )[/tex]
What are the degree and leading coefficient of the polynomial?
Answer:
Degree: 9
Coefficient: -1
Step-by-step explanation:
The degree of a polynomial is equivalent to the highest degree of all its terms.
The term with the highest degree in this polynomial is y^9
what is the awnser to 65.9- 45.902=
Answer:
19.998? or is there something else to it
For each triangle find the value of x
Answer:
x = 20
Step-by-step explanation:
The sum of the angles in a triangle is 180. A right triangle has one angle of 90. Thus, the sum of the other two angles will be 90. So, 90+31 = 121 and 180-121 = 59. (3x-1) = 59. Solve for x. This would mean that x would be 20. 3*20 = 60 and 60-1 = 59. All the angles add together would get 180: 59+90+31.
Write the equation of the line that passes through the points (3, 4) and (5, 8)
Answer:
y=2x-2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(8-4)/(5-3)
m=4/2
m=2
y-y1=m(x-x1)
y-4=2(x-3)
y=2x-6+4
y=2x-2
which inequality is true?
PLS help with this immediately no links or guesses
Answer:
B all real numbers greater than 0
What is the length of the missing leg? help me pleaseee die in 5 mins
Answer:
A is 21!!
Step-by-step explanation:
Brainliest Please!
Katia is baking. She uses 2 ⅛ cups of sugar for cookies and 1 ⅗ cups of sugar for a cake. How much total sugar did Katia use?
Answer:
3.725
Step-by-step explanation:
because you add 2.125 (2 1/8) and 1.6 (1 3/5) to get 3.725
A company is going to make a storage container with sheet steel walls The container will be in the shape of a rectangular prism If the sheet steel costs 30 for each square meter how much will the sheet cost it total The sides are 7m 3m and 3m
Answer:
3060
Step-by-step explanation:
First we need to calculate the total surface area of the prism
TSA = 2(lw+wh+lh)
l is the length of the prism
w is the width of the prism
h is the height of the prism
Let
L = 7m
W = 3m
H = 3m
Substitute
TSA = 2(7(3)+3(3)+7(3))
TSA = 2(21+9+21)
TSA = 2(30+21)
TSA = 2(51)
TSA = 102m²
Hence the total surface area of the prism is 102m²
Since sheet steel costs 30 for each square meter, then;
1m² = 30
102m² = x
Cross multiply
x = 30*102
x = 3060
Hence the sheet with the dimension will cost 3060
the diagram shows a part of a regular 10 sided polygon
work out the size of the angle marked x
Answer:
b
Step-by-step explanation:
b
find the square rootV 196
Answer:
The answer is 14
Step-by-step explanation:
The square root 196
√196 = 14
Thus, The answer is 14
-TheUnknownScientist
What's the x plz help
Answer:
The answer for x is ten
pls help quick what is 1/8+2/5
Answer:
21/40
Step-by-step explanation: here is a calculator to help you with fractions: https://www.calculatorsoup.com/calculators/math/mixednumbers.php
What is the slope of the line below?
The image is a graph of an x-axis and a y-axis. A line is drawn which passes through the points (2,3) and (-2,-7).
A. 5
B. 0.2 or 15
C. 2.5 or 52
D. 0.4 or 25
Answer:
The awnser is C. but please know I may be wrong
Step-by-step explanation:
Ms. Morrison is purchasing a house and needs to finance a $150,000 mortgage from
the bank with an annual percentage rate (APR) of 3.8%. She is financing it over 30
years and making monthly payments. What is the monthly payment?
Samantha and Luis are attempting to dentermine the average number of library books that seventh-grade students check out at one time. Samantha surveys every other seventh grade students
Answer: Your question is incomplete
But if the attached image is the complete question “whose sample is the most random”, then your answer is:
Luis’ sample.
Step-by-step explanation:
A random sample is one where each member is selected at random.
It is the kind of sampling where each member has an equal chance of being selected.
Samantha and Luis are trying to determine the number of library books that seventh graders check out. Their focus is;
1.) Seventh graders and
2.) Library books
Samantha surveys seventh graders leaving the library while Luis surveys seventh graders at random in the school cafeteria.
Samantha’s survey is more focused because each member of her sample was leaving the library meaning that they had handled books.
But Luis’ sample is more random because he takes his survey from all seventh graders (seventh graders in the cafeteria). With his random sampling, there is a high probability that each member never handled library books.