Screenshot below will hold the question.

Answer:

a=-54/7

Step-by-step explanation:

-35=5+7(a+2)

by opening the bracket we have

-35=5+7a+14

-35=7a+19

collect like terms

we have:

-35-19=7a

-54=7a

a=-54/7

Answer:

a = -54/7

Step-by-step explanation:

multiply 7 with the number in brackets

-35 = 5 + 7(a + 2)

-35 = 5 + 7a + 14

then add the numbers without symbols

-35 = 19 + 7a

make a the subject

-7a = 19 + 35

-7a = 54

divide the subject with the same number + the answer

-7a ÷ -7 = 54 ÷ -7

a = -54/7 or -7 5/7

hope this helps :)

The surface area of the new toy is given as follows:

1,439 in².

The surface area of a figure is given by the sum of the surface area of all it's compositions. This figure is given by a cylinder and a rectangular prism.

The surface area of a cylinder with radius r and height h is given by the following formula:

[tex]S = 2\pi r(r + h)[/tex]

In this problem, the dimensions are:

r = 3 in, h = 16 in.

Hence:

[tex]S = 2\pi \times 3(3 + 19) = 132\pi[/tex]

The surface area of a rectangular prism of length l, width w and height h is given as follows:

[tex]S = 2(lw + lh + wh)[/tex]

In this problem, the dimensions are:

l = 24 in, h = 10 in, w = 8 in.

Hence the surface area is:

S = 2 x (24 x 10 + 24 x 8 + 10 x 8) = 1024 in²

It is the sum of the surface areas, hence:

[tex]132\pi + 1024 = 1439 \text{in}^2[/tex]

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Answer: Here you go :)

Step-by-step explanation:

Hope it helps!

The expression is simplified to give 2 ( m² + m + 2Im ) = 0

Given the expression;

(1+m)²= (1-m)²+ 4lm,​

Expand the expression

( 1 +m) ( 1 + m) = ( 1 + m) ( 1 - m) + 4Im

1 + m + m + m² = 1 - m + m - m² + 4Im

collect like terms

1 + 2m + m² = 1 - m² + 4Im

1 - 1 + m² + m² + 2m + 4Im

2m² + 2m + 4lm = 0

simplify

2 ( m² + m + 2Im ) = 0

Thus, the expression is simplified to give 2 ( m² + m + 2Im ) = 0

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Answer:

yes dear u need not to pay before viewing answer

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Carey's weekly salary before tax is  $1300.

The mathematical operation that would be used to determine the required value is division. Division is a mathematical operation that entails grouping a number into equal parts using another number.

In order to determine Carey's weekly salary before tax, divide the yearly salary by the number of weeks in a year.

Carey's weekly salary before tax = yearly salary / number of weeks in a year

$67,600 / 52 = $1300

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Answer:

9900

Step-by-step explanation:

You start with 300, and add 300 32 times (once for every 3 months in 8 years).

[tex]300+9600=9900[/tex]

Answer:

15 quarters, 10 nickels

Step-by-step explanation:

[tex]q+n=25[/tex]

[tex]0.25q+0.05n=4.25[/tex]

multiply the first equation by -0.25 and add the second equation to it

[tex]-0.25q-0.25n=-6.25\\0.25q+0.05n=4.25[/tex]
________________
                [tex]-0.2n=-2[/tex]

[tex]n=\frac{-2}{-0.2} =10[/tex]   has 10 nickels

[tex]q=25-n=25-10=15[/tex]  has 15 quarters

10(.05) +15(0.25) = 0.5 + 3.75 = 4.25

Hope this helps

Step-by-step explanation:

1 meter = 1000 mm

the area of 1.6 m² means the side length of the square is

sqrt(1.6) = 1.264911064... m = 1,264.911064... mm

to create a square out of the rectangular pattern he needs to put e.g. 42 patterns along the 45 mm side and stack 45 patterns on top of the 42 mm side.

the minimum number of needed patterns we get via the last common multiple (LCM) of 42 and 45.

for this we use the prime factorization :

45 ÷ 2 no

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 3 no

5 ÷ 5 = 1

45 = 3² × 5¹

42 ÷ 2 = 21

21 ÷ 2 no

21 ÷ 3 = 7

7 ÷ 3 no

7 ÷ 5 no

7 ÷ 7 = 1

42 = 2¹ × 3¹ × 7¹

the LCM is the product of the longest streaks of each used prime factor.

LCM(42, 45) = 2¹ × 3² × 5¹ × 7¹ = 2×9×5×7 = 630

(i) he needs 210 patterns to form the smallest square.

this will be

14×45 mm on one side = 630 mm

15×42 mm on the other side = 630 mm

14×15 = 210 patterns.

(ii)

the limit per side length is as established

1,264.911064... mm

starting with the minimum of 630 mm how often can we add 42 mm in one direction and 45 mm in the other, and keep a 15 : 14 ratio between these numbers ?

and we need integer numbers, as we cannot use parts of the patterns (only full patterns).

45 × x <= 1264

x <= 1264/45 = 28.08888888... = integer 28

42 × y <= 1264

y <= 1264/42 = 30.0952381... = integer 30

30/28 = 15/14

so, the ratio is maintained for these numbers.

that means as maximum we can put

30×28 = 840 patterns as square inside the max. allowed area.

the dimensions of this max. square are therefore

30×42 = 1260 mm

28×45 = 1260 mm

the area of this square is then

1260mm × 1260 mm = 1,587,600 mm² = 1.5876 m²

Answer:

14ft

Step-by-step explanation:

12 yard pipe equals 36ft. Divided equally 3 times gives 3 pipes at 12ft per pipe. 2 of those are divided in half, making 4 6ft pipes. 1 of the 6ft pipes is cut into 3 2ft pipes. you now have 3 pipes at 2ft, 3 pipes at 6ft and 1 pipe at 12ft. the longest 2 pieces are 12ft and 6ft making 18ft. 2 shoetest pieces equal 4ft. 18ft minus 4ft equals 14ft.

Answer:

71

Step-by-step explanation:

Evaluate for x=12

(8)(12)−25

(8)(12)−25

=71

Answer:

71

Step-by-step explanation:

To evaluate [tex]8x - 25[/tex] when [tex]x = 12[/tex], we have to replace x with 12 in the expression:

[tex]8x - 25[/tex]

⇒ [tex]8(12) -25[/tex]

⇒ [tex]96 - 25[/tex]

⇒ [tex]\bf 71[/tex]

The solution to the given simultaneous equation; x + 2y = -4, 2x + 5y = 1 using substitution method is x = -22 and y = 9

x + 2y = -4

2x + 5y = 1

Using Substitution method

From equation (1)

x = -4 - 2y

Substitute x = -4 - 2y into equation (2)

2x + 5y = 1

2(-4 - 2y) + 5y = 1

-8 - 4y + 5y = 1

- 4y + 5y = 1 + 8

y = 9

Substitute y = 9 into

x + 2y = -4

x + 2(9) = -4

x + 18 = -4

x = -4 - 18

x = - 22

Therefore, the solution to the given simultaneous equation; x + 2y = -4, 2x + 5y = 1 using substitution method is x = -22 and y = 9

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Using the binomial distribution, there is a 0.3474 = 34.74% probability of getting one wrong number.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are given by:

p = 0.15, n = 10.

The probability of getting one wrong number is P(X = 1), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

P(X = 1) = C(10,1) x (0.15)¹ x (0.85)^9 = 0.3474

0.3474 = 34.74% probability of getting one wrong number.

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Answer:

c

Step-by-step explanation:

The measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

In the figure, lines BD and QS are parallel. Two parallel lines B D, and Q S are intersected by a line AT at C, and R respectively such that the angle ∠DCR is 77 degrees.

We know that the angle ∠DCR & ∠SRT and ∠DCR & ∠SRT are corresponding angles. Then they are equal to each other.

∠DCR = ∠SRT = 77°

∠CRQ = ∠CRS

We know that the angle ∠CRQ and ∠CRS are supplementary angles. Then we have

∠CRQ + ∠SRT = 180°

∠CRQ + 77° = 180°

∠CRQ = 103°

Then the measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.

The diagram is given below.

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Answer:

(4,8)

hi hi hi hi hi hi hi hi

Answer:

37.5

Step-by-step explanation:

So whenever you want to find "x" percent of a number, you just do: [tex]\frac{x}{100} * n = \text{x\% of n}[/tex]. You're essentially converting the percentage to it's decimal value by dividing by 100.

Given this information, we're solving for x, instead of x% of n. In this case n = 56,000, and x% of 56,000 is 21,000

[tex]\frac{x}{100} * 56000 = 2100[/tex]

Divide both sides by 56,000

[tex]\frac{x}{100} = \frac{21,000}{56,000}[/tex]

Multiply both sides by 100

[tex]x = 100(\frac{21,000}{56,000})[/tex]

Simplify:

[tex]x = 37.5\%[/tex]

This can be generally thought of as:

[tex]x=100(\frac{part}{whole})[/tex]

where part = partial amount, or how much is after finding what x% is of the whole amount, but in this case we know what it is, we just don't know what the "x" percent is.

We get $593,940

Answer:

Solution Given:

1 second = $ 521

19 minutes=19*60=1140 seconds

1140 seconds =$521*1140 =$593,940

Answer:

$593,940

Step-by-step explanation:

$521 for every second

First, you need to multiply 60 with 19, since there are 60 seconds in a minute.

We get: 60 × 19 = 1140

Now multiply $521 with 1140

We get: 521 × 19 = 593,940

Final result: $593,940

Hope this helps :)

Answer:

C

Step-by-step explanation:

[tex]\cos E=\frac{11}{18} \\ \\ E=\cos^{-1} \left(\frac{11}{18} \right) \\ \\ E \approx 52.33^{\circ}[/tex]

The second number line best shows how to solve –4 – (–8). This can be obtained by finding the value of –4 – (–8) and checking which number line has the required arrow mark.

The value of  –4 – (–8) is obtained.

–4 – (–8) =  –4 + 8

–4 – (–8) = 4

The arrow should move from zero to - 4 and the second arrow should move from - 4 to 4.

From the question given the number lines,

The first arrow is moving from zero to - 4.

First condition is satisfied.

The second arrow is moving from - 4 to  8.

Second condition is not satisfied.

The first arrow is moving from zero to - 4.

First condition is satisfied.

The second arrow is moving from - 4 to  4.

Second condition is satisfied.

Hence the second number line best shows how to solve –4 – (–8).

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Answer: 9 and 2/3 cases  

Step-by-step explanation:

6 goes into 58 9 times to make 54 so makes 4 left over 4/6 simplified makes 2/3.

To ship 58 items with 6 items per case, you will need 9 complete cases and 1 additional case with the remaining 4 items, making a total of 10 cases.

We have,

To find the number of cases required to ship 58 items when there are 6 items per case, we can use division.

Number of cases = Total items / Items per case

Number of cases = 58 items / 6 items per case

Number of cases = 9 with a remainder of 4

When we divide 58 items by 6 items per case, we get 9 with a remainder of 4.

This means that 9 cases can be fully filled with 6 items each, and there will be 4 items left that won't fit in a complete case.

Therefore,

To ship 58 items with 6 items per case, you will need 9 complete cases and 1 additional case with the remaining 4 items, making a total of 10 cases.

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The complete question:

How many cases are required to ship 58 items if there are 6 items per case?

The volume of the cylinder in discuss in which case, the radius of the cylinder is 3 inches and the height is inches is; V = 141.3in³.

The cylinder in discuss according to the task content has radius, 3 inches and height, 5 inches.

Since the volume of a cylinder by convention is given as; V = πr²h

Therefore, the volume of the cylinder in discuss is;

V = π (3²)×5

V = 3.14 × 45

V = 141.3in³

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If a /b = p/q, then (a + b)/b = b/(a+d) exists FALSE.

Let a, b, c, d be the four numbers, then

if a : b = c : d then (a + b) : b :: (c + d) : d.

If a : b :: c : d then (a - b) : b :: (c - d) : d.

Given equation,

[tex]$\Rightarrow \frac{a}{b}=\frac{p}{q}$$[/tex]

Adding 1 on both sides of the equation, we get

[tex]$&\Rightarrow \frac{a}{b}+1=\frac{p}{q}+1 \\[/tex]

[tex]$&\Rightarrow \frac{a+b}{b}=\frac{p+q}{q}[/tex]

This rule exists also comprehended as the Componendo property of fractions.

Therefore, [tex]$\frac{a+b}{b}=\frac{p+q}{q}$$[/tex] then a = pb + q but the hypothesis says that

a = (p+b) / q.

If a /b = p/q, then (a + b)/b = b/(a+d) exists FALSE.

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Without using general formula we will solve it in bit lengthy manner

For first half

Time=Distance/Speed

For second half

Time

So

Average speed

Option C

The answer is 412.3 km/h.

The formula to find average velocity is :

[tex]\boxed {V_{avg} = \frac{d_{1}+d_{2}}{t_{1}+t_{2}}}[/tex]

Let's find t₁ and t₂.

Now, let's substitute in the formula to get the answer.

The volume of the solid is which is a cone is 100.48 [tex]km^{3}[/tex].

Given a cone of radius 4 km and height being 6 km.

We are told to find the volume of the cone.

Volume is basically the amount of a substance that a container can hold in its capacity.Its value cannot be equal to zero or negative. It is basically amount of filling in a container.

Volume of cone is 1/3 [tex]\pi r^{2} h[/tex].

Volume =1/3 [tex]\pi 4^{2} *6[/tex]

=1/3 π*16*6

=32π

=32*3.14

=100.48[tex]km^{3}[/tex]

Hence if the radius of the cone is 4 km and height be 6 km then the volume of the cone is 100.48[tex]km^{3}[/tex].

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The correct option regarding Talia factoring is given by:

Talia needs to factor out a negative from one of the groups so the binomials will be the same.

The expression is given by:

(15x² - 3x) + (-20x + 4).

Her first step was:

3x(5x - 1) + 4(-5x + 1)

After that, she did not factor out anything more out of the expression. However, looking at the two terms of the addition, we can realize that:

(-5x + 1) = -(5x - 1), hence she should factor out the negative.

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Answer:

$1137.87

Step-by-step explanation:

Frist, we will find the hourly rate.

Given 15 hours = $502,

1 hour = [tex]\frac{502}{15} \\[/tex] = [tex]33\frac{7}{15}[/tex]

Note: Will leave the rate as a fraction as to maintain maximum accuracy.

34 hours = [tex]33\frac{7}{15}*34[/tex] = $1137.87 (nearest cent)

An example of an exponential graph function has been attached and its' properties are as below.

The general formula for exponential functions is: f(x) = aˣ, a > 0, a ≠ 1.

The reasons for the restrictions are because;

If a ≤ 0, then when you raise it to a rational power, you may not get a real number.

The graph of an exponential function y = 2ˣ is shown in the attached file. Here are some properties of the exponential function when the base is greater than 1.

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Answer:

Dependent variable: time(months) or [tex]t[/tex]

Independent variable: 6

Step-by-step explanation:

[tex]h=24+6t[/tex]

(h=height)

Answer:

y = 1/3x - 3

Step-by-step explanation:

We can find the equation of the line, by finding the slope and combine with our y-intercept (-3).

We need to use the slope formula to find the slope.

Thus, we have (-3 - (-2)) / 0 - 3 = -1/-3 = 1/3

So our equation is y = -1/3x - 3