What value of $k$ will make $4x^2 - 20x + k$ the square of a binomial?

Answer:

The altitude of the trapezoid is 60 feet.

Step-by-step explanation:

Trapezoid

Sum of the bases: B+b=280 feet

Area of the trapezoid: A=8,400 feet^2

Altitude of the trapezoid: h=?

The formula to calculate the area of a Trapezoid is:

A = (1/2) (B+b) h

Replacing the given values:

8,400 feet^2 = (1/2) (280 feet) h

(1/2) (280 feet) = (140 feet)

8,400 feet^2 = (140 feet) h

Solving for h: Dividing both sides of the equation by 140 feet:

8,400 feet^2 / (140 feet) = (140 feet) h / (140 feet)

60 feet = h

h = 60 feet

Answer: The altitude of the trapezoid is 60 feet.

Answer:

60

Step-by-step explanation:

Answer:

29.03 units

Step-by-step explanation:

x^2 = 10^2 + 19^2 - 2*19*20 cos 122

=   100 + 361 - 720 * -0.52992

= 842.54

x = 29.03

Answer:

20 hours

hope it helps

Step-by-step explanation:

total earnings was $240 but to find how much he made working you first have to deduct the $80 bonus  

240 - 80 = 160

so he made $160 working now to find out how many hours worked you have to divide by 8 because he got paid $8.00 an hour

160 ÷ 8 = 20

Answer:

20hrs

Step-by-step explanation:

We need to find out how many hours she worked last week.

The bonus added $80 to the money she got from her hours worked so lets take that away:

240-80=160

Since she gets $8/hr  we should divide 160 by 8

160÷8=20

Answer: the answer is 6ft

Step-by-step explanation:

3 times 1 times 2 = 6ft

Number of gallons of water would it take to fill the tank two-thirds full is,

⇒ 30 gallons

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

An aquarium tank is 3 feet long, 1 foot wide, and 2 feet high.

Hence, Volume of tank is,

⇒ V = 3 x 1 x 2

⇒ V = 6 feet³

Hence, Number of gallons of water would it take to fill the tank two-thirds full is,

⇒ 2/3 of 6

⇒ 4 feet³

⇒ 4 × 7.5

⇒ 30 gallons

Thus, Number of gallons of water would it take to fill the tank two-thirds full is,

⇒ 30 gallons

Learn more about the multiplication visit:

https://brainly.com/question/10873737

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It's going to be 7/10

Answer:

B

Step-by-step explanation:

Since AB = AC = 8 then the triangle is isosceles and

∠C = ∠B = 30° ( base angles of an isosceles triangle )

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the base angles from 180, hence

∠A = 180° - (30 + 30)° = 180° - 60° = 120° → B

Answer:

A x 5

Step-by-step explanation:

Answer:

take all evaporation numbers and add them together to get the answer u r looking for

Step-by-step explanation:

Answer:

[tex]y=cos(x+\pi )[/tex]

Step-by-step explanation:

From the graph, we can see that y = -1 when x  = 0.

So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.

1. y = cos(x + pi/2) = cos(0 + pi/2) = 0

2. y = cos(x+2pi) = cos(0+2pi) = 1

3. y = cos(x+pi/3) = cos(0+pi/3) = 1/2 = 0.5

4. y = cos(x+pi) = cos(0+pi) = -1

Therefore, the equation of this graph is y = cos(x+pi) = cos(0+pi) = -1.

Answer:

3n+5

Step-by-step explanation:

Answer:

Opposite angles of a parallelogram are congruent.

Step-by-step explanation:

Given:

KLMN is a parallelogram.

KN ║ LM and KL ║MN.

To prove:

∠N ≅ ∠L

∠M ≅ ∠K

Proof:

∠N ≅ ∠L since the opposite angles of a parallelogram are congruent.

∠M ≅ ∠K since the opposite angles of a parallelogram are congruent.

Answer: Parallelogram KLMN Given

KL¯¯¯¯¯∥NM¯¯¯¯¯¯¯ and Kn---------llLM Definition of parallelogram

m∠K+m∠N=180°

m∠L+m∠M=180°

m∠K+m∠L=180° Same-Side Interior Angles Theorem

m∠K+m∠N=m∠K+m∠L

m∠L+m∠M=m∠K+m∠L Substitution Property of Equality

m∠N=m∠L

m∠M=m∠K Subtraction Property of Equality

∠N≅∠L

and ∠M≅∠K

Angle Congruence Postulate

Step-by-step explanation:

I took the test and got a 100

[tex]\frac{422}{8}=52.75mph[/tex]

A.

[tex]average=\dfrac{distance}{time}\\\\\text{We have}\\\\distance=422\ miles\\\\time=8\ hours.\\\\\text{Substitute:}\\\\\boxed{x=\dfrac{422\ miles}{8\ hours}=52.75\ mph}[/tex]

Answer: 5h represents the number of hours Rob actually spent on the project.

Step-by-step explanation:

Let Rob planned that he will spend x hours in his project.

According to the question,

He spent 25% more time on his project than he planned.

That is,  his actual time = x + 25% of x = 125% of x

Again according to the question,

He spent an extra h hours on his project.

That is,  25% of x = h

[tex]\frac{25\times x}{100} = h[/tex]

[tex]x=\frac{100h}{25}[/tex]

x = 4h

Thus,  his actual time = 125% of x = 125% of 4h = [tex]\frac{125\times 4h}{100}[/tex] = 5h

Which is the required expression.

Answer:

5h and (h/0.25)1.25

Step-by-step explanation:

This means he planned to spend \dfrac{\maroonD{h}}{\greenD{25\%}}\cdot100\%  

25%

h

​  ⋅100%start fraction, start color maroonD, h, end color maroonD, divided by, start color greenD, 25, percent, end color greenD, end fraction, dot, 100, percent hours on the research project.

Hint #33 / 6

Because 25\%25%25, percent means 252525 per hundred, we can write it in equivalent forms.

\begin{aligned} 25\%&=\dfrac{25}{100}\\\\ &=0.25 \end{aligned}  

25%

​    

=  

100

25

​  

=0.25

​

Answer:

x= 0.4

Step-by-step explanation:

We need to solve and find the value of x

7 1/3x = 1.6 ÷ 6/11

Converting mixed fraction into improper fraction

22/3 x = 1.6 ÷ 6/11

Converting ÷ sign by X and reciprocating the term

22/3 x = 1.6 * 11/6

Now divide both sides by 3/22

x = 1.6 * 11/6 * 3/22

x = 1.6 * 1/2 * 1/2

x = 1.6/4

x = 0.4

S0, x= 0.4

Answer:

v = 9

Step-by-step explanation:

Use the method of cross- multiplying

[tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex] ⇒ ad = bc

8v = 12 × 6

8v = 72 ( divide both sides by 8 )

v = 9

Answer:

[tex]v=9[/tex]

Step-by-step explanation:

The given equation is

[tex]\frac{v}{12}=\frac{6}{8}[/tex].

We multiply both sides of the equation by 12 to obtain,

[tex]12\times \frac{v}{12}=\frac{6}{8}\times 12[/tex].

This implies that;

[tex]v=\frac{3}{4} \times 12[/tex]

This gives

[tex]v=\frac{3}{1} \times 3[/tex]

[tex]v=3\times 3[/tex]

[tex]v=9[/tex]

[tex]\dfrac{5x^4+10x^3-7x+1}{x+2}=(5x^4+10x^3-7x+1):(x+2)[/tex]

[tex]_+\begin{matrix}(5x^4&+&10x^3&-&7x&+&1)&:&(x+2)&=5x^3-7\\-5x^4&-&10x^3\end{matrix}\\\overline{_+\begin{matrix}\ \ =&&&&=&\ \ \ -&7x&+&1\\&&&&&&7x&+&14\end{matrix}}\\\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\ 15}[/tex]

[tex]\dfrac{5x^4+10x^3-7x+1}{x+2}=(5x^4+10x^3-7x+1):(x+2)=5x^3-7+R(15)\\\\5x^4+10x^3-7x+1=(x+2)(5x^3-7)+15[/tex]

Final answer:

Long division is a method used to divide two polynomials in algebra. It involves arranging the dividend and divisor, determining the term of the quotient, subtracting and repeating until there are no more terms left to bring down.

Explanation:

In algebra, long division is a method used to divide two polynomials. It is especially useful when the dividend (the polynomial being divided) has a higher degree than the divisor (the polynomial dividing the dividend).

Here's a step-by-step explanation:

Let me know if you need further assistance or if there's anything else I can help you with!

Answer: 252 feet tall

Step-by-step explanation:

1) make a proportion

x/18=140/10

2)solve

10x=140*18

x=140*18/10

x=14*18

x=252

3) Answer

The building is 252 feet tall

Answer:

The right answer is 1 unit or A

Step-by-step explanation:

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The given ratio is [tex]\frac{18}{27}[/tex]

9 is the common factor of 18 and 27

divide numerator and denominator by 9

[tex]\frac{18/9}{27/9} =\frac{2}{3}[/tex]

hence [tex]\frac{2}{3}[/tex] is proportion with [tex]\frac{18}{27}[/tex]

Answer:

D

Step-by-step explanation:

note that the values in the domain map to the values in the domain as

- 1 → 2 ( that is 1 + 3 = 2 )

3 → 6 ( that is 3 + 3 = 6 )

5 → 8 ( that is 5 + 3 = 8 )

In each case 3 is added to the value in the domain(x) to obtain the value in the range ( y = f(x) )

Hence f(x) = x + 3 → D

Answer:

21 students

Step-by-step explanation:

90 x .10 = 9

80 x .15 = 12

9 + 12 = 21 students

The amount that is direct-deposited bi-weekly is 404.30.

To calculate the bi-weekly direct deposit amount, we need to follow these steps:

1. Calculate the gross pay for a week:

 Gross pay per week = Hourly wage * Hours worked per week

 Gross pay per week = $8.60/hr * 32 hr/wk

 Gross pay per week = $275.20

2. Calculate the total deductions per week:

 Total deductions rate = FICA rate + federal tax rate + state tax rate

 Total deductions rate = 7.65% + 10.6% + 8.25%

 Total deductions rate = 26.5%

 Total deductions per week = Gross pay per week * Total deductions rate

 Total deductions per week = $275.20 * 26.5%

 Total deductions per week = $73.049

 3. Calculate the net pay for a week:

 Net pay per week = Gross pay per week - Total deductions per week

 Net pay per week = $275.20 - $73.049

 Net pay per week = $202.151

4. Calculate the bi-weekly net pay:

 Bi-weekly net pay = Net pay per week* 2

 Bi-weekly net pay = $202.151 * 2

 Bi-weekly net pay = $404.302

Since the net pay is calculated to the nearest cent, we can round the bi-weekly net pay to the nearest cent as well:

Bi-weekly net pay (rounded) = $404.30

Therefore, the amount that is direct-deposited bi-weekly is 404.30.

The answer is: $404.30.

Answer:

4) 80 5) 96 6) 50 7) 28 8) 17 9) 14 10) 58

Step-by-step explanation:

4) 41+39 5) 28+32+46 6) 13+37 7) 45-17 8) 39-22 9) 31-17 10) 18+40

Answer:

B. 14

Step-by-step explanation:

The sum of infinite geometric series is given by

[tex]\frac{a}{1-r}[/tex]

0.126126126... = [tex]\frac{126}{1000}+\frac{126}{1000000}+\frac{126}{1000000000}[/tex]

Here a =126/1000, r= 1/1000

0.126126126... = [tex]\frac{126/1000}{1-1/1000}[/tex] =126/999 = 14/111

∴ 0.126126126... = 14/111

So, the numerator of the reduced fraction is 14.

Answer:

B. 14

Step-by-step explanation:

Answer:

Step-by-step explanation: To find a y intercept you must find what y is when x is 0 so because it already tells you on the table the y intercept is 4. To find slope take 2 x intercepts and 2 y intercepts. For this well take the 0,4 and 5,1. The take the y from both pairs and minus them so it will look like 4 minus 1. Then draw a line under the equation under this line do the same thing but with the x's from both pairs so 0-5 then you will get as a result of both -3/5 as your slope.

Answer:

slope: -3/5

y-intercept: (0, 4)

slope-intercept form: y = -3/5x + 4

Step-by-step explanation:

To find the slope of this line, you would take two points from the table and substitute their coordinates into the slope formula.

Slope formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

I'm going to use the points (0, 4) and (5, 1). You can really use any point from the table. Substitute these points into the formula to find the slope.

(0, 4), (5, 1) → [tex]\frac{1-4}{5-0} \rightarrow \frac{-3}{5}[/tex]

This means the slope of the line is -3/5.

The y-intercept will always have the value of x be 0 (so the point is solely on the y-axis), so by looking at the table we can see that the y-intercept is at (0, 4).

Since we have the slope and a point of the line, we must use point-slope form to find the equation of the line in slope-intercept form. Substitute in the point (0, 4) --you could use any point from the table-- and the slope -3/5 into the point-slope form equation.

point-slope form: y - y1 = m(x - x1) --you'll be substituting the point coordinates and slope into y1, x1, and m.

y - (4) = -3/5(x - (0))

Simplify.

y - 4 = -3/5x

Add 4 to both sides.

y = -3/5x + 4 is the equation of the line in slope-intercept form (you have both the slope and the y-intercept in this form).

Answer:

30°                                

Step-by-step explanation:

No. of sides in dodecagon = 12

No. of angles = 12

Since its regular, all sides and all angles are equal.

total rotational angle = 360°

since no. of angles = 12

and all angles are equal,

rotational angle at which, it will co - incide with itself = [tex]\frac{360}{12}[/tex]

                                                                                     = 30°

A regular dodecagon will be onto itself it is rotated about the central angle 30°.

Answer: 30°

Step-by-step explanation:

Answer:

l = 2 1/2 ft

Step-by-step explanation:

The formula for A is l*w for a rectangular length

A= lw

Putting in what we know

8 1/2 = l * 3 2/5

I will change mixed numbers to improper fractions

8 1/2 = (2*8+1)/2 = 17/2

3 2/5 = (5*3+2)/5 = 17/5

17/2 = l*17/5

Multiply both sides by 5/17 to isolate l

5/17* 17/2 = l* 17/5 * 5/17

5/2 = l

Changing this back to a mixed number

2 1/2 = l

if the ∡E = ∡F = 90°, that means for that quadrilateral of BEGF, the other angles are ∡B = ∡G = 90°, which means is a square, meaning all its sides are equal, therefore

[tex]\bf y + 5 = 3y\implies 5=2y\implies \cfrac{5}{2}=y\implies 2\frac{1}{2}=y[/tex]