Find P on line segment CD that is 3/4 the distance from C(0, 0) to D (0, 12).

Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.

Here in the question it is given that,

We have to find the number of seats in each row.

Let us assume that the number of seats in each row be x.

From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,

Number of seats in one row = Number of rows + 7

x = Number of rows + 7

⇒ Number of rows = x - 7

Total number of seats in the auditorium can be written as,

⇒ (Number of seats in one row)(Number of rows) = Total number of seats

(x)(x - 7) = 2244

x² - 7x = 2244

⇒ x² - 7x - 2244 = 0

By using quadratic formula we can find the root,

x = (-b ± √b² - 4ac)/2a

here in the question, a = 1, b = -7, c = -2244

√b² - 4ac = √(-7)² - 4(1)(-2244)

√b² - 4ac = √49 + 8976

√b² - 4ac = √9025

√b² - 4ac = 95

x = (-b ± √b² - 4ac)/2a

x = (7 ± 95)/2

x = 102/2 or x = -88/2

⇒ x  = 51 or x = -44

Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.

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Answer: Mary can expect to answer 60 questions in a 150 minutes

Step-by-step explanation:

150 divided by 30 = 5

5 x 12 = 60

Applying the intersecting secants theorem, the length of segment KL is approximately, 45.8.

According to the intersecting secants theorem, if two lines from a point outside a circle intersect the circle, then the product of the length of one line segment and its portion outside the circle is equal to the product of the length of the other line segment and its portion outside the circle.

Using the theorem, we have:

MN * MO = ML * MK

Substitute:

21 * 48 = 22 * KL

1,008 = 22KL

1,008/22 = KL

KL = 45.8 (nearest tenth)

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Answer:

55 in²

Step-by-step explanation:

Base x Height

Answer

Step by step explantion:

bsf= 26

Eliana:98

SS teacher=203

David=55

Step-by-step explanation:

m= music

bsf: m

eliana:4m-6

David:2m+3

SS teacher: 2(4m-6)+7

m+4m-6+2m+3+8m-12+7

382=15m-7

7+ +7

389=15m

/15m /15m

m=26

multiply 26 to each one of them

Answer:

the value of 3b ÷ a is 3 ÷ 70

Step-by-step explanation:

The computation is shown below:

Given that

a × b = 70

So it could be write as

a = 70 ÷ b

And, the value of 3b ÷ a is

= 3b ÷ 70 ÷ b ÷ 1

= 3b ÷ 70b

= 3 ÷ 70

Hence, the value of 3b ÷ a is 3 ÷ 70

Answer:

Step-by-step explanation:

1) The base is the number 3

2) the power is 12

3) it shoud give you 3^12

4) It should give you 531441

5) You mutiply both exponents together

The length of side AB in right angled triangle ABC  will be 48 cm.

Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.

Given,

∠B= 90°, AC = 96 cm, ∠C = 30°

Now, we know, Trignometric ratio sin θ in triangle can be given by-:

sin θ = \(\frac{perpendicular}{hypotenuse}\)

From given figure,

Perpendicular= AB= ?

and Hypotenuse= AC = 96

and θ= 30°

Hence,

sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)

\(\frac{1}{2} = \frac{AB}{96}\)                                      (∵ sin 30°= 1/2)

\(AB=\frac{96}{2}\)

\(AB= 48 cm\)

Thus, AB= 48 cm

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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?

Answer: The answer is D. 35.3

Step-by-step explanation: Because the triangle has to add up to 180 and 41.3 + 103.4 = 144.7. Then you could either do 180-144.7 = 35.3 or you could add 144.7 + 35.3. Hope this helps

The value of angle C based on the information is A. 35.3°

It's important to know that the total sum of angles in a triangle is 180°.

In this case, the following can be deduced:

Angle A = 41.3°

Angle B = 103.4°

Therefore, Angie C will be:

= Total angle - {Angle A + Angle B}

= 180° - (41.3° + 103.4°)

= 180° - 144.7°

= 35.3°

Therefore, the correct option is D.

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A.  The payback period is 7.2 years. The net present value of the proposed investment is 3720.55.

B. No, the project does not meet the company's cash payback criteria.

C.  Yes, the project does meet the net present value criteria for acceptance.

A. The truck costs $55,440 and generates annual cost savings of $7,700. So the payback period is the cost of the truck divided the expected amount the truck will generate.

                $55,440 / $7,700 = 7.2 years

To solve for the net present value, we say

Net Present Value = ∑ [(Cash inflow in period t) / (1 + \(r^{t}\)] - Initial Investment.

NPV = (($7,700 / (1 + 0.08)¹) = 7 129.63

+ ($7,700 / (1 + 0.08)²) = 6601.51

+ .($7,700 / (1 + 0.08)³ = 6112.51

+ ($7,700 / (1 + 0.08)⁴) = 5659.73

+ ($7,700 / (1 + 0.08)⁵) = 5240.49

+ ($7,700 / (1 + 0.08)⁶) = 4 852.31

+ ($7,700 / (1 + 0.08)⁷) = 4492.88

+($7,700 / (1 + 0.08)⁸)  = 4160.07

+ ($27,600 / (1 + 0.08)⁸)) = 14911.42

- $55,440

We add all these values together and subtract by  $55,440

7 129.63 + 6601.51 + 6112.51 + 5659.73 + 5240.49 +4 852.31 + 4492.88 + 4160.07 + 14911.42 - $55,440

59160.55 - 55,440

NPV = 3720.55

B. The cash payback period of the project is 7.2 years. The company's cash payback criteria state that a project should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life, which would be 4 years which is 50% of 8 years. Since 7.2 years is greater than 4 years, the project does not meet the company's cash payback criteria.

C. The positive NPV of $3,720.55 shows that embarking on the prooject will be valuable to the company. This means the project meets the NPV criteria for acceptance.

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Answer: 0.18km2

Step-by-step explanation:

60mx3km=0.18km2

-3(p-1)+9p+2

10-4(m+1)

4g-2g-3(g-2)

hope it helps

stay safe healthy and happy.

Answer:

6p+5

-4m+6

-g+6

Step-by-step explanation:

1st Equation

-3(p-1)+9p+2

-> -3p+3+9p+2

=> 6p+5

2nd Equation

10 - 4(m + 1)

=> 10-4m-4

=> -4m+6

3rd Equation

4g - 2g - 3(g - 2)

=> 4g-2g-3g+6

=> -g+6

The evaluated value of x from the line geometry given is 36.

An angle is the point where two lines meet. From the given diagram, the sum of the angles on the line is 180 degrees.

Take the sum to have

x + 3x + x = 180

Simplify

4x + x = 180

5x = 180

Divide both sides by 5

5x/5 = 180/5

x = 36

Hence the value of x from the diagram is 36

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Answer:

Step-by-step explanation:

\(\angle JKH = \angle GFH\) (alternate angles)

\(\angle JHK = \angle GHF\)  (vertically opposite angles)

So answer is (A) AA Similarity Postulate.

Answer:

9 1/2

Step-by-step explanation:

19/2=19.5

Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

If there are 31 horses competing in a show, then the blue, red, and yellow ribbons can be awarded in 26970 different ways.

As per the question statement, 31 horses are competing in a show.

We are required to calculate the number of ways in which the blue, red and yellow ribbons can be awarded.

To solve this question, first, we need to know a basic rule of horse shows, which is the 1st place or the winner is awarded with a blue ribbon, the second place or the runners-up is awarded with a red ribbon and the third place or the second runners-up is awarded with a yellow ribbon.

That is, in simpler terms, we have to calculate the number of different ways, in which the first, second and third places can be achieved between 31 different horses, each having equal probability of winning.

To solve this question, we just need to know the formula of permutation which goes as \([(nPr)=\frac{n!}{(n-r)!} ]\),  i.e., we are to select an ordered set or "r" from a set of "n".

As per our question, (n = 31) and (r = 3), and using these in the above mentioned formula of permutation, we get

\((31C)=\frac{31!}{(31-3)!}=\frac{31!}{28!} =\frac{28!*29*30*31}{28!}=(28*29*30)=26970.\)

That is, the blue, red and yellow ribbons can be awarded in a show with 31 horses as contestants in 26970 different ways.

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Answer:

291870 kilotons

Step-by-step explanation:

Since the country cuts its carbon content by 1.1% each year. The initial value at the first year is 50000. Therefore this can be represented by the exponential function:

y = a(b)ˣ ⁻ ¹

where y is the amount of carbon emission in kilotons in x years.

a = 50000, b = 100% - 1.1% = 98.9% = 0.989

y = 50000(0.989)ˣ ⁻ ¹

In the first year: y = 50000(0.989)¹ ⁻ ¹ = 50000

In the second year: y = 50000(0.989)² ⁻ ¹ = 49450

In the third year: y = 50000(0.989)³ ⁻ ¹ = 48906

In the fourth year: y = 50000(0.989)⁴ ⁻ ¹ = 48368

In the fifth year: y = 50000(0.989)⁵ ⁻ ¹ = 47836

In the sixth year: y = 50000(0.989)¹ ⁻ ¹ = 47310

The total emission in 6 years = 50000 + 49450 + 48906 + 48368 + 47836 + 47310 = 291870 kilotons

Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given two triangles, Where the base of these triangles are same

And also given that the two angles are the same.

Since,

Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).

Thus, the third angle is also equal

From AAS:

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,

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After answering the presented question, standard deviation t Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)

A statistic that expresses the variability or variation of a bunch of values is the standard deviation. A high standard deviation indicates that the values are more distributed, whereas a low standard deviation indicates that the numbers are closer to the set mean. The standard deviation is a measure of how far the data are from the mean (or ). When the standard deviation is small, the data tends to cluster around the mean; when it is great, the data is more spread. The standard deviation represents the average variability of the data collection. It displays the average deviation from the mean of each score.

Next, we need to find the t-value for a 90% confidence interval with 8 degrees of freedom (n-1):

t = t(0.05, 8) = 1.860

Now we can calculate the lower and upper bounds of the confidence interval:

Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)

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Answer:

Option B is correct

Step-by-step explanation:

Original expression is |8 - 1| = 7 = distance between number 1 and number 8

=> Option B is correct

Hope this helps!

The number line model that matches the expression |8 - 1| which is correct option(B)

The graph can be defined as a pictorial representation or a diagram that represents data or values.

The expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given the expression as |8 - 1|,

The value of the expression would give us 7. Meaning that the distance between coordinate 8 and 1 is 7 units.

The graphs given models the expression, |8 - 1|.

Option A, would match |-8 -1| = 5 units

Option B, would match |8 - 1| = 7 units.

Therefore, the answer is option (B).

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By algebra properties and base change formula, the value of x of the exponential function 4ˣ ⁺ ³ = 7 is equal to 1 / ㏒₇ 4 - 3

In this question we find an exponential function that must be solved, this can be done by combining algebra properties and base change formula. Change base formula is a property that changes the base of a logarithm into another, defined below:

㏒ₐ x = ㏒ₙ x / ㏒ₙ a

Where:

First, write the entire expression:

4ˣ ⁺ ³ = 7

Second, use logarithm operators on both sides:

㏒₄ 4ˣ⁺³ = ㏒₄ 7

Third, use logarithm properties to simplify the expression:

(x + 3) · ㏒₄ 4 = ㏒₇ 7 / ㏒₇ 4

x + 3 = 1 / ㏒₇ 4

Fourth, clear x within the expression by algebra properties:

x = 1 / ㏒₇ 4 - 3

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Answer:

"proportional to"

Step-by-step explanation:

The sign ∝ means 'is proportional to'. This is used to show that one variable of value is proportional to another value or variable.

Example:

Hope this helps.

According to the angles between intersecting secant and tangent, the value of

angle DF is 52 degrees

angle PQR = 49 degrees

The value of angle DF is solved using the angles of intersecting secant out side the circle

The theorem give the formula in the form

44 = 1/2 (140 - DF)

88 = 140 - DF

DF = 140 - 88

DF = 52 degrees

Using intersection of tangents, for the second figure

exterior angle = 1/2 (major arc - minor arc)

major arc = 360 - 131 = 229

PQR = 1/2 (229 - 131)

PQR = 49 degrees

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Answer:

\(z^{12}\)

Step-by-step explanation:

\((z^{3})^4\) = \(z^{12}\)

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Answer: \(35x < 4-5x+3x^2\) is \(x < \frac{1}{3}\) or \(x > \frac{4}{3}\)

Step-by-step explanation:

A) To generate the table of values, we can substitute different values of x into the equation and solve for y.

x             y

-2        26

-1        12

0         4

1         2

2        10

To plot the graph of the function, we can use the table of values and plot the corresponding points on a graph with a scale of 4 for the y-axis and 2cm to 1 unit along the x-axis. The graph should look like a parabola opening upwards.

c) To solve for the root of the equation 4-5x+3x^2=0, we can use the graph and find the x-coordinate of the point where the graph intersects the x-axis. This point is also known as the x-intercept or the root of the equation. From the graph, we can see that the root is approximately x=0.83.

To solve the equation 3x^2 -5x=2, we can rearrange it to the form 3x^2 -5x-2=0 and factor it as (3x+1)(x-2)=0. This gives us two solutions: x=-1/3 and x=2.

To determine the range of values of x for which 35x​<4-5x+3x^2, we can rearrange the inequality to the form 3x^2-40x+4>0 and factor it as (3x-1)(x-4/3)>0. This means that either (3x-1) and (x-4/3) are both positive or both negative.

When (3x-1)>0 and (x-4/3)>0, we get x>1/3 and x>4/3, which means x>4/3.

When (3x-1)<0 and (x-4/3)<0, we get x<1/3 and x<4/3, which means x<1/3.

Therefore, the range of values of x for which 35x<4-5x+3x^2 is x<1/3 or x>4/3.

Answer:

C

Step-by-step explanation:

just did it