In the Diagram of parallelogram HIJK below, the diagonals HJ and IK are perpendicular, as shown. If HJ is 10 inches and IK is 24 inches long, then why must HK be 13 iches long?

Two parallel lines have same slopes so we need to find the slope of the line which passes through the given points.

Suppose : A = ( - 2 , 7 ) & B = ( 4 , 4 )

Slope = y ( B ) - y ( A ) / x ( B ) - x ( A )

Slope = 4 - 7 / 4 - ( - 2 )

Slope = - 3 / 4 + 2

Slope = - 3 / 6

Slope = - 1 / 2

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As you know The coefficient of x is the slope of the line in slope-intercept form.

Thus we have to find the option which x has - 1 / 2 as the coefficient .

Look we have that in D so the correct answer is D .

Answer:

12 correct answers

Step-by-step explanation:

It is given that :

The probability of a student guessing the correct answer for a five choice multiple choice question is [tex]$\text{P(correct)}=0.2$[/tex]

Number of multiple choice questions = 60

So the number of correct answers that a student are expected to guess correctly on the test is :

[tex]$=60 \times 0.2$[/tex]

= 12

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

Direct proportion equation:

We have:

Using the equation to find the value of k:

The equation of the line:

Correct choice is A

Answer:

FV= $3,352.98

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $5,400

Number of periods (n)= 5 years

Interest rate (i)= 10%

To calculate the future value (FV), we need to use the following formula:

FV= PV / (1 + i)^n

FV= 5,400 / (1.1^5)

FV= $3,352.98

Answer:

B. -2_x_4÷3 this answer are not sure

Answer:

D

Step-by-step explanation:

-5 < 6x +3

-8 < 6x

-(4/3) < x

I use < to represent 'no no smaller than'

Answer:

x = 7, -1

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

you were right.

hope this helps

Answer:

6

Step-by-step explanation:

1)

-2+12x = 11x+4 [ corresponding angle formed by two parallel lines are equal ]

2)

NOW, Simple simplify....

Answer: 15

Step-by-step explanation:

The answer is because if you divide 14,130 by 3.14. You'll get 4500 and then divide that by 300 and your finally is 15

The radius of the inflated beach ball is equal to 58 inches.

Surface Area of a Sphere. A = 4 π r². The volume of a Sphere. V = (4 ⁄ 3) π r³. Where r is the radius of the circle.

Given: The volume of the sphere is 14,310 inches³

we know the volume of the sphere is  4/3 πr³

Thus equating we get

4/3 × 3.14×r³=14310

r³=3417.99

r³=3418

r=58.463 or 58 (approx)

Learn more about sphere here:

https://brainly.com/question/2855746

#SPJ6

Answer:

a + 9

Step-by-step explanation:

Given that :

Melissa's current age = a

Melissa's age in 9 years will be will be expressed as :

Melissa's current age + number of years from present time

Thus ;

Expression to represent Melissa's age in 9 will be :

a + 9

Thus ;

Melissa's in 9 years = a + 9

Answer:

[tex]v=400,000 \times (2)^d[/tex]

Step-by-step explanation:

Given that,

The value of a house is 400,000 in 2015 and it doubles every decade.

Let v be the value of the house.

We need to find an equation for v in terms of d (the number of decades since 2015).

It shows that the function is exponential. So,

[tex]v=ab^d[/tex]

Where

a = Initial Value = 400000

b = rate = 2

d = number of decades

v = the current value of the home

So,

[tex]v=400,000 \times (2)^d[/tex]

Answer:

17-2x^2=-21

Step-by-step explanation:

17-1x=-21

17-21=x

-4=x/x=-4

Answer: -0.75

1/8 - 1(7)/8 = -3/4= -0.75

Answer:

[tex]\frac{1}{8} -1\frac{7}{8}[/tex]

[tex]\frac{1}{8} -\frac{15}{8}[/tex]

[tex]\frac{1-15}{8}[/tex]

[tex]-\frac{14}{8}[/tex]

[tex]-\frac{7}{4}[/tex]

[tex]-1\frac{3}{4}[/tex]

Step-by-step explanation:

Step-by-step explanation:

Let a be the total score of Div. A

Let b be the total score of Div. B

given,

[tex] \frac{a}{15} - \frac{b}{20} = 2[/tex]

as equation 1.

and

[tex]b - a = 160 \\ - a + b = 160[/tex]

as equation 2.

Now multiply equation 2 by 1/20 to eliminate b to solve for a.

[tex] ( - a)( \frac{1}{20} ) + (b)( \frac{1}{20} ) = ( \frac{1}{20} )(160) \\ - \frac{a}{20} + \frac{b}{20} = 8[/tex]

take this new equation as equation 3.

now we will use equation 1 + equation 3 to eliminate b to solve for a.

[tex] ( \frac{a}{15} + ( - \frac{a}{20} )) + ( - \frac{b}{20} + \frac{b}{20} ) = 2 + 8 \\ \frac{a}{60} = 10 \\ a = 60 \times 10 \\ = 600[/tex]

Div.A total score = 600

Average Score = Total Score / Number of students.

[tex] \frac{600}{15} \\ = 40[/tex]

Answer:

60 clockwise

Step-by-step explanation:

Given:

The figure of two semicircles with diameters 6 cm and 5 cm.

To find:

The area of the combined figure.

Solution:

It is given that the diameters of the semicircles are 6 cm and 5 cm so their radii are 3 cm and 2.5 cm respectively.

Area of a semicircle is:

[tex]A=\dfrac{1}{2}\pi r^2[/tex]

So, the combined area of two semicircles with radii 3 cm and 2.5 cm is:

[tex]Area=\dfrac{1}{2}\pi (3)^2+\dfrac{1}{2}\pi (2.5)^2[/tex]

[tex]Area=\dfrac{1}{2}\pi (9)+\dfrac{1}{2}\pi (6.25)[/tex]

[tex]Area=14.137167+9.817477[/tex]

[tex]Area=23.954644[/tex]

Round the value to the nearest tenth (one decimal place.

[tex]Area\approx 24.0[/tex]

Therefore, the area of given figure is 24.0 sq. cm.

Answer:

Step-by-step explanation:

[tex]\frac{X}{2} =\frac{X+2}{3} \\\\3x=2x+4\\\\x=4[/tex]

hope it helps....

Answer:

1- 24

2- $96

3- $7.75

4- 37

5- 11

6- 54

7- $38

8- 12

9- $46

10- 59

Answer:

1=200

2=300

3=400

4=400

Step-by-step explanation:

Each year they get 100 more dollars. If you have any questions, just ask!

Answer:

659.6 ft

Step-by-step explanation:

x = 140 / tan 23  

x = 329.82(rounded to hundredth)

so total ground distance between the cables = 2x = 2(329.82) = 659.64 feet

Answer: 255.988°

Step-by-step explanation:

Use SOH-CAH-TOA (O=opposite, A=adjacent(side), H=hypotenuse)

They gave us the quest to find the adjacent side, so we can cross off SOH. The angle of elevation is 38 and the angle is adjacent to the right angle(side) and they gave us the opposite which is 200. Now we can also cross off the CAH because they didnt give us or ask for the hypotenuse. SO now solving time.

tan(38)=[tex]\frac{200}{x}[/tex], since x is on the bottom we switch.

x=[tex]\frac{200}{tan(38)}[/tex]

x=255.988°

Answer: I took a screen shot of your answer hope this helps

Step-by-step explanation:

pleas make brainly  

Answer:

AD = 19

Step-by-step explanation:

Here, we want to find the length of AD

To do this, we will use the illustration drawn below in the attachment

Since B is the midpoint of AC, and BC = 8; then AB will also be 8

Mathematically;

AD = AB + BD

AD = 8 + 11

AD = 19

Answer:

2a. aₙ = 12 * -2ⁿ⁻¹; a₈ = -1536

2b. aₙ = 4 * 3ⁿ⁻¹; a₈ = 8748

Step-by-step explanation:

The geometric sequence formula is aₙ = a₁ * rⁿ⁻¹.

2a:

a₈ = 12 * -2⁸⁻¹ {Subtract 1 from 8 to get 7}

a₈ = 12 * -2⁷ {2⁷ is 128. Since the exponent is odd, this will be negative.}

a₈ = 12 * (-128) {Multiply 12 by -128 to get -1536.

a₈ = -1536

2b:

a₈ = 4 * 3⁸⁻¹ {Subtract 1 from 8 to get 7)

a₈ = 4 * 3⁷ {7 is the 3rd number after 4 (a multiple of 4). As a result, this will end in a 7. 3⁷ is 2187.}

a₈ = 4 * 2187 {Multiply 4 by 2187 to get 8748}

a₈ = 8748

Answer:

4. (2,1) 5. (-2,1) 6. (8, 80)

Step-by-step explanation:

2x + 4y - 2x + 2y = 8 - 2

6y = 6

y = 1

2x + 4 = 8

2x = 4

x = 2

(2,1)

3x + 4y + 6x - 4y = -2 - 14

8x = -16

x = -2

-6 + 4y = -2

4y = 4

y = 1

(-2,1)

multiply first equation by 4

4y = 40x

4y + 40x + 6y = 40x + 800

10y = 800

y = 80

80 = 10x

x = 8

(8, 80)

Answer:

1st expression=4n

2nd expression=16n²=4n×4n

3rd expression=8n=2×4n

so

GCF=4n

Answer:

The symbol (∞) is read as infinity. and indicates that the set is unbounded to the right on a number line. Interval notation requires a parenthesis to enclose infinity. The square bracket indicates the boundary is included in the solution.

Step-by-step explanation: