Factor the expression:
15x-6xy

Answer:

x + x - x = x

explanation:

give us the actual formula lol

Answer: 59

Step-by-step explanation:

The expression that is equivalent to the perimeter of the rectangle in the image shown is, 6x + 8.

To find the perimeter of a rectangle, add all the four sides of the rectangle. The following formula can be used:

Perimeter (P) = 2(length + width).

In the rectangle shown below, the dimensions are:

Length of rectangle = 2x + 3

Width of rectangle = x + 1

Substitute into the perimeter each expression of the dimensions:

Perimeter = 2[(2x + 3) + (x + 1)]

Open the parentheses by applying the distributive property of equality:

Perimeter = 2(2x + 3 + x + 1)

= 2(3x + 4)

= 2(3x) +2(4)

= 6x + 8

Therefore, the expression is, 6x + 8.

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Answer:

$0.10 (nearest cent)

10.5¢

Step-by-step explanation:

Given:

To find the approximate unit price per ounce, divide the cost of the can by the number of ounces in the can:

[tex]\implies \dfrac{0.89}{8.5}=0.104705882...[/tex]

Therefore, the approximate unit price per ounce is $0.10 (nearest cent) or 10.5¢ (nearest half cent).

Dimensions of the Rectangle are : 16 feet by 13 feet .

A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal . A rectangle has two dimensions. we can measure its length and, perpendicular to that, its width.

Rectangle is 3 feet longer than it is wide and its area is 208 sq-feet .

Area of Rectangle = l×b  ( Where l = length , b = breadth )

Therefore , Let X be the the width of rectangle . then from given it's length is (X+3).

∴ X × (X+3) = 208

∴ [tex]x^{2}[/tex]+3X-208 = 0

(X+16)(X-13) = 0

X = -16 & X = 13

Distance can't be negative so Width = X = 13 feet.

∴ Length = X+3 = 16 feet.

Thus the Dimensions are 16 feet by 13 feet .

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Answer:

x ≥ 72/5

8.6 ≤ x -5 4/5= 8.6 ≤ x -29/5

8.6 ≤ x -29/5= x ≥ 72/5

1. f(x) - cubic function -- polynomial , g(x) - linear function

similar

The function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y-intercept = 4

x - intercepts = -2.68

Function g(x)

Domain: x > 0

Range: -4 < y < ∞

y - intercept = -4

x - intercepts = none

By comparing the key features above, we can conclude that the common features in both functions are their range

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Answer:

-2

Step-by-step explanation:

Given,

g(x) = f(4)

or, 2 - 4x = 3*4 - 2

or, 2 - 4x = 10

or, 2 - 10 = 4x

or, -8 = 4x

or, x = -2

The non-real roots of the polynomial x³ - 10x² + 29x - 30  are; x = 2 + i or 2 - i

We are given the polynomial as;

x³ - 10x² + 29x - 30

We are told that the real root of the polynomial is -6. Thus, (x + 6) is a factor of the polynomial.

Now, we can use polynomial long division to get;

x³  -  10x²  +  29x  -  30

- divisor  * x²     x³  -  6x²        

remainder      -  4x²  +  29x  -  30

- divisor  * -4x¹     -  4x²  +  24x    

remainder             5x  -  30

- divisor  * 5x⁰             5x  -  30

remainder                0

Quotient :  x² - 4x + 5  Remainder:  0

          x²    -    4x   +   5_______

(x + 6) | x³  -  10x²  +  29x  -  30

         -  x³  -  6x²

                     -4x²  +  29x  -  30

                   -  - 4x²  +  24x

                                    5x  -  30

                                 -  5x -   30

                                             0

Now, using quadratic calculator to find the roots of the quotient, we get;

x = 2 + i or 2 - i

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By evaluating a revenue equation, we will see that she earned $139 last week.

We know that Isha is a pet sitter, and she earns $5 for each cat and $12 for each dog.

So, if she pet sats for x cats and y dogs, the revenue will be:

R(x, y) = $5*x + $12*y

In this case we know that she pet sat for 11 cats and 7 dogs, then we have:

x = 11

y = 7

So we need to evaluate the above revenue function, we will get:

R(11, 7) = $5*11 + $12*7

R(11, 7) = $55 + $84

R(11, 7) = $139

Isha earned $139 last week.

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Answer:

Step-by-step explanation:

[tex]\frac{22w}{55}[/tex]

divide both side by 11

[tex]\frac{2w}{5}[/tex]

The sum of the two complex numbers will give:

(-4 + i) + (10 - 5i) = 6 - 4i

So the correct option is the third one.

Let's assume we have two complex numbers which are:

A = a + bi

B = c + di

The sum between these two complex numbers is:

A + B = (a + bi) + (c + di)

Taking i as a common factor we can rewrite:

(a + bi) + (c + di) = a + c + (b + d)i

And that is the general sum.

Here we want to solve:

(-4 + i) + (10 - 5i)

Again, if we take i as a common factor we can rewrite:

-4 + 10 + (1 - 5)*i

6 - 4i

So the correct option is the third one.

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The volume of this shape is 628 cm³.

What is a volume?

It is given that,

r=5

h=8

Then volume=π(5²)×8

                     =3.14×25×8

                     =628 cm³

Hence, The volume of this shape is 628 cm³.

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Answer:

[tex]60[/tex]

Step-by-step explanation:

Using the exterior angle theorem, [tex]y=35^{\circ}+25^{\circ}[/tex].

Answer:

10x²+8x-6

Step-by-step explanation:

5x²+4x+5x²×2+4x-3

=10x²×2+8x-3

=10x²+8x-6

After solving the equation the length of AB is [tex]2\sqrt{3}[/tex]

What do you mean by trigonometry?

Trigonometry  “triangle” and  “measure”) is a branch of mathematics that studies the relationship between the side lengths and angles of triangles.

A trigonometric ratio is the ratio between the edges of a right triangle.

The sine function (sin) defined as the ratio of the opposite side of the angle to the hypotenuse.

In the given triangle ABC , use sin ratio to find AB.

tan θ = P/B

tan 30 = AB/6

[tex]\frac{1}{\sqrt{3} } =AB/6[/tex]

AB = [tex]\frac{6}{\sqrt{3} }[/tex] = [tex]\frac{6}{\sqrt{3} }\times \frac{\sqrt{3}}{\sqrt{3}}= \frac{6\sqrt{3}}{3}=2\sqrt{3}[/tex]

Therefore, length of AB is [tex]2\sqrt{3}[/tex]

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The square root of 15 is approximately 4.

To approximate the square root of 15, we can find the perfect squares that are closest to 15. The perfect squares that are closest to 15 are 9 and 16. Since 15 is closer to 16, we can say that the square root of 15 is slightly less than 4.

Another approach could be:

The square root of 15 is approximately 3.87. Rounding to the nearest integer gives us 4. To round a number, we look at the number following the place value we are rounding to. If it is greater than or equal to 5, we round up. If it is less than 5, we round down. In this case, the digit following the ones place is 8, which is greater than 5, so we round up to 4.

Answer:

D

Step-by-step explanation:

base= y2-y1

height = x3-x1

so (1/2)×(y2-y1)×(x3-x1)

The number of volunteers recruited for the first 5 weeks is; 486 people

A geometric sequence is defined as a sequence in which the result of the division of consecutive terms is always the same, called common ratio r.

The nth term of a geometric sequence is given by:

aₙ = a₁rⁿ⁻¹

where;

a₁ is the first term

r is the common ratio

In this question, on the first week there are 6 people, and since each new people involve three more, the common ratio is 3, hence the parameters for the geometric sequence are:

a₁ = 6

r = 3

Hence the number of people after n weeks is:

aₙ = 6(3)ⁿ⁻¹

Thus, the number of volunteers recruited for the first 5 weeks is;

a₅ = 6(3)⁵⁻¹

a₅ = 6 * 3⁴

a₅ = 486

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It will take 38 weeks a student to save enough money for the ticket.

Mathematical operations come in several types, with division being one. The phrases or numbers are divided into the same number of components during this operation.

Given,

a student must save at least $675 plus 3% tax to buy a round-trip ticket to London.

3% of 675

= 3 x 675 / 100

= 20.25

The student has $98 saved already.

Now student needs ($675 - $98) + 20.25 = $577 + 20.25

= $597.25

If the student earns $32 per week and plans to save half of the earnings each week toward the ticket cost.

That means, $32 / 2 = $16 per week.

To find the amount of enough money:

Divide $597.25 by $16.

597.25 /16

= 37.328125

≈ 38 weeks

Therefore, student will save for 38 weeks.

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Answer: x = 0.375

Step-by-step explanation:

Equation: 8x + 4 = 7

Subtract 4 on both sides

8x = 3

Divide by 8 on both sides

x = 3/8 is 0.375 decimal

x = 0.375 (0.38 round-up)

Answer:

Step-by-step explanation:

Four more than the product of a number and 8 is equal to 7.

4 + 8x = 7

8x = 7 - 4

8x = 3

x = 3/8

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

check

4 + 8 x 3/8 = 7

4 + 3 = 7

7 = 7

the answer is good

The statement "In a symmetric distribution, the first quartile will always equal the third quartile" is true

The given statement is "In a symmetric distribution, the first quartile will always equal the third quartile"

The symmetric distribution is defined as the distribution that occurs when the values of variables appear at regular frequencies. Usually the mean, mode and the median all are same point in the symmetric distribution.

In the symmetric distribution the left side of the graph will be the mirror image of the right hand side of the graph. So the first quartile will always equal the third quartile.

Therefore, the given statement is true

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Answer:

D

Step-by-step explanation:

(7+-6)/2

(7-6)/2

1/2

(-6+(-8)/2

(-6-8)/2

-14/2

-7

(.5,-7)

The decimal point is to be placed three places to the left.

What are decimal numbers?

When we divide a whole number into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.

Given that, in the question, the product of a decimal number between 350 and 400 and 0.48 results in the numbers 182136. As 0.48 is just 48/100, let's take a decimal number between 350 and 400.

If the number is 370.1, for example, we can write it as 3701/10 because it has one decimal point.

Our denominator will be 1000, because both the denominators are 100 and 10, which is equivalent three decimal places to the left of the result when we multiply 48/100 by 3701/10.

The result provided to us should therefore be written as 182.136, with the decimal point moved three spaces to the left.

The decimal point is to be placed three places to the left.

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Answer:

The unit rate in cost per roll is $0.83 per roll.

what is unit rate? how to calculate unit rate of cost?

Unit rate is a type of ratio that compares the quantity of two different types of units. It is calculated by dividing the cost of a given quantity of an item by the number of units in that quantity. For example, if a bag of apples costs $4 and there are 5 apples in the bag, the unit rate of cost for the apples is $0.80 per apple ($4/5= $0.80). Another example would be if a carton of eggs costs $2.50 and there are 10 eggs in the carton, the unit rate of cost for the eggs would be $0.25 per egg ($2.50/10 = $0.25). Unit rate is a useful tool for understanding the cost of items, especially when comparing items of different sizes or quantities. It can also be used to calculate the cost of a certain number of items, as long as the unit rate is known.

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Answer:

cosβ = -1/2

Step-by-step explanation:

Since cos2β = 3/4 and β is in quadrant III, the value of cosβ must be negative. We can find the exact value of cosβ by using the identity cos2β = 2cos^2β - 1. Substituting 3/4 for cos2β and solving for cosβ, we get:

3/4 = 2cos^2β - 1

cos^2β = 1/4

cosβ = 1/2 or -1/2

Since cosβ is negative in quadrant III, the value of cosβ is -1/2. Thus, the answer is cosβ = -1/2.

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Answer: Therefore, the correct formula is {a}_{21}  = 2000 * 0.5^{20}.

Step-by-step explanation:

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant factor called the common ratio. In this case, the common ratio is 0.5, since each term is found by dividing the previous term by 2.

To find the nth term in a geometric sequence, we can use the formula:

a_n = a_1 * r^(n-1)

where a_1 is the first term in the sequence, a_n is the nth term, and r is the common ratio. In our case, the first term is 2000, the nth term is the 21st term, and the common ratio is 0.5. Therefore, the formula we need to use is:

a_21 = 2000 * 0.5^(21-1)

    = 2000 * 0.5^20

Therefore, the correct formula is {a}_{21}  = 2000 * 0.5^{20}.