Section 5.2-10. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).-2x+3y = 15-x-3y = 12

We are asked to find the final area in square centimeters.

We must first convert the measurements of the poster into centimeters:

1.2m = 120cm

0.9m = 90cm

Area = length * width

= 120*90

= 10800 square centimeters.

Answer:

It's already in its simplest form.

Step-by-step explanation:

I'm writing a book/document on this topic but it's not finished. I suspect there is an error in this question because it's practically impossible to factorise it into integers.

The quadratic polynomial in the numerator has imaginary roots because 5 squared is less than 20 times 4.

ax² + bx + c;

if ( b² < 4ac ) { 'solution is imaginary' }

The quadratic equation will explain the above.

The function rule represents how much money is still owed is B = 3000 - 150m

A function is used to show the relationship between the data given. This can be illustrated with the variables.

Here, the person bought the first car for $3,000 and make payments of $150 each month.

Let B represent the balance.

The function to illustrate this will be:

B = 3000 - 150(m)

B = 3000 - 150m

where B = balance

m = number of months

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lillyvong13, this is the solution:

Cost of the ticket to a New York Jets game = $ 225

Savings up to now = $ 18

Difference = 225-18 = 207

Number of weeks = 9

Let x to represent the amount of money Gary must save each week for buying the ticket, as follows:

x = 207/9

x = 23

Gary must save $ 23 at the end of 9 weeks to have enough money to buy the ticket

Answer:

Assuming you're trying to find where the lines intersect (their solution), the point where they intersect is (1/2 , 1).

Step-by-step explanation:

When you are trying to find the point where two lines intersect, you have to find the x and y values of that point. To do that, just set the lines equal to each other.

First, since y must equal y:

y = y

-4x + 3 = 4x - 1

Now solve for x:

-8x + 3 = -4

-8x = -4

8x = 4

x = 1/2

We just found the x value of the shared point. Now we need to find the y value of that point. Again, since the two lines share this point, plugging in the x value will result in the same y value for both lines.

So just plug in x to any of the equations: (I think y=4x-1 is easier)

y(1/2) = 4(1/2) - 1     or      y = 4(1/2) - 1  (it doesn't matter how you write it)

y(1/2) = 2 - 1           or      y = 2 - 1

y(1/2) = 1

So the point is:

(1/2 , 1)

To check you can plug in the y value you find, 1 in this case, and solve for x. If you get the same x value as before, everything is correct.

So:

(1) = -4x + 3

-2 = -4x

1/2 = x    or    x = 1/2

Great! Everything is correct.

This may seem like a very long process, but it is very easy. Just find the x and y values that the lines share by setting the lines equal to each other.

Given data:

The given equation is c+(4-3c)-2=0

The given equation can be written as,

c+4-3c-2=0

-2c+2=0

-2c=-2

c=1

Thus, the value of c is 1, so option C) is correct.

Given:

Required:

To find the independent and dependent variable.

Explanation:

In the given equation,

The dependent variable = k(d)

The independent variable = d

Final Answer:

The dependent variable = k(d)

The independent variable = d

We know that a a childresn spend more hours napping when they are youngers therefore we have a negative correlation

We have the following:

The intersection with the x-axis is when the value of y is 0, that is, the computer already has a value of 0 and has no commercial value.

we found it like this

which means that in 10 years, the computer does not represent a commercial value

to calculate the number of years that have passed when the computer has a value of 2000, y = 2000, therefore we replace

This means that in a total of 5 years the value of the computer will be $ 2000

Answer: 24 mph

Step-by-step explanation:

If she can run 12 mph/ 12 miles per hour

She runs for 2 hours

12 · 2 = 24

The sequence 2,7,12,... given is an arithmetic progression. This is because it has a common difference.

Given:

first term, a = 2

common difference, d = second term - first term = 7 - 2 = 5

d = 5

n = 38

The sum of an arithmetic progression is given by;

Therefore, the sum of the first 39 terms of the series is 3,591

For 6 sandwiches and 3 dozen cookies, the total time taken by Brenda would be 33 minutes.

Given is Brenda who must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich, and 45 minutes to make a dozen cookies.

If she makes [x] sandwiches and [y] dozen cookies, then the total time she would take to make them can be written as -

t = 4x + 3y

For 6 sandwiches and 3 dozen cookies, we can write -

t(6, 3) = 4 x 6 + 3 x 3 = 24 + 9 = 33 minutes

t(6, 3) = 33 minutes

Therefore, for 6 sandwiches and 3 dozen cookies, the total time taken by Brenda would be 33 minutes.

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{Complete question is given below -

She must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich, x, and 45 minutes to make a dozen cookies, y.}

3 combinations:

3 quarters and 6 dimes

5 quarters and 1 dime

1 quarter and 11 dimes

1) Remember that a dime corresponds to $0.10 and a quarter to $0.25. And the value we want to find is $1.35

2) As we can see the last digit on $1.35 is 5 then we can infer that we're going to need an odd number of quarters ($0.25). Also, notice that we need whole numbers for the quantities of each coin. In other words, multiples of 0.10 and 0.25 whose sum yields to $1.35. So let's do it step by step:

So, we can write out the following list of combinations:

q (quarter) 3 q = 3 x 0.25 = $ 0.75

d (dimes) 6 d = 6 x 0.10 = $ 0.60

0.60 + 0.75 = 1.35

2.2) Another possible combination:

q (quarter) 5 q = 5 x 0.25 = $ 1.25

d (dimes) 1 d = 1 x 0.10 = $ 0.10

0.10+1.25= 1.35

2.3)

q (quarter) 1 q = 1 x 0.25 = $ 0.25

d (dimes) 11 d = 11x 0.10 = $ 1.10

0.25+1.10 = 1.35

3) Hence, considering that we need to combine dimes and quarters and their sum must be lesser than $1.35 We have three combinations with whole numbers of dimes and quarters:

3 quarters and 6 dimes

5 quarters and 1 dime

1 quarter and 11 dimes

To find the equation of the line we just need to find the beta constants. In order to do this we have (they provided us with) the following system of equations:

Let us subtract the second equation to the first one:

This implies that

Now, let us replace this value we just got into the second equation to find beta_0:

At last,

Then, the equation of the line is just

Answer:

f(-8)= -112

Step-by-step explanation:

-2(-8)^2 + 2(-8)

-2(-64) + 16

-128 + 16

= -112

hope this helped

have a good day :)

Answer: 8m

Explanation:

Given:

To find the height(h) of the tree, we can use ratio since they are similar triangles.

Triangle 1

Triangle 2

So,

Therefore, the height of the tree is 8m.

a The value of (2.3 × 10⁴) × (1.5 × 10^-2) is 3.45 × 10^2

b. The value of (3.6 × 10^-5) ÷ (1.8 × 10^2) is 2 × 10^-3. This illustrates the concept of standard form.

The standard form is simply used in Mathematics to illustrate the numbers that are either too large or too small.

It's important to note that the multiplication of exponents is an addition and the division of the power is subtraction.

Therefore, (2.3 × 10⁴) × (1.5 × 10^-2) will be:

= (2.3 × 1.5) × (10^(4-2)

= 3.45 × 10^2

Also, (3.6 × 10^-5) ÷ (1.8 × 10^2) will be:

= (3.6 ÷ 1.8) × 10^(-5 + 2)

= 2 × 10^-3.

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Answer:

Options A and C

Explanation:

We want to find out which arithmetic sequence(s) contain the term 34.

For an arithmetic sequence to contain the term, 34, the corresponding n-value must be an integer.

Option A

Set tn = 34

Solve for n:

The 8th term of this sequence is 34.

Option B

A sequence cannot have a decimal nth term, therefore, the sequence does not contain 34.

Option C

T1 = 12, d=5.5

The 5th term of this sequence is 34, therefore, it contains the term 34.

Option D

3,7,11,...

Using the nth term of an arithmetic sequence formula:

A sequence cannot have a decimal nth term, therefore, the sequence does not contain 34.

The sequences in Options A and C contain the term 34.

Answer:

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

Step-by-step explanation:

In the equation, [tex]y=mx+b[/tex], the "m" represents the slope, and the b represents the y-intercept.

We know the slope is 5, so we already know part of the equation: [tex]y=5x+b[/tex]

To solve for the "b" part or y-intercept, we can simply plug in a known point on the line, which was given to be (-7, -29)

This gives us the following equation:

[tex]-29 = 5(-7) + b\\\text{simplify}\\-29 = -35 + b\\\text{add 35 to both sides}\\6=b[/tex]

Answer: y = 5x + 6

Step-by-step explanation:

1. Do point-slope formula {(y - y1) = m(x - x1})

(y - 29) = 5(x - 7)

Distribute

(y - 29) = 5x - 35

Subtract 29 on both sides

Cancel out y - 29 - 29

y = 5x + 6

Answer:

a) degree 5; monomial

b) degree 7; polynomial

c) degree 3; polynomial

d) degree 2; polynomial

e) degree 3 polynomial

Explanation.

A polynomial is a mathematical expression containing coefficients and variables.

An example of a polynomial is 42x^5 + 23 x^3 - 2x.

A monomial is a polynomial that contains only one term. For example, x^4, 34x^5, 2x, etc.

Having that in mind, we go through the expressions and place them in one of either category.

a) 7^5

This contains only one term, meaning it is monomial; its highest exponent is 5, meaning it is of degree 5.

b) 5^7 + 7^2

This contains two terms, meaning it is a polynomial; its highest exponent is 7, meaning its degree is 7.

c) 7^3 + 11^2 − 13 + 112

This expression contains four terms - it is a polynomial; its highest exponent is 3, meaning its degree is 3.

d) + 2 + 3^2

This contains three terms, meaning it is a polynomial; its highest exponent is 2, meaning its degree is 2.

e) 11^3 − 7^3

This contains 2 terms, meaning it is a polynomial; its highest exponent is 3, meaning it is of degree 2.

ANSWER:

STEP-BY-STEP EXPLANATION:

Since we know a side and the hypotenuse, we can rule out tangent and cotangent, since these are related to the two legs.

Therefore, if we want to know that side we must apply sine or cosine, just like this:

Therefore, the way to calculate the value of the missing side is by means of the sine of the angle R

The probability that Jim, Bruce and Valerie are selected in that​ order is P = 1/680

Given,

Number of students in a class = 17

Jim, Bruce and Valerie are 3 of the 17.

Three of students from the class are randomly chosen to deliver their reports during the next class meet.

We have to find the probability that Jim, Bruce and Valerie are selected in that​ order;

Here,

The total number of possible selection;

S = ⁿCr

Where, n = 17 and r = 3

Then,

S = ¹⁷C₃

S = 17! / 14! x 3!

S = 680

Therefore,

The probability that Jim, Bruce and Valerie are selected in that​ order is P = 1/680

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No solutions

Explanation

Step 1

replace Eq(1) in Eq (2)

Step 2

subtract x in both sides

6=2 is false, it means there is not solution for both equations,

The domain is all the possible input values, and the range is all the possible output values.

So according to this function (Given in the question).

The domain is [-3, 5] and the range is [-5, 4]

That is all to this question.

(a) Whole number and integer

(b) Negative integer

(c) Negative integer

Positive, negative, and zero numbers all fall under the category of integers. The word "integer" is a Latin word that signifies "whole" or "intact." Therefore, fractions and decimals are not considered to be integers. A number line is a graphic representation of positive and negative integers. The use of integers on a number line facilitates mathematical procedures. The right-side number is always greater than the left-side number. Due to the fact that they are greater than 0, positive numbers are positioned to the right of zero. All natural numbers and 0 are included in a group of numbers known as whole numbers. They belong to the category of real numbers, which excludes fractions, decimals, and negative numbers. Numbers used for counting are also regarded as whole numbers.

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Last year, Susan had $20,000 to invest. She invested some of it in an account that paid 10% simple interest per year, and she invested the rest in an account that paid 7% simple interest per year. After one year, she received a total of $1790 in interest. How much did she invest in each account?

Let

x ------> amount invested in an account that paid 10% simple interest per year

20,000-x ------> amount invested in an account that paid 7% simple interest per year

so

The formula of simple interest is equal to

I=P(rt)

In this problem we have that

10%=0.10

7%=0.07

x*(0.1)+(20,000-x)*(0.07)=1,790

solve for x

0.10x+1,400-0.07x=1,790

0.03x=1,790-1,400

0.03x=390

x=$13,000

therefore

Given that one of the ships travels at 12 nautical miles per hour, then after 1.5 hours, it will travel 12*1.5 = 18 miles

The other ship will travel 22*1.5 = 33 miles

The angle of 145° is measured with respect to the positive x-axis. Then, respect the negative x-axis, its measure is 180° - 145° = 35°

We have to use trigonometric functions to find x1, y1, x2, and y2, as follows:

sin(55°) = y1/18

sin(55°) *18 = y1

14.7 = y1

cos(55°) = x1/18

cos(55°)*18 = x1

10.3 = x1

sin(35°) = y2/33

sin(35°)*33 = y2

18.9 = y2

cos(35°) = x2/33

cos(35°)*33 = x

-27 = x2 (the minus sign comes from the graph)

The distance between two points (x1, y1) and (x2, y2) is computed as follows:

Substituting with the values found,

Given 7 women and 10 men;

a) the top 3 are all men:

Therefore, the probability that the top 3 are all men is:

b) the top 3 are all women:

Therefore, the probability that the top 3 are all women is:

c) 2 men and 1 woman;

Therefore, the probability that the top 3 finishers are 2 men and 1 woman is:

d) 1 man and 2 women;

Therefore, the probability that the top 3 finishers are 1 man and 2 women is:

SOLUTIONS

Using factor theorem to solve the equation below:

20+50-8 times 3

70 -24

46 is answer

Answer:

10(5)-24 ----) 50-24 -----) 26

Step-by-step explanation:

answe is 26