what are two ways of determining the distance between two points

Answer:

66

Step-by-step explanation:

since BD and BC are congruent, angle C and angle D are equal. this means 6x-9=3x+24. If you solve this equation you get x=11. If you plug it into either 6x-9 or 3x+24 you get 57. 180-(57+57)=66

Answer:

D

Step-by-step explanation:

f(x) = x^2+1 at x=-1, f(-1)=1+1=2

Answer:

She has 12 quarters.

Step-by-step explanation:

You have two unknowns, the number of quarters and the number of dimes. You need one equation per unknown, so you need two equations. One equation deals with the number of coins. The other equation deals with the values of the coins.

The first step is to choose variables. We can go with x and y, but I prefer to choose q and d, so I remember more easily what they represent.

Let q = number of quarters.

Let d = number of dimes.

Let's deal with the numbers of coins first.

"Georgina has 14 more dimes than quarters"

She has q number of quarters, but the number of dimes is 14 more than the number of quarters. d is 14 more than q. Our first equation is

d = q + 14

Now we deal with the values of the coins.

We don't know yet the actual numbers of dimes and quarters, so we use d and q to represent those numbers.

One dime is worth $0.10; d number of dimes is worth 0.1d.

A quarter is worth $0.25; q number of quarters is worth 0.25q.

The total value of the dimes and quarters is the sum of the values of the two sets of coins:

0.1d + 0.25q

We are told "Georgina has $5.60 in quarters and dimes."

This gives us our second equation.

0.1d + 0.25q = 5.6

Now we have a set of two equations in two variables:

d = q + 14

0.1d + 0.25q = 5.6

There are several methods for solving a system of equations. Since the first equation is already solved for a variable, d, we can use the substitution method.

We rewrite the second equation, but we substitute q + 14 for d in the second equation.

Second equation:

0.1d + 0.25q = 5.6

Substitute q + 14 for d:

0.1(q + 14) + 0.25q = 5.6

Distribute on the left side:

0.1q + 1.4 + 0.25q = 5.6

Combine like terms on the left side:

0.35q + 1.4 = 5.6

Subtract 1.4 from both sides:

0.35q = 4.2

Divide both sides by 0.35:

q = 12

There are 12 quarters.

(You are asked only the number of quarters, so you can stop here. I will continue to find also the number of dimes for 2 reasons. 1) You see how it's done, so it will help with other problems. 2) By finding the numbers of dimes and quarters, then we can check if our solution is correct, which I will do below at the end.)

Now we use the first equation, d = q + 14. We substitute 12 for q and solve for d.

d = q + 14

d = 12 + 14

d = 26

There are 26 dimes.

Check:

We check the numbers of coins:

26 - 12 = 14 The number of dimes is indeed 14 more than the number of quarters.

We check the values of the coins:

0.1(26) + 0.25(12) = 2.6 + 3 = 5.6 The value of the coins is indeed $5.60.

Our answer is correct.

Answer: Actual distance = 37.5 miles

Step-by-step explanation:

Let x be the actual distance

Given information

Length on map = 7.5 inches

Scale = 1 inch : 5 miles

Set up proportion

[tex]\frac{7.5}{x} =\frac{1}{5}[/tex]

Cross multiply to convert out of fraction form

[tex]7.5*5=1*x[/tex]

[tex]\boxed{x=37.5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

It depends a lot on where you live. But I would assume the answer is apples. I hope this helps you out and have a nice day! :)

Answer:

4.10526315789

Step-by-step explanation:

Answer: 4.10526315789

Step-by-step explanation:

Answer:

C; B

Step-by-step explanation:

The direct/explicit formula for a geometric sequence is the following:

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

Where aₙ represents the term n, a represents the initial value, and r represents the common ratio.

Therefore, to find the nth term, we just need to find the initial value and the common ratio.

1)

-8, 24, -72, 216...

The common ratio is the ratio between each consecutive term. Do two to confirm that they are indeed the same. Thus:

[tex]r=24/-8=-3\\r=-72/24\stackrel{\checkmark}{=}-3[/tex]

So, the common ratio is -3. And the initial value is -8. Thus, putting them into our equation:

[tex]a_n=-8(-3)^{n-1}[/tex]

Thus, the eighth term will be:

[tex]a_8=-8(-3)^{8-1}\\a_8=-8(-3)^7\\a_8=17496[/tex]

C

2)

Again, find the common ratio.

2, -14, 98, -686...

[tex]-14/2=-7\\98/-14\stackrel{\checkmark}{=}-7[/tex]

The common ratio is -7. The initial value is 2. Thus:

[tex]a_n=2(-7)^{n-1}[/tex]

And the sixth term will be:

[tex]a_6=2(-7)^{6-1}\\a_6=2(-7)^5\\a_6=-33614[/tex]

B

Answer:  48

There are many approaches to estimating stuff like this, so there isn't one set answer. My approach is shown below.

========================================================

1 min = 60 sec

30 min = 1800 sec (multiply both sides by 30)

1/2 hr = 1800 sec (replace "30 min" with "1/2 hr")

The value 2014 is fairly close to 1800, so roughly every half hour we have a prize being won. This is an overestimate.

There are 24 hours in a day, so 24*2 = 48 half-hour periods in a day, meaning we have an estimated 48 prizes in a full day. This is an overestimate as well.

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

Extra info:

If you're curious about finding the more accurate value, then you could follow these steps

1 prize = 2014 seconds

x prizes = 86400 seconds (number of seconds in a full day)

1/x = 2014/86400

1*86400 = x*2014

86400 = 2014x

2014x = 86400

x = 86400/2014

x = 42.8997020854021

Round down to get x = 43. We round down because there isn't enough time to get that 44th prize. The value 43 is fairly close to 48, and we can see our earlier estimate of 48 was an overestimate.

Answer:

3/2

Step-by-step explanation:

if u divide two fractions, it is same as multiplying with its reciprocal

Answer:

7.7 ft

Step-by-step explanation:

The third longest side is also the second shortest side.

The 14 ft side of quadrilateral ABCD corresponds to the 6 ft side of quadrilateral EFGH.

14/6 = 18/x

7/3 = 18/x

7x = 18 * 3

7x = 54

x = 54/7

x = 7.7

Answer: D. 7.7 feet

Answer:

Step-by-step explanation:

7.7

Answer:

True

Step-by-step explanation:

We know that distance = rate * time

21 miles = 7 miles per hours * 3 hours

21 miles = 21 miles

True

Answer:

[tex]\frac{1}{9^4}[/tex].

Step-by-step explanation:

[tex]9^{-4}[/tex]

= [tex]\frac{1}{9^4}[/tex]

= [tex]\frac{1}{9 * 9 * 9 * 9}[/tex]

= [tex]\frac{1}{81 * 81}[/tex]

= [tex]\frac{1}{6561}[/tex]

= 0.0001524157903.

Hope this helps!

Answer:

Is there supposed to be some "dots" or something

Answer:

24 and 48

Today, the son is 24 years old, and the father is 48 years old.  

Step-by-step explanation:

(x - 10) + (2x - 10) = 52

3x + 20 = 52

3x = 72

x = 24

The father is 2 times his son's age.

2x

= 2(24)

= 48

So, the son is 24 and the father is 48.

10 years ago, son was 14 and father was 38, if added, this adds up to 52, so we know our calculations are correct.

Answer:

So the son’s age is 24 and the father’s is 48. Ten years ago, they were 14 and 38, which adds up to 52.

Step-by-step explanation:

If the son’s age is x, the father’s age is 2x.

Ten years ago:

(x - 10) + (2x - 10) = 52

3x + 20 = 52

3x = 72

x = 24

2x = 48

Hey there! I'm happy to help!

to find the volume of a sphere, you cube the radius, multiply it by 4/3, and then multiply it by π.

First, we have to find the radius. To find the surface area you square the radius and multiply it by 4 and then π.

Let's do that formula backwards on our surface area to find the radius.

We divide by π

100÷π=100

We divide by 4.

100÷4=25

We find the square root.

√25=5

Now, we use our radius in the volume formula.

5³=125

125×4/3=500/3

We multiply by π.

500/3π

Therefore, the volume of a sphere if its surface area is 100π ft² is 500/3π ft³.

Have a wonderful day! :D

Answer:

V=166.66[tex]\pi[/tex] ft³

Step-by-step explanation:

The surface area of a sphere is 4[tex]\pi[/tex]r²

100[tex]\pi[/tex]=4

100[tex]\pi[/tex]/4

25=r²

r=5

Now that we know the radius is 5, we can find the volume.

v=4/3[tex]\pi[/tex](5)³

v=(5*5*5*4)/3*[tex]\pi[/tex]

V=166.66[tex]\pi[/tex]

Answer:

First, find the cost function of DoItRight Housekeeping:

The y-intercept(b), representing the initial cost, can be calculated by substituting in values to the function:

[tex]f(x)=12x+b\\26=12(1.5)+b\\b=26-18=8[/tex]

Therefore, the function for two companies are:

When comparing the two functions, it's shown how CleanIt has a greater y-intercept than DoltRight, meaning that CleanIt has a greater initial cost than DotRight. The y-intercept is when the graph intercepts the y-axis, therefore, the coordinates there would be (0, y-value), which, in this case for CleanIt company, will be (0, 16). While CleanIt has a greater y-intercept(initial cost), DoItRight has a greater slope, meaning they cost more per hour.

Answer:

the answer is 60.7

Step-by-step explanation:

60 to has a between numbers like given in the picture

so as number line it's

60.1 . 60.2 60.3 60.4 60.5 60.6 60.7 60.8 and continue

if u get any 3 digit number like 600 to 650 in number line

u do it like it the same 600.1 600.2.... and go on

Answer:

63½ or 63.5

Step-by-step explanation:

65-60=5

10points=5

1point=?

1×5/10= ½

that means the sequence continues after adding ½ i.e

60..60½...61...61½...62...62½...63...63½...64..64½...65

you have been asked the 8th number which is 63½

Answer:

see below

Step-by-step explanation:

x + 3y = 5,

y = –x + 3

Substitute the point into each equation and verify that it is true

x + 3y = 5,  2 +3(1) = 5   5 = 5  true

y = -x +3    1 = -2+3     1=1  true

(2,1) is a solution

Answer:

D,A,A,A,

Step-by-step explanation:

that's the real answer

1d

2a

2a

2a

God bless

Answer:

y = 5[tex]\sqrt{6}[/tex]

Step-by-step explanation:

JLT forms the special 90-60-30 right triangle and the side length for the given measure follows as 2a-a[tex]\sqrt{3}[/tex]-a

since the side length that sees 90 degrees is 10 then x = 5

according to Euclidian theorem :

y^2 = LK*KI (LK = 15 -x, KI = 15)

y^2 = 10*15

y^2 = 150 find the root for both sides

y = 5[tex]\sqrt{6}[/tex]

Answer:

Unpainted  surface area = 514.28 cm²

Step-by-step explanation:

Given:

Side of cube = 20 Cm

Radius of circle = 20 / 2 = 10 Cm

Find:

Unpainted  surface area

Computation:

Unpainted  surface area = Surface area of cube - 6(Area of circle)

Unpainted  surface area = 6a² - 6[πr²]

Unpainted  surface area = 6[a² - πr²]

Unpainted  surface area = 6[20² - π10²]

Unpainted  surface area = 6[400 - 314.285714]

Unpainted  surface area = 514.28 cm²

Answer:

44 degrees.

Step-by-step explanation:

The 3 small triangles are isosceles  so m < a = m < b , therefore

m < a = (180 - 92) / 2 = 44 degrees.

m < f = m < a ( they are both subtended on the circle by the same chord (cd)),

So m < f = 44.

Answer:Holly drank 12 bottles in a week.

Step-by-step explanation:

First change the fraction 1 2/5 litre into a decimal, by doing this, we can know how many litres are there in 2/5.

So= 1 2/5

= 2 ÷5 = 0.4

= 1 + 0.4 = 1.4 liters

1.4 liters is the amount of water in a bottle.

Next, also change the fraction 2 2/5 litres into a decimal.

So=2 2/5

= 2÷5 = 0.4

= 2 + 0.4 = 2.4 liters

She drinks 2.4 liters a day.

To find how many bottles she drank in 1 week, we must multiply the amount of water she drinks in a day to the days in a week.

So= 1 week= 7 days

= 1 day= 2.4 liters

So= 2.4 × 7 = 16.8

She drinks 16.8 in a week.

To find how much bottles she drank in a week, we must divide the amount of liters she drank in one week to the amount of liters are there in a bottle.

So= 16.8 ÷ 1.4= 12 bottles

Holly drinks 12 bottles in a week.

I hope this helps! I'm sorry if it's wrong and complicated.

Answer:

G. $70

Step-by-step explanation:

$420 for 7 hours

$270 for 4 hours

Each of the above already includes the fixed fee.

Now we subtract the bottom line from the top line:

$420 - $270 = $150

$7 hours - 4 hours = 3 hours

$150/3 hours = $50/hour

For 4 hours, the hourly fee is $50/hour * 4 hours = $200.

Since the total charge for 4 hours is $270, then fixed fee is

$270 - $200 = $70

Answer: $70

The fixed fee that the mechanic charges is $70. Therefore, option G is the correct answer.

Given that, a mechanic charges a fixed fee plus an hourly rate for each hour he works. He charges $420 for 7 hours and $270 for 4 hours.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the mechanic charges x dollars per an hour.

The difference in the charges = $420 - $270 = $150

Difference in the hours = 7 hours - 4 hours = 3 hours

Now, x=150/3 = 50

So, $50 per hour is the mechanic charges for service.

For 4 hours, the hourly fee is 50 × 4 = $200.

Since the total charge for 4 hours is $270, then fixed fee is

$270 - $200 = $70

The fixed fee that the mechanic charges is $70. Therefore, option G is the correct answer.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

Answer:

Step-by-step explanation:

area of rectangle=120

find area of CPD

area=1/2  (area of the rectangle)

area =  1/2×120=60

The area of triangle CPD IS 30 square units.

If the area of the rectangle is 120, then the area of triangle CPD is 30.

The area of a rectangle is given by the formula:

Area = length × width

In this case, the length of the rectangle is 120/width.

The area of a triangle is given by the formula:

Area = (1/2) × base × height

The base of triangle CPD is the width of the rectangle, and the height of triangle CPD is half the length of the rectangle.

Therefore, the area of triangle CPD is:

(1/2) × width × (120/width) = 30

So the answer is 30.

Learn more about triangle here: brainly.com/question/2773823

#SPJ2

Answer:

His gain percent would have been 8%

Step-by-step explanation:

The key to answering this question is to first calculate the price at which the wheat flour was bought.

Mathematically;

% profit = (selling price-cost price)/cost price * 100%

Let the cost price be $x

Thus;

% profit = (30-x)/x * 100

20 = 100(30-x)/x

20x = 3000-100x

100x + 20x = 3000

120x = 3000

x = 3000/120

x = Rs 25

So let’s assume he sold at Rs 27

His profit would have been 27-25 = 2

His gain or loss percentage would’ve been;

2/25 * 100/1 = 200/25 = 8% (gain, since selling price is greater than the cost price)

Answer:

a=13

Step-by-step explanation:

-90=-6a-12

-6a=-78

a=13

Answer:

a=13 well as u can see the other comment already gave an explanation of y it is a=13 and i completely agree with it have a nice afternoon,night,or day to u

Step-by-step explanation:

Answer:

The greatest common factor of the expression is 25x

Step-by-step explanation:

Here, we are interested in giving the greatest common factor of the expression.

We can do this by factorization till we have no common factors left.

the expression is;

100x^2 -250xy + 75x

we start with the common factor x;

x(100x -250y + 75)

The next thing to do here is to find the greatest common factor of 100,250 and 75.

The greatest common factor here is 25.

Thus, we have;

25x(4x -10y + 3)

There is no more factor to get from the terms in the bracket. This simply means that the terms in the bracket are no longer factorizable

So the greatest common factor we have is 25x

Answer:

[tex]slope=\frac{1}{2}[/tex]

Step-by-step explanation:

Use the following equation:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change of the x-axis, otherwise known as the slope.

Insert the values:

[tex](1_{x1},2_{y1})\\(5_{x2},4_{y2})[/tex]

[tex]\frac{4-2}{5-1}=\frac{2}{4} =\frac{1}{2}[/tex]

The slope is [tex]\frac{1}{2}[/tex].

:Done

Answer:

1/2

Step-by-step explanation:

The formula for slope is: y1-y2/x1-x2

The points given are: (x-coordinate, y-coordinate)

In the formula:

y1 is the y-coordinate of the first point

y2 is the y-coordinate of the second point

x1 is the x-coordinate of the first point

x2 is the x-coordinate of the second point

This said, we can plug our points in.

2-4/1-5

Subtract.

-2/-4

Simplify.

-1/-2

The negatives will cancel each other out.

1/2

The slope of the line that cuts through the points (1,2) and (5,4) is 1/2.

Answer:

The answer is below

Step-by-step explanation:

From the diagram of the flask attached, the diameter of the cylinder is 1 inch and its height (h) is 3 inches. The radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch

The volume of the cylinder = πr²h = π(0.5)² × 3 = 2.36 in³

While for the sphere the diameter is 4.5 in. The radius of the sphere R = diameter / 2 = 4.5/2 = 2.25

The volume of the sphere = 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³

Volume of the flask = The volume of the cylinder  + The volume of the sphere = 2.36 + 47.71 = 50.07 in³

If the sphere and the cylinder are dilated by a scale factor of 2. For the cylinder its height (h') = 3/2 = 1.5 inch and its radius (r') = 0.5/2 = 0.025

The new volume of the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³

While for the sphere The radius of the sphere R' = 2.25 / 2 = 1.125

The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³

New Volume of the flask = The new volume of the cylinder  + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³

The ratio of the new volume to original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125

The resulting volume would be 0.125 times the original volume

Answer:

50.07 and 8 times

Step-by-step explanation:

1) Calculate volume of each figure using according formulas.

You should get:

Sphere: 47.71in^3

Cylinder: 2.36in^3

Now let's add, and you should get 50.07.

2) Let's dilate the dimensions/flask by 2 (multiply by 2)

4.5 * 2 = 9

1 * 2 = 2

3 * 2 = 6

Now with these dimensions you should get:

Sphere: 381.7in^3

Cylinder: 18.85in^3

This should add up to 400.55in^3

Divide new by original. 400.55 / 50.07 = 8

So it is 8 times larger.