Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°.

Answer:

(8,-10)

Step-by-step explanation:

step 1

Find the slope of line KL

K(-6,8),L(6,0)

m=(0-8)/(6+6)

m=-8/12=-2/3

step 2

Find the slope of the line that is parallel to KL

we know that

If two lines are parallel , then their slopes are the same

therefore

The slope of the parallel line to KL is m=-2/3

step 3

Find the equation of the line parallel to KL that pass through the point M

M(-4,-2)

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

substitute

y+2=-(2/3)(x+4)

step 4

Verify the points

we know that

If the point lie on the line, then the point must satisfy the equation of the line

case a) (-10,0)

substitute the value of x and the value of y in the equation and then compare the result

-10+2=-(2/3)(0+4)

-8=-8/3 -----> is not true

therefore

The point is not on the line

case b) (-6,2)

substitute the value of x and the value of y in the equation and then compare the result

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

4=4/3 -----> is not true

therefore

The point is not on the line

case c) (0,-6)

substitute the value of x and the value of y in the equation and then compare the result

-6+2=-(2/3)(0+4)

-4=-8/3 -----> is not true

therefore

The point is not on the line

case d) (8,-10)

substitute the value of x and the value of y in the equation and then compare the result

-10+2=-(2/3)(8+4)

-8=-8 -----> is true

therefore

The point is on the line

Answer:

Step-by-step explanation:

It's the right isosceles triangle.

Right triangle with angles 45°, 45°, 90°. The sides are in ratio 1 : 1 : √2

(look at the picture).

Therefore

x = 7

y = 7√2

Answer:

Acute

Step-by-step explanation:

Note the definitions:

Obtuse: At least one of the angles are greater than 90°

Equilateral: All angles are congruent & equal to 60°

Acute: All angles are less than 90°

Right: At least one angle is equal to 90°

In this case, the triangle is a D) acute, for it fits the requirement for being an acute... all angles are less than 90°.

~

Hello There!

The triangle shown in the image would be an acute triangle

An acute triangle is a triangle where all three sides are less than 90°

In the image, none of the angles shown are greater than 90° so this

is an example of an acute triangle

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - [tex]\frac{5}{2}[/tex] and (a, b) = (- 6, 2), so

y - 2 = - [tex]\frac{5}{2}[/tex] (x - (- 6)), that is

y - 2 = - [tex]\frac{5}{2}[/tex] (x + 6) ← in point- slope form

An equation in point slope form for this line y - 2 = -5/2  (x + 6) .

The point slope form of a straight line in geometry is used to represent the equation of a straight line using its slope 'm' and a point(x, y) that lies on the given line.

equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Now,  m = - 5/2

and (a, b) = (- 6, 2)

So, the equation of line be

y-2=  -5/2 (x+6)

Hence,

y - 2 = -5/2  (x + 6) in point- slope form.

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The Addition Property of Equality allows us to add the same amount to both sides of an equation, so if x = 5, by adding 3 to both sides, x + 3 would be 8.

The Addition Property of Equality is a principle of mathematics that states: if you add the same amount to both sides of an equation, the equation remains balanced. So, if we take the equation x = 5, according to the Addition Property of Equality, we can add 3 to both sides of the equation. This will give us: x + 3 = 5 + 3. Therefore, x + 3 = 8.

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Answer:

Variability is when there is no consistency.

Step-by-step explanation:

Variation in data can be due to various factors. Variability can also be called the spread of data.

Standard deviation is a measure of variability as standard deviation measures the spread of data.

!!

Answer:

option D: 27.5 square units

Step-by-step explanation:

Divide the polygon in 6 figures

see the attached figure

Area of figure 1 (right triangle)

A1=(1/2)(3)(3)=4.5 units²

Area of figure 2 (rectangle)

A2=(1)(3)=3 units²

Area of figure 3 (rectangle)

A3=(1)(3)=3 units²

Area of figure 4 (right triangle)

A4=(1/2)(3)(3)=4.5 units²

Area of figure 5 (right triangle)

A5=(1/2)(4)(5)=10 units²

Area of figure 6 (right triangle)

A6=(1/2)(1)(5)=2.5 units²

The total area is equal to

At=A1+A2+A3+A4+A5+A6

At=4.5+3+3+4.5+10+2.5=27.5 units²

Answer:

Option D.

Step-by-step explanation:

As we know area of a triangle = [tex]\frac{1}{2}\times Base\times Height[/tex]

1. Area of ΔJKL = [tex]\frac{1}{2}\times(\text{Distance of L from base JK})\times (JK)[/tex]

= [tex]\frac{1}{2}\times (3)\times (5)[/tex]

=7.5 square units

2. Area of ΔIJL = [tex]\frac{1}{2}\times(\text{Distance of J from base IL})\times (IL)[/tex]

=  [tex]\frac{1}{2}\times (3)\times (5)[/tex]

= 7.5 square units

3. Area of triangle IKL = [tex]\frac{1}{2}\times(\text{Distance of H from base IL})\times (IL)[/tex]

= [tex]\frac{1}{2}\times (5)\times (5)[/tex]

= [tex]\frac{25}{2}=12.5[/tex] square units

Now area of ΔJKL + ΔIJL + ΔIKL = 7.5 + 7.5 + 12.5

= 27.5 square units

Option D. is the answer.

Answer:

{0}

Step-by-step explanation:

14 + 8m = 14 - 3m - 5m

Combine like terms

14 + 8m = 14 - 8m

Add 8m to each side

14 +8m +8m = 14 -8m +8m

14 +16m = 14

Subtract 14 from each side

14-14 +16m = 14-14

16m = 0

Divide by 16

16m/16 = 0/16

m = 0

Answer:

{0}

Step-by-step explanation:

The given equation is

[tex]14+8m=14-3m-5m[/tex]

We need to find the solution set of given equation.

Combine like terms on the right side of the given equation.

[tex]14+8m=14+(-3m-5m)[/tex]

[tex]14+8m=14+(-8m)[/tex]

[tex]14+8m=14-8m[/tex]

Add 8m on both sides.

[tex]14+8m+8m=14-8m+8m[/tex]

[tex]14+16m=14[/tex]

Subtract 14 from both sides.

[tex]14+16m-14=14-14[/tex]

[tex]16m=0[/tex]

Divide both sides by 16.

[tex]m=\frac{0}{16}[/tex]

[tex]m=0[/tex]

Therefore, the solution set is {0}.

Answer:

2

Step-by-step explanation:

2 is the constant of proportionality in the equation y = 2x . When two variables are directly proportional to each others . Where k is called the constant of proportionality . Thus in the question x and y are proportional variables

Answer:

you are correct

Step-by-step explanation:

area = 6 × 3 = 18 in²

Answer:

Yes!You got it correct!

Step-by-step explanation:

Good job!

Answer:

x=8 ?

Step-by-step explanation:

Answer:

The function f(x) intercepts the x-axis at (0,0), thus it touches the x-axis once.The graph of the function g(x) does not intercept the x-axis at all.

Step-by-step explanation:

In this question you first form the table for values of x with corresponding values of f(x) that you will use to graph the function f(x)=x².Then do the same for the function g(x)=x²+2.Take a point from the parent function f(x) and compare it with its image in the function g(x) to identify the transformation that occurred.Graph the two equations to visually see the x-intercepts in both equations.

In the parent function f(x)=x² form a table as shown below;

x                      f(x)=x²          coordinate to plot

-3                     -3²=9                (-3,9)

-2                      -2²=4                (-2,4)

-1                        -1²=1                 (-1,1)

0                         0²=0               (0,0)

1                           1²=1                 (1,1)

2                          2²=4               (2,4)

3                           3²=9               (3,9)

Use the coordinates to plot the graph of f(x)=x² on a graph tool and see the number of x-intercept values

In the function g(x)=x²+2 also form your table for values of g(x) with corresponding values of x

x                              g(x)=x²+2                                          coordinate to plot

-3                          -3²+2=9+2=11                                          (-3,11)

-2                          -2²+2=4+2=6                                          (-2,6)

-1                           -1²+2=1+2=3                                             (-1,3)

0                            0²+2=2                                                    (0,2)

1                             1²+2=1+2=3                                              (1,3)

2                            2²+2=4+2=6                                             (2,6)

3                            3²+2=9+2=11                                             (3,11)

Use the coordinates to plot the graph of g(x)=x²+2  on a graph tool to determine the number of x intercept values

You can determine the transformation that occurred too, how?

Take a point on the parent function f(x) and compare it with its image in the function g(x)

Let take point (-3,9) and compare it to (-3,11).You notice x coordinate did not change but the y coordinate shifted 2 units upwards along the y-axis.To determine this dilation you subtract the coordinates of object point from that of image point.

[tex]=(\frac{0-0}{11-9}) =(\frac{0}{2} )=(0,2)[/tex]

The dilation was (0,2)

Solution

From the graphs, the function f(x), intercepts the x-axis at (0,0), thus it touches the x-axis once.The graph of the function g(x) does not intercept the x-axis at all.

Answer:

12

Step-by-step explanation:

We are given the following equation and we are to solve for the variable r and find its value:

[tex] - 1 . 5 ( 4 - r ) = - 1 2 [/tex]

Expanding the brackets to get:

[tex]6-1.5r=-12[/tex]

[tex]-1.5r=-12-6[/tex]

[tex] - 1 . 5 r = - 1 8 [/tex]

[tex] r = \frac { - 1 8 } { - 1 . 5 } [/tex]

r = 12

Answer:

-4

Step-by-step explanation:

-1.5 (4 - r) = -12

(4 - r) = [tex]\frac{-12}{-1.5}[/tex]

-r =  [tex]\frac{12}{1.5}[/tex] - 4

r = 4 -  [tex]\frac{12}{1.5}[/tex] = -4

Step-by-step explanation:

[tex]1 \div 2 \times base \times height = area[/tex]

[tex]1 \div 2 \times x \times 42.2 = \ 369.25 \[/tex]

[tex]x = 369.25 \div 21.1[/tex]

[tex] = 17.5[/tex]

Answer:

Base = 17.5 inches.

Step-by-step explanation:

Given  : A triangle has an area of 369.25 square inches. The height of the triangle is 42.2 inches.

To find : What is the length of the base of the triangle.

Solution : We have given

Area of triangle = 369.25 square inches.

Height =  42.2 inches.

Area of triangle = [tex]\frac{1}{2}*base*height[/tex].

Plugging the values.

369.25 =  [tex]\frac{1}{2}*base*42.2[/tex].

On multiplying both sides by 2

369.25 * 2 = base * 42.2

738.5 = base * 42.2

On dividing both sides by 42.2

Base = 17.5 inches.

Therefore, Base = 17.5 inches.

Answer:

Red

Step-by-step explanation:

P = 30/120 = 1/4

The spinner is divided into 8 equal sections.  1/4 of 8 is 2.  So we're looking for a color that appears on exactly 2 of the sections.

The color is red.

Answer:

Step-by-step explanation:

First, factor the denominator: (x-5)(x+4)

Since the denominator already has the two values, you only need to multiply it by (x+3), which means you need to multiply the numerator by (x+3):

(x-1)(x+3)/(x-5)(x+4)(x+3)

(x-1)(x+3) then simplifies to [tex]x^2+2x-3[/tex]

The problem is solved by calculating that there are 24 nickels and 12 dimes to make a total of $2.40, given that there are twice as many nickels as dimes.

The subject of this question is Mathematics, specifically dealing with simple money-based equations. In the problem you're presented with, you've been asked to figure out the number of nickels and dimes that make up $2.40, given that there are twice as many nickels as there are dimes.

First, we can start by understanding the value of each coin. A nickel is worth $0.05, and a dime is worth $0.10. With the condition expressed in the problem, let's express the number of dimes as x, thus the number of nickels would then be 2x.

Because of their respective values, the total value of the dimes would be 0.10x and the total value of the nickels would be 0.05 × 2x or 0.10x. Adding both together, we'd have 0.10x + 0.10x = 0.20x, which we know equals $2.40 from the problem. Solving the equation 0.20x = 2.40 gives us x = 12. That's your number of dimes. The nickels would be 2 × 12 = 24. So, the answer to your problem would be 24 nickels and 12 dimes.

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Answer:

The volume of this pyramid is 16 cm³.

Step-by-step explanation:

The volume [tex]V[/tex] of a solid pyramid can be given as:

[tex]\displaystyle V = \frac{1}{3} \cdot b \cdot h[/tex],

where

Here's how to solve this problem with calculus without using the previous formula.

Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.

Refer to the sketch attached. Let the vertical distance from the vertice be [tex]x[/tex] cm.

As a result, the length of a side of the square will be

[tex]\displaystyle \frac{x}{3}\times 4 = \frac{4}{3}x[/tex].

The area of the square will be

[tex]\displaystyle \left(\frac{4}{3}x\right)^{2} = \frac{16}{9}x^{2}[/tex].

Integrate the area of the horizontal cross-section with respect to [tex]x[/tex]

[tex]\displaystyle \begin{aligned}\int_{0}^{3}{\frac{16}{9}x^{2}\cdot dx} &= \frac{16}{9}\int_{0}^{3}{x^{2}\cdot dx}\\ &= \frac{16}{9}\cdot \left(\frac{1}{3}\int_{0}^{3}{3x^{2}\cdot dx}\right) & \text{Set up the integrand for power rule}\\ &= \left.\frac{16}{9}\times \frac{1}{3}\cdot x^{3}\right|^{3}_{0}\\ &= \frac{16}{27}\times 3^{3} \\ &= 16\end{aligned}[/tex].

In other words, the volume of this pyramid is 16 cubic centimeters.

Answer:

16cm3

Step-by-step explanation:

Answer:

yes! total calories= 535

Step-by-step explanation:

answer:

Donna Dieter is trying to keep her lunches under 600 calories. Today she had a peanut butter sandwich, one cup of vegetable soup, an apple, and a glass of milk. Did she stay under her goal?

YES

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ \cline{1-1} B=\stackrel{183\times 183}{33489}\\ h=110 \end{cases}\implies V=\cfrac{1}{3}(33489)(110)\implies V=1227930[/tex]

Answer:

V =1127930 m^3

Step-by-step explanation:

The volume is

V = 1/3 B h

where B is the area of the base

B = area of the square

B = 183*183 since it is a square

B = 33489

V = 1/3 *(33489) * 110

V =1127930 m^3

For this case we have to:

Let[tex]u = x + 1[/tex]

So:

[tex]u ^ 2-4u + 2 = 0[/tex]

We have the solution will be given by:

[tex]u = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = 1\\b = -4\\c = 2[/tex]

Substituting:

[tex]u = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (1) (2)}} {2 (1)}\\u = \frac {4 \pm \sqrt {16-8}} {2}\\u = \frac {4 \pm \sqrt {8}} {2}\\u = \frac {4 \pm \sqrt {2 ^ 2 * 2}} {2}\\u = \frac {4 \pm2 \sqrt {2}} {2}[/tex]

The solutions are:

[tex]u_ {1} = \frac {4 + 2 \sqrt {2}} {2} = 2 + \sqrt {2}\\u_ {2} = \frac {4-2 \sqrt {2}} {2} = 2- \sqrt {2}[/tex]

Returning the change:

[tex]2+ \sqrt {2} = x_ {1} +1\\x_ {1} = 1 + \sqrt {2}\\2- \sqrt {2} = x_ {2} +1\\x_ {2} = 1- \sqrt {2}[/tex]

Answer:

[tex]x_ {1} = 1 + \sqrt {2}\\x_ {2} = 1- \sqrt {2}[/tex]

Answer: 1st - x = 1 + √2 & 4th- x= 1 - √2

Step-by-step explanation:

Answer:

[tex]{\boxed{\text{A. }\math{k = -7}}[/tex]

Step-by-step explanation:

The general rule for vertical translation of a function ƒ(x) ⟶ ƒ(x) + k .

A positive value of k means that the graph is shifted up by k units.

The graph of ƒ(x) was shifted from (0, 1) to (0, -6).

[tex]\text{The graph was shifted down by seven units, so }{\boxed{\mathbf{k = -7}}[/tex]

The value of k is -7.

Vertical translation refers to the up or down movement of the graph of a function.

Here, the shape of the function remains the same.

It is also known as the movement/shifting of the graph along the y-axis.

In vertical translation, each point on the graph moves k units vertically and the graph is said to translated k units vertically.

The general rule for vertical translation of a function,

f(x)= g(x) + k .

here, the graph is shifted up by k units.

As, seen from the graph of g(x) is shifted from point (0, 1) to (0, -6).

Hence, the graph is shifted by -7 units.

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Answer:

1/32768

Step-by-step explanation:

First, solve the parenthesis:

2^3 = 2 * 2 * 2 = (2 * 2) * 2 = (4) * 2 = 8

Next, solve the outer power. Note that it has a negative sign, which means that after you solve for the power sign, you have to put the number under 1.

(8)^-5 = 1/(8 * 8 * 8 * 8 * 8) = 1/32768

1/32768 is your answer.

~

Answer:

A) 1/2^15

Step-by-step explanation:

edge2021

Answer:

90 recipes

Step-by-step explanation:

we know that

Fiona posted a total 216 recipes in 36 weeks

using proportion

Find out  how many recipes did she upload in 15 weeks'

Let

x -----> the number of recipes

[tex]\frac{216}{36}\frac{recipes}{weeks}=\frac{x}{15}\frac{recipes}{weeks} \\\\x=216*15/36\\\\x= 90\ recipes[/tex]

Answer:

27/1000

Step-by-step explanation:

To solve this, you would distribute the power 3 to the numerator and denomerator. 3^3 is 27 and 10^3 is 1000. So you get 27/1000

Answer:

the value is 27/1000 in other words the answer to your question is B

A = -120

AX = -240

X = 2

Step-by-step explanation:

∵ x + 4y - z = -14

∵ 5x + 6y + 3z = 4

∵ -2x + 7y + 2z = -17

\left[\begin{array}{ccc}1&4&-1\\5&6&3\\-2&7&2\end{array}\right]=\left[\begin{array}{ccc}-14\\4\\-17\end{array}\right]

∴ A = 1(6×2 - 3×7) + (-4)(2×5 - 3×-2) + (-1)(5×7 - 6×-2)

∴ A = 1(12 - 21) + (-4)(10 - -6) + (-1)(35 - -12)

∴ A = -9 + (-4)(16) + (-1)(47) = -9 - 64 - 47 = -120

To find X replace the column of X by the column of the answer

\left[\begin{array}{ccc}-14&4&-1\\4&6&3\\-17&7&2\end{array}\right]

∴ AX = -14(6×2 - 3×7) + (-4)(4×2 - 3×-17) + (-1)(4×7 - 6×-17)

∴ AX = -14(12 - 21) + (-4)(8 - -51) + (-1)(28 - -102)

∴ AX = 126 + (-4)(59) + (-1)(130) = 126 - 236 - 130 = -240

∴ X = AX/A = -240/-120 = 2  

Answer:

A     -120

Ax   -240

Ay    360

Az    -480

x    2

y    -3

z    4

Step-by-step explanation:

Answer:

C. 21

Step-by-step explanation:

g(x) = x² - 4

Give: x = 5

Plug in 5 for x in the equation:

g(5) = 5² - 4

Simplify. Remember to follow PEMDAS. First, solve the exponent, then subtract:

g(5) = (5 * 5) - 4

g(5) = 25 - 4

g(5) = 21

C. 21 is your answer.

~

Answer:

46%

Step-by-step explanation:

440 + 480 = 920

2000 / 920 =46%

Answer:

One cinnamon chip scone provides 46% of the daily recommended calorie intake of 2000 calories for an adult woman.

Step-by-step explanation:

Consider the provided information.

The Starbucks cinnamon chip scone has 480 calories-more calories than a 440 calorie McDonald's double cheeseburger.

First calculate the calories in Starbucks cinnamon chip scone .

Starbucks cinnamon has 480 calories-more than a 440 calorie cheeseburger.

The calories in Starbucks cinnamon = 480+440 = 920

Now we need to find the One cinnamon chip scone provides what percent of the daily recommended calorie intake of 2000 calories for an adult woman.

Find what percentage of 2000 is 920 as shown.

[tex]\frac{920}{2000}\times 100[/tex]

[tex]\frac{920}{20}[/tex]

[tex]46\%[/tex]

Hence, One cinnamon chip scone provides 46% of the daily recommended calorie intake of 2000 calories for an adult woman.

Answer:

D.

Increase by more than 0.25 dollars.

Step-by-step explanation:

What is the gross margin %?

Margin % = (2.50/1.00) * 100 = 250%

If the cost goes up 0.25 what will the  selling price have to do to maintain a markup of 250%?

250% =(x/1.25) * 100%

Divide by 100%

250 / 100 = x / 1.25

2.5 = x / 1.25  

Multiply both sides by 1.25

2.5 * 1.25 = x

3.125 = x

But that is really not the question. The question is, how much higher is that now than it used to be?

3.125 - 2.50 = 0.625 cents.

So you would have to increase the selling price by more than 0.25

Answer:

90-35=55

Hope this helps! <3