f (a) = 3a + 2, When
f(a) = 11

Answer:

In 6 years, Ralph will be only twice as old as Sara

Step-by-step explanation:

Answer:

The answer is C, 3x+4

Step-by-step explanation:

The “in four years” part translates to +4. The 3x translates to 3 times his current age. Hope this helped :)

Answer:

P=12

12=2(w+5)(multiply what's in the brackets with 2)

12=2w+10(take away 10 from each side)

2=2w(divide by 2 from each side)

1=w

do the same for the rest

P=14

2=w

P=16

3=w

P=18

4=w

Step-by-step explanation:

Answer:

\(w=\dfrac{P-10}{2}\)

\(\large\begin{array}{|c|c|c|c|c|}\cline{1-5}P&12&14&16&18\\\cline{1-5}w&1&2&3&4\\\cline{1-5}\end{array}\)

Step-by-step explanation:

Given dimensions of a rectangle:

Therefore, the expression for the perimeter of the rectangle is:

To solve for w in terms of P, rearrange the equation to make isolate w:

\(\implies P=2(w+5)\)

\(\implies P=2w+10\)

\(\implies P-10=2w\)

\(\implies \dfrac{P-10}{2}=w\)

\(\implies w=\dfrac{P-10}{2}\)

To create a table of values for P = 12, 14, 16 and 18, substitute these values of P into the equation for w.

\(\begin{aligned}P=12 \implies w&=\dfrac{12-10}{2}\\w&=\dfrac{2}{2}\\w&=1\end{aligned}\)

\(\begin{aligned}P=14 \implies w&=\dfrac{14-10}{2}\\w&=\dfrac{4}{2}\\w&=2\end{aligned}\)

\(\begin{aligned}P=16 \implies w&=\dfrac{16-10}{2}\\w&=\dfrac{6}{2}\\w&=3\end{aligned}\)

\(\begin{aligned}P=18 \implies w&=\dfrac{18-10}{2}\\w&=\dfrac{8}{2}\\w&=4\end{aligned}\)

Table of values

\(\large\begin{array}{|c|c|c|c|c|}\cline{1-5}P&12&14&16&18\\\cline{1-5}w&1&2&3&4\\\cline{1-5}\end{array}\)

Answer: 12x^2+4

Step-by-step explanation:

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Angles adjacent to 148° are vertical angles and are equal. The measure of either of the angles adjacent to the 148° angle is 32° because it is supplementary to 148°. 85° + w + 32° = 180°, so m∠w is 63°.

The two angles adjacent to 148° are vertical angles and are equal

either of the angles adjacent to the 148° = 180° - 148° = 32° {supplementary angles}

85° + w + 32° = 180°

w + 117° = 180°

w = 180° - 117° {subtract 117° from both sides}

w = 63°

In summary, angles adjacent to 148° are vertical angles and are equal. The measure of either of the angles adjacent to the 148° angle is 32° because it is supplementary to 148°. 85° + w + 32° = 180°, so m∠w is 63°.

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First, let's graph the polygon:

Now, let's prove it's a parallelogram by showing that the segments NP and RQ are parallel, and NR and PQ are parallel as well.

Let's prove that the angular coefficient is the same for NR and PQ

Then they're parallel, just to confirm, let's do the same for NP and RQ

Then it's parallel as well.

Answer:

9x - 21 because of explanation given in the image above hopefully it helps :)

-15x + 43!!

have a great day!

Mikey had two mice that were about the same age and weight. Mikey fed each of the two mice a different feed for a month. The line of mouse 2 must be greater than line of mouse 1 in the graph.

Based on your description, it sounds like the weight of mouse 2 increased at a faster rate than mouse 1 over the course of the month. This could be shown on a graph as two lines, one representing the weight of mouse 1 and the other representing the weight of mouse 2.

The line for mouse 2 would be higher, indicating that its weight increased more than that of mouse 1. The x-axis would represent time (in days), and the y-axis would represent weight. The complete graph is attached.

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Answer:

a) Since np >= 5 and n(1-p) >= 5, the approximation is justified

b) 0.7

c) 0.0725

d) 0.5098 = 50.98% probability that a sample proportion, p,would differ from p = 0.70 by as much as 0.05

Step-by-step explanation:

We use the normal distribution and the central limit theorem to solve this question.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

In this question, we have that:

\(p = 0.7, n = 40\)

a. Show that this sample size is large enough to justify using the normal approximation to thesampling distribution of p.

We need that: np >= 5, n(1-p) >= 5. So

np = 40*0.7 = 28 > 5

n(1-p) = 40*0.3 = 12 > 5

Since both conditions are satisfied, the approximation is justified.

b. What is the mean of the sampling distribution of p if the real estate agents are correct?

This is \(\mu = p = 0.7\)

c. What is the standard deviation of the sampling distribution of p if the real estate agents are correct?

This is \(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.7*0.3}{40}} = 0.0725\)

d. If the real estate agents are correct, what is the probability that a sample proportion, p,would differ from p = 0.70 by as much as 0.05?

This is the pvalue of Z when X = 0.7 + 0.05 = 0.75 subtracted by the pvalue of Z when X = 0.7 - 0.05 = 0.65. So

X = 0.75

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.75 - 0.7}{0.0725}\)

\(Z = 0.69\)

\(Z = 0.69\) has a pvalue of 0.7549

X = 0.65

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.65 - 0.7}{0.0725}\)

\(Z = -0.69\)

\(Z = -0.69\) has a pvalue of 0.2451

0.7549 - 0.2451 = 0.5098

0.5098 = 50.98% probability that a sample proportion, p,would differ from p = 0.70 by as much as 0.05

Answer:

hypotenuse = 10 cm

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse (h) is equal to the sum of the squares on the other 2 legs.

h² = 8² + 6² = 64 + 36 = 100 ( take square root of both sides )

h = \(\sqrt{100}\) = 10

Answer:

The 12 magnets for $34.68 as the unit price is lower.

Step-by-step explanation:

→ Find the cost per magnet for 12

34.86 ÷ 12 = $2.89

→ Find the cost per magnet for 3

9.57 ÷ 3 = $3.19

Answer:

8.3 ft

Step-by-step explanation:

Hypotenuse is the longest side

Opposite is the side opposite the angle

Adjacent is the remaining side

Draw the triangle out, and you'll find that the hypotenuse (length of ladder) is 12ft, and that you are looking for the adjacent side (length of the foot of the ladder to the building). Rule out the opposite side (side of building) as it is not needed. The appropriate trigonometric formula is then the \(cos(angle) = \frac{adjacent}{hypotenuse}\), rearranged to find the adjacent side is \(adjacent = cos(angle)*hypotenuse\)  

substitute the values in and you get cos(46) x 12 = 8.335900446

If RS = ST point S is called midpoint of RT. The given statement is true.

Given that, RS = ST.

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

Here, RS = ST point S is called midpoint of RT.

The line segment RT and its midpoint S is shown on the figure below.

Therefore, the given statement is true.

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Answer:

use pythogoras therom to solve it and its say to find base its formula is h square - psquare

Answer: f(x^2) = x^2 - 5

The geometric center of the graph under the function is 5/3

The equation of the function is given as:

f(x) = 3 - |x - 2|

The interval is given as:

x ∈ [0, 3]

The geometric center (gc) of the graph under the function is calculated using

gc = ∫x f(x) dx/∫f(x) dx

Substitute the known values in the above equation

gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx

Integrate the numerator and the denominator of the above equation

gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]

Recall that the interval is given as x ∈ [0, 3]

Substitute the interval values in the above equation.

The equation is then simplified using a graphing calculator.

So, we have

gc = (65/6)/(13/2)

Express the quotient expression as a product

gc = (65/6) * (2/13)

Divide 65 by 13

gc = 5/6 * 2

Divide 2 by 6

gc = 5/3

Hence, the geometric center of the graph under the function is 5/3

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Answer:

that's cool how is your day going

Step-by-step explanation:

Answer:

Oh well, How was ur day? and i hope you have a wonderful day or night

Step-by-step explanation:

Answer:

8 footballs

18 basketballs

36 baseballs

24 softballs

Step-by-step explanation:

Let f = footballs

f = 8

Let b = basketballs

b = 2+2f = 2 +2(8) = 2 +16 = 18

Let B = baseballs

B = 5f -4 = 5(8) -4 = 40-4 = 36

Let s = softballs

s = 6+1/2B = 6+1/2(36) = 6+18 = 24

The total is 86

f+b+B +s = 86

8+18+36+24 = 86

86=86

There are 8 footballs.

Two more than twice the number of footballs are basketballs:

2f + 2 = b

f = number of footballs

b = number of basketballs

In the first statement, there are 8 footballs. So, f = 8

2(8) + 2 = b

16 + 2 = b

18 = b

Therefore, there are 18 basketballs.

Four less than 5 times the number of footballs are baseballs:

5f - 4 = a

f = number of footballs

a = number of baseballs

In the first statement, there are 8 footballs. So, f = 8

5(8) - 4 = a

40 - 4 = a

36 = a

Therefore, there are 36 baseballs.

Six more than half of the baseballs are softballs:

a/2 + 6 = s

a = number of baseballs

s = number of softballs

In the third statement, there are 36 baseballs. So, a = 36

(36)/2 + 6 = s

18 + 6 = s

24 = s

Therefore, there are 24 softballs.

Best of Luck!

Option D, which is the closest choice to 933.33, is 930. As a result, 930 fraction acres is a plausible estimate of the amount of acres on which Mr. Bailey will plant soybeans

A fraction is a number that represents a portion of a whole or a ratio between two quantities in mathematics. It is represented as a top number (numerator) over a bottom number (denominator) divided by a horizontal line, also known as a vinculum. The fraction 3/4, for example, represents three-quarters of a whole that has been divided into four equal parts. Proper fractions, improper fractions, and mixed numbers are all ways to express a fraction. A suitable fraction is one in which the numerator is less than the denominator, for example, 2/5.

Mr. Bailey intends to plant soybeans on 4 of every 9 acres, which equates to (4/9) of the total acres he farms.

If he intends to cultivate 2,100 acres, the number of acres planted with soybeans is:

(4/9) x 2,100 = 933.33

We must round this amount to the next whole number because he cannot plant soybeans on a fraction of an acre.

Option D, which is the closest choice to 933.33, is 930. As a result, 930 acres is a plausible estimate of the amount of acres on which Mr. Bailey will plant soybeans.

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Answer:

y is just being multiplyed by -4 :)

Step-by-step explanation:

in other words -4x

Answer:

y = -4x

Step-by-step explanation:

Answer:

159???????

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

No, because for x = 7, there are two values of y

Answer:

\(\huge\boxed{\sf No.}\)

Step-by-step explanation:

For a relation to act as a function, the x-values (domain) of the relation should NOT be repeated.

Here,

In domain(x-values), 7 is being repeated. Hence, the relation is not a function.

\(\rule[225]{225}{2}\)

Answer:

= 1799   or   224.875

     8

Step-by-step explanation:

5³ − (6/48) + 10²

= 125 - (0.125) + 100

= 224.875

or

5³ − (6/48) + 10²

= 125 - 1/8 + 100

= -1/8 + 225

= (225 * 8)/8 - 1/8

= (225 * 8-1) / 8

= 1799   or   224.875

     8

Answer:

\(\huge \boxed{\frac{1799}{8} }\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

\(\displaystyle 5^3-(\frac{6}{48} )+10^2\)

Solving for exponents:

\(\displaystyle 125-(\frac{6}{48} )+100\)

Adding or subtracting:

\(\displaystyle -(\frac{1}{8} )+100+125\)

\(\displaystyle -(\frac{1}{8} )+225\)

\(\displaystyle -(\frac{1}{8} )+\frac{1800}{8}\)

\(\Rightarrow \ \displaystyle \frac{1799}{8}\)

\(\rule[225]{225}{2}\)

Answer:

1.5 pounds

Step-by-step explanation:

3/2 = 1.5

Answer: (4.92, -0,91)

Step-by-step explanation:

This should be C on edge 2021

Answer:

C: (4.92, –0.91)

Step-by-step explanation:

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