The function g is defined by g(x)=ax−7, where a is a constant. Find a, if the graph of g passes through the point ( 1/3 ,−2).

Answer:

0, 2 and - 6

Step-by-step explanation:

To find the zeros of f(x), equate f(x) to zero, that is

x(x - 2)(x + 6) = 0

Equate each factor to zero and solve for x

x = 0

x - 2 = 0 ⇒ x = 2

x + 6 = 0 ⇒ x = - 6

Answer:

b.

Step-by-step explanation:

x=0,−2+√17,−2−√17

Decimal Form:

x=0,2.12310562…,−6.12310562

Answer:

The correct answer is 5

Step-by-step explanation:

To find this, start by multiplying them in any order. For ease, we'll multiply the first and last.

-2/3 * -3 = 2

Now we take that and multiply it by the remaining term.

2 * 2 1/2 = 5

Answer: option c

Step-by-step explanation:

By definition, if you have:

[tex]\sqrt[n]{x}[/tex]

you can rewrite it has following:

[tex]x^{\frac{1}{n}}[/tex]

Therefore, keeping the above on mind, you can rewrite the expression given in the problem, as you can see below:

[tex]15x^{\frac{1}{3}}y^{\frac{1}{5}}=(15\sqrt[3]{x})(\sqrt[5]{y})[/tex]

Both terms are multiples of 15, then take the 15th root of both and multiply the exponents by 15. Therefore you obtain:

[tex]15\sqrt[15]{x^5y^3}[/tex]

The answer is:

c. [tex]15\sqrt[15]{x^{5}y^{3}}[/tex]

To express the expression using a radical we must remember that:

Transforming radical to exponential form:

[tex]\sqrt[n]{x}=x^{\frac{1}{n}}\\\sqrt{x}=x^{\frac{1}{2} }[/tex]

So, the given expression is:

[tex]15x^{\frac{1}{3}}y^{\frac{1}{5}}[/tex]

Its radical form will be:

[tex]15\sqrt[3]{x}\sqrt[5]{y}[/tex]

Then, the expression could be also equivalent to:

[tex]15\sqrt[3]{x}\sqrt[5]{y}=15\sqrt[15]{x^{5}}\sqrt[15]{y^{3}}\\\\15\sqrt[15]{x^{5}}\sqrt[15]{y^{3}}=15\sqrt[15]{x^{5}y^{3}}[/tex]

Have a nice day!

ANSWER

1. k=13

2. x=-10

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 3x - 10[/tex]

To find f(x+5), plug in (x+5) wherever you see x.

This implies that:

[tex]f(x) = {(x + 5)}^{2} + 3(x + 5) - 10[/tex]

Expand:

[tex]f(x) = {x}^{2} + 10x + 25+ 3x + 15- 10[/tex]

Simplify to obtain

[tex]f(x) = {x}^{2} + 13x + 30[/tex]

We now compare with,

[tex]f(x) = {x}^{2} + kx + 30[/tex]

This implies that:

[tex]k = 13[/tex]

To find the smallest zero of f(x+5), we equate the function to zero and solve for x.

[tex]{x}^{2} + 13x + 30 = 0[/tex]

[tex] {x}^{2} + 10x + 3x + 30 = 0[/tex]

[tex]x(x + 10) + 3(x + 10) = 0[/tex]

[tex](x + 3)(x + 10) = 0[/tex]

[tex]x = - 10 \: or \: x = - 3[/tex]

The smallest zero is -10.

Answer:

k=13 while x =-10 :)

Step-by-step explanation:

Answer:

its 5

Step-by-step explanation:

what you do is put then like this 33346678 then you add them and you get 40

then see how meny there are so here we have 8 so we devid by 8 and get 5

Mean is the average of the data set

Work:

Total: 3 + 3 + 3 + 4 + 6 + 6 + 7 + 8 = 40

Mean = 40/8 = 5

Explanation:

To find the mean of a data set, add all the values together and divide by the number of values in the set.

So

First, count the number values in your data set.

Next, sum up all values in your data set, it means you need to add all together

Last, to find mean(average) = sum of all values / total number

Step-by-step explanation:

h=8m

b=2m

we know,

A=b×h

=2m×8m

=16m²

Answer:

14

Step-by-step explanation:

1,4,9,16,25,36,49,64,81,100,121,144,169,196

In order to match each of the pairs you need to divide the numerator by the denominator to make it into a decimal.

Below are the pairs:

21/25 = 84%

13/20 = 65%

2/5 = 40%

3/4 = 75%

3/5 = 60%

21/25 = 84%

13/20 = 65%

2/5 = 40%

3/4 = 75%

3/5 = 60%

Answer: is there a picture or something like that?

Step-by-step explanation:  

Answer:

6-12j

Step-by-step explanation:

Best regards

The algebraic expression is: 12j - 6

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ The formula for area of a trapezoid is a+b/2*h

a=3

b=8

h=4

3+8=11

11/2=5.5

5.5*4=22

Final answer:

The area of the trapezoid is 22 square inches

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ The formula for area of a trapezoid

The area of the trapezoid is 22 square inches is a+b/2*h

a=3, b=8, h=4

3+8=11

11/2=5.5

5.5*4=22

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

DOGE

[tex]\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{xy}{2}=28\implies \stackrel{\textit{cross-multiplying}}{xy=56}\implies y=\cfrac{\stackrel{\stackrel{k}{\downarrow }}{56}}{x}[/tex]

The equation that represents an inverse variation with a constant of 56 is:

             Option: D

         D.   [tex]\dfrac{xy}{2}=28[/tex]                  

Inverse Variation--

It is a relationship between two variables such that it is given in the form that:

If x and y are two variables then they are said to be in inverse variation if there exist  a constant k such that:

[tex]y=\dfrac{k}{x}[/tex]

i.e.

[tex]xy=k[/tex]

Here the constant of variation is 56

i.e. k=56

Hence, we have:

[tex]xy=56\\\\i.e.\\\\xy=28\times 2\\\\i.e.\\\\\dfrac{xy}{2}=28[/tex]

              Hence, option: D is the correct answer.

adequate notice of leave

Answer:

at least a 2 week notice

Step-by-step explanation:

Answer:

4*4*4 = 4³

Step-by-step explanation:

Claire has 4 stamps.

Julia has 4 times as many as Claire or 4*4 = 4².

Damon has 4 times as many as Julia or 4*4*4 = 4³

Final answer:

The two positive integers in question are 8 and 3, as they satisfy both conditions: one integer is 5 less than the other and their product equals 24.

Explanation:

The problem asks us to find two positive integers where one is 5 less than the other and their product equals 24. Let's denote the larger integer as 'x'. Then, the other integer would be 'x - 5'. We can set up the equation:

x(x - 5) = 24

Which simplifies to:

x² - 5x - 24 = 0

By factoring this quadratic equation, we end up with:

(x - 8)(x + 3) = 0

We are given the numbers are positive integers, so we take the positive root which is:

x = 8

Subsequently, the smaller integer would be:

8 - 5 = 3

So the two integers are 8 and 3.

I would use the pythagorean theorem to find the lengths of each side. a² + b² = c².

Side AB is one we're looking for. If you make other right triangle with that same side you can see that one length is 4 and the other is 3. So, 4² + 3² = c² → 25 = c² → 5 = c. Side AB is length 5.

Side AC is another. Do the same with that side and you get that one length is 4 and the other is 3. (This is the same one as above) so side AC is length 5.

Side BC is the last one. One of the lengths is 1 and the other is 1 → 1² + 1² = c² → 2 = c² → 1.414213562 = c so side BC is approximately length 1.41.

Add each length up and you get a perimeter of roughly 11.4

Answer:

8

Step-by-step explanation: i got it wrong and it tole me the answer.

Answer: D: 8

Step-by-step explanation:

Happy cheating

Let the soup can be represented by = s

Let the tuna can be represented by = t

Let the error of the scale in grams be represented by = e

4 cans of soup and 3 cans of tuna are placed on a correct scale and reads 80 ounces.

A can of soup and a can of tuna are placed on this scale, and it reads 24 ounces.

Two cans of tuna weigh 18 ounces on the bad scale.

Now equations becomes:

[tex]4s+3t=80[/tex]   ....(1)

[tex]s+t+e=24[/tex]    .... (2)

[tex]2t+e=18[/tex]     ..... (3)

From equation 3 we get

[tex]e=18-2t[/tex]

Putting this in equation 2

[tex]s+t+18-2t=24[/tex] = [tex]s-t=6[/tex]   ..... (4)  

Now we will solve equations 1 and 4.

Multiplying equation (4) by '4' we get, [tex]4s-4t=24[/tex]

Now subtracting this from equation 1, we get

[tex]7t=56[/tex]

[tex]t=8[/tex]

Now 4s+3t=80 ,

[tex]4s+24=80[/tex]

[tex]4s=56[/tex]

s = 14

And s+t+e = 24

14+8+e = 24

e = 2

Hence, a can of tuna weighs 8 ounces, a can of soup weighs 14 ounces and the amount of error is 2 ounces.

To find the amount of error in the scale and the correct weight of each type of can, set up a system of equations. Solve the equations to find that the amount of error in the scale is 0 ounces and the correct weight of each can is 15 ounces for soup and 9 ounces for tuna.

To find the amount of error in the scale and the correct weight of each type of can, we need to set up a system of equations.

Let's assume the weight of a can of soup is 's' and the weight of a can of tuna is 't'. From the given information, we can write the following equations:

1. s + t = 24   (equation 1)

2. 4s + 3t = 80  (equation 2)

We also know that two cans of tuna weigh 18 ounces on the bad scale. Therefore, we can write:

3. 2t = 18

From equation 3, we can solve for t: t = 18/2 = 9 ounces.

Substitute the value of t in equation 1 to find s: s + 9 = 24. Solving for s gives s = 15 ounces.

So, the amount of error in the scale is 24 - (15 + 9) = 24 - 24 = 0 ounces. The correct weight of each type of can is 15 ounces for soup and 9 ounces for tuna.

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Answer:

D - 56.6 MPH is the faster

Step-by-step explanation:

Find the unit rate by dividing the miles by hours

A. 589/11 = 53.55 MPH

B. 360/7 = 51.43 MPH

C. 111/2 = 55.5 MPH

D. 283/5 = 56.6 MPH

After calculating the speed for each option by dividing the distance by time, option D is found to be the fastest with a speed of 56.6 mph.

To find out which rate is the fastest, we need to calculate the speed for each option by dividing the distance by the time.

The speed is the distance traveled per unit of time, typically expressed in miles per hour (mph).

Comparing the calculated speeds, option D is the fastest with a speed of 56.6 mph.

Answer:

8/15

Step-by-step explanation:

there are 8 pints of lemonade totally. These 8 pints are divided into 15 glasses in equal amounts.

So each glass contains 8/15 pints of lemonade.

Hope i helped you:)

Answer:

0.53 repeated 3

Step-by-step explanation:

Just do 8 divided by 15 and you get 0.53333333333, which is just 0.53 with a little slash over the top. Hope this helps :)

Answer:

Step-by-step explanation:

11x+11

or you could do

11(x+1)

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

Given: [tex]4x-6=2x-2[/tex]

To solve for x, we need to isolate the x values on one side of the equation. Let's start by subtracting 2x from both sides.

[tex]2x-6=-2[/tex]

To further isolate x on one side of the variable, we should add 6 to both sides.

[tex]2x=4[/tex]

Finally, we need to take the coefficient of 2 off of the x to solve for x. To do this, divide both sides by the coefficient, 2.

[tex]\frac{2x}{2} = \frac{4}{2}[/tex]

[tex]x=2[/tex]

Answer: x=2

Step-by-step explanation:

* Hopfully the helps:) Mark me the brainliest:)!!

Answer:

use the formula A = 1/2ab(sin C)

Step-by-step explanation:

add the 32+0.05 to find the n

Answer: 32 liters

Step-by-step explanation:

W(0)= 32 so the glass tanks volume is 32

Answer:

22/45

Step-by-step explanation:

Let A be the event of drawing a multiple of 2,  

So,  

p(A)=  23/45

Now, let A' be the opposite(complementary) event which means not drawing a multiple of 2

From the properties of probability, the sum of an event’s probability and its opposite(complementary) event’s probability is equal to 1.

p(A)+p(A')=1

We have to find the probability of not drawing a multiple of two i.e. p(A')

p(A')=1-p(A)

=1 - 23/45

=  (45-23)/45

=22/45

So the probability of not drawing a multiple of 2 from the hat is 22/45.

Final answer:

The probability of not drawing a multiple of two from the numbers 30 to 74, given the probability of drawing a multiple of two is 23/45, is computed by subtracting 23/45 from 1, resulting in a probability of 22/45.

Explanation:

The probability of not drawing a multiple of two is simply calculated by subtracting the probability of drawing a multiple of two from 1, as these probabilities are complementary.

Given that the probability of drawing a multiple of 2 is 23/45, we can find the probability of not drawing a multiple of two by doing the following:

1 - (probability of drawing a multiple of 2) = 1 - (23/45) = 22/45.

Therefore, the probability of not drawing a multiple of two is 22/45.

The equation of the graph is y= -(x+3)^2 +1

Choice A is the correct answer

The equation of the given graph is:

            [tex]y=-(x-3)^2+1[/tex]

We know that the general equation of a downward parabola with vertex at (h,k) is given by the formula:

      [tex]y=a(x-h)^2+k[/tex]

where a<0

Here in each of the options we have a= 1 or -1

but as a has to be less than 1 this means that a= -1

Also, we have: (h,k)= (3,1)

i.e. h=3 and k=1

Hence, putting the values of h,k and a in the general equation we get:

      Hence, the equation of parabola is:

       [tex]y=-(x-3)^2+1[/tex]

Find the GCF (Greatest Common Factor) of both numbers. It is 3.

Divide both numbers by the GCF.  

The simplest form is 1/3.

Answer:

[tex]\boxed{\bold{\frac{1}{3}}}[/tex]

Step-by-step explanation:

Simplify [tex]\bold{\frac{3}{9} }[/tex]

Find a number that goes into 3 and 9 evenly

Number: 3

Divide to simplify

3 ÷ 3 = 1

9 ÷ 3 = 3

Rewrite fraction

[tex]\bold{\frac{1}{3}}[/tex]

Regards,

             Mordancy

Answer:

[tex]f(x)=x^3+x^2-4x-4[/tex]

Step-by-step explanation:

From the graph, the x-intercepts are;

[tex]x=-2[/tex]

[tex]x=-1[/tex]

[tex]x=2[/tex]

These are root of the polynomial function represented by the given graph.

By the remainder theorem;

[tex]f(-2)=0,f(-1)=0,f(2)=0[/tex]

According to the factor theorem, if [tex](x-a)[/tex] is a factor of [tex]f(x)[/tex], then [tex]f(a)=0[/tex]

This implies that;

[tex](x+2),(x+1),(x-2)[/tex] are factors of the required function.

Hence; [tex]f(x)=(x+1)(x-2)(x+2)[/tex]

We expand using difference of two squares to obtain;

[tex]f(x)=(x+1)(x^2-4)[/tex]

We expand using the distributive property to get;

[tex]f(x)=x^3-4x+x^2-4[/tex]

Rewrite in standard form to obtain;

[tex]f(x)=x^3+x^2-4x-4[/tex]

Answer:

Choice A: f(x) = x^3 + x^2 − 4x − 4

Step-by-step explanation:

Here's a great and simple answer.

Ok first we need to take the x intercepts to solve.

If we look at the graph we see the x ints are -2,+1 and +2.

To solve we need to put them into factor form

= (x-2) (x+2) and (x+1)

Simplify: (x-2) (x+2) = (x^2-4) and (x+1)

Now we take (x^2-4) and (x+1) and multiply them to find our answer

(x^2-4) (x+1)

= x^2(x) and x^2(1) = x^3 and x^2.

now the other: -4(x) and -4(+1) = -4x and -4

We have nothing common here so we just join them

= x^3 + x^2 - 4x - 4, and that is the same as choice A.

Answer:

x=-2

Step-by-step explanation:

Carry over the 5 to the other side of the equal sign and do its reverse. So 3-5=-2 which means x is equal to -2.

Answer:

x=-2,x=-8

Step-by-step explanation: