Express each ratio as a fraction in lowest terms.
1) 3 goals in 6 attempts:
2) 5 quarters out of 15 coins:
Express each rate as a unit rate.
If the answer is in dollars and cents, it must begin with a dollar sign ($).
3) $197 for 4 theater tickets:
(Price per ticket in dollars and cents)
mph (Answer rounded to nearest tenth of a
4) 111.7 miles in 8.4 hours:
mile per hour.)​

Answer:

4(r+4)(r-4)

Step-by-step explanation:

If you factor it out, then it will be 4(r+4)(r-4). You can double check by multiplying it.

For this case we must factor the following expression:

[tex]4r ^ 2-64[/tex]

We take common factor 4:

[tex]4 (r ^ 2-16)[/tex]

We factor the expression within the parenthesis:

[tex]4 [(r-4) (r + 4)][/tex]

Finally we have that the factored expression is:

[tex]4 [(r-4) (r + 4)][/tex]

Answer:

[tex]4 [(r-4) (r + 4)][/tex]

Answer:

The value of f[ g(x) ] = 7x + 27

Step-by-step explanation:

It is given that, f( x ) = 7x + 13 and g( x ) = x + 2

To find the value of f(g(x))

g(x) = x + 2 and 7x + 13   (given)

Let g(x) = x + 2

f [ g(x) ] = 7(x + 2) + 13  [ substitute the value of g(x) in f(x) ]

 = 7x + 14 + 13

 = 7x + 27

Therefore the value of f[ g(x) ] = 7x + 27

Answer:

Total distance mouse traveled in 3 hours = [tex]\frac{3}{24}[/tex] of a mile

The mouse traveled the same distance in each hour. So in order to find the distance covered in 1 hour we have to divide the distance covered in 3 hours by 3. This will give us the distance that the mouse traveled in one hour.

So, the distance traveled in one hour will be = [tex]\frac{3}{24} \div 3 = \frac{3}{24} \times \frac{1}{3} =\frac{1}{24}[/tex] of a mile

The error which Matt made was that he divided only the denominator of the expression by 3, this probably was a calculation error.

Correct conclusion will be: Mouse travel 1/24 of a mile each hour

Answer:

Matt should have divided 3 by 3, not 24 by 3. (C.)

Step-by-step explanation:

since its a whole number you do not divide it at all.

Also:

Answer:

C. 52 cm

Step-by-step explanation:

A full circle has a degree measure of 360 degrees.

Minor arc DE is intercepted by a central angle of 120 degrees.

120 degrees is 1/3 of 360 degrees, so the length of minor arc DE is 1/3 of the circumference of the circle.

length of minor arc DE = (120/360) * 2 * pi * r

length of minor arc DE = (1/3) * 2 * 3.14 * 25 cm

length of minor arc DE = 52.3333... cm

Answer:

the correct answer is 52.

Step-by-step explanation:

I just got it correct.

C. x=2

To complete the table, let's plug in the x-values into [tex]f(x)[/tex] and [tex]g(x)[/tex], so:

For [tex]f(x)[/tex]:

[tex]If \ x=0: \\ \\ f(0)=9(0)+7=7 \\ \\ \\ If \ x=1: \\ \\ f(1)=9(1)+7=16 \\ \\ \\ If \ x=2: \\ \\ f(2)=9(2)+7=25[/tex]

For [tex]g(x)[/tex]:

[tex]If \ x=-2: \\ \\ g(-2)=5^{-2}=0.04 \\ \\ \\ If \ x=-1: \\ \\ g(-1)=5^{-1}=0.2 \\ \\ \\ If \ x=2: \\ \\ g(2)=5^{2}=25[/tex]

From this, the complete table is:

[tex]\left|\begin{array}{c|c|c}x & f(x)=9x+7 & g(x)=5^{x}\\-2 & -11 & 0.04\\-1 & -2 & 0.2\\0 & 7 & 1\\1 & 16 & 5\\2 & 25 & 25\end{array}\right|[/tex]

From the table, you can see that [tex]f(x)=g(x)=25[/tex] when [tex]x=2[/tex] so the correct option is C. x=2. But what does [tex]x=2[/tex] mean? It means that at this x-value, the graph of the linear function [tex]f(x)[/tex] and the graph of the exponential function [tex]g(x)[/tex] intersect and the point of intersection is [tex](2,25)[/tex]

Answer:

H

Step-by-step explanation:

Solve each equation for y.

First equation:

8x + 6 = 2y

2y = 8x + 6

y = 4x + 3

This line has y-intercept 3, and slope 4.

Second equation:

12x - 3 = 3y

3y = 12x - 3

y = 4x - 1

This line has y-intercept -1 and slope 4.

Since the two lines have the same slope and different y-intercepts, they are parallel lines.

Answer: H

Answer:

The correct answer is H.

Step-by-step explanation:

In order to solve this exercise we have two paths. The first one uses less calculation than the second.

First way of solution: Isolate the variable [tex]y[/tex] in the right hand side of each equation. To do this you only need to divide the first equation by 2, and then divide the second equation by 3. Thus, you will obtain [tex]4x+3=y[/tex] and [tex]4x-1=y[/tex].

Now, notice that both lines have the same slope, so they are parallel. But before to give a definite answer we need to check if both lines are the same or not. Evaluate at [tex]x=0[/tex], in the first equation you have [tex]y=3[/tex] and in the second one [tex]y=-1[/tex]. As they have different intercepts with the X-axis, they parallel.

Second way of solution: Solve the system of equations. Isolate [tex]y[/tex] in the first equation:

[tex]4x+3=y[/tex].

Then, substitute this expression in the second equation:

[tex]12x-3=3(4x+3)[/tex]

[tex]12x-3=12x +9[/tex].

Which is equivalent to [tex]0=9+3[/tex] and this is impossible. Hence, the system of equations has no solution and the lines are parallel.

Answer:

c. x = 6 only

Step-by-step explanation:

In order to calculate the zeros of f(x), we need to set it equal to zero and find the corresponding values of x.

[tex]x^{2}-12x+36=0[/tex]

Using the midterm breaking, we can split -12x into two such terms whose sum will be -12x and product will be 36x². These two terms are -6x and -6x

So, the above expression can be written as:

[tex]x^2-6x-6x+36=0\\\\ x(x-6)-6(x-6)=0\\\\ (x-6)(x-6)=0\\\\ (x-6)^{2}=0\\\\ x-6=0\\\\ x=6[/tex]

This means, the zero of f(x) occurs at x = 6 only.

Answer:

The correct answer option is A. $4,400.

Step-by-step explanation:

Cost of the tuition and fees for 1 year = $12,500

Grants and scholarships for 1 year = $6500

Cost of room and board for 1 year = $8200

Cost for work study for 1 year = $9800

So basically, Marcel pays = (tuition and fees + cost of room and board)

                                          = $12,500 + $8,200 = $20,700

He can pay through the (grants and scholarships + cost for work-study) =  $6,500 + $9,800 = $16,300

Therefore, Marcel needs to borrow = $20,700 - $16,300 = $4,400

Answer:

The answer is A

Step-by-step explanation:

Answer:

∠DFE=119°

Step-by-step explanation:

step 1

Find the measure of angle BFD

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

∠BFD=(1/2)[arc BD+arc CE]

substitute the given values

∠BFD=(1/2)[38°+84°]

∠BFD=61°

step 2

Find the measure of angle DFE

we know that

∠BFD+∠DFE=180° -----> linear pair (supplementary angles)

substitute

61°+∠DFE=180°

∠DFE=180°-61°=119°

Answer:

2 2/5

Step-by-step explanation:

5/6 x-4 = -2

Add 4 to each side

5/6 x-4+4 = -2+4

5/6 x = 2

Multiply by 6/5 to isolate x

6/5 *5/6 x = 6/5 *2

x = 12/5

Changing this from an improper fraction

5 goes into 12   2 times with 2 left over

x = 2  2/5

Step-by-step explanation:

Six less than five times a number is at least thirty- four

n - number

a)

5n - 6 ≥ 34           add 6 to both sides

5n ≥ 40           divide both sides by 5

n ≥ 8

b) in the attachment

c) n ∈ [8, ∞)

Answer:

t>2

Step-by-step explanation:

We are given:

3t+9>15.

Subtract 9 on both sides:

3t+9-9>15-9

Simplify:

3t+0>6

3t>6

Divide both sides by 3:

t>6/3

Simplify:

 t>2

Answer:

t > 2.

Step-by-step explanation:

3t + 9 > 15

3t + 9 - 9 > 15 - 9

3t  > 6

t > 2.

Answer:

Choice A.

Step.-by-step explanation:

y=√x

y=x² -1

Substituting the values in choice A:

1.2 = √1.5 = 1.2247     Approximately equal.

1.2 = (1.5)^2 - 1 = 1.25   Approximately equal.

Choice B.

-1.2 = √-1.5  which is imaginary so NOT this one.

Choice C

-1.2 = √1.5 = -1.2247

-1.2 = (1.5)^2 - 1 = 1.25  NO.

Choice D

We have the non real value √-1.5 again so NOT this one.

Answer: Option A

A.(1.5,1.2)

Step-by-step explanation:

We have the following system of equations

[tex]y=\sqrt{x}[/tex]

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

the solution of the system will be all points that satisfy both equations at the same time

For (1.5,1.2)

[tex]y=\sqrt{1.5}=1.2[/tex]

[tex]y=(1.5)^2 -1=1.2[/tex]

Both equations are satisfied

Note that we can discard options B and D because the domain of the equation [tex]y =\sqrt{x}[/tex] does not include the negative numbers.

We can discard option C because the range of the function [tex]y =\sqrt{x}[/tex] does not include the negative numbers.

Finally the answer is the option A

The answer of -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] is 0.06237948089

Step-by-step explanation:

To solve this problem -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] we must start with

1. Solve this bracket [9 (-8.9 + 9/5) .01] at first

2. Multiply the answer of the bracket by 66.9

3. Multiply -3(8/9) and divide the answer by the product of the previous

   step

In [9 (-8.9 + 9/5) .01]

∵ (-8.9 + 9/5) = (-8.9 + 1.8) = -7.1

∴ [9 (-8.9 + 9/5) .01] = [9 (-7.1).01]

∵ 9(-7.1)(.01) = -0.639

∴ [9 (-8.9 + 9/5) .01] = -0.639

∵ 66.9 [-0.639] = -42.7491

∵ [tex]-3(\frac{8}{9})=\frac{-8}{3}[/tex]

∴ -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] = [tex]\frac{-8}{3}[/tex] ÷ -42.7491

∴ -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] = 0.06237948089

The answer of -3(8/9) ÷ 66.9[9 (-8.9 + 9/5) .01] is 0.06237948089

Learn more:

You can learn more about decimals in brainly.com/question/1774450

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Answer:

-1 edge

Step-by-step explanation:

...

1st-1

2nd –i

I just did it on edge :D

Answer:

So we have (-1,3), (-2,2) and (-5,-1).

Step-by-step explanation:

So we need to find the equation of the line that is parallel to the blue line going through point P.

The slope of the blue line (count the rise/run) is 1/1=1.

Parallel lines have the same slope.  

So y=mx+b is the slope-intercept form where m is the slope and b is the y-intercept.

So since the blue line has slope 1 and parallel lines have the same slope then the line going through point P will have slope 1 too.

Point P is actually the y-intercept of the line going through P.

So the equation that is parallel to the blue line going through point P is y=1x+4. b was 4 because it was the y-intercept.

You can also just write y=1x+4 as y=x+4.

Testing the points:

(-4,2)?

Does y=x+4 for this point?  2=-4+4 which gives us 2=0 so no for this point.

(-1,3)?

Does y=x+4 for this point?  3=-1+4 which gives us 3=3 so yes for this point.

(-2,2)?

Does y=x+4 for this point?  2=-2+4 which gives us 2=2 so yes for this point.

(4,2)?

Does y=x+4 for this point?  2=4+4 which gives us 2=8 so no for this point.

(-5,-1)?

Does y=x+4 for this point?  -1=-5+4 which gives -1=-1 so yes for this point.

So we have (-1,3), (-2,2) and (-5,-1).

Answer:BCE

Step-by-step explanation:I jus did it on EDGE

Answer:

I believe it's A, because all triangles have 3 vertices.

Step-by-step explanation:

Answer:

Figure A

Step-by-step explanation:

We are given that a  statement

''If is is an triangle , then it has three vertices.

We have to find that which diagram represents the given statement

From first diagram

If triangle then it have three vertices because intersection of triangle and three vertices is triangle.

From second diagram

Intersection region of three vertices and triangle is three vertices.

So, from second diagram we cannot say if a triangle then it has three vertices.

Hence, figure A represent the given statement.

Answer:

you would divide the two numbers. 2 divided by 11 is 0.18

Answer:

0.181818182 or rounded is 0.18

Step-by-step explanation:

to turn any fraction into a decimal you always do numerator divided by denominator

Answer:

D)150 ≤ w ≤ 500

Step-by-step explanation:

Let  be the number of word in Kylie's essay.

We know that the essay has to have a minimum word count of 150, so the length of the essay must be greater or equal than 150 words; remember that in mathematics we say greater or equal with the sign: ≥, so we can express the statement as:

Which is equivalent to

We also know that the essay has to have a maximum word count of 500 words, so the length of the essay must be lest or equal than 500 words; remember that we can say the same using the symbol ≤, so we can express the statement as:

Now, we can join our tow inequalities in a compounded one:

The length w of an essay is typically represented by a compound inequality of form a < w < b, where a and b represent the range of acceptable lengths. Without specific details, we can't provide a more precise inequality.

From the question, it seems that the length w of the essay might be compared to a word count that is too short or too long. This could translate into an inequality such as a < w < b, where a and b represent the acceptable range of the essay length in words. Unfortunately, without specific values for 'too short' and 'too long', we cannot give a more precise answer. However, the type of compound inequality we are talking about is known as a 'conjunction' or 'and' inequality, represented by a < w < b or a ≤ w ≤ b if including the exact lower and upper bounds.

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Answer:

1/5

Step-by-step explanation:

There are 30 contestants.  16 are men, which means 14 are women.

All 14 women wear glasses.  Since 20 of the contestants wear glasses, that means there are 6 men who wear glasses.

So the probability that a randomly selected contestant will be a male with glasses is 6/30 or 1/5.

Answer:

3 and 4: B

Step-by-step explanation:

As per the property of traversal lines, when two parallel lines are cut by traversal then the corresponding angles formed are equal.

In given case ∠6 is corresponding angle of ∠8 and ∠8 is corresponding to ∠18.

Hence option B is correct for 3 and statements!

If lines are ||, corresponding angles are equal.

Answer:

If lines are ||, corresponding angles are equal.

Step-by-step explanation:

yep

No Solution

Brainliest Please :)

Answer:

6

Step-by-step explanation:

9^3 ÷2 the inverse is 9÷3×2 =9÷3=3×2=6 the answer is 6

2 x 10^(10 - 2)

2 x 10^(8)

2 x 100,000,000

200, 000, 000

Answer:

[tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form

[tex]f(x)=\dfrac{1}{3}x-\dfrac{1}{3}[/tex] - function notation

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points (-2, -1) and (1, 0).

Substitute:

[tex]m=\dfrac{0-(-1)}{1-(-2)}=\dfrac{1}{3}[/tex]

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

[tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form

[tex]y+1=\dfrac{1}{3}(x+2)[/tex]          use the distributive property

[tex]y+1=\dfrac{1}{3}x+\dfrac{2}{3}[/tex]           subtract 1 = 3/3 from both sides

[tex]y=\dfrac{1}{3}x-\dfrac{1}{3}[/tex]

Answer:

Point slope form : [tex]y-0=\frac{1}{3}(x-1)[/tex]

Function notation : [tex]f(x)=\frac{1}{3}(x-1)[/tex]

Step-by-step explanation:

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the point slope form of line is

[tex]y-y_1=m(x-x_1)[/tex]

Where, m is slope.

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

From the given graph it is clear that he line passes through the points (-2,-1) and (1,0). Slope of the line is

[tex]m=\frac{0-(-1)}{1-(-2)}=\frac{1}{3}[/tex]

The point is (1,0) and slope is 1/3. So, the point slope form of the line is

[tex]y-0=\frac{1}{3}(x-1)[/tex]

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

Therefore the point slope form is [tex]y-0=\frac{1}{3}(x-1)[/tex].

Replace y by f(x) to write the equation in function notation.

[tex]f(x)=\frac{1}{3}(x-1)[/tex]

Therefore the function notation is [tex]f(x)=\frac{1}{3}(x-1)[/tex].

Answer:

B

Step-by-step explanation:

The function is

[tex]y=\sqrt{x-4}[/tex]

use the graph tool to visualize the graph as below

Answer:

B

Step-by-step explanation:

The given equation is :

[tex]y=\sqrt {x-4}[/tex]

This is a equation of a half parabola because general equation of a parabola with its as x-axis is:

[tex]y^2={x-a}[/tex]

Where a is the vertex of the parabola. If square root is taken, then there will be one positive and one negative. So,

The positive represents the upper side of the parabola.

Hence,  [tex]y=\sqrt {x-4}[/tex] represents upper parabola with x -axis is its axis and vertex at (4,0). Option B is correct.

Answer:

My blue dot is the y-intercept.

My red dot is my x-intercept.

Please look at the graph.

Step-by-step explanation:

I can show you my graph and mark it where the x-intercepts and y-intercepts are.

Let's begin.

We have y=2/3 x+4.

Compare this to the slope-intercept form, y=mx+b where m is the slope and b is the y-intercept.

You should see that m=2/3 and b=4.

This means the slope is 2/3 and the y-intercept is 4.

Don't forget slope means rise/run.

So once we graph 4 (plot a point) on the y-axis, then we will use our slope to get to one more point.  The slope here tells us to rise 2 and run 3.

Now sometimes our graph is not accurate when drawing by hand so there is a way without graphing that you can find the x- and y-intercepts.

The x-intercept is when the y-coordinate is 0.

The y-intercept is when the x-coordinate is 0.

So to find the x-intercept, I'm going to set y to 0 and solve for x. Like so,

0=2/3 x +4

Subtract 4 on both sides:

-4=2/3 x

Multiply both sides by the reciprocal of 2/3 which is 3/2:

3/2 (-4)=x

Simplify:

-12/2=x

Simplify:

-6=x

Symmetric Property:

x=-6

So the x-intercept is (-6,0).

I actually already have the y-intercept since my equation is in y=mx+b (slope-intercept form).  But if it wasn't you could just set x to 0 and solve for y. Like so:

y=2/3 (0)+4

y=0+4

y=4

The y-intercept is (0,4).

Let's go to our graph now.

Answer:

After I had submitted my answer it gave me this answer

Step-by-step explanation:

Answer:

f(x) = x

Step-by-step explanation:

f(x) = x is of the form y = mx + b.

y = mx + b is the slope-intercept form of the equation of a line, so its graph is a line.

f(x) = x^2 has a variable to the second power, so its graph is a parabola, and not a line.

f(x) = |x| has an absolute value, so its graph is shaped like a V. It is not a line.

Answer:

20% markup

Step-by-step explanation:

10,000 x 1.20 = 12,000

Answer:

20%

Step-by-step explanation:

10,000×120%=12,000

Answer:

5h -2

Step-by-step explanation:

(6h + 1) - (h+3)

= 6h + 1 - h -3

= 5h -2

6h +1 - h+3

Subtract like terms:

6h - h = 5h

1-3 = -2

The answer becomes 5h-2

Answer:

A. 111.65

Step-by-step explanation:

This scenario can be interpreted like a triangle ABC where A and B are islands and C is the point from where the captain is 160 miles from island B.

a = 160

b = 260

c = 250

Law of cosines

[tex]c^2 = a^2 + b^2 - 2(ab)Cos(C)\\Arranging\ as\\2ab \ cos\ C = a^2+b^2-c^2\\2(160)(260)\ cos\ C = (160)^2+(260)^2- (250)^2\\83200\ cos\ C=25600+67600-62500\\83200\ cos\ C=30700\\cos\ C= \frac{30700}{83200}\\cos\ C=0.36899\\C = arccos\ (0.36899)\\C = 68.35[/tex]

The internal angle is 68.35°

We have to find the external angle to find the bearing the captain should turn

Using the rule of supplimentary angles:

The external angle = 180 - 68.35 = 111.65°

Therefore, the captain should turn 111.65° so that he would be heading straight towards island B.

Hence, option 1 is correct ..

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

AB = 250 feet

AC = 260 feet

BC = 160 feet

We need to find the angle C that is heading straight towards island B.

We will apply "Law of cosine":

[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}\\\\\cos C=\dfrac{160^2+260^2-250^2}{2\times 160\times 260}\\\\\cos C=0.368\\\\C=\cos^{-1}(0.368)\\\\C=68.40^\circ[/tex]

Exterior angle would be

[tex]180-68.40=111.65^\circ[/tex]

Hence, Option 'a' is correct.