9. Write the equation of a line that is PERPENDICULAR to 6x+3y=15 and passes
through the coordinate (12,-5).

Answer: 12x^6y^3-28x^4y^5+8x^4y^4-4x^3y^4

Step-by-step explanation:

The requierd product of 4x³y³ and (3x³-7xy²+2xy-y) is:

12x⁶y³ - 28x⁴y⁵ + 8x⁴y⁴ - 4x³y⁴

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The monomial and the polynomial are given in the question, as follows:

4x³y³ × (3x³-7xy²+2xy-y)

To find the product of the monomial 4x³y³ and the polynomial (3x³-7xy²+2xy-y), we need to multiply each term in the polynomial by the monomial and then add the results.

(4x³y³) × (3x³) = 12x⁶y³

(4x³y³) ×  (-7xy²) = -28x⁴y⁵

(4x³y³) ×  (2xy) = 8x⁴y⁴

(4x³y³) ×  (-y) = -4x³y⁴

⇒ 12x⁶y³ - 28x⁴y⁵ + 8x⁴y⁴ - 4x³y⁴

Therefore, the product of 4x³y³ and (3x³-7xy²+2xy-y) is:

12x⁶y³ - 28x⁴y⁵ + 8x⁴y⁴ - 4x³y⁴

Learn more about the polynomial here:

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Answer:

Her height would be 162.56 centimeters tall.

Step-by-step explanation:

There are 12 inches in 1 foot so that would mean that 1 foot has 30. 48 centimeters.

30.48 x 5 = 152.4

Add the 4 extra inches so 4 inches in centimeters is 10.16

152.4 + 10.16 = 162.56

Answer:

0.5cm

Step-by-step explanation:

Using the sine rule

Answer:

c = 0.5 cm

Step-by-step explanation:

Using the Sine rule in the triangle, then

[tex]\frac{c}{sin15}[/tex] = [tex]\frac{2}{sin105}[/tex] ( cross- multiply )

c × sin105° = 2 × sin15° ( divide both sides by sin105°

c = [tex]\frac{2sin15}{sin105}[/tex] ≈ 0.5 cm ( to the nearest tenth )

Answer:

Company B will charge cheaper in 5 hours

Step-by-step explanation:

Step one:

Given data

Company A

charges $25 per hour and a $300 equipment fee

let the total be

A= 300+25t---------------1

Company B

charges $50 per hour and a $125 equipment fee.

let the total be

A= 125+50t---------------2

put t = 5 in the two expressions above

A= 300+25t---------------1

A= 300+25*5

A=300+125

A=$425

B= 125+50t---------------2

B= 125+50*5

B=125+250

B=$375

Answer:

A = 25t + 300 B = 50t + 125

company B is $50 cheaper than company A for 5 hours of landscaping

Answer:

For Literature = 90 pages

For Grammar = 60 pages

Step-by-step explanation:

An English book consists of two sections, literature and grammar, in a ratio of 3:2. How much of each type of content will be needed to make a book of 150 pages?

Literature : Grammar

3 : 2

Total number of Proportion = 3 + 2 = 5

For Literature

= 3/5 × 150 pages

= 90 pages

For Grammar

= 2/5 × 150 pages

= 60 pages

Answer:

140

Step-by-step explanation:

The two non supplementary angles not supplementary to x = the sum of those two angles. So the sum = 57 + 83 = 140

x = 140

Answer:

£15

Step-by-step explanation:

Angad : Nick = 5 : 1

Let

Nick share = x

Angad share = x + £60

Angad : Nick

5 : 1 = x + £60 : x

5/1 = x + 60 / x

Cross product

5 * x = 1 * x + 60

5x = x + 60

5x - x = 60

4x = 60

x = 60/4

x = 15

Nick get £15

Answer:

2.5 ounces drip from the faucet per hour.

Step-by-step explanation:

You can figure this out by dividing the amount of water (7.5) by the hours (3).

7.5/3 = 2.5

To check your work you can do the same for the other combinations.

10/4=2.5, 12.5/5=2.5....

I hope this helped :)

Answer:

Average rate of change for given function is: -2

Step-by-step explanation:

Given function is:

[tex]f(x)=x^2-6x+8\\x_12= 1\\x_1 = 3[/tex]

In order to find the rate of change, we have to find the value of function on x1 and x2

So,

[tex]f(x_1) = (3)^2-6(3)+8 = 9-18+8 = -1\\f(x_2) = (1)^2-6(1)+8 = 1-6+8 = 3[/tex]

The formula for finding the rate of change is:

[tex]Rate\ of\ change = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

Putting the values, we get

[tex]=\frac{3-(-1)}{1-3}\\=\frac{3+1}{-2}\\=\frac{4}{-2}\\= -2[/tex]

Hence,

Average rate of change for given function is: -2

Answer:

Step-by-step explanation:

Answer:

[tex] 2 \dfrac{1}{4} [/tex]

Step-by-step explanation:

[tex] -5 \dfrac{1}{2} + 7 \dfrac{3}{4} = [/tex]

[tex] = -5 \dfrac{2}{4} + 7 \dfrac{3}{4} [/tex]

[tex] = 7 \dfrac{3}{4} - 5 \dfrac{2}{4} [/tex]

[tex] = 2 \dfrac{1}{4} [/tex]

Answer:

__________________the answer is C _____________

Answer:

C.

Step-by-step explanation:

The y intercept is when x=0

so (0, -7) is the y-intercept

slope is found when you subtract y-y1/x-x1

-10- (-7) / 9-0

-3/9

simplified is -1/3

slope is -1/3 and y intercept is (0, -7)

Answer:

Height of the building = 77 ft.

Step-by-step explanation:

Let the height of the building (AB) = h feet

It's given that height of a woman (ED) = 5 feet 3 inches

                                                              ≈ 5 feet + [tex]\frac{3}{12}[/tex] ft

                                                              ≈ 5.25 ft

Length of the shadow (BC) of the building = 55 ft

Length of the shadow (DC) of the woman = 45 in ≈ 3.75 ft

Since, both the triangles ABC and EDC are similar, their corresponding sides will be proportional.

By the property of similar triangles,

[tex]\frac{AB}{ED}= \frac{BC}{DC}[/tex]

[tex]\frac{h}{5.25}=\frac{55}{3.75}[/tex]

h = [tex]\frac{55\times 5.25}{3.75}[/tex]

h = 77 ft

Therefore, height of the building will be 77 ft.

Answer:

$392

Step-by-step explanation:

Given the expression :

Total cost = 20a + 13c

a = adult

c = student

The total cost for 4 adults and 24 students

a = 4 ; c = 24

Total cost :

20(4) + 13(24)

80 + 312

= $392

Answer:

the expression is (36+5)³

Answer:

Step-by-step explanation:

Substitute the value for x.

f(-5) = 3(-5) - 2

f(-5) = -15 - 2

f(-5) = -17

Answer:

jhvcvghvrxthrcftgv

Step-by-step explanation:

hkhvyyiytvhjh

Answer:

hhhhhhh

Step-by-step explanation:jujujujjujjjju

Answer:

Let x be the number

"five times a number"

5x

"six less than five times a number"

5x-6

"is at least 29" >29 (greater than or equal too)

5x - 6 > 29

5x > 35 (add +6 to both sides retains the dense if the inequality)

x>7 (divide both sides by +7 retains the sense of Inequailty)

Check:

Is 5(7) - 6 > 29?

35 - 6 > 29 ?

29 > 29? yes, they are equal.

Try 50:

Is 5(50) - 6 > 29 ?

250 - 6 > 29?

244 > 29 ? yes

Answer:

5x - 6 = 29

Answer:

There is not a proportional relationship

Step-by-step explanation:

The first and second hour the pay is $9.50/hour, but in the third hour the pay is $11/hour. Then in the fourth hour it changes again to $10/hourIf there was a proportional relationship there would need to be a constant rate of change in pay.

Answer:

Yes, the proportional relationship is 9.50

Step-by-step explanation:

In the graph that you have attached this picture with, hours x 9.50 = pay.

Hope this helps :D

The number of red counters and the number of green counters that were in the bag originally is: 10 red and 8 green counters.

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For this case, let we had:

R numbers of red counters, and G number of green counters originally.

Then, total counters in the bag originally = R +G

One counter out of R+G counters can be chosen in R+G ways. But one green counter out of R+G counters can be chosen in G ways.

Thus, probability of taking green counter out in one random picking is:

[tex]\dfrac{G}{R + G}[/tex]

It is given that this probability is 4/9. Therefore, we get:

[tex]\dfrac{G}{R+G} = \dfrac{4}{9}\\\\\\9G = 4R + 4G\\\\5G = 4R[/tex](first equation)

When 4 more red counters and 2 more green counters were added, then:

One counter out of R+G+6 counters can be chosen in R+G+6 ways. But one green counter out of R+G+6 counters can be chosen in G+2 ways (since there are G+2 green counters in the considered bag) ways.

Thus, probability of taking green counter out in one random picking is:

[tex]\dfrac{G+2}{R + G+6}[/tex]

It is given that this probability is 10/23. Therefore, we get:

[tex]\dfrac{G+2}{R+G+6} = \dfrac{10}{23}\\\\\\23G + 46 = 10R + 10G + 60\\\\13G = 10R + 14[/tex](second equation)

Thus, we got a system of two linear equations as:

[tex]5G = 4R\\13G = 10R + 14[/tex]

From first equation, getting the value of G in terms of R,

[tex]G = \dfrac{4R}{5}\\[/tex]

Now, substituting this with G in the second equation, we get:

[tex]\\13\left(\dfrac{4R}{5} \right) =10R + 20\\\\52R = 50R + 20\\2R = 20\\R = 10[/tex]

From this value of R, and the value of G in terms of R, we get:

[tex]G = \dfrac{4R}{5}\\\\ = \dfrac{4 \times 10}{5} = 8[/tex]

Thus, R = 10 and G = 8.

Thus, the number of red counters and the number of green counters that were in the bag originally is: 10 red and 8 green counters.

Learn more about probability here:

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Answer:

4x -12

Step-by-step explanation:

is that what u needed lol

Step-by-step explanation:

-24 ==== ( 2×-6=-12___-12×2= -24)

Answer:

m = 2, b = 4.6

Step-by-step explanation:

The slope intercept formula is y = mx + b, So you can substitute for the values given.

Answer:

B

Step-by-step explanation:

Its very simple try not to waste your points

Answer:

2

Step-by-step explanation:

because 8 and 4 to get the shape smaller you divide it by 2 so you times 1 *2 to get the bigger one

Answer:

[tex]m\angle N=57^{\circ}[/tex]

Step-by-step explanation:

From the isosceles-base theorem, the measure of the angles adjacent to the pair of congruent sides of the triangle are equal. Since the problem declares [tex]LM\cong LN[/tex], the remaining unknown angles are equal ([tex]m\angle N=m\angle M[/tex]). The sum of the interior angles of a triangle always add up to [tex]180^{\circ}$[/tex].

Therefore:

[tex]m\angle N\cdot 2+66=180,\\m\angle N\cdot 2=114,\\m\angle N=\fbox{$57^{\circ}$}[/tex] .

Answer:

LMN is rectangle in L so LMN= 180° ; ML=66°;N=?  N= 180°- 66°=114=114/2= 57° so N=57°

Step-by-step explanation:

When the angle at the top is close to 0 °, the two of the base get less than 180 °, or less than 90 ° for each. If the angle at the top is 60 °, the other two are: 180 - 60 = 120 °, and each is: 120/2 = 60 °.

Answer:

1) d 2) b

Step-by-step explanation:

1) 36÷24 = 1.5 15×1.5= answer

2) 4÷3.2= 1.25 7.5÷1.25= answer