based on the function h(t), what will be the account value five years after the account is opened?

The Lewis family and the Perry family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 15 L per hour. The water output rate for the Perry family's sprinkler was 40 L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850 L . How long was each sprinkler used

Answer:

Hours of use of sprinkler by Lewis family is 30 hours.

Hours of use of sprinkler by Perry family is 35 hours.

Step-by-step explanation:

Let W = hours of use by Lewis family

65 - W = hours of use by Perry family

Then;

15W + 40*(65 - W) = 1850

15W + 2600 - 40W = 1850

(15 - 40)W = 1850 - 2600

-25W = −750

W = 750/25 = 30

Therefore;

W = 30

65 - W = 65 - 30 = 35

Hence,

Hours of use by Lewis family is 30 hours.

Hours of use by Perry family is 35 hours.

Answer:

it is A or the first one

Step-by-step explanation:

The graph represents the system y = 1/2x + 3 and y = 3/2x - 1 is the lines and passes by (0, 3) and (4, 5), Option A.

Two equation of lines is  given y = 1/2x + 3 and y = 3/2x - 1.
A graph to be identified showing the coordinate.

A line can be defined by a shortest distance between two points is called as a line.

Here, slope of equations of lines y = 1/2x + 3 and y = 3/2x - 1 are 1/2 and 3/2 and intercept is 3 and -1 now matching this with option we identified option A contains both the lines and passes by (0, 3) and (4, 5).

Thus, The graph represents the system  y = 1/2x + 3 and y = 3/2x - 1 is the lines and passes by (0, 3) and (4, 5) ,Option A.  

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Answer:

(A) 1

Step-by-step explanation:

We know that the formula is x = (m/m+n) (x2-x1) + x1.

But the trick to the question which is why everyone is getting it wrong is because it asks for F to D not D to F.

The reason everyone else was getting 4 was because they were using this.

They solved the equation x = (8/8+5) (9-[-4]) -4 where it was D to F. This equation does turn out to be 4 but it is incorrect.

However, the correct equation (because it is supposed to be F to D) is

x = (8/8+5) (-4 -9) +9 which is in fact equal to 1.

I also just took the quiz and got 100%.

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Answer:

x² + 2x + 3

Step-by-step explanation:

(f + g)(x) = f(x) + g(x), thus

f(x) + g(x)

= 4x + 5 + x² - 2x - 2 ← collect like terms

= x² + 2x + 3

Answer:

14 units

Step-by-step explanation:

All we have to pay attention to in this problem is B, so we can ignore the rest of the triangle. B is 5 units directly to the left of line l, meaning that B' must be 5 units to the right of line l. This would put B' 2 units to the left of line m. That means that B" would be 2 unit to the right of line m, as that is how reflections work. Adding up all of the difference in units you have a 10 unit shift from B to B', and then a 4 unit shift from B' to B". Now adding 4+10=14 units.

Answer:

$26.

Step-by-step explanation:

His original salary was $20. It increased by 20%. In other words, the total salary he earns is now:

[tex]20+20(.3)=20(1.3)=26[/tex]

His new salary is $26.

Note: For the second step, I used the distributive property.

[tex]20(1)+20(.3)=20(1+.3)=20(1.3)[/tex]

Answer:

You've given Uncle Sam an interest-free loan of your money for a full year. ... If you had received your expected refund incrementally as part of your pay, you could have used it to pay bills, start an emergency fund or save for something special.You are at the mercy of the IRS, which already is at the mercy of a frequently late-acting Congress when it comes to tax laws. If Congress and the IRS are slow, then so is your receipt of your refund.

Answer:

All negative numbers

Step-by-step explanation:

They are not whole numbers

Answer:

0

Step-by-step explanation:

Since negative numbers are not considered whole numbers, they are not included here. All natural numbers are whole numbers but not all whole numbers are natural numbers. 0 is a whole number but it doesn't count as a natural number which makes the answer 0

Answer:

380 square inches

Step-by-step explanation:

We are given the measurements of the Rectangular Prism as

8 inches by 9 inches by 10 inches

Where based on the order of arrangement:

8 inches = Length

9 inches= Width

10 inches = Height

Step 1

Find the amount of wrapping paper needed

Perimeter = 2L + 2W

= 2 × 8 + 2 ×9

= 16 + 18

= 34 inches

Base = L × W

= 8 × 9

= 72 inches

Surface Area of the Rectangular Prism =PH + 2B

Where P = Perimeter

H = Height

B = Base

= 34 × 10 + 2× 72

= 340 + 144

= 484 square inches

The area of the Rectangular prism = 484 square inches

Step 2

So we were told that she used wrapping paper the measured 2 feet by 3 feet.

We would convert the values in feet to inches

1 ft = 12 inches

Length = 2 ft = 2 × 12 = 24 inches

Width = 3 ft = 3 × 12 = 36 inches

We find the area of the wrapping paper

Length × Width = 24inches × 36 inches = 864 square inches.

Step 3

The amount of square inches of wrapping paper left over is calculated as:

Area of the wrapping paper used - Area of the Rectangular prism

= 864 square inches - 484 square inches

= 380 square inches.

Therefore, the amount of square inches of wrapping paper left over is 380 square inches.

Answer:

Step-by-step explanation:

1/8 + c = 4/5

c = 4/5 - 1/8

c = 4/5 × 8/8 - 1/8 × 5/5

= 32+5 / 40

= 37/40

Hope this helps

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Answer:

y = 0.5x + 2

Step-by-step explanation:

the y-intercept is 2, as shown in the graph

the slope is 0.5. this is because while the x-value goes up by 2, the y-value goes up by one (from 0, 2 to 2, 3).

using the slope formula of rise / run, you get 1/2, which is equal to 0.5

Answer:

c

Step-by-step explanation:

Answer:

Both a relation and a function

Step-by-step explanation:

Replicates itself every 14 minutes, which is exponential function

Answer:

8

Step-by-step explanation:

BD is 32 units.

BE is half of BD

3x - 8 = 32/2

3x - 8 = 16

3x = 16 + 8

3x = 24

3/3x = 24/3

x = 8

Answer:

Solution,

Diagonals of rectangle bisects each other.so,

2 BE = BD

2( 3x - 8 ) = 32

6x - 16 = 32

Add 16 on both sides

6x - 16 + 16 = 32 + 16

Simplify

6x = 48

divide both sides of equation by 6

6x/6 = 48/6

calculate

X = 8

Hope this helps...

Good luck on your assignment..

Answer:

The answer is c.

Step-by-step explanation:

[tex]a_{1} =-1*(-4)x^{n-1}[/tex]

[tex]a_{1} =-1(-4)^{1-1}[/tex]

[tex]a_{1} =-1(-4)^{2} \\a_{1} =-1(1)\\a_{1} =-1[/tex][tex]a_{2} =-1(-4)^{2-1} \\a_{2} =-1(-4)^{1} \\a_{2} =-1(-4)\\a_{2}=4[/tex][tex]a_{3}=-1(-4)^{3-1} \\a_{3}=-1(-4)^{2} \\a_{3}=-1(16)\\a_{3}=-16[/tex]

Answer:

D

Step-by-step explanation:

Mathematically, the mid segment of a trapezoid is exactly the average of the 2 parallel bases

What this means is that to find the length of the trapezoid, we will need to find the average of the two parallel bases

Mathematically, this is same as adding the two bases and dividing the result by 2.

Hence we can say it is exactly one-half the length of the sum of the two parallel bases

Based on the information given, the composition of transformations that will bring about a pair of similar, not congruent triangles is D. a rotation, then a dilation.

A congruent triangle simply means when two triangles have exactly the same side and angles.

Therefore, the composition of transformations that will bring about a pair of similar, not congruent triangles is a rotation, then a dilation.

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Answer:

CPCTC

Step-by-step explanation:

You already proved that triangle BAD is congruent to CAD, this means that all of the corresponding angles and sides with be congruent (CPCTC). That means BD is congruent to CD. Hope this helps!

Answer:  3/5

Step-by-step explanation:

[tex]\dfrac{a}{a+2}+\dfrac{3}{20}=\dfrac{a+3}{(a+2)+3}\\\\\\\dfrac{a}{a+2}\bigg(\dfrac{20}{20}\bigg)+\dfrac{3}{20}\bigg(\dfrac{a+2}{a+2}\bigg)=\dfrac{a+3}{a+5}\\\\\\\dfrac{23a+6}{20(a+2)}=\dfrac{a+3}{a+5}\\\\\\(23a+6)(a+5)=20(a+2)(a+3)\\\\\\23a^2+121a+30=20a^2+100a+120\\\\\\3a^2+21a-90=0\\\\\\a^2+7a-30=0\\\\\\(a+10)(a-3)=0\\\\\\a=-10\quad a=3[/tex]

Since "a" is a positive integer, disregard a = -10

So the only valid answer is a=3   →  a+2=5

[tex]\dfrac{a}{a+2}=\large\boxed{\dfrac{3}{5}}[/tex]

Answer:

c = 6√2 cm

Step-by-step explanation:

a² + b² = c²

6² + 6² = c²

36 + 36 = c²

108 = c²

c = ± √108 = ± 6√2

Since the side length of a triangle can't be negative, c = -6√2 is an extraneous solution; therefore the answer is c = 6√2.

Answer:

72 cm or 6 square root of 2

Step-by-step explanation:

a^2+b^2=c^2

6^2+6^2=c^2

36+36=72

c= 72 cm.  or 6 square root of 2

hope this helps.

Answer:

Step-by-step explanation:

If F and H are midpoints of sides of rectangle then FH is parallel to the other side of rectangle so FH is perpendicular to the EG. That means the lenght of FH is equal to lenght of rectangle, and the lenght of EG is equal to width of rectangle.

So the area of the rectangle:  [tex]A_{rectangle}=EG\cdot FH[/tex]

FH ⊥ EG so the area of quadrangle EFGH:

[tex]A_{_{EFGH}}=\frac12EG\cdot FH=\frac12A_{rectangle}[/tex]

no matter the location of segment EG

The area of EFGH is always One-half of the area of the rectangle.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have given that;

the kite EFGH is inscribed in a triangle and F and H are midpoints and EG is parallel to the side of rectangle.

The kite consists of 2 triangle that are EFG and EHG.

Now,

In a triangle EFG is,

= 1/2 x EG x h......(1)

where h is the height from F to EG

Also the area of EHG:

= 1/2 x EG x h₁

where is the height from H to EG

We also know that h₁ + h is the width of the rectangle and EG is the length of the rectangles.

Area of Kite = = 1/2 x EG x h + 1/2 x EG x h₁

Also, The area of a rectangle is rectangle length × rectangle width.

Thus, The Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle.

Hence, The statement describes how the location of segment EG affects the area of EFGH is the area of EFGH is always One-half of the area of the rectangle.

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Answer:

The constant term is 240. It represents the initial daily revenue.

Step-by-step explanation:

It is given that Tico's Taco Truck is trying to determine the best price at which to sell tacos, the only item on the menu,  to maximize profits.

The owner can calculate the daily revenue using the polynomial  expression

where x is the number of $1 increases in the taco price.

Constant term does not contain any variable.

In the given expression 240 is free from variable x. So, the constant term is 240.

The value of expression is 240 for x=0. Since x is the number of $1 increases in the taco price, therefore 240 is the daily revenue when the taco price is not increased or the taco price increased by 0.

Therefore the constant term is 240 and it represents the initial daily revenue.

Answer:

17

Step-by-step explanation:

You would make the 10.01 a 10 and the 7.07 a 7.

Answer:

Marcus will receive a total of $17,542.2 when he redeems the certificate of deposit (CD) at the end of 10 years

Step-by-step explanation:

Principal(p)=$13,000

Rate(r)=3.0%

Period(n)=12 months

Time(t)=10 years

A=p(1+r/n)^nt

=13,000(1+0.03/12)^12*10

=13,000(1+0.0025)^120

=13,000(1.0025)^120

=13,000(1.3494)

=17,542.2

A=$17,542.2

Marcus will receive a total of $17,542.2 when he redeems the certificate of deposit (CD) at the end of 10 years

Answer:

[tex]y=\frac{5}{6}x+5[/tex]

Step-by-step explanation:

Well this is actually really simple we just have to look at the line and see what attributes it has so we can make an equation.

So slope intercept form is [tex]y=mx+b[/tex].

Like to find the y intercept we know it is the point that the line touches the y axis which is 5.

Now for the slope, the slope is how far each points are from each other on a line so to find the slope we can use the following formula [tex]\frac{y^2-y^1}{x^2-x^1}[/tex].

So to do this we need two points that are on the line we can use (-6,0) and (6,10).

So y2 is 10 and y1 is 0 so 10-0 is 10 and 6 - -6 is 12 so the slope is 10/12 and we have to simplify it to 5/6 so the slope is 5/6 and now we have to put it in slope intercept -> [tex]y=\frac{5}{6}x+5[/tex]

Answer:

The answer is option D.

Step-by-step explanation:

Because -3/-5 = 3/5 since the negative sign cancel each other.

Hope this helps you

Answer:

The fourth  option

Step-by-step explanation:

-3/5 is the same as - 3/5 or 3/-5 (it doesn't matter where the negative sign goes-on the side, numerator, or denominator)

-(-3/-5) is basically negative of -3/-5

-3/-5 is the not the same as -3/5

Answer:

4th Graph

Step-by-step explanation:

Step 1: Find (f + g)(x)

-x² + 3x + 5 + x² + 2x

3x + 5 + 2x

5x + 5

Step 2: Graph

Answer:

option d on edge trash

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

If you were to divide a negative number by a negative number, or multiply a negative number by a negative number, you would change the sign to positive as two negatives make a positive.

Answer:

False

Step-by-step explanation:

if you multiply two negative integers, you will get a positive result

For example

(-1) x (-2) = 2   (the sign of the answer is different from the sign of the two negative integers that we multiplied)

Answer:

Step-by-step explanation:

Let s represent the speed of the bus.

From the information given, the bus needs to cover a distance of 240 km in less than 5 hours. The formula for calculating the speed of the bus, s is expressed as

Speed, s = distance covered by the bus/ time taken to cover the distance

Therefore,

Speed, s = 240/5 = 48 km/hr

A higher speed would ensure the bus covers the distance in less than 5 hours. Therefore, the inequality that represents the speed (s) of the bus would be

s ≥ 48