21. Given h(x) = -x-14, if h(x) = -2, find x.

Answer:

Step-by-step explanation:

The binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

Given that binomial  (x+5) is a factor of x² + 8x + 15.

We need to find the other factor.

Let us solve x² + 8x + 15=0

x² + 5x +3x+ 15=0

x(x+5)+3(x+5)=0

(x+3)(x+5)

So the other binomial factor is x+3.

Hence, the binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.

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The blank in the statement should be filled in with "ΔVYZ." which is proven by the definition of congruence.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbolΔ.

Since S, T, and U are midpoints in ΔVYZ, it follows that:

ST is a median of ΔVYZ, meaning it bisects the side VZ into two equal parts.

TU is a median of ΔVYZ, meaning it bisects the side VY into two equal parts.

SV is a median of ΔVYZ, meaning it bisects the side YZ into two equal parts.

Using the definition of congruence, two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in measure. Since medians bisect their corresponding sides, it follows that all three pairs of corresponding sides in ΔYST, ΔTUZ, and ΔSVU are equal in length.

Furthermore, since the medians divide the triangle into two smaller triangles that are similar to the original triangle, it follows that the corresponding angles in ΔYST, ΔTUZ, and ΔSVU are equal in measure.

Therefore, ΔYST ≅ ΔTUZ ≅ ΔSVU ≅ ΔVYZ.

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This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.

What is inequality?

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

We can write the first inequality as x + y <= 12

This inequality represents the constraint that Mav can work at most 12 hours in total between both jobs.

The second inequality represents the constraint that Mav must earn no less than $140 in a given week, which can be written as:

15x + 10y >= 140

To graph the system of inequalities, we can plot the lines corresponding to x + y = 12 and 15x + 10y = 140 on the coordinate plane and shade the region that satisfies both inequalities.

The solution to the system of inequalities will be the values of x and y that lie in the shaded region.

One possible solution is x = 4 and y = 8, which means that Mav works 4 hours of lifeguarding and 8 hours of landscaping in a given week, earning a total of 15 * 4 + 10 * 8 = $120.

Hence, This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.

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Answer:

Step-by-step explanation:

You want inequalities, their graph, and a possible solution satisfying Mav's requirement for at most 12 total hours spent lifeguarding at $15 per hour and landscaping at $10 per hour, with an income of at least $140.

The required relations can be written ...

  x + y ≤ 12 . . . . . . . total hours

  15x +10y ≥ 140 . . . . total earnings

The inequalities need to be solved for y to match the answer format requirements.

  inequality 1: y ≤ 12 -x . . . . . . . . . . subtract x

  inequality 2: y ≥ 14 -1.5x . . . . . . divide by 10, subtract 1.5x

The attached graph shows a couple of possible solutions. The solution space is the doubly-shaded area bounded by vertices ...

  (4, 8), (12, 0), and (9 1/3, 0)

Mav will make the most money working 12 hours lifeguarding (x, y) = (12, 0).

She can just meet her income requirements by working 8 hours lifeguarding and 2 hours landscaping (x, y) = (8, 2).

One possible solution is 4 hours lifeguarding and 8 hours landscaping.

The angle that the ladder makes with the ground is ∠B = 67.38°.

The distance between the ladder from the building is 5 feet.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Given that a 13-foot ladder is placed up against a wall.

The ladder's top touches the wall at a height of 12 feet.

As per the given question, we have the right triangle ΔABC

Using sine ratio to find angle ∠B as:

sin ∠B = AC/ AB

sin ∠B = 12/13

∠B = sin ⁻¹(12/13)

∠B = 67.38°

Now, using Pythagoras's theorem to find distance x as:

AC² + BC² = AB²

12² + x² = 13²

144 + x² = 169

x² = 169 - 144

x² = 25

x = 5

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Answer: Solutions for x - 4,4,-5 and for y - 3,-3, 0

Step-by-step explanation: I wrote the solutions in order. To solve this question I combined both equations to eliminate the y variable to solve for x. It looked like this :  [tex]x^2+x=20[/tex]. I brought the 20 to the other side and got [tex]x^2+x-20=0[/tex]. Then I factored and got [tex](x+5)(x-4)[/tex] which means x = -5 and x = 4. Finally I plugged in these values into the equation to find the possible y values.

The total weight of the liquid in the tank which is hemisphere in shape is 16,415 pounds.

The density and mass are related to each other with the formula -

Density = mass/volume

So, we have the density. We need to calculate the volume of hemisphere which will be accomodating the liquid. Then we will find the mass.

Volume of hemisphere = 2/3πr³, where r represents radius.

Volume = 2/3×π×5³

Performing multiplication, division and taking cube

Volume = 261.8 feet³

Now, mass = density × volume

Mass = 62.7 × 261.8

Performing multiplication

Mass = 16,414.86 pounds

Rounding off

Mass = 16,415 pounds

Thus, the mass of liquid will be 16,415 pounds.

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Answer:

Step-by-step explanation:

Find the GCF:

12, 24, 36

8, 16, 24, 32

GCF is 24

The lowest amount of boxes the teacher could buy would be 2 boxes of Rulers and 3 boxes of Protractors. I hope this helped

The number of different necklaces that Ginger can make, with the same ratio of pink to white beads is 5 necklaces.

To find the number of necklaces, find the smallest equivalent ratio of pink to white beats used to make the necklace.

Pink beads : White beads

30 : 35

( 30 / 5 ) : ( 35 / 5 )

6 : 7

To find the find the number of beads, divide the number of pink beads available by the number of pink beads in the ratio:

= 30 / 6

= 5 necklaces

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Answer: x = 22

Step-by-step explanation:

Subtract 34 from both sides.
x + 34 - 34 = 56-34 --> x = 22

The extra information "XY = YZ" would demonstrate that the parallelogram WXYZ is a parallelogram.

Theorem: The area of a triangle is roughly half the area of a parallelogram if they share a base and are situated between the same parallels.

These bisectors meet at a 90-degree angle.

And it indicates that they are parallel.

We discover that there are four congruent triangles, with XY parallel to WZ and WX parallel to YZ even though they are perpendicular to one another.

In addition, contrasting angles are equal.

The properties of the parallelogram are these two latter results.

Therefore, the additional fact "XY = YZ" would demonstrate that the triangular WXYZ is a parallelogram.

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The total number of ways to form 3 groups comprising of 3, 3 and 2 students is calculated by multiplying the individual numbers of ways, which results in 280.

The formula for calculating the number of unique ways to form three groups comprising of 3, 3, and 2 students is given by:

Number of ways = Number of ways to select 3 first-year students from 5 first-year students x Number of ways to select 3 second-year students from 3 second-year students x Number of ways to select 2 students from 8 students

=[tex]5C3 x 3C3 x 8C2[/tex]

= 10 x 1 x 28

= 280

Therefore, there are 280 unique ways to form three groups comprising 3, 3, and 2 students. This can be seen by considering the total number of possible arrangements of the 8 students into 3 groups of 3, 3 and 2. First, we need to select 3 students from 5 first-year students in 5C3 ways, which is equal to 10. Second, we need to select 3 students from 3 second-year students in 3C3 ways, which is equal to 1. Finally, we need to select 2 students from 8 students in 8C2 ways, which is equal to 28. Therefore, the total number of ways to form 3 groups comprising of 3, 3 and 2 students is calculated by multiplying the individual numbers of ways, which results in 280.

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Answer:

34 bricks is the greatest amount Mary could have used

Step-by-step explanation:

Tammy received 19 phone calls on the first evening, 13 phone calls on the second evening, and 76 phone calls on the third evening.

Let's use algebra to solve the problem.

Let x be the number of phone calls Tammy received on the first evening.

According to the problem, she received 6 fewer calls on the second evening than on the first evening. This means that the number of phone calls she received on the second evening is x - 6.

The problem also states that she received 4 times as many calls on the third evening as she did on the first evening. This means that the number of phone calls she received on the third evening is 4x.

We know that Tammy received a total of 108 phone calls over the three evenings. We can use this information to set up an equation:

x + (x - 6) + 4x = 108

Simplifying the equation:

6x - 6 = 108

Adding 6 to both sides:

6x = 114

Dividing both sides by 6:

x = 19

Therefore, Tammy received 19 phone calls on the first evening, 13 phone calls (19 - 6) on the second evening, and 76 phone calls (4 x 19) on the third evening.

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Complete question is:

Over the last three evenings, Tammy received a total of 108 phone calls at the call center. The second evening, she received 6 fewer calls than the first evening. The third evening, she received 4 times as many calls as the first evening. How many phone calls did she receive each evening?

P(A)=1/5, P(B)=7/20, P(A and B)= 7/100. The events A and B are independent.

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).

1) P(A)=1/5, P(B)=7/20, P(A and B)= 7/100

Here, P(A and B)= P(A)×P(B)

= 1/5 × 7/20

= 7/100

So, the events A and B are independent.

2) P(A)=13/20, P(B)=13/20, P(A and B)= 169/400

Here, P(A and B)= P(A)×P(B)

= 13/20 × 13/20

= 169/400

So, the events A and B are independent.

3) P(A)=7/10, P(B)=2/5, P(A and B)= 21/100

Here, P(A and B)= P(A)×P(B)

= 7/10 × 2/5

= 14/50

So, the events A and B are not independent.

2) P(A)=1/5, P(B)=1/5, P(A and B)= 1/25

Here, P(A and B)= P(A)×P(B)

= 1/5 × 1/5

= 1/25

So, the events A and B are independent.

Therefore, options 1, 2 and 4 are correct answers.

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Answer:-3

Step-by-step explanation: -7 -4

Answer:

if its 50,000k for example it is gonna be Loan term in years is 7 it depends on the price

Step-by-step explanation:

The distance between the foot of the ladder from the bottom of the wall is 40 meters.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Here,
The distance between the foot of the ladder from the bottom of the wall can be found by using the Pythagorean theorem.

The ladder is the hypotenuse, with a length of 50m

The distance from the wall to the ground is 30m

The distance from the wall to the foot of the ladder is x

Using the Pythagorean theorem:

x² + 30² = 50²

x² + 900 = 2500

x² = 1600

x = 40

So, the distance between the foot of the ladder from the bottom of the wall is 40 meters.

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The mean, also known as the average, is a central value that represents the typical value of a set of data.

To calculate the mean, you add up all the values in the data set and divide by the number of values. The mean provides a general sense of the distribution of the data and helps to identify any patterns or trends. In the stem-and-leaf plot, the mean can be calculated by adding up all the values and dividing by the number of throws. The mean in this case is 4.62 feet, which indicates that a typical throw of the ball results in 4.62 feet. This value can be used to gain a better understanding of the overall performance of the ball thrower and provide insight into how far the ball is typically thrown.

It is important to note that the mean is sensitive to outliers or extreme values, so it may not accurately reflect the typical value of the data in all cases. However, in this particular case, the mean provides a useful representation of the typical performance of the ball thrower.

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Answer:d

Step-by-step explanation:

The correct equations for the measures of the unknown angles x and y are:

x = cos(a), y = sin(a).

The trigonometric functions (sin, cos, tan) are mathematical functions that describe the relationships between the sides and angles of a right triangle. Given an angle a in a right triangle, we can use these functions to find the values of the side ratios for that angle. For example:

sin(a) = opposite side / hypotenuse

cos(a) = adjacent side / hypotenuse

tan(a) = opposite side / adjacent side

In these expressions, "opposite side" refers to the side opposite the angle a, "adjacent side" refers to the side adjacent to the angle a, and "hypotenuse" refers to the longest side in the right triangle (the one opposite the right angle).

The inverse trigonometric functions[tex](sin^-1, cos^-1, tan^-1)[/tex] are the reverse of the trigonometric functions. Given a value of a trigonometric function, the inverse function returns the measure of the angle (in radians) for which that value is the result. For example:

[tex]sin^-1(y) = a (where y = sin(a))cos^-1(x) = a (where x = cos(a))tan^-1(t) = a (where t = tan(a))[/tex]

So, the correct equations for the measures of the unknown angles x and y are:

[tex]x = cos^-1(x)y = sin^-1(y)[/tex]

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Answer:

(x-1)(x+1)(x+3)

Step-by-step explanation:

[tex]x^3+3x^2-x-3\\=x^2(x+3)-1(x+3)\\=(x^2-1)(x+3)\\=(x-1)(x+1)(x+3)[/tex]

If  a petrol station wants to make 100% profit. the cost of fuel per litre at this petrol station is 1.4 pence.

Given, the formula to calculate the cost of fuel per litre:

(1 + 100) X + X 160 C = cost of oil per barrel.

Where :

X = cost of oil per litre

C= rate of fuel duty tax in %.

We know that fuel duty is 50% and oil costs £128 per barrel, so we can substitute these values into the equation:

(1 + 100) X + X 160 * 0.5 = 128

Expanding the equation:

100 X + 80 X = 128

180 X = 128

Dividing both sides by 180:

X = 128/180 = 7/10 = 0.7

So, the cost of oil per litre is 0.7 pence.

The petrol station wants to make 100% profit, so we add the profit to the cost of oil per litre:

0.7 + 0.7 * (100/100) = 1.4 pence

Therefore, the cost of fuel per litre at this petrol station is 1.4 pence.

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Answer: No

Step-by-step explanation:

Valid only for numbers less than 40.

P(40) = 412 which is not a prime number

Answer:

So, the rational number is [tex]\frac{52}{12}[/tex] .

Step-by-step explanation:

Let x be the other number.

We know ,

[tex]\frac{7}{36}[/tex] + x = [tex]\frac{5}{6}[/tex]

To find x, we need to convert both to have a common denominator.

So, if we multiply [tex]\frac{7}{36}[/tex] by [tex]\frac{10}{36}[/tex]  ,

[tex]\frac{10}{1}[/tex] × [tex]\frac{7}{36}[/tex] + x = [tex]\frac{56}{10}[/tex]

After multiplication the fraction  [tex]\frac{7}{36}[/tex] becomes [tex]\frac{70}{360}[/tex]  .

[tex]\frac{70}{360}[/tex]+ x =  [tex]\frac{56}{10}[/tex]

Now we have common denominator of 360in both fraction,

Now,

we can simplify the equation ,

[tex]\frac{70}{360}[/tex]  + x = [tex]\frac{56}{10}[/tex]

70 + 360x = 56 × 36

2520 + 360x = 2016

504 + 360x = 2016

360x = 1512

x = [tex]\frac{1512}{360}[/tex]

   =[tex]\frac{52}{12}[/tex]

So, the rational number is [tex]\frac{52}{12}[/tex] .

The probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.

To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we need to use the data from the survey. Let's assume that the survey results are summarized in the following table (attached) :

From this table, we can see that the probability of a worker living more than 5 miles from work is 35%. We can also see that the probability of a worker riding their bicycle is 50%, and the probability of a worker living more than 5 miles from work and riding their bicycle is 20%.

To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we can multiply the probabilities of these two events:

P(Lives > 5 miles and Rides Bicycle) = P(Lives > 5 miles) x P(Rides Bicycle | Lives > 5 miles)

= 35% x (20%/35%)

= 0.5714 or 57% (rounded to the nearest whole percent)

Therefore, the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.

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V Prism is V = B × h=9.5*4=38

the volume of a sphere is V = 4/3 π r³=4/3*22/7*9.5=10.47

V=10.47+38=48.476

A measurement of three-dimensional space is volume. It is frequently expressed in numerical form using SI-derived units, as well as different imperial or US-customary units. In contrast to how much space the container actually occupies, the volume of a container is typically thought of as its capacity, or the amount of fluid it could hold. Volume was initially measured using naturally occurring vessels of a comparable shape and then with standardized containers. Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects in the zero, one, and two dimensions have no volume.

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The mean of the given data is 22.39.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Let us form a table by give data

Score          Frequency        Midpoint(x)          fx

1-7                    13                       4                      52

8-10                  1                        9                       9

11-15                 19                      13                     247

16-20               20                      18                    360

21-35               19                       28                   532

36-50               20                     43                  860

Mean=∑fx/N

=52+9+247+360+532+860/13+1+19+20+19+20

=2060/92

Mean=22.39

Hence, the mean of the given data is 22.39.

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