The directions are write and solve two step equations

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: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

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:

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

The probability of drawing a green followed by a black marble from a bag containing 25 marbles without replacement is found by multiplying the individual probabilities of each event. These are 4/25 for the green marble and 7/12 for the black marble after the first draw.

The subject of this question is probability within the field of Mathematics, suitable for a High School level student. The probability of drawing a green and black marble without replacement is a two-step probability problem. Given that there are 5 purple, 2 yellow, 4 green, and the rest black out of 25 marbles, we first need to calculate the total number of black marbles, which is 25 - (5 + 2 + 4) = 14. The probability of drawing a green marble first is 4 out of 25, which simplifies to 4/25. After a green marble is drawn, there are now 24 marbles left in the bag, with 14 being black. Therefore, the probability of then drawing a black marble is 14/24 or 7/12. To find the combined probability of both events occurring sequentially, we multiply the individual probabilities: (4/25) * (7/12). This calculation will give us the final probability of drawing a green and then a black marble without replacement.

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:

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:

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:

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:

For this equation I used the fact that S and U are congruent (because Line ur and rs are equal and lines UT and TS are equal. All the interior angles need to add to 360 degrees. U+R+S = 340 so T has to equal 20 degrees.

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)

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: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.

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:

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:

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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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:

13.4 grams of a 120 gram sample will remain radioactive after 30 minutes.

Step-by-step explanation:

Given : A radioactive substance has a decay rate of 0.073 per minute.

To find : How many grams of a 120 gram sample will remain radioactive after 30 minutes?          

Solution :

Using decaying formula,  

[tex]y(t)=y_o e^{-rt}[/tex]

Where, [tex]y_o=120[/tex] is the initial amount

r=0.073 is the decay rate

t=30 minute is the time

Substitute the value in the formula,

[tex]y(30)=120\times e^{-0.073\times 30}[/tex]

[tex]y(30)=120\times e^{-2.19}[/tex]

[tex]y(30)=120\times 0.1119[/tex]

[tex]y(30)=13.428[/tex]

[tex]y(30)=13.4[/tex]

Therefore, 13.4 grams of a 120 gram sample will remain radioactive after 30 minutes.

Answer:

13.4

Step-by-step explanation:

Substitute the given values into the formula: A(t)=Pert. Where P is the initial mass, r is the rate of decay, and t is time.  Note, the rate is negative because we are finding the rate of decay.  

A=120e−(0.073)(30)≈13.4

So, about 13.4 grams will remain after 30 minutes.

The length of the wire is bent into a square, making each side equal to 7x/4. The area of a square is found by squaring the length of one side, so the area, as a function of , is (7x/4)^2 or 49x^2/16.

The given information is that the length of the wire is 7x, and it is bent into a square. In a square, all sides are equal. Therefore, we can say that the length of each side of the square is 7x/4.

To find the area of a square, we simply square the length of one side. Thus, the area A of the square, expressed as a function of x, is (7x/4)^2 or 49x^2/16.

Therefore, the question's answer is that the area A of the square can be expressed as the function 49x^2/16.

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Final answer:

To express the area A of a square in terms of z, assuming the wire length is 7z, calculate the side length a as 7z/4 and then square it to get A = (7z/4)². If x is correct and unrelated to z, more information is needed.

Explanation:

To express the area A of a square as a function of z, given that a wire of length 7x is bent into the shape of a square, we follow these steps:

The perimeter of the square is equal to the length of the wire, which is 7x.

Since the perimeter P of a square is 4 times one of its sides a, we can write P = 4a. Therefore, 7x = 4a.

To find the side length a, we divide 7x by 4: a = 7x/4.

The area A of a square is the square of one of its sides, so A = a². By substituting a with 7x/4, we get A = (7x/4)².

Finally, we need to write the equation in terms of z. Here, it seems there might be an issue with the question, as there is no direct relationship provided between x and z. Assuming there's a typographical error and that the wire length is actually 7z, we can write a = 7z/4 and A = (7z/4)².

If x is indeed correct and unrelated to z, more information is required to express A as a function of z.

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: The answer is 3m/s

Step-by-step explanation:

Answer: The runner’s average speed is 3 m/s.

Step-by-step explanation:

Hi, to solve this problem we have to multiply the length of the track (402.2 meters) by the times that joe ran around it (8.25 times).

So, mathematically speaking:

Now that we have this result, we have to divide it by the time ( 1,119.803 sec), to obtain the speed rate.

In conclusion, the runner’s average speed is 3 m/s.

Feel free to ask for more if it´s necessary or if you did not understand something.

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:

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:

[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 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:

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:

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: -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]