Triangles ABC and DEF are similar.
Find the length of segment AC.

Answer:

Step-by-step explanation:

S = [tex]\left[\begin{array}{cc}4&1\\-1&-2\end{array}\right][/tex]

T = [tex]\left[\begin{array}{cc}-5&0\\-4&3\end{array}\right][/tex]

ST = [tex]\left[\begin{array}{cc}4&1\\-1&-2\end{array}\right][/tex] × [tex]\left[\begin{array}{cc}-5&0\\-4&3\end{array}\right][/tex] = [tex]\left[\begin{array}{cc}14(-5)+1(-4)&(4)0+1(3)\\(-1)(-5)+(-2)(-4)&(-1)0+(-2)(3)\end{array}\right][/tex] =

= [tex]\left[\begin{array}{cc}-24&3\\13&-6\end{array}\right][/tex]

TS = [tex]\left[\begin{array}{cc}-5&0\\-4&3\end{array}\right][/tex] × [tex]\left[\begin{array}{cc}4&1\\-1&-2\end{array}\right][/tex] = [tex]\left[\begin{array}{cc}(-5)(4)+(0)(-1)&(-5)(1)+(0)(-2)\\(-4)(4)+3(-1)&(-4)(1)+(3)(-2)\end{array}\right][/tex] =

= [tex]\left[\begin{array}{cc}-20&-5\\-19&-10\end{array}\right][/tex]

ST ≠ TS

Answer:

Step-by-step explanation:

64

because the small triangle at the top is isoscel and has the base angles BDE and BED = (180 -48)/2 =66

angle BDE is congruent to DAC = 66, because 2 || BE and AC are cut by transversal BA

angle ADC = 180 -50 -66 = 64

Answer:

z = 5

Step-by-step explanation:

-0.25z = -1.25

-1.25 ÷ -0.25 = 5

z = 5

Answer:

10 belts

Step-by-step explanation:

6.5 meters of cord / 0.625 meters per belt = 10.4 belts

Because 0.4 meters of cord is not enough for a belt, the answer is 10.

Answer:

1

Step-by-step explanation:

An expression contains variables which can be represented by using the alphabets like a, b, c, m, x, y, z, etc. We can form different expressions using various numbers and variables. The expression equivalent to x+(-3)+(-2) - 2 is x-7 = 0. The correct option is B.

An expression or also called the algebraic expression is defined as the mathematical statement which contains numbers, variables and an arithmetic operation between them.

In order to factorize or simplify the expression, we should know how to combine the like terms, factor a number, order of operations. The given equation can be simplified as:

x + (-5) -2 = 0

x - 7 = 0

Thus the correct option is B.

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Your question is incomplete most probably your full question was;

Which expression is equivalent to x+(-3)+(-2) - 2

A. x-3 = 0

B. x - 7 = 0

C. x - 4 = 0

D. x- 3 = 0

Answer:

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

Step-by-step explanation:

[tex]16^{x}[/tex] = [tex]\frac{1}{64}[/tex] , that is

[tex](4^2)^{x}[/tex] = [tex]\frac{1}{4^3}[/tex]

[tex]4^{2x}[/tex] = [tex]4^{-3}[/tex]

since bases on both sides are equal , both 4 then equate exponents

2x = - 3 ( divide both sides by 2 )

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

Answer:

x = 5, y = -2

Step-by-step explanation:

2x + 5y = 0 --- Equation 1

Equation 1×3: 6x + 15y = 0 --- Equation 2

3x - 4y = 23 --- Equation 3

Equation 3×2: 6x - 8y = 46 --- Equation 3

We will be eliminating 6x from Equation 2.

Equation 3-2: 6x - 8y - 6x - 15y = 46-0

-23y = 46

y = 46 ÷ -23

y = -2

Substitute y = -2 into Equation 1:

2x + 5y = 0

2x + 5(-2) = 0

2x + (-10) = 0

2x - 10 = 0

2x = 10

x = 10 ÷ 2

x = 5

Answer:no it does not

Step-by-step explanation:

In order for it to round up it would have to be 82.5 or higher.

Answer:

No. To round up to 83 the number has to be 82.5 or higher.

(x, y) = (0, -7) and ((28/5 , 21/5)) , as found by solving the system of linear equations.

A system of linear equations is a set of two or more linear equations. Linear equations refer to the equations that involve two or more variables in the form of "ax + b".

Given: 2x - y = 7x² + y² = 49

to find: Values of x and y.

Finding:

Solving the system of two linear equations, by deriving the value of one variable from an equation and substituting it in the other equation and solving for the two variables.

eqn1 2x - y = 7

y = 2x - 7

eqn2  x² + y² = 49O

substituting the value of y from eqn1,

we get: x² + (2x - 7)² = 49

x² + 4x² + 49 - 28x = 49

5x² -28x = 0

x ( 5x - 28) = 0

x = 0, x = 28/5

For x = 0, y = -7 (in eqn1)=>

(x, y) = (0, 7)

For x = 28/5

y = 2(28/5) - 7

= (56 - 35) / 5

= 21 / 5

(x,y) = (28/5 , 21/5)

Hence, (x, y) = (0, -7) and (28/5 , 21/5), as found by solving the system of linear equations.

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When it's the > or ≥ sign, the shade/region will be above the graph.

When it's the < or ≤ sign, the shade/region will be below the graph.

Thus, the answer is below.

Answer:

m∠2= 97

Step-by-step explanation:

When 2 angles are supplementary, they add up to 180 degrees.

We are told that angle 1 is 83 and the angle 1 and 2 are supplementary

So, angle 1 and 2 add up to 180, let's subtract 83 from 180 to find measure of angle 2

180-83=97

hope this helps! feel free to ask any questions

Answer:

[tex]B= \frac{S + 7}{A}[/tex]

Step-by-step explanation:

We are given the following equation:
S = BA - 7

And we want to solve it for B.

This is a literal equation, and to solve these, we need to isolate the variable we are solving for (in this case, B) on one side.

Here's the equation again:
S = BA - 7

We can start by adding 7 to both sides (removes it from the right side).

S = BA - 7

+7        +7

________________

S + 7 = BA

Now, divide both sides by A to isolate B. Remember that we're dividing both S AND 7 by A.

(S + 7) = BA

÷A       ÷A

[tex]\frac{S+7}{A} = B[/tex]

This can be rewritten to be: [tex]B = \frac{S + 7}{A}[/tex]

You can also write it as  [tex]B = \frac{S}{A} +\frac{7}{A }[/tex] if you wish.

The algebraic expression is '4d' for the phrase "The product of 4 and the depth of the pool."

Expressing algebraically means to express it concisely yet easily understandable using numbers and letters only. Most of the Mathematical statements are expressed algebraically to make it easily readable and understandable.

Here, we are asked to represent the phrase "The product of 4 and the depth of the pool" algebraically.

The depth of the pool is an unknown quantity. So let it be 'd'.

Then product of two numbers means multiplying them.

We write the above statement as '4  x d' or simply, '4d' ignoring the multiplication symbol in between.

The question is incomplete. Find the complete question below:

Translate the following phrase into an algebraic expression. Use the variable d to represent the unknown quantity. The product of 4 and the depth of the pool

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Answer:

-2.5 , -1 , 15.03 , 15.32

-10 , -6 1/2 , -1 , 0

0.02 , 0.2 , 2.02 , 2.2

Step-by-step explanation:

Answer:

-2.5 , -1 , 15.03 , 15.32

-10 , -6 1/2 , -1 , 0

0.02 , 0.2 , 2.02 , 2.2

Step-by-step explanation:

Answer:

3/14 of a liter of salt

Step-by-step explanation:

Step one:

given

tot amount of salt= 5/7 of a liter of salt

that is 1*5/7= 5/7 liters

She used 1/2 of a liter for an experiment

Required:

the remaining amount of salt

Step two:

we are going to subtract the salt used for the experiment from the total

= 5/7-1/2

= 10-7/14

= 3/14

The remainder is 3/14 of a liter of salt

Answer:

752 pies will be made form the 2,528 pound pumpkin

Step-by-step explanation:

Here, we want to know the number of pies that will be made from the given number of purée

Firstly, we need to know the number of cups in 2,528-pound pumpkin purée

Mathematically, 1 pound = 1.92 cups

So , 2528 pound will be 2,528/1.92 = 1,316.67 cups

1 3/4 cups is needed to make a pie

So the number of pies that 1,316.67 cups will

make would be;

1316.67 divided by 1 3/4

= 1316.67/1.75 = 752 approximately

Answer:

x= 2

Step-by-step explanation:

so you add the values given in the brackets and leave X as it is (do this on both sides of the equation.

1. (x + 5)(x+4)= (x+12)(x+1)

2. multiply the parenthesis on both sides or one at a time

so,  [tex]x^{2}[/tex]+5x+4x+20 = [tex]x^{2}[/tex]+12+1x+12

3. cancel like terms which we have [tex]x^{2}[/tex] so remove that.

5x+4x+20=12+1x+12

4. collect like terms.

9x + 20 = 13x + 12

5. move like terms.

9x-13x=12-20 = -4 = -8

6. x= [tex]\frac{-4}{-8}[/tex]  divide both sides by 4 or basically simplify 4 divided by 8

which leaves u with

x= 2

hope this helps x, let me know if u have any questions. photomath is an app that helps too.

Answer: 24m+28

Step-by-step explanation:

you would distribute the -4 threw eveything

so it would be 24m+28

Answer:

9.1 = a+4

Step-by-step explanation:

The right side has two different values, variable a, constant 4.

The left side has the constant 9.1.

If both sides are equal, then

a + 4 should equal 9.1

Answer:

9.1 = a+4

Step-by-step explanation:

Answer:

I hope this helps:))

Step-by-step explanation:

Answer:

12n - 8

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define Expression

4(3n - 2)

Step 2: Expand

Answer:

4(3n-2)

=> 12n-8

=> 12n=8

=> n=8/12

=> n= 2/3

Answer:

567

Step-by-step explanation:

rghjbvcdfghjk

Answer:

567

Step-by-step explanation:

five hundred and sixty seven

Answer:

11

Step-by-step explanation:

SInce the x vales are the same, you just have to look at the y values. 7 is how much from -4? So do 7-(-4)

Answer: 11

Hope this helps :)

Answer:

50.265m^3

Step-by-step explanation:

because the formula for solving this problem is πr^2•height and then to finish solving it would have to be put into cubed as it's 3d

The one digit number is 4 and three digit number is 727.

Let us consider the one digit number be a and three digit number be b. Given that their sum is equal to 731.

a + b = 731 : equation 1

Also, their product is equal to 2908.

a × b = 2908 : equation 2

Now, from equation 1, the value of b is

b = 731 - a : equation 3

Putting the value of b in equation 2, we get

a (731 - a) = 2908

731a - a² = 2908

a² - 731a + 2908 = a

Using middle term splitting, the equation can be written as

a² - 727a - 4a + 2908 = 0

a(a - 727) - 4(a - 727) = 0

a - 4 = 0 and a - 727 = 0

a = 4, 727

Now, putting the value of a in equation 3, we get

b = 731 - 4 and 731 - 727

b = 727, 4

Thus, the one digit number is 4 and three digit number is 727.

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Answer:

C.) completely randomized experimental design

Step-by-step explanation:

Edge 2020

The experimental design used by Betty is completely randomized experimental design. Hence, option A is correct.

A process used to confirm or deny a theory, as well as assess the effectiveness or possibility of something that has never been performed before, is called an investigation.

By showing what happens when a particular element is modified, experiments shed light on causation relationships. Experiments have a wide range of objectives and sizes, but always depend on a repeatable process and a logical examination of the outcomes. Additionally, there are experiments conducted in nature.

As Betty is wants to bake a perfect cookie, and she has enough batter. She is testing to bake the batter at different temperatures to see that what is the ideal temperature to make perfect cookies. So, this is completely randomized experimental design.

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Answer:

D.

Step-by-step explanation: