Given: AB = DC, AC = DB
Prove: AABC= ADCB
Look at the proof. Name the postulate you would use to prove the two triangles are congruent.
Given: AB DC, AC = DB
Prove: AABC= ADCB
AB= DC
Given
AC DB
Given
BC BC
Reflexive Property
of Congruence
AABC ADCB
?
B
D
C

Answer:

For the function [tex]$f(x)=4 x-3$[/tex] the average rate change from x is equal 1 to x is equal 2 is 4 .

Step-by-step explanation:

A function is given f(x)=4x-3.

It is required to find the average rate change of the function from x is 1 to x is 2 . simplify.

Step 1 of 2

A function f(x)=4 x-3 is given.

Determine the function [tex]$f\left(x_{1}\right)$[/tex] by putting the value of x=1 in the given function.

[tex]$$\begin{aligned}&f(1)=4(1)-3 \\&f(1)=1\end{aligned}$$$$f(1)=1$$[/tex]

Determine the function [tex]$f\left(x_{1}\right)$[/tex] by putting the value of x is 2 in the given function.

[tex]$$\begin{aligned}&f(2)=4(2)-3 \\&f(2)=5\end{aligned}$$[/tex]

Step 2 of 2

According to the formula of average rate change of the equation [tex]$\frac{\Delta y}{\Delta x}=\frac{f\left(x_{2}\right)-f\left(x_{2}\right)}{x_{2}-x_{1}}$[/tex]

Substitute the value of [tex]$f\left(x_{1}\right)$[/tex] with, [tex]$f\left(x_{1}\right)$[/tex] with [tex]$3, x_{2}$[/tex] with 2 and [tex]$x_{1}$[/tex] with 1 .

[tex]$$\begin{aligned}&\frac{\Delta y}{\Delta x}=\frac{5-1}{1} \\&\frac{\Delta y}{\Delta x}=4\end{aligned}$$[/tex]

Answer: 81/100



Step-by-step explanation:

I don't guarantee you I am right but..

first, solve for the exponents after substituting the numbers in

3/5 x 3/5 is 9/25

since b's exponent is negative, you change the fraction into its reciprocal and then do it with the exponent but positive

2/3^-3 to 3/2^3 and 3/2 x 3/2 is 9/4

then you mutiply both numbers to get 9/4 x 9/25 is 81/100

Answer:

The table that has the y-value as 2 for each input

Step-by-step explanation:

The table that has the y-value as 2 for each input. This is because as x increases by 1, the y-value is increasing by 0, so the slope is 0/1 or 0. The vertical line doesn't have a zero slope, since it's undefined,  because if you take any two points the "run" is 0, thus you would be dividing by 0, the slope cannot be defined.

Answer:

11 and 19

Step-by-step explanation:

X + (X+8) = 30

Open bracket

X plus X + 8 = 30

2x + 8= 30

Collect like terms

2x = 30 - 8

2x = 22

X=11

And x + 8 = 11 + 8= 19

Answer:

x = -3

y = 9

Step-by-step explanation:

6x + 3y = 9 ⇒ ( 1 )

Divide the whole equation by 3.

2x + y = 3 ⇒ ( 2 )

-9x - 2y = 9 ⇒ ( 3 )

Let us take equation (2) and make y the subject of the equation.

2x + y = 3

y = 3 - 2x ⇒ ( 4 )

Now let us take equation (3) and find the value of x.

For that, we can replace y with ( 3 - 2x ).

Let us solve it now.

-9x - 2y = 9

-9x - 2 ( 3 - 2x ) = 9

-9x -6 + 4x = 9

-5x - 6 = 9

-5x = 9 + 6

-5x = 15

Divide both sides by (-5).

x = -3

And now let us take equation (4) to find the value of y.

For that, we can replace x with -3.

Let us solve it now.

y = 3 - 2x

y = 3 - 2 × -3

y = 3 + 6

y = 9

4.59 g will be the amount of substance that will be present after 5 year.

Given: 16g of radioactive substance

            8g left after 8 year

Concept: In a chemical reaction, the half-life of a species is the time it takes for the concentration of that substance to drop to half its original value. In a first-order reaction, the half-life of the reactant is ln(2)/λ, where λ (also referred to as k) is the reaction rate constant.

The half-life is given as 5 years, so the amount remaining after 9 years will be found by using the steps done below:

Remaining amount of radioactive substance = initial × (1/2)^(t/(half-life))

Remaining substance = (16 g)×(1/2)^(9/5) ≈ 4.59 g

After 9 years i.e., after 8 years have passed

About 4.59 g of the substance remains.

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Answer:

Hence the expression [tex]$$(4z-y)(z-6)=4z^2-yz-24z+6y$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{matrix}{} & {} & {} & {} & 4z & - & y \\ \times & {} & {} & {} & z & - & 6 \\ \end{matrix}$$[/tex]

_________________

[tex]$$\begin{matrix}{} & {} & {} & - & 24z & + & 6y \\ 4{{z}^2} & - & yz & {} & {} & {} & {} \\ \end{matrix}$$[/tex]

_________________

[tex]$$\begin{matrix}4{{z}^2} & - & yz & - & 24z & + & 6y \\ \end{matrix}$$[/tex]

The function is assigning to each element of one set exactly one element from the other set.

First table represent a function.

Second table not represent a function (for -1 are four different numbers).

Third table represent a function.

Fourth table not represent a function (for -6 are two differen numbers 5 and 9)

Both climbers rested on the wall at a constant height for 2 minutes.

The illustrative graph that represents the climbers' movement is added as an attachment

From the attached graph, we have the following observation

The difference between the endpoints of both horizontal line is

Difference = 6- 4 = 2

Difference = 7 - 5 = 2

This means that both Brynn and Abby stopped for 2 minutes

Hence, the true statement about is that (d) Both climbers rested on the wall at a constant height for 2 minutes.

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The probability that a randomly selected light bulb will last between 825 hours and 900 is 0.477.

From the information given, a standard deviation below the mean will be:

= 750 - 75 = 675

Two standard deviations below the mean will be:

= 750 - 75(2)

= 600

In this case, we ant to know the probability that make up the areas. This is illustrated in the graph.

In conclusion, the correct option is 0.477.

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Answer:

6 1/4

Step-by-step explanation:

ad 2 and 3 get 5 ad 3 and 2 get five now u have 5/4 uh oh the 4 is full

take 1 from the 5 over 4 and turn that one into 6 and turn the 4/4 to 1/4

boom 6 1/4

Answer:

210° , 330°

Step-by-step explanation:

using the sides of the 30- 60- 90 triangle

with legs 1, [tex]\sqrt{3}[/tex] and hypotenuse 2 , then

[tex]sin^{-1}[/tex] [tex]\frac{1}{2}[/tex] = 30° ← related acute angle

since [tex]sin^{-1}[/tex] - [tex]\frac{1}{2}[/tex]

then angle is in third / fourth quadrants , then required angles are

180° + 30° = 210° ← in third quadrant

360° - 30° = 330° ← in fourth quadrant

The test statistic for this procedure is using two sample T-test is 0.458.

Definition of Two Sample T-test

A variation of the Student's t-test used to determine if two sample means are substantially different is known as the two sample T-test (also known as Welch's t-test, Welch's adjusted T, or unequal variances t-test). The test's degrees of freedom have been changed, which generally boosts the test's power for samples with unequal variance.

T-Test Statistic for The Procedure

It is given that mean of the differences = 1.33

And, the standard deviation of the differences, standard error = 2.90

The test static formula is given as,

t = (estimate - hypothized value) / standard error

Here,  t is the t- test statistic, and estimate is the mean of the differences.

Since it is given that all conditions are met, the hypothized value can be taken as 0

Substituting substituting estimate = 1.33 and standard error = 2.90 in the t-test statistic formula, we get,

t = (1.33-0)/2.90

or t = 0.458

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The equations are both the same with a slope of 2 and y-intercept of 3.

A line is the distance between two points. Given the equations below;

2y - 4x = 6

y = 2x + 3

___________

y - 2x = 3

y = 2x + 3

The equations are both the same with a slope of 2 and y-intercept of 3. The graph of the equation is plotted below.

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The regression equation is y = 3.231x + 10.138

The regression model that fits the data is a linear model.

This is so because as x increases by 1, the y value increases by an almost constant rate

To determine the regression equation, we make use of a graphing calculator

From the graphing calculator, we have the following summary:

The regression equation is then calculated as;

y = bx + a

Where

b = SP/SSX = 56.55/17.5 = 3.23143

a = MY - bMX = 18.22 - (3.23*2.5) = 10.1381

So, we have:

y = 3.23143x + 10.1381

Approximate

y = 3.231x + 10.138

Hence, the regression equation is y = 3.231x + 10.138

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The  dimensions of the microwave cup-of-soup package are:

Radius = 3.39cm, and Height = 9.27cm.

Computed using differentiation.

The microwave cup-of-soup package is in the shape of a cylinder.

Thus, its volume can be shown as, V = πr²h, where r is its radius in cm and h is its height in cm.

The volume is given to be 450 cm³.

Thus, we can say that,

πr²h = 450,

or, h = 450/(πr²) ... (i).

The cost of the microwaveable cup-of-soup package is given as:

The bottom is made of styrofoam at 0.03 cents/cm².

The area of the bottom = πr².

Therefore, the cost of the bottom = πr²(0.03) cents.

The side is made of styrofoam at the rate of 0.03 cents/cm².

The area of the side = 2πrh = 2πr{450/(πr²)}. {Taking h = 450/(πr²) from (i)}.

Therefore, the cost of the side = 2πr{450/(πr²)}(0.03) cents.

The top is made of glued paper at the rate of 0.08 cents/cm².

The area of the top = πr².

Therefore, the cost of the top = πr²(0.08) cents.

Therefore the total production cost function can be written as:

C = πr²(0.03) + 2πr{450/(πr²)}(0.03) + πr²(0.08) cents,

or, C = 0.03πr² + 0.08πr² + 27/r cents,

or, C = 0.11πr² + 27/r cents ... (ii).

We are asked to minimize the cost function.

To minimize it, we follow these steps:

Differentiating both sides in (ii) with respect to the radius,

dC/dr = 0.22πr - 27/r² ... (iii).

To get the points of inflections, we equate this to zero, to get,

dC/dr = 0.22πr - 27/r² = 0,

or, 0.22πr - 27/r² = 0,

or, 0.22πr = 27/r²,

or, r³ = 27/0.22π,

or, r = ∛(27/0.22π) = 3.393 cm.

To check whether the cost C, is minimum or maximum at the point, we calculate the second order differential, and if it's greater than 0, then we get a minimum and vice-versa.

Thus, differentiating both sides of (iii), with respect to the radius r, we get:

d²C/dr² = 0.22π + 54/r³.

0.22π + 54/r³ is greater than 0, for all values of r, since r is always greater than 0 {radius of an object cannot be negative}.

Thus, the radius at which the cost is minimized is 3.393 cm.

The corresponding height will be 450/(πr²) = 9.274 cm.

Thus, the dimensions of the microwave cup-of-soup package are:

Radius = 3.39cm, and Height = 9.27cm.

Computed using differentiation.

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To convert an integer to a fraction you must choose an expression that does not alter the numerical value. You can do this with multiples of the number, for example, for 100:

100/1 = 200/2 = 300/3 = 400/4 = 100

Another example, for 500:

500 = 500/1 = 1000/2 = 1500/3 = 2000/4

Answer:

Step-by-step explanation:I actually depends on what your solving like if you are solving a question is says solving 16 times a random fraction, you just simply add one under 16. And it will make it 16/1

The logarithm of 10 to base 10 is 1

The given parameters are:

So, the logarithm expression can be represented as:

[tex]\log_{10}10[/tex]

The law of logarithm states that:

[tex]\log_{x}x = 1[/tex]

The above means that;

When the base and the number are the same, the logarithm is 1

So, we have:

[tex]\log_{10}10 = 1[/tex]

Hence, the logarithmic value is 1

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Answer:

(1,3)

Step-by-step explanation:

since they are open circles they will not have brackets instead they will have parentheses.

one answer for this number line (graph) is (1,3)

Answer: 74.52 if the question is how far she swims

Step-by-step explanation:

What the given proof is trying to show us is that; ∠3 = 126°

From the attached line, we see that angle 1 and angle 3 form a straight line. Now, since we know that angles on a straight line sum up to 180°, then it means that they are supplementary.

We are given;

1) ∠1 and ∠2 are supplementary

2) ∠1 = 36°

Thus from definition of complementary angles, we can say that;

36° + ∠2 = 90°

Subtraction property of equality when applied gives;

∠2 = 54°

We are told that ∠2 and ∠3 are linear pairs and as such;

∠2 + ∠3 = 180° from linear pairs theorem.

By substitution property of equality we have;

54° + ∠3 = 180°

Solving gives ∠3 = 126°

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Answer:

742 is 7.42x10^2

0.053 inches is 5.3x10-2 inches

Step-by-step explanation:

The goal is to convert he number into a format that has one digit to the left of the decimal point.  When moving the decimal point more to the left, each step reduces the number by a factor of 10/

742

74.2 is the original number reduced by 10.  To keep the number valid, we need to multiply by 10, which can be written as 74.2 x 10.

7.42 is reduced by another factor of 10:  7.42 x10x10  This is the same as 7.42x10^2

742 is 7.42x10^2

0.053

0.53 is the original number multiplied by 10.  To keep the number valid, we need to divide by 10, which can be written as 0.53x10^-1

5.3 is the original number divided by another factor of 10.  This can be written as 5.3x10^-2

0.053 inches is 5.3x10-2 inches

The roots of a polynomial function tells us about the position of the equation on a graph and the roots also tells us about the complex and imaginary roots. So, Roots of chords are similar to the roots of polynomial functions.

A real root of a polynomial function is the point where the graph crosses the x-axis (also known as a zero or solution). For example, the root of y=x^2 is at x=0.

Roots can also be complex in the form a + bi (where a and b are real numbers and i is the square root of -1) and not cross the x-axis. Imaginary roots of a quadratic function can be found using the quadratic formula.

A root can tell you multiply things about a graph. For example, if a root is (3,0), then the graph crosses the x-axis at x=3. The complex conjugate root theorem states that if there is one complex root a + bi, then a - bi is also a complex root of the polynomial. So if you are given a quadratic function (must have 2 roots), and one of them is given as complex, then you know the other is also complex and therefore the graph does not cross the x-axis.

So, The roots of a polynomial function tells us about the position of the equation on a graph and the roots also tells us about the complex and imaginary roots. So, Roots of chords are similar to the roots of polynomial functions.

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3) Vertical angles are congruent.

4) Corresponding angles tehorem

5) Transitive property of congruence

Answer:

C

Step-by-step explanation:

on edge

Answer:

4 gifts

Step-by-step explanation:

4÷4=0

so you get each other a gift so there none to spare

Answer:

12 gifts

Step-by-step explanation:

If there are 4 people, and each person brings a gift for each of the other three people, that means that there are 12 gifts at the party. Let's say there are four people: A, B, C, and D. Person A would have to bring 3 gifts to give  B, C, and D. Similarly, B would bring a gift each for A, C, D. C would bring a gift for A, B, D. Lastly, D would bring a gift for A, B, and C. Each person brings three gifts to give to the other three people at the party, and 3*4 people is 12. I hope that makes sense.

Answer:

[tex]5)\ \ \left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4=4x^{\frac{4}{5}}y^{\frac{2}{5}}[/tex]

[tex]6)\ \ \frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }=1[/tex]

Step-by-step explanation:

[tex]\left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4[/tex]

[tex]=x^{\frac{8}{10}}y^{\frac{4}{10}} +3x^{\frac{4}{5}}y^{\frac{4}{10} }[/tex]

[tex]=x^{\frac{4}{5}}y^{\frac{2}{5}} +3x^{\frac{4}{5}}y^{\frac{2}{5} }[/tex]

[tex]=x^{\frac{4}{5}}y^{\frac{2}{5}}\times(1+3)[/tex]

[tex]=4x^{\frac{4}{5}}y^{\frac{2}{5}}[/tex]

……………………………………

[tex]\frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }[/tex]

[tex]=\frac{(2+7) \times\sqrt{9^{5}} }{\sqrt{9^{2}} \times \sqrt{9^{5}} }[/tex]

[tex]=\frac{9 \times\sqrt{9^{5}} }{9 \times \sqrt{9^{5}} }[/tex]

[tex]=1[/tex]

Answer:

Point-slope form of equation given as [tex]$y-2=-2(x+2)$[/tex].

Slope-intercept form of equation is given as [tex]$y=-2 x-2$[/tex].

Step-by-step explanation:

In the question, it is given that the slope of a line is -2 and it passes from (-2,2).

It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.

To do so, first find the values which are given in the question and put it in the formula of point-slope form. Simplify the equation to rewrite as slope-intercept form.

Step 1 of 2

Passing point of the line is (-2,2).

Hence, [tex]$x_{1}=-2$[/tex] and

[tex]$$y_{1}=2 \text {. }$$[/tex]

Also, the slope of the line is -2.

Hence, m=-2

Substitute the above values in point-slope form of equation given by [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]

[tex]$$\begin{aligned}&y-y_{1}=m\left(x-x_{1}\right) \\&y-2=-2(x-(-2) \\&y-2=-2(x+2)\end{aligned}$$[/tex]

Hence, point-slope form of equation given as y-2=-2(x+2).

Step 2 of 2

Solve y-2=-2(x+2) to write it as slope-intercept form given by y=mx+c.

[tex]$$\begin{aligned}&y-2=-2(x+2) \\&y-2=-2 x-4 \\&y=-2 x-4+2 \\&y=-2 x-2\end{aligned}$$[/tex]

Hence, slope-intercept form of equation is given as y=-2x-2.

Answer:

Hence the expression [tex]$$(3rs-7)(3rs-4)=9r^2s^2-33rs+28$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{matrix}{} & {} & {} & {} & 3rs & - & 7 \\ \times & {} & {} & {} & 3rs & - & 4 \\ \end{matrix}$$[/tex]

_________________

[tex]$$\begin{matrix}{} & {} & {} & - & 12rs & + & 28 \\ {} & {} & 9{{r}^2}{{s}^2} & - & 21rs & {} & {} \\ \end{matrix}$$[/tex]

________________

[tex]$$\begin{matrix}{} & {} & 9{{r}^2}{{s}^2} & - & 33rs & + & 28 \\ \end{matrix}$$[/tex]

Answer:

28

Step-by-step explanation:

Simple solution:

Each one was 5 years younger 5 years ago, so subtract 5 from 38 for each one.

38 - 5 - 5 = 28

The sum of their ages was 28.

Algebra solution:

Kate is x years old now.

Gift is y years old now.

The sum of their ages now is x + y.

The sum of their ages is 38, so x + y = 38.

5 years ago:

Kate was x - 5 years old.

Gift was y - 5 years old.

The sum of their ages 5 years ago was x - 5 + y - 5 = x + y - 10.

Substitute 38 for x + y.

The sum of their ages was 38 - 10 = 28