Find x [Angles and Segment]

Answer:

They can buy 13meals if they buy 100 gallons of gasoline.

Step-by-step explanation:

3.50 PER gallon so 1 gallon is $3.50

if they buy 100 gallons you have to multiply 3.50 by 100 which gives you 350. you subtract 350 from 1000 so 1000-350 and get 650. now, you divide 650 by 50 because each meal is $50. And you get 13 so there you have it.

Final answer:

The family can buy 13 meals.

Explanation:

To find the number of meals the family can buy, we need to calculate the total cost of gasoline and subtract it from the total budget.

The family buys 100 gallons of gasoline at a cost of $3.50 per gallon, so the total cost of gasoline is 100 * $3.50 = $350.

The remaining budget for meals is $1,000 - $350 = $650.

The cost of each meal is $50, so the family can buy $650 / $50 = 13 meals.

Answer:

h=2×6/8

x^2=h^2+4

x=5/2

Answer:

The interest paid is $1575.

Step-by-step explanation:

Given is:

Monthly loan payment = $1857

Loan amount = $300000

Rate = 6.3% annual

So, monthly rate will be = [tex]6.3/12/100=0.00525[/tex]

Hence, we will calculate the interest for month.

[tex]0.00525\times300000=1575[/tex] dollars

So, interest paid = $1575.

Principle paid = [tex]1857-1575=282[/tex] dollars

Answer:

Step-by-step explanation:

When the points designating each triangle are considered in order, they are seen to be in clockwise order. Segment FG is oriented to the west, while corresponding segment VW is oriented to the east. This means the figure could have been rotated 180° or reflected across a point. Either way, some translation may be necessary to align the figures as shown.

Possible transformations include ...

___

If one of the triangles is reflected across the midpoint of GW, it will coincide with the other triangle. Hence only one reflection across a chosen point is required. Of course, reflection across a point is identical to rotation 180° about that point. For any other point of reflection or rotation, translation will be involved.

Answer:

rotation, then translation

Step-by-step explanation:

rotation, then translation

Answer:

The answer is between 2 to 3 scoops.

Answer:

The only logical answer would be between 2 and 3 scoops

Answer:

The value of a is 10 and the value of b is 6

Step-by-step explanation:

* Lets revise how to solve the problem

- Remember in the number with exponent

-  a^n × a^m = a^(n + m)

- a^n ÷ a^m = a^(n - m)

Lets solve the problem

∵ [tex]\frac{7^{2}.7x^{8}}{7x^{4}}[/tex]

- Lets use the rule above

∵ [tex]7^{2}.7^{8}=7^{2+8}=7^{10}[/tex]

∴ [tex]\frac{7^{2}.7^{8}}{x^{4}}=\frac{7^{10}}{7^{4}}[/tex]

∵ [tex]\frac{7^{10}}{7^{4}}=\frac{7^{a}}{7^{4}}[/tex]

∴ a = 10

∵ [tex]\frac{7^{10}}{7^{4}}=7^{10-4}=7^{6}[/tex]

∵ [tex]7^{6}=7^{b}[/tex]

∴ b = 6

* The value of a is 10 and the value of b is 6

Answer: 10 and 6 for the next one its 2, 3, and 8

Step-by-step explanation: i hope this helps :)

Answer:

Step-by-step explanation:

Tough question.

Spiritual.

Love (if ever there was a misused word, it is love). I used to ask my classes what this sentence means "I love hunting." Try that one on. I don't know if you are dating someone, but how can you say "I love you." and "I love hunting." and not have something terribly wrong with the definition of the verb. One implies treasuring someone. The other means outfoxing a fox and murder.

Religion. Why are there so many different ones? The claim that there is only one true one makes the definition elusive to say the least. And it has caused a great deal of trouble.

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

Geometry: You have to know what a line segment is before you can say that one segment bears a relationship to another one.

You have to be able to define a point before you can calculate an intersection point of 2 lines or 2 curves or more.

You have to be able to define almost any term in geometry so that you can restrict enough to make it useful.

If tangents are drawn from the same spot, then they will be equal.

Since tangents AB and AC both start from point A, and go to the same circle, then:

AC = AB.

That means the statement:

'If AC is equal to 10cm, then segment AB is equal to 20cm'

is false

(if a AC  = 10cm, then AB would =  20cm as well)

_____________________________________

Answer:

False

Answer:

The given statement is false.

Step-by-step explanation:

We have been given a statement. We are supposed to determine whether our given statement is true or not.

Segments AC and AB are tangent to circle E. If AC is equal to 10 cm, then segment AB is equal to 20 cm.

We know that tangents of circle from same external point are congruent.

We can see that both tangents AB and AC are drawn from same point A, so AB will be equal to AC.

Since [tex]AB=20[/tex] and [tex]AC=10[/tex], therefore, our given statement is false.

Answer:

The smallest number of colors needed to color the vertices of so that no two adjacent vertices share the same color.

the smallest value of possible to obtain a k-coloring.

Final answer:

The chromatic number for a map is the minimum number of colors needed to color the regions of the map such that no two adjacent regions have the same color.

Explanation:

The chromatic number for a map is the minimum number of colors needed to color the regions of the map such that no two adjacent regions have the same color.

The chromatic number can vary depending on the specific map and its regions. To determine the chromatic number, one approach is to use a graph-theoretic representation of the map, where each region corresponds to a vertex and adjacent regions are connected by edges. Then, a graph coloring algorithm can be used to find the minimum number of colors needed to properly color the regions of the map.

Answer:

Part 1) [tex]-17\frac{8}{9}[/tex] -----> [tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}[/tex]

Part 2) [tex]-15.11[/tex] ------> [tex]-12.48-(-2.99)-5.62[/tex]

Part 3) [tex]-19\frac{8}{9}[/tex] -----> [tex]-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})[/tex]

Part 4) [tex]-201.65[/tex] -----> [tex]-353.92-(-283.56)-131.29[/tex]

Part 5) [tex]74[/tex] ------> [tex]83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})[/tex]

Step-by-step explanation:

Part 1) we have

[tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}[/tex]

To calculate the subtraction convert the mixed numbers to an improper fractions

[tex]6\frac{4}{9}=\frac{6*9+4}{9}=\frac{58}{9}[/tex]

[tex]3\frac{2}{9}=\frac{3*9+2}{9}=\frac{29}{9}[/tex]

[tex]8\frac{2}{9}=\frac{8*9+2}{9}=\frac{74}{9}[/tex]

substitute

[tex]-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=-\frac{(58+29+74)}{9}=-\frac{161}{9}[/tex]

Convert to mixed number

[tex]-\frac{161}{9}=-(\frac{153}{9}+\frac{8}{9})=-17\frac{8}{9}[/tex]

Part 2) we have

[tex]-12.48-(-2.99)-5.62[/tex]

To calculate the subtraction eliminate the parenthesis first

[tex]-12.48-(-2.99)-5.62=-12.48+2.99-5.62=-15.11[/tex]

Part 3) we have

[tex]-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})[/tex]

To calculate the subtraction convert the mixed numbers to an improper fractions

[tex]19\frac{2}{9}=\frac{19*9+2}{9}=\frac{173}{9}[/tex]

[tex]4\frac{1}{9}=\frac{4*9+1}{9}=\frac{37}{9}[/tex]

[tex]3\frac{4}{9}=\frac{3*9+4}{9}=\frac{31}{9}[/tex]

substitute

[tex]-\frac{173}{9}-\frac{37}{9}-(-\frac{31}{9})[/tex]

Eliminate the parenthesis

[tex]-\frac{173}{9}-\frac{37}{9}+\frac{31}{9}=\frac{(-173-37+31)}{9}=-\frac{179}{9}[/tex]

Convert to mixed number

[tex]-\frac{179}{9}=-(\frac{171}{9}+\frac{8}{9})=-19\frac{8}{9}[/tex]

Part 4) we have

[tex]-353.92-(-283.56)-131.29[/tex]

To calculate the subtraction eliminate the parenthesis first

[tex]-353.92+283.56-131.29=-201.65[/tex]

Part 5) we have

[tex]83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})[/tex]

To calculate the subtraction convert the mixed numbers to an improper fractions

[tex]83\frac{1}{5}=\frac{83*5+1}{5}=\frac{416}{5}[/tex]

[tex]108\frac{2}{5}=\frac{108*5+2}{5}=\frac{542}{5}[/tex]

[tex]99\frac{1}{5}=\frac{99*5+1}{5}=\frac{496}{5}[/tex]

substitute

[tex]\frac{416}{5}-\frac{542}{5}-(-\frac{496}{5})[/tex]

Eliminate the parenthesis

[tex]\frac{416}{5}-\frac{542}{5}+\frac{496}{5}=\frac{(416-542+496)}{5}=\frac{370}{5}=74[/tex]

Answer:

[tex]y=\frac{-4}{3}x+\frac{-4}{3}[/tex] slope-intercept form

[tex]y+4=\frac{-4}{3}(x-2)[/tex] point-slope form

Step-by-step explanation:

Equation of a line in point-slope form is y-y_1=m(x-x_1) where m is the slope and b is the [tex](x_1,y_1)[/tex] is a point on the line.

So the m, slope, can be found by calculating the rise/run from one to another point on the line.

So let's start at (2,-4) and count to (-4,4).

So the rise is 8 and the run is -6.

The slope is therefore 8/-6=-8/6=-4/3.

Now if you didn't want to count because you can't count all the time.

You could line up the two points and subtract vertically, then put 2nd difference over 1st difference.

Like this:

(  2  ,   -4)

(-4  ,      4)

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

6          -8

So the slope is -8/6=-4/3.

Anyways now using any point on the line as [tex](x_1,y_1)[/tex] along with the slope we found we can finally put into our equation for point-slope form:

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

with [tex](x_1,y_1)=(2,-4)[/tex] and [tex]m=\frac{-4}{3}[/tex].

This gives us:

[tex]y-(-4)=\frac{-4}{3}(x-2)[/tex]

[tex]y+4=\frac{-4}{3}(x-2)[/tex]

We probably want to put into y=mx+b form; not 100% sure so I will give you choices:

y=mx+b is called slope-intercept form because it tells us the slope is m and the y-intercept is b.

[tex]y+4=\frac{-4}{3}(x-2)[/tex]

Distribute the -4/3 to the terms inside the ( ):

[tex]y+4=\frac{-4}{3}x+\frac{8}{3}[/tex]

Subtract 4 on both sides:

[tex]y=\frac{-4}{3}x+\frac{8}{3}-4[/tex]

Simplify the (8/3)-4:

[tex]y=\frac{-4}{3}x+\frac{-4}{3}[/tex]

Answer:

Step-by-step explanation:

The train uses

[tex]\frac{400gallons}{200miles}[/tex]

If you reduce that you get that the train uses

[tex]\frac{2gallons}{1mile}[/tex]

To find the slope of the line, we will use the 2 points on the coordinate plane where the graph goes through:  (0, 0) and (400, 200)

Applying the slope formula:

[tex]m=\frac{200-0}{400-0}=\frac{1}{2}[/tex]

Answer:

6 miles per gallon

slope = 6

Step-by-step explanation:

Answer:

r = 7

Step-by-step explanation:

let r = x

equation becomes

7x-15= x+27

Let the Left side AND Right side both equal y

y = 7x - 5

y = x + 27

graph these 2 equations. You should get 2 straight lines that intersect at x = 7, y = 34. (see attached)

recall at the start we let r = x, if we replace x with r again, we get r = 7

Answer:

Part a. t = 7.29 years.

Part b. t = 27.73 years.

Part c. p = $3894.00

Step-by-step explanation:

The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.

Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!

Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!

Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!

Answer:

  "demand"

Step-by-step explanation:

Vocabulary question.

  "Demand" refers to the quantity of goods and services that consumers are willing to buy at a given price.

Answer:

[tex]tan(\theta)=-\frac{7}{6}[/tex]

[tex]sec(\theta)=\frac{\sqrt{85} }{6}[/tex]

[tex]cos(\theta)=\frac{6\sqrt{85} }{85}[/tex]

[tex]sin(\theta)=-\frac{7\sqrt{85}}{85}[/tex]

[tex]cosec(\theta)=-\frac{\sqrt{85}}{7}[/tex]

Step-by-step explanation:

[tex]cot (\theta) = -\frac{6}{7}[/tex]

a) Since,

[tex]tan(\theta) = \frac{1}{cot(\theta)}[/tex]

[tex]tan(\theta) = \frac{1}{-\frac{6}{7} }=-\frac{7}{6}[/tex]

b) Also, according to the Pythagorean identity:

[tex]sec^{2}(\theta)=1+tan^{2}(\theta)[/tex]

Using the value of tan([tex]\theta[/tex]), we get:

[tex]sec^{2}(\theta)=1+(-\frac{7}{6} )^{2}\\\\ sec^{2}(\theta)=\frac{85}{36}\\\\ sec(\theta)=\pm \sqrt{\frac{85}{36} } \\\\ sec(\theta)=\pm \frac{\sqrt{85} }{6}[/tex]

Since, secant is positive in 4th quadrant, we will only consider the positive value. i.e.

[tex]sec(\theta)=\frac{\sqrt{85} }{6}[/tex]

c) Since,

[tex]cos(\theta)=\frac{1}{sec(\theta)}[/tex]

Using the value of secant, we get:

[tex]cos(\theta)=\frac{1}{\frac{\sqrt{85} }{6} } =\frac{6\sqrt{85} }{85}[/tex]

d) According to Pythagorean identity:

[tex]sin^{2}(\theta)=1-cos^{2}(\theta)\\sin(\theta)=\pm \sqrt{1-cos^{2}(\theta)}[/tex]

Since, sine is negative in fourth quadrant, we will consider the negative value. Using the value of cosine, we get:

[tex]sin(\theta)=-\sqrt{1-(\frac{6\sqrt{85} }{85})^{2}}=-\frac{7\sqrt{85}}{85}[/tex]

e) Since,

[tex]cosec(\theta)=\frac{1}{sin(\theta)}[/tex]

Using the value of sine, we get:

[tex]cosec(\theta)=\frac{1}{-\frac{7\sqrt{85} }{85}}=-\frac{\sqrt{85}}{7}[/tex]

Answer:

9

Step-by-step explanation:

[tex]\tt distance=\sqrt{(1-1)^2+(-4-5)^2}=\sqrt{0^2+9^{2}}=\sqrt{9^2} =9[/tex]

The formula for distance between two points is:

[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}[/tex]

In this case:

[tex]x_{2} =1\\x_{1} =1\\y_{2} =-4\\y_{1} =5[/tex]

^^^Plug these numbers into the formula for distance like so...

[tex]\sqrt{(1-1)^{2} + (-4-5)^{2}}[/tex]

To solve this you must use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

First we have parentheses. Remember that when solving you must go from left to right

[tex]\sqrt{(1-1)^{2} + (-4-5)^{2}}[/tex]

1 - 1 = 0

[tex]\sqrt{(0)^{2} + (-4-5)^{2}}[/tex]

-4 - 5 = -9

[tex]\sqrt{(0)^{2} + (-9)^{2}}[/tex]

Next solve the exponent. Again, you must do this from left to right

[tex]\sqrt{(0)^{2} + (-9)^{2}}[/tex]

0² = 0

[tex]\sqrt{0 + (-9)^{2}}[/tex]

(-9)² = 81

[tex]\sqrt{(0 + 81)}[/tex]

Now for the addition

[tex]\sqrt{(0 + 81)}[/tex]

81 + 0 = 81

√81

^^^This can be further simplified to...

9

***Remember that the above answers are in terms of units

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

<1 = 100

<2 = 80

Step-by-step explanation:

Angle 1 and angle 2 are supplementary

Supplementary angles add to 180 degrees

<1 + <2 = 180

The angles are in a ratio of 5 to 4

Multiply by x to get the measure of each angle

<1 = 5x  <2 = 4x

5x+4x = 180

Combine like terms

9x = 180

Divide by 9

9x/9 =180/9

x =20

<1 = 5x = 5*20 = 100

<2 = 4x = 4*20 = 80

Answer:

he's right

Step-by-step explanation:

or she i dont discriminate

Answer:

Test statistic = z = 1.01264

Step-by-step explanation:

p = 0.25

q = 1 - p = 0.75

n = 520

x = 140

[tex]psample = \frac{x}{n} = \frac{140}{520} = 0.26923[/tex]

[tex]z = \frac{psample - p}{\sqrt{\frac{p*q}{n} } } =\frac{0.26923 - 0.25}{\sqrt{\frac{0.25 * 0.75 }{520} } } = \frac{0.01923}{\sqrt{\frac{0.1875}{520} } } = \frac{0.01923}{\ 0.01899} = 1.01264[/tex]

Explanation:

Step 1: find the mean of the data

Step 2: subtract the mean from every data value

Step 3: find the absolute values of the differences from Step 2

Step 4: find the mean of the absolute values from Step 3. This is the MAD.

_____

The mean and absolute value have their usual definitions.

The mean is the sum of a set of numbers, divided by the number of numbers in the set.

The absolute value is the numerical value of a number with its sign changed to positive, if it isn't already. For example, |-1| = 1 and |1| = 1. The vertical bars signify the absolute value of their contents.

Step-by-step explanation:

The only exception to that is that when you have a negative outside of the absolute value symbol, you will get a negative answer.

Ex: -|3| = -3

I am joyous to assist you anytime.

Answer:

-44 4/9

Step-by-step explanation:

-36 4/9-(-10 2/9)-(18 2/9)

-36 4/9+10 2/9 = 26 6/9

26 6/9 - (18 2/9)= -44 4/9

The correct answer to the given fraction after simplification is equal to [tex]-44\frac{4}{9}[/tex] .

" Simplification is defined as the reduce the given expression, fraction or problem into the easiest form."

Convert mixed fraction to proper fraction

[tex]p\frac{q}{r} = \frac{(r\times p)+q}{r}[/tex]

According to the question,

Given fraction,

[tex]-36\frac{4}{9}- (-10\frac{2}{9})-(18\frac{2}{9})[/tex]

Simplify the given fraction using conversion mixed fraction to proper fraction we get,

[tex]\frac{-328}{9}+ \frac{92}{9}- \frac{164}{9}\\\\= \frac{-328+92-164}{9}\\ \\= \frac{-400}{9}\\ \\= -44\frac{4}{9}[/tex]

Hence, Option(A) is the correct answer.

Learn more about simplification here

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Answer:

See below in bold.

Step-by-step explanation:

Ship's vector:

Horizontal component = 30 cos 30  = 25.98.

Vertical component = 30 sin(-30) = -15.

So it is <25.98, -15).

The current's vector:

Horizontal component =  5 sin 20 = 1.71.

Vertical component = 5 cos 20 = 4.7.

So it is <1.71, 4.7>.

The ship's vector representing its actual motion is 30.73 mph east of north.

To solve this problem, we can break down the velocities of the ship and the water current into their horizontal and vertical components. The ship's vector can be represented as:

Ship's Vector: 30 mph at an angle of 30° south of east

Breaking this down into horizontal and vertical components:

Horizontal Component = 30 mph * cos(30°) = 25.98 mph east

Vertical Component = 30 mph * sin(30°) = 15 mph south

The water current's vector can be represented as:

Water Current's Vector: 5 mph at an angle of 20° east of north

Breaking this down into horizontal and vertical components:

Horizontal Component = 5 mph * cos(20°) = 4.75 mph north

Vertical Component = 5 mph * sin(20°) = 1.71 mph east

To find the ship's actual motion, we can add the horizontal and vertical components together:

Horizontal Component = 25.98 mph east + 4.75 mph north = 30.73 mph east of north

Vertical Component = 15 mph south + 1.71 mph east = 16.71 mph south of east

Therefore, the ship's vector representing its actual motion is 30.73 mph east of north.

The equation for this scenario is  6b= 42.

B= 42/6= 7

The value of b that makes the equation true is 7.

Hope this helps!

Answer:

6b = 42

b = 7 for the equation to be true.

Step-by-step explanation:

If Leo has b boxes of pencils with each containing 6 pencils, it means that the total number of pencils Leo has is dependent on the number of boxes given that the number in each box is known.

The product of the number of boxes with the number in each box gives the total number of pencils Leo has. This may be expressed mathematically as

= b × 6

= 6b

Given that Leo has 42 pencils, it means that

6b = 42

Dividing both sides by 6,

b = 42/6 = 7

It means he has 7 boxes.

Answer:

Given is :

4 different alarm systems were installed in the vault.

Each of the four systems detects theft with a probability of .99 independently of the others.

For solving this question, we have to first find the probability that none works.

It will be given as:

As there is 0.01 probability that all four systems will fail to detect theft. As all are independent, we get probability as: [tex](0.01)^{4}[/tex]

Now, we have to find the probability that at least one system detects the theft, it is given by:  [tex]1 -(0.01)^{4}[/tex]

Final answer:

To find the height of the building, we use the tangent function with the angle of depression and the horizontal distance from the point to the building's base, resulting in a building height of 22 meters when rounded to the nearest meter.

Explanation:

To calculate the height of the building when the angle of depression from the top of the building to a point P on the ground is 23.6 degrees and the distance from P to the foot of the building is 50 meters, we can use trigonometry.

Specifically, we use the tangent function which relates the angle of a right triangle to the ratio of the opposite side (height of the building in this case) over the adjacent side (distance from P to the foot of the building).

Let's denote the height of the building as H. Thus, we have:

tan(23.6°) = H / 50

From this, we can solve for H:

H = 50 × tan(23.6°)

Rounding to the nearest meter, the height of the building is 22 meters.

Answer:

∠R = 36.06°, ∠Q = 90.81°

Step-by-step explanation:

I used the Law of Cosines to find angle R first.  If you use the Law of Sines, the main angle is the same, but it differs in the decimal value.  Since you started the process with the Law of Cosines, I used it again.  Setting up to find angle R:

[tex]36^2=48^2+60^2-2(48)(60)cosR[/tex] and

1296 = 2304 + 3600 - 5760cosR so

-4608 = -5700cosR and

.8084210526 = cosR

Taking the inverse cosine to find the angle,

R = 36.06

That means that Q = 180 - 36.06 - 53.13 so

Q = 90.81

Answer:

  see below

Step-by-step explanation:

The Law of Cosines tells you ...

  a² = b² + c² -2bc·cos(A)

Substituting the given values gives you ...

  a² = 4² +7² -2(4)(7)cos(52°)

Answer:

  c)  (-2, 6)

Step-by-step explanation:

Subtracting the second equation from the first gives ...

  (y) -(y) = (x^2 +3x +8) -(2x +10)

  0 = x^2 +x -2 . . . . . simplify

  0 = (x -1)(x +2) . . . . factor

Solutions for x are 1 and -2. The corresponding y-values are ...

  y = 2{1, -2} +10 = {2, -4} +10 = {12, 6}

The solutions are (1, 12) and (-2, 6). The only matching choice is (-2, 6).

Answer:

Step-by-step explanation:

You must use a combination:

[tex]_nC_k=\dfrac{n!}{k!(n-k)!}[/tex]

We have n = 16, k = 3.

Substitute:

[tex]_{16}C_3=\dfrac{16!}{3!(16-3)!}=\dfrac{13!\cdot14\cdot15\cdot16}{2\cdot3\cdot13!}\qquad\text{cancel}\ 13!\\\\=\dfrac{14\cdot15\cdot16}{2\cdot3}=\dfrac{7\cdot5\cdot16}{1}=560[/tex]

The number of possible selections is 560.

The library is to be given 3 books as a gift. The books will be selected from a list of 16 titles.

Here we used the combination

[tex]= nC_n\\\\= 16C_3\\\\= \frac{16!}{3!(16-3)!}\\\\ = \frac{16!}{3!13!}\\\\ = \frac{16\times 15\times 14\times 13!}{13!3!}\\\\ = \frac{16\times 15\times 14}{3\times 2\times 1}\\[/tex]

= 560

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