Write and solve an equation to find the measure of the unknown angle.​

Answer:

[tex]\dfrac{y^2}{36}-\dfrac{x^2}{45}=1.[/tex]

Step-by-step explanation:

Since vertices and foci lie on the y-axis, the equation of the hyperbola is

[tex]\dfrac{y^2}{b^2}-\dfrac{x^2}{a^2}=1.[/tex]

If the vertices are at points (0,±6), then [tex]b=6.[/tex]

If the foci are at points (0,±9), then [tex]c=9.[/tex]

Note that

[tex]c^2=b^2+a^2,[/tex]

then

[tex]9^2=6^2+a^2,\\ \\a^2=81-36,\\ \\a^2=45.[/tex]

The equation of the hyperbola is

[tex]\dfrac{y^2}{36}-\dfrac{x^2}{45}=1.[/tex]

Answer:

The height is 17 ft

Step-by-step explanation:

The surface area of a rectangular prism is

SA = 2(LW +WH + LH)

where L = length, W = width, and H = height

We know SA = 930, L = 12, and W = 9

930 = 2(12*9 +9H + 12H)

Divide each side by 2

930/2 = 2/2(12*9 +9H + 12H)

465 = (12*9 +9H + 12H)

Combine like terms

465 = 84+21H

Subtract 84 from each side

465-84 = 84-84+21H

357 = 21H

Divide by 21

357/21=21H/21

17 = H

The height is 17 ft

Answer:

Height is 17 ft.

Step-by-step explanation:

Given: Rectangular Prism is also called cuboid

          Length, L = 12 ft.    and   width, W = 9 ft.

          Surface Area of cuboid, SA = 930 ft.²

To find: height , H

The surface area of a rectangular prism or cuboid

SA = 2(LW +WH + LH)

930 = 2(12×9 +9H + 12H)

[tex]\frac{930}{2}=108 +9H + 12H[/tex]

465 = 108 + 9H + 12H

108 + 9H + 12H  = 465

21H + 108 =  465

21H = 465 - 108

21H = 357

[tex]H=\farc{357}{21}[/tex]

H = 17  

therefore, Height is 17 ft.

Answer:

Step-by-step explanation:

-50 plus so above the number so like -51.5

If paul's account balance is less than - $50 the possible balance for Paul's account should be in the range of - $50.9 to - $50.1.

Range defines possible values in between two values that are some distance apart on the number line. The range can also be defined as the possible values from the least value to the greatest value.

Given that Paul's account balance is less than - $50.

∴ The possible balance for Paul's account can be in the range of

- $50.9 to - $50.1 because if he had an amount which is less than - $51 then the given statement should have been mentioned.

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Answer:

Simplify 32 • 35.

37

310

Step-by-step explanation:

• = Multiplication

Also by the process of elimination, 32+35 is not 37

Answer:

32x35=1120

Step-by-step explanation:

Answer:

$1.42

Step-by-step explanation:

Change = Amount She Pays With - The Cost of the Book

y=10-8.58

y=$1.42

Answer:

First we must subtract 10 into 8.58, which will equal 1.42

so she will have $1.42 change back

Answer:

C.12 1/2

Step-by-step explanation:

5=2/5a

Multiply each side by 5/2 to isolate a

5/2 * 5 = 5/2 * 2/5 a

25/2 = a

12 1/2 = a

Answer:

x=32

Step-by-step explanation:

(32-5)^(2/3)=9

Answer:

No

Step-by-step explanation:

Here we are taking only one measurement:  the height of one person.  Strictly speaking, this is NOT a statistical question.

"List the heights of a sample of 50 first-graders" would definitely be a stat. question.

The question 'How tall is Sam?' is not a statistical question. Statistical questions expect a variety of responses, not a singular answer. Height is typically measured in feet or centimeters.

The question 'How tall is Sam?' is not considered a statistical question. A statistical question is one in which the answer varies and requires data collection for multiple items or individuals to answer. It is one for which you don't expect to get a single answer. Instead, you expect to get a variety of different answers, and you're interested in the distribution and tendency of those answers. For instance, 'How tall are the students in a class?' is a statistical question because it would result in a variety of answers and we could analyze that data set.

The unit for height in this context typically is measured in feet or centimeters.

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Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

To calculate m use the slope formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (2, 1)

m = [tex]\frac{1-6}{2-1}[/tex] = - 5, hence

y = - 5x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 6), then

6 = - 5 + c ⇒ c = 6 + 5 = 11

y = - 5x + 11 → A

Answer:

[tex]y=-5x+11[/tex]

Step-by-step explanation:

Given :  Points (1,6) and (2,1)

To Find : Which of the following is the equation of a line that passes through the points (1,6) and (2,1) ?

Solution:

[tex](x_1,y_1)=(1,6)\\(x_2,y_2)=(2,1)[/tex]

Now to find the equation of a line that passes through the points (1,6) and (2,1) we will use two point slope form

Two point slope form : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Substitute the values

[tex]y-6=\frac{1-6}{2-1}(x-1)[/tex]

[tex]y-6=-5(x-1)[/tex]

[tex]y-6=-5x+5[/tex]

[tex]y=-5x+11[/tex]

So, Option A is true.

Hence The equation of a line that passes through the points (1,6) and (2,1) is[tex]y=-5x+11[/tex]

Answer:

1 solution

Step-by-step explanation:

Set it equal to 0

0=3/4x+12

Subtract 12

-12=3/4x

Multiply by 4

-48=3x

Divide by 3

X = -16

The equation has an infinite number of solutions

Given equation is,

[tex]y=\frac{3}{4}x+12[/tex]

We can write the given equation as,

[tex]3x-4y+12=0[/tex]

[tex]For x=1\\y=\frac{51}{4}\\For x=2\\y=\frac{27}{2}\\For x=3\\y=\frac{57}{4}[/tex]

In the above given equation for the different values of x gives the different solution of y.

Hence, the given equation has an infinite number of solutions.

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Answer:

45 miles

Step-by-step explanation:

if 1 in = 15 mi     so put x=15

3 is 3 times 1 so x=3 and 3*15=45

Your answer is 45 miles.

Answer:

The slope is 5

Step-by-step explanation:

This equation is in slope intercept form

y = mx +b

where m is the slope and b is the y intercept

y = 5x+4

where 5 is the slope and 4 is the y intercept

Answer:

Step-by-step explanation:

The slope-intercept form of the equation of a line:

y = mx + b

m - slope

b - y-intercept

We have the equation y = 5x + 4

Therefore the slope is m = 5

Answer:226,432.80

Step-by-step explanation:

Final answer:

Javier's total financed price for his home, excluding the longer-term interest but including the cost of buying points, is $97,920. This total includes the initial mortgage of $96,000 after a 20% down payment on a $120,000 home and the $1,920 spent on purchasing two points to reduce the interest rate.

Explanation:

Javier's home cost $120,000, and he was required to make a 20% down payment. Twenty percent of $120,000 is $24,000, which is the down payment amount. Therefore, the initial loan amount is $120,000 - $24,000 = $96,000.

Buying points typically costs 1% of the loan amount per point to lower the interest rate by a certain percentage. It is not specified how much the rate was lowered by purchasing 2 points, but we can calculate the cost. Two points on a $96,000 loan is 2% of $96,000, which equals $1,920.

Thus, the total financed price of the home, not counting interest payments over the term of the mortgage but including the cost of the points, is the initial loan amount plus the cost of the points: $96,000 initial loan + $1,920 for points = $97,920.

Bases have bitter taste. (1)

Answer:

Bitter taste would belong to a base

Step-by-step explanation:

Answer: 82 2/3 yards squared

Step-by-step explanation: The formula for area is l × w = A. Because of this, you need to multiply the two numbers.

1. Make 10 1/3 into an improper fraction.

10 1/3 = 31/3

2. Multiply!

31/3 × 8/1 = 248/3

3. Simplify

3 goes into 248 82 times with 2 left over (82 2/3)

D. Three debts added to four fortunes will be one fortune.

Debts=negative, so -3

Fortunes= positive, so 4

-3+4=1

3debt+4fortune=1fortune

Or, 4fortune-3debt=1fortune

4-3=1

Answer:

D. Three debts added to 4 fortunes will be one fortune.

Step-by-step explanation:

Given : A modern equation involving positive and negative integers would be -3+4=1.

To find : How would Brahmagupta have represented this equation.

Solution : We have given that -3+4=1.

Here, - sing represent by debt and + sign represent by fortune .

In given statement  3  is with debt and 4 is with fortune and 1 with fortune.

Then we can see,  Three debts added to 4 fortune will be one fortune.

Therefore, D. Three debts added to 4 fortunes will be one fortune.

Answer:Simplifying

y = -2x + -3

Reorder the terms:

y = -3 + -2x

Solving

y = -3 + -2x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Simplifying

y = -3 + -2x

Step-by-step explanation:Simplifying

y = x + 6

Reorder the terms:

y = 6 + x

Solving

y = 6 + x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Simplifying

y = 6 + x

Answer:

Step-by-step explanation:

ΔNPM and ΔABM are similar. Therefore the sides are in proportion:

[tex]\dfrac{AM}{NM}=\dfrac{BM}{PM}[/tex]

We have

[tex]AM=71.5\ ft-22\ ft=49.5\ ft\\NM=71.5\ ft\\BM=x\\PM=97.5\ ft[/tex]

Substitute:

[tex]\dfrac{49.5}{71.5}=\dfrac{x}{97.5}[/tex]       cross multiply

[tex]71.5x=(49.5)(97.5)[/tex]

[tex]71.5x=4826.25[/tex]           divide both sides by 71.5

[tex]x=67.5[/tex]

Answer:

LM = 23 units

Step-by-step explanation:

triangle KLN and triangle MLN are congruent.

The segment LM is equal to segment LK.

Also, MN is same as KN, thus we can write:

[tex]MN=KN\\25=14x-3\\25+3=14x\\28=14x\\x=2[/tex]

Since, x = 2, we can get the side length LM:

[tex]LM=LK=9x+5\\LM=LK=9(2)+5\\LM=23[/tex]

Hence, LM = 23 units

Answer:

LM = 23 units

Step-by-step explanation:

From figure we can see an isosceles triangle KNM

KN = NM

NL is the perpendicular from N to KM,

Therefore KL = LM

To find the value of x

From figure we can write,

14x - 3 = 25

14x = 25 + 3 = 28

x = 28/14 = 2

To find LM

LM = KL

we have KL = 9x + 5

Therefore LM = 9x + 5 = (9 * 2) + 5  = 23 units

Answer: -216

Step-by-step explanation:

To solve the exercise you must use the formula shown below:

[tex]Sn=\frac{(a_1+a_n)n}{2}[/tex]

Where:

[tex]a_1=152\\a_n=a_{24}[/tex]

You should find  [tex]a_{24}[/tex]

The formula to find it is:

[tex]a_n=a_1+(n-1)d[/tex]

Where d is the difference between two consecutive terms.

[tex]d=138-152=-14[/tex]

Then:

[tex]a_{24}=152+(24-1)(14)=-170[/tex]

Substitute it into the first formula. Therefore, you obtain:

[tex]S_{24}=\frac{(152-170)(24)}{2}=-216[/tex]

Answer:

Sn = -216

Step-by-step explanation:

We are given the following sequence and we are to find the sum of the given sequence if there are 24 terms in it:

[tex] 152, 138, 124, ... [/tex]

We know that the formula of sum for an arithmetic sequence is given by:

[tex]S_n =\frac{n(a_1+a_n)}{2}[/tex]

where [tex]a_1[/tex] is the first term (124)and [tex]a_n[/tex] is the last term [tex]a_{24}[/tex].

To find [tex]a_1[/tex], we will use the following formual:

[tex]a_n=a_1+(n-1)d[/tex]

[tex]a_24=152+(24-1)(-14)[/tex]

[tex]a_{24}=170[/tex]

Substituting the given values in the above formula to get the sum:

[tex]S_n =\frac{24(152-170)}{2}[/tex]

[tex]S_n=-216[/tex]

Answer:

Part 1) [tex]sin(2x)=8\frac{\sqrt{5}}{81}[/tex]

Part 2) [tex]cos(2x)=\frac{79}{81}[/tex]

Part 3) [tex]tan(2x)=8\frac{\sqrt{5}}{79}[/tex]

Step-by-step explanation:

Part 1) Find sin(2x)

we know that

[tex]sin(2x)=2sin(x)cos(x)[/tex]

we have

[tex]sin(x)=\frac{1}{9}[/tex]

Find cos(x)

Remember that

[tex]sin^{2}(x)+cos^{2}(x)=1[/tex]

substitute

[tex](\frac{1}{9})^{2}+cos^{2}(x)=1[/tex]

[tex]cos^{2}(x)=1-(\frac{1}{9})^{2}[/tex]

[tex]cos^{2}(x)=1-(\frac{1}{81})[/tex]

[tex]cos^{2}(x)=\frac{80}{81}[/tex]

[tex]cos(x)=\frac{\sqrt{80}}{9}[/tex]

[tex]cos(x)=4\frac{\sqrt{5}}{9}[/tex] -----> is positive because angle x belong to the I quadrant

Find sin(2x)

we have

[tex]sin(x)=\frac{1}{9}[/tex]

[tex]cos(x)=4\frac{\sqrt{5}}{9}[/tex]

so

[tex]sin(2x)=2sin(x)cos(x)[/tex]

[tex]sin(2x)=2(\frac{1}{9})(4\frac{\sqrt{5}}{9})[/tex]

[tex]sin(2x)=8\frac{\sqrt{5}}{81}[/tex]

Part 2) Find cos(2x)

we know that

[tex]cos(2x)=cos^{2}(x)-sin^{2}(x)[/tex]

we have

[tex]sin(x)=\frac{1}{9}[/tex]

[tex]cos(x)=4\frac{\sqrt{5}}{9}[/tex]

so

[tex]cos(2x)=(4\frac{\sqrt{5}}{9})^{2}-(\frac{1}{9})^{2}[/tex]

[tex]cos(2x)=\frac{80}{81}-\frac{1}{81}[/tex]

[tex]cos(2x)=\frac{79}{81}[/tex]

Part 3) Find tan(2x)

we know that

[tex]tan(2x)=\frac{sin(2x)}{cos(2x)}[/tex]

we have

[tex]sin(2x)=8\frac{\sqrt{5}}{81}[/tex]

[tex]cos(2x)=\frac{79}{81}[/tex]

so

[tex]tan(2x)=\frac{8\frac{\sqrt{5}}{81}}{\frac{79}{81}}[/tex]

[tex]tan(2x)=8\frac{\sqrt{5}}{79}[/tex]

Using trigonometric identity functions, when Sinx equals 1/9, Sin(2x) equals 2√80/729, Cos(2x) equals 79/81, and Tan(2x) equals 162√80/56831.

The question asks for the values of Sin(2x), Cos(2x), and Tan(2x) when Sinx = 1/9 (x in Quadrant 1). To solve for these values, we can use the identity formulas. If given that sinx = 1/9, it follows that cosx = √(1 - sin²x) = √(1 - (1/81)) = √(80/81) because in quadrant 1, the cosine value is positive. Therefore:

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Answer:

The correct answer is

Z⁶Y³/Z⁶Y⁴ = 1/Y

Step-by-step explanation:

Points to remember

1).  xᵃ * xᵇ = xᵃ⁺ᵇ

2).  xᵃ/xᵇ = xᵃ⁻ᵇ

3).  x° = 1

4). x⁻ᵃ = 1/xᵃ

The given expression is Z⁶Y³/Z⁶Y⁴

To find the simplification of expression

Z⁶Y³/Z⁶Y⁴ =  Z⁶⁻⁶ * Y³⁻⁴

 =  Z° * Y⁻¹ = 1 * 1/Y = 1/Y

Therefore the value of given expression  Z⁶Y³/Z⁶Y⁴ is 1/Y

Answer:i might be wrong but i believe its b

Step-by-step explanation:

Answer:

A : 1/4

B : 19/100

C : 3/50

Step-by-step explanation:

There are 25 prime numbers from 1 to 100.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

25/100 = 1/4

There are 19 numbers that contain 9.

9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, and 99.

19/100

There are 6 numbers that are prime and contain 9.

19, 29, 59, 79, 89, 97.

6/100 = 3/50

Answer:

n° = 62°

p° = 62°

q° = 118°

v° = 84°

w° = 138°

Step-by-step explanation:

angle ABC is 118°

so

m° + 118° = 180

m° = 180° - 118°

m° = 62°

n° = m° = 62° (corresponding angles are equal since AB is parallel to DC, and BC)

p° = n° = 62° (vertical angles are equal)

q° + n° = 180° (linear pair angles)

q° + 62° = 180°

q° = 180° - 62°

q° = 118°

v° + 96° = 180° (linear pair angles)

v°  = 180° - 96°

v° = 84°

w° + 42° = 180 (linear pair angles)

w° = 180° - 42°

w° = 138°

Answer:

n° = 62°

p° = 62°

q° = 118°

v° = 84°

w° = 138°

Step-by-step explanation:

angle ABC is 118°

so

m° + 118° = 180

m° = 180° - 118°

m° = 62°

n° = m° = 62° (corresponding angles are equal since AB is parallel to DC, and BC)

p° = n° = 62° (vertical angles are equal)

q° + n° = 180° (linear pair angles)

q° + 62° = 180°

q° = 180° - 62°

q° = 118°

v° + 96° = 180° (linear pair angles)

v°  = 180° - 96°

v° = 84°

w° + 42° = 180 (linear pair angles)

w° = 180° - 42°

w° = 138°

Answer:

The correct option is 1.

Step-by-step explanation:

The given table shows the mean daily temperature in Idaho during a week in January.

Sunday = 0.7°F

Monday = -1.2°F

Tuesday = -1.8°F

Wednesday = 1.1°F

Thursday = 0°F

Friday = 0.2°F

Saturday = -0.4°F

Arrange the temperature in ascending order.

-1.8°F, -1.2°F, -0.4°F, 0°F, 0.2°F, 0.7°F, 1.1°F

It means the lowest mean temperature was on Tuesday and the highest mean temperature was on Wednesday.

Therefore the correct option is 1.

Answer:

The lowest mean temperature was on Tuesday.

THIS IS THE EXACT ANSWER ON TTM

Step-by-step explanation:

Answer:

The probability of an event can help in determining that how much chance is there of the event to occur. The probability is between 0 to 1 always. Closer value to 1 means that the event has more chance of occurrence while a probability close to zero means the event is less likely to occur.

Step-by-step explanation:

Answer:

For tingle #1

We can find angle C using the triangle sum theorem: the three interior angles of any triangle add up to 180 degrees. Since we know the measures of angles A and B, we can find C.

[tex]C=180-(A+B)[/tex]

[tex]C=180-(21.24+27.14)[/tex]

[tex]C=131.62[/tex]

We cannot find any of the sides. Since there is noting to show us size, there is simply just not enough information; we need at least one side to use the rule of sines and find the other ones. Also, since there is nothing showing us size, each side can have more than one value.  

For triangle #2

In this one, we can find everything and there is one one value for each.

- We can find side c

Since we have a right triangle, we can find side c using the Pythagorean theorem

[tex]b^2=a^2+c^2[/tex]

[tex]4^2=2^2+c^2[/tex]

[tex]16=4+c^2[/tex]

[tex]12=c^2[/tex]

[tex]c=\sqrt{12}[/tex]

[tex]c=2\sqrt{3}[/tex]

- We can find angle C using the cosine trig identity

[tex]cos(C)=\frac{adjacent}{hypotenuse}[/tex]

[tex]cos(C)=\frac{2}{4}[/tex]

[tex]C=arccos(\frac{2}{4} )[/tex]

[tex]C=60[/tex]

- Now we can find angle A using the triangle sum theorem

[tex]A=180-(B+C)[/tex]

[tex]A=180-(90+60)[/tex]

[tex]A=30[/tex]

For triangle #3

Again, we can find everything and there is one one value for each.

- We can find angle A using the triangle sum theorem

[tex]A=180-(B+C)[/tex]

[tex]A=180-(90+34.88)[/tex]

[tex]A=55.12[/tex]

- We can find side a using the tangent trig identity

[tex]tan(C)=\frac{opposite-side}{adjacent-side}[/tex]

[tex]tan(34.88)=\frac{7}{a}[/tex]

[tex]a=\frac{7}{tan(34.88)}[/tex]

[tex]a=10.04[/tex]

- Now we can find side b using the Pythagorean theorem

[tex]b^2=a^2+c^2[/tex]

[tex]b^2=10.04^2+7^2[/tex]

[tex]b^2=149.8[/tex]

[tex]b=\sqrt{149.8}[/tex]

Answer:

Quadrant II

Step-by-step explanation:

Quadrant II points are characterized by a negative X value but a positive Y value (-x,y).

Since -10 is negative and 9 is positive, this point lies on quadrant II.

Answer:

quadrant III

Step-by-step explanation:

Answer:

The IQR is 0.2999999999999998

Step-by-step explanation:

You take the 3rd quartile and the 4th and you subtract them.

3rd-4th=IQR

Answer:

0.3

Step-by-step explanation:

5.5, 6.0, 6.2, 6.2, 6.3, 6.4, 6.5, 6.5, 6.8, 6.7

Median: 6.35

Lower quartile: 6.2

Upper quartile: 6.5

Interquartile range: 6.5 - 6.2 = 0.3

Answer:

16.6 ft

Step-by-step explanation:

Use Law Of Sines to solve this:

(Sin 7)/9 = (Sin 13)/x

Cross multiply...

x(Sin 7) = 9(Sin 13)

Divide both side by Sin 7

x = [9(Sin 13)]/(Sin 7)

 x = 16.61254121

Answer:

16.6 ft

Step-by-step explanation:

There is No Absolute Solution

9x+3 = 9x+5 has zero solutions.

The solution of an equation can be found by finding the value of the variable in the equation.

9x+3 = 9x+5

⇒ 3 = 9x - 9x + 5

⇒ 3 = 5

But 3 ≠ 5

The variables canceled each other out and we found that the given equation doesn't have a solution. Thus the equation has no solution.

Therefore, we have determined that the given equation 9x+3=9x+5 has zero equations.

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