Expand and simplify
(5x + 2)(x + 2)

Answer:

5y²

Step-by-step explanation:

Prime factorizing each term :

⇒ 30y¹⁰ = 5 x 3 x 2 x y¹⁰

⇒ 15y⁶ = 5 x 3 x y⁶

⇒ 5y² = 5 x y²

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

From this, we understand the GCF of the numbers are :

⇒ 5 × y²

⇒ 5y²

An equation that describes the graph is [tex]y=-x^{2} +1[/tex]

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

"It is a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. "

For given question,

The graph describes the parabola.

The parabola opens downward, so the equation of the parabola would be,

[tex]y=-x^{2}[/tex]

We know that, for a function f(x) is transformed to f(x) + c if c > 0 then the graph of the function moves up by c units.

if c < 0 then the graph of the function moves down by c units.

As the graph of the parabola moves down by 1 unit, the equation of the parabola would be,

[tex]y=-x^2+1[/tex]

Therefore, the equation that describes the graph is [tex]y=-x^{2} +1[/tex]

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Answer:

Pentagon

Step-by-step explanation:

Because as you can see, a regular pentagon is bigger than then the hexagon. If it's both in the circle below, the pentagon will most likely have an big advantage in this.

What will happen if marquis doesn't file taxes in April is that; nothing will happen, but marquis will miss out on his potential refund.

Withholding in this regards by his employers simply means how much is being taken out of your paycheck in taxes.

Now, withholding tax is basically an advance payment of income tax which may be used to offset or reduce tax liabilities. In this case, since the employer has withheld $200 in federal income taxes from his paychecks, what it means is that if he doesn't file taxes in April, nothing will happen, but he will miss out on his potential refund.

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Answer:

2,4,8,11,22, or 44

Step-by-step explanation:

To figure out how many rings would be in each full row with no leftovers, we need to find all the factors of 88 (outside of 1 and 8) which are 2,4,8,11,22, and 44. Since the question does not give any more information on how big the rows need to be, I can't narrow this down any further, however if I had to choose I would say rows of 8 by 11 would be the best.

Hope this helps! :)

The area of the triangle DEF is 2 square units

The given parameters are:

D(9,-8), E(8,-3), and F(2,-5),

The area of the triangle is calculated using:

Area = 0.5|x1 * (y2 -y3) + x2 * (y1 -y3) + x3 * (y2 -y1) |

This gives

Area = 0.5|9 * (-3 + 5) + 8 * (-8 + 5) + 2 * (-3 + 8) |

Evaluate

Area = 0.5|4|

Expand

Area = 2

Hence, the area of the triangle DEF is 2 square units

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Answer:

68

Step-by-step explanation:

[tex]4+\left(11-3\right)^2\\(11-3)=8\\=4+8^2\\=4+64\\=68[/tex]

Answer:

2/3

Step-by-step explanation:

Probability (b or e) :

⇒ There are 3 b's and 3 e's in the word "bumblebee"

⇒ P (b or e) = No. of b's and e's / Total letters

⇒ P (b or e) = 3 + 3 / 9

⇒ P (b or e) = 6/9

⇒ P (b or e) = 2/3

Answer:

[tex]\tan \theta = \dfrac{8}{15}[/tex]

Step by step explanation:

[tex]\text{Given that,}\\\\~~~~~~~\sin \theta = \dfrac{8}{17}\\\\\implies \sin^2 \theta = \dfrac{64}{289}\\\\\implies 1-\cos^2 \theta = \dfrac{64}{289}\\\\\implies \cos^2 \theta = 1-\dfrac{64}{289}\\\\\implies \cos^2 \theta = \dfrac{225}{289}\\\\\implies \cos \theta =\pm\sqrt{\dfrac{225}{289}}\\\\\implies \cos \theta = \pm\dfrac{15}{17}[/tex]

[tex]\text{In quadrant I, all ratios are positive, so,}~ \cos \theta = \dfrac{15}{17}\\\\\text{Now,}\\\\\tan \theta = \dfrac{\sin \theta }{\cos \theta}\\\\\\~~~~~~~~=\dfrac{\tfrac{8}{17}}{\tfrac{15}{17}}\\\\\\~~~~~~~~=\dfrac{8}{17} \times \dfrac{17}{15}\\\\\\~~~~~~~=\dfrac{8}{15}[/tex]

Answer:

C

Step-by-step explanation:

-4x+2<6

-4x<4

x<-1

because the sign doesnt have a line under it, it is an open hole

Answer:

[tex]\text{P(green)} =\frac{45}{139}[/tex]

Step-by-step explanation:

The total number of candies is :

= 42+45+20+32

= 139

Then

we have 45 green out of 139 candies.

Then

[tex]\text{P(green)} =\frac{45}{139}[/tex]

Note : 45/139 is already simplified.

Answer:

5

Step-by-step explanation:

the gradient is 5

change in Y over change in X

The property identity of multiplication is applied in the given statement.

The properties of multiplication are:

From the property identity, you know that the product between any number by the number 1 equals that number. Example: 3 • 1=3.

The question shows 10=10•1. Like, it was shown previously, this occurs due to the identity property of multiplication.

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Answer:

Step-by-step explanation:

Answer:

A and E

Step-by-step explanation:

A is already given by the basic fact that DE = FG. this makes the 2 lines automatically also congruent.

but this does not tell us anything about EF.

E and F could be very close together or far apart, and still DE = FG can be true in either case.

and that is why B, C and D could be true, but they are not in all cases true, and therefore these statements are in general false.

Answer:

27 units

Step-by-step explanation:

6 (base) × 9 (height) = 54

54 × 1/2 = 27

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

so in this case we have the provided ones (2005 , 12000) and (2010 , 12250)

[tex](\stackrel{x_1}{2005}~,~\stackrel{y_1}{12000})\qquad (\stackrel{x_2}{2010}~,~\stackrel{y_2}{12250}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12250}-\stackrel{y1}{12000}}}{\underset{run} {\underset{x_2}{2010}-\underset{x_1}{2005}}} \implies \cfrac{12250 -12000}{2010 -2005}\implies \cfrac{250}{5}\implies \underset{\textit{rate of change}}{50}[/tex]

Answer:

Step-by-step explanation:

As it is a second order equation, it means that it has two possible answers and they are [tex]x_1[/tex] and [tex]x_2[/tex].

The famous quadratic formula for solving any second order equation is the following:

[tex]x_{1} = \frac{-b + \sqrt{b^2 - 4 ac}}{2a}\\x_{2}=\frac{-b - \sqrt{b^2 - 4 ac}}{2a}[/tex]

Where a is the coefficient of [tex]x^2[/tex], b is the coefficient of x, and c is the free term. In other words,

[tex]a = 3\\b=4\\c=-2[/tex]

as the equation should be in the following form:

[tex]a x^2 + bx+c = 0[/tex]

Therefore the possible answer should be the following,

[tex]\frac{-4 + \sqrt{4^2 - 4*3*(-2)}}{2*3}=\frac{-4 +\sqrt{16 + 24}}{6} =\frac{-4 + \sqrt{40}}{6}=\\ \frac{-4 + \sqrt{4*10}}{6} = \frac{-4 + 2\sqrt{10}}{6}[/tex][tex]\frac{2*(-2 + \sqrt{10})}{2*3} = \frac{-2 + \sqrt{10}}{3}[/tex]

by dividing the numerator and denominator by 2, we can deduce the following,

The number of players in the team would be 15 which can bring to the tournament.

A soccer squad collected $1511 to attend a competition. They spent $933.50 on a bus rental and $38.50 for each player on food.

A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

Let the number of players would be x

As per the given information, the required solution would be as:

Total budget = (per player meal)(x players) + bus rent

1511 = 38.50x + 933.50

Rearrange the terms and solve for x

1511 - 933.50 = 38.50x

577.50 = 38.50 x

Divide both sides by 38.50 into above equation,

x = 15

Therefore, the number of players in the team would be 15 which can bring to the tournament.

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Considering the area of the hole, it is found that there is a 4.9% probability of hitting a ball into the circular hole.

The area of a circle of radius r is given by:

[tex]A = \pi r^2[/tex]

In this problem, the hole has a diameter of 1 ft, hence it is radius is of r = 1 ft/2 = 0.5 ft, and it's area is given by:

[tex]A = \pi \times (0.5)^2 = 0.7854 \text{ft}^2[/tex]

Hence the probability is given by:

p = 0.7854/16 = 0.049 = 4.9%

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Answer:

A

Step-by-step explanation:

We are asked to find the amount of interest earned on $16,500 than $15,000 with APYs of 4.1% for a year.

We will use simple interest formula to solve our given problem.

I= prt

i= amount of interest

p=principal amount

r= interest rate in decimal form

t= time in years

4.1%=  41/100= 0.041

$16,500 times 0.041 -  $15,000 times 0.041

(16,500- 15,000) times 0.041

(1,500) times 0.041

So the answer is $61.50

I hope this is right, have a nice day.

The probability of picking two snacks of the same type is 0.308.

The probability of picking 2 potato will be:

= 6/14 × 5/13

= 0.429 × 0.385

= 0.165

The probability of picking 2 doritos will be:

= 5/14 × 4/13

= 0.357 × 0.308

= 0.110

The probability of picking 2 corn curls will be:

= 3/14 × 2/13

= 0.214 × 0.154

= 0.033

Therefore, the probability of picking two snacks of the same type will be:

= 0.165 + 0.110 + 0.033

= 0.308

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Answer:

C: is a function because each input (x) has exactly one output( y).

Step-by-step explanation:

A function is when one input (x) has exactly one output (y).

A: is not a function because -4 is paired with two different y values.

B: is not a function because -4 is paired with two different y values.

C: is a function because each input (x) has exactly one output( y).

D: is not a function because -1 is paired with two different y values.

The translated vertices are:

The vertices of the original figure are:

Now we want to apply a translation of four units to the right and 2 units down, then each point (x, y) becomes (x + 4, y - 2).

This means that the translated vertices are:

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Answer:

CE = 3.2 cm

DH = 4.5 cm

Explanation:

Given:

MNPR ≅ CEDH

≅ - means approximately equal

Lengths of the shape:

MN = CE = 3.2 cm

NP = ED = 6.5 cm

PR = DH = 4.5 cm

RM = HC = 9 cm

In order to find equation, first find slope:

[tex]\sf slope : \dfrac{y_2 - y_1}{x_2 - x_1} \quad where \ (x_1, y_1) , \ (x_2, y_2) \ are \ points[/tex]

Given points: (-3, 7) and (6, -5)

[tex]\rightarrow \sf slope : \dfrac{-5-7}{6-(-3)} =-\dfrac{4}{3}[/tex]

Equation:

[tex]\sf y- y_1 = m(x - x_1)[/tex]

insert values

[tex]\rightarrow \sf y - 7 = -\dfrac{4}{3} (x -(-3))[/tex]

[tex]\rightarrow \sf y = -\dfrac{4}{3} x - 4 +7[/tex]

[tex]\rightarrow \sf y = -\dfrac{4}{3} x +3[/tex]

Answer:

50-20 or perimeter-2length

Step-by-step explanation:

15 inches is the width