8 points
Find the measure of the arc or
angle indicated. Assume that
lines which appear tangent are
tangent. *
F
E
46°
?
?
570
D
с
T
O 123
O 149
O 167
O 93

Answer:

(i) [tex]y = 2x(x-5)[/tex]

(ii)  zeros:  x = 0 and x = 5

axis of symmetry:  x = 2.5

(iii)  vertex:  (2.5, -12.5)

(iv) see attached

Step-by-step explanation:

Part (i)

Factor:  [tex]y=2x^2-10x[/tex]

Factor out the common term [tex]2x[/tex]:

[tex]\implies y=2x(x-5)[/tex]

Part (ii)

Zeros occur when [tex]y=0[/tex]

[tex]\implies 2x(x-5)=0[/tex]

Therefore:

[tex]\implies 2x=0 \implies x=0[/tex]

[tex]\implies (x-5)=0 \implies x=5[/tex]

So the zeros are x = 0 and x = 5

The axis of symmetry of a parabola is x = a where a is the midpoint of the zeros.

[tex]\textsf{midpoint of zeros}=\dfrac{0+5}{2}=2.5[/tex]

Therefore, the axis of symmetry is [tex]x=2.5[/tex]

Part (iii)

The axis of symmetry is the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute this into the given equation.

[tex]\implies 2(2.5)^2-10(2.5)=-12.5[/tex]

So the vertex is (2.5, -12.5)

Part (iv)

Plot the zeros and the vertex.

As the leading coefficient is positive, the parabola will open upwards, so the vertex is the minimum point.

Draw the axis of symmetry, then sketch the parabola, ensuring each side of the axis of symmetry is symmetrical.

*see attached*

Answer:

Final answer -

Area of paperboard = [tex]565.92 \: inches {}^{2} [/tex]

hope helpful :D

236 x 0.126

29.736 MB have been downloaded

Answer:

Step-by-step explanation:

Divide the numerator by the denominator.

Write down the whole number part of the quotient.

Take the remainder and write it over the original denominator.

Find midpoint coordinates:

[tex]\rightarrow \sf (\dfrac{-1+3}{2} ), \ (\dfrac{7+(-1)}{2} )[/tex]

[tex]\hookrightarrow \sf (1, \ 3)[/tex]

Find the gradient of MN:

[tex]\dashrightarrow \sf \dfrac{-1-7}{3-(-1)}[/tex]

[tex]\dashrightarrow \sf -2[/tex]

slope of perpendicular bisector:

[tex]\rightarrow \sf \dfrac{1}{2}[/tex]

Equation:

[tex]\sf \rightarrow y = \dfrac{1}{2}x+\dfrac{5}{2}[/tex]

Answer:

[tex]y=\dfrac12x+\dfrac52[/tex]

Step-by-step explanation:

M = (-1, 7)

N = (3, -1)

[tex]\sf slope\:of\:MN=\dfrac{y_n-y_m}{x_n-x_m}= \dfrac{-1-7}{3-(-1)}=-2[/tex]

If two lines are perpendicular to each other, the product of their slopes will be -1.  Therefore, the slope (m) of the line perpendicular to MN is:

[tex]\sf \implies -2 \times m=-1[/tex]

[tex]\sf \implies m=\dfrac12[/tex]

If the line bisects the line MN, it will intersect it at the midpoint of MN:

[tex]\begin{aligned}\textsf{Midpoint of MN} & =\left(\dfrac{x_m+x_n}{2},\dfrac{y_m+y_n}{2}\right)\\ & =\left(\dfrac{-1+3}{2},\dfrac{7+(-1)}{2}\right)\\ & =(1,3)\end{aligned}[/tex]

Finally, use the point-slope form of the linear equation with the found slope and the midpoint of MN:

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

[tex]\implies y-3=\dfrac12(x-1)[/tex]

[tex]\implies y=\dfrac12x+\dfrac52[/tex]

Answer:

Step-by-step explanation:

It would be about 3.14 as since it is only 1 inch pi is multiplyed by one and when rounding pi to the hundreths you get 3.14 hope this helps

Answer:

P = 184 yards

C = 175.84 centimetres

P = 212 m

Step-by-step explanation:

P = 2(150 yards) + 2(92 yards)

P = 300 yards + 184 yards

P = 184 yards

C = 2(3.14) × (28 centimetres)

C = 6.28 × (28 centimetres)

C = 175.84 centimetres

P = 104 m + 32 m + 76 m

P = 212 m

Answer:

I believe it would be 9.

Step-by-step explanation:

Finding Dialation: 16/12 = 1.3
Height: 16/1.3 = 12
Width: 12/1.3 = 9

Answer:

(5*2) + (1/2)(2+2+2)*4)

Step-by-step explanation:

Area of Triangle = (1/2)(2 + 2 + 2 )* 4)

Area of Rectangle = 5 * 2

Total Area = (5*2) + (1/2)(2+2+2)*4)

Answer:

B

Step-by-step explanation:

B is the best answer because it's a lot of students and unbiased

c=30p

$450

Setting up an equation lets us solve this question quickly. It also lets us create a relationship that can be used to find the cost of admission for any number of people.

Writing the Equation

As stated in the question, c will represent the total cost and p will represent the number of people admitted. Additionally, 30 will be the coefficient because it represents the cost per person. The variable p will take on the coefficient because it is the independent variable. Remember that the independent variable is the one that you can control. On the other hand, c is the dependent variable because it depends on the p variable.

Solving the Equation

To solve the equation for 15 people, plug 15 in for p.

Then, multiply out to solve

⠀

Explanation :

⠀

We know,

[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = \dfrac{4}{3} \pi {r}^{3} }}}[/tex]

⠀

Here,

⠀

Substituting the values in the formula :

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times3.14 \times {\bigg(7 \bigg)}^{3} }}}[/tex]

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times 343 }}}[/tex]

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4 \times 3.14 \times 343}{3} }}}[/tex]

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4308.08}{3}}}}[/tex]

⠀

[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = 1436.02 }}}[/tex]

⠀

Therefore,

[tex]6i~~ + ~~2\sqrt{3}j\implies < \stackrel{a}{6}~~,~~\stackrel{b}{2\sqrt{3}} > \\\\[-0.35em] ~\dotfill\\\\ \stackrel{magnitude}{\sqrt{a^2+b^2}}\implies \sqrt{6^2+(2\sqrt{3})^2}\implies \sqrt{36+(2^2\cdot 3)}\implies \sqrt{36+12}\implies \sqrt{48} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{direction}{tan^{-1}\left( \cfrac{b}{a}\right)}\implies tan^{-1}\left( \cfrac{2\sqrt{3}}{6} \right)\implies tan^{-1}\left( \cfrac{\sqrt{3}}{3} \right) \\\\\\ tan^{-1}\left( \cfrac{1}{\sqrt{3}} \right)\implies 30^o[/tex]

Answer:

betweennnnnnn 8 and 9!!! :)

Answer:

  19 -d

Step-by-step explanation:

The number Johnson has left is found by subtracting the number he gave away from the number he started with.

  19 -d . . . . . . . number of ice cream bowls left

Answer: ( -[tex]\sqrt{5}[/tex] / 3)

Step-by-step explanation:

sin(angle) = opposite/hypotenuse

opposite =2

hypotenuse = 3

solve for adjacent side with pythagorean theorum

opposite^2 + adjacent^2 = hypotenuse^2

2^2 + adjacent^2 = 3^2

4 + adjacent^2 = 9

adjacent^2 = 9 - 4

adjacent^2 = 5

adjacent = [tex]\sqrt{5}[/tex]

-[tex]\sqrt{5}[/tex] since it is in the second quadrant

cosx = (adjacent/hypotenuse)

cosx = (-[tex]\sqrt{5}[/tex]/3)

(-[tex]\sqrt{5}[/tex]/3)

Answer:

$933.12

Step-by-step explanation:

So 20% of $1,080 is 216.

1080 - 216 is 864

8% of 864 is 69.12

864 + 69.12 would be $933.12

Answer:

SA = 434 ft^2

Step-by-step explanation:

We are going to exclude the floor since we are assuming he won't paint the floor. The shed has 5 sides since we aren't going to consider the floor.

length - L

width - W

height - H

surface area - SA

H = 8 ft

L = 14 ft

W = 7 ft

To calculate the area of each side or surface of the shed,

since there are two sides/ surfaces with the same are except for the roof, we will multiply the areas by 2.

Surface area:

SA = 2 × (W×H + L×H) + L×W

SA = 2 × (7×8 + 14×8) + 14×7

SA = 434 ft^2

Answer:

472 :)

Step-by-step explanation:

47.2/0.1 = 472

Have an amazing day!

Please rate and mark brainliest!!

Answer:

A

Step-by-step explanation:

It because I think it is the correct

Answer:

The only true statement is :

The graph of the function is a parabola

Step-by-step explanation:

f(x) = x² – 5x + 12

Option 1: The value of f(–10) = 82  

Reason : f(-10) = (-10)² – 5(-10) + 12 = 100 + 50 + 12 = 162 ≠ 82

Option 2: The graph of the function is a parabola  [tex]\huge\checkmark[/tex]

Option 3: The graph of the function opens down

Reason : the coefficient of x² is 1 ,which is a positive number then the graph opens up.

Option 4: The graph contains the point (20, –8)

Reason : f(20) = 312 ≠ -8

Option 5: The graph contains the point (0, 0)

Reason : f(0) = 12 ≠ -8

Answer:

ABC

Step-by-step explanation:

Answer:

this answer is 0.83

Step-by-step explanation:

5/8 is 0.625, 3/4 is 0.75 and 0.625 divided by 0.75 is 0.83

Answer: 5/6

All you have to do is combine the two equations, like so [tex]\frac{5*4}{8*3}[/tex]

Multiply [tex]\frac{20}{24}[/tex]

Then simplify [tex]\frac{5}{6}[/tex]

Answer:

Random

Step-by-step explanation:

The internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units.

Quadrilaterals are figures formed by four line segments and whose sum of internal angles equals 360°. By geometry we know that the area of a trapezoid is the average of the length of the two bases (B, b), in inches, multiplied by the height of the quadrilateral.

A = 0.5 · (B + b) · h   (1)

By trigonometry the measure of the longer base and the height of the isosceles trapezoid are, respectively:

B = b + 2 · l · cos θ   (2)

h = l · sin θ   (3)

Where θ is an internal angle, in degrees.

By (2) and (3) in (1):

A = 0.5 · (2 · b + 2 · l · cos θ) · (l · sin θ)

A = (b + l · cos θ) · (l · sin θ)

A = b · l · sin θ + l² · sin θ · cos θ

A = b · l · sin θ + 0.5 · l² · sin 2θ  (4)

If we know that b = 6 in and l = 4 in, then the area of the isosceles trapezoid is represented by the following function:

A = 24 · sin θ + 8 · sin 2θ   (5)

Now we determine the angle associated to the maximum area by graphic approach.

According to this approach, the internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units. [tex]\blacksquare[/tex]

To learn more on trapezoids, we kindly invite to check this verified question: https://brainly.com/question/8643562

Step-by-step explanation:

7.2

5

24

2345

6303

-3

2467.2

5

24

2345

6303

-3

246

The linear function is given by table B and the equation y = ( 1/2 )x + 3.2

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution

On a graph, a linear equation forms a straight line. On a graph, a nonlinear equation produces an S-curve, a bell curve, or another nonlinear shape.

Given data ,

Let the linear function be represented as A

Now , the value of A is

Let the x values be x = { 0 , 2 , 4 , 6 , 8 }

Let the y values be y = { 3.2 , 4.2 , 5.2 , 6.2 , 7.2 }

Now , the equation of line is y - y₁ = m ( x - x₁ )

where m is the slope

m = ( 4.2 - 3.2 ) / ( 2 - 0 )

m = 1/2

On simplifying , we get

y - 3.2 = ( 1/2 ) ( x - 0 )

Adding 3.2 on both sides , we get

y = ( 1/2 )x + 3.2

Hence , the linear function is y = ( 1/2 )x + 3.2

To learn more about linear equations click :

https://brainly.com/question/10185505

#SPJ7

Answer:

Step-by-step explanation:

The figure has 2 triangular and 3 rectangular faces.

This is a right triangular prism.

Find the area of each face and add up to get the total surface area.

Each triangle has base of 10 and height of:

Total surface area is

Answer:

12+6.25pi= 31.63495408 Ft squared

Step-by-step explanation:

Area of each individual triangle is 3 by 4 by 1/2

Area of each semicircle is 1/2 2.5 ^2 pi

Answer:

this would be 2

Step-by-step explanation: