which angle pair is a pair of alternate interior angles.

Answer:

672

Step-by-step explanation:

Given:

The base of a prism is a right triangle with legs measuring 16 feet and 4 feet.

Height of the prism is 14 feet.

To find:

The volume of the triangular prism.

Solution:

The area of a triangle is:

[tex]Area=\dfrac{1}{2}\times b\times h[/tex]

Where, b is base and h is height of the triangle.

The base of a prism is a right triangle with legs measuring 16 feet and 4 feet. It means the base of the triangle is 16 feet and height is 4 feet. So, the area of the base of the prism is:

[tex]B=\dfrac{1}{2}\times 16\times 4[/tex]

[tex]B=32[/tex]

Now, the volume of a triangular prism is:

[tex]V=Bh[/tex]

Where, B is base area and h is the height.

Putting [tex]B=32,h=14[/tex] in the above formula, we get

[tex]V=32\times 14[/tex]

[tex]V=448[/tex]

Therefore, the volume of the triangular prism is 448 cubic feet.

Given:

The graph of the system of inequalities.

To find:

The system of inequalities.

Solution:

From the given graph it is clear that the first line passes through the points (0,2) and (1,-1). So, the equation of the boundary line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-2=\dfrac{-1-2}{1-0}(x-0)[/tex]

[tex]y-2=-3x[/tex]

[tex]y=-3x+2[/tex]

The shaded region lies above the line and the boundary line is a solid line. So, the sign of inequality must by ≥.

[tex]y\geq -3x+2[/tex]

The second line passes through the points (0,-2) and (3,0). So, the equation of the boundary line is:

[tex]y-(-2)=\dfrac{0-(-2)}{3-0}(x-0)[/tex]

[tex]y+2=\dfrac{2}{3}x[/tex]

[tex]y=\dfrac{2}{3}x-2[/tex]

The shaded region lies above the line and the boundary line is a solid line. So, the sign of inequality must by ≥.

[tex]y\geq \dfrac{2}{3}x-2[/tex]

Therefore, the system of inequalities contains two linear inequalities [tex]y\geq -3x+2[/tex] and [tex]y\geq \dfrac{2}{3}x-2[/tex].

Answer:

Don't have them

lol

Answer:

addition property of equality

Step-by-step explanation:

9514 1404 393

Answer:

  B, C, E

Step-by-step explanation:

When the central angles are congruent, the corresponding triangles are congruent:

  ΔJHK ≅ ΔLHM . . . . selection E

and the base chords are congruent:

  ML ≅ JK . . . . selection B

The subtended arcs are also congruent, so adding arc LK to each will result in congruent arc measures:

  arc MLK ≅ arc LKJ . . . . selection C

Answer:

3m:20m

Step-by-step explanation:

2km to m = 2000

300:2000

(divide both sides by 100)

300/100=3

2000/100=20

3:20

Answer:

3 : 20

Step-by-step explanation:

2km = 2000

Ratio:

300 : 2000 =

150 : 1000 =

75 : 500 =

15 : 100 =

3 : 20

An equation that models the considered calorie consumption by Jonathan is y = mx + 6k, where m is the number of calorie per buiscuit, and k is the number of calorie per package of pemmican.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

We're specified that:

Let we take:

m = number of calories per buiscuit that Jonathan eats.

Then, for x buiscuits, it would be [tex]m \times x[/tex] calories, or in short [tex]mx[/tex] calories.

Let k = number of calories per package of pemmican, then:

for 6 packages of pemmican, it would be [tex]6 \times k[/tex] calories, or in short [tex]6k[/tex] calories.

Thus, total calories Jonathan consumes = y = calories from x buiscuits + calories from 6 packages of pemmican.

or, we get:

[tex]y = mx + 6k[/tex]

Thus, an equation that models the considered calorie consumption by Jonathan is y = mx + 6k, where m is the number of calorie per buiscuit, and k is the number of calorie per package of pemmican.

Learn more about forming equations here:

https://brainly.com/question/11938672

Answer:

4x^2 - 14x + 19

Step-by-step explanation:  

A = LW

A = (2x-3) (2x-3)

4x^2 - 6x - 6x + 9

Combine like terms:

4x^2 - 12x + 9

-2(x - 5) (for both ovals)

(4x^2 - 12x + 9) -2(x - 5)

4x^2 - 12x + 9 - 2x + 10

Group then combine like terms:

4x^2 - 12x - 2x + 10 + 9

4x^2 - 14x + 19

Sorry for being 10 days late but here is the answer for anybody that needs this! :D

Answer:

A i did this one already

Step-by-step explanation:

Answer:25

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

because you have to multiply to get the parentheses off.

Answer:

1.

Equation: y = -4x + 7

Slope: -4

y-intercept = 7

2.

Equation: y = 2/3x - 3

Slope: 2/3

y - intercept: -3

3.

Equation: y = 5/4x - 3/2

Slope: 5/4

y - intercept: -3/2

4.

Equation: y = -1/2x + 4

Slope: -1/2x

y - intercept: 4

Answer: for C it is that 1/2 is half of an whole therefore 1/2 is  half is less than the rest

for D you will have to add more 1/2 for it to be greater than but for now, it is less than.

for E you will have to add more 1/2 for it to be greater than

Answer:

Step-by-step explanation:

Inscribed angle = 130°/2 = 65°

Answer:

5x^2−10x−2

Step-by-step explanation:

I hope this is what you are looking for I just added (5x^2 – 9) + (-10x + 7)

Answer:

the line plot in the bottom right corner

Step-by-step explanation:

Answer:

D is the correct graph.

Step-by-step explanation:

First you put the entries in ascending order, because that's how the line plot needs to be ordered.

1/4, 3/8, 1/2, 3/4, 7/8, 1, 1 1/4

So right there, you can rule out A.

You can rule out C because 1/4 does not occur 5 times in the data set.

B is incorrect because 3/8 isn't on the line plot at all.

Please let me know if you have questions.

Answer:

Step-by-step explanation:

g(x) =(1/4 x)²

g(x)  = 4x² will be the equation of the parabola.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, two parabolas f(x) and g(x),

From the general equation of the parabola,

y = a(x – h)² + k or x = a(y – k)² +h.

Here (h, k) denotes the vertex.

As we can see in our case, the vertex is (0, 0)

Thus, the equation of the parabola will be

y = ax²

Since the given parabola passes through the point (1, 4)

Substitute the values,

4 = a(1)²

a = 4

therefore, the equation of the parabola g(x) will be,

g(x)  = 4x²

Learn more about function here:

https://brainly.com/question/29633660

#SPJ7

Answer:

The correct anser for delta math is 68%

Step-by-step explanation:

I gave up on delta math

Answer:

18

Step-by-step explanation:

The key of this leaf stem-leaf plot is:

4 | 5 = 45

Therefore, the data points that represents children with weight that is less than 50 pounds would be as follows:

First row => 12, 13, 15, 15 15, 16, 16, 19

Second row => 23, 25

Third row => 33, 35, 37, 38, 39

Fourth row => 44, 45, 45

Therefore, the number of children that weigh less than 50 pounds = 18

Answer:

Acute and isosceles

Step-by-step explanation:

Acute triangle because with all sides equal, all the angles are acute

Isosceles triangles have (at least) 2 equal sides. This is actually an equilateral triangle, where all 3 are equal. A scalene triangle has 3 unequal sides.

Answer:

3π

Step-by-step explanation:

period = 3π

Answer:

25.899sq.metres

Step-by-step explanation:

Area of this section of wood = Area of the sector

Area of the sector = theta/360 * πr²

r is the radius

theta is the central angle

Substitute

Area of the sector = 85.3/360 * πr²

Area of the sector = 85.3/360 * 3.14(5.90)²

Area of the sector = 85.3/360 * 109.3034

Area of the sector = 9,323.58002/360

Area of the sector = 25.899

Hence the area of the section of wood  is 25.899sq.metres

Answer: BC = 5.83

Step-by-step explanation:

Luckily, the triangle is placed on the graph nicely so we can count the legs of the triangle:

AB = 5

AC = 3

BC = ?

To find BC, we can simply use the Pythagorean Theorem:

[tex]a^{2}+b^{2}=c^{2}[/tex]

5^2 + 3^2 = c^2

25 + 9 = c^2

34 = c^2

Now square root to find c, or BC.

[tex]\sqrt{34}=\sqrt{c^{2} }[/tex]

c = 5.83 (rounded by nearest hundredth)

Answer:

It will take approximately 68.2 years for the Caribou population to reach 21,000.

Step-by-step explanation:

The population P of Caribou in the Yukon is modeled by P=6x²-120x+1250 where x is the number of years from today.

If the population P of Caribou in the Yukon is 21000, then, replacing you get:

21000= 6x²-120x+1250

So:

0= 6x²-120x+1250 -21000

0= 6x²-120x - 19750

This is a quadratic function of the form: 0= ax²+ bx +c, where: a=6, b= -120 and c=-19750

To solve a quadratic function and determine the value of x you can use the expression:

[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]

Replacing the values ​​of a, b and c and solving you get:

[tex]x1,x2=\frac{-(-120)+-\sqrt{(-120)^{2}-4*6*(-19750) } }{2*6}[/tex]

[tex]x1,x2=\frac{120+-\sqrt{14400+474000 } }{12}[/tex]

[tex]x1,x2=\frac{120+-\sqrt{488400 } }{12}[/tex]

[tex]x1,x2=\frac{120+-698.86 }{12}[/tex]

So:

[tex]x1=\frac{120+698.86 }{12}[/tex]

x1= 68.24 ≅ 68.2

and

[tex]x2=\frac{120-698.86 }{12}[/tex]

x2= -48. 24 ≅ -48.2

As time cannot be negative, it will take approximately 68.2 years for the Caribou population to reach 21,000.

Answer: 54

Total = 90

x : y = 2: 3

5p = 90

1p= 90/5= 18

Larger Angle= =18*3= 54

Answer:

4,140 degrees

Step-by-step explanation:

Mathematically, the sum of interior angles of a polygon is;

(n-2)180

where n is the number of sides the polygon has

Mathematically;

we will be replacing n by 25 here

So, we have;

(25-2)180

= 23 * 180 = 4,140 degrees

Answer:

V= 2* L*B*H

Step-by-step explanation:

Although we are not given the dimension of the rectangular prisms in this question

The volume of a rectangular prism is

V= L*B*H

Since the number of the prism is two

Hence the volume of the two prisms

V= 2* L*B*H

Therefore, when the plugin the dimensions of the prism into the expression above, you will get the volume of the two prisms combined