The pentagons ABCDE and PQRST are similar.
Find the length x of ST.
D
S
2
4.
A
4.8
P
E
4.8
T
13
3.6
C
5
B
R
6
O

An expression has numbers, variables, and mathematical operations. The other factor of the given binomial is a²+7a+10 except (a+5) is (a+2).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

To find the other factor of the binomial a²+7a+10, we can write it as,

[tex]a^2+7a+10\\\\=a^2+5a+2a+10\\\\=a(a+5)+2(a+5)\\\\=(a+5)(a+2)[/tex]

Thus, the other factor of the given binomial is a²+7a+10 except (a+5) is (a+2).

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Answer:

(a + 2)

Step-by-step explanation:

Answer: B) x=5, x=1

Step-by-step explanation:

To start multiply everything in the expression by 2

[tex]0.5x^{2} -3x+2.5\\x^{2} -6x+5[/tex]

Now factor the trinomials for when a=1

So you must find two numbers that add to -6 and multiply to 5

In this case, the numbers are -1 and -5

[tex]x^{2} -6x+5\\(x-1)(x-5)[/tex]

Now set each of the factors equal to 0 and solve for x

[tex]x-1=0\\x-1+1=0+1\\x=1[/tex]

[tex]x-5=0\\x-5+5=0+5\\x=5[/tex]

The shape of the cross section formed from slicing the pyramid is called; a triangle

We are told that it is a pyramid with a base that is a pentagon with all sides the same length.

Now, the Pyramid's ap-ex is usually constructed by isosceles triangles. Thus, when they are sliced from its ap-ex to from the vertex, in the cross section a triangle will be formed, This triangle will be an isosceles triangle.

In conclusion, the shape of the cross section formed from slicing the pyramid is a triangle.

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Answer:

61.90 ft

Step-by-step explanation:

Perimeter: the boundary that surrounds a shape

1) Find the perimeter of the semicircle using this formula: [tex]\frac{1}{2} *2\pi r[/tex], where [tex]r[/tex] is the radius, and π is 3.14 (according to the question).

1.1) We need to find the radius first.

Radius = Diameter ÷ 2

So, 10 ÷ 2 = 5

1.2) Input the values into the semicircle formula.

[tex]\frac{1}{2} *2(3.14)(5)[/tex]

1.3) solve for the perimeter of the semicircle.

[tex]\frac{1}{2} *31.4[/tex]

= 15.7

2) Find the perimeter of the triangle and the rectangle.

= [tex]6 + 12.2 + 14 + 14[/tex]

= 46.2

3) Add them.

= [tex]46.2 + 15.7[/tex]

= 61.9 ft

3) Round the answer (61.9) to the nearest hundredth (according to the question).

= 61.90 ft

As per the total length of the arc of a semicircle, the outer perimeter of this figure is 61.9 feet.

A semicircle that has a radius of 'r' units, has the total length of it's arc is

= πr units

In the given figure, the semicircle has a diameter = 10 feet.

Therefore, the radius of the semicircle

= 10/2 feet

= 5 feet

Now, the total length of it's arc is

= πr units

= 3.14 × 5 feet

= 15.7 feet

Therefore, the outer perimeter of this figure is

= (12.2 + 6 + 14 + 15.7 + 14) feet

= 61.9 feet

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[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{vertex}{(-3~~,~~5)}\qquad y=a[x-(-3)]^2+5\implies y=a(x+3)^2+5 \\\\\\ \textit{we also know that} \begin{cases} x=-1\\ y=2 \end{cases}\qquad 2=a(-1+3)^2+5\implies -3=a(2)^2 \\\\\\ -3=4a\implies -\cfrac{3}{4}=a~\hfill \boxed{y=-\cfrac{3}{4}(x+3)^2+5}[/tex]

Answer:

Step-by-step explanatio the way the question is phrased Is confusing

Answer:

Step-by-step explanation:

The markings on the figure show this to be a parallelogram. That means opposite sides are congruent. Because the sides are parallel, "alternate interior" angles are also congruent.

__

Angle y forms a linear pair with the one marked 83°, so is supplementary to it:

  y = 180°-83° = 97°

__

The angle marked y is an exterior angle to the triangle containing the angle marked (7x -5)°. As such, it is equal to the sum of the remote interior angles, the one marked (7x -5)° and the unmarked one that is congruent to (3x +32)°.

  (7x -5) +(3x +32) = 97 . . . . . angle relations in the left-side triangle

  10x +27 = 97 . . . . . . . collect terms

  10x = 70 . . . . . . . . subtract 27

 x = 7 . . . . . . . . divide by 10

__

The side marked Z is congruent to the opposite parallel side, so ...

  z = 19

__

The missing measures are ...

_____

Additional comment

You can also find the value of y by adding up the interior angles of the right-side triangle. The one not shown there is "alternate interior" to the one marked (7x -5)°, hence has the same measure. This gives ...

  (7x -5) +(3x +32) +83 = 180

Subtracting 83° from both sides gives the equation we used above.

[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2-r^2)~~ \begin{cases} R=\stackrel{larger}{radius}\\ r=\stackrel{smaller}{radius}\\[-0.5em] \hrulefill\\ R=50\\ r=36 \end{cases}\implies \begin{array}{llll} A=\pi (50-36)\implies A=14\pi \\\\\\ A\approx 44.0 \end{array}[/tex]

The domain is represented by the set of values of the time, that is, the horizontal axis, and the domain of the given function is represented by t ∈ [0, 4.5].

All functions are relations in which there is no value of the domain related to more than one value of the range, functions in explicit form related the variable of the range in terms of the variable of the domain.

Based on the information shown in the graph, the domain is represented by the set of values of the time, that is, the horizontal axis, and the range is represented by the set of values of the height, that is, the vertical axis.

Hence, the domain is represented by the set of values of the time, that is, the horizontal axis, and the domain of the given function is represented by t ∈ [0, 4.5].

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Answer:

ength l = 1 in

width w = 14 in

height h = 2.5 in

diagonal d = 14.3 in

total surface area Stot = 103 in2

lateral surface area Slat = 75 in2

top surface area Stop = 14 in2

bottom surface area Sbot = 14 in2

volume V = 35 in3

Answer:

177

Step-by-step explanation:

the number of sit-ups is going up in 4s , so if i take the 33 sit ups she does on the 5th day i add 4 to that 12 times , so you just do 33+12 and multiply that by 7 since thats how many days she has until 12.

Answer:

no. 4

Step-by-step explanation:

=25x - 125/x^2 - 25

=25(x-5) / x^2 - 5^2

=25(x-5) / (x-5) (x+5) <use of formula a^2 - b^2=(a-b) (a+b)>

=25/x+5 <cut (x-5) on both side>

Answer:

555

Step-by-step explanation:

The packs the colors came in and the colors do not matter. The initial value of crayons is 555.

Answer:

Surface area of the rectangular prism=

Step-by-step explanation:

Given Dimensions of the rectangular prism are:

[tex]Length(L)=16yards[/tex]

[tex]Width(w)=2yards[/tex]

[tex]Height(H)=1.5yards[/tex]

Surface Area of a rectangular prism=

                                          [tex]2(L*W+W*H+H*L)[/tex]

                                          [tex]=2(16*2+2*6+6*16)[/tex]

                                          [tex]=2(32+12+96)[/tex]

                                          [tex]=2(140)[/tex]

                                     [tex]=140yards^2[/tex]

The surface area of the rectangular prism is [tex]140yards^2[/tex]

Answer:

779

Step-by-step explanation:

Aiming to get the value of formula

Given that

50° + 80² = 140°.

:: Cos140² = 100 + 700²³ - R²

kaw of ousines axivox. T

·· R² = 607246

R≈ 780 miles

• The result is T80 miles

If the wrong discion criterion is used, the potential lose in value for the firm is $209.07.

The  correct decision criterion is the net present value. Net present value is the present value of after-tax cash flows from an investment less the amount invested. The internal rate of return is the discount rate that equates the after-tax cash flows from an investment to the amount invested

The net present vaue and the internal rate of return can be calculated using the financial calcuator.

Project S:

I = 6%

NPV = 291.74

IRR = 17.86%

Project I:

Cash flow in year 0 = $-2150

Cash flow each year from year 1 to 4 = 765

I = 6%

NPV = 500.81

IRR = 15.78%

If the wrong criteria is used, Project S would be chosen.

Loss in value = 500.81 - 291.74 = $209.07.

Here are the cash flows used:

WACC: 6.00%

Year 0 1 2 3 4

CF S -$1,025 $380 $380 $380 $380

CF I -$2,150 $765 $765 $765 $765

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Answer:

Molly would be 1 years old.

Step-by-step explanation:

"In three years..."

(m+3) will be Molly's age then.

(h+3) will be Heidi's age then.

(h+3) = 2(m+3) :: given.

.

Subsitute what we know about m, which is it equal h-4.

.

(h+3) = 2(m+3)

(h+3) = 2m + 6

substitute m=h-4

(h+3) = 2(h-4) +6

h +3 = 2(h -4) +6

h +3 = 2h -8 +6

h +3 = 2h -2

h = 2h -8 +3

-h = -5

h = 5

Heidi is 5 years old now.

.

m = h-4

m = 5-4

m = 1

Molly is 1 years old now.

Answer:

50+3+80+1+40+4+70+2

Step-by-step explanation:

Pls thank if correct

Dont get mad if not correct.

Hope this helps <3

The number of degrees that have been turned by the car when it travels from town a to town b will be 1080°.

From the information given, it was stated that it took a car 3 hours to travel from town a to town b and the wheel of a car completes a rotation.

In this case, a rotation is 360°, since there are 3 rotations, the degrees will be:

= 360 × 3

= 1080°

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Answer:

63

Step-by-step explanation:

You get the answer by multiplying the radius by 2 to get the diameter and then multiplying the result by pi or 3.14, which gives you 62.83 and then round it up which is 63

The perfect square trinomial will be [tex]\rm x^2+14x+49[/tex] ,  [tex]x^2-24x+144[/tex]Expression 2 and 4 are correct.

A mathematical expression with three terms or three monomials is called a trinomial. Polynomials having only three terms are known as trinomials.

The second and fourth expression seems to be the perfect square let's check it.

Expression 2;

[tex]x^2 + 14x+49 \\\\ x^2+7x+7x+49 \\\\ x(x+7)+7(x+7)\\\\ (x+7)(x+7) \\\\ (x+7)^2[/tex]

Expression 4;

[tex]x^2-24 x +144 \\\\ x^2-12x-12x+144 \\\\ x(x-12)-12(x-12) \\\\ (x-12)^2[/tex]

Hence the perfect square trinomial will be [tex]\rm x^2+14x+49[/tex] ,  [tex]x^2-24x+144[/tex] .Expressions 2 and 4 are correct.

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Answer:

Options 2 and 4

Step-by-step explanation:

Answer:

63 + 10

Step-by-step explanation:

when you do parenthesis and the number is next to another one with no symbol you multiply so 4-2 = 2 2 x 5 = 10 giving you 63 + 10

Answer: B 3m/s²

Step-by-step explanation: Acceleration is difference in speed /time = 15-0/5

Answer:

3 is the answer

Step-by-step explanation:

answer up above

Answer:

See below ~

Step-by-step explanation:

a)

b)

c)

d)

e

Answer:

length = 20 feet and width = 5 feet

Step-by-step explanation:

Volume is equal to volume = height * width * length. The questions tells us the total volume is 200 cubic feet and that the lenght is equal to length = 4w. Set up the equation 4w * w * 2 = 200 cubic feet. Multiply to get 8w^2 = 200 and solve for w.

Answer:

2 x 10 x 4 + (4 + 10) x 2 x 6 = 80 + 168 = 248