Find the value of each expression in simplest form. Show all work

Answer:

x= -3 straight up

Step-by-step explanation:

2x+9 = 7x + 24

simplify

x= -3

Integrate both sides with respect to t :

∫ dy/dt dt = ∫ -12t ² dt

y(t) = -4t ³ + C

Use the initial condition to solve for C :

5 = -4•0³+ C

C = 5

So

y(t) = -4t ³ + 5

and the answer is D.

Alternatively, you can directly apply the fundamental theorem of calculus:

[tex]\dfrac{\mathrm dy}{\mathrm dt}=-12t^2\implies y(t)=y(0)+\displaystyle\int_0^t -12u^2\,\mathrm du[/tex]

[tex]\implies y(t)=5-4u^3\bigg|_0^t[/tex]

[tex]\implies y(t)=5-4t^3[/tex]

Answer:

4

Step-by-step explanation:

Significant figures are whole numbers, without any decimals, the four numbers are therefore significant.

Answer:

∠2=37°

Step-by-step explanation:

Given:

∠1=4x°

∠2=∠4 (Vertical Angle Theorem)

∠3=90°

∠4=(3x+1)°

∠4=∠2 (Vertical Angle Theorem)

∠1+∠2+∠3=180° (We use this equation in the next step)

∠1+∠3+∠4=180°

Thus, ∠2=(3x+1)°, making:

(4x)°+(3x+1)°+90°=180°

7x+91=180

7x=89

x=12

This means:

∠1=4x=4(12)=48°

∠2=3x+1=3(12)+1=37°

∠3=90°

∠4=3x+1=3(12)+1=37°

Answer:

1/6, 2/3, 15/18

Step-by-step explanation:

get a common denominator

2/3 times 6

15/18 times 1

1/6 times 3

new fractions : 12/18, 15/18, 3/18

so it would be 3/18, 12/18, 15/18

then just revert it back to the original fraction and you have your answer

Answer:

There were total 2900 seats in the theater.

Step-by-step explanation:

Given that:

Seats filled by students = 1247 seats

Vacant seats = 57%

Total percentage of seats = 100%

Percentage of seats filled by students = (100-57)%

Percentage of seats filled by students = 43%

Let,

x be the total number of seats.

43% of x = 1247

[tex]\frac{43}{100}x=1247\\0.43x=1247[/tex]

Dividing both sides by 0.43

[tex]\frac{0.43x}{0.43}=\frac{1247}{0.43}\\x=2900[/tex]

Hence,

There were total 2900 seats in the theater.

Answer:

37x4

4x30=120

4x7=28

120+28=148

this is how i show my work. it has never failed me

Step-by-step explanation:

37×4

4×30

4×7=28

120+28=148

Answer:

82.88%

Step-by-step explanation:

Given that:

Mean (μ) = 16.7 pounds

Standard deviation (σ) = 3.8 pounds

Number of pounds eaten = 11.5 = x

P(11.5 ≥ x ≤11.5)

P(x ≤ 11.5) :

Zscore = (x - μ) / σ

Zscore = (11.5 - 16.7) / 3.8

Zscore = - 5. 2 / 3.8

Zscore = −1.368421

P(Z ≤ - 1.3684) = 0.085593 (Z probability calculator)

P(x ≥ 11.5) ;

Zscore = (x - μ) / σ

Zscore = (11.5 - 16.7) / 3.8

Zscore = - 5. 2 / 3.8

Zscore = −1.368421

P(Z ≥ - 1.3684) = 0.91441 (Z probability calculator)

P(Z ≥ - 1.3684) - P(Z ≤ - 1.3684)

0.91441 - 0.085593 = 0.828817

0.828817 * 100% = 82.88%

Answer:

.77 is the answer

Step-by-step explanation:

Answer:

0.77 is the anwser:)))))))))))

Answer:

There is significant evidence at 0.05

Step-by-step explanation:

Given that:

After performing hypothesis., with confidence level being α = 0.05 ; The researcher decides to reject the Null. The conclusion will be ;

There is significant evidence to reject the Null at confidence level of 0.05

Answer:

FIFTY - FIVE THOUSAND FIVE HUNDRED AND FIFTY-FIVE

Step-by-step explanation:

Answer: The rectangular lot is 12x8 meters

Step-by-step explanation: Perimeter of a geometric figure is the sum of all its sides.

A rectangle is a quadrilateral that has opposite sides parallel and equal, which means, and suppose l is length and w is width:

P = 2l + 2w

The perimeter of the lot is 40m, thus:

2l + 2w = 40

Area of a rectangle is calculated as:

A = length x width

The lot has area of 96, thus:

lw = 96

Solving the system of equations:

2l + 2w = 40 (1)

lw = 96 (2)

Isolate l from (1):

2l = 40 - 2w

l = 20 - w (3)

Substitute (3) in (2):

w(20-w) = 96

[tex]-w^{2}+20w=96[/tex]

[tex]-w^{2}+20w-96=0[/tex]

There are many methods to determine the roots of a quadratic equation. One of them is using the sum and product of those roots.

[tex]sum = \frac{-b}{a}[/tex]

[tex]sum=\frac{-20}{-1}[/tex]

sum = 20

[tex]prod=\frac{c}{a}[/tex]

[tex]prod=\frac{-96}{-1}[/tex]

prod = 96

The roots of the quadratic equation are numbers which the sum results in 20 and product is 96:

w₁ = 12

w₂ = 8

If we substitute w to find l, the numbers will be l₁ = 8 and l₂ = 12.

Since length is bigger than width, the rectangular lot Mang Jose has to plant mushrooms measures 12m in length and 8m  in width

Answer:

0.05 or 5/100

Step-by-step explanation:

Answer:

Answer:

81

Step-by-step explanation:

9 × -9 = -81

-81 × -1 = 81

Answer:

81

Step-by-step explanation:

9*-9=- 81

-81*-1= 81

Replace c with 50 and solve for f:

50 = 5/9(f-32)

Multiply both sides by 9:

450 = 5(f-32)

Distribute the right side:

450 = 5f -160

Add 160 to both sides:

610 = 5f

Divide both sides by5:

F =610/5

F = 122

Answer:

122 = F

Step-by-step explanation:

C = 5/9 ( F - 32)

Let C = 50

50 = 5/9 ( F - 32)

Multiply each side by 9/5

9/5 *50 = 9/5 *5/9 ( F - 32)

90 =  ( F - 32)

Add 32 to each side

90+32 = F -32+32

122 = F

Answer:

55

Step-by-step explanation:

180 - 82 - 43 = 55

I think this is right! I hope you have a good day and stay safe!

Answer:

1 gram

Step-by-step explanation:

Rounded, it is one gram or one whole, you round the whole number.

Answer:

Answer:

6 days

210 pages

Step-by-step explanation:

As stipulated by the question, let the number of days Amir has been reading be x and the number of pages he had read to be y.

Now since he reads 35 pages per day.

Then mathematically;

y = 35x

For Jesse, He started reading a day before, this means that the number of days he had read would be x + 1. Since he reads 30 per day, the total number of pages he would have read is 30(x+1)

To find the number of days which is x, we have to assume that at a point in time, the number of books they would have read would be the same meaning that

Also; y = 30(x + 1)

Equating the two situations

35x = 30(x + 1)

35x = 30x + 30

35x -30x = 30

5x = 30

x = 30/5

x = 6 days

This means that it will take Amir 6 days to catch Jese.

The number of books they would have read by then is y = 35x = 30(x + 1)

= 35 * 6 or 30(6+1)

= 210

Step-by-step explanation:

Answer: dude above me copied

Step-by-step explanation:

1. y = 35x

2. y = 30x + 1

3. y = 35x

   y = 30 x + 1

4. Its more convenient to substitute y because It's easier.

    35x = 30(x + 1)

5.  35x = 30x + 1

    35x = 30x + 30

    35x -30x = 30

    5x = 30

    x = 6    (30/5 = 6)

    35 x 6 = 210 (y)

6. Both people have read 210 pages and it takes amir 6 days to catch up.

Answer:

[tex]y = 164[/tex]

Step-by-step explanation:

Given

[tex]y = 8x + 4[/tex]

Where

[tex]x = number\ of\ comic\ books[/tex]

[tex]y = total\ cost[/tex]

Required

Find y when x = 20

To do this, we simply substitute 20 for x in [tex]y = 8x + 4[/tex]

[tex]y = 8*20 + 4[/tex]

[tex]y = 160 + 4[/tex]

[tex]y = 164[/tex]

Hence, 20 comic books cost 164

Answer:

7

down

3x-6

Step-by-step explanation:

g(x)=3x-6

f(x)=3x+1

Thus, g(x) is just f(x)-7

Answer:

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

The range is the difference between the largest and smallest numbers. The mid range is the average of the largest and smallest number.

Hope this helps!

Answer:

s + r - l

Step-by-step explanation:

This is an arithmetic progression question.

The formula to get the terms of an AP is;

L_n = a + (n - 1)d

Where;

a is first term

n is number of term

d is difference between terms

Thus, second term is;

L_2 = a + d

Third term is;

L_3 = a + (3 - 1)d

L_3 = a + 2d

Similarly, L_4 = a + 3d

Now we are told that;

Sum of the first 2 numbers is s;

Sum of the second and third number is l

Sum of the last two numbers is r

Thus;

a + (a + d) = s - - - (eq 1)

(a + d) + (a + 2d) = l - - - (eq 2)

(a + 2d) + (a + 3d) = r - - - (eq 3)

Thus, sum of the first and last term will be;

L_1 + L_4 = a + (a + 3d)

Now,from earlier;

(a + 2d) = r - (a + 3d)

Also;

(a + d) = s - a

Thus, plugging them into the eq 2 gives;

(s - a) + r - (a + 3d) = l

Expanding we have;

s + r - 2a - 3d = l

d = (s + r - 2a - l)/3

Thus;

L_1 + L_4 = a + (a + (3(s + r - 2a - l)/3))

= 2a + s + r - 2a - l = s + r - l

Answer:

Each of the twin beds: 5 decorative pillows

Each of the queen beds: 11 decorative pillows

Step-by-step explanation:

Let the number of pillows used for each twin bed be x

Let the number of pillows used for each queen bed be y

she decorated 1 twin bed and 2 queen beds and used a total of 27 pillows. Thus;

x + 2y = 27 - - - (eq 1)

Also, she used

37 pillows to spruce up 3 twin beds and 2 queen beds. Thus;

3x + 2y = 37 - - - (eq 2)

From eq 1, x = 27 - 2y

Thus;

3(27 - 2y) + 2y = 37

81 - 6y + 2y = 37

81 - 4y = 37

4y = 81 - 37

4y = 44

y = 44/4

y = 11

x = 27 - 2(11)

x = 27 - 22

x = 5

Thus, she used 5 decorative pillows for each of the twin beds and 11 decorative pillows for each of the queen bed

Answer:

imm a bit sorry I could only answer the international one as the national is equal to international place value system

Step-by-step explanation:

eight hundred ninety three thousand four hundred fifty one

hth tth th h t o

8 9 3 4 5 1

I hope you understand

Answer:

60,000

Step-by-step explanation:

Jane-2000

Peter-ratio of 5=25000

Marta-ratio of 7=35000

25000+35000

60000

Answer:

$6,000

Step-by-step explanation:

If [tex]y[/tex] is the amount of money a child receives, and [tex]x[/tex] is the total amount being divided among the children, then

Jane's share:  [tex]y = \frac{4}{4+5+7} * x = \frac{4}{16}x[/tex]

Peter's share:  [tex]y = \frac{5}{4+5+7} * x = \frac{5}{16}x[/tex]

Martha's share:  [tex]y = \frac{7}{4+5+7} * x = \frac{7}{16}x[/tex]

We know Jane got $2000, so we can use that to solve for [tex]x[/tex]:

[tex]\frac{4}{16} x = 2000[/tex]

[tex]x = \frac{16}{4} * 2000 = 8000[/tex]

Plug this x value in to find how much Peter and Martha received:

[tex]\frac{5}{16} * 8000 + \frac{7}{16} * 8000 = $6000[/tex]

Answer:

C. y - 3 = -2(x - 4)

Step-by-step explanation:

The equation of the line can be written in point-slope form as y - b = m(x - a),

Where,

m = slope

(a, b) = coordinates of a point on the line.

Find slope (m) using the points (4, 3) and (5, 1)

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{5 - 4} = \frac{-2}{1} = -2 [/tex]

m = -2.

Substitute a = 4, b = 3, and m = -2, into y - b = m(x - a), the equation that best fits the graph would be:

✔️y - 3 = -2(x - 4)