Dana helped her dad build a sandbox for her younger sister. The sandbox is shaped like a rectangular prism that is 4 1 2 feet long and 4 feet wide. Dana used bags of sand to fill the sandbox 1 2 of a foot deep. Each bag contains 1 2 of a cubic foot of sand. How many bags of sand did Dana use?

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x + cos²x = 1

Consider the left side

[tex]\frac{1-tan^2x}{1+tan^2x}[/tex]

= [tex]\frac{1-\frac{sin^2x}{cos^2x} }{1+\frac{sin^2x}{cos^2x} }[/tex] ← multiply numerator/ denominator of the whole fraction by cos²x

= [tex]\frac{cos^2x-sin^2x}{cos^2x+sin^2x}[/tex]

= [tex]\frac{cos^2x-sin^2x}{1}[/tex]

= cos²x - sin²x

= cos²x - (1 - cos²x)

= cos²x - 1 + cos²x

= 2cos²x - 1

= right side , thus proven

[tex]\frac{1 - \tan^2(x)}{1 + \tan^2(x)}\\= \frac{\frac{\cos^2(x)}{\cos^2(x)} - \frac{\sin^2(x)}{\cos^2(x)}}{\frac{\cos^2(x)}{\cos^2(x)} + \frac{\sin^2(x)}{\cos^2(x)}}\\= \frac{\frac{\cos^2(x) - \sin^2(x)}{\cos^2(x)}}{\frac{\cos^2(x) + \sin^2(x)}{\cos^2(x)}}\\= \frac{\cos^2(x) - \sin^2(x)}{\cos^2(x)} \cdot \frac{\cos^2(x)}{\cos^2(x) + \sin^2(x)}\\= \frac{(\cos^2(x) - \sin^2(x)) \cdot \cos^2(x)}{\cos^2(x) \cdot (\cos^2(x) + \sin^2(x))}\\= \frac{\cos^2(x) - \sin^2(x)}{\cos^2(x) + \sin^2(x)}[/tex]

[tex]= \cos^2(x) - \sin^2(x)\\= \cos^2(x) - (1 - \cos^2(x))\\= \cos^2(x) - 1 + \cos^2(x)\\= 2\cos^2(x) - 1[/tex]

Answer:

0,6

Step-by-step explanation:

Answer: Y= -7/3x + 6

Answer:

[tex]5(n + 4)^{\frac{3}{2} }[/tex]  

I hope this helps!

Let the shorter piece be x. The longer piece is 4 times the length of the other, so it is 4x.

4x + x = 160.

5x = 160

x = 32

4x = 128

The length of the shorter piece is x, which is 32.

Answer:

Solving steps:

find the value of y when x = 1

=> y = 8(1)

multiply 8 by 1

=> y = 8

Hey there!

ORIGINAL EQUATION: y = 8x

This one should be quite easy to answer because we already have the value of x. (x = 1) all we have to do is find the y-value and where it is on the number line.

NEW EQUATION: y = 8(1)

SIMPLIFY IT!

y = 8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

$24

Step-by-step explanation:

Ava + her 3 friends = 4 people total.

The bill was $96

To split this evenly among 4 people we can divide the bill by 4.

96/4 = 24

Therefore each person would pay $24.

Hope this helps! :)

Answer:

The marathon runner runs 1 mile every 10 minutes.

Step-by-step explanation:

9/2 miles is equal to 4.5 miles. 3/4 hours is equal to 45 minutes.

Answer:

9:22

Step-by-step explanation:

Find the LCM Least common multiple of all three numbers (minutes)

3,4,5  LCM is 60

Divide each one into the LCM

60/3 = 20

60/4 =  15

60/5 =  12

Totals =82

add that to the time 8:00

82 is an Hour and 22 minute so it would be 9:22

I looked at other problems and this is how they solved it.  I hope it helps

Step-by-step explanation:

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

m = (4-0)/(0-(-8))

m = 4/8

y = mx + c

4 = (4/8)(0) + c

c = 4

Thus, the equation is y = (4/8)x + 4

Answer:40

Step-by-step explanation: because 70 times 2 = 140 and you add 40 will equal 180 because every triangle equals 180

The measure of angle m<P is 40 degrees

The given triangle is an isosceles triangle where:

m<R = m<Q

Taking the sum of the interior angles, we will have:

m<P + ,m<Q + m<R  = 180

70 + 70 + m<P = 180

m<P = 180 - 140

m<P= 40 degrees

Hence the measure of angle m<P is 40 degrees

Larn more angles in a triangle here: https://brainly.com/question/25215131

Answer: 32ft²

Step-by-step explanation:

The area of a trapezoid is given by the formula: A = [(b1+b2)/2] x h, where b1 and b2 are the two bases, and h is the height.

In our situation, b1 = 3, and b2 = 5. The height is given as 2.

Plugging these numbers into our formula:

A = (b1+b2)/2 x h

A = [(3+5)/2] x 2

A = (8/2) x 2

A = 4 x 2

A = 8ft²

8ft² is the area of one trapezoid. If Mr. Smith wants to fit 4 of these shapes into the room, the combined area will be 4 x 8 = 32ft².

Have a nice day :)

Answer:

[tex]\frac{12}{49}[/tex]

explanation:

Use the keep change flip method. This consists of literally flipping a fraction to make the denominators alike, allowing for faster solves and multiplication.

[tex]2\frac{1}{3}[/tex] is [tex]\frac{7}{3}[/tex], so flip 7/3 so it is 3/7, matching up with 4/7.

Next, multiply.

4 x 3

7 x 7

4 x 3 is 12. Write 12 as a numerator.

7 x 7 is 49. Write 49 as a denominator.

Therefore, the answer is [tex]\frac{12}{49}[/tex]

Simplifying? We cannot simplify this number due to a lack of factors.

The right answer will be both I and II

I. In the effective rate formula, n is equal to one.

II.The nominal rate is 7.918%.

Compound interest is the interest on a loan or deposit that accrues on both the initial principal and the accumulated interest from previous periods.

The formula for the compound interest is given as:

[tex]A=p(1+\dfrac{r}{n})^{nt}[/tex]

Here

A= amonut

P= principle

r=rate of interest

t=time period

n=for how much time compunded

Thus we can see in the question it is compounded annually so n = 1 and the rate is given as 7.918%

Thus the right answer will be both I and II

I. In the effective rate formula, n is equal to one.

II.The nominal rate is 7.918%.

To know more about compound interest follow

https://brainly.com/question/24924853

Given :

You decide to run at least 7.5 miles per week during the week to train for the cross-country season in the fall.

During one week, you run 2 miles on Sunday and 2.5 miles on Wednesday.

To Find :

How many more miles, m, do you need to run before the week is over.

Solution :

Total number of miles we travelled till Wednesday :

t = miles run on Sunday + miles run on Wednesday

t = 2 + 2.5 miles = 4.5 miles.

Now, number of miles remaining :

R = Total target - t

R = 7.5 - 4.5 miles

R = 3 miles.

Therefore, we need to run 3 more miles before the week is over.

Hence, this is the required solution.

Answer:

The truck will need to make 3 trips.

Step-by-step explanation:

First, we need to find the volume that the truck can carry. Using the dimensions of the truck and the volume formula, we have:

[tex]V=lwh\\V=8.5\times5\times3.5\\V=148.75\text{ ft}^3[/tex]

Since we need to move a total of 400 cubic feet, we will divide that amount by the truckload capacity (volume).

[tex]400 \div 148.75 \approx 2.689[/tex]

In context, he will need to take three truck loads: two loads will be full, and the third will not be full.

Answer: 18

Step-by-step explanation:

Answer:

No, these equations are not parallel.

Step-by-step explanation:

The equation [tex]y=0[/tex] is a vertical line. This equation, in fact, is the y-axis.

The equation [tex]x=0[/tex] is a horizontal line. This equation, in fact, is the x-axis.

These lines are perpendicular, not parallel.

Answer:

x <4

Step-by-step explanation:

hope it helps

for any question comment me ❤❤

Answer:

x = 1 and x = 3

Step-by-step explanation:

Let's solve your system by substitution.

y=2x+1;y=3x

Step: Solvey=2x+1for y:

y=2x+1

Step: Substitute2x+1foryiny=3x:

y=3x

2x+1=3x

2x+1+−3x=3x+−3x(Add -3x to both sides)

−x+1=0

−x+1+−1=0+−1(Add -1 to both sides)

−x=−1

−x

−1

=

−1

−1

(Divide both sides by -1)

x=1

Step: Substitute1forxiny=2x+1:

y=2x+1

y=(2)(1)+1

y=3(Simplify both sides of the equation)

Answer:

x=1 and y=3

Answer:

-15625

Step-by-step explanation:

Hope this helped !! :)

Have a good day.

Answer:

[tex]in standard notation \: 9 { \times 10}^{ - 4} = 0.0009[/tex]

1750 litres.............50 cars

1960 litres.............n cars

so n x 1750 = 1960 x 50

n = 98000 : 1750

n = 56

56 cars tanks will be filled

Answer:

56

Step-by-step explanation:

1750 divided by 50 to find out how much litres each car gets. =35

so 35 litres per car so divide 1960 by 35. =56

56 cars can be filled

CHECK ANSWER.

the six extra cars so 35 multiplied by 6. =210

1750+210=1960!

Answer: One triangle

Step-by-step explanation:

-The triangle's dimensions are defined and fixed.

-Given the fixed dimensions, only one unique triangle can be constructed.

-Hence, only one triangle of the dimensions 7.2cm, 6.9cm and 12.8 cm can be formed.

Answer:

1

Step-by-step explanation:

The correct shape would be a scalene triangle, which can't be bent and twisted and still have the same side lengths.

Answer:

tenths

Step-by-step explanation:

the 2 is in the ones place and the 5 is in the hundreds meaning the 3 would be in the tenths

Answer:

Yes

Step-by-step explanation:

9 can go into 8397 evenly without any remainders.

Answer:

8397/9= 933

8397 is divisible by 9 if you divide 8397 by 9 and the quotient is an integer. The easiest way to determine if 8397 is divisible by 9 is to calculate the sum of the digits in 8397. If the sum of the digits is divisible by 9, then 8397 is divisible by 9.

8+3+9+7= 27

27 is divisible by 9

Step-by-step explanation:

The total distance the bird flew in feet is 140 feet

Given the following parameters

The angle of elevation = 30 degrees

Height =  70 feet

total distance the bird flew in feet (D)

Using the SOH CAH TOA identity

sin 30 = 70/D
D = 70/sin30

D = 140eet

Hence  the total distance the bird flew in feet is 140 feet

Learn more on SOH CAH TOA here: https://brainly.com/question/20734777

Answer:

$560

Step-by-step explanation:

1/5th the original price just means 20%

20% of 700 is 140

700*.20= 140

Since it's 20% off that means subtraction

700-140=560

Hope this helps!