Indicate the equation of the given line in standard form. Show all your work for full credit. the line containing the median of the trapezoid whose vertices are R(-1,5)S(1,8) T(7,-2) U(2,0)

Answer:

$135

Step-by-step explanation:

Givens:

1) Jenny + Dan = $330

2) Jenny = $60 + Dan

Substitute Jenny's value into equation 1

(Dan = D)

$60 + D + D = $330

2D = $270

D = $135

Hope this helps :)

Answer:

14

Step-by-step explanation:

Evaluate exponents, followed by brackets, multiplication and addition

Given

3² + (- 2 + 3) × 5

= 9 + 1 × 5 ← exponents and bracket

= 9 + 5 ← multiplication

= 14 ← addition

Answer:

The correct answer is 14.

Step-by-step explanation:

I'll give you an a hint. You'd need to know about the order of operations is parenthesis, exponent, multiply, divide, add, and subtract.

First, do parenthesis.

(-2+3)=1

3²+1*5

Next, exponent.

3²=3*3=9

9+1*5

Then, multiply.

5*1=5

Finally, add.

9+5=14

So, the correct answer is 14.

I hope this helps!

Answer:

B. 68%.

Step-by-step explanation:

We have been given that driving times for students' commute to school is normally distributed, with a mean time of 14 minutes and a standard deviation of 3 minutes.

First of all, we will find z-score of 11 and 17 using z-score formula.

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{11-14}{3}[/tex]

[tex]z=\frac{-3}{3}[/tex]

[tex]z=-1[/tex]

[tex]z=\frac{17-14}{3}[/tex]

[tex]z=\frac{3}{3}[/tex]

[tex]z=1[/tex]

We know that z-score tells us a data point is how many standard deviations above or below mean.

Our z-score -1 and 1 represent that 11 and 17 lie within one standard deviation of the mean.

By empirical rule 68% data lies with in one standard deviation of the mean, therefore, option B is the correct choice.

Answer: 68%

Step-by-step explanation: ya boy just took le test :-)

Answer:

{-0.36, 8.36) to the nearest hundredth.

Step-by-step explanation:

x^2 - 8x = 3

(x - 4)^2 - 16 = 3

(x - 4)^2 = 19

Taking square roots:

x - 4 = +/- √19

x =  4 +/- √19

x = {-0.36, 8.36} to nearest 1/100.

For this case we have the following expression:

[tex]x ^ 2-8x = 3[/tex]

We must complete squares.

So:

We divide the middle term between two and we square it:

[tex](\frac {-8} {2}) ^ 2[/tex], then:

[tex]x ^ 2-8x + (\frac {-8} {2}) ^ 2 = 3 + (\frac {-8} {2}) ^ 2\\x ^ 2-8x + (- 4) ^ 2 = 3 + 16[/tex]

We have to, by definition:

[tex](a-b) ^ 2 = a ^ 2-2ab + b ^ 2[/tex]

Then, rewriting:

([tex](x-4) ^ 2 = 19[/tex]

To find the roots, we apply square root on both sides:

[tex]x-4 = \sqrt {19}[/tex]

We have two solutions:

[tex]x_ {1} = \sqrt {19} +4\\x_ {2} = - \sqrt {19} +4[/tex]

Answer:

([tex](x-4) ^ 2 = 19\\x_ {1} = \sqrt {19} +4\\x_ {2} = - \sqrt {19} +4[/tex]

Answer:

Vertify is an identity

Sin2x=2cotx(sin^2x)  

starting from the right-hand side

2cotx(sin^2x)

=2(cosx/sinx)(sin^2x)

=2(cosx/sinx)(sin^2x)

=2sinxcosx=sin2x

ans:right-hand side=left-hand side

Step-by-step explanation:

Step-by-step explanation:

sin^2x = 2cotx sin^2x

Rewrite right side as fractions:

sin^2x = [tex]\frac{2}{1}[/tex] * [tex]\frac{cosx}{sinx}[/tex] * [tex]\frac{(sinx)(sinx)}{1}[/tex]

Multiply together [tex]\frac{cosx}{sinx}[/tex] and [tex]\frac{(sinx)(sinx)}{1}[/tex] :

sin^2x = [tex]\frac{2}{1}[/tex] * [tex]\frac{(cosx)(sinx)(sinx)}{sinx}[/tex]

Cancel out sinx on top and bottom:

sin^2x = [tex]\frac{2}{1}[/tex] * [tex]\frac{(sinx)(cosx)}{1}[/tex]

Multiply together 2 and (sinx)(cosx):

sin^2x = 2sinxcosx

Substitute sin^2x in for 2sinxcosx:

sin^2x = sin^2x

Answer:

It can be B or C (B is closer to being correct); neither are worded perfectly correct. Definitely not A or C.

Step-by-step explanation:

I am a math teacher and whoever created this question didn't cover everything.

The answer is all numbers greater than 10, not just rational (irrational should also be included) and not just whole numbers (fractions and decimals should be included).

Answer:

(B)a rational number infinitely close to 10 but greater than 10, and all other rational numbers greater than 10

Step-by-step explanation:

x> 10 means all numbers greater than 10

(A)10 and every whole number greater than 10

False, does not include 10

(B)a rational number infinitely close to 10 but greater than 10, and all other rational numbers greater than 10

True

(C)11 and every whole number greater than 11

False, it only included integers. 10.5 is a solution but not included here

(D)a rational number infinitely close to 10 but greater than 10, and all other whole numbers greater than 10

False, it only included whole numbers. 10.5 is a solution but not included here

The answer should really be real numbers, not rational numbers.  

Irrational numbers can be solutions.  But given the choices given, B is the best solution.

Answer:

P = -2600/3 t + 25600/3

P = -8200/3

Step-by-step explanation:

t is the time in years since 1990, so two points on the line are (5, 4200) and (8, 1600).

Using the points to find the slope:

m = (y₂ − y₁) / (x₂ − x₁)

m = (1600 − 4200) / (8 − 5)

m = -2600/3

Now writing the equation in point-slope form:

P − 4200 = -2600/3 (t − 5)

Converting to slope-intercept form:

P − 4200 = -2600/3 t + 13000/3

P = -2600/3 t + 25600/3

In 2003, t = 13:

P = -2600/3 (13) + 25600/3

P = -8200/3

The linear formula for the moose population is P = -800t + 8200. The moose population predicted by this model for the year 2003 is 2,400.

In this question, we are given that in 1995 the moose population was 4200 and by 1998 it was 1600. This change in population mimics a linear relationship. We are asked to find the formula for this line and then predict the moose population in 2003.

We know that 1995 corresponds to t = 5 (since t is the years since 1990) and 1998 corresponds to t = 8. Therefore we can find the slope of the line (m) as (4200- 1600) / (5 - 8) = -800 per year. Since we know that the line crosses the point (5,4200), we can find the y-intercept, denoted as (b), using the formula y = mx + b.

Substitute m = -800, x = 5, and y = 4200 into the equation and solve for b

4200 = -800 * 5 + b

This simplifies to b= 4200 + 4000 = 8200

Therefore, the formula is P = -800t + 8200

To predict the moose population in 2003, simply substitute t = 13 into the formula (since 2003 is 13 years since 1990). Therefore,

P = -800 * 13 + 8200 = 2400

Therefore, the model predicts that the moose population in 2003 would be 2400.

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Answer:

The correct answer option is A. Loss of 9 oz.

Step-by-step explanation:

We are given that a cat's weight change -8 oz. while she was sick. It means that the cat lost 8 ounces of weight.

We are to determine whether which of the given answer options show a greater change in weight.

The correct answer for this is: loss of 9 oz which is a greater loss than 8 oz.

Answer:

420

Step-by-step explanation:

Amount in the 45% solution + amount in the 70% solution = amount in the 45% solution

0.15 × 350 + 0.70 × V = 0.45 × (350 + V)

52.5 + 0.70V = 157.5 + 0.45V

0.25V = 105

V = 420

You need 420 mL of the 70% solution.

After setting up and solving a weighted average equation, the result reveals that you would need 1050 mL of the 70% alcohol solution to achieve the desired 45% alcohol solution.

To solve this problem, we can use the concept of weighted averages. The final volume of alcohol in the 45% solution will be the sum of the alcohol in the 15% solution and the 70% solution. Let's denote the volume of the 70% solution we need to add as X ml. So, the equation will be:

0.15 × 350 + 0.70 × X = 0.45 × (350 + X)

Solving this equation will give us the amount of 70% solution needed. After simplifying, you get:

52.5 + 0.7X = 157.5 + 0.45X

Further simplification gives:

0.7X - 0.45X = 157.5 - 52.5

Therefore, X = 1050 ml. So, you will need 1050 ml of the 70% solution.

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Answer:

P=110in

Step-by-step explanation:let me know if it's correct i'm not 100% sure

Answer:

110 inches

Step-by-step explanation:

The perimeter is basically the sum of all sides

In this case, it will be

25+25=50 for 2 opposite sides

30+30= 60 for 2 other opposite sides

hence 50+60= 110 inches

Answer:Y=7

Step-by-step explanation:

-8x-3y = -13    (eq 1)

-3x-2y = -11    (eq 2)

First, multiply equation 1 by 2.

-16x-6y = -26

Second, multiply equation 2 by 3.

-9x-6y = -33

Subtract the system of equations:

-16x-6y = -26

-9x-6y = -33

-7x = 7

x = -1

Substitute this value into one of the original equations to solve for y

-3x-2y = -11

-3(-1)-2y = -11

3-2y = -11

-2y = -14

y = 7

Really hope this helps  :)

Hey There!

We have been given:

[tex]8x + 3y = 13 \\ 3x + 2y = 11[/tex]

Find the lcm of 3 and 2 to eliminate one equation:

3 * 2 = 6

2 * 3 = 6

Multiply each equation to get to 6:

[tex]2(8x + 3y = 13)\\ 16x + 6y = 26[/tex]

[tex]3(3x + 2y = 11)\\ 9x+6y=33[/tex]

Eliminate:

[tex]16x + 6y = 26\\ -(9x+6y=33)\\ -9x - 6y=-33[/tex]

Simplify:

[tex]16x + 6y = 26\\ -9x - 6y=-33 \\ 7x = -7[/tex]

Solve for x by dividing 7 in both sides:

[tex]7x = -7\\ x = -1[/tex]

Solve for y by substituting x in any equation with -1:

[tex]8(-1) + 3y = 13[/tex]

Simplify:

[tex]-8 + 3y = 13[/tex]

Add 8 in both sides:

[tex]3y = 21[/tex]

Solve for y by dividing 3 in both sides:

[tex]y = 7[/tex]

The value of x is -1 and the value of y is 7

Our answers:

x = -1

y = 7

Answer:

y = -2x+1

Step-by-step explanation:

We have a point and a slope, so we can use the point slope form of a line

y-y1 = m(x-x1)  where m is the slope and (x1,y1) is the point

y-3 = -2(x--1)

y-3=-2(x+1)

Distribute the 2

y-3 = -2x-2

Add 3 to each side

y-3+3 = -2x-2+3

y = -2x+1

This is in slope intercept form

Answer:

729

Step-by-step explanation:

1/3^-2×3^-4×(-1)^2

=3^2×3^4/1

=9×81

=729

For this case we have the following expression:

[tex]\frac {1} {3^ {- 2} * x^{ - 4} * y ^ 2}[/tex]

We must evaluate the expression to:

[tex]x = 3\\y = -1[/tex]

So:

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

[tex]\frac {1} {\frac {1} {3 ^ 2} * \frac {1} {3 ^ 4} * 1} =\\\frac {1} {\frac {1} {3 ^ 2} * \frac {1} {3 ^ 4}} =\\\frac {1} {\frac {1} {9} * \frac {1} {81}} =\\\frac {1} {\frac {1} {729}} =\\\frac {729} {1} =\\729[/tex]

Answer:

Option B

Answer:

It a delta notation that change in y over change in x

Answer:

C

Step-by-step explanation:

Edge 2021

Answer:

[tex]\large\boxed{A=54\ m^2}[/tex]

Step-by-step explanation:

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdor h[/tex]

b₁, b₂ - bases

h - height

We must use the Pythagorean theorem:

[tex]x^2+8^2=10^2[/tex]

[tex]x^2+64=100[/tex]              subtract 64 from both sides

[tex]x^2=36\to x=\sqrt{36}\\\\x=6\ m[/tex]

We have b₁ = 6 + 6 = 12m, b₂ = 6m and h = 8m.

Substitute:

[tex]A=\dfrac{12+6}{2}\cdot6=\dfrac{18}{2}\cdot6=(9)(6)=54\ m^2[/tex]

For this case we have to:

[tex]x \leq \frac {5} {4}[/tex]: Represents all values less than or equal to[tex]\frac {5} {4}.[/tex]

[tex]x \geq \frac {5} {2}[/tex]: Represents all values greater than or equal to [tex]\frac {5} {2}.[/tex]

As the inequalities include the sign "=", then the borders of the graphs will be closed.

[tex]\frac {5} {4} = 1.25\\\frac {5} {2} = 2.5[/tex]

The word "or" indicates one solution or the other, so the correct option is graph B

ANswer:

Option B

Answer:

SECOND graph.

Step-by-step explanation:

Given compound inequality,

[tex]x \leq \frac{5}{4}\text{ or }x \geq \frac{5}{2}[/tex]

[tex]\because \frac{5}{4}=1.25\text{ or }\frac{5}{2}=2.5[/tex]

[tex]\implies x \leq 1.25\text{ or }x\geq 2.5[/tex]

If x ≥ 1.25

In the number line closed circle on 1.25 and shaded left side from 1.25,

If x ≤ 2.5

In the number line closed circle on 2.5 and shaded right side from 2.5

Hence, SECOND option is correct.

Answer:

add up the lengths of all the sides of the ceiling,is there a diagram that comes with this or something?

Step-by-step explanation:

Answer: multiply

Step-by-step explanation: you must multiply length x width

Answer:

9.093

Step-by-step explanation:

Of means multiply

.7 * 12.99

9.093

Answer:

9,093

Step-by-step explanation:

Yes. You take 70% of 12,99 [multiply].

I am joyous to assist you anytime.

Answer:

38

Step-by-step explanation:

less than 45

Answer:38

Step-by-step explanation:

Answer:

[tex]\large\boxed{234\,\text{students}}[/tex]

Step-by-step explanation:

In this question, we're trying to find how many students are going to the homecoming dance.

To find the answer, we need to use some information that was provided to us from the question.

Important information:

With the information above, we can solve the question.

To make this simple, we're going to need to figure out how much of 325 is 72%, due to the fact that we need to find the 72% of students that are going to the dance (out of 325 students).

To do this, we would multiply 325 by 0.72

[tex]325*0.72=234[/tex]

When you multiply, you should get 234.

This means that 234 students from the school are going to the dance.

Approximately 234 out of 325 students at Wilson High School, which constitutes about 72% of the whole body, are attending the homecoming dance.

The subject of this question is mathematics, specifically a practical application of percentage calculations. In this scenario, we need to determine the number of students from Wilson High School attending the homecoming dance if 72% of the total student body, which comprises 325 students, is attending.

To solve this, we multiply the total number of students (325) by the percentage of students attending the dance in decimal form (0.72). So, 325 * 0.72 will give us the number of students attending the dance.

After calculating, we find that 234 (rounded to the nearest whole number) students are planning to attend the homecoming dance at Wilson High School.

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Answer:

13 square units

Step-by-step explanation:

First of all, you need to identify that ABCD is a rectangle (AB=CD and AD=BC).

The area of a rectangle is calculated by multiplying the length and the width.

Secondly, we use the Pythagoras’s theorem to calculate side CD and AD (the length and width). I’ve added some labels to your original diagram (see picture attached) so that it’s easier to understand.

The Pythagoras’s theorem is a^2 + b^2 = c^2 (c is the hypotenuse).

So, for side CD:

3^2 + 1^2 = (CD)^2

9 + 1 = (CD)^2

CD = √ 10

and for side AD:

4^2 + 1^2 = (AD)^2

16 + 1 = (AD)^2

AD = √17

Lastly, to calculate the area:

√10 x √17 = 13.04

Your answer is 13 square units.

Hope this helped :)

Answer:

Option B. 13 square units

Step-by-step explanation:

Area of a parallelogram is defined by the expression

A = [tex]\frac{1}{2}(\text{Sum of two parallel sides)}[/tex] × (Disatance between them)

Vertices of A, B, C and D are (3, 6), (6, 5), (5, 1) and (2, 2) respectively.

Length of AB = [tex]\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]

                      = [tex]\sqrt{(5-6)^{2}+(6-3)^{2}}[/tex]

                      = [tex]\sqrt{10}[/tex]

Since length of opposite sides of a parallelogram are equal therefore, length of CD will be same as [tex]\sqrt{10}[/tex]

Now we have to find the length of perpendicular drawn on side AB from point D or distance between parallel sides AB and CD.

Expression for the length of the perpendicular will be = [tex]\frac{|Ax_{1}+By_{1}+C|}{\sqrt{A^{2}+B^{2}}}[/tex]

Slope of line AB (m) = [tex]\frac{y-y'}{x-x'}[/tex]

                                 = [tex]\frac{6-5}{3-6}=-(\frac{1}{3} )[/tex]

Now equation of AB will be,

y - y' = m(x - x')

y - 6 = [tex]-\frac{1}{3}(x-3)[/tex]

3y - 18 = -(x - 3)

3y + x - 18 - 3 = 0

x + 3y - 21 = 0

Length of a perpendicular from D to side AB will be

= [tex]\frac{|(2+6-21)|}{\sqrt{1^{2}+3^{2}}}[/tex]

= [tex]\frac{13}{\sqrt{10}}[/tex]

Area of parallelogram ABCD = [tex]\frac{1}{2}(AB+CD)\times (\text{Distance between AB and CD})[/tex]

= [tex]\frac{1}{2}(\sqrt{10}+\sqrt{10})\times (\frac{13}{\sqrt{10} } )[/tex]

= [tex]\sqrt{10}\times \frac{13}{\sqrt{10} }[/tex]

= 13 square units

Option B. 13 units will be the answer.

Answer:

20 sweets.

Step-by-step-explanation:

Let Colin have x sweets.

The Henry gets x+15 sweets

Then according to the ratios:

5/2 = x+15/x

5x = 2x + 30

3x = 30

x = 10.

So Colin has 10 sweets.

The ratio of Brian's sweets to Colin's  sweets  is  4: 2 or 2:1.

So Brian has 2 * 10 = 20 sweets.

Answer:

[tex]\large\boxed{5x\times(3x^2-5)=15x^3-25x}[/tex]

Step-by-step explanation:

[tex]5x\times(3x^2-5)\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\=(5x)(3x^2)+(5x)(-5)\\\\=15x^3-25x[/tex]

The resulting product of the functions using the distributive property is

15x³ - 25x.

Product is an operation carried out when two or more variables, numbers, or functions are multiplied together.

Given the expression 5x(3x² - 5)

Taking the product:

5x(3x² - 5)

Expand using the distributive property

= 5x(3x²) - 5x(5)

= (5×3)(x × x²) - 25x

= 15x³ - 25x

Hence the resulting function is 15x³ - 25x.

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Answer:

[tex]\large\boxed{D.\ a^2+2ah+h^2+3a+3h+5}[/tex]

Step-by-step explanation:

[tex]f(x)=x^2+3x+5\\\\f(a+h)\to\text{exchange x to (a + h)}:\\\\f(a+h)=(a+h)^2+3(a+h)+5\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\ \text{and the distributive property}\\\\f(a+h)=a^2+2ah+h^2+3a+3h+5[/tex]

Answer:

[tex]\large\boxed{\dfrac{6}{5x^{10}}}[/tex]

Step-by-step explanation:

[tex]\sqrt{\dfrac{72x^{16}}{50x^{36}}}\qquad\text{simplify}\\\\=\sqrt{\dfrac{36x^{16}}{25x{^{20+16}}}}\qquad\text{use}\ (a^n)(a^m)=a^{n+m}\\\\=\sqrt{\dfrac{36x^{16}}{25x^{20}x^{16}}}\qquad\text{cancel}\ x^{16}\\\\=\sqrt{\dfrac{36}{25x^{20}}}\qquad\text{use}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\ \text{and}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{\sqrt{36}}{\sqrt{25}\cdot\sqrt{x^{10\cdot2}}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{6}{5\sqrt{(x^{10})^2}}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\dfrac{6}{5x^{10}}[/tex]

Answer:

Step-by-step explanation:

The slope-intercept of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

=========================================

[tex]f(x)=2x-5\to m=2[/tex]

From the table of function g(x) we have:

x = 2 → y = 0

x = 4 → y = 5

Calculate the slope:

[tex]m=\dfrac{5-0}{4-2}=\dfrac{5}{2}=2.5[/tex]

The slope of f(x) is equal to 2.

The slope of g(x) is equal to 2.5.

2 < 2.5

Answer:

B. g(x) has a greater slope

Step-by-step explanation:

Given the function f(x) =2x-5 and g(x), g(x) has a greater slope.

f(x) = 2

g(x) = 2.5

Answer:

The two numbers are 5 and 10.

Step-by-step explanation:

We need to solve the following system of equations:

We know that:

A + B = 15

A/B = 2

Solving the system of equations we have:

A/B = 2 ⇒ A = 2B

Then:

2B + B = 15 ⇒ 3B = 15 ⇒ B = 5

Then, we need to find A:

A = 10

Answer:

The two numbers are 5 and 10

Step-by-step explanation:

Let x be one number and y be the other number

Their sum is 15

x+y = 15

The quotient is 2

x/y =2

Rewriting this equation by multiplying by y

x/y * y = 2*y

x = 2y

Substitute this into the first equation

2y+ y = 15

Combine like terms

3y = 15

Divide by 3 on each side

3y/3 =15/3

y=5

Now we can find x

x = 2y

x =2(5)

x=10

Answer:

[tex]f(a)=1+5a^2[/tex]

[tex]f(a+h)=1+5a^2+10ah+5h^2[/tex]

[tex]\frac{f(a+h)-f(a)}{h}=10a+5h[/tex]

Step-by-step explanation:

We are given [tex]f(x)=1+5x^2[/tex].

Find [tex]f(a)[/tex].  All this means is replace [tex]x[/tex] in [tex]f(x)=1+5x^2[/tex] with [tex]a[/tex].

[tex]f(x)=1+5x^2[/tex]

[tex]f(a)=1+5a^2[/tex]

Find [tex]f(a+h)[/tex]. All this means is replace [tex](a+h)[/tex] in [tex]f(x)=1+5x^2[/tex] with [tex](a+h)[/tex].

[tex]f(x)=1+5x^2[/tex]

[tex]f(a+h)=1+5(a+h)^2[/tex]

[tex]f(a+h)=1+5(a+h)(a+h)[/tex]

[tex]f(a+h)=1+5(a^2+2ah+h^2)[/tex]

[tex]f(a+h)=1+5a^2+10ah+5h^2[/tex]

Find [tex]\frac{f(a+h)-f(a)}{h}[/tex]. So we got to put some parts together; the parts above:

[tex]\frac{f(a+h)-f(a)}{h}[/tex]

[tex]\frac{(1+5a^2+10ah+5h^2)-(1+5a^2)}{h}[/tex]

Now in the first ( ) I see 1+5a^2 and in the second ( ) I see 1+5a^2, so this means you have (1+5a^2)-(1+5a^2) which equals 0.

[tex]\frac{10ah+5h^2}{h}[/tex]

Now assuming h is not 0. we can divide top and bottom by h.

[tex]\frac{10a+5h}{1}[/tex]

[tex]10a+5h[/tex]

To calculate the values for the quadratic function f(x) = 1 + 5x^2, substitute the necessary values for x. The difference quotient involves a simplification process of the terms after substitution.

The problem is to evaluate the function f(x) = 1 + 5x^2 at a given value a and at a + h, and then to find the difference quotient which is part of the process to find the derivative of the function. First, we calculate f(a), then f(a + h), and lastly the difference quotient f(a + h) - f(a) / h.

To get f(a), we substitute x with a in the function, so we get:

f(a) = 1 + 5a^2

For f(a + h), we substitute x with (a + h):

f(a + h) = 1 + 5(a + h)^2

Now to find the difference quotient (f(a + h) - f(a)) / h:

(f(a + h) - f(a)) / h = (1 + 5(a + h)^2 - (1 + 5a^2)) / h

We can simplify this further by expanding and combining like terms, eventually canceling out the h in the denominator. However, without further expansion and simplification, the expression is already accurate.

Answer: not a black marble: 4/5

Red marble: 3/10

Step-by-step explanation: Count the number of marbles.

5+2+3=10

The total number of marbles that aren’t black are 8 out of 10. The fraction is 8/10. It can be simplified to 4/5.

The number of red marbles is 3 out of 10. As a fraction, it’s 3/10.