5. 4x2 - 31x + 21
Factoring

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\text{Calculate what fraction of 30 is 18 and convert it to percent:}\\\\\dfrac{18}{30}=\dfrac{18:6}{30:6}=\dfrac{3}{5}\\\\\dfrac{3}{5}\cdot100\%=\dfrac{300}{5}\%=60\%[/tex]

[tex]\bold{METHOD\ 2:}\\\\\begin{array}{ccc}30&-&100\%\\\\18&-&p\%\end{array}\qquad\text{cross multiply}\\\\\\(30)(p)=(18)(100)\\\\30p=1800\qquad\text{divide both sides by 30}\\\\\dfrac{30p}{30}=\dfrac{1800}{30}\\\\p=60[/tex]

Final answer:

18 is 60% of 30, calculated by dividing 18 by 30 and then multiplying the result by 100.

Explanation:

Calculating the Percentage

To determine what percentage 18 is of 30, you can use the formula for calculating percentages:

Divide the number you want to find the percentage of (18 in this case) by the total number or 'whole' value (which is 30).

Multiply the result from step 1 by 100 to find the percentage.

So, the calculation is (18 ÷ 30) × 100, which equals 60%. Therefore, 18 is 60% of 30.

Answer:

80cents per pound

Step-by-step explanation:

24 divided by 30 is .8

Answer:

19??

Step-by-step explanation:

Answer:

yes it is 19 all you have to do is add 12 and 7

Answer:

  (-1/4)(2x +5y)

Step-by-step explanation:

Multiply and divide by -1/4:

  [tex]-\frac{1}{2}x-\frac{5}{4}y=\dfrac{(-\frac{1}{4})(-\frac{1}{2}x-\frac{5}{4}y)}{-\frac{1}{4}}=\left(-\dfrac{1}{4}\right)(-4)\left(-\dfrac{1}{2}x-\dfrac{5}{4}y\right)\\\\=\left(-\dfrac{1}{4}\right)\left(2x+5y)[/tex]

Answer:

The amount which real estate agency gets is $  21,010  .

Step-by-step explanation:

Given as :

The selling price for a house = $ 382,000

The commission rate for real estate agency = 5.5 %

The commission rate for the agent = 30 %

So, the commission which real estate agency get = 5.5 % of $ 382,000

I.e the commission which real estate agency get = 0.055 × $ 382,000

Or, the commission which real estate agency get = $ 21,010

Again ,

The commission which agent get = 30 % of $ 382,000

I.e the commission which agent get = 0.3 × $ 382,000

Or, the commission which agent get = $ 114,600

Hence The amount which real estate agency gets is $  21,010  . answer

The agent earns a commission of $6,303 from the $382,000 house sale. This is calculated by first determining the real estate agency's commission of 5.5% on the sale price, which is $21,010. Then calculating 30% of this figure, which is the agent's earnings.

To calculate the total commission the agent will receive, you first have to calculate how much the real estate agency gets, and then calculate the agent's earnings based on that number.

The real estate agency's commission is 5.5% of the total sold price of the house. This can be calculated as:

(5.5 / 100) * $382,000 = $21,010

The agent then receives 30% of this amount, which you calculate as:

(30 / 100) * $21,010 = $6,303

Therefore, the agent earns a commission of $6,303 from the sale of the house.

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Answer:

75% decrease

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

Answer:

Tanya's average speed was [tex]\frac{1}{2}[/tex] laps per minutes.

Step-by-step explanation:

Tanya walked 15 laps on an indoor track in 30 minutes.

Therefore, the average speed of Tanya is [tex]\frac{15}{30} = \frac{1}{2}[/tex] laps per minutes.

Calculation:

The average speed formula is given by [tex] V = \frac{\textrm {Distance covered}}{\textrm {Number of munutes spent}}[/tex]

The distance is 15 laps.

The time is 30 minutes.

Therefore, [tex]V = \frac{15}{30}[/tex] laps per minute.

After simplification, [tex]V = \frac{1}{2}[/tex] laps per mins.

Therefore, Tanya's average speed was [tex]\frac{1}{2}[/tex] laps per minute. (Answer)

Answer:

[tex]\large\boxed{\dfrac{3x+6}{x-4}\div\dfrac{2x^2+9x+10}{x^2+4x}=\dfrac{3x(x+4)}{(x-4)(2x+5)}}[/tex]

Step-by-step explanation:

Just like that

[tex]\dfrac{3x+6}{x-4}\div\dfrac{2x^2+9x+10}{x^2+4x}=\dfrac{3x+6}{x-4}\cdot\dfrac{x^2+4x}{2x^2+9x+10}\\\\=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{2x^2+4x+5x+10}=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{2x(x+2)+5(x+2)}\\\\=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{(x+2)(2x+5)}\qquad\text{cancel}\ (x+2)\\\\=\dfrac{3x(x+4)}{(x-4)(2x+5)}[/tex]

Answer: The value of x is 40

Step-by-step explanation:

Given triangle SRT,

Angle SRT = 20 and Angle SRT = Angle STR

To find Angle STU:

We know that

The sum of all interior angles of triangle is equal to 180.

Angle SRT + Angle STR + Angle RST =180

Also, Angle SRT = Angle STR =20

20+20+Angle RST=180

Angle RST=140.

Now. The exterior angle of triangle is equal to sum of opposite interior angles of triangle,

Angle STU=4x=Angle RST+Angle SRT

4x=20+140

4x=160

x=40

Therefore, The value of x is 40

Answer: 729

Step-by-step explanation: 1st term X common ratio(desired term-1)

The 7th term in the sequence is -2187.

To find the 7th term in the sequence 1, -3, 9, -27, ..., we can observe that each term is obtained by multiplying the previous term by -3. Therefore, to find the 7th term, we start with the first term 1 and repeatedly multiply by -3:

So, the 7th term in the sequence is -2187.

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5/7 x 7/3

Multiply the numerators together and the denominators:

(5 x 7) / (7 x 3)

35/21 reduces to 5/3 = 1 2/3

There were 980 student desks originally.

Step-by-step explanation:

Number of desks purchased = 295

Desks bought for teacher = 50

Desks for students = No. of desks purchased - desks bought for teachers

Desks for students = 295 - 50 = 245

This is 1/4 of number of original student desks.

Let x be the number of original student desks.

According to statement;

[tex]\frac{1}{4}\ of\ x=245\\\frac{1}{4}x=245[/tex]

Multiplying both sides by 4;

[tex]4*\frac{1}{4}x=245*4\\x=980[/tex]

There were 980 student desks originally.

Keywords: subtraction, multiplication

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[tex](fog)(x) = -x[/tex]

Step-by-step explanation:

The composition is calculated by putting the other function in place of variable

Given

[tex]f(x) = x - 1\\g(x) = -x+1[/tex]

The composition will be:

[tex](fog)(x) = g(x) -1\\=(-x+1) -1\\=-x+1-1\\=-x[/tex]

Hence,

[tex](fog)(x) = -x[/tex]

Keywords: Composition, Functions

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Answer:

199.8°

Step-by-step explanation:

The circle has radius r = 7 ft.

Now, the circumference of the circle is given by the formula C = 2πr

So, [tex]C = 2 \times \frac{22}{7} \times 7 = 44[/tex] ft.

Now, 44 ft arc length is equivalent to 360°  

Hence, 24.42 ft arc length is equivalent to [tex]\frac{360}{44} \times 24.42 = 199.8[/tex] degree.

Therefore, the central angle is 199.8° (Answer)

Answer:

15

Step-by-step explanation:

Answer:

3*5

Step-by-step explanation:

GCF of 45 and 75 = 15

15: 1,3,5,15

3 and 5 are prime numbers so: 3*5=15

Answer:

2x-5

Step-by-step explanation:

(4x-7)-(2x-2)=4x-2x-7-(-2)=2x-7+2=2x-5

Answer:

2x-5

Step-by-step explanation:

A point B is (1 , -9)

Step-by-step explanation:

The formula of the slope of a line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points

lie on the line

We need to find a point B that makes that true

Assume that point B is (x , y)

∵ Point A = (5 , 3)

∵ Point B = (x , y)

∴ [tex]x_{1}=5[/tex] and [tex]x_{2}=x[/tex]

∴ [tex]y_{1}=3[/tex] and [tex]y_{2}=y[/tex]

- Substitute these values in the formula of m

∴ [tex]m=\frac{y-3}{x-5}[/tex]

∵ m(A , B) = 3

- Equate the formula of the slope by 3

∴ [tex]\frac{y-3}{x-5}=3[/tex]

- By using cross multiplication

∴ y - 3 = 3(x - 5)

- Simplify the right hand side

∴ y - 3 = 3x - 15

- Add 3 for both sides

∴ y = 3x - 12

To find point B chose any value for x and substitute it in the

equation to find y

∵ x = 1

∴ y = 3(1) - 12 = 3 - 12

∴ y = 9

∴ Point B = (1 , -9)

V.I.N: You can find many values of point B by chose different values of x and find the corresponding values of y

A point B is (1 , -9)

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Answer:

x=60.4

Step-by-step explanation:

Add 7.6 on both sides

1/4x=15.1

Multiply both sides by 4

x= 60.4

Answer:13 hours

Step-by-step explanation:

So you would divide 737 (miles) by 11 (hours) in order to find how far he traveled in 1 hour. You should get 67. So he travels at 67 miles in 1 hour. Then you would divide 871(total miles) by 67(distance traveled in 1 hour) to find out how many hours it took to travel 871. You should get 13(hours).

Hoped it helped.

Answer:

[tex]log_{b}(b^{x r}) [/tex]

Step-by-step explanation:

A picture of the question is shown in the figure attached. There we can see that the step corresponding to Properties of exponents is the option:

[tex]log_{b}(b^{x r}) [/tex]

which is equivalent to

[tex]log_{b}((b^{x})^{r}) [/tex]

This question is based on the property of exponents.Therefore, the correct option is (c), [tex]\bold{log _a(b^{x r})}[/tex].

Given that :

[tex]\bold{log_a(M^r)}[/tex]

In this question, we have choose appropriate correct option for for given expression.

According to the question,

It is given that,

[tex]\bold{log_a(M^r)}[/tex]                                                                                            ...(1)

Now, substitute the value of M = [tex]\bold{b^{x}}[/tex]. We get,

Thus, [tex]\bold{log_a(M^r)} = \bold{log _a((b^{x})^r)}[/tex]                                                            ...(2)

As we know that, by using the property of exponents,

[tex]\bold{(x^{m})^n = x ^{mn}}[/tex]

Now, applying this property in expression (2).

We get,

[tex]\bold{log _a((b^{x})^r)} = \bold{log _a(b^{x r})}[/tex]

Therefore, the correct option is (c), [tex]\bold{log _a(b^{x r})}[/tex].

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The product of 3 factorial is 6.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

We have to find the value of 3 factorial.

By the definition of factorial, factorial of any natural number can be defined as,

a factorial = 1 × 2 × ....... × (a - 1) × a

Here we have to find 3 factorial.

3 factorial can be written as,

3 factorial = 3 × 2 × 1 = 6 × 1 = 6

Hence the required product of 3 factorial is 6.

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Answer: 19.5

Step-by-step explanation:

Answer:

The relationship between number of animals owned and the number of vet bills is an example positive correlation.

Step-by-step explanation:

Correlation:

Now, as the number of animals increase the number of vet bills will increase. Thus, it could be said that increase in one variable leads to increase in another variable.

Thus, the given relationship is an example of positive relationship or a positive correlation.

Answer:

Option(D)

Finger Painting can be hard for children to control, but helps free their tension

Explanation:

Finger painting is a form of art in which the paintings or drawings are created by using fingers instead of a pen, pencil or brush.In this the fingers are dipped in paint and then the drawings are made by using bare hands.

This is a hard technique to make a painting or illustration and hence can be hard for children to control, but since it involves sensing touch, it helps release the tension and soothe the mind of the person who does painting using this method.

Answer:

 2[tex]\frac{1}{2}[/tex] cups

Step-by-step explanation:

Given, a recipe uses 8[tex]\frac{3}{4}[/tex] cups of milk for every 3[tex]\frac{1}{2}[/tex] cups of oatmeal.

So, For each 8.75 cups of milk ,3.5 cups of oatmeal is required.

Or,

we can say 3.5 cups of oatmeal require 8.75 cups of milk.

Thus,

1 Cup of oatmeal will require  [tex]\frac{8.75}{3.5}[/tex] cups of milk.

                                              =   2.5 cups of milk .

Thus answer is 2.5 cups, Which we can write 2 + 0.5 cups

                                                                      =  2[tex]\frac{1}{2}[/tex] cups (In mixed form)

Step-by-step explanation:

[tex](6i)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=6^3i^3\\\\\text{If}\ i=\sqrt{-1},\ \text{then}\\\\6^3i^3=216(-i)=-216i\\\\\text{else}\\\\6^3i^3=216i^3[/tex]

Final answer:

The expression equivalent to (6i)^3 is -216i, achieved by cubing the digit 6 to get 216 and remembering that i^3 is -i.

Explanation:

To find an expression equivalent to (6i)^3, we follow the rules of exponentiation and imaginary numbers. First, we cube the digit part, which is 6, to get 6^3 = 216. Next, we cube the imaginary unit i. Recall that i is the imaginary unit where i^2 = -1. Thus, i^3 is the same as i^2 multiplied by i, which equals to -i.

Combining these, we obtain (6i)^3 = 6^3 * i^3 = 216 * (-i) = -216i. This is the simplified form of the original expression.

The area of pasture is 60000 square feet.

Step-by-step explanation:

Perimeter of rectangular pasture = 1000 feet

Width of pasture = w

Length of pasture = l = w+100

We know that,

Perimeter = 2(Length+width)

[tex]1000=2(w+100+w)\\1000=2(2w+100)\\1000=4w+200\\1000-200=4w\\800=4w\\4w=800[/tex]

Dividing both sides by 4

[tex]\frac{4w}{4}=\frac{800}{4}\\w=200[/tex]

Width is 200 feet.

Length = w+100 = 200+100 = 300 feet

Area of pasture = A = Length * Width

[tex]Area\ of\ pasture=300*200\\Area\ of\ pasture=60000 \ ft^2[/tex]

The area of pasture is 60000 square feet.

Keywords: rectangle, area

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The question is about calculating the area of a rectangular pasture given its perimeter and relation between its length and width. After setting up equations based on the given conditions and calculating, the area of the pasture is found to be 60,000 square feet.

The subject of this question is Mathematics, specifically dealing with the calculation of area from given perimeter and length-width relationship in a rectangle. Let's denote the width of the rectangular pasture as 'w', and its length would then be 'w+100'.

The formula for the perimeter of a rectangle is 2*(length + width). As given, the perimeter is 1000 feet, so we set up the equation: 1000 = 2*(w+100 + w).

Simplify this to get the width 'w' which is 200 feet and the length is 'w+100', so 300 feet.

The area of a rectangle is calculated by the formula length*width, therefore, calculating gives 200*300 = 60,000 square feet.

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Answer:

6

Step-by-step explanation:

Because you have to added than reverse the question than it will give you your answer backwards

Answer:

Speed = 39.3 miles/hr

Time = 6.5 hrs.

Distance = Speed x time

= 39.3 x 6.5

= 245.45 miles (approx.)

Hope this helps!

Answer:

Speed = 39.3 miles/hr

Time = 6.5 hrs.

Distance = Speed x time

= 39.3 x 6.5

= 255.45 miles (approx.)

Step-by-step Explanation:

Answer:

see explanation

Step-by-step explanation:

Let ∠4 be x then ∠6 is [tex]\frac{1}{8}[/tex] x

∠4 and ∠6 are same side interior angles and are supplementary, thus

x + [tex]\frac{1}{8}[/tex]x = 180

Multiply through by 8 to clear the fraction

8x + x = 1440, that is

9x = 1440 ( divide both sides by 9 )

x = 160

Hence ∠4 = 160° and ∠6 = 160° ÷ 8 = 20°

Answer:

[tex]m \angle 4 = 160 \°\\m \angle 6 = 20 \°[/tex]

Step-by-step explanation:

From the graph, we can say that

[tex]m \angle 6 + m \angle 4 = 180 \°[/tex]

Because they are consecutive interior angles, and they sum 180° by definition. So, the reason of third statement is "by definition of consecutive interior angles".

We already know that

[tex]m \angle 6 = \frac{1}{8} \times m \angle 4[/tex]

But,

[tex]m \angle 6 + m \angle 4 = 180 \°\\m \angle 6 = 180\° - m \angle 4[/tex]

Replacing this, we have

[tex]180\° - m \angle 4=\frac{1}{8}(m \angle 4)\\(\frac{1}{8}+1) (m\angle 4)=180\°\\\frac{9}{8}(m\angle 4) = 180 \°\\ m \angle 4 = \frac{180(8)}{9}= 160\°[/tex]

Then,

[tex]m \angle 6 + m \angle 4 = 180 \°\\m \angle 6 + 160\° =180\°\\m \angle 6 = 180-160=20[/tex]

Therefore, the measures of these two angles are

[tex]m \angle 4 = 160 \°\\m \angle 6 = 20 \°[/tex]