The radius of a cylindrical gift box is (3x+4) inches. The height of the gift box is three times the radius. What is the surface area of the cylinder? Write your answer as a polynomial in a standard form.

Answer:

Explanation:

add 13 to both sides of the equation.

17+13=−8x.

30=−8x.

divde both sides by −8.

30−8=x⇒x=−308=−154.

As a check.

Step-by-step explanation:

Answer:

Step-by-step explanation:

17 = -13 - 8x....add 13 to both sides

17 + 13 = -13 + 13 - 8x

30 = -8x...now divide both sides by -8

-30/8 = (-8/-8)x

-30/8 = x.....reduce

- 15/4 = x <===

Answer:

3x(9x^2+1) or C on edge

Step-by-step explanation:

did the test on edge and i got it right :

The polynomial that is factored completely is 5x^2 - 17x + 14, as it can be fully factored into (5x - 7)(x - 2) using the quadratic formula or factoring by inspection.

The question requires us to determine which polynomial is factored completely. We have four options to consider.

Hence, the polynomial that is factored completely is 5x^2 - 17x + 14.

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We can ise Pythagorean triplet which is ( 12 , 16 , 20 )

Therefore the answer is 16.

Step-by-step explanation:

Or we can use Pythagoras theorem , stated as ;

( hyp )^2 = ( adj )^2 + ( opp )^2

hyp ( hypotenuse ) = 20

We can assume the adj ( adjacent ) = 12

By substituting the values ,

20^2 = 12^2 + ( adj )^2

400 = 144 + ( adj )^2

400 - 144 = ( adj )^2

256 = ( adj )^2

Take the square root of both sides

✓256 = adj

16 = adj

Therefore the length of the other leg which is the adjacent( adj ) side is 16.

The length of the other leg is 16

To find the length of the other leg of a right triangle, given one leg is 12 and the hypotenuse is 20, we use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c).

This relationship is given by:

a² + b² = c²

1.  Here, one leg (a) is 12 and the hypotenuse (c) is 20. So we can write:

12² + b² = 20²

2.  Calculating the squares gives:

144 + b² = 400

3. Subtract 144 from both sides to find b²:

b² = 256

4. Finally, take the square root of both sides to find b:

b = √256 = 16

Thus, the length of the other leg is 16.

Answer:

The sum of the roots of a polynomial is 5/3, the product of the same polynomial is -11. Write the polynomial function in standard form.n:

Answer:

f(x) = x³ - 7x - 6

Step-by-step explanation:

Given that the zeros are x = - 1, x = - 2 and x = 3 then the corresponding factors are

(x + 1), (x +2) and (x - 3)

The polynomial is then the product of the factors, that is

f(x) = (x + 1)(x + 2)(x - 3) ← expand the first pair using FOIL

     = (x² + 3x + 2)(x - 3) ← distribute

     = x³ - 3x² + 3x² - 9x + 2x - 6 ← collect like terms

     = x³ - 7x - 6

[tex]

kx+12=3kx \\

12=2kx \\

x=\frac{12}{2k} \\

x=\frac{6}{k}

[/tex]

Hope this helps.

Answer: x=6/k

Step-by-step explanation:

kx + 12 = 3kx and subtract k from both sides

12=3kx-kx then simplify

12=2kx, now divide both sides by two

12/2=kx simplify again

6=kx divide next

6/k=x finally, switch sides to get x=6/k

Hope this helps, have a BLESSED and wonderful day, as well as a safe one!

-Cutiepatutie ☺❀❤

=============================================

Explanation:

A triangle is only possible if you can add two sides and have that sum be larger than the third side. This is the triangle inequality theorem.

Choice A is ruled out because the second and third sides add to 7+7 = 14, but that's not larger than the first side 15.

Choice B is a similar story: 6+8 = 14 is not larger than 14 (the first side)

Choice C as well: 6+7 = 13 is not larger than 14

------

Choice D is the answer because

15+7 > 9

15+9 > 7

7+9 > 15

These three inequalities show that picking any two sides of this triangle, then adding them up, leads to a sum larger than the third side.

Answer:

Step-by-step explanation:

x^2 + 2x + 1 = 17

x^2 + 2x = 17 - 1

x^2 + 2x = 16

x^2 + 2x + 1 = 16 + 1

(x + 1)(x + 1) = 17

(x + 1)^2 = 17

x + 1 = sqrt 17

x = -1 (+ - ) sqrt 17

x = -1 + sqrt 17 or x = -1 - sqrt 17 <===

Answer:

x = -1 + square root 17

Step-by-step explanation:

I took the test

Answer:

two solutions : 9   ; -9

Step-by-step explanation:

x²=81

means : x² - 81 =0   but 81 = 9²

use identity ; a² - b² = (a-b)(a+b)

x² -9² = 0     : (x-9)(x+9)=0

x-9=0 or x+9 = 0

x =9 or x = -9

Answer:

(y + 2)(y + 3)

Step-by-step explanation:

Answer:

product

Step-by-step explanation:

Answer:

The Correct Answer is product of powers

Step-by-step explanation:

Answer:

Let's write this out in an equation.

y = 4 + 7x

The mathematical equation 'Y is 4 more than the product of 7 and x' can be written as 'Y = 7x + 4' where Y is the dependent variable and x is the independent variable. This is a standard form linear equation.

The subject of this question is Mathematics, and it appears to be targeted at a Middle School level. The statement 'Y is 4 more than the product of 7 and x' is a mathematical equation that can be written as Y = 7x + 4. Here, '7x' refers to the product of 7 and x, and the '+ 4' indicates that Y is 4 more than this product. It is a linear equation in variable x.

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Answer:

2. The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.

Step-by-step explanation:

The total lunch budget of the company  =  $150

Total number of employees  = 20

The cost of 1 roast beef sandwich = $5

The cost of 1 tuna sandwich = $5

r represents the number of roast beef sandwiches provided.

t represents the number of tuna sandwiches provided.

Now, consider the given statements:

Here, total number of sandwiches purchased  = Total number of employees

⇒ r +  t = 20   .... (1)

Also, as each type of sandwich costs $5.

So, the cost of r roast beef sandwiches = r x ( Cost of  1  beef sandwich)

= r x ( $5) = 5 r

And, the cost of t tuna sandwiches = t x ( Cost of  1  tuna sandwich)

= t x ( $5) = 5 t

Total cost of (r +t) sandwiches = Total Lunch Budget

⇒ 5 r +  5 t = 150   .... (2)

Hence, from (1) and (2) the above situation can be represented as:

r +  t = 20  

5 r +  5 t = 150

Hence, the company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.

The diagonal of square is 9.90 units long.

Step-by-step explanation:

Given,

Length of each side of square= s = 7 units

Diagonal of square = s√2

Putting s = 7

Diagonal of square = [tex]7*\sqrt{2}[/tex]

Diagonal of square = 7 * 1.414

Diagonal of square = 9.898

Rounding off to nearest hundredth

Diagonal of square = 9.90 units

The diagonal of square is 9.90 units long.

Keywords: square, diagonal

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Answer:

d = 9.9 units

Step-by-step explanation:

The step by step explanation is in the picture below

Answer:

All that you would have to do is add 10 more blocks to show that its 10 more than 43

Answer:

w = I /2 - 4

Step-by-step explanation:

half the length : I /2

4 less than half the length : I /2 - 4

To match the requirements : w= I /2 - 4

[tex]\text{Hey there!}[/tex]

[tex]\text{Is 6(6 + x) equivalent to 6x + 3?}[/tex]

[tex]\text{Kind of yes, and kind of no}[/tex]

[tex]\text{But in order for you to solve for this equation you have to use the distribute}\\\text{ property}[/tex]

[tex]\text{The distributive property formula is}\rightarrow\text{a(b + c) = a(b) + a(c) = ab + ac}[/tex]

[tex]\text{Let's solve for the equation, shall we?}[/tex]

[tex]\text{6(6 + x)}\\\text{6(6) + 6(x)}\\\text{6(6) = 36}\\\text{36 + 6(x)}\\\text{6(x) = 6x}\\\boxed{\text{\underline{36+6x}}}[/tex]

[tex]\text{36 + 6x}\neq \text{6x+ 36}[/tex]

[tex]\text{So, thus your answer has to be NO}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

Step-by-step explanation:

Let, it will take x years to be of same height for these trees.

We know that 1 ft = 12 inches.

8 ft = [tex]12\times8 = 96 inch[/tex]. 2 ft = 24 inch.

After x years, the height of type A will be (96 + 6x) inch and the height of type B will be (24 + 15x) inch.

We need find the value of x, for which 96 + 6x = 24 + 15x or, 9x = 72 or, x = 8.

Answer:

Function 1.

Step-by-step explanation:

The rate of change of Function 2 = (18.75 - 14.25)/ (5 - (-1))

=  4.5 / 6

= 3/4 or 0.75.

For Function 1 it is  5/6 or 0.83

So Function 1 has greatest rate of change.

Speed of boat in still water is 12 km/hr and speed of current is 9 km/hr

Solution:

From given,

Downstream distance = 213 km

Time taken for downstream = 11 hours

Thus, speed is given as:

[tex]\text{Downstream speed} = \frac{\text{Downstream distance}}{\text{time taken}}[/tex]

[tex]\text{Downstream speed} = \frac{231}{11} = 21[/tex]

Thus downstream speed is 21 km/hr

Also,

Upstream distance = 213 km

Time taken for upstream = 77 hours

Thus, speed is given as:

[tex]\text{Upstream speed} = \frac{\text{Upstream distance}}{\text{time taken}}\\\\\text{Upstream speed} = \frac{231}{77} = 3[/tex]

Thus upstream speed is 3 km/hr

If the speed downstream is "a" km/hr and the speed upstream is "b" km/hr , then:

[tex]\text{Speed in still water } = \frac{1}{2}(a+b)\\\\\text{Speed of current } = \frac{1}{2}(a-b)[/tex]

Here, a = 21 and b = 3

Therefore,

[tex]\text{Speed in still water } = \frac{1}{2}(21+3) = \frac{24}{2} = 12\\\\\text{Speed of current } = \frac{1}{2}(21-3) = \frac{18}{2} = 9[/tex]

Thus speed of boat in still water is 12 km/hr and speed of current is 9 km/hr

The speed of boat in still water is 12 km/hr as:

Let speed of Boat be 'b' and speed of Current be 'c'.

Distance given is 210 miles.

Therefore speed for downstream = 210 ÷ 10=21 mph

speed for upstream =3mph

Now we can form the two equations as :

i) b+c = 21 ......(i) For downstream

ii) b-c = 3.........(ii) For Upstream

Solving by substitution method :

From equation (ii) c = b - 3 Substitute this value of c in equation

(i) we get b + b - 3 = 21

Therefore b = 12. Now substitute the value of b in any of the equations above (i) or (ii) and get c= 9

b= 12 and c = 9.

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Answer:

5+4w=7

Step-by-step explanation:

Answer:

Look at the picture.

x < 0 and y < 0

Answer:

Hypotenuse = 20

Step-by-step explanation:

As we know that in 30 60 90 triangle

Short leg = X

Hypotenuse = 2X

Perpendicular = X[tex]\sqrt{3}[/tex]

Short leg = X = 10

Hypotenuse = 2X = 10*2 = 20

Final answer:

In a 30-60-90 triangle, the hypotenuse is twice the length of the shortest leg. Therefore, with a shortest leg of 10, the hypotenuse is 20.

Explanation:

The student has asked about the length of the hypotenuse in a 30-60-90 triangle where the shortest leg is given as 10. In a 30-60-90 triangle, the ratios of the sides are 1:√3:2. Since the shortest leg (the one opposite the 30° angle) is known to be 10, we can find the hypotenuse by multiplying the length of the shortest leg by 2.

Thus, the hypotenuse is 20.

To summarize the process, if the shortest leg a is known, then the hypotenuse c is calculated using the formula: c = 2a. Given that a = 10, the calculation would be c = 2 × 10 = 20.

Answer:

y=0

Step-by-step explanation:

Parallel lines never intersect therefore you need to find what y=-5 would look like on a graph (look at the image for reference, it is the blue line). Because it is a straight line then you just need to find what would make a straight line across the origin, therefore you would have to do y=0 (the red line on the image.)

The reason for putting y=0 or y=-5 is because the y value will ALWAYS stay the same and the x value will continue going on and on, without intersecting.

According to the construction described  ∠ DEF ≅ ∠GEF by SSS congruence theorem

How to show that the two angles are congruent

Statement        Reason

DE ≅ GE              given

DF ≅ GF               given

EF ≅ FE                reflexive property

Δ DEF ≅ Δ GEF   SSS congruence theorem

∠ DEF ≅ ∠GEF    CPCTC

Answer:

x = 18.5

Step-by-step explanation:

Multiply 5 and 3.7.

Which equals 18.5.

Check: 18.5 / 3.7 = 5.√

Answer:

[tex]10\frac{1}{2}\ \frac{acres}{hour}[/tex]

Step-by-step explanation:

The correct question is:

Darcy harvests 8 3/4 ​ acres of corn every 5/6​  of an hour. Darcy harvests corn at a constant rate. How many acres does she harvest per hour?

we know that

To find out the corn rate harvested per hour or the unit rate, divide the number of acres of corn harvested by the total time it takes

so

[tex]8\frac{3}{4} :\frac{5}{6}[/tex]

Convert mixed number to an improper fraction

[tex]8\frac{3}{4}=8+\frac{3}{4}=\frac{8*4+3}{4}=\frac{35}{4}[/tex]

substitute

[tex]\frac{35}{4} :\frac{5}{6}=\frac{210}{20}=\frac{21}{2}\ \frac{acres}{hour}[/tex]

Convert to mixed number

[tex]\frac{21}{2}\ \frac{acres}{hour}=\frac{20}{2}+\frac{1}{2}=10\frac{1}{2}\ \frac{acres}{hour}[/tex]

Answer:

[tex]10\frac{1}{2}[/tex] or [tex]\frac{21}{2}[/tex]

The correct inequality is: C. $114,840.00(1 + 0.04)^2 > $115,362.00.

It correctly applies compound interest to determine when the house value exceeds $114,840.00.

To determine the number of years [tex](\( f \))[/tex] after purchase that the value of Isaac's house will be more than $114,840.00, we can use the formula for compound interest.

The formula for compound interest is given by:

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

Where:

- A is the future value of the investment/asset.

- P is the initial principal amount (the initial value of the investment/asset).

-  r  is the annual interest rate (expressed as a decimal).

- n is the number of years the asset is invested for.

In this case:

- [tex]\( P = \$104,400.00 \)[/tex] (the initial value of the house).

- r = 0.04 (the annual rate of increase, which is 4% expressed as a decimal).

- We want to find the value of n when [tex]\( A > \$114,840.00 \)[/tex].

So, the inequality to represent this scenario is:

[tex]\[ \$114,840.00 < \$104,400.00(1 + 0.04)^n \][/tex]

Now, let's compare this inequality with the options provided:

A. [tex]\( \$114,840.00(1 + 0.04)^{n+1} > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( n + 1 \) instead of \( n \)[/tex] in the exponent.

B. [tex]\( \$114,840.00(0.04)^2 > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( (0.04)^2 \)[/tex] instead of [tex]\( (1 + 0.04)^n \)[/tex].

C. [tex]\( \$114,840.00(1 + 0.04)^2 > \$115,362.00 \)[/tex] - This option is correct. It uses the correct formula for compound interest and compares it to the threshold value of [tex]\$114,840.00[/tex].

D. [tex]\( \$114,840.00(1 - 0.04)^2 > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( (1 - 0.04)^2 \) instead of \( (1 + 0.04)^n \).[/tex]

Therefore, the correct inequality is option C:

[tex]\[ \$114,840.00(1 + 0.04)^2 > \$115,362.00 \].[/tex]

Correct question is:

Isaac purchased a house for $104,400.00.

Every year, Isaac makes improvements so that the value of the house goes up by 4% Which of the following inequalities can be used to determine the number of years after purchase, f, that the value of Isaac's house will be more than $114,840.00?

[tex]A. $114,840.00(1+0.04)^r+1 > $115,362.00[/tex]

[tex]B. $114,840.00(0.04)^2 > $115,362.00[/tex]

[tex]C. $114,84000(1+0.04)^2 > $115,362.00[/tex]

[tex]D. $114,84000(1-0.04)^2 > $115,362.00[/tex]

Answer:

The length of the intercepted arc for circle S is  (1/2)π ft

9514 1404 393

Answer:

  45 cm

Step-by-step explanation:

The ratio of length to width is the same for the drawing as for the field.

  length/width = L/(30 cm) = (120 yd)/(80 yd)

  L = (30 cm)(3/2) = 45 cm . . . . . . multiply by 30 cm and simplify

The field should be 45 cm long on the drawing.

Final answer:

The soccer field in Lexie's scale drawing should be 45 centimeters long, using a scale factor based on the given width of 30 centimeters and the real soccer field's dimensions.

Explanation:

Lexie is scaling a real soccer field to a drawing, with the real field's dimensions being 120 yards long and 80 yards wide. When converting these dimensions to a scale drawing where the width is 30 centimeters, we need to find the drawing's length. To do this, we will use a scale factor.

First, we find the actual scale factor based on the given dimensions:

Actual width of soccer field = 80 yards

Width in the drawing = 30 centimeters

To convert yards to centimeters, we need to know that 1 yard equals 91.44 centimeters. Given this, the actual width in centimeters is 80 yards * 91.44 cm/yard = 7312 centimeters.

Now, we calculate the scale factor:

Scale factor = Width in the drawing / Actual width in centimeters = 30 cm / 7312 cm

Using this scale factor, we can find the length for the drawing:

Actual length of soccer field = 120 yards

Actual length in centimeters = 120 yards × 91.44 cm/yard = 10972.8 centimeters

Length in the drawing = Actual length in centimeters × Scale factor = 10972.8 cm × (30 cm / 7312 cm)

Calculating this gives us:

Length in the drawing = 45 centimeters

Therefore, the length of the soccer field in Lexie's drawing should be 45 centimeters.

Answer:

Graph of quadratic opening downward and linear sloping up to the left. They intersect at point negative 3, negative 1 and point 1, negative 5

Step-by-step explanation:

we have

[tex]-x^{2} -3x-1=-x-4[/tex]

we can separate the expression above into two equations

[tex]y=-x^{2} -3x-1[/tex] ----> equation A

This is a quadratic equation ( vertical parabola) open downward (the leading coefficient is negative)

[tex]y=-x-4[/tex] ----> equation B  

This is a linear equation with negative slope (decreasing function).so linear sloping up to the left

The solution of the original expression are the x-coordinates of the intersection point both graphs

using a graphing tool

The intersection points are (-3,-1) and (1,-5)

see the attached figure

Answer: C is the correct choice

Step-by-step explanation: