please help me with this please

1)  [tex]2^{5+3}[/tex] = [tex]2^{8}[/tex]  (By Product rule of exponents [tex]a^{m} *a^{n} = a^{m+n}[/tex])

2) [tex]m^{5+7}[/tex] = [tex]m^{12}[/tex]  (By Product rule of exponents [tex]a^{m} *a^{n} = a^{m+n}[/tex])

3) [tex]b^{4+2} = b^{6}[/tex]    (By Product rule of exponents [tex]a^{m} *a^{n} = a^{m+n}[/tex])

4) [tex]x^{2+1}*y^{2} = x^{3}y^{2}[/tex]   (By Product rule of exponents [tex]a^{m} *a^{n} = a^{m+n}[/tex])

5) [tex]x^{4+5}*y^{1+1} = x^{9}y^{2}[/tex]    (By Product rule of exponents [tex]a^{m} *a^{n} = a^{m+n}[/tex])

6) [tex]2^{4 - 3} = 2^{1} = 2[/tex]   ( By Quotient rule of exponents [tex]a^{m} /a^{n} = a^{m-n}[/tex])

7) [tex]c^{8 - 5} = c^{3}[/tex]    ( By Quotient rule of exponents [tex]a^{m} /a^{n} = a^{m-n}[/tex])

8) [tex]x^{4 - 4} = x^{0} = 1[/tex]  ( By Quotient rule of exponents [tex]a^{m} /a^{n} = a^{m-n}[/tex])

9) [tex]a^{2- 3} = a^{-1}[/tex]  ( By Quotient rule of exponents [tex]a^{m} /a^{n} = a^{m-n}[/tex])

10) [tex]m^{5*10} = m^{50}[/tex] (Power of a power rule [tex](a^{m})^{n} = a^{m*n}[/tex])

11) [tex]5^{2*2} = 5^{4}[/tex]  (Power of a power rule [tex](a^{m})^{n} = a^{m*n}[/tex])

12) [tex]\frac{x^{2*2} }{y^{3*2} } = \frac{x^{4} }{y^{6} }[/tex]   (Power of a quotient rule [tex]( \frac{a}{b} )^{m} = \frac{a^{m} }{b^{m} }[/tex])

13) [tex]a^{1*3} b^{2*3} =a^{3} b^{6}[/tex]   (Power of a power rule [tex](a^{m})^{n} = a^{m*n}[/tex])

14) [tex]c^{2*5} d^{3*5} =c^{10} d^{15}[/tex]   (Power of a power rule [tex](a^{m})^{n} = a^{m*n}[/tex])

15) [tex](m^{2-2} )^{2} = (m^{0} )^{2} = 1^{2} =1[/tex]   (Power of a quotient rule [tex]( \frac{a}{b} )^{m} = \frac{a^{m} }{b^{m} }[/tex]  and Zero exponent rule [tex]a^{0} = 1[/tex])

16) [tex]\frac{y^{2*0} }{z^{7*0} } = \frac{y^{0} }{z^{0} } = 1[/tex]   (Power of a quotient rule [tex]( \frac{a}{b} )^{m} = \frac{a^{m} }{b^{m} }[/tex]  and Zero exponent rule [tex]a^{0} = 1[/tex])

17) [tex]\frac{1}{k^{2} }[/tex]       ( Negative Exponent rule [tex]a^{-m} = \frac{1}{a^{m} }[/tex] )

18) [tex]g^{3*-2} h^{3*-2} = g^{-6} h^{-6} = \frac{1}{g^{6}h^{6} }[/tex]   ( Negative Exponent rule [tex]a^{-m} = \frac{1}{a^{m} }[/tex] )

19) [tex]( x^{3-2} y^{3-2} )^{5} = (xy)^{5} =x^{5} y^{5}[/tex]  (By Quotient rule of exponents [tex]a^{m} /a^{n} = a^{m-n}[/tex] )

20) [tex](m^{2-3} n^{2-2} )^{4} =(m^{-1}n^{0})^{4} = m^{-4} = \frac{1}{m^{4} }[/tex]  (Power of a quotient rule [tex]( \frac{a}{b} )^{m} = \frac{a^{m} }{b^{m} }[/tex]  and Zero exponent rule [tex]a^{0} = 1[/tex]) ( Negative Exponent rule [tex]a^{-m} = \frac{1}{a^{m} }[/tex] )

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Answer:

The tangent line using limits/ derivatives is  y=42x-42

Step-by-step explanation:

Answer:

f(x) = (3·x^2 + x - 4)·(2·x^3 + 3·x + 1)

f(x) = 3·x^2·2·x^3 + 3·x^2·3·x + 3·x^2·1 + x·2·x^3 + x·3·x + x·1 - 4·2·x^3 - 4·3·x - 4·1

f(x) = 6·x^5 + 9·x^3 + 3·x^2 + 2·x^4 + 3·x^2 + x - 8·x^3 - 12·x - 4

f(x) = 6·x^5 + 2·x^4 + x^3 + 6·x^2 - 11·x - 4

f'(x) = 30·x^4 + 8·x^3 + 3·x^2 + 12·x - 11

tangent at x = 1

f(1) = 6·1^5 + 2·1^4 + 1^3 + 6·1^2 - 11·1 - 4 = 0

f'(1) = 30·1^4 + 8·1^3 + 3·1^2 + 12·1 - 11 = 42

t(x) = f'(1)·(x - 1) + f(1)

t(x) = 42·(x - 1) + 0

t(x) = 42·x - 42 + 0

t(x) = 42·x - 42

The liters of gas that Alonso need to fill his gas tank is 71.92279 liters.

It was stated that Alonso's car holds a maximum of 19 gallons of gas.

It is important to note that 1 gallon = 3.78541 liters.

Therefore, the number of liters will be calculated by multiplying the value. This will be:

= 19 × 3.78541

= 71.92279 liters.

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Explanation

Step 1

as the triangles are similar

Step 2

solve for x

so, the anwer

Answer:

Never True

Step-by-step explanation:

The equation is not balanced.

Answer: 84.

Step-by-step explanation: If you add the width 5cm and 2cm, it gives you 7cm, then length x width so 12x7= 84(cm).

If I am wrong, I am truly sorry, I haven't done area in a long time.

Answer:

Manny.

Step-by-step explanation:

Because they split cleaning on Thursday and Manny finished first, then on Friday Manny will clean more stalls because they are faster.

Answer:

72 minutes

Step-by-step explanation:

150

-78

72

Answer:

Step-by-step explanation:

1) 2hours??

2) 150-78=72mins

3)24x4=96

96x60=5760

The measure of angle ∠EAD is 29° and ∠CAB is 119°.

So, according to the image ∠CAF is 180°.

Obtain, ∠EAD as follows:

Similarly, ∠CAF = ∠CAB + ∠BAF

Obtain, ∠CAB as follows:

Therefore, the measure of angle ∠EAD is 29° and ∠CAB is 119°.

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The correct question is given below:
Find the following angle measures.

mEAD =

mCAB =

Question: Simplify the expression 1 + 0.25 (8 + 12) - 0.3 × 2​

Solution:

Distributing 0.25 in the sum we obtain:

Performing each of the operations we obtain:

So the correct answer is

There is strong positive association between the variables.

The strength of the linear link between two variables is assessed using correlation coefficients. A correlation coefficient with a value over zero denotes a positive link, whereas one with a value below zero denotes a negative relationship. A statistical indicator of how strongly two variables are linearly related is the correlation coefficient. From -1 to 1, its values are possible. A correlation coefficient of -1 indicates a perfect negative, or inverse, correlation, in which the values in one series rise as the values in the other fall, and the other way around. A value of 1 indicates a direct link that is 100 percent positive. There is no linear link when the correlation coefficient is zero.

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Answer:

Yes, Nevin scored 96 points.

Step-by-step explanation:

[tex](58 \times 1.75) - (22 \times .25)[/tex]

[tex]101.5 - 5.5 = 96[/tex]

Answer:

The answer is A

Step-by-step explanation:

y=-0.5x + 225

This is because every month 50 cents which can be written as 0.5 is taken off the account so it would be negative. Since X =  the number of months, you would multiply it by 0.5, hence -0.5x. Since 225 is the orginial balance you would add that.

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The volume V of the described solid S is 3.48 π and this can be described by performing the integration and using the given data.

Given: The base of S is the region enclosed by the parabola [tex]$y=2-3 \mathrm{x}^2$[/tex] and the x-axis.

Cross-sections perpendicular to the y-axis are squares.

To determine the x-intercept by substituting (y = 0) in the given function.

[tex]$&0=2-3 \mathrm{x}^2 \\[/tex]

[tex]$&x^2=\frac{2}{3} \\[/tex]

[tex]$&x=\pm \sqrt{\frac{2}{3}}[/tex]

The volume of solid S is given by: [tex]$\mathrm{V}=\pi \mathrm{r}^2 \mathrm{~h}$[/tex]

where [tex]$\mathbf{r}=\mathbf{y}\sqrt{x}[/tex] and h = dx.

[tex]$&\mathrm{dV}=\pi\left(2-3 \mathrm{x}^2\right)^2 \mathrm{dx} \\[/tex]

[tex]$&\mathrm{dV}=\pi\left(9 \mathrm{x}^4-12 \mathrm{x}^2+4\right) \mathrm{dx}[/tex]

Now, integrate the above expression.

[tex]$&\int \mathrm{dV}=\int_0^{\sqrt{2 / 3}} \pi\left(9 \mathrm{x}^4-12 \mathrm{x}^2+4\right) \mathrm{dx} \\[/tex]

[tex]$&\mathrm{V}=\pi\left[\left(9 \frac{\mathrm{x}^5}{5}-\frac{12 \mathrm{x}^3}{3}+4 \mathrm{x}\right)\right]_0^{\sqrt{2 / 3}}[/tex]

Simplify the above expression, we get

[tex]$&\int \mathrm{dV}=\int_0^{\sqrt{2 / 3}} \pi\left(9 \mathrm{x}^4-12 \mathrm{x}^2+4\right) \mathrm{dx} \\[/tex]

[tex]$&\mathrm{V}=\pi\left[\left(9 \frac{\mathrm{x}^5}{5}-\frac{12 \mathrm{x}^3}{3}+4 \mathrm{x}\right)\right]_0^{\sqrt{2 / 3}}[/tex]

Simplify the above expression.

[tex]$$\mathrm{V}=\pi\left[\left(9 \frac{\left(\sqrt{\frac{2}{3}}\right)^5}{5}-\frac{\left(\sqrt{\frac{2}{3}}\right)^3}{3}+4\left(\sqrt{\frac{2}{3}}\right)\right]\right.$$\alpha[/tex]

Now, simplify the above expression by using the arithmetic operations.

V ≈ 3.48 π

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perpendicular gradients are egual to -1 when multiplying them which means

Step-by-step explanation:

.Ma×Mb=-1

Ma=-1/Mb

Answer:

Explanation:

Given the function, g(x) below:

We evaluate g(x) for x=1,2 and 3:

We see that whenever x increases by 1, the value of g(x) triples.

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

Explanation:

Add up the values

1 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4 = 30

Then divide by the sample size n = 10 since there are 10 items in this list

30/10 = 3

The mean is 3.

---------------

An example in real life

Imagine that the numbers given represent the number of cookies that 10 people have. Person A has 1 cookie, person B has 2 cookies, person C has 2 cookies, person D has 3 cookies, and so on.

Adding up all the cookies gets us 30 total. Imagine all the cookies are placed on a plate somewhere.

To split the cookies evenly among the 10 people, we divide by 10 to get 30/10 = 3. This means each person gets 3 cookies, which is exactly the arithmetic mean.

a. Natasha says her answer is 11.75. Therefore, she is correct.

b. The possible error that was made was that Jorge shifted the decimal backward.

A quotient is a quantity created by the division of two numbers in mathematics. The quotient is widely used in mathematics and is also known as the integer component of a division, a fraction, or a ratio. A decimal is a number with a whole and a fractional part. Decimal numbers are between integers and represent a numerical value for a whole plus some fraction of a whole.

From the information, it should be noted that Natasha and Jorge were asked to find the quotient to the decimal division problem 18.8÷1.6.

a. It should be noted that the division of the decimals will be:

= 18.8 ÷ 1.6

= 11.75

This can easily be done with a calculator.

b. One can easily know who is correct through the use of a calculator or mentally. The fact that Jorge got 1.175 is incorrect.

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The surface area will be the surface area of the rectangular prism, plus the surface area of the triangular prism, minus the area of the base of the triangular prism, so:

For the rectangular prism:

For the triangular prism:

The area of the base of the triangular prism is:

Therefore:

The quotient of 8 divided by one-third, multiply 8 by 3. Option C

Fractions are simply defined as part of a whole element, set or quantity.

The different types of fractions are;

Examples of simple fractions include; 1/2, 1/5

Examples of proper fractions include; 2/3 . 4/6

Examples of mixed fractions include; 2 1/4, 3 6/7

Examples of improper fractions include;5/4, 6/54

From the information given, we have;

8 ÷ 1/3

Take inverse of the divisor and multiply

8 × 3/1

24

Then, multiplying 8 by 3 is 24

Hence, the value is 3

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The order of the color of the 39th skittle is: yellow

By adding numbers to the given sequence and examining the repetition, order-based issues in mathematics can be addressed. Once the proper order number has been determined, numbering the other objects will be a breeze.

The answer is a bag of Skittles in the following color order: red, orange, brown, yellow, green, and blue.

The hue of the 39th skittle that they consumed is:

There are six hues in all.

Red is repeated once again after number 6. The order for the red is as follows:

[1, 6,12,18,24,30,36]

39 is yellow, 38 is brown, and 37 is orange.

Consequently, the 39th skittle is colored in the following order: yellow

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First let's find the value of x using the Pythagorean theorem in the left small triangle:

Now, finding the value of y with the Pythagorean theorem in the right small triangle, we have:

The area of the triangle is calculated with the formula:

Where b is the base and h is the height relative to this base. Using b = 6 + y and h = x, we have:

Answer:

the answer is 27.5

Step-by-step explanation:

the decimal point should be placed in the ones place...I think

Answer:

hope this helped

Step-by-step explanation:

Multiply the height of Rectangle by the scale factor. This will give you the height of Rectangle

Multiply the width of Rectangle by the scale factor. This will give you the width of Rectangle

Multiply the height and width of Rectangle to find the area

The proof that "u" is a subspace of "v" is given below.

Suppose that t:v->w is a linear transformation where "v" and "w" are vector spaces.

Let "z" be the subspace of "w".

Since "t" is a linear transformation, the zero vector of "w" is in "z".

Let x, y ∈ U.

Then t(x), t(y) ∈ z.

Since, "z" is a subspace of "w".

So, "z" is closed under vector addition.

Thus, t(x) + t(y) ∈ z.

Now, t(x) + t(y) = t(x + y), since, t is a linear transformation.

Therefore, t(x + y) ∈ z.

Thus, x + y ∈ u.

Therefore, "u" is closed under vector addition.

Hence proved.

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Answer: E

Step-by-step explanation: On the y axis go 6 spaces up and E will be 6 spaces to the right.

As x and 68° are alternate interior angles, so, x = 68°.

We are given a set of parallel lines and a transversal.

We can see that:

The type of angle pairs is alternate interior angles.

( as it forms an inverted F-shape)

Now, these angles are 68° and x°.

So, we know that, the alternate interior angles are equal to each other.

So, we get that:

x = 68°

Therefore, as x and 68° are alternate interior angles, so, x = 68°.

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[tex]\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=5.2\\ A=26.58 \end{cases}\implies 26.58=\cfrac{1}{2}(5.2)h \\\\\\ 26.58=2.6h\implies \cfrac{26.58}{2.6}=h\implies 10.22\approx h[/tex]

For students who earned a score of 21 or higher on the quiz

The cumulative frequency = 16

The relative frequency  = 32%

The number of times a specific value appears in the data is its frequency (f). A variable's distribution is its frequency pattern, or the collection of all conceivable values and the frequencies corresponding to those values.

To get relative frequency, we will take this cumulative number and divide by the total number of students. number of 21 or more / total number of students = 16 / 50 = 0.32 or 32%.

The cumulative frequency of students who earned a score of 21 or higher on the quiz is =16.

Total frequency is = 4+8+15+7+7+3+4+2=50.

So the relative cumulative frequency is

= 16 / 50

= 0.32 or 32%.

Hence , the relative cumulative frequency when students who earned a score of 21 or more is 0.32.

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Answer:

Step-by-step explanation:

1) Find the table

To find the numbers on the table, just substitute the number for x

If x = 0

y=-4x+3

y=-4(0) + 3

y= 0 + 3

y= 3

If x = 1

y=-4x+3

y=-4(1)+3

y= -4 + 3

y= -1

You can see a pattern, each x makes it go down by 4.

So the following will be...

if x = 2 -> -5

if x = 3 -> -9

2) Now fill in the table with the points

(0, 3) (Taken from the table, the x and y)

(1, -1)

(2, -5)

(3, -9)

3) Afterward draw a line through it. You will get your graph.