Evaluate 5^-2



A. 1/25
B. -10
C. 1/10
D. -25

Answer:

A. -4

Step-by-step explanation:

J= Jake's Number

A= Amy's Number

2j = 3j+2

-j = 2

j = -2

check: 2(-2) = 3(-2)+2

-4 = -6+2

-4 = -4 (correct)

Jake's number is -2. Amy's is -4

Answer:

There would be 144 red cars.

Step-by-step explanation:

3:5 is equal to 3/5

240 * (3/5) = 144

Answer:

90 red cars

Step-by-step explanation:

sum the parts of the ratio 3 + 5 = 8 parts

divide 240 by 8 to find one part of the ratio

240 ÷ 8 = 30 ← 1 part of the ratio

3 parts = 3 × 30 = 90 ← number of red cars

5 parts = 5 × 30 = 150 ← number of blue cars

Answer:

E

Step-by-step explanation:

The expression given is:  sec β - cos β ( i will write "beta" instead of the symbol β)

We know that [tex]sec(x)=\frac{1}{cos(x)}[/tex]

Substituting this into the the expression and doing some algebra manipulation, we have:

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

Using the identity  [tex]cos^{2}(x)+sin^{2}(x)=1\\[/tex] (also [tex]sin^{2}(x)=1-cos^{2}(x)[/tex]), we can now write:

[tex]\frac{1-cos^{2}(beta)}{cos(beta)}\\=\frac{sin^2(beta)}{cos(beta)}\\=\frac{sin(beta)*sin(beta)}{cos(beta)}\\=\frac{sin(beta)}{cos(beta)}*sin(beta)[/tex]

We know [tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex], substituting this, we have:

[tex]\frac{sin(beta)}{cos(beta)}*sin(beta)\\=tan(beta)*sin(beta)[/tex]

Answer choice E is the right answer.

The expression sec β - cos β in terms of sine and cosine simplifies to sin2 β. This is achieved by knowing that secant is the reciprocal of cosine and using the Pythagorean identity in trigonometry.

To write the expression in terms of sine and cosine, we start by remembering that secant is the reciprocal of cosine, so sec β = 1/cos β. So, the expression sec β - cos β is equivalent to 1/cos β - cos β.

However, to remove the quotient from the expression, we multiply through by cos β to get 1 - cos2 β. So the expression sec β - cos β simplifies to 1 - cos2 β.

But remember, based on the Pythagorean identity in trigonometry, 1 - cos2 β is also equivalent to sin2 β. So that's our final simplified expression in terms of sine and cosine.

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Answer:

x=3/2,  x=-4

Step-by-step explanation:

2x^2 + 5x - 12

First lets see if we can factor this

(2x    ) ( x      )

-12 = -1*12     1*-12

    -  2*6        2 * -12

    -  3*4       3 * -4

2 * one of these pairs - the other pair = +5  

2*4 -3 = 5

Put the -3 in the first spot and the 4 in the second spot

(2x-3)  ( x+4)

Using the zero product property

2x-3 =0     x+4=0

2x=3             x=-4

x = 3/2

Answer:

Part a) The number of visits mus be greater than or equal to [tex]4[/tex]

Part b)

with season pass

The total cost is [tex]\$64[/tex]

without season pass

The total cost is [tex]\$58.5[/tex]

Step-by-step explanation:

Let

x---> the number of visit to the water park

y---> the total cost to visit the water park per person

we know that

[tex]y=(14.50+5)x=19.5x[/tex]  

so

Part a) How many visits to the water park would you have to use for the season pass to be a better deal?

For [tex]y=\$64[/tex]

Substitute the value of y in the equation and solve for x

[tex]64=19.5x[/tex]

[tex]x=64/19.5=3.28\ visits[/tex]

therefore

The number of visits mus be greater than or equal to [tex]4[/tex]

Part b) What would the total cost be for 3 visits with and without a season pass?

with season pass

The total cost is [tex]\$64[/tex]

without season pass

The total cost for [tex]x=3\ visits[/tex] is

[tex]y==19.5(3)=\$58.5[/tex]  

Answer:

[tex]x^2+6x+6y=0[/tex]

Step-by-step explanation:

The distance between the parabola focus and the directrix is 3, then

[tex]p=3.[/tex]

Parabola vertex is placed on the perpendicular line to the directrix and this perpendicular line passes trough the focus. Its equation is x=-3 and parabola vertex coordinates are (-3,1.5).

Branches of the parabola go in negative y-direction, then the equation of the parabola is

[tex](x-(-3))^2=-2\cdot 3(y-1.5),\\ \\(x+3)^2=-6(y-1.5),\\ \\x^2+6x+9=-6y+9,\\ \\x^2+6x+6y=0.[/tex]

Answer:

y2=-12x

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

To find how many times 6 x 10^5 power is greater tan 3 x 10^4 power, we divide the first number by the second. Write an equation!

(6 x 10^5)/(3 x 10^4)=

To divide them, we simply subtract the exponents. 5-4=1.

(6 x 10^1)/(3 x 10^1)

60/30=20

Your answer is 20.

Hope this helps!

Answer:

Your answer would be A)6x105 is 20 times larger than 3x104

All u have to do is get your answer from 6x10^5(which is 600,000) and 3x10^4(which is 30,000) and divide it by each other       So it would be   600,000/30,000=20  =^.^=

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

Remove parenthesis 3(-x+(2x+1))=x-1

Collect the like terms 3(-x+2x+1)=x-1

Multiply parenthesis by 3 3(x+1)=x-1

Move terms 3x+3=x-1

Collect the like terms and calculate 3x-x=-1-3

Divide both sides by 2 2x=-4

Answer: x=-2

Step-by-step explanation:

Answer: [tex]2\sqrt{30}[/tex]

Step-by-step explanation:

               120

                 ∧

             12   10

             ∧     ∧

           3  4  2  5

               ∧

             2  2

  [tex]\sqrt{120}[/tex]

= [tex]\sqrt{2*2*2*3*5}[/tex]

= [tex]2\sqrt{2*3*5}[/tex]

= [tex]2\sqrt{30}[/tex]

Answer:

y ≈ 0.7

Step-by-step explanation:

locate [tex]\frac{\pi }{4}[/tex] on the x-axis, move up the vertical line until meeting the graph then the horizontal reading gives y ≈ 0.7

Arrows on a line mean that the line continues forever in that direction. If there are two arrows in both directions along a line, then you have a geometric line. If you only have one arrow, then it is a ray. Having no arrows indicates a segment.

Answer:

3* (b+9) = 4

Step-by-step explanation:

b is the unknown number

Three times the sum of a number and 9 is 4.

3* (b+9) = 4

To translate 'Three times the sum of a number and 9 is 4' into an equation, you represent the unknown number by 'b' and write the equation as 3(b + 9) = 4. Solve for 'b' by distributing the 3 and then isolating 'b' to get b = -23/3.

Translating the sentence 'Three times the sum of a number and 9 is 4' into an equation involves identifying the phrases that represent mathematical operations and the variable represented by b. The sentence describes a two-step mathematical process: finding the sum of a number (b) and 9, and then multiplying that sum by 3 to get 4. This can be written as an equation: 3(b + 9) = 4.

To solve for the unknown, which in this case is b, we first distribute the 3 inside the parentheses: 3b + 27 = 4. Then we isolate the b on one side by subtracting 27 from both sides of the equation: 3b = 4 - 27, which simplifies to 3b = -23. Finally, we divide both sides by 3 to get b on its own: b = -23/3.

Answer:

a. y= -1/5x+1

Step-by-step explanation:

If we have 2 points , we can find the slope using the formula

m = (y2-y1)/(x2-x1)

  = (-1-2)/(10--5)

   =(-1-2)/(10+5)

  = -3/15

  = -1/5

The slope if -1/5

We can use the point slope form of a line to write an equation

y-y1= m(x-x1)

y-2 = -1/5(x--5)

y-2 =-1/5(x+5)

Distribute the -1/5

y-2=-1/5x -1

Add 2 to each side

y-2+2 = -1/5x -1+2

y = -1/5x+1

Step-by-step explanation:

Use this formula: Y2 - Y1

                              X2 -X1

Then, use point slope form: y - Y1 = m (x - X1)

Finally, it'll reveal your answer!!! :)

Answer:

7. n = 5r + 10

9.  [tex] 28.50j + 18s \le 100 [/tex]

Step-by-step explanation:

7.

The table gives you these values

2   20

4    30

6    40

8    50

The left side goes up by 2 each time while the right side goes up by 10 each line.

Using that pattern, fill in a few extra lines. I did it below in bold.

0    10

1     15

2   20

4    30

6    40

8    50

The line 0, 10 shows you that b in y = mx + b is 10. Also from the fist line to the second line, as x goes from 0 to 1, a difference of 1, y goes from 10 to 15, a difference of 5. The slope is difference in y over difference in x, so

slope = m = 5/1 = 5.

The equation is

y = mx + b

y = 5x + 10

The problem uses n instead of y and r instead of x, so you get

n = 5r + 10

9.

One pair of jeans costs $28.50. j is the number of jeans. j number of jeans cost 28.50j.

One shirt costs $18. s is the number of shirts. s number of shirts cost 18s.

The total cost is the cost of the jeans plus the cost of the shirts.

The total cost is 28.50j + 18s.

She can spend up to $100. The total cost of the jeans and shirts can be less than $100 or exactly $100, but it cannot be more than $100.

cost of jeans and shirts must be less than or equal to $100

[tex] 28.50j + 18s \le 100 [/tex]

Answer:

3. - 1 52/57

4.  -1 23/135

5. -3 31/36

Step-by-step explanation:

3.  Note the answer will be a negative number because one of the numbers is negative and the other is positive. When we do the division  use positive numbers . Then we can just plug in  the negative.

It looks like  114 will only divide once into 218  because 2*114 = 228 .

So the whole number part is 1. Now subtract 114 from 218  we get  104.

So we have the mixed number 1 104/114. These numbers in the fraction are positive so we divide by 2 to simplify.

This gives us 1 52/57

Finally plug in the negative and we have -1 52/57 (answer)

Q4. In a similar fashion to the above  158 / 135 = 1 and the fraction part is (158-135) / 135 =  23/135,so the answer is  -1 23/135  ( note its negative because of the -135).

Q5.

-834 / 216

216 divides 3 times into 834 and the remainder is 834 - 3 * 216

= 834 - 648 =  186

so the mixed number is -3 186/216

Now simplify 186/216:-

divide each number by 2 , we get  93/108

3 will divide into 93 and 108 giving 31/36

Now plug in the negative.

So the answer is -3 31/36

Answer:

3. [tex]-1\tfrac{52}{57}[/tex]

4. [tex]-1\tfrac{23}{135}[/tex]

5. [tex]-3 \tfrac{31}{36}[/tex]

Step-by-step explanation:

3.

To find :  the quotient when we divide -218 by 114

Solution : As in −218÷114 one of the numbers is negative and the other is positive, quotient must be negative .

[tex]\frac{-218}{114}=\frac{-109}{57}=-1\tfrac{52}{57}[/tex] ( mxed fraction )

( see fig (i) )

4.

To find : the quotient when we divide 158 by 135

Solution: As in 158÷(−135) one of the numbers is negative and the other is positive, quotient must be negative .

[tex]\frac{158}{-135}=-1\tfrac{23}{135}[/tex] ( mixed fraction )

( see fig (ii) )

5.

To find : −834÷216

Solution :

As in −834÷216 one of the numbers is negative and the other is positive, quotient must be negative .

[tex]\frac{-834}{216}=\frac{-417}{108}=\frac{-139}{36}=-3 \tfrac{31}{36}[/tex]

( see fig iii )

The answer is x > -4

To get this answer, you divide both sides by 5. This is to undo the multiplication that happens to the 'x' in '5x'. Note that 5x means 5*x or 5 times x, where x is just a placeholder for some unknown number.

Saying x > -4 means you can pick any number larger than -4.

i can help you with points if you would like

pls consider it i have alot

B. (0, 9)

Reflection across x=a is represented by the transformation ...

... (x, y) ⇒(2a-x, y)

Reflection across y=b is represented by the transformation ...

... (x, y) ⇒ (x, 2b-y)

The double reflection, across x=2, y=1 will result in the transformation ...

... (x, y) ⇒ (2·2-x, y) ⇒ (4-x, 2·1-y) ⇒ (4-x, 2-y)

For (x, y) = X(4, -7), the transformed point is ...

... X''(4-4, 2-(-7)) = X''(0, 9)

The double reflection across x=2 and y=1 transforms the point X(4, -7) to X''(0, 9), illustrating the sequential application of reflection transformations (4-x, 2-y).

The correct answer is option B.

A reflection across the vertical line x=a is represented by the transformation (x, y) ⇒ (2a-x, y). Similarly, a reflection across the horizontal line y=b is represented by the transformation (x, y) ⇒ (x, 2b-y). The double reflection, across x=2 and y=1, can be expressed by applying these transformations sequentially.

Starting with the point (x, y), the first reflection across x=2 yields (2·2-x, y), and then, the reflection across y=1 gives (4-x, 2·1-y). Combining these transformations, the double reflection is represented by the transformation (x, y) ⇒ (4-x, 2-y).

Now, applying this double reflection to the given point X(4, -7), we get X''(4-4, 2-(-7)) = X''(0, 9). Therefore, the transformed point after the double reflection is X''(0, 9) making option B the correct option.

Learn more about Transformations here:

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Answer:

$29.50

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Melinda: y = 10x + 22

George: y = 13x + 10

13x + 10 = 10x + 22

-10x          -10x          

 3x   + 10 =         22

         -10         -10

3x            =         12

÷3                      ÷3

  x            =          4

Lets say Y is the amount they will save.

So Melinda's savings could be described by the equation Y=22+10X, where X is the number of weeks. The same goes to George, but his equation would be Y=10+13X.

To save the same amount, their equations must match:

22+10X = 10+13X

Solving this, one gets

12 = 3x

=> 4=x

So the answer is 4 weeks.

The question requires understanding of real estate value, equity, and mortgage calculations related to buying a house. Freda's equity is the entire value of her house at $250,000. Ben has paid off a portion of his loan and has an equity of $100,000 in his home.

The question provided deals with the financial aspects of purchasing a house and understanding real estate value, equity, and mortgage calculations. Helena purchasing a house for $210,000 would fall under the mathematics or business subject area as it involves financial calculations.

Freda's house situation, where she bought a house for $150,000 in cash and its current value is $250,000, tells us that her equity in the property would be the entire value of the house, which is $250,000, since she owes nothing to the bank.

As for Ben, he initially purchased his house for $100,000 and made a 20% down payment. He took a loan from the bank to cover the remaining 80%, later paid off $20,000 of it, and his house value has increased to $160,000. Ben's remaining loan balance would be the original borrowed amount minus what he has already paid back. Since he had taken 80% of $100,000, that would have been $80,000 initially, minus the $20,000 paid, leaves him with a $60,000 debt. The equity that Ben has in his house is the current market value minus the debt, which is $160,000 - $60,000, giving him an equity of $100,000.

In another scenario provided, Joanna is looking to determine how much she can afford in terms of a house loan with yearly payments of $12,000 at an interest rate of 4.2% over a 30-year period. She would need to apply the formula for calculating a mortgage payment and the total amount paid over the course of the loan.

Helena's total monthly payments are approximately $2,361.17. The closest answer choice is C. $2330.20.

Principal and Interest:

Down payment = 5% of $210,000 = $10,500

Loan amount = $210,000 - $10,500 = $199,500

Using a mortgage calculator, the monthly principal and interest payment for a 15-year loan at 4.5% interest on $199,500 is $1595.54.

PMI (Private Mortgage Insurance):

Loan-to-value ratio (LTV) = $199,500 / $200,000 = 99.75%

Based on the table, the PMI premium for a 15-year fixed-rate loan with an LTV of 95.01% to 97% is 0.79%.

Annual PMI premium = 0.79% of $199,500 = $1575.05

Monthly PMI premium = $1575.05 / 12 = $131.25

Property Taxes:

Annual property taxes = 3.5% of $200,000 = $7000

Monthly property taxes = $7000 / 12 = $583.33

Homeowners Insurance:

Monthly homeowners insurance = $600 / 12 = $50

Total Monthly Payments:

Principal and Interest: $1595.54

PMI: $131.25

Property Taxes: $583.33

Homeowners Insurance: $50 Total: $2350.12

Complete Question:

Helena is purchasing a house for $210,000, with a 15 -year fixed-rate mortgage at 4.5% interest. She has made a 5% down payment. The house is valued at $200,000, and the local tax rate is 3.5%. Her homeowners insurance is $600 per year. What are her total monthly payments? (Use the table below to calculate PMI premiums.)

[tex]\begin{tabular}{lcccl} Base-To-Loan\% & \multicolumn{2}{c}{ Fixed Rate Loan } & \multicolumn{2}{c}{ ARM 2\%+1 Year Cap } \\& $30 {yrs}$ & $15 {yrs}$ & $30 {yrs}$ & $15 {yrs}$ \\$95.01 \%$ to $97 \%$ & $0.90 \%$ & $0.79 \%$ & ${n} / {a}$ & ${n} / {a}$ \\$90.01 \%$ to $95 \%$ & $0.78 \%$ & $0.26 \%$ & $0.92 \%$ & $0.81 \%$ \\$85.01 \%$ to $90 \%$ & $0.52 \%$ & $0.23 \%$ & $0.65 \%$ & $0.54 \%$ \\$85 \%$ and Under & $0.32 \%$ & $0.19 \%$ & $0.37 \%$ & $0.26 \%$\end{tabular}[/tex]

A. 2654.23

B. 2894.71

C. 2330.20

D. 2202.72

The system results in a false statement

Answer:

$9

Step-by-step explanation:

The artist buys 8 brushes that cost $5 each, then all brushes cost

[tex]\$5\cdot 8=\$40.[/tex]

He pays $94 for all brushes and cans of paint, then all cans of paint cost

[tex]\$94-\$40=\$54.[/tex]

If he buys 6 cans of paint, then one can of paint costs

[tex]\$54:6=\$9.[/tex]

Answer:

3/8

Step-by-step explanation:

1/8 + 1/4 =

We need to get a common denominator of 8

1/8 + 1/4 * 2/2

1/8 + 2/8

3/8

Answer:0.16 and 6%

Step-by-step explanation:

Answer:

(f+g)(x) = -4^x + 5x - 2

Step-by-step explanation:

if f(x) = -4^x - 8 and g(x) = 5x + 6,

(f+g)(x) = f(x) + g(x)

= -4^x - 8 + 5x + 6

= -4^x + 5x - 2

Answer:

-4^x + 5x - 2

Step-by-step explanation:

By the additive property of function, (f+g)(x) = f(x) + g(x)

Given f(x) = -4^x - 8 and g(x) = 5x + 6

(f+g)(x) = f(x) + g(x)

= -4^x - 8 + 5x + 6

= -4^x + 5x - 2

Answer:

16 logs

Step-by-step explanation:

4 logs in 2 hours

8 logs in 4 hours

12 logs in 6 hours

16 logs in 8 hours

Answer:

16

Step-by-step explanation:

16 Because 2 divided by 8 equals 4 then 4x4=16