Solve for z.

–2.9 + 4.2z = –14.73 − 12.74 + 0.3z

z =

Answer:

The answer to this question can be described as follows:

-5 with multiplicity 3

9 with multiplicity 2

-1 with multiplicity 1

Step-by-step explanation:

Given:

[tex]\Rightarrow f (x) = (x + 5)^3(x - 9)^2(x + 1)[/tex]

Solve the above equation:

[tex]\Rightarrow f (x) = (x + 5)(x + 5)(x + 5)(x - 9)(x - 9)(x + 1)\\[/tex]

The roots of the polynomial are as follows:

 [tex]\Rightarrow (x-x_1)(x-x_2)(x-x_3)......(x-x_n)\\\\\Rightarrow x_1,x_2,x_3.........x_n[/tex]

That's why the roots are:

5 with multiplicity 3

9 with multiplicity 2

-1 with multiplicity 1

Answer:

answer:

a. -5 with multiplicity 3  

d. 9 with multiplicity 2

f. -1 with multiplicity 1

Step-by-step explanation:

Answer:

16.485 feet

Step-by-step explanation:

Given that tire is 5.25 feet tall

any circular shape is as tall as its diameter.

we can say that diameter of tire is 5.25 feet.

in one rotation tire will start from one point of tire and reach it again.

it is like on a circle moving from on one point and then reaching to same point.

and we know that distance covered on moving on the point of circle is equal to circumference.

Thus, measure of circumference would help to find how many feet the tractor will travel in 1 rotation.

circumference of circle is given by [tex]\pi D[/tex]

where D is the diameter of circle.

we will us 3.14 as value of [tex]\pi[/tex]

thus, circumference of circle is[tex]\pi * 5.25 = 3.14*5.25 = 16.485[/tex]

Hence, tractor would travel 16.485 feet in one rotation.

Answer:

Step-by-step explanation:

  -2/7+0 = 0+-2/7 . . . . commutative property of addition

The commutative property allows you to swap the order of operands being summed.

  0+-2/7 = -2/7​ . . . . identity element of addition

The identity element for addition is 0. That is, adding 0 to anything does not change its value.

Answer:

p = - 5i or p = 5i

Step-by-step explanation:

Noting [tex]\sqrt{-1}[/tex] = i

Given

p² = - 25 ( take the square root of both sides )

p = ± [tex]\sqrt{-25}[/tex] = ± [tex]\sqrt{25(-1)}[/tex] = ± 5i

Thus

p = - 5i or p = 5i

Because p squared is equal to -25, the square root of -25 is equal to p.

Because of this, finding the square root of -25 will give us our answer.

[tex]\sqrt{-25}[/tex] = 5i

Therefore, p = 5i or p = [tex]\sqrt{-25}[/tex].

Hope this helped! :)

Answer:

141

Step-by-step explanation:

We need to first find the volume of the cannonballs and then, divide the volume of the closet by the volume of the cannonballs.

The radius of the spherical cannonball is 0.75 feet.

The volume of a sphere is:

[tex]V = \frac{4}{3} \pi r^3[/tex]

where r = radius

Therefore, the volume of the cannonballs is:

[tex]V = \frac{4}{3} * \pi * 0.75^3\\\\V = 1.77 ft^3[/tex]

Therefore, the number of cannonballs that can fit the closet is:

250 / 1.77 = 141.24

Since the number is a maximum and it must be a whole number, the number of cannonballs that can fit the closet is 141.

Answer:on the circle

Step-by-step explanation:

Point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a center of the circle at D(-1, 3)

And point G(-10, 1) is on the circle.

We know the standard equation of the circle when a center is given:

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]

Where r is the radius of the circle and (h, k) is the center of the circle.

Here (h, k) ⇒ (-1, 3)

The circle equation becomes:

[tex]\rm (x+1)^2+(y-3)^2=r^2[/tex]

Put the point on the circle equation to get the radius of the circle:

[tex]\rm (-10+1)^2+(1-3)^2=r^2[/tex]

[tex]\rm (-9)^2+(-2)^2= r^2\\\\\rm 81+4 = r^2\\\\ \rm r = \sqrt{85} \ units[/tex]

Equation of circle is:

[tex]\rm (x+1)^2+(y-3)^2=85[/tex]

Now put the point J(-3, 12 ) in the circle equation:

[tex]\rm (-3+1)^2+(12-3)^2=85[/tex]

4+ 81 ⇒ 85

It means point J is lying on the circle.

Thus, point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

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it should be 271.94

Answer:

299/100*85=$254.15 + 7% = 254.15/100*107= $ 271.9405

Step-by-step explanation:

1. $299/100*85=$254.15 + 7% sales Tax =  $ 271.9405

Answer:

$10579.49

Step-by-step explanation:

The formula for amount gotten after a period of time (in years) on a principal which is compounded continuously is given as:

[tex]A = P(1 + r)^t[/tex]

where P = principal (amount borrowed)

r = interest rate

t = number of years

Peter accumulated $7,500 in credit card debt with interest rate as 3.5% per year and he does not make any payments for 10 years.

Therefore, his debt is:

[tex]A = 7500(1 + \frac{3.5}{100})^{10}\\ \\A = 7500 (1 + 0.035)^{10}\\\\A = 7500(1.035)^{10}\\[/tex]

A = $10579.49

He will owe $10579.49 after 10 years

Answer:

A= $10,643.01

Step-by-step explanation:

if you are rounded to the nearest cent

Identify the values of each variable in the formula. Remember to express the percent as a decimal.

A=?

P= $7,500

r= 0.035

t= 10 years

For compounding continuously, use the formula A=Pert.

Substitute the values in the formula and compute the amount to find

A= 7,500e [tex]x^0.035.10[/tex][tex]x^{0.035.10}[/tex]

A= $10,643.01

Answer:

x = -(a - b)/b

Step-by-step explanation:

Solve for x:

a = b (1 - x)

a = b (1 - x) is equivalent to b (1 - x) = a:

b (1 - x) = a

Divide both sides by b:

1 - x = a/b

Subtract 1 from both sides:

-x = (a - b)/b

Multiply both sides by -1:

Answer: x = -(a - b)/b

Answer:

circumference = 2πr

2×π×6

12πmm

Given:

Radius of circle = 6 mm

Work out :

Workout the circumference of this circle?

Formula used:

Circumference of circle = 2πr

Solution:

According to the question,

Circumference of circle = 2πr

= 2 × π × 6

= 12 π mm

Answer: m√M = 98°

Step-by-step explanation:

x + x + 6 + 3x - 16 = 180

5x - 10 = 180

5x = 180 + 10

x = 190 / 5 = 38

m√M = 3x - 16

= 3(38) - 16

= 98°

Answer:

m<M = 98 deg

Step-by-step explanation:

Theorem

The sum of the measures of the angles of a triangle is 180 degrees.

Now we set the sum of the measures of the angles equal to 180 and solve for x.

3x - 16 + x + 6 + x = 180

5x - 10 = 180

5x = 190

x = 38

Now that we know x, we substitute x with 38 in the expression for the measure of angle M.

m<M = 3x - 16

m<M = 3(38) - 16

m<M = 114 - 16

m<M = 98

Answer & Step-by-step explanation:

When we see (f + g)(x), it means that we are adding together f(x) and g(x).

f(x) = 4x + 1

g(x) = x² - 5

(f + g)(x) = (4x + 1) + (x² - 5)

Combine like terms and make sure x² is in the front of the expression so you are following the rules of exponents when in standard form.

(f + g)(x) = x² + 4x - 4

So, (f + g)(x) equals x² + 4x - 4

The volume of the given pyramid is 106.1 cubic foot.

Given:

The perimeter of the base is 15.8 feet

The base of the pyramid is square given of side say L .

Thus, from the formula of perimeter of square,

⇒ 4*L = 15.8 feet

∴  L = 3.95 feet

Now the base area of the pyramid is [tex]L^{2}[/tex] as it is a square .

∴ Base area = 3.95*3.95 square feet

= 15.6025 square foot

Now, formula for volume of the pyramid

=  1/3 * base area * height

⇒ Volume = 1/3 * 15.6025 * 20.4 cubic foot

∴ Volume = 106.097 cubic foot

Thus volume of the given pyramid is 106.1 cubic foot rounded off to nearest tenth.

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Answer:

x° = ∠OBR = ∠ABC (base angles of a cyclic isosceles trapezoid)

Step-by-step explanation:

APRB form a cyclic trapezoid

∠APO  = x° (Base angle of an isosceles triangle)

∠OPR  = ∠ORP (Base angle of an isosceles triangle)

∠ORB = ∠OBR (Base angle of an isosceles triangle)

∠APO + ∠OPR + ∠OBR = 180° (Sum of opposite angles in a cyclic quadrilateral)

Similarly;

∠ORB + ∠ORP + x°  = 180°

Since ∠APO = x° ∠ORB = ∠OBR and ∠OPR  = ∠ORP we put

We also have;

∠OPR = ∠AOP = ∠BOR (Alternate interior angles of parallel lines)

Hence 2·x° + ∠AOP = 180° (Sum of angles in a triangle) = 2·∠OBR + ∠BOR

Therefore, 2·x° = 2·∠OBR, x° = ∠OBR = ∠ABC.

Answer: the 5 in the parentheses on the second line should be negative. Also, where did the 23 go?? That's a mistake too.

Step-by-step explanation: 3 - 8 = -5 so

23(2 - 4) + 5(3 - 8)

23(-2) + 5(-5)

(-46) + (-25)

-71

(at least, I think so unless there was a mistake in the equation)

Answer:

Choice C

Step-by-step explanation:

f: initial value of 200 decreasing at a rate of 4%

g: initial value of 40 increasing at a rate of 8%

f is decreasing so it must go down starting at 200

That eliminates a and d

g is increasing and starts at 40  That eliminates a

We must look at b and c

g is increasing faster than f is decreasing

Choice C

Answer:

[tex]10[/tex]

[tex]16[/tex]

Explanation:

A rational number is a number that can be expressed as the quotient or fraction of two integers.

Answer: D

Step-by-step explanation:

the scale factor is 6

Triangle ABC  has the lengths  4,2,4   and DEF has the lengths 24,12,24

so for the triangle ABC's lengths to become triangle DEF  is is supposed to be multiplied by 6

4*6= 24

2*6= 12

4*6= 24

Complete Question:

The scatter plot shows the number of oranges picked, in hundreds, in relation to the number of lemons harvested, in hundreds, by several farmers. According to the plot, which value is the best estimate of the correlation coefficient of the data?

A.-0.2

B. -0.9

C. 0.9

D. 0.2

*See attachment for the scatter plot

Answer:

C. 0.9

Step-by-step explanation:

If we take a good look at the scatter plot in the attachment showing numbers if oranges picked in relation to number of lemons harvested, we can infer that there's a strong positive correlation between both variables.

Thus, both variables are moving in the same direction. As one variable increases, the other variable increases. Also, the data points represented on the plot seem clustered close to the line rather than farther away.

This will suggest a positive correlation coefficient that is closer to 1.

From the options given above, the best estimate of the correlation coefficient would be 0.9.

The answer is C. 0.9

Answer:

230

Step-by-step explanation:

9 times 20 = 180

divide by 2 = 90

7 times 20 = 140

140 + 90 = 230

Answer:

A=230 cm2

Step-by-step explanation:

A1= L x W             HEIGHT OF TRIANGLE=16-7=9

A1=20 x 7

A1=140 cm2

A2=1/2 x B x H

A2=1/2 x 20 x 9

A2=90 CM 2

Answer:

a. 2(^3 sqrt 3) - ^3 sqrt 18

Step-by-step explanation:

got it right on edge

[tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex][tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex][tex]2(\sqrt[3]{3})-\sqrt[3]{18}[/tex] option (A)  is Correct.

The problem can be solved by following steps.

The expression given is [tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex]

So , The first step we will do is Rationalize the figure

= [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }}{\sqrt[3]{9}*\sqrt[3]{9} }[/tex]

The product of radicals with the same index equals the radical of the product:[tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9*9^2} }[/tex]

Simplify using exponent with same base

[tex]a^{n}*a^{m} = a^{a+m}[/tex]

= [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^1+^2} }[/tex]

Calculate the sum or difference: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^3} }[/tex]

Simplify the radical expression: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {{9} }[/tex]

Calculate the power : [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{9} }[/tex]

Cross out the common factor: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{3} }[/tex]

Factor Greatest Common Factors : [tex]\frac{3*2\sqrt[3]{3}-\sqrt[3]{18} }{3}[/tex][tex]3*2\sqrt[3]{3}-\sqrt[3]{18}}[/tex]

Reduce the fraction : [tex]2\sqrt[3]{3}-\sqrt[3]{18}}[/tex]

Hence the First option is correct

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Answer:

Can you please tell me what is the area of the given triangle?

Answer:

(5s + 8) is the missing factor.

Step-by-step explanation:

The given expression is 5s² + 23s + 24

We have to convert the given expression into the factored form.

One factor of the expression has been given as (x + 3)

5s² + 23s + 24 = 5s²+ 15s + 8s + 24

                        = 5s(s + 3) + 8(s + 3)

                        = (5s + 8)(s + 3)

So the factors of the expression will be (s + 3) and (5s + 8)

Therefore, the missing factor of the given expression is (5s + 8).

Answer:

x >13/9

Step-by-step explanation:

(1/4)(5x−3) > (1/2)x + (1/3)

Distribute

5/4x - 3/4 > 1/2x + 1/3

Multiply each side by 12 to get rid of fractions

12*5/4x -12* 3/4 >12* 1/2x +12* 1/3

15x -9 > 6x +4

Subtract 6x from each side

15x-6x-9 > 6x-6x+4

9x -9> 4

Add 9 to each side

9x-9+9 > 4+9

9x > 13

Divide by 9

9x/9 >13/9

x >13/9

Answer:

Explanation:

Answer:

The answer is 7n3 + 6.

Step-by-step explanation:

To simplify, remove the parentheses and combine like terms.

The standard form of the given expression is 7n³+6.

The given expression is (4+2n³)+(5n³+2).

To add any two expressions group the like terms.

Here, 4+2n³+5n³+2

= (2n³+5n³)+4+2

= 7n³+6

Therefore, the standard form of the given expression is 7n³+6.

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Answer:

yes distribute . . .

Step-by-step explanation:

the 6 to the 9 and the 4

6(9) - 6(4)=30

Answer:

d. Summarized account information

Step-by-step explanation:

Answer:

89595/100000

Step-by-step explanation:

Answer:

4 yards

Step-by-step explanation:

the formula for finding the volume of a shape is volume= to length times with times how tall it is. In this case we do not have the hight so we make a formula. 5 and 3/4 times 10 times hight = to 230. If you do the math you get 4 yards as the answer.

Answer:4 yards

Step-by-step explanation: