Rewrite 5x²+35x using distributive property

Answer:

Step-by-step explanation:

The GCF of 42 and 50 is 2.

Although a part of your question is missing, you might be referring to this full question "Devaughn is 8 years younger than Sydney. The sum of their ages is 84. What is Sydney's age?"

Sydney is 46 years old.

Let s be the age of Sydney.

Let d be the age of Devaughn.

As Devaughn is 8 years younger than Sydney, therefore

s = d + 8  (1)

It is given that sum of their ages is 84.

s + d = 84 (2)

Substituting the value of s from equation 1 into equation (2), we get,

d + 8 + d = 84

2d + 8 = 84

2d = 76

d = 76/2 = 38 years old

Now, find the value of s by substituting the value of d in equation 1.

s = d + 8

s = 38 + 8

s = 46 years old

So, Devaughn is 38 years old and Sydney is 46 years old.

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The prompt that examines linear functions and ordered pairs are given below.

1) Here are the ordered pairs for each point:

Point A: (4, 9)

Point B: (6, 3)

Point C: (1, 3)

Point D: (8, 7)

Point E: (8, 9)

See the attached graph.

2) Part A: The completed table and graph for Derek is given as attached.

Part B: Derek makes 10 bracelets in 5 hours.

3) The ordered pairs are given in the labelled graph accordingly.

4) Deanna's coordinates plane is labelled and attached accordingly. The correct answer is Option B (5,8)

5) The other ordered pairs that could be the vertext are Options A - E. See the attached image (Miguel's Squre

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Answer:

83360 cm

Step-by-step explanation:

1 m = 1000 cm

83.36 m = ? cm

We Take

83.36 x 1000 = 83360 cm

So, 83.36 m = 83360 cm

Answer:

Axis of symmetry =1

vertex =(1,2)

y intercept =0

min/max= -6,2

domain= 0,1,2

range =y≥1,2

Answer:

I cannot understand the question

The perimeter of the regular polygon with 15 sides, each measuring 11 cm and an apothem of 18.4 cm, is approximately 166.05 cm.

What is polygon?

A polygon is a two-dimensional geometric shape that is made up of straight lines connecting a sequence of points, which are called vertices.

To find the perimeter of a regular polygon with 15 sides, we need to know the length of each side. However, we are given the apothem, which is the distance from the center of the polygon to the midpoint of any side.

We can use the apothem and the number of sides to find the length of each side using the formula:

length of each side = 2 × apothem × tan(π/n)

where n is the number of sides and π is the mathematical constant pi (approximately equal to 3.14159).

Substituting the given values, we get:

length of each side = 2 × 18.4 cm × tan(π/15)

length of each side ≈ 11.07 cm

Now that we know the length of each side, we can find the perimeter by multiplying it by the number of sides:

perimeter = number of sides × length of each side

perimeter = 15 × 11.07 cm

perimeter ≈ 166.05 cm

Therefore, the perimeter of the regular polygon with 15 sides, each measuring 11 cm and an apothem of 18.4 cm, is approximately 166.05 cm.

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8 degrees and 20 degrees are the required measures of the two angles.

The sum of the interior angles of any quadrilateral is 360 degrees. We know two of the angles already: 311° and 21°. Let's call the other two angles x and y. We know that the ratio of x to y is 2:5, which means we can write:

x = 2k

y = 5k

where k is a constant of proportionality.

We can now write an equation based on the sum of the interior angles:

311 + 21 + x + y = 360

Substituting the expressions for x and y:

311 + 21 + 2k + 5k = 360

Simplifying:

332 + 7k = 360

Subtracting 332 from both sides:

7k = 28

Dividing both sides by 7:

k = 4

Now we can find the values of x and y:

x = 2k = 2(4) = 8

y = 5k = 5(4) = 20

Therefore, the two angles in a ratio of 2:5 are 8 degrees and 20 degrees.

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Answer: C, 125

Step-by-step explanation: That is the slope of the line, which remains constant. The slope represents the distance over the time, and distance divided by time equals the speed. This means that the speed remains constant throughout.

The range of scores is large, from 17 to 94, indicating a widespread in performance among the students. The histogram visualization complements the 5-number summary and gains a better understanding of the distribution of the exam scores.

What is the range of the data set?

To find the range in a data set, you have to subtract the largest value from the smallest value.

Based on the 5-number summary of the data (17, 47, 76, 81, 94), we can draw the following conclusions about the performance on the exam:

The minimum score on the exam was 17.

The maximum score on the exam was 94.

The median score on the exam was (76+81)/2 = 78.5, which means that half of the students scored above 78.5 and a half scored below.

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1), which is 81-47=34.

The IQR provides a measure of the spread of the middle 50% of the data.

hence, The range of scores is large, from 17 to 94, indicating a widespread in performance among the students. The histogram visualization complements the 5-number summary and gains a better understanding of the distribution of the exam scores.

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The three statements that are true about the lines are: Line WZ has the same slope as line XY. Line YX has a greater slope than line ZY, and Line XW has a lesser slope than line YZ.

A linear equation has the form y = mx + b, where m is the slope of the line and b is the y-intercept, or the y-coordinate of the line's intersection with the y-axis. The slope measures how steep a line is, or how quickly the y-coordinate changes for every unit change in the x-coordinate. A line has a positive slope if it is moving upward from left to right, and a negative slope if it is moving downward. The line's intersection point with the y-axis, or the value of y when x is equal to 0, is known as the y-intercept.

Because both lines travel through the same point (0, -3) and have a slope of 1/3, line WZ and line XY have the same slope.

Given that both lines pass through the same point (3, 0), line YX has a bigger slope than line ZY.

Because line XW passes through points (-4, 1) and (3, 3), which have a little change in y over a large change in x, as opposed to line YZ, which passes through points (0, -3) and (3, 0), which have a large change in y over a small change in x, line XW has a lower slope than line YZ.

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Answer:

A. B. C.

Step-by-step explanation:

The correct matches for the probability of falling below the z-score are:

-0.08: 0.4681

0.63: 0.7357

-2.7: 0.0035

1.95: 0.9744

Explain probability

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability is calculated by dividing the number of favourable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, science, economics, and finance, to make predictions and decisions based on uncertain events.

According to the given information

To match the probability of falling below a given z-score, we need to use a standard normal distribution table or a calculator with a built-in normal distribution function. Here are the probabilities for each z-score:

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The domain restrictions on the function [tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex] are the x values -9, 0, 3, 4 and 9

From the question, we have the following function that can be used in our computation:

[tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex]

Next, we set the denominator to 0 and solve for x

So, we have

81 - x²: x = ±9

2x² - 6x: x = 0 and x = 3

x² + 2x - 6x: x = 0 and x = 4

Hence, the domain restrictions are the x values -9, 0, 3, 4 and 9

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The statement "About 16% of the students scored 74 or below" is true for the given normal distribution of test scores with an average of 78 and a standard deviation of 4.

Standard deviation is a measure of the amount of variation or dispersion of a set of values from their mean (average) value. It is calculated as the square root of the variance of a set of data. A smaller standard deviation indicates that the values are tightly clustered around the mean, while a larger standard deviation indicates that the values are more spread out.

In the given question,

About 16% of the students scored 74 or below is true. This is because of the empirical rule for normal distributions, which states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. So, if the average score is 78 and the standard deviation is 4, a score of 74 falls one standard deviation below the mean, which represents about 16% of the total data.

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Answer:

About 97.5%  of the students scored 86 or below.

Step-by-step explanation:

To find the constant k for this type of bacteria, we can use the formula for exponential growth:

N(t) = N0 * e^(kt)

where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, e is Euler's number (approximately 2.71828), and k is the constant we're looking for.

We know that the bacteria doubles in number every 25 minutes, which means that after 25 minutes, the number of bacteria will be 2 times the initial number (N0). Therefore, we can write:

N(25) = 2 * N0

Substituting this into the formula, we get:

2 * N0 = N0 * e^(k*25)

Dividing both sides by N0 and simplifying, we get:

2 = e^(25k)

Taking the natural logarithm of both sides, we get:

ln(2) = 25k

Solving for k, we get:

k = ln(2)/25 ≈ 0.0278

Therefore, the equation for modeling the exponential growth of this type of bacteria is:

N(t) = N0 * e^(0.0278t)

*IG:whis.sama_ent

well, the markup is 1,776.33 - 1,315,80 = 461.33.

now, if we take 1315.80(origin amount), what is 461.33 off of it in percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 1315.80 & 100\\ 461.33& x \end{array} \implies \cfrac{1315.80}{461.33}~~=~~\cfrac{100}{x} \\\\\\ 1315.8x=46133\implies x=\cfrac{46133}{1315.8}\implies x\approx 35[/tex]

Answer:

$232,241.07

Step-by-step explanation:

To calculate the total amount in the account after 30 years of depositing $3,000 each year and earning 6% interest compounded annually, we can use the formula for the future value of an annuity:

FV = P * (((1 + r)^n - 1) / r)

where:

FV is the future value of the annuity

P is the periodic payment (in this case, $3,000 per year)

r is the interest rate per compounding period (in this case, 6% per year, compounded annually)

n is the number of compounding periods (in this case, 30 years)

Substituting the given values, we get:

FV = $3,000 * (((1 + 0.06)^30 - 1) / 0.06)

Using a calculator, we get:

FV ≈ $232,241.07

Therefore, the total amount in the account after 30 years, rounded to the nearest cent, is $232,241.07.

Therefore, we can predict that approximately 5,845,200 people left on cruises from this state in the year 2010.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

This linear equation depicts the number of passengers embarking on cruises from a certain state between 2005 and 2009.

It goes like this:

y = 117,000x + 4,919,200

For example, if x = 0, which represents the year 2005, then y = 4,919,200. If x = 1, which represents the year 2006, then y = 4,919,200 + 117,000 = 5,036,200. Similarly, if x = 2, which represents the year 2007, then y = 4,919,200 + 2(117,000) = 5,153,200.

y = 117,000(5) + 4,919,200

y = 5,845,200

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Question:

The number of people, y, leaving on cruises from a certain state from 2005 to 2009 can be approximated by y=117,000x+4,919,200, where x is the number of years after 2005.

Answer: it’s 8.25

Step-by-step explanation: because it’s in between 8 and 8.5. Thank god

The exponential function is y=5.[tex]2^x[/tex].

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Here the exponential function is [tex]y=ab^x[/tex]

Since (-3,5/8) is on the graph, -[tex]\frac{5}{8}[/tex]=[tex]ab^{-3}[/tex] -----> 1

Since (3, 40) is on the graph, 40=[tex]ab^3[/tex] ------> 2

So, [tex]\frac{ab^3}{ab^{-3}}=\frac{40}{\frac{-5}{8}}[/tex]

=> [tex]b^{3+3}=8\times8[/tex]

=> [tex]b^6=2^6[/tex]

=> b = 2

put b=2 into 2 then,

=> 40= [tex]a\times2^3[/tex]

=> 8a=40

=> a =5

Then the exponential function is y=5.[tex]2^x[/tex].

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Answer:

$526.75 i believe

Step-by-step explanation:

Answer:

39.96

Step-by-step explanation:

the shape is a parallelogram ao the formula is base x height

A=10.8 x 3.7

A=39.97

Answer:

To estimate the difference, we need to round each number to the nearest whole number and then subtract the rounded numbers.

Rounding each number to the nearest whole number, we get:

10 rounded to the nearest whole number is 10

19 rounded to the nearest whole number is 19

19 rounded to the nearest whole number is 19

4 rounded to the nearest whole number is 4

19 rounded to the nearest whole number is 19

-2 rounded to the nearest whole number is -2

Subtracting the rounded numbers, we get:

10 - 19 - 19 - 4 - 19 - (-2) = 10 - 19 - 19 - 4 - 19 + 2 = -49

Therefore, the estimated difference is -49.

The area of a figure in the shape of a parallelogram is 74.4 m2 . If the height of the parallelogram is 6 m, the length of the parallelogram is 12.4 meters.

A parallelogram is a four-sided plane figure with opposite sides parallel and equal in length. It is a special type of quadrilateral, which is a polygon with four sides.

The opposite sides of a parallelogram are parallel, which means they have the same slope and never intersect. The opposite sides are also equal in length, which means they have the same distance between them.

The adjacent angles of a parallelogram are supplementary, which means they add up to 180 degrees. This property is known as the parallelogram law, which states that the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of its sides.

The area of a parallelogram can be calculated by multiplying the base by the height. The base is one of the parallel sides, and the height is the perpendicular distance between the base and the opposite side.

The area (A) of a parallelogram is given by the formula:

A = base x height

where the base is the length of one of the sides of the parallelogram and the height is the perpendicular distance between the base and the opposite side.

In this problem, we are given the area of the parallelogram as 74.4 m² and the height as 6 m. Let the length of the parallelogram be denoted by b. Then, we can use the formula for the area of a parallelogram to write:

74.4 m² = b x 6 m

Solving for b, we get:

b = 74.4 m² / 6 m

b = 12.4 m

Therefore, the length of the parallelogram is 12.4 meters.

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Answer:

Step-by-step explanation:

40 de grese

Answer:

52°

Step-by-step explanation:

The angle between two secants drawn from the point outside the circle is half the difference of the intercepted arcs.

    [tex]\sf \boxed{\bf \angle \ Y =\dfrac{far \ arc - near \ arc}{2}}[/tex]

     [tex]\sf \angle Y = \dfrac{m\overset{\frown}{GK} - m\overset{\frown}{CE}}{2}\\\\50 = \dfrac{152-m\overset{\frown}{CE}}{2}[/tex]

    [tex]50*2 = 152 - m\overset{\frown}{CE}\\\\100 = 152 - m\overset{\frown}{CE}[/tex]     

 [tex]100 + m\overset{\frown}{CE} = 152\\\\[/tex]  

           [tex]\sf m\overset{\frown}{CE}= 152 - 100\\\\m\overset{\frown}{CE} = 52^\circ[/tex]

The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

Given equation :

y=(x−2)2−8

y = 2x - 4 - 8

= 2x - 12

The final equation is y = 2x - 12.

Compare this equation with slope and y-intercept formula :

y = mx+c

So that c = -12

The value of y-intercept according to the solution is -12.

To find the vertex. Let's assume x=0; Substitute in the equation

y = 2(0) -12

y = -12

The first vertex will be (0, -12)

If x = 1; y = 2(1) -12

y = -10

Then the second vertex will be (1, -10).

Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

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Answer:

A.  h'(2) = 5

B.  m'(2) = -24

C.  y = 8x - 31

D.  j'(2) = 3/25 = 0.12

Step-by-step explanation:

When differentiating composite functions, use the chain rule.

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\$\left[f\left(g(x)\right)\right]'=f'\left(g(x)\right) \cdot g'(x)$\\\end{minipage}}[/tex]

Chain Rule: The derivative of a composite function is the product of the derivative of the outer function evaluated at the inner function and the derivative of the inner function.

Using the chain rule, if h(x) = g(f(x)) then h'(x) = g'(f(x)) ⋅ f'(x).

To find h'(2), substitute x = 2 into the differentiated equation:

[tex]\begin{aligned}h'(x)& = g'(f(x)) \cdot f'(x)\\\\\implies h'(2)& = g'(f(2)) \cdot f'(2)\\& = g'(5) \cdot 1\\& = 5 \cdot 1\\&=5\end{aligned}[/tex]

Therefore, h'(2) = 5.

Using the chain rule, if m(x) = f(x²) then m'(x) = f'(x²) ⋅ 2x.

To find m'(2), substitute x = 2 into the differentiated equation:

[tex]\begin{aligned}m'(x) &= f'(x^2) \cdot 2x\\\\\implies m'(2) &= f'(2^2) \cdot 2(2)\\&=f'(4) \cdot 4\\&=-6 \cdot 4\\&=-24\end{aligned}[/tex]

Therefore, m'(2) = -24.

To find the slope of the tangent line to the graph of k at x = 4, substitute x = 4 into the derivative of k(x).

If k(x) = f(g(x)) then k'(x) = f'(g(x)) ⋅ g'(x).

Therefore, the slope of the tangent line is:

[tex]\begin{aligned}k'(x) &= f'(g(x)) \cdot g'(x)\\\\\implies k'(4) &= f'(g(4)) \cdot g'(4)\\&= f'(5) \cdot 4\\&= 2 \cdot 4\\&= 8\end{aligned}[/tex]

Now calculate k(x) when x = 4:

[tex]\begin{aligned}k(x)&=f(g(x))\\\\\implies k(4) &= f(g(4))\\&=f(5)\\&=1\end{aligned}[/tex]

To write the equation of the tangent line, substitute the found slope m = 8 and point (4, 1) into the point-slope equation:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-1&=8(x-4)\\y-1&=8x-32\\y&=8x-31\end{aligned}[/tex]

Therefore, an equation for the line tangent to the graph of k at x = 4 is:

To find the derivative of j(x) use the quotient rule.

[tex]\textsf{If\;\;$j(x)=\dfrac{g(x)}{f(x)}$\;\;then:}\\\\\\j'(x)=\dfrac{f(x)g'(x)-g(x)f'(x)}{(f(x))^2}[/tex]

To calculate j'(2), substitute x = 2 into the equation:

[tex]\begin{aligned} \implies j'(2)&=\dfrac{f(2)g'(2)-g(2)f'(2)}{(f(2))^2}\\\\&=\dfrac{5 \cdot 1-2 \cdot 1}{(5)^2}\\\\&=\dfrac{5-2}{25}\\\\&=\dfrac{3}{25}\\\\&=0.12\end{aligned}[/tex]

Therefore, j'(2) = 3/25 = 0.12.

the result of the division is: [tex]x^2 - 5x - 15 - 43/(x - 3)[/tex].

To divide  [tex](x^3 - 8x^2 + 2) by (x - 3)[/tex], we can use polynomial long division:

 [tex]x^2 - 5x - 15[/tex]

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

[tex]x - 3 | x^3 - 8x^2 + 0x + 2[/tex]

    [tex]- (x^3 - 3x^2)[/tex]

     -----------------

  [tex]-5x^2 + 0x[/tex]

           [tex]- (-5x^2 + 15x)[/tex]

             -------------

                 [tex]-15x + 2[/tex]

                 [tex]- (-15x + 45)[/tex]

                      -----------

                              -43

Therefore, the result of the division is: [tex]x^2 - 5x - 15 - 43/(x - 3)[/tex]

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The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.

Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.

cos(35°) = adjacent side (FH) / hypotenuse (GH)

We know that FH = 18.4 in. So, we can write the equation as:

cos(35°) = 18.4 / GH

GH = 18.4 / cos(35°)

GH = 18.4 / 0.81915

=  22.46 inches

So, the length of GH, the hypotenuse, is approximately 22.46 inches.

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