If g(x) is the inverse of f(c) what is the value of f(g(2)) ?

Answer:

0

Step-by-step explanation:

The given limit is

[tex]\lim_{x \to \infty} \frac{x^2+x-22}{4x^3- 13}[/tex]

Divide both the numerator and the denominator by the highest power of x in the denominator.

[tex]=\lim_{x \to \infty} \frac{\frac{x^2}{x^3}+\frac{x}{x^3}-\frac{22}{x^3}}{\frac{4x^3}{x^3}- \frac{13}{x^3}}[/tex]

This simplifies to;

[tex]=\lim_{x \to \infty} \frac{\frac{1}{x}+\frac{1}{x^2}-\frac{22}{x^3}}{4- \frac{13}{x^3}}[/tex]

As [tex]x\to \infty, \frac{c}{x^n} \to 0[/tex]

[tex]=\lim_{x \to \infty} \frac{0+0-0}{4- 0}=0[/tex]

The limit is zero

➷ We'll work from here:

9x = 180

To isolate x, you would need to divide both sides by 9

x = 180/9

Solve:

x = 20

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer: ❤️Hello!❤️ x = 20

Step-by-step explanation:  Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  

2*x+3*x+4*x-(180)=0  

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  9x - 180  =   9 • (x - 20)  

Step  2  :

Equations which are never true :

2.1      Solve :    9   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

2.2      Solve  :    x-20 = 0  

Add  20  to both sides of the equation :  

                     x = 20  

Answer:

Step-by-step explanation:

The formula of a volume of a rectangle prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have V = 72 cm³, w = 2 cm and h = 4 cm. Substitute:

[tex](2)(4)l=72[/tex]

[tex]8l=72[/tex]          divide both sides by 8

[tex]l=9\ cm[/tex]

Answer:

d.   a_n = 6n - 4.

Step-by-step explanation:

The common difference (d)  is 8-2 = 14-8 = 20-14 = 26-20 = 6.

This is an Arithmetic Sequence with the first term (a1) is 2.

The general form of the explicit formula is a_n = a1 + d(n - 1)  so this sequence has  the formula:

a_n = 2 + 6(n - 1)

a_n = 2 + 6n - 6

a_n = 6n - 4.

The sequence is an illustration of an arithmetic sequence.

The explicit formula is: (d) [tex]a_n = 6n - 4[/tex]

We have:

[tex]a_1 = 2[/tex] -- the first term

Next, we calculate the common difference (d)

[tex]d = a_2 - a_1[/tex]

So, we have:

[tex]d = 8 -2[/tex]

[tex]d = 6[/tex]

The explicit formula is calculated using:

[tex]a_n = a_1 + (n - 1)d[/tex]

So, we have:

[tex]a_n =2 + (n - 1) \times 6[/tex]

Open bracket

[tex]a_n = 2 + 6n - 6[/tex]

Collect like terms

[tex]a_n = 6n - 6 + 2[/tex]

[tex]a_n = 6n - 4[/tex]

Hence, the explicit formula is: (d) [tex]a_n = 6n - 4[/tex]

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Answer:

I think it's 53 miles

Step-by-step explanation:

After flat fee of $1.75 leaves him $13.25. Then use the remainder to calculate miles. Each dollar allows 4 miles × 13 = 52+1=53

The inequality is:

             [tex]1.75+0.25x\leq 15[/tex]

The solution of the inequality is:

                    [tex]x\leq 53[/tex]

Let Eddie could travel x miles.

It is given that:

A cab charges $1.75 for the flat fee and $0.25 for each mile.

This means that the fee charged by Eddie if he travels x miles excluding the flat fee is:

                   $  0.25x

Total amount the cab will charge Eddie is:

              1.75+0.25x

Also, it is given that:

He has only $ 15 to spend this means that he can spend no more than 15 on riding in a cab.

Hence, the inequality is given by:

            [tex]1.75+0.25x\leq 15[/tex]

Now on solving the inequality i.e. finding the possible values of x from the inequality.

We subtract both side of the inequality by 1.75 to obtain:

[tex]0.25x\leq 13.25[/tex]

Now on dividing both side of the inequality by 0.25 we get:

[tex]x\leq 53[/tex]

Hence, Eddie could travel less than or equal to 53 miles .

Answer:

B, 3x - 5

Step-by-step explanation:

Factor by grouping to get (3x - 5)(2x + 3).

Factor 6x2−x−15

6x2−x−15

=(3x−5)(2x+3)

Answer:

(3x−5)(2x+3)

Answer:

  2 and 3/7 pounds

Step-by-step explanation:

Convert the mixed number to an improper fraction

12 1/7 becomes 85/7

This represents 5 bags, so divide it by 5 to see what one bag should weigh...

(85/7)/5 becomes (85/7)/(5/1)

which becomes

(85/7)*(1/5)      (division is the same as multiplying by the reciprocal)

   85/35  

     17/7      (reduce the fraction by factoring out a 5 from top and bottom)

       2 and 3/7 pounds

Answer:

852

Step-by-step explanation:

The correct answer would be A.

A.

You can distribute the 8

Distribute 8 to a and multiply them = 8a

Distribute 8 to -6 and multiply them = -48

= 8a-48

Answer:

48

Step-by-step explanation:

There are 3 events that are taking place.

Rolling a die which has 6 possible outcomes.

Flipping a coin which has 2 possible outcomes.

Spinning a spinner which has 4 possible outcomes.

Since the outcome of each event is independent of the other, the total possible outcomes will be equal to the product of outcomes of each event.

i.e.

Total outcomes = 6 x 2 x 4 = 48

The sample space of the experiment contains all the possible outcomes. so the number of elements in the sample space of this experiment will be 48

Answer:

The correct answer option is 48.

Step-by-step explanation:

Here in this experiment, three events are taking place that include rolling a die, flipping a coin and spinning a spinner.

The possible outcomes of each of these events are:

Rolling a die - 6

Flipping a coin - 2

Spinning a spinner - 4

Therefore, we can find the number of elements in the sample space of this environment by multiplying their possible outcomes.

Number of elements = 6 × 2 × 4 = 48

Answer:

length of base is 10

Step-by-step explanation:

The area of the entire firgure is 1600 cm^2.  There are 4 equal sized pennants, so each pennant is 1600/4 = 400

the bottom pennant has area 400 and is triangular shaped.  the area of a triangle is 1/2 b h.  

A = 1/2 b h       given height is 80 and area is 400.  plug these values in

400 = 1/2 b (80)

400 = 40 b       divide both sides by 40

b = 10

Answer:

[tex]x=-0.75[/tex]

Step-by-step explanation:

The given equation is

[tex]4^{-5x-7}=6^{2x-1}[/tex]

We take logarithm of both sides to base 10.

[tex]\log(4^{-5x-7})=\log(6^{2x-1})[/tex]

[tex](-5x-7)\log(4)=(2x-1)\log(6)[/tex]

We expand the brackets to get;

[tex]-5x\log(4)-7\log(4)=2x\log(6)-\log(6)[/tex]

Group similar terms;

[tex]-7\log(4)+\log(6)=2x\log(6)+5x\log(4)[/tex]

[tex]-7\log(4)+\log(6)=(2\log(6)+5\log(4))x[/tex]

[tex]\frac{-7\log(4)+\log(6)}{(2\log(6)+5\log(4))}=x[/tex]

[tex]x=-0.752478[/tex]

To the nearest hundredth.

[tex]x=-0.75[/tex]

Answer:

Step-by-step explanation:

[tex]n,\ n+2,\ n+4-\text{three consecutive even integers}\\\\\text{The equation:}\\\\n+(n+2)+(n+4)=-72\\\\n+n+2+n+4=-72\qquad\text{combine like terms}\\\\3n+6=-72\qquad\text{subtract 6 from both sides}\\\\3n+6-6=-72-6\\\\3n=-78\qquad\text{divide both sides by 3}\\\\\dfrac{3n}{3}=-\dfrac{78}{3}\\\\n=-26\\\\n+2=-26+2=-24\\\\n+4=-26+4=-22[/tex]

Answer:

35° and 85°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Since one angle = 60° then the sum of the other 2 angles = 120°

Sum the parts of the ratio 7 + 17 = 24 parts, hence

[tex]\frac{120}{24}[/tex] = 5° ← value of 1 pat of the ratio, hence

7 parts = 7 × 5° = 35°

17 parts = 17 × 5° = 85°

note that 60° + 35° + 85° = 180°

Answer:

The 3 angles are 36.87, 53.13 and 90 degrees.

Step-by-step explanation:

This right  triangle ABC  has sides 3, 4 and 5 units.

To find the angles:

sin A - 3/5  gives m <  A =  36.87 degrees

sin B = 4/5 gives m < B = 53.13 degrees.

QUESTION 1

The given logarithm is

[tex]\log_{243}(27)[/tex]

Let [tex]\log_{243}(27)=x[/tex].

We rewrite in exponential form to get;

[tex]27=243^x[/tex]

We rewrite both sides of the equation as an index number to base 3.

[tex]3^3=3^{5x}[/tex]

Since the bases are the same, we equate the exponents.

[tex]3=5x[/tex]

Divide both sides by 5.

[tex]x=\frac{3}{5}[/tex]

[tex]\therefore \log_{243}(27)=\frac{3}{5}[/tex]

QUESTION 2

The given logarithm is

[tex]\log_{25}(\frac{1}{5} )[/tex]

We rewrite both the base and the number as power to base 5.

[tex]\log_{5^2}(5^{-1})[/tex]

Recall that: [tex]\log_{a^q}(a^p)=\frac{p}{q} \log_a(a)=\frac{p}{q}[/tex]

We apply this property to obtain;

[tex]\log_{5^2}(5^{-1})=\frac{-1}{2}\log_5(5)=-\frac{1}{2}[/tex]

Dana’s waking rate in miles per hour is 3 mph.

I did 3/4 x 4 = 3 because she walked 1/4 a mile and I needed to figure out the miles per one whole hour.

I hope this made sense and helped you.

[tex]f'(x)[/tex] exists and is bounded for all [tex]x[/tex]. We're told that [tex]f(0)=-8[/tex]. Consider the interval [0, 3]. The mean value theorem says that there is some [tex]c\in(0,3)[/tex] such that

[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}[/tex]

Since [tex]f'(x)\le9[/tex], we have

[tex]\dfrac{f(3)+8}3\le9\implies f(3)\le19[/tex]

so 19 is the largest possible value.

Given a differentiable function with f(0) = -8 and f'(x) ≤ 9 for all x, we use the Mean Value Theorem to find that f(3), at its largest, can be 1.

In this mathematics problem, we are given that f is a differentiable function with f(0) = -8 and its derivative f'(x) ≤ 9 for all x. We aim to calculate the possible maximum value of f(3). To do this, we apply the Mean Value Theorem for the interval [0, 3]. By this theorem, there exists a number 'c' in this interval such that the derivative at that point is equal to the slope of the secant line through the points (0, f(0)) and (3, f(3)). Thus, we get the equation: f(3) - f(0) = f'(c). Rearranging this, we get f(3) = f(0) + f'(c). Substituting the given values, f(3) = -8 + f'(c).

Since we know f'(x) ≤ 9 for all x, this means f'(c) ≤ 9 as well. Replacing this in the equation we get f(3) ≤ -8 + 9 = 1. Hence, the largest possible value for f(3) is 1.

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Answer:

27

Step-by-step explanation:

We figure out the scale factor first, which is the number of times one radius is of the other.  We call the scale factor, k.

To get how many times larger is the volume of similar spheres, we will need to cube the scale factor.

Since it is given that radius of Sphere A is 3 times that of Sphere B, we can say that the scale factor (k) = 3. Hence, the volume of Sphere A would be k^3 times the volume of Sphere B.

So,  [tex]k^3\\=(3)^3\\=27[/tex]

Hence, the volume of sphere A is 27 times the volume of sphere B.

Answer:

12+2 =14

Step-by-step explanation:

Answer: 1 and 13.

Step-by-step explanation: Because of the total, we know that the first number has to be less than 5, but greater than 0. to start in the median, let's use 3.

3+12 = 15.

That won't work, so let's try 2.

2+12 = 14.

There's the answer.

Answer:

1 hour

Step-by-step explanation:

1/4 of 4 is 1

Answer:one hour

Step-by-step explanation:

Probability of an event is the measure of its chance of occurrence.  The probability that the post box will outweigh the Kellogs box is 0.4129 approximately.

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.

If we have

[tex]X \sim N(\mu, \sigma)[/tex]

(X is following normal distribution with mean [tex]\mu[/tex] standard deviation [tex]\sigma[/tex])

then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

[tex]P(Z \leq z) = P(Z < z) )[/tex]

Also, know that if we look for Z = z in z-tables, the p-value we get is

[tex]P(Z \leq z) = \rm p \: value[/tex]

Suppose that a random variable X is formed by [tex]n[/tex] mutually independent and normally distributed random variables such that:

[tex]X_i = N(\mu_i , \sigma^2_i) ; \: i = 1,2, \cdots, n[/tex]

And if

[tex]X = X_1 + X_2 + \cdots + X_n[/tex]

Then, its distribution is given as:

[tex]X \sim N(\mu_1 + \mu_2 + \cdots + \mu_n, \: \: \sigma^2_1 + \sigma^2_2 + \cdots + \sigma^2_n)[/tex]

If, for the given case, we assume two normally distributed random variables as:

X = variable assuming weights of boxes of Post Corn Flakes
Y = variable assuming weights of boxes of Kellogs

Then, as per the given data, we get:

[tex]X \sim N(\mu = 64.1, \sigma = 0.5)\\Y \sim N(\mu = 63.9, \sigma = 0.4)[/tex]

Then,  the probability that the Post box will outweigh the Kellogs box can be written as:

[tex]P(X > Y)[/tex]

Or,

[tex]P(X -Y > 0)[/tex]

We need to know about the properties of X-Y.

Also, since [tex]E(aX) = aE(X), Var(aX) = a^2Var(X)[/tex], thus,

[tex]-Y \sim N(-63.9, 0.4)[/tex]

As both are independent(assuming), thus,

[tex]X - Y \sim N(\mu = 64.1 - 63.9, \sigma = 0.5 + 0.4) = N(0.2, 0.9)[/tex]

Using the standard normal distribution, we get the needed probability as:

[tex]P(X -Y > 0) = 1 - P(X - Y \leq 0) \\P(X -Y > 0)= 1- P(Z = \dfrac{(X-Y) - \mu}{\sigma} \leq \dfrac{0 - 0.2}{0.9})\\P(X -Y > 0) \approx 1 - P(Z \leq -0.22)[/tex]

Using the z-tables, the p-value for Z = -0.22 is 0.4129

Thus, [tex]P(X > Y) = P(X - Y > 0) \approx 0.4129[/tex]

Thus, the probability that the post box will outweigh the Kellogs box is 0.4129 approximately.

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The probability that a randomly selected Post box outweighs a Kellogg's box is approximately 50%.

To find the probability that the Post box will outweigh the Kellogg's box, we need to calculate the difference in weights between the two brands and then determine the probability that this difference is positive.

Let X be the weight of a box of Post Corn Flakes and Y be the weight of a box of Kellogg's Corn Flakes.

We are given that:

- For Post Corn Flakes, X ~ N(μ = 64.1, σ = 0.5)

- For Kellogg's Corn Flakes, Y ~ N(μ = 63.9, σ = 0.4)

We want to find P(X > Y), which is the probability that a randomly selected box of Post Corn Flakes weighs more than a randomly selected box of Kellogg's Corn Flakes.

Now, let Z = X - Y. We are interested in finding P(Z > 0).

The mean and standard deviation of Z can be calculated as follows:

- Mean of Z: μ_Z = μ_X - μ_Y = 64.1 - 63.9 = 0.2 oz

- Standard deviation of Z: σ_Z =[tex]sqrt(σ_X^2 + σ_Y^2) = sqrt(0.5^2 + 0.4^2)= sqrt(0.25 + 0.16)= sqrt(0.41) = 0.64 oz[/tex]

Now, we standardize Z:

Z = (X - Y - μ_Z) / σ_Z

Therefore,

P(Z > 0) = P((X - Y - μ_Z) / σ_Z > 0)

         = P((X - Y) > μ_Z)

         = P((X - Y) > 0.2)

Now we look up the z-score corresponding to Z = 0.2:

z = (0.2 - μ_Z) / σ_Z

  = (0.2 - 0.2) / 0.64

  = 0

The probability that Z is greater than 0 is equal to the probability that the standardized Z-score is greater than 0, which is 0.5.

Therefore, the probability that the Post box will outweigh the Kellogg's box is 0.5 or 50%.

Answer:

480 feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

2  on  top goes  to  last  on  the  bottom  or  b  goes  to  d

1st one one top goes to the 2nd one on bottom or a goes to b

last one on top goes to the third one on bottom or d goes to c

The last two witch are 3rd on top and first one together

Hope this helped it took me a long time :)

The x and y coordinates on the circle will be such that they satisfy the equation of the unit circle.

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

A unit circle refers to a circle with unit radius (r = 1 unit) and positioned at center ( coordinates of origin = (h,k) = (0,0))

Thus, the equation of unit circle would be:

[tex]x^2 + y^2 =1[/tex]

Getting expression for y in terms of x,

[tex]x^2 + y^2 =1\\\\y = \pm \sqrt{1 - x^2}[/tex]

Using this equation to evaluate x for all given y:

[tex]\pm \dfrac{\sqrt{5}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{5}{9} = 1 - x^2\\\\x^2 = \dfrac{4}{9}\\\\x = \pm \dfrac{2}{3}[/tex]

From the options available, the fourth block seems valid.

Thus, we get:

[tex]y = \pm \dfrac{\sqrt{5}}{{3}} \rightarrow \left(\dfrac{2}{3}, y\right)[/tex]

[tex]\pm \dfrac{\sqrt{7}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{7}{9} = 1 - x^2\\\\x^2 = \dfrac{2}{9}\\\\x = \pm \dfrac{\sqrt{2}}{3}[/tex]

From the options available, the fourth block seems valid.

Thus, we get: [tex]y = \pm \dfrac{\sqrt{7}}{{3}} \rightarrow \left(\dfrac{\sqrt{2}}{3}, y\right)[/tex]

[tex]\pm \dfrac{3}{5} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{9}{25} = 1 - x^2\\\\x^2 = \dfrac{16}{25}\\\\x = \pm \dfrac{4}{5}[/tex]

From the options available, the fourth block seems valid.

Thus, we get: [tex]y = \pm \dfrac{3}{5} \rightarrow \left(\dfrac{4}{5}, y\right)[/tex]

[tex]\pm \dfrac{2\sqrt{2}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{8}{9} = 1 - x^2\\\\x^2 = \dfrac{1}{9}\\\\x = \pm \dfrac{1}{3}[/tex]

From the options available, the fourth block seems valid.

Thus, we get: [tex]y = \pm \dfrac{2\sqrt{2}}{{3}} \rightarrow \left(\dfrac{1}{3}, y\right)[/tex]

Thus, the x and y coordinates on the circle will be such that they satisfy the equation of the unit circle.

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Answer:

a. [tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]

Step-by-step explanation:

The given system of equation is

[tex]9x-4y-5z=9[/tex]

[tex]7x+4y-4z=-1[/tex]

[tex]6x-6y+z=-5[/tex]

The coefficient matrix is :

[tex]\left[\begin{array}{ccc}9&-4&-5\\7&4&-4\\6&-6&1\end{array}\right][/tex]

The constant matrix is

[tex]\left[\begin{array}{c}9\\-1\\-5\end{array}\right][/tex]

The augmented matrix is obtained by  combining the coefficient matrix and the constant matrix.

[tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]

The correct choice is A

in short, we simply split the total amount by the given ratio, so we'll split or divide 1020 by (15 + 2) and then distribute accordingly.

[tex]\bf \cfrac{petunias}{geraniums}\qquad 15:2\qquad \cfrac{15}{2}~\hspace{7em}\cfrac{15\cdot \frac{1020}{15+2}}{2\cdot \frac{1020}{15+2}}\implies \cfrac{15\cdot \frac{1020}{17}}{2\cdot \frac{1020}{17}} \\\\\\ \cfrac{15\cdot 60}{2\cdot 60}\implies \cfrac{900}{120}\implies \stackrel{petunias}{900}~~:~~\stackrel{geraniums}{120}[/tex]

The total number of geraniums in the greenhouse is 120. This was determined by calculating the value of each 'part' in the provided petunia to geranium ratio and then multiplying the number of geranium 'parts' by this value.

The question provides a ratio of petunias to geraniums in the greenhouse, which is 15:2. This is the same as saying for every 15 petunias, there are 2 geraniums. If you combine the parts of the ratio, you get a total of 17 parts (15 petunias + 2 geraniums). We know that the total number of flowers in the greenhouse is 1020.

Now, we'll figure out what each 'part' is equal to in the real world. To do that, we divide the total number of flowers by the total number of parts, so 1020 ÷ 17 = 60. This tells us each 'part' in our ratio is equal to 60 flowers.

From there, since we need to find the number of geraniums, we multiply the number of geranium 'parts' by the value of each 'part'. So, the number of geraniums in the greenhouse is 2 (The geranium 'parts') x 60 = 120 geraniums.

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Answer:

Part a) The volume of the prism Q is two times the volume of the prism P

Part b) The volume of the prism Q is two times the volume of the prism P

Step-by-step explanation:

Part 18) we know that

The volume of a rectangular prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

a) Suppose the bases of the prisms have the same area, but the height of prism Q is twice the height of prism P. How do the volumes compare?

Volume of prism Q

[tex]VQ=B(2h)=2(Bh)[/tex]

Volume of prism P

[tex]VP=Bh[/tex]

Compare

[tex]VQ=2VP[/tex]

so

The volume of the prism Q is two times the volume of the prism P

b) Suppose the area of the base of prism Q is twice the area of the base of prism P. How do the volumes compare?

Volume of prism Q

[tex]VQ=(2B)h=2(Bh)[/tex]

Volume of prism P

[tex]VP=Bh[/tex]

Compare

[tex]VQ=2VP[/tex]

The volume of the prism Q is two times the volume of the prism P

Answer:

p = 4

j = 21

Step-by-step explanation:

Joey = j

Pat = p

j = p + 17

(j+6) = 2*(p + 6) + 7      Simplify this. Remove the brackets.

j + 6 = 2p + 12 + 7        combine like terms    

j + 6 = 2p + 19               Subtract 6 from both sides

j +6-6 = 2p +19-6

j = 2p + 13

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

Equation j = 2p + 13 and j = p + 17

2p + 13 = p + 17                 Subtract p from both sides

2p-p+13 =p-p + 17

p + 13 = 17                         Subtract 13 from both sides

p = 17-13

p = 4

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

j = p + 17

j = 4 + 17

j = 21

Answer:

Joey is 21; Pat is 4

Step-by-step explanation:

The problem statement supports two equations in Joey's age (j) and Pat's age (p):

j - p = 17

(j +6) -2(p +6) = 7

Subtracting the second equation from the first, we have ...

(j -p) -((j +6) -2(p +6)) = (17) -(7)

p +6 = 10 . . . . . simplify

p = 4 . . . . . . . . . subtract 6

J = 17 +4 = 21

Joey is 21; Pat is 4.