A park designer wanted to place a fountain so that it was close to both the slide and the swings. Refer to the coordinate grid shown. Each unit on the grid represents 100 ft.

(A) find the distance from the slide to the foundation show your work.

(B) if each jump = 100ft, how far is it from the slide to the fountain?


Please show your work :)

Answer:

1,450 & 1,500

Step-by-step explanation:

it occured 7 times each

sorry for my hand writing

Answer:

Step-by-step explanation:

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

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

m - slope

b - y-intercept

We have the equation in a standard form:

[tex]6x+3y=12[/tex]

Convert:

[tex]6x+3y=12[/tex]             subtract 6x from both sides

[tex]6x-6x+3y=-6x+12[/tex]

[tex]3y=-6x+12[/tex]              divide both sides by 3

[tex]\dfrac{3y}{3}=\dfrac{-6x}{3}+\dfrac{12}{3}[/tex]

[tex]y=-2x+4[/tex]

So, its a multiplying question - the product. Also there are multiple answers from x = negative anything to positive 14, so i chose a number.

The product of -2 and a number minus six is greater than -18.

-2 · (x - 6) > -18

-2 · (7 - 6) > -18

-2 · (1) > -18

-2 > -18

x = 7, or anything lower than 15.

On the number line btw, -2 is bigger than -18

Answer:

60

Step-by-step explanation:

36+6=42

42+6=48

48+6=54

54+6=60

Answer:

The yield to maturity of the bonds is 11%

Explanation:

Price at which the bonds is currently trading = 283.30$

Face Value = $1000

Coupon rate = 2%

Hence the coupon bond rate = $1000 ×2%

= [tex]1000\times \frac{2}{100}[/tex]

=$20

Years to maturity: 20 years

Formula used:  

=[tex]\frac{(C+ (\frac{(F-P)}{n}))}{(\frac{(F+P)}{2})}[/tex]

Where C is the bond coupon rate

F is the face value

P is the price

N is the number of years

=[tex]\frac{(20 +(\frac{(1000-283.30)}{20})}{(\frac{(1000+283.30)}{2})}[/tex]

=11%

The yield to maturity of the bonds is 11%

Answer:

The number of solutions of the system is zero

Step-by-step explanation:

we have

a) [tex]x+y=2[/tex]

Isolate the variable y

[tex]y=-x+2[/tex] ----> equation A

This is the equation of the line in slope intercept form

where

The slope is m=-1

The y-intercept is b=2

b) [tex]2x+2y=8[/tex]

Isolate the variable y

[tex]2y=-2x+8[/tex]

[tex]y=-x+4[/tex] ----> equation B

This is the equation of the line in slope intercept form

where

The slope is m=-1

The y-intercept is b=4

Remember that

If two lines are parallel, then their slopes are the same

In this problem the lines A and B are parallel lines with different y-intercept

so

The lines don't intersect

therefore

The system has no solution

Answer:

a. 16 gallons

b. 32

Step-by-step explanation:

Let the full capacity of the tank is x gallons.

a. It is given that 12 gallons of water fill a tank to [tex]\frac{3}{4}[/tex] capacity.

Hence, we can write [tex]\frac{3x}{4} = 12[/tex]

⇒ [tex]x = \frac{4 \times 12}{3} = 16[/tex] gallons.

b. If the tank is filled to capacity, then there will be 16 gallons of water, with which [tex]\frac{16}{\frac{1}{2} } = 32[/tex] numbers of half-gallon bottles of be filled with water. (Answer)

Answer:

here is the answer

 A system of equations is a collection of two or more equations with a same set of unknowns. 

Answer:

5 miles

Step-by-step explanation:

0.5 x 10

= 5

Answer:

5 Miles

Step-by-step explanation:

1/5 of an hour would be 12 minutes. If it is 1/2 mile every 1/5 our, you hike 1 mile for 2/5.

1/5 = 1/2

2/5 = 1

3/5 = 1 1/2

4/5 = 2

5/5 = 2 1/2

So if 1 hour is 2 1/2 miles, you multiply it by 2, or add it withh its same number, which is,

5 miles.

Answer:

a. After 2 weeks the first plant will be taller.

b. After 10 weeks the second plant will be taller.

c. After 4 weeks both the plant will be of the same height.

d. This is the condition for the height of the first plant is greater than that of the second plant.

Step-by-step explanation:

The first plant was 5 cm tall and the second plant was 4 cm.

Again, the first plant has grown 0.5 cm a week and the second plant has grown 0.75 cm a week.

So, the height of the first plant after W weeks will be (5 + 0.5W) cm. and the height of the second plant after W weeks will be (4 + 0.75W) cm.

a. After 2 weeks the first plant will be (5 + 2× 0.5) = 6 cm.

And after 2 weeks the second plant will be (4 + 2 × 0.75) = 5.5 cm

So, after 2 weeks the first plant will be taller.

b. After 10 weeks the first plant will be (5 + 10× 0.5) = 10 cm.

And after 10 weeks the second plant will be (4 + 10 × 0.75) = 11.5 cm

So, after 10 weeks the second plant will be taller.

c. If 5 + 0.5w = 4 + 0.75w, give w = 4 weeks, then this means that after 4 weeks both the plant will be of the same height.

d. If, 5 + 0.5w > 4 + 0.75w, then it means that this condition is for the height of the first plant will be more than the second plant. (Answer)

a. After 2 weeks: First plant: 6 cm (taller), Second plant: 5.5 cm b. After 10 weeks: First plant: 10 cm. Second plant: 11.5 cm (taller) c. Solution to 5+0.5w=4+0.75w is w=4, where both plants are equal in height (5 cm). d. Inequality 5+0.5w>4+0.75w indicates the first plant is taller before w=4 weeks.

a. To determine which plant is taller at the end of 2 weeks, let's calculate their heights:

- First plant after 2 weeks: [tex]\( 5 + 0.5 \cdot 2 = 5 + 1 = 6 \)[/tex] cm

- Second plant after 2 weeks: [tex]\( 4 + 0.75 \cdot 2 = 4 + 1.5 = 5.5 \)[/tex] cm

Since 6 cm (first plant) > 5.5 cm (second plant), the first plant is taller at the end of 2 weeks.

b. Now, let's calculate their heights after 10 weeks:

- First plant after 10 weeks: [tex]\( 5 + 0.5 \cdot 10 = 5 + 5 = 10 \) cm[/tex]

- Second plant after 10 weeks: [tex]\( 4 + 0.75 \cdot 10 = 4 + 7.5 = 11.5 \) cm[/tex]

Since 11.5 cm (second plant) > 10 cm (first plant), the second plant is taller at the end of 10 weeks.

c. The equation given is [tex]\( 5 + 0.5w = 4 + 0.75w \)[/tex]. This equation represents the point in time (number of weeks, w) when both plants will have the same height. Solving for w:

[tex]\[ 5 + 0.5w = 4 + 0.75w \][/tex]

Subtract 0.5w from both sides:

[tex]\[ 5 = 4 + 0.25w \][/tex]

Subtract 4 from both sides:

[tex]\[ 1 = 0.25w \][/tex]

Divide both sides by 0.25:

[tex]\[ w = \frac{1}{0.25} = 4 \][/tex]

Therefore, w = 4  represents the number of weeks after which both plants will have the same height, which is 5 cm.

d. The inequality [tex]\( 5 + 0.5w > 4 + 0.75w \)[/tex] represents the point in time (number of weeks, w) when the first plant's height (5 cm + 0.5w) exceeds the second plant's height (4 cm + 0.75w). Solving for w:

[tex]\[ 5 + 0.5w > 4 + 0.75w \][/tex]

Subtract 4 from both sides:

[tex]\[ 1 + 0.5w > 0.75w \][/tex]

Subtract 0.5w from both sides:

[tex]\[ 1 > 0.25w \][/tex]

Divide both sides by 0.25:

[tex]\[ w < \frac{1}{0.25} = 4 \][/tex]

Therefore, the solution to [tex]\( 5 + 0.5w > 4 + 0.75w \)[/tex] represents the number of weeks w when the first plant is taller than the second plant. This happens for ( w < 4 ) weeks.

Use long division (see attached image below) to divide 250 over 9. The image shown has a red quotient of 27 and a blue remainder of 7.

This means there will be 27 full boxes with 9 cookies each. That accounts for 27*9 = 243 cookies so far. The remaining 7 won't be able to fill a full box as we're 2 short.

-------

A shortcut is to use a calculator to divide 250/9 = 27.778, then you ignore the decimal portion and focus solely on the whole part 27.

-------

Amy will have 27 full boxes of cookies, which is determined by dividing the total number of cookies by the number of cookies per box.

To find out how many full boxes Amy will have when selling 250 chocolate chip cookies in boxes of 9, you can divide the total number of cookies by the number of cookies per box.

Number of full boxes = Total number of cookies / Cookies per box

Number of full boxes = 250 cookies / 9 cookies per box

Using division:

Number of full boxes ≈ 27.777...

Since Amy can't have a fraction of a box, she will have 27 full boxes of cookies.

To learn more about the division operation click here :

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Answer:

No Solution.

Step-by-step explanation:

x-3y=-4

2x-6y=6

-----------

simplify 2x-6y=6 into x-3y=3

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

x-3y=-4

x-3y=3

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

x-3y=-4

-(x-3y)=-1(3)

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

x-3y=-4

-x+3y=-3

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

0=-7

no solution

The equations x - 3y = -4 and 2x - 6y = 6 represent a system with parallel lines that do not intersect, therefore there are no solutions to this system of equations.

Let's solve the system of equations using the method of substitution or elimination. First, look at the two given equations:

It's clear that Equation 2 is simply Equation 1 multiplied by 2. This implies the two equations are multiples of each other, which could mean the system has an infinite number of solutions or no solutions. Let's simplify Equation 2 to confirm:

Divide Equation 2 by 2:

2x/2 - 6y/2 = 6/2

x - 3y = 3

This new equation contradicts Equation 1 (x - 3y = -4), which indicates that there are no solutions since the two lines are parallel and will never intersect.

Answer:

a. 1 cup of yellow and 1.75 cups of blue

b. 4 cups of yellow and 7 cups of blue

Step-by-step explanation:

a. We can multiply both sides of this ratio by an number of our choice to get an equivalent ratio. 2:3.5 = 1: 1.75. (We are multiplying by 1/2)

b. 2 : 3.5 = 4 : 7 (We are multiplying by 2)

The missing terms in the geometric sequences are 360 and 1080 for sequence B, and 0.2 and 0.02 for sequence C.

In this question, we're working with geometric sequences. A geometric sequence is a sequence in which you multiply by a constant to get from one term to the next.

For sequence B, we notice that 120 is three times 40, so we're multiplying by 3 each time. Thus, the next two terms would be 360 (120 * 3) and 1080 (360 * 3).

For sequence C, we're dividing by 10 to get from one term to the next (200 / 10 = 20, 20 / 10 = 2). Thus, the missing terms would be 0.2 (2 / 10) and 0.02 (0.2 / 10).

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Answer: 80 miles for the first ship, and 150 miles for the other.

Explanation:

First thing we should do is correspond each number with a letter:

Let x be the distance travel by ship heading east

Let y be the distance travel by ship heading south

y = x + 70 -- (1)

sqrt(x^2 + y^2) = 170 -- (2)

Subtract (1) into (2):

sqrt(x^2 + (x + 70)^2) = 170

x^2 + x^2 + 140x + 4900 = 28900

2x^2 + 140x - 24000 = 0

x ^2 + 70x - 12000 = 0

(x - 80)(x + 150) = 0

x = 80 or -150

Since the distance for the first ship can’t be negative, therefore, x = 80 -- (3)

Subtract (3) into (1), therefore, y = 150

Hope this helps! :)

Answer: 1.14

Step-by-step explanation:

hate how you gotta pay just to see an answer

The required sales tax on purchases of $18.95 is $1.14.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Amount = $18.95
Sales tax applies is 6% on the amount,
Now,
Sales tax is given as,
tax = amount × tax percentage / 100
tax = 18.95 × 6 / 100
tax = 1.14

Thus, the required sales tax on purchases of $18.95 is $1.14.

Learn more about percentages here:

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Answer:

2) -2(3x - 7) = -6x + 14

3) Add 4x to both sides

4) Subtract 14 from both sides

5) Divide both sides by -2

Step-by-step explanation:

Answer:

y=x+3

Step-by-step explanation:

y-y1=m(x-x1)

m=(y2-y1)/(x2-x1)

m=(4-3)/(1-0)

m=1/1=1

y-3=1(x-0)

y-3=x

y=x+3

Answer:

y=mx+b form; m is the slope

Step-by-step explanation:

So the slope would be the m

Answer: -a/b

Step-by-step explanation:

ax+by=c right?

then slope = -a/b

Answer:

B. 30cm³

Step-by-step explanation:

Volume of a prism=length×Breadth×Height(L×B×H)

Where Length(L)=5-cm, Breadth(B)= 2-cm Height(H)=3-cm

∴Volume=5×2×3=30 cm³

Answer:A

Step-by-step explanation:

The bottles are represented by b. Each bottle costed 2.10, so it's 2.10b. Then he also bought a pizza for 12.99. The total of all of it was 21.39.

Answer:

A. 2.10b+12.99=21.39; 4 bottles

Step-by-step explanation:

Answer:

1. -6, -24, -96, -384, -1,536

2. 3, 12, 21, 30, 39

Step-by-step explanation:

1. Given

[tex]a_1=-6\\ \\a_n=4a_{n-1}[/tex]

Find [tex]a_2, \ a_3,\ a_4,\ a_5:[/tex]

[tex]a_2=4a_{2-1}=4a_1=4\cdot (-6)=-24\\ \\a_3=4a_{3-1}=4a_2=4\cdot (-24)=-96\\ \\a_4=4a_{4-1}=4a_3=4\cdot (-96)=-384\\ \\a_5=4a_{5-1}=4a_4=4\cdot (-384)=-1,536[/tex]

2. Given

[tex]a_1=3\\ \\a_n=a_{n-1}+9[/tex]

Find [tex]a_2, \ a_3,\ a_4,\ a_5:[/tex]

[tex]a_2=a_{2-1}+9=a_1+9=3+9=12\\ \\a_3=a_{3-1}+9=a_2+9=12+9=21\\ \\a_4=a_{4-1}+9=a_3+9=21+9=30\\ \\a_5=a_{5-1}+9=a_4+9=30+9=39[/tex]

The car would be worth $13,000 in the year 2011.

To calculate the value of the car in the year 2011, we need to find the depreciated value of the car each year from 2007 to 2011. The value of the car depreciates by 5% each year, which means it retains 95% of its value each year. Here are the calculations:

Therefore, in the year 2011, the car would be worth $13,000 to the nearest hundred dollars.

Answer:

-6(p+13)

Step-by-step explanation:

-5(3p+3)+9(-7+p)

-15p-15-63+9p

-15p+9p-15-63

-6p-15-63

-6p-78

simplify

-6(p+13)

Answer:

-6p-78

Step-by-step explanation:

Khan

BTW: Its 100% correct

Answer:Another way to graph a linear function is by using its slope m, and y-intercept. ... The y-intercept is the point on the graph when x =0 x = 0 . The graph crosses the y-axis at (0,1) .

Answer:

Step-by-step explanation:

When you have a linear equation, the y-intercept is the point where the graph of the line crosses the y-axis.

Answer:

○ C. [tex]\displaystyle y = \frac{1}{2}x + 10[/tex]

Step-by-step explanation:

9 = ½[−2] + b

−1

[tex]\displaystyle 10 = b \\ \\ y = \frac{1}{2}x + 10[/tex]

** Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES], so −2 becomes ½.

I am joyous to assist you anytime.

Judy needs to buy 4 packages of cookies for her party, with each package containing 6 cookies to serve her 24 friends.

Judy wants to buy some cookies for her birthday party, ensuring each of her 24 friends receives one cookie. Cookies are sold in packages of 6. To calculate the number of packages she needs, divide the total number of friends by the number of cookies in a package.

Calculation: 24 friends ÷ 6 cookies per package = 4 packages

Judy needs to buy 4 packages of cookies to have enough for each friend to have one cookie.

Answer:

0.0003333333 is the answer

Answer: 0.00033333333

Step-by-step explanation: U divide, or if ur having trouble with that, use Google.

Hope this helped u :)

Answer:

12

Step-by-step explanation:

12/3=4

4+8=12

24-12=12