in parallelogram ABCD the measure of m
A) 82.5
B) 97.5
C) 120
D) 130

Answer:

[tex]y = -0.25x -1.5[/tex]

Step-by-step explanation:

Given

[tex](x,y) = \{(-12,1.5)(-1,-1.25),(5,-2.75),(8,-3.5)\}[/tex]

Required

The function rule (in slope intercept)

First, we calculate the slope (m) using:

[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]

This gives:

[tex]m = \frac{-1.25 -1.5}{-1 - -12}[/tex]

[tex]m = \frac{-2.75}{11}[/tex]

[tex]m = -\frac{2.75}{11}[/tex]

[tex]m = -0.25[/tex]

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

This gives:

[tex]y = -0.25(x - -12) + 1.5[/tex]

[tex]y = -0.25(x +12) + 1.5[/tex]

Open bracket

[tex]y = -0.25x -3 + 1.5[/tex]

[tex]y = -0.25x -1.5[/tex]

Yes

Step-by-step explanation:

As u can see in the diagram labelled 1-4 u can see 4 triangles ,

Answer:

4·x² + 24·x = 45

Step-by-step explanation:

The total area of the frame and picture needed by the photographer = 80 in²

The size of the picture that will be in the frame = 5 × 7 inch

The length of the picture = 7 inches

The width of the picture = 5 inches

Let x represent the width of the frame, we get;

The width of the total area = The width of the picture + 2 × The width of the frame

Therefore, the width of the total area = 5 + 2·x

The length of the total area = The length of the picture + 2 × The width of the frame

Therefore, the length of the total area = 7 + 2·x

We get;

The total area = Total length × Total width

∴ The total area = (5 + 2·x) × (7 + 2·x)

We are given that the total area = 80, therefore, by transitive property of equality, we have;

(5 + 2·x) × (7 + 2·x) = 80

35 + 10·x + 14·x + 4·x² = 80

4·x² + 24·x = 80 - 35 = 45

∴ 4·x² + 24·x = 45

Therefore, the quadratic equation that can be used in solving for the width is 4·x² + 24·x = 45.

Answer:

The answer is 4x^2+24x=45

Step-by-step explanation:

I got it right on my test.

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Answer:

x = -17

Step-by-step explanation:

7(2x + 3) = 12x - 13

Distribute

7*2x +7*3 = 12x-13

14x +21 = 12x-13

Subtract 12x from each side

14x-12x+21 = 12x-12x-13

2x+21 = -13

Subtract 21 from each side

2x+21-21 = -13-21

2x = -34

Divide by 2

2x/2 = -34/2

x = -17

Answer:

x=11

Step-by-step explanation:

The angles given are alternate exterior angles and alternate exterior angles are equal if the lines are parallel

5x+9 = 6x-2

Subtract 5x from each side

5x+9-5x = 6x-2-5x

9 = x-2

Add 2 to each side

9+2 =x-2+2

11=x

Now,

5x + 9 ( vertically opposite angle )

Then,

5x + 9 = 6x - 2 ( corresponding angle )

x = 11

I hope you understand...

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Answer:

1144

Step-by-step explanation:

100 + 98 + 96 +.... + 78+76 =

(12-0)/2 (176)  

(6.5) (176) = 1144

The sum of the series will be 1068.

We have the following expression -

[tex]\sum_{i=0}^{12} 100 - 2i[/tex]

We have to rewrite the series as the sum.

A series in mathematics is the sum of a list of numbers that are generated according to some pattern.

We have the following expression -

[tex]\sum_{i=0}^{12} 100 - 2i[/tex]

The terms of this series can be calculated by calculating the value of the function at different values of i.

The series is as follows -

100 + 98 + 96 +.... + 78+76

This is an arithmetic progression with a = 100 and d = - 2 and n = 12. The sum of this series is -

[tex]S = \frac{n}{2} \times {2a + (n-1)d}[/tex]

S = [tex]\frac{12}{2} [{2 \times 100 + (12 -1)(-2)] = 6[200+ 11 \times -2] = 6[200 -22][/tex]

S = 6 x 178 = 1068

The sum of the series will be 1068.

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Answer:

[tex]y = \sqrt{\frac{x- a}{2b}}[/tex]

Step-by-step explanation:

Step 1:  Make y the subject of this formula

[tex]x- a = a - a - 2by^{2}[/tex]

[tex]\frac{x- a}{2b} = \frac{2by^{2}}{2b}[/tex]

[tex]\sqrt{\frac{x- a}{2b}} = \sqrt{y^{2}}[/tex]

[tex]\sqrt{\frac{x- a}{2b}} = y[/tex]

Answer:  [tex]y = \sqrt{\frac{x- a}{2b}}[/tex]

Answer:

n=5

Step-by-step explanation:

7n+2=4n+17

Subtract 2 from both sides

7n=4n+15

Subtract 4n

3n=15

Divide by 3

n=5

I hope it helps!

Answer:

7n+2=4n+17

7n+2−2=4n+17−2

7n=4n+15

7n−4n=4n+15−4n

3n=15

3n/3=15/3

n=5

OAmalOHopeO

Answer:12kg

Step-by-step explanation:

8kg+4kg=12kg

the 4kg came from the half block

se um bloco pesa 8 kg meio bloco pesa 4 kg então é só juntar 8+4=12

Answer:

=> 12πr²

Step-by-step explanation:

The Surface area of sphere is 4πr²

so the surface area of sphere with radius 3x will be

=> 4×3πr²

=> 12πr²

Answer:

-4, 3 and 6

Step-by-step explanation:

Given

See attachment for complete question

Required

The roots of the polynomial

We have:

[tex]y = x^3 + 72[/tex]

[tex]y = 5x^2 + 18x[/tex]

When the above functions are plotted, the x-coordinate of the point of intersection are: -4, 3 and 6

Hence, the roots are: -4, 3 and 6

Answer:

it is -4, 3, 6.

Answer:

6pi=2pi(r)(120/360)

r=9

C=(pi)d

C=(pi)18

c=18pi

Step-by-step explanation:

Answer:

Step-by-step explanation:

The measurement of AC = 6pi

120/360 * pi * 2 * R = 6*pi                The pi values cancel out.

1/3 * 2 * R =  6                                    Multiply by  3

2R = 18                                               Divide by 2

R = 9

the circumference = 2 * pi * R

C = 2 * pi *9

C = 18 * pi

Now you want the measurement of arc AB

120 = 6 * pi

30 = x

120/30 = 6pi/x            Cross multiply

120 * x = 180 * pi         Divide by 120

x = 180 pi / 120

x = 3/2 * pi

So the measurement of arc AB = 1.5 * pi

Answer:

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Step-by-step explanation:

4x² - 3, x less than/equal to 0

Step-by-step explanation:

y = (-1/2)[(x+3)^½]

(x+3)^½ = -2y

Square both sides,

(x+3) = (-2y)²

x+3 = 4y²

x = 4y²-3

Interswitch x and y

Inverse is 4x²-3

Domain of inverse is the range of f.

The range of f is less than/equal to 0

Because at x = -3, f(x) = 0

For x > -3, f(x) is negative

Domain of inverse is x less than/equal to 0

the first/upper one

the other point cloud is too compact to leave a clear clue about any slope

Answer:

Step-by-step explanation:

6 ÷ (⅔) = 6 × (3/2) = 9

There are nine ⅔-cup servings per pitcher.

Answer:

x=136

Step-by-step explanation:

Answer:

FS = 48

Step-by-step explanation:

The distance from the vertex to the centroid is twice the distance from the centroid to the midpoint, so

FB = 2 BS = 2 × 16 = 32

Then

FS = FB + BS = 32 + 16 = 48

Answer:

4

Step-by-step explanation:

x=3

x2 means 3 square (+3)

3×3+3

=9+3

12÷3

4

Answer:

a =7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp side/ adj side

tan 45 = 7/a

a tan 45 = 7

a = 7/ tan 45

a = 7 / (1)

a = 7

Answer:

PC = 14.42 cm

Step-by-step explanation:

If a tangent and secant are drawn from a point outside a circle, then the product of the lengths of the segments of the secant is equal to the square of the length of the tangent.

PC² = PB × BD

PC² = 4 × 52

PC² = 208

PC = [tex]\sqrt{208}[/tex]

PC = 14.42 cm

The length of PC=14.42 cm.

when a tangent and secant are drawn from a point outside a circle, then the multiplication of the lengths of the segments of the secant is equal to the square of the length of the tangent.

PC² = PB × BD

Use the given value in above formula we get,

PC² = 4 × 52

PC² = 208

[tex]PC = \sqrt{208}[/tex]

Therefore we get the value of PC is,PC = 14.42 cm.

Therefor the length of PC=14.42 cm.

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Answer:

D: 6.04

Step-by-step explanation:

100*1.08 = 108

108*0.87 = 93.96

100-93.96 = 6.04

Step-by-step explanation:

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it really helps!

Answer:

since b is 348421 and we are looking for b21 it is 348421(12)

Answer:

87.12

Step-by-step explanation:

Answer:

12.5

Step-by-step explanation:

Answer:

B. y=1/3x+4

Step-by-step explanation:

Hi there!

We are given the line PQ and we want to find the line that is perpendicular to it

Perpendicular lines have slopes that are negative and reciprocal. When they are multiplied together, the result is -1

So first, let's find the slope of the line PQ

The point P is given as (-8, 7) and the point Q is given as (-4, -5)

The formula for the slope calculated from two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where ([tex]x_{1}[/tex] [tex]y_1[/tex]) and ([tex]x_2[/tex], [tex]y_2[/tex]) are points

We have the needed information for the slope, but let's label the values of the points to avoid any confusion

x1=-8

y1=7

x2=-4

y2=-5

Now substitute into the formula (m is the slope, and remember: the formula contains SUBTRACTION):

m=[tex]\frac{(-5-7)}{(-4--8)}[/tex]

simplify

m=[tex]\frac{-5-7}{-4+8}[/tex]

add

m=-12/4

divide

m=-3

So the slope of the line PQ is -3

As said above, perpendicular lines have slopes that have a product of -1

So to find the slope of the line perpendicular to PQ, use this formula:

-3m=-1

divide both sides by -3

m=1/3

The only line that has a slope of 1/3 is B (y=1/3x+4), so B is the answer.

Hope this helps!

Answer:

7/2 =x

Step-by-step explanation:

The triangles are similar so we can write a ratio to solve

2         4

---- = -------

x        7

Using cross products

2*7 = 4x

14 = 4x

14/4 = 4x/4

7/2 =x

Answer:

[tex]x=3\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{4}{2} :\frac{7}{x}[/tex]

x · 4 = 7 · 2

4x = 14

4x ÷ 4 = 14 ÷ 4

x = 3.5

Answer:

[tex]x \geqslant 1[/tex]

Step-by-step explanation:

[tex] \sqrt{x + 6 - 7} = \sqrt{x - 1} \\ \\ x - 1 \geqslant 0 \\ x \geqslant 1[/tex]

Answer:

7

Step-by-step explanation:

Thing about centroids is they create segments that are spilt with one piece [tex]\frac{1}{3}[/tex] and the larger piece [tex]\frac{2}{3}[/tex] .

So, if the whole segment is 21, then the large piece is [tex]\frac{2}{3}[/tex] of 21. The small piece is [tex]\frac{1}{3}[/tex] of 21.

TE = 21 · [tex]\frac{1}{3}[/tex] = [tex]\frac{21}{3}[/tex] = 7