Is the following relation a function?

Answer:

[tex]\frac{1}{25}[/tex]

Step-by-step explanation:

using the rule of exponents

• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex], then

[tex]5^{-2}[/tex] = [tex]\frac{1}{5^{2} }[/tex] = [tex]\frac{1}{25}[/tex]

[tex]3x-\dfrac{1}{5}(10x+5)=6\qquad\text{use distributive property}\\\\3x-\left(\dfrac{1}{5}\right)(10x)-\left(\dfrac{1}{5}\right)(5)=6\\\\3x-2x-1=6\qquad\text{add 1 to both sides}\\\\\boxed{x=7}[/tex]

Answer:

$887,761.38

Step-by-step explanation:

The principal amount the home is valued is $375,000 and it increases at a rate of 9% a year which is 0.09 and the amount of time it grew is 10 years. Therefore:

[tex]A_{final}=375000(1+0.09)^{10}=375000(1.09)^{10}=887761.38[/tex]

After 10 years the house is worth $887,761.38 if this trend continues

Answer:

$887,761.38

i know this i s the answer because i had a quiz.

PLz mark brainlest

Answer:

31. Yes (Y)

WXYZ ~ DABC

S.F.=4

32. Yes (Y)

GHIJ ~ KLMN

S.F.=2/3

33. Missing length: 16

34. Missing length: 30

35. x=7

36. x=10

Step-by-step explanation:

31. The polygons are similar if:

WX/DA=XY/AB

Then:

WX/DA=24/6→WX/DA=4

XY/AB=16/4→XY/AB=4

Like WX/DA=4=XY/AB, the polygons WXYZ and DABC are similar

Scale Factor: S.F.=XY/DA=XY/AB→S.F.=4

32. The polygons are similar if:

GH/KL=HI/LM=IJ/MN=GJ/KN

Then:

GH/KL=6/9=(6/3)/(9/3)→GH/KL=2/3

HI/LM=4/6=(4/2)/(6/2)→HI/LM=2/3

IJ/MN=4/6=(4/2)/(6/2)→IJ/MN=2/3

GJ/KN=4/6=(4/2)/(6/2)→GJ/KN=2/3

Like GH/KL=HI/LM=IJ/MN=GJ/KN=4, the polygons GHIJ and KLMN are similar

Scale Factor: S.F.=GH/KL=HI/LM=IJ/MN=GJ/KN→S.F.=2/3

33. If the polygons are similar, their sides must be proportional, then:

x/24=10/15

Simplifying the fraction on the right sides of the equation, dividing the numerator ans denominator by 5:

x/24=(10/5)/(15/5)

Dividing:

x/24=2/3

Solving for x: Multiplying both sides of the equation by 24:

24(x/24)=24(2/3)

Multiplying:

x=8(2)

x=16

34. If the polygons are similar, their sides must be proportional, then:

54/63=(54/9)/(63/9)→54/63=6/7

48/56=(48/8)/(56/8)→48/56=6/7

x/35=6/7

Solving for x: Multiplying both sides of the equation by 35:

35(x/35)=35(6/7)

Multiplying:

x=5(6)

x=30

36. (8x-2)/63=42/49

Simplifying the fraction on the right sides of the equation, dividing the numerator ans denominator by 7:

(8x-2)/63=(42/7)/(49/7)

Dividing:

(8x-2)/63=6/7

Solving for x: Multiplying both sides of the equation by 63:

63(8x-2)63=63(6/7)

Multiplying:

8x-2=9(6)

8x-2=54

Adding 2 both sides of the equation:

8x-2+2=54+2

Adding:

8x=56

Dividing both sides of the equation by 8:

8x/8=56/8

Dividing:

x=7

37. (6x-6)/63=42/49=30/35

Simplifying the fractions

(6x-6)/63=(42/7)/(49/7)=(30/5)/(35/5)

Dividing:

(6x-6)/63=6/7

Solving for x: Multiplying both sides of the equation by 63:

63(6x-6)63=63(6/7)

Multiplying:

6x-6=9(6)

6x-6=54

Adding 6 both sides of the equation:

6x-6+6=54+6

Adding:

6x=60

Dividing both sides of the equation by 6:

6x/6=60/6

Dividing:

x=10

The formula of a slope:

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

We have the points (-4, 2) and (-2, 2). Substitute:

[tex]m=\dfrac{2-2}{-2-(-4)}=\dfrac{0}{-2+4}=0[/tex]

Answer:

The coordinates of orthocenter of the triangle are (1,5).

Step-by-step explanation:

The given vertices are A(0,6), B(4,6) and C(1,3).

Orthocenter of a triangle is the intersection point of all altitudes.

The product of slopes of two perpendicular lines is -1.

The slope of AB is

[tex]m_{AB}=\frac{y_2-y_1}{x_2-x_1}=\frac{6-6}{4-0}=0[/tex]

The slope of AB is 0, therefore slope of line which is perpendicular to AB is [tex]\frac{-1}{0}[/tex].

Point slope form of a line is

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

Where, m is the slope.

The equation of altitude on AB form C is

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

[tex]0=x-1[/tex]

[tex]x=1[/tex]                              ..... (1)

Slope of BC is

[tex]m_{BC}=\frac{y_2-y_1}{x_2-x_1}=\frac{6-3}{1-4}=1[/tex]

The slope of BC is 1 therefore the slope of altitude on BC from A is -1.

The equation of altitude on BC from A is

[tex]y-6=-1(x-0)[/tex]

[tex]y=-x+6[/tex]                         ..... (2)

Using (1) and (2) we get

[tex]x=1, y=5[/tex]

The  intersection point of two altitudes is (1,5). Therefore coordinates of orthocenter of the triangle are (1,5).

Answer:

Correct choice is D

Step-by-step explanation:

Plot points (12, 16), (13, 18), (13, 10), (14, 16), (15, 9), (15, 8), (16, 17), (17, 23) on the coordinate plane. On this coordinate plane x represents age in years and y represents texting speed in words per minute.

Option A is false. Consider points A(12,16) and C(13,10). For these points x-coordinates increases, but y-coordinates decreases. Therefore, as age increases, texting speed doesn't increase.

Option B is false. Consider points A(12,16) and B(13,18). For these points both x-coordinates and y-coordinates increases. Therefore, as age increases, texting speed increases too.

Option C is false. Consider points C(13,10) and F(15,8). For these points y-coordinates decreases, but x-coordinates increases. Therefore, as texting speed decreases, age increases.

Option D is true, there is no clear relationship between age and texting speed.

Answer:

The Answer is D. No, there is no clear relationship between age and texting speed.

Step-by-step explanation:

Answer: the equation is slope-intercept form y = -2/3x

Answer:

yes

Step-by-step explanation:

one way to help is to just do 1x5=5 and add on the two zeros  to get 500

Answer:

True

Step-by-step explanation:

10 * 5 = 50

If we ad a zero to one of the numbers, we add a zero to the answer

100 * 5 = 500

10 * 50 = 500

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=\stackrel{doubled}{2r}\\ h=\stackrel{\textit{divided by 3}}{\frac{h}{3}} \end{cases}\implies V=\cfrac{\pi (2r)^2\left( \frac{h}{3} \right)}{3} \\\\\\ V=\cfrac{\pi (2^2r^2)\left( \frac{h}{3} \right)}{3}\implies V=\cfrac{~~\frac{4\pi r^2 h}{3}~~}{3}\implies V=\cfrac{4\pi r^2 h}{3\cdot 3}\implies \stackrel{\frac{4}{3}\textit{ of the original}}{V=\cfrac{4}{3}\cdot \cfrac{\pi r^2 h}{3}}[/tex]

Final answer:

When the radius is doubled and the height is divided by 3 in the volume formula for a cone, the new volume is 4/3 of the original volume.

Explanation:

The student has provided the formula 1/3 π r^2 • h, which represents the volume of a cone.

To find the ratio of the new volume to the original volume after the radius (r) is doubled and the height (h) is divided by 3, we must substitute these changes into the formula and simplify.

Original volume formula is V = 1/3 π r^2 • h.

If the radius is doubled (2r) and the height is divided by 3 (h/3), the new volume formula becomes

V' = 1/3 π (2r)^2 • (h/3).

After simplification, the new volume becomes V' = 1/3 π 4r^2 • h/3, which further simplifies to V' = 4/9 π r^2 • h.

Therefore, the ratio of the new volume V' to the original volume V is 4/3.

Answer:

120 dollars

Step-by-step explanation:

6 hours per day, for 2 days, leads to a total of 12 hours (2*6 = 12)

If it takes 2 gallons of gas to run the boat for 1 hour, then it will take 24 gallons to run for 12 hours. We can see this if we have the ratio below

2 gallons: 1 hour

12*(2 gallons): 12*(1 hour) .... multiply both sides by 12

24 gallons: 12 hours

Now multiply this gallon count (24) by the cost per gallon ($5) and we get to 5*24 = 120

Answer:5%

Step-by-step explanation:

Given, cost of two table lamps including tax = $42

Therefore, cost of one table lamp including tax =[tex]\frac{42}{2}[/tex]=21$

Given, cost of one table lamp before tax = $20

Hence tax amount on each lamp = $21 - $20 = $1

Hence tax rate payed[tex]=\frac{\text {tax amount}}{\text {Sale Price}}\times 100[/tex]

[tex]=\frac{1}{20}\times {100}=5\%[/tex]

Answer:

a. 9.34 billions of pounds.

b. 14.37 billions of pounds.

Step-by-step explanation:

We have been given that cheese production in a country is currently growing at a rate of 4% per year. the equation [tex]y=8.3*(1.04)^{x}[/tex] models the cheese production in the country from 2003 to 2009. In this equation l, y is the amount of cheese produced in billions of pounds and x represents the number of years after 2003.

a. To find the total cheese production in the country in 2006 we will substitute x= 3 in our given equation as 2006-2003=3.

[tex]y=8.3*(1.04)^{3}[/tex]

[tex]y=8.3*1.124864[/tex]  

[tex]y=9.3363712[/tex]

Therefore, the cheese production in year 2006 will be 9.34 billions of pounds.

b. To find the total cheese production in the country in 2017 we will substitute x= 14 in our given equation as 2017-2003=14.

[tex]y=8.3*(1.04)^{14}[/tex]

[tex]y=8.3*1.7316764476028035[/tex]

[tex]y=14.37291451510326905[/tex]

Therefore, the cheese production in year 2017 will be 14.37 billions of pounds.

Answer:

Given the equation: [tex]y = 8.3(1.04)^x[/tex]        ......[1]

where

y is the amount of cheese produced in billions of pounds and

x represents the number of years after 2003

Since, this equation models the cheese production in the country from 2003 to 2009.

(a)

we have to find the total cheese production in the country in 2006.

Substitute x = 3 years(i.e, 2003 -2006) in [1] to solve for y;

[tex]y = 8.3(1.04)^{3}[/tex]

Simplify:

y = $9.3363712

Therefore, the total cheese production in the country in 2006 is, $9.34.

(b)

we use  the equation to predict the total amount of cheese produced in the country in 2017.

We have x = 14 years.

Substitute in [1] we get;

[tex]y = 8.3(1.04)^{14}[/tex]

Simplify:

y = $14.3729145151

Therefore, the estimate total amount of cheese produced in the country in 2017 is, $14.37

Answer:

Step-by-step explanation:

Make circles. 4 circles. Then divide the beads to your circles. The one's you have leftover is your remainder. Hope that helps.

Answer:

Assume that the cost of the milk is x.

We are given that a sandwich costs 0.75$ more than the cost of milk. This means that:

cost of sandwich = cost of milk + 0.75

cost of sandwich = x + 0.75

Now, the customer bought 4 sandwiches and 4 containers of milk at the cost of 7$.

We will transform this into an equation as follows:

total cost = cost of 4 sandwiches + cost of 4 containers of milk

7 = 4(x+0.75) + 4(x)

Solve the above equation to get x as follows:

7 = 4x + 3 + 4x

7-3 = 8x

8x = 4

x = 0.5

Therefore:

cost of milk = x = $0.5

cost of sandwich = x+0.75 = 0.5+0.75 = $1.25

Answer:

$1.25

Step-by-step explanation:

Answer:

Corresponding Parts of Congruent Figures. The word corresponding refers to parts that match between two congruent triangles. You can identify corresponding angles and corresponding sides. First, name the corresponding angles.

Step-by-step explanation:

In geometry, two figures are congruent if they have the same size and shape. To verify congruence, all corresponding sides and angles of two figures must match in size and measure. For instance, given two triangles ABC and DEF, they would be congruent if their corresponding sides and angles were equal.

In geometric terms, two figures are congruent if they have the same size and shape. This means all corresponding sides and angles of the two figures are equal. In order to determine if two shapes are congruent, you need to match each part of one shape with a corresponding part on the other and see if they are of the same size and angle.

For instance, if you have two triangles ABC and DEF, these triangles would be congruent (often written as △ABC≅△DEF) if the sides AB=DE, BC=EF, and AC=DF and angles ∠A=∠D, ∠B=∠E and ∠C=∠F. This is the principle of corresponding parts of congruent figures being congruent.

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Answer:

Step-by-step explanation: If you are trying to figure out how many gallons the whole family uses, the answer is 99 gallons.The reason is is because it says 2.2 gallons a minute and it takes 9 minutes for a shower. So you multiply 9 by 2.2 which would give you 19.8. Then you multiply it by 5 isnce it says 5 people take a shower.

Answer:

99 gallons

Step-by-step explanation:

Let as assume we need to find how many gallons of water does the family use for showering every morning.

It is given that every minute 2.2 gallons of water flows from a shower.

Total number of family members = 5

Average time of shower = 9 minutes per person every morning.

Total time of shower = [tex]9\times 5=45[/tex] minutes

1 minute = 2.2 gallons

45 minute = 2.2 × 45  gallons

45 minute = 99 gallons

Therefore, in every morning 99 gallons of water was used by the family

Answer:

$6.15 an hour

Step-by-step explanation:

To find how much money our raise is, we can multiply the percent times our salary

6 * .025 = .15

Our raise is 15 cents an hour

Take what we were making plus our raise

6+.15

$6.15

This is what we will be making per hour.

Answer:

How much is 44 out of 100 written as a percentage? Convert fraction (ratio) 44 / 100 Answer: 44%

Step-by-step explanation:

44% of the total free throws are made.

We have a basketball player made 44 out of 100 attempted free throws.

Assume the percent of free throws be [x]%. We can write -

[x] = (44/100) x 100

[x] = 44%

Therefore, 44% of the total free throws are made.

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Answer:

x=0.996

Step-by-step explanation:

[tex]3e^{2x} +5=27[/tex]

To take natural log ln , we need to get e^2x alone

Subtract 5 on both sides

[tex]3e^{2x}=22[/tex]

Now we divide both sides by 3

[tex]e^{2x}=\frac{22}{3}[/tex]

Now we take 'ln' on both sides

[tex]ln(e^{2x})=ln(\frac{22}{3})[/tex]

As per log property we can move exponent 2x before ln

[tex](2x)ln(e)=ln(\frac{22}{3})[/tex]

The value of ln(e) = 1

[tex]2x=ln(\frac{22}{3})[/tex]

Divide both sides by 2

[tex]x=\frac{ln(\frac{22}{3})}{2}[/tex]

x= 0.996215082

Round to nearest thousandth

x=0.996

Hello There,

The answer is:

10 movies

Hope this helps have a great day :)

Answer:↓

98+36864

Step-by-step explanation:

Answer:

y = 1/3 x +1

Step-by-step explanation:

y-5=1/3(x-12)

Distribute the 1/3

y-5 = 1/3x -1/3 *12

y-5 = 1/3 x -4

Add 5 to each side

y-5+5 = 1/3 x-4+5

y = 1/3 x +1

Answer:

x≠-12; x≠0

Step-by-step explanation:

A fraction denominator cannot be 0.

3x(x+12)≠0

if you multiply a number by zero, the product is also zero

3x≠0

x≠0

x+12≠0

x≠-12

Answer:

Step-by-step explanation:

We are given value of sine trigonometric ratio = 0.9123.

We need to find the angle in degrees whose measure has a sine of 0.9123.

So, we need to find the value of [tex]sin^{-1}(0.9123)[/tex].

On plugging [tex]sin^{-1}(0.9123)[/tex] in calculator, we get

65.82°.

Now, we need to round it to the nearest whole degree.

Therefore, 65.82°≈ 66°.

Answer:

Step-by-step explanation: Arrange your numbers in numerical order.

Count how many numbers you have.

If you have an odd number, divide by 2 and round up to get the position of the median number.

If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

Final answer:

The formula for finding the median depends on whether the total number of data values is odd or even. If it is odd, the median is the middle value when the data is ordered from least to greatest. If it is even, the median is the average of the two middle values when the data is ordered.

Explanation:

The formula for finding the median depends on whether the total number of data values is odd or even. If it is odd, the median is the middle value when the data is ordered from least to greatest. If it is even, the median is the average of the two middle values when the data is ordered. For example, if you have the data set 2, 4, 6, 8, 10, the median would be 6 because it is the middle value. But if you have the data set 2, 4, 6, 8, the median would be (4+6)/2 = 5 because it is the average of the two middle values.

Answer:23

Step-by-step explanation:

92/4

Answer:

Jack is 6 and Mom is 30

Step-by-step explanation:

J = Jacks age

M = Mom's age

5J = M

In 6 years, so add 6 to the age

3(J+6) = (M+6)

We have a system of 2 equations and 2 unknowns

Lets simplify the 2nd equation

3(J+6) = (M+6)

3J + 18 = M+6

Substituting M =5J

3J + 18 = 5J +6

Subtract 3J from each side

3J-3J + 18 = 5J-3J +6

18 = 2J+6

Subtract 6 from each side

18-6 = 2J+6-6

12 = 2J

Divide each side by 2

12/2 = 2J/2

6=J

Jack is 6

We still need to find Mom's age

M = 5J

     = 5*6

    =30

Mom is 30

Answer:

11/16

Step-by-step explanation:

Answer:

Decimal: 0.6875 Fraction: 2.75/4

Step-by-step explanation:

To convert percent into a decimal you move the decimal point two places to the left. So 68.75% is equal to 0.6875.

To find the fraction form we know that 68.75% is 68.75/100 because percent is of one hundred. We can simply 68.75/100 by dividing the numerator and denominator by 25 and we get 2.75/4.  So 68.75% as a fraction is 2.75/4.