Consider the relationship 3r+2t=18

A. write the relationship as a function r=f(t)

B. Evaluate f(-3)

C. solve f(t)= 2

Answer:

[tex] \sqrt{2}[/tex]

Step-by-step explanation:

You can multiply by sqrt 6/sqrt 6 to get rid of the sqrt in the denominator. This leaves you with 2(sqrt 3)(sqrt 6)/sqrt 36. The sqrt's in the numerator can be multiplied to get 2(sqrt 18). The sqrt 36 can be simplified to just 6. Sqrt 18 can be split into sqrt 9 and sqrt 2. The sqrt 9 can be taken out and simplified as 3. 3x2=6. This leaves you with 6(sqrt 2)/6. The 6 in the numerator cancels the 6 in the denominator and just leaves sqrt 2.

Answer:

aaaaaaaaaaa

Step-by-step explanation:

let's recall that, on the number line, for the positive side, the farther from zero, the larger the number, thus 100 is a much larger number than 10.

now, on the negative side of the number line, the farther from zero, the smaller the number, thus -1 is much much larger number than -1,000,000,000.

is -3 ≥ -15, is -3 larger or equals to -15, well, certainly is not equal but is certainly larger, yes.

Answer:

Step-by-step explanation:

Graph the absolute value function y = |x|.  This is v-shaped and opens up.

Now translate the entire graph 2 units to the left.  You will then have the graph of y=|x+2|​.

Answer:

I is at -7

Step-by-step explanation:

Step 1 : Find the distance between point F and G.

Point G is at 2

Point F is at 8

The distance between them is of 6 points/numbers.

Step 2 : Find I

Point H is -1

Point I will be 6 points/numbers behind point H so you have to count backwards.

Going 6 points/numbers backwards will bring you to -7 which is point I.

Therefore, I is -7.

!!

Answer:

A(x+2)(x-3)(x+6) where A is a constant.

If you want to change the order in that multiplication you can.

Read answer for my options on what your answer could look like.

Let me know the choices or if you have any questions.

Step-by-step explanation:

It says which like you have choices...

But I can give you several polynomials with those zeros.

By factor theorem if you have -6 is a zero then x+6 is a factor.

By factor theorem if you have -2 is a zero then x+2 is a factor.

By factor theorem if you have  3 is a zero then x-3 is a factor.

So a polynomial with those factors I mentioned is:

(x+6)(x+2)(x-3)

or

4(x+6)(x+2)(x-3)

or

-12(x+6)(x+2)(x-3)

or

1.4(x+6)(x+2)(x-3)

and so on....

I guess you could also say

4(x+6)(x+2)(x-3)^3.

It didn't say it had to have this multiplicity of 1.

Anyways I think you are probably looking for an option that says something like this:

A(x+6)(x+2)(x-3)

where A is a constant.

Keep in mind multiplication is commutative so it could be written as

A(x+2)(x-3)(x+6) or something similar to that.

Answer:

The x-intercepts are (5,0) and (7,0)

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

a is a coefficient

(h,k) is the vertex

In this problem we have

(h,k)=(6,-5)

substitute

[tex]y=a(x-6)^{2}-5[/tex]

Find the coefficient a

with the y-intercept (0,175) substitute the value of x and the value of y in the equation

For x=0, y=175

[tex]175=a(0-6)^{2}-5[/tex]

[tex]175=36a-5[/tex]

[tex]36a=180[/tex]

[tex]a=5[/tex]

substitute

[tex]y=5(x-6)^{2}-5[/tex]

Find the x-intercepts

Remember that the x-intercepts are the values of x when the value of y is equal to zero

For y=0

[tex]0=5(x-6)^{2}-5[/tex]

[tex]5(x-6)^{2}=5[/tex]

simplify

[tex](x-6)^{2}=1[/tex]

square root both sides

[tex]x-6=(+/-)1[/tex]

[tex]x=6(+/-)1[/tex]

[tex]x=6(+)1=7[/tex]

[tex]x=6(-)1=5[/tex]

therefore

The x-intercepts are (5,0) and (7,0)

Final answer:

To make a 4 percent ethanol mixture, 4000 gallons of 6 percent ethanol gasoline must be added to 2000 gallons of gasoline with no ethanol.

Explanation:

To determine how many gallons of gasoline containing 6 percent ethanol must be added to 2,000 gallons of gasoline with no ethanol to achieve a mixture that is 4 percent ethanol, we can use a simple algebraic equation.

Let x be the number of gallons of 6 percent ethanol gasoline we need to add. The total amount of ethanol in the new mixture will be 0.06x gallons since 6 percent of the x gallons is ethanol. We need the mixture to have 4 percent ethanol overall, so we can set up the equation: 0.06x / (2000 + x) = 0.04. We're calculating the proportion of ethanol in the total mixture, which includes the initial 2000 gallons plus the x gallons we're adding.

Multiplying both sides of the equation by (2000 + x) to eliminate the fraction gives us 0.06x = 0.04(2000 + x), which simplifies to 0.06x = 80 + 0.04x. Subtracting 0.04x from both sides gives us 0.02x = 80, and dividing both sides by 0.02 gives us x = 80 / 0.02. This simplifies to x = 4000.

Thus, 4000 gallons of 6 percent ethanol gasoline must be added to the 2000 gallons of non-ethanol gasoline to achieve a 4 percent ethanol mixture.

Answer:

<4,22>.

Step-by-step explanation:

This question involves the concepts of addition and scalar multiplication of vectors. It is given that the vector u = <-4, 1> and v = <-1, 6>. To find -2u, simply multiply -2 with the elements of u. This will give:

-2u = <-4*-2, 1*-2> = <8, -2>.

Similarly:

4v = <-1*4, 6*4> = <-4, 24>.

Hence,

-2u + 4v = <8, -2> + <-4, 24> = <8-4, -2+24> = <4,22>.

So the correct answer is <4,22>!!!

To find -2u + 4v, we will perform vector addition after scaling vectors u and v by -2 and 4, respectively.
First, we scale the vector u by -2. To do this, we multiply each component of vector u by -2:
u = <-4, 1>
-2u = -2 * <-4, 1> = <(-2)*(-4), (-2)*1> = <8, -2>
Now, we scale the vector v by 4. To do this, we multiply each component of vector v by 4:
v = <-1, 6>
4v = 4 * <-1, 6> = <4*(-1), 4*6> = <-4, 24>
Now that we have -2u and 4v, we can add these two vectors together. We do this by adding the corresponding components:
-2u + 4v = <8, -2> + <-4, 24>
Adding the x-components:
8 + (-4) = 4
Adding they-components:
-2 + 24 = 22
Hence, the resultant vector of -2u + 4v is:
-2u + 4v = <4, 22>
So the solution to -2u + 4v is the vector <4, 22>.

Answer:

B.

Step-by-step explanation:

The triangle is equilateral, therefore its angles are 60°.

Answer:

Options A and B.

Step-by-step explanation:

An ellipse is represented by the equation [tex]\frac{(x+5)^{2}}{625}+\frac{(y-7)^{2}}{49}=1[/tex]

We have to find the foci of the given ellipse.

Ellipse having equation [tex]\frac{(x-h)^{2}}{a^{2} }+ \frac{(y-k)^{2} }{b^{2} }=1[/tex]

Then center of this ellipse is represented by (h, k) and foci as (c, 0) and (-c, 0).

And c is represented by c² = a² - b²

So we co relate this equation with our equation given in the question.

a = √625 = 25

b = √49 = 7

and c² = (25)² - (7)²

c² = 625 - 49 = 576

c = ±√576

c = ±24

Now we know center of the ellipse is at (-5, 7) so foci can be obtained by adding and subtracting x = 24 from the coordinates of the center.

Center 1 will be [(-5+24=19), 7] ≈ (19, 7)

Center 2 will be [(-5-24=-29), 7] ≈ (-29, 7)

Therefore, options A and B are correct.

Answer:

A and B

Step-by-step explanation:

Answer:

The correct option is 32

Step-by-step explanation:

The given expression is:

m∠1 = 3y – 6

m∠1= 90°

Now arrange the value of angle in the given equation:

3y-6=90

Move the constant to the R.H.S

3y= 90+6

3y= 96

Now divide both the terms by 3

3y/3=96/3

y=32

Thus the correct option is 32....

Answer:

[tex]\Huge \boxed{10-N=8+N}[/tex]

Step-by-step explanation:

Difference: should be subtract.

N: should be a number.

Sum: Add

Therefore, the correct answer is 10-N=8+N.

Hope this helps!

Answer:

10-N=8+N

Step-by-step explanation:

10-N=8+N represents "the difference between ten and a number is the sum of eight and a number''.

You should go in order of PEMDAS:

P - parenthesis

E - exponents

M - multiplication

D - division

A - addition

S - subtraction

Answer:

[tex] y = 6(2.5)^x [/tex]

Step-by-step explanation:

[tex] y = ab^x [/tex]

Use (0, 6) and solve for a:

[tex] 6 = ab^0 [/tex]

[tex] 6 = a \times 1 [/tex]

[tex] a = 6 [/tex]

Use a = 6 and (1, 15) and solve for b.

[tex] 15 = 6b^1 [/tex]

[tex] 15 = 6b [/tex]

[tex] 6 = 2.5 [/tex]

[tex] y = 6(2.5)^x [/tex]

Answer:

see explanation

Step-by-step explanation:

Obtain the exponential function by substituting the given points into the equation.

Equation in form

y = a [tex]b^{x}[/tex]

Using (0, 6), then

6 = a [tex]b^{0}[/tex] = a ⇒ a = 6

Using (1, 15), then

15 = 6 [tex]b^{1}[/tex] = 6b ( divide both sides by 6 )

[tex]\frac{15}{6}[/tex] = b, hence

b = [tex]\frac{5}{2}[/tex]

Exponential equation is y = 6 [tex](\frac{5}{2}) ^{x}[/tex]

Answer:

The correct answer is option 1)  (6,7)

Step-by-step explanation:

Points to remember

Mid point formula

Let (x₁, y₁) and (x₂, y₂) be the end points of a line segment, then the coordinates of the midpoint of the line segment is given by

[(x₁ + x₂)/2, (y₁ + y₂)/2]

To find the coordinates of B

Let A(x₁, y₁) =  (-4, 3), and M(1, 5)

Coordinates of B be (x₂, y₂)

We have,

[(x₁ + x₂)/2, (y₁ + y₂)/2] = (1, 5)

(x₁ + x₂)/2 = 1

(-4 + x₂)/2 = 1

-4 + x₂ = 2

x₂ = 2 + 4 = 6

(y₁ + y₂)/2 = 5

(3 + y₂)/2 = 5

3+ y₂ = 10

y₂ = 10 - 3 = 7

Therefore coordinates of B(6,7)

The correct answer is option 1)  (6,7)

Final answer:

The coordinates of point B, which lies diametrically opposite to A on circle M with a known center at (1, 5), are determined to be (6, 7).

Explanation:

Since segment AB is the diameter of circle M, and we know the coordinates of A (-4, 3) and center M (1, 5), we can find B by using the fact that the center of the circle is the midpoint of the diameter. The midpoint formula states that the midpoint M can be found using the following formulas:

Mx = (Ax + Bx) / 2

My = (Ay + By) / 2

Therefore, to find Bx and By, we can rearrange the formula:

Bx = 2Mx - Ax

By = 2My - Ay

Solving this gives us B as:

Bx = 2(1) - (-4) = 6

By = 2(5) - 3 = 7

So the coordinates of point B are (6, 7).

Answer:

Option C is correct.

Step-by-step explanation:

-10<3x-4<8

Solving the given equation,

we know that if a<b<c then a<b and b<c

s0, -10<3x-4 and 3x-4<8

Solving to find the value of x

-10<3x-4

Switching sides,

3x-4>-10

3x > -10 +4

3x > -6

x > -6/3

x > -2

3x-4 < 8

3x < 8+4

3x < 12

x < 12/3

x < 4

s0, x >-2 and x < 4

-2 < x <4

Option C is correct.

-10 < 3x-4 < 8

Isolate x

First add 4 to each side:

-6 < 3x < 12

Divide each side by 3:

-2 < x < 4

The inequality signs do not contain equal to, so you would have open circles on both -2 and positive 4.

This means x is greater than -2 and less than 4, which is shown as the 3rd choice.

Answer:

False.

Step-by-step explanation:

The function f(x) =2x is not an logarithmic function. Rather, it is a linear function. The reason for this is that in f(x) = 2x, there is no log or ln involved on the right hand side of the equation. It is the polynomial of the first degree, which means it is a straight line function. It is important to note that for any value of x, the value of the function changes with the same proportion. This is because the derivative of the function is a constant, which means that the rate of change is constant. The graph of the function will be a line passing from the origin and (1,2) and will have the positive slope. Therefore, f(x) is not a logarithmic function, which means that the statement is false!!!

Answer:

(20+x)*2=x-6

40+2x=x-6

40=-x-6

46=-x

check:

x=-46

20-46*2=-46-6

-26*2=-52

-52=-52

x=-46

Answer:

x1=-14;x2=-26

Step-by-step explanation:

|x+20|=6

x+20=6

x+20=-6

Answer:

[tex]m=\dfrac{5}{2}[/tex]

Step-by-step explanation:

If the equation of the line is

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

then m represents the slope of the line and b represents the y-intercept of the line. This equation is called the equation of the line in the slope form.

Rewrite the equation of the line in the slope form

[tex]y-4=\dfrac{5}{2}(x-2)\\ \\y-4=\dfrac{5}{2}x-\dfrac{5}{2}\cdot 2\\ \\y-4=\dfrac{5}{2}x-5\\ \\y=\dfrac{5}{2}x-1[/tex]

Thus, the slope of the line is

[tex]m=\dfrac{5}{2}[/tex]

The slope of a line whose equation is [tex]y-4 = \frac{5}{2}(x-2)[/tex] is [tex]\frac{5}{2}[/tex]

In this case;

The equation in question is;

[tex]y-4 = \frac{5}{2}(x-2)[/tex]

Combining like terms;

[tex]y= \frac{5}{2}x-5+4[/tex]

The equation of the line is

[tex]y= \frac{5}{2}x-1[/tex]

From the equation the slope of the line is [tex]\frac{5}{2}[/tex], while

The y-intercept is -1

Keywords: Slope, Equation of a straight line, y-intercept,  

Level: High school  

Subject: Mathematics  

Topic: Equation of a straight line  

Sub-topic: Slope/gradient of a line

Answer:

2.5 inches

Step-by-step explanation:

If Jeff has a big scoop of ice cream that is 10 inches tall and it melts by 25% in a minute, the height of the ice cream after one minute is 2.5 inches.

You have to find what 25% of 10 inches is.

25% of 10 inches = 2.5 inches

Therefore, the height of the ice cream after one minute is 2.5 inches.

Answer: 7.5 inches tall

Step-by-step explanation: if 25% of the ice cream melted, it means 75% is remaining, therefore you say 75÷100 =0.75 then you multiply it by 10 inches to get 7.5 inches.

 i don't know all about them but a few are

1) What you are doing on one side do it on other side

eg -

x-10 = 5

x-10 + 10 = 5 + 10 [adding 10 on both the sides]

x= 15

or

10x = 100

10x/10 = 100/10

x = 10

or

x/ 10 = 10

x/10 * 10 = 10 * 10

x = 100

I hope you have understood

Answer:

[tex]4(2+\sqrt{2})\text{ square unit}[/tex]

Step-by-step explanation:

Given function that shows the area of the opening,

[tex]A(\theta)=16 \sin\theta (\sin \theta + 1)[/tex]

If [tex]\theta = 45^{\circ}[/tex]

Hence, the area of the opening would be,

[tex]A(45^{\circ})=16 \sin 45^{\circ} (\cos 45^{\circ} + 1)[/tex]

[tex]=16\times \frac{1}{\sqrt{2}}\times (\frac{1}{\sqrt{2}}+1)[/tex]

[tex]=16(\frac{1}{2}+\frac{1}{\sqrt{2}})[/tex]

[tex]=8+\frac{16}{\sqrt{2}}[/tex]

[tex]=8+4\sqrt{2}[/tex]

[tex]=4(2+\sqrt{2})\text{ square unit}[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

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

[tex]g(x)=f(x+1)[/tex]

so

Find the function f(x+1)

substitute the variable x for the variable (x+1) in the function

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

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

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

so

[tex]g(x)=4x+2[/tex]

Find the y-intercept

The y-intercept of g(x) is the point (0,2) (value of y when the value of x is equal to zero)

Find the x-intercept

The x-intercept of g(x) is the point (-0.5,0) (value of x when the value of y is equal to zero)

therefore

The graph in the attached figure

Answer:

C: (-0.5,0), (0,2)

Step-by-step explanation:

Answer:

[tex]x=-\frac{6}{7}[/tex]

[tex]y=-17\frac{6}{7}[/tex]

Step-by-step explanation:

We are given the following system of equations that we are to solve:

[tex] y = 8 x - 1 1 [/tex] - (1)

[tex] y = x - 1 7 [/tex] - (2)

Since the left hand side of both the equations is the same so we will equate the right hand sides of both the equations to get:

[tex]8x-11=x-17[/tex]

[tex]8x-x=-17+11[/tex]

[tex]7x=-6[/tex]

[tex]x=-\frac{6}{7}[/tex]

Substituting this value of [tex]x[/tex] in (1) to find [tex]y[/tex]:

[tex]y=8(-\frac{6}{7})-11[/tex]

[tex]y=-17\frac{6}{7}[/tex]

Final answer:

The solution to the system of equations y = 8x - 11 and y = x - 17 is found by setting the equations equal to each other and solving for x, then substituting back to find y. The solution is x = -6/7 and y = -125/7.

Explanation:

To solve the system of equations, you want to find a single value for x and y that satisfies both equations simultaneously. The given equations are:

y = 8x - 11

y = x - 17

Since both equations are equal to y, we can set them equal to each other and solve for x:

8x - 11 = x - 17

Now, let's get all the x terms on one side and the numbers on the other:

8x - x = -17 + 11

7x = -6

Dividing both sides by 7 gives us:

x = -6/7

Now that we have x, we can substitute it back into one of the equations to find y:

y = 8(-6/7) - 11

y = -48/7 - 11

Convert -11 to a fraction,

y = -48/7 - 77/7

y = -125/7

The solution to the system of equations is x = -6/7 and y = -125/7.

Answer:

The correct answer is last option 78.5%

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where r is the radius of circle

Area of square = a²

Where 'a' is the side length of square

To find the area of circle

Here r = 10 cinches

Area =  πr²

 =  3.14 * 10²

 = 3.14 * 100 = 314

To find the area of square

Here a = 20 inches

Area = a²

 = 20²

 = 400

To find the probability percentage

Probability = area of circle/Area of square

 = (314/400)*100

 78.5 %

Answer:

[tex]\sqrt{7^{2}+5^{2}  }[/tex]

Step-by-step explanation:

Since the whole base of the triangle is 14, we can half it to find the base of one triangle which is 7.

Pythagoras Theorem states a² + b² = c²

In this case a² = 7 and b² = 5 so,

a² + b² = c²

a² = 7 and b² = 5

7² + 5² = c²

49 + 25 = c²

74 = c²

√74 = c

Answer:

21

Step-by-step explanation:

To find the greatest common factor between a set of numbers, you can list the factors of those numbers and find the largest one they each have in common.

A factor of a number is a number which can be multiplied against another number to get your original number.

Factors of 21: 1, 3, 7, 21

Factors of 63: 1, 3, 7, 9, 21, 63

Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105

21 is the greatest factor which all three have in common.

Answer:

21

Step-by-step explanation:

GCF of 21, 63 and 105

Break these numbers into prime factors

21 = 3*7

63 = 9*7 = 3*3*7

105 = 15*7 = 3*5*7

There is a 3, 7 in  all the terms

The largest number of 3's in the terms is 1

The largest number of 7's is 1

Multiply the largest number of terms together

3*7 =21

[tex]20-20\cdot0.15=\boxed{17}[/tex]

Comic book cost is reduced from 20 dollars to 17 dollars.

Hope this helps.

r3t40

Answer:

A $20 comic book is reduced to $17

Step-by-step explanation:

Consider the provided information.

A bookstore is having a sale. All comic books are reduced 15%.

We need to Fill the blank to show a  correct representation of this sale.

A $20 comic book is reduced to?​

The cost of books are reduced to 15% that means now you need to pay only 85% of the price.

Therefore,

[tex]\frac{85}{100}\times 20=0.85\times20 =17[/tex]

Hence, A $20 comic book is reduced to $17

Answer:

Step-by-step explanation:

Put the coordinates of the points to the each inequality, and check the inequality:

A. (1, -5)

y < -3x + 3

-5 < - 3(1) + 3

-5 < -3 + 3

-5 < 0     CORRECT

y < x + 2

-5 < 1 + 3

-5 < 3      CORRECT

B. (1, 5)

y < -3x + 3

5 < -3(1) + 3

5 < -3 + 3

5 < 0     FALSE

C. (5, 1)

y < -3x + 3

1 < -3(5) + 3

1 < -15 + 3

1 < -12     FALSE

D. (-1, 5)

y < -3x + 3

5 < -3(-1) + 3

5 < 3 + 3

5 < 6      CORRECT

y < x + 2

5 < -1 + 2

5 < 1      FALSE

Answer:

h = 3+1.5x

Step-by-step explanation:

We start at a height of 3 inches

Then we growth at a rate if 1.5 inches per month, where x is the number of months

1.5x

Add them together

3+1.5x

The height is

h = 3+1.5x

Answer:

c on edge 2020

Step-by-step explanation:

i just did the assignment

The solution of the exponential function is option (C) [tex]x=\frac{ln3}{2}[/tex] is the correct answer.

The natural log is the logarithm to the base of the number e and is the inverse function of an exponential function. It is denoted by ln x.

For the given situation,

The function is 5e^2x - 4 = 11

⇒ [tex]5e^{2x} - 4 = 11[/tex]

⇒ [tex]5e^{2x} = 11+4[/tex]

⇒ [tex]5e^{2x} = 15[/tex]

⇒ [tex]e^{2x} = \frac{15}{5}[/tex]

⇒ [tex]e^{2x} = 3[/tex]

Taking ln on both sides,

⇒ [tex]ln e^{2x} = ln3[/tex]                       [∵ ln e = 1 ]

⇒ [tex]{2x} = ln3[/tex]

⇒ [tex]x=\frac{ln3}{2}[/tex]

Hence we can conclude that the solution of the exponential function is option (C) [tex]x=\frac{ln3}{2}[/tex] is the correct answer.

Learn more about natural log function here

https://brainly.com/question/27945885

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