The archway of the main entrance of a university is modeled by the quadratic equation y = -x2 6x. the university is hanging a banner at the main entrance at an angle defined by the equation 4y = 21 − x. at what points should the banner be attached to the archway?

Answer:

Step-by-step explanation

2 * [3 * (16 + 1)] - 8 =

2 * [3 * 17] - 8 =

2 * 51 - 8

102 - 8 =

94

Median is the central tendency of the data and always exists in the middle of the data set.

The Median is the middlemost value of the numbers arranged in the ascending orders. Median is the central tendency of the data and always exists in the middle of the data set.

The process of finding the median if the number of data points is even is as follows:

( if the number of data pints were even then we just need to arrange the numbers and cross the high/low pair and only one data point will be left which acts as the Median of the data set)

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The probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.

From the information given, we have to find the probability for each fruit. This will be:

Almond = 12/50 = 0.24

Cashew = 10/50 = 0.2

Mixed = 6/50 = 0.12

Peanut = 14/50 = 0.28

Pecan = 8/50 = 0.16

Therefore, the probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.

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L = 2W

perimeter = 2( L + W ) = 20 .

2 ( 2W + W ) = 20

6 W = 20

W = 20/6

= 10/3

L = 20/3

Answer:

10/3

Step-by-step explanation:

Given properties of the rectangle:

Given this we want to find the width of the perimeter.

Creating a system of equation:

First off we know that perimeter = 2L + 2W

We also know that the perimeter of this rectangle is 20 cm

So we can say that 20 = 2L + 2W

We also know that the length of this rectangle is twice the width or in other words l = 2w

So we have the two equations, 20 = 2l + 2w and l = 2w

Solving the system:

We are going to use the substitution method to solve this system.

The substitution method works when you have two equations, one can be just a plain equation but the other must have one of the variables defined ( by itself on either side of the equal sign )

If you have one of the variables defined, you can plug it in ( substitute ) into the other equation and solve for the other variable.

Plugging in the defined variable into the other equation

Equation : 20 = 2l + 2w

Defined variable : l = 2w

==> plug in l = 2w

20 = 2(2w) + 2w ( now we solve )

==> multiply 2 and 2w

20 = 4w + 2w

==> combine like terms

20 = 6w

==> divide both sides by 6

20/6 = w

==> simplify fraction

10/3  = w

The width = 10/3

Checking our work:

First we must solve for length as well

Solving for length by plugging in width into either equation

l = 2w

==> plug in w = 10/3

l = 2(10/3)

==> multiply 2 and 10/3

l = 20/3

Now to check our we we plug in the length and width into both equations, if both are true then our answer is correct

Equation 1 : 2l + 2w = 20

==> plug in l = 20/3 and w = 10/3

2(20/3) + 2(10/3) = 20

==> simplify multiplication

40/3 + 20/3 = 20

==> add fractions

20 = 20

Equation 2 : l = 2w

==> plug in l = 20/3 and w = 10/3

20/3 = 2(10/3)

==> multiply 2 and 10/3

20/3 = 20/3

Both are correct so our final answer is correct as well! :)

Answer:

The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle

The Leg Rule (or Leg geometric mean theorem) relates the length of each leg of a right triangle with the segments projected by them on the hypotenuse.

Step-by-step explanation:

The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Notice the triangle used with this rule. The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.

Answer:

  The sine of the angle = the length of the opposite side. the length of the hypotenuse.

  The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.

  The tangent of the angle = the length of the opposite side. the length of the adjacent side.

Step-by-step explanation:

Answer:

c = a√2

Step-by-step explanation:

Apply the 45º-45º-90º Triangle Theorem to find the length of the hypotenuse of the triangle.

since there is no measure, I will write you the formula:

c (hypotenuse) = a√2

Step-by-step explanation:

the answer is C since y is less than. meaning that the line should be dashed and below the graph.

comment if you have any doubts.

Check the picture below.

Answer:

Probability=number of specific outcomes/total of all possible outcomes

There are 5 blue marbles and a total of 15 marbles.

So the probability of drawing a blue marble from the jar is:

5/15

1/3

Step-by-step explanation:

Hope this helps

Answer:

If you entered the function correctly there is not a range  

Step-by-step explanation:

Answer: {y|-♾<y<0}

Step-by-step explanation: i’m taking this summer school class

The probabilities are:

The probability of getting a particular color of marble, is given by the quotient between the number of marbles of that color and the total number of marbles.

Here we have:

So the total number is 5 + 7 + 4 + 8 = 24.

Then:

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Answer:

h=70°

Step-by-step explanation:

h + 110° = 180° {linear pair angles}

h = 180° - 110°

h = 70°

Answer:

h=70

pa brainliest po kuya/ate

Step-by-step explanation:

pa brainliest po

Answer:

-10 is the opposite of 10

Step-by-step explanation:

-10 is the opposite of 10 ,because The sum of a number and its opposite equals to zero.

450t+550t=4,000

1000t=4000

t=4000/1000

t=4 hours they will be 4,000 apart.

------------------------------------------

20t+12(4.5-t)=70

20t+54-12t=70

8t=70-54

8t=16

t=16/8

t=2 hours at 20 mph.

proof

20*2+12(4.5-2)=70

40+12(2.5)=70

40+30=70

70=70

The employee that has the larger pay increase is Jane. Her income is larger by £65.

Percentage is the fraction out of an amount that is usually expressed as a number out of hundred.

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Answer:

14

Step-by-step explanation:

|-14|=14

Division is one of the four fundamental arithmetic operations. The number of pints of water Scott drank yesterday is 4.2 pints.

Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

A rope was 14.35 inches long. Megean cut the rope into 7 pieces of equal length. Therefore, the length of each piece of rope in inches will be,

Length of piece = 14.35 inches/7 = 2.05 inches

Scott drank 3.5 bottles of water yesterday . Each bottle contained 1.2 pints of water. Therefore, the number of pints of water Scott drank yesterday is,

Number of pints = 3.5 bottles × 1.2 pints = 4.2 pints

Hence, The number of pints of water Scott drank yesterday is 4.2 pints.

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Answer:

  B: 610; A: 202,000

  D: 253; C: 2,007,000

Step-by-step explanation:

These are all expressions that can be calculated as is, or that can be simplified a little bit by taking advantage of the distributive property and other properties of addition and multiplication. The idea is to look for numbers that show up more than once, and rearrange the expression so they only show up once.

__

This is a straight addition problem. The two "176" values have opposite signs, so cancel when they are added. Using the associative and commutative properties of addition, we can rearrange this to ...

   597 +13 +(-176 +176)

  = 597 +13

This can further be rearranged to ...

  = (597 +3) +(13 -3)

  = 600 +10

  = 610

__

The factor 2020 can be put outside parentheses using the distributive property:

  = 2020(173 -73)

  = 2020×100

  = 202,000

__

The value 15 is repeated. Terms using it can be combined using the distributive property.

  = 15(17 -1) +13

  = 15(16) +13

  = 240 +13

  = 253

Another way to look at this one is to use the factoring of the difference of squares.

  = (16 +1)(16 -1) +(-15 +13)

  = 16² -1² +(-2)

  = 256 -3

  = 253

__

Again, we can focus on rearranging so 2019 only needs to show up once.

  = 2019(890 +110) -12000

  = 2019×1000 -12×1000

  = (2019 -12)×1000

  = 2,007,000

Answer:the answer is 352

Step-by-step explanation: mike can find the sum by adding the two numbers 145+237=352 to make it simpler you can start by adding the hundreds then the tens and then the ones.

Answer:

15) 3.2

17) 13.4

Step-by-step explanation:

To find the missing lengths, you need to use the Pythagorean theorem:

a² + b² = c²

In this form, "c" represents the length of the hypotenuse and "a" and "b" represent the lengths of the other two sides.

You are trying to find one of the side lengths (not the hypotenuse) in 15). To find the other length, you can plug the other values into the equation and simplify to find "b".

15)    a = 4.1     c = 5.2

a² + b² = c²                                    <----- Pythagreom Theorem

(4.1)² + b² = (5.2)²                          <----- Plug values in for "a" and "c"

16.81 + b² = 27.04                         <----- Raise numbers to the power of 2

b² = 10.23                                      <----- Subtract 16.81 from both sides

b = 3.2                                           <----- Take the square root of both sides

You are trying to find the hypotenuse in 17). Since you have been given the lengths of the other sides, you can plug them into the equations and simplify to find "c".

17)   a = 4.4      b = 12.7

a² + b² = c²                                      <----- Pythagreom Theorem

(4.4)² + (12.7)² = c²                           <----- Plug values in for "a" and "b"

19.36 + 161.29 = c²                          <----- Raise numbers to the power of 2

180.65 = c²                                      <----- Add

13.4 = c                                            <----- Take the square root of both sides

The true statement about is the graph has a range of {y|-∞ < y < ∞} and decreases as x approaches 0.

A logarithm function is a type of function that represents the inverse of an exponential function. Mathematically, a logarithmic function is written as [tex]y =log_ax[/tex].

The domain of the given logarithm function f(x) = logx is (x > 0) and its graph wouldn't touch the vertical axis but moves to the right.

Also, the logarithmic function increases as the value of x increases. Thus, this function would decrease when x approaches zero (0).

In conclusion, we can deduce that the range of this function is -∞ < y < ∞.

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Answer:

domain:

c. The graph has a domain of {x|0<x<∞} and approaches 0 as x decreases.

and pretty sure the range is:

b. The graph has a range of {y|-∞<y<∞}and decreases as x approaches 0.

because all real numbers

Step-by-step explanation:

hope this helped

Answer:

P = 156 units

Step-by-step explanation:

the perimeter (P) is the sum of the 3 sides of the triangle.

tangents from an external point to the circle are congruent , that is

HK = HJ ( substitute values )

13x - 8 = 7x + 4 ( subtract 7x from both sides )

6x - 8 = 4 ( add 8 to both sides )

6x = 12 ( divide both sides by 2 )

x = 2

Then

HK = HJ = 7x + 4 = 7(2) + 4 = 14 + 4 = 18

and

KI = IL = 21

then

GL = GJ = 60 - 21 = 39

Thus

P = HK + KI + IG + GJ + JH = 18 + 21 + 60 + 39 + 18 = 156 units

Answer:

Step-by-step explanation:

The triangles are congruent when corresponding sides are congruent.

__

ΔFGH ≅ ΔABC means corresponding sides are ...

  (GH, BC) = (V, 16)

  (HF, CA) = (48, W)

Corresponding sides being congruent means ...

  V = 16

  W = 48

The inequality that can be used  to determine the number of boxes of donuts, d, they must sell in order to meet their goal is $1500 ≥ $575 + $5d.

Here are inequality signs and what they denote:

Total amount that needs to be raised ≥ amount made at the fruit sale + (profit per box x number of boxes)

$1500 ≥ $575 + $5d

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The equation on the graph is shown (I really hope this helps)

Equation of the translated graph is;

⇒y = cos(x - 30) - 1

What is equation of translated graph?

Equation of the translated graph is solved as;

g(x) = f(x + k) + C

Where, k and C are points.

Given that;

The equation is;

y = cos x

Since, Graph of function y = cosx is translated by (30, -1).

So, Equation of translated graph will be;

y = cos(x - 30) - 1

Hence, The equation of the translated graph will be;

⇒ y = cos(x - 30) - 1

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Using the triangle sum theorem, the value of angle ACB in the triangle is: B. 50°.

According to the triangle sum theorem, the sum of all the angles in a triangle equals 180 degrees.

90 + 7x - 20 + 4x = 180

70 + 11x = 180

11x = 180 - 70

11x = 110

11x/11 = 110/11

x = 10

m∠ACB = 7x - 20

Plug in the value of x

m∠ACB = 7(10) - 20

m∠ACB = 50° (option B).

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[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: 5 < b = 6 \: \: \: or \: \: \: b - 5 = 6 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b - 5 = 6 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b = 6 + 5 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\dashrightarrow \: \: \underline{ \boxed{\mathbf \red{ \: \: b = 11 \: \: }}} \\ \end{gathered}[/tex]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

[tex]\begin{gathered}\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \small \color{blue}{ \underline{\boxed{ \begin{array}{cc} \small \underline{\underline{\bf{ \color{red}{{ \orange \bigstar \: MᴏʀE \: IᴅᴇɴᴛɪᴛɪᴇS \: \orange \bigstar}}}}} \\ \\ \: \frak{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \: \frak{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \: \frak{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \: \frak{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \: \frak{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \: \frak{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \: \frak{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \: \frak{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \\ \: \end{array} }}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \: \: [/tex]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

^०^

Answer:  B.   5/13

This is the same as writing [tex]\frac{5}{13}[/tex]

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

Reason:

We have two given sides of this right triangle. Use the pythagorean theorem to find the missing side.

a = 5 and b = 12 are the two known legs; c is the unknown hypotenuse

[tex]a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+12^2}\\\\c = \sqrt{25+144}\\\\c = \sqrt{169}\\\\c = 13\\\\[/tex]

The hypotenuse is exactly 13 units long. This is a 5-12-13 right triangle.

Now we can compute sine of theta

[tex]\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{5}{13}\\\\[/tex]

This points us to choice B as the final answer.

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