10v+6=-54

What is happening to the variable?


How do you solve for the variable?

Answer: t=15

Step-by-step explanation:

ST=9. BC=3

ST/BC=

9/3=3 ==> with this information, we can conclude that triangle ABC needs to be stretched by a scale factor of 3 in order to become triangle RST.

t=RS

RS=AB*3

RS=5*3

RS=15

t=15

The perimeter of one of the triangles is 28 inches.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

From the given information the diagonal of the rectangle will be,

d = √(12² + 3.5²)

d = √(144 + 12.25).

d = √156.25.

d = 12.5.

We know, Perimeter is the sum of the lengths of all the sides.

Therefore, P = 12.5 + 12 + 3.5 inches.

P = 28 inches.

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You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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The correct answer of the operation is option B: 4x^2 - 9.

To perform the operation (2x-3)(2x+3), we can use the FOIL method, which stands for First, Outer, Inner, Last. Let's go through the steps:

First: Multiply the first terms of each binomial.

(2x)(2x) = 4x^2

Outer: Multiply the outer terms of each binomial.

(2x)(3) = 6x

Inner: Multiply the inner terms of each binomial.

(-3)(2x) = -6x

Last: Multiply the last terms of each binomial.

(-3)(3) = -9

A binomial is a two-term algebraic expression that contains variable, coefficient, exponents and constant, a binomial is an expression that has two unlike terms connected through an addition or subtraction operator in between.  

Now, let's combine the like terms:

4x^2 + 6x - 6x - 9

Notice that the terms 6x and -6x cancel each other out.

Simplifying further, we have:

4x^2 - 9

The correct answer is option B: 4x^2 - 9.

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Answer:

11x+60° =93

11x =93-60

x=33/11

x=3

z+93 = 180 (being angles in st. line)

z=180-93

z= 87

Answer:

x=3

z=87

Step-by-step explanation:

Using the vertical angles rule, we can set 11x+60=93, solve for x:

\(11x+60=93\\11x=33\\x=3\)

Since two angles on a line add up to 180, we can find z by setting 180=z+93, solve for z:

\(180=93+z\\87=z\)

Answer:

2/9 = approximately 0.22.

Step-by-step explanation:

There are a total of 12 possible outcomes when the spinner is spun once, so the probability of getting a result that is not green is 8/12, or 2/3. Similarly, the probability of getting green on the second spin is 4/12, or 1/3.

To find the probability of getting a result that is not green on the first spin and green on the second spin, you can multiply the probabilities of each individual event. Therefore, the probability of getting not green then green is (2/3) * (1/3) = 2/9 = approximately 0.22.

Alternatively, you could also use the principle of complementary probabilities to calculate the probability of getting not green on the first spin and green on the second spin. The probability of getting not green on the first spin is 1 - (4/12) = 8/12 = 2/3, and the probability of getting green on the second spin is still 4/12 = 1/3. Multiplying these probabilities gives a result of (2/3) * (1/3) = 2/9 = approximately 0.22.

Answer:  

x = -2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

6 - 9x = 5x - 9x + 16

Step 2: Solve for x

Answer:

\(x=-2\)

Step-by-step explanation:

\(We\ are\ given,\\6-9x=5x-9x+16\\6-9x=-4x+16\ [Resolving\ like\ terms\ in\ RHS]\\-9x+4x=16-6[Transposing\ variables\ to\ LHS\ and\ constants\ to\ RHS]\\-5x=10[Simplifying]\\x=\frac{10}{-5}[Dividing]\\x=-2 [Finding\ the\ value\ of\ x]\)

I got 9 7/9 by using a calculator

The vertex of the reflected figure over x axis will be A'(3 , -4) , B'(-1 , -3), C'(4 , -10) , D'(2 , 3), the correct option is (c) .

In the question ,

it is given that ,

the Polygon ABCD is reflected over x axis .

the vertices of the Polygon ABCD is A(3, 4), B(-1, 3), C(4,10) & D(2,-3)  .

We know that when the point (x , y) is reflected over the x axis the point becomes (x, -y) .

the point A(3,4) after reflection becomes A'(3 , -4) .

the point B(-1 , 3) after reflection becomes B'(-1 , -3) .

the point C(4 , 10) after reflection becomes C'(4 , -10) .

the point D(2 , -3) after reflection becomes D'(2 , -(-3)) = (2 , 3) .

Therefore , The vertex of the reflected figure over x axis will be A'(3 , -4) , B'(-1 , -3), C'(4 , -10) , D'(2 , 3) .

The given question is incomplete , the complete question is

Polygon ABCD has vertices (3, 4), (-1, 3), (4,10) & (2,-3) was reflected over the x-axis. Which would be vertex of the reflected figure?

(a) (-3,-4)

(b) (-4,-10)

(c) (-1, -3)

(d) (2,-3)

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Answer:

a) 81

b) 2401

c) 100

d) 78125

Step-by-step explanation:

a) \(3^{2}\) x \(3^{2}\)  = \(3^{4}\)  When the bases are the same and you are multiplying powers, you add the exponents.

\(3^{4}\) means 3x3x3x3 or 81

b) 7 x \(7^{4}\) = \(7^{5}\) When the bases are the same and you are multiplying powers, you add the exponents.  When you do not see an exponent like the number 7, the exponent is 1.

7 = \(7^{1}\)

\(7^{4}\) means 7x7x7x7x or 2401

c) \(\frac{10^{9} }{10^{7} }\)  = \(10^{2}\)  When the bases are the same and you are dividing, you subtract the exponents.

\(10^{2}\) means 10x10 = 100

d) \(\frac{5^{8} }{5}\)= \(5^{7}\) When the bases are the same and you are dividing, you subtract the exponents.

\(5^{7}\) means 5x5x5x5x5x5x5 =

Answer:

a) \(\sf 3^4\)

b) \(\sf 7^5\)

c) \(\sf 10^2\)

d) \(\sf 5^7\)

Step-by-step explanation:

a) → → →

\(\sf 3^2 \times 3^2\) (Apply exponent rule)

\(\sf 3^{2+2}\) ( Add numbers)

\(\bf 3^4\)

b) → → →      

\(\sf 7 \times 7^ 4\) (Apply exponent rule)

\(\sf 7^{1+4}\) (Add numbers)

\(\bf 7^5\)

c) → → →

\(\sf 10^9 \div10^7\) (Apply exponent rule)

\(\sf 10^{9-7}\) (Add numbers)

\(\bf 10^2\)

d) → → →

\(\sf 5^8 \div 5\) (Apply exponent rule)

\(\sf 5^{8-1}\) (Add numbers)

\(\bf 5^7\)

____________________

Hope this helps!

Have a great day!

Eva's account balance after t years can be represented by the exponential growth function:

A(t) = 1500 * (1 + 0.04)^t

The value of Lamount's house after t years can be represented by the exponential growth function:

V(t) = 255000 * (1 + 0.06)^t

Brian's investment value after t years can be represented by the exponential growth function:

I(t) = 2000 * (1 + 0.16)^t

In these equations, A(t) represents the account balance, V(t) represents the house value, and I(t) represents the investment value after t years. The exponent represents the growth rate, where (1 + r) is used to account for the growth percentage (e.g., 0.04 for 4% growth rate).

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Answer:

64ft

Step-by-step explanation:

since all sides of a square and the same and equal then all the dimensions will be the same

Answer:

One.

Step-by-step explanation:

It is a linear equation. This means that x is raised to the first power, which there can only be one solution.

Answer:

Hi, the correct answer to your question is Y,X would be (29,11)

ONE SOLUTION

Step-by-step explanation:

First you have to... solve for y

Y equals 2x+7

Next you have to use the variable y and put in into an equation.

2x+7 - 3x = -4 (Also) :) - x = -11

Now you have to solve the equation for the variable x

Which will be 11 (x will be 11)

Finally you have to use x to solve for y

2(11)+7 = 29

Now we have 11 and 29 so the answer to your question will be

= (29,11)

Also this means it has one solution

Btw this is a linear equation...

Hope this helps you! :)

Answer:

 525 miles

Step-by-step explanation:

Two unit rates are given in this problem:

miles per gallon

gallons per mile

Since we want to find miles, the appropriate rate to use is miles per gallon:

\(distance = \frac{miles}{gallon} (gallons)\\distance = \frac{35 miles}{gallon} (15 gallons) = 525\)

Answer:

D. EF is longer than EG.

Step-by-step explanation:

I took the quiz

1. In 2008, there were approximately 28.2 million live Christmas trees sold in the U.S

2. The linear regression equation that models the set of data above is C = 0.28t + 27.28.

3. From 2004 to 2011, the number of Christmas trees sold in the U.S. increased by approximately 0.28 million trees each year.

4. In 2008, there were approximately 28.4 million live Christmas trees sold in the U.S.

5. Why is this the case: A. The data are not perfectly linear. The regression equation gives only an approximation.

By using the data values in the table, the number of live Christmas trees that were sold in the year 2008 can be calculated as follows;

t = 0 + (2008 - 2004) years.

t = 4 years.

At t = 4 years on the table, approximately 28.2 million live Christmas trees sold in the U.S.

Part 2.

Based on the table, we can logically deduce that the y-intercept or initial value is (0, 27.1).

y = mx + b ≡ C = mt + b

b = (547.6 - 538.6)/(105 - 72.2)

b = 0.28

Therefore, the required linear regression equation is given by;

C = 0.28t + 27.28

Part 3.

Based on the slope of the above linear regression equation, the number of Christmas trees sold in the U.S. from 2004 to 2011 increased by approximately 0.28 million trees each year.

Part 4.

For the number of live Christmas trees sold in year 2008, we have:

C(4) = 0.28(4) + 27.28

C(4) = 28.4 million.

Part 5.

The answers to parts 1 and 4 are different because the data set do not have a perfectly linear relationship and the linear regression equation gives only an approximated value, not an exact value.

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Answer:

Step-by-step explanation:

Sure! I'll perform the mathematical operations using the given numbers and apply the rules of precision. Please find the results below:

(9.11) + (6.232)

The sum of 9.11 and 6.232 is 15.342.

(7.4023) x (19)

The product of 7.4023 and 19 is 140.844.

(9.162) - (2.39)

The difference between 9.162 and 2.39 is 6.772.

(0.00482) x (213)

The product of 0.00482 and 213 is 1.02786.

(8.73) / (5.198)

The division of 8.73 by 5.198 is 1.67920734.

(7644) / (0.13)

The division of 7644 by 0.13 is 58,800.

Please note that the results are rounded to the appropriate number of decimal places based on the precision rules.

Answer:

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Step-by-step explanation:

Given;

Total Months = 14

Total Words = 1920

Required

Find the time spent in Portugal and time spent in Brazil

Let P represent Portugal and B represent Brazil; This implies that

\(P + B = 14\) ---- Equation 1

Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that

\(130P + 150B = 1920\) --- Equation 2

Make P the subject of formula in equation 1

\(P = 14 - B\)

Substitute 14 - B for P in equation 2

\(130(14 - B) + 150B = 1920\)

Open Bracket

\(1820 - 130B + 150B = 1920\)

\(1820 + 20B = 1920\)

Subtract 1820 from both sides

\(1820 - 1820 + 20B = 1920 - 1820\)

\(20B = 100\)

Divide both sides by 20

\(\frac{20B}{20} = \frac{100}{20}\)

\(B = 5\)

Substitute 5 for B in \(P = 14 - B\)

\(P = 14 - 5\)

\(P = 9\)

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Answer:

B

Step-by-step explanation:

After adding them all together, we end up with 351. There are 12 numbers, so we do 351/12, getting 29.25.

Answer:

i think the answer is B because 3/4 is more than 2/3

Answer:

its b.

Step-by-step explanation:

if you convert them, so they both have the same dominator, nadias recipe ends up needing more flour.

Answer:

k

Step-by-step explanation:

-3k minus -3k

-2k-(-3k)

-2k+3k

k

The most appropriate choice for Basic Proportionality Theorem will be given by -

x = 5 is the correct answer

What is Basic Proportionality Theorem?

If a line is drawn parallel to third side of a triangle, intersecting the other two sides of the triangle, the other two sides are  divided in the same ratio.

Here,

In the figure, two parallel lines are given

By Basic Proportionality Theorem,

\(\frac{x}{x+5} = \frac{x-2}{x+1}\\\)

\(x(x +1) = (x - 2)(x + 5)\\x^2 +x = x^2 + 5x - 2x -10\\x = 3x -10\\3x - x = 10 \\ 2x = 10\\x = \frac{10}{2}\\x = 5\)

x = 5 is the correct answer

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Answer:

area of trapezium=1/2 h(length 1+length2)

1/2*5*(13+6)

1/2*5*19

Answer:

Area = 47.5cm^{2}

Step-by-step explanation:

Area = 1/2 (a+b) × height

Area = 1/2 (6 + 13) × 5

  Area = 1/2 (19) × 5

    Area = 47.5cm^{2}

The answers to all limits are:

(a) lim x → a [ f(x) + 2g(x)] =  -6,

(b) lim x → a [h(x) − 3g(x) + 1] = 13

(c) lim x → a [ f(x)g(x)] = -8

(d) lim x → a [g (x)]² = 16

(e) lim x → a 3√6 + f(x) / 2g(x)

The central limit theorem states that if you take sufficiently large samples from a population, the samples' means will be normally distributed, even if the population isn't normally distributed.

here, we have,

(a) lim x → a [ f(x) + 2g(x)]

= lim x → a f(x) + 2 lim x → a g(x) (using algebraic limit theorem)

= 2 + 2(-4)

= -6

(b) lim x → a [h(x) − 3g(x) + 1]

= lim x → a h(x) - 3 lim x → a g(x) + lim x → a 1 (using algebraic limit theorem)

= 0 - 3(-4) + 1

= 13

(c) lim x → a [ f(x)g(x)]

= lim x → a f(x) * lim x → a g(x) (using algebraic limit theorem)

= 2 * (-4)

= -8

(d) lim x → a [g(x)]²

= [lim x → a g(x)]^2 (using algebraic limit theorem)

= (-4)^2

= 16

(e) lim x → a 3√6 + f(x) / 2g(x)

= [3√6 + lim x → a f(x)] / [2 lim x → a g(x)] (using algebraic limit theorem)

= [3√6 + 2] / [2(-4)]

= (-3√6 - 2) / 8

Therefore, the answers to all limits are:

(a) lim x → a [ f(x) + 2g(x)] =  -6,

(b) lim x → a [h(x) − 3g(x) + 1] = 13

(c) lim x → a [ f(x)g(x)] = -8

(d) lim x → a [g (x)]² = 16

(e) lim x → a 3√6 + f(x) / 2g(x)

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Complete question:

1. Given that

lim

x → a f(x) = 2, lim

x → a g(x) = −4, lim

x → a h(x) = 0

find the limits.

(a) lim

x → a [ f(x) + 2g(x)]

(b) lim

x → a [h(x) − 3g(x) + 1]

(c) lim

x → a [ f(x)g(x)] (d) lim

x → a [g(x)]2

(e) lim

x → a

3

√6 + f(x) (f ) lim

x → a

2

g(x)

a. To find the probability that exactly four of the contracts experience cost overruns, we use the binomial probability formula:

P(X = 4) = (20 choose 4) * 0.2^4 * (0.8\()^16\)

where "X = the number of contracts that experience cost overruns". Using a calculator, we get:

P(X = 4) ≈ 0.2835

b. To find the probability that fewer than three of the contracts experience cost overruns, we need to find the probability that 0, 1, or 2 contracts experience cost overruns. We can use the binomial probability formula for each of these values and add the probabilities together:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= (20 choose 0) * 0.2^0 * (0.8)^20 + (20 choose 1) * 0.\(2^1\) * (0.8\()^19\) + (20 choose 2) * 0.\(2^2\) * (0.8\()^18\)

Using a calculator, we get:

P(X < 3) ≈ 0.1792

c. To find the probability that none of the contracts experience cost overruns, we use the binomial probability formula:

P(X = 0) = (20 choose 0) * 0.2^0 * (0.8)^20

Using a calculator, we get:

P(X = 0) ≈ 0.0115

d. The mean number of contracts that experience cost overruns is given by the formula:

μ = n*p

where "n" is the number of contracts sampled (20) and "p" is the probability of a cost overrun (0.2). Thus, we have:

μ = 20 * 0.2

μ = 4

e. The standard deviation of the number of contracts that experience cost overruns is given by the formula:

σ = sqrt(np(1-p))

Plugging in the values, we get:

σ = sqrt(200.2(1-0.2))

σ ≈ 1.79

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Answer:

50% or 1/2

Step-by-step explanation:

Because there are 4 animals in the barn, if two animals leave (out of 4), then there are 50% of the animals in the barn and 50% of the animals leaving the barn.

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Answer:

D. \(\frac{(x-7)^2}{8^2} -\frac{(y-2)^2}{7^2}\)

Step-by-step explanation:

hope this helps

Answer:  D has the largest perimeter

Step-by-step explanation:

The top numbers of fractions describe the vertex and  the bottom number square rooted tells you how long each or wide each part of the asymptote rectangle is.

A.

P = 2(11) + 2(3)

P = 22+6

P=28

B.

P = 2(4) + 2(9)

p = 8 +18

P = 26

C.

P = 2(5) + 2(9)

P = 10 +18

P = 28

D.

P =  2(8) + 2(7)

P = 16 +14

P = 30