Find the length of segment AC if AB is 7, BC is 12 and B is between a A and C

Answer:

5 years

Step-by-step explanation:

18= 9(1.15)^x

Divide each side by 9

18/9= 9/9 *(1.15)^x

2 = 1.15 ^x

Take the  log on each side

log (2) = log (1.15^x)

log 2 = x log 1.15

Divid each side by log (1.15)

log 2 / log 1.15 = x log 1.15/ log 1.15

log 2 / log 1.15 = x

4.959484455 = x

To the nearest year

5 years

bAnswer:

B)

Step-by-step explanation:

Rise over run is another term for slope, with we can use to derive a linear equation.

The term rise over run in technical terms is the change of y over the change of x.

To find the rise over run, subtract the y terms and divide that by the x terms.

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

You can use this to derive a linear equation as earlier mentioned by plugging in given points.

For example, a line passes through (3,4) with a rise over run of 3.

[tex]y=mx+b[/tex]

[tex]4=3(3)+b[/tex]

[tex]4=9+b[/tex]

[tex]b=-5[/tex]

So therefore the y intercept is -5, and the equation is [tex]y=3x-5[/tex]

Answer:

a = 2

Step-by-step explanation:

Let's find the equation of the line using the 2 points given.

Let's call -1 as x_1 and -5 as y_1

also, 4 as x_2 and 5 as y_2

The equation of line is :

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Let's plug the points and get the equation of the line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y+5=\frac{5+5}{4+1}(x+1)\\y+5=2(x+1)\\y+5=2x+2\\y=2x-3[/tex]

Now, to find a, we substitute a in x and 1 in y of the equation of the line we just got:

[tex]y=2x-3\\1=2(a)-3\\1=2a-3\\2a=4\\a=\frac{4}{2}=2[/tex]

Answer: [tex]a=2[/tex]

Step-by-step explanation:

We know that this line passes through the point [tex](a,1)[/tex] where "a" is the  unknown x-coordinate of that point and 1 is the y-coordinate.

We also know that this line passes through the points (-1, -5) and (4, 5).

Then, in order to find the value of "a", we can plot the known points and draw the line (Observe the image attached).

You can observe in the image attached that the point whose y-coordinate is 1 is the point (2,1). Therefore, the value of "a" is:

[tex]a=2[/tex]

Answer:

The company earned 68 billion dollars in the year 2008..

Step-by-step explanation:

This is because  the time t is the number of years since the END of 2008. The  time t = 0 at the end of 2008, so the earnings = 0^2 + 10(0) + 68 = 68 billion.

Answer:

option B

Step-by-step explanation:

A particular company's net sales is modeled by the expression (t² + 10t + 68)

Where t represents number of years since the end of year 2008.

In this expression 68 is the constant term which represents the earning of the company before 2008. or in year 2008.

The company earned 68 billion dollars in 2008.

Therefore, option B is the answer.

[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] ~\dotfill\\\\ g(x)=3(x-\stackrel{h}{2})^2+(\stackrel{k}{-5})\qquad \qquad \stackrel{\textit{vertex}}{(2,-5)}[/tex]

Answer: period

Step-by-step explanation:

Answer:

The correct option is A.

Step-by-step explanation:

It is given that a driver runs over a nail, puncturing the tire without causing a leak.

Tire of a car represents a periodic function because after a particular time the tire comes its initial stage and that particular time interval is called a period.

It means period is the key feature of the function representing the nail’s travel can be used to determine the amount of time it takes for the nail to reach the same orientation it had when it entered the tire.

Therefore the correct option is A.

Answer:

Step-by-step explanation:

Rewrite the first equation

[tex]-6y=-50-4x\\\\4x-6y=-50[/tex]

Now we have the following system of equations

[tex]4x-6y=-50\\5x-6y=-49[/tex]

To solve the system of equations multiply the first equation by -1 and add it to the second equation

[tex]-1*4x-(-1)*6y=-50*(-1)\\\\-4x+ 6y=50[/tex]

[tex]-4x+ 6y=50[/tex]

        +

[tex]5x-6y=-49[/tex]

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

[tex]x + 0 =1\\\\x=1[/tex]

Now substitute the value of x in any of the two equations and solve for y

[tex]5(1)-6y=-49[/tex]

[tex]5-6y=-49[/tex]

[tex]-6y=-49-5[/tex]

[tex]-6y=-54[/tex]

[tex]y=\frac{54}{6}[/tex]

[tex]y=9[/tex]

The solution is:

[tex](1,\ 9)[/tex]

Answer:

13

Step-by-step explanation:

Two factors of -48... that means two numbers which multiplied together give a result of -48, like -6 and 8 for example.

The difference of those two factors is -19.  There not that many possible factors for -48, so if we list them we'll be able to spot a pair with a difference of 19.

A first list of factors for -48 is: -1 and 48, -2 and 24, -3 and 16, -4 and 12, -6 and 8.

We can create another list by inverting the signs: 1 and -48, 2 and -24, 3 and -16, 4 and -12, 6 and -8.

The question says the difference of the two factors is 19...  can you spot in each list a pair of factors having a difference of 19?   I see -3 and 16 and also 3 and -16.

The question also say the one of the greatest absolute value is positive... so that  means it's a pair with +16, not -16.

The pair of factors we're looking for is then -3 and 16. They are factors of -18, they have a difference of 19, and the one with the greatest absolute value is positive.

The sum of -3 and 16 is 13.

Answer:

Point

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

I got it right on E2020

Answer:

x =20

Step-by-step explanation:

We can use proportions to solve

$240         320

----------- = ------------

15                x

Using cross products

240x = 320 * 15

240x =4800

Divide by 240 on each side

240x/240 = 4800/240

x =20

By finding the cost per square yard from Joanna's initial purchase ($16 per sq yd), we can calculate that she can buy 20 square yards of carpet for $320.

To find out how many square yards of carpet Joanna can buy for $320 using the same rate, we first need to determine the cost per square yard based on her $240 purchase. She can buy 15 square yards for $240, so by dividing the total cost by the number of yards, we find the cost per square yard.

Cost per square yard = Total cost / Number of square yards = $240 / 15 sq yds = $16 per sq yd.

Now, we can use the cost per square yard to find out how many square yards she can get for $320. We divide the total amount she's willing to spend by the cost per square yard.

Square yards for $320 = Total amount to spend / Cost per square yard = $320 / $16 per sq yd = 20 sq yds.

Therefore, Joanna can buy 20 square yards of carpet for $320.

Answer:

∠ACD≅∠CAB

Step-by-step explanation:

According to SAS postulate if two sides and the included angle of ΔDAC are same to two sides and the included angle of ΔBCA. Then ΔDAC≅ΔBCA

But for the given figure  

∠DAC≅∠BCA and

CA=AC   (common in both triangle)

Hence we need ∠ACD≅∠CAB to prove that ΔDAC≅ΔBCA

D

(-71+1) + 0 = (-71+1)

This is because the whole equation involves addition thus it is an example of associative property of addition

Answer:

(-71 + 1) + 0 = (-71 +1)

Step-by-step explanation:

Given 3 numbers: a,b,c

Associative property of addition: (a + b) + c = a + (b + c)

On this case: a= -71

b = 1

c = 0

(a + b) + c = (-71 + 1) + 0 = -70 + 0 = -70

(-71 + (1 + 0)) = (-71 + 1) = -70

Both the sums are equal to -70 and hence the associative property of addition for the three numbers a= -71, b = 1, c= 0 holds.

All the other options in the question contain a reference to variable i and does not have the same three values a,b,c on both sides of the equality. So they do not represent the associative property.

Answer:

Option C.

[tex]a=6\sqrt{3}[/tex]

[tex]b=12[/tex]

[tex]c=6\sqrt{2}[/tex]

Step-by-step explanation:

step 1

Find the value of a

we know that

[tex]tan(60\°)=a/6[/tex]

Remember that

[tex]tan(60\°)=\sqrt{3}[/tex]

so

[tex]a/6=\sqrt{3}[/tex]

[tex]a=6\sqrt{3}[/tex]

step 2

Find the value of b

we know that

[tex]cos(60\°)=6/b[/tex]

Remember that

[tex]cos(60\°)=1/2[/tex]

so

[tex]6/b=1/2[/tex]

[tex]b=12[/tex]

step 3

Find the value of c

we know that

[tex]cos(45\°)=c/b[/tex]

[tex]cos(45\°)=c/12[/tex]

Remember that

[tex]cos(45\°)=\sqrt{2}/2[/tex]

[tex]c/12=\sqrt{2}/2[/tex]

[tex]c=6\sqrt{2}[/tex]

Answer:

C.

Step-by-step explanation:

Answer:

[tex]s(x)=10(1.03)^{x}[/tex]

Step-by-step explanation:

Let

x -----> the number of weeks

S ----> the number of members in the science club

In this problem we have a exponential function of the form

[tex]s(x)=a(b)^{x}[/tex]

where

a is the initial value

b is the base

we have

[tex]a=10\ membrers[/tex]

[tex]r=3\%[/tex]

[tex]b=100\%+3\% =103\%=103/100=1.03[/tex]

substitute

[tex]s(x)=10(1.03)^{x}[/tex]

Answer:

1) the factored form is  y= ( x-5 ) ( x+4 )

2) the vertex is (4.5, -0.25)

3) the y intercept is when x equals 0 so it is at (0,20)

4) it opens upward and the vertex is (4.5, -0.25) the x intercepts are (4,0) and (5,0) and the y intercept is  (0,20)

5)

a. it dips  between 4 seconds and 5 seconds so the x intercepts are (4,0) and (5,0)

b. it is taken at the vertex aka the lowest point so the height is -0.25

Answer:

Part 1:

[tex]y= (x-4)(x-5)[/tex]

Part 2:

[tex](\frac{9}{2}, - \frac{1}{4})[/tex]

Part 3:

[tex]Y=20[/tex]

Part 5:

The height:

[tex]-\frac{1}{4}[/tex]

The time:

[tex]\frac{9}{2}[/tex]s

Step-by-step explanation:

[tex]y = x^{2}  -9x+20[/tex] Is a quadratic equation.

Part 1:

We use [tex]x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}[/tex] to factor quadratic equations

[tex]y = x^{2}  -9x+20[/tex]

a=1 b=-9 c=20

[tex]x = \frac {-(-9) \pm \sqrt {(-9)^2 - 4(1)(20)}}{2(1)}[/tex]

[tex]x = \frac {9 \pm \sqrt {81 -80}}{2}[/tex]

[tex]x = \frac {9 \pm {1}}{2}[/tex]

we solve both possibilities

[tex]x = \frac {9 + {1}}{2}=5[/tex]

[tex]x = 5[/tex]  

[tex]x = \frac {9 -{1}}{2}=4[/tex]

[tex]x=4[/tex]

The factored form would be

[tex]y= (x-4)(x-5)[/tex]

Part 2:

We use the formula to find the x coordinate of the vertex of a parabola

[tex]V_{x}=\frac{-b}{2a}[/tex]

[tex]y = x^{2}  -9x+20[/tex]

a=1 b=-9 c=20

[tex]V_{x}=\frac{9}{2}[/tex]

Now we substitute the value of x in [tex]y = x^{2}  -9x+20[/tex] to find the value of the coordinate y of the vertex

[tex]y = \ (\frac{9}{2} )^{2}   -9(\frac{9}{2}) +20\\ y=  \frac{81}{4} -\frac{81}{2} +20\\ y= -\frac{1}{4}[/tex]

The vertex of the parabola is

Vertex:

[tex](\frac{9}{2}, - \frac{1}{4})[/tex]

Part 3:

the y-intercept is when the value of x = 0.

We substitute this value in [tex]y = x^{2}  -9x+20[/tex]

[tex]y = 0^{2}  -9(0)+20= 20[/tex]

The y-intercept is [tex]y=20[/tex]

Part 5:

A.

Between 4s and 5s

B and C.

Erin's photograph is taken at the lowest point of the roller coaster.

The lowest point of the parabola is the vertex.

The coordinate y of the vertex gives us the height and the coordinate x the time.

The height:

[tex]-\frac{1}{4}[/tex]

It is negative because it is below the point we take as zero.

The time:

[tex]\frac{9}{2}[/tex]s

Part 4:

The answer is the graph

Answer:

L = 4d + 54

when d = 31 days

L = 4(31) + 54

L = 124 + 54

L = 178 miles

Step-by-step explanation:

The length of the road after 35 days of construction is 76 miles.

The length of the road after 35 days can be calculated using the given function L(d) = 41 + d, where L represents the length in miles and d represents the number of days of construction. To find the length after 35 days, we substitute d = 35 into the function.

L(35) = 41 + 35

L(35) = 76

Therefore, the length of the road after 35 days of construction is 76 miles.

Learn more about Lengthening of road here:

https://brainly.com/question/34454511

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Answer:

All are valid

Step-by-step explanation:

Px - 43 = -42x + Q (rearrange)

x = (Q+43) / (P + 42)  <----Substitute options for P & Q into this equation to see which combination gives exactly 1 solution for x

A) P=42, Q = 42; x = (42+43) / (42+42) = 1.011 (only 1 solution = valid)

B) P=43, Q = -42; x = (-42+43) / (43+42) = 0.012 (only 1 solution = valid)

C) P=-43, Q = -43; x = (-43+43) / (-43+42) = 0 (only 1 solution = valid)

D) P=42, Q = 43; x = (42+43) / (42+42) = 1.023 (only 1 solution = valid)

Answer:

       =25 %

Step-by-step explanation:

Percent decrease equals (original minus new) / original * 100 %

Percent decrease = (85-64)/ 85 * 100%

                              = 21/85 * 100%

                              =.247058824 * 100%

                              =24.7058824%

       To the nearest percent

                              =25 %

Answer:

"Y intercept is1 "

Step-by-step explanation:

The slope is (-1 - 2)/[8 - (-4)] = -3/12 = -(1/4)

(-1/4) = (y - 2)/(x + 4) => -x - 4 = 4y - 8

-x + 4 = 4y

y = (-1/4)x + 1 so that the y-intercept is 1

Answer:

"Y intercept is1 "

The slope is (-1 - 2)/[8 - (-4)] = -3/12 = -(1/4)

(-1/4) = (y - 2)/(x + 4) => -x - 4 = 4y - 8

-x + 4 = 4y

y = (-1/4)x + 1 so that the y-intercept is 1

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

These are the terms of a geometric sequence with n th term formula

[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

r = [tex]\frac{-48}{64}[/tex] = [tex]\frac{36}{-48}[/tex] = - [tex]\frac{3}{4}[/tex]

the first term a = 64, hence

[tex]a_{n}[/tex] = 64 [tex](-3/4)^{n-1}[/tex]

ANSWER

C. 28

EXPLANATION

The given expression is

[tex] {x}^{2} - 7x + 10[/tex]

We want to evaluate this function at x=-2.

We just have to substitute x=-2 into the given expression.

In other words, we have to replace x with -2 wherever we see x in the expression

[tex]{( - 2)}^{2} - 7( - 2) + 10[/tex]

We evaluate the exponent to get

[tex]4 - 7( - 2) + 10[/tex]

We multiply next to get:

[tex]4 + 14+ 10[/tex]

We now add to obtain:

[tex]28[/tex]

The correct answer is C

Answer:

Step-by-step explanation:

Let Waldo's speed = W

Let Ralph's speed = W + 15

A

Waldo's distance = speed * Time

Time = 4 hours.

Speed = w

distance = 4 * w

B

Ralph's speed is W + 15. It's not clear if you need a number. We'll get around to that later.

C

Ralph traveled  4*(W + 15)

D

4w + 70 + 4(W + 15) = d

You really can't get a definite answer to these questions. Even if you knew whether they were heading away from each other or towards each other it wouldn't help.

Picture needed. not enough info

Answer:

a² + b² = c², where a and b are the legs and c is the hypotenuse.

Answer:

Step-by-step explanation:

To build the equation we need to get  the value.

120,000

Lets add the percent which is 1.055 since it is 5.5% added to nothing increasing

120,000(1.055)x

Answer:

120000(1.055)x

Step-by-step explanation

Answer:

The answer is 79.875

Hope this helps!

Answer:

79.875

Step-by-step explanation:

79.875

8/639

-56

______

079

-072

_______

0070

-0064

_______

0060

-0056

________

0040

-0040

________

0000

Answer:

the right answer is point

Step-by-step explanation:

The Undefined term that is used to define an angle is; a point.

An angle is defined as the union of two rays with a common endpoint. The common end point is known as the vertex of the angle while the rays are known as the sides of the angle.

Now, angle can be named in different ways like use of capital letters, vertex of the angle, by placing any number or symbol at the vertex in the interior of the angle and other ways.

However, the undefined term that is used to define an angle is called "point".

Read more about angle at; https://brainly.com/question/7620723

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Answer: C

Step-by-step explanation:

1 + 2sin(x+pi)

1 is adding to the y, so it is a vertical shift of 1 unit,

2 is a stretch because it is multiplying to the sin,

and pi is adding to the x, so it is a phase shift.

Answer:

Step-by-step explanation:

The y-intercept of the function represended in the graph is 4 → (0, 4).

The table C. represents a linear function with a greater y-intercept (0, 5) → 5.

Answer:

51-10sqrt(2)

Step-by-step explanation:

(a-b)^2=a^2-2ab+b^2

(5sqrt(2)-1)^2=(5sqrt(2))^2-2(5sqrt(2))(1)+1^2

                     =5^2(2)-2(5sqrt(2))(1)+1^2

                    =25(2)-10sqrt(2)+1

                    =50-10sqrt(2)+1

                    =51-10sqrt(2)