Solve the system of equations by the addition method.
3x + 4y = 7
6x - 4y= 2

Taking into account the definition of a system of linear equations, the textbook store sold 141 math textbooks and 282 psychology textbooks.

A system of linear equations is a set of linear equations (that is, a system of equations in which each equation is of the first degree) in which more than one unknown appears.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

p + m= 423

p=2m

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first one you get:

2m + m= 423

3m=423

m= 141

Substituting this value in the second equation you get:

p= 2m

p= 2×141

p= 282

Finally, 141 math textbooks and 282 psychology textbooks were sold by the textbook store.

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The confidence interval estimate for the mean of the population at 95% is [$282.70, $317.30].

Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.

CI = μ ± z x (SD / √n)

where CI = confidence interval

μ = sample mean

z = found by using a z-score table

SD = sample standard deviation

n = sample size

At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.

(100 - 95) / 2 = 2.5

100 - 2.5 = 97.5

Find 0.975 in the z-table to get the value of z.

At p = 0.95, z = 1.96

Plug in the values and solve for the confidence interval.

CI = μ ± z x (SD / √n)

CI = 300 ± 1.96 x (45 / √26)

CI = 300 ± 17.30

CI = [$282.70, $317.30]

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Answer:

Step-by-step explanation:

We know that perpendicular lines have opposite-reciprocal slopes.

Given line:

Its slope is 2 and the perpendicular line has a slope of - 1/2.

Let's find the line with the slope of - 1/2:

Answer:

c

Step-by-step explanation:

Answer:

135 degrees

Step-by-step explanation:

a triangle rule is sum of all three angles equal 180

We know one angle of the triangle angle is 45 degrees because of the corresponding angle below it

So we just subtract 45 from 180

180-45=135

hopes this helps please mark brainliest

For the given equation 4x + 3y =21 the slope intercept form is given by y = (-4/3)x + 7.

Graph is attached.

As given in the question,

Given equation is equal to :

4x + 3y = 21

To get the slope intercept form of the given equation we have,

Subtract 4x from both the sides of the given equation we have,

4x + 3y - 4x = 21 - 4x

⇒ 3y = 21 - 4x

Now divide by 3 on both the sides of the equation we get,

3y / 3 = (-4/3)x + (21/3)

⇒ y = (-4/3) x + 7

Graph of the given equation in slope intercept form y = (-4/3) x + 7 is attached.

When x = 0 ⇒ y = 7

y= 0 ⇒ x = 21 /4

Therefore, for the given equation 4x + 3y =21 the slope intercept form is given by  y = (-4/3)x + 7.

Graph is attached.

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The set which is equivalent and equal to the given set; {1, 2, 3, ...} is; Z+.

It follows from the task content that the set which is equivalent to the given set; {1, 2, 3, ...} is to be determined.

Since the numbers in the set are all integers and which happen to be positive integers.

Hence, the best representation of a set which is equivalent to the given set as given in the task content is; Z+.

The set of positive integers is represented as Z+. It implies all the integers greater than 0.

Hence, the set which is equivalent to the given set; {1, 2, 3, ...} is; Z+.

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The difference between exponents [tex](a^n)^m = a^{mn}[/tex] and [tex]a^nb^n = (ab)^n[/tex] has been described below

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2 \times 2 \times 2 \times 2[/tex]

Here, 2 is multiplied by itself 4 times.

If [tex]a^m = a \times a \times a \times....... \times a[/tex] (m times), a is the base and m is the index.

The laws of index are-

[tex]a^m \times a^n = a^{m + n}\\a^m \div a^n = a^{m-n}\\a^0 = 1\\a^{-n} = \frac{1}{a^n}\\\\a^m b^m = (ab)^m\\(\frac{a}{b})^n = \frac{a^n}{b^n}[/tex]

In case of  [tex](a^n)^m = a^{mn}[/tex], the base is single but in case of [tex]a^nb^n = (ab)^n[/tex], the base is a product of two numbers

If the base can be expressed as a product of different numbers,

[tex]a^nb^n = (ab)^n[/tex] is used

If the base cannot be expressed as a product, then [tex](a^n)^m = a^{mn}[/tex] is used

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In completing the square method, considering the equation X^2 - 5x = 6 the student should add 25 / 4 to both sides of the equation

The quadratic equation is an equation of the form

ax^2 + bx + c

The completing the square method is on of the methods of solving equations of the form above

The factor to be added on the both sides of the equation while using the completing the square method is

(b / 2a)^2

compared to the equation in the problem X^2 - 5x = 6 it is

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There are 102 grams of copper in 12 cm³ of copper.

A unit rate means a rate for one of something.

Given that 1 cm³ of copper have mass of 8.5 grams

Therefore, 12 cm³ = 12*8.5 = 102 grams

Hence, There are 102 grams of copper in 12 cm³ of copper.

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The length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.

According to the question,

We have the following information:

The first side of a triangle is 2 feet longer than the second. The third side is 5 feet shorter than twice the second. The perimeter is 49 feet.

Let's take the second side to be x feet.

So, we have the following sides:

First side = (x+2) feet

Third side = (2x-5) feet

Perimeter = 49

x+x+2+2x-5 = 49

4x-3 = 49

Adding 3 on both the sides:

4x = 49+3

4x = 52

Dividing by 4 on both the sides:

x = 52/4

x = 13 feet

First side = 2+13

First side = 15 feet

Third side = 2*13-5

Third side = 26-5

Third side = 21 feet

Hence, the length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.

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Answer:

See below

Step-by-step explanation:

.105    is    105   THOUSANDTHS    or   105/1000

  Divide top and bottom by '5'

    to get   21/100

The cost of the appointment without insurance is $200. Isaiah has an insurance plan throw his employer with a $50 monthly premium and a $20 copay. then Isaiah will have to pay his doctor $ 20

Insurance co-pay is a pre-determined amount that a person with medical insurance pay every time they use medical services. The co-pay is a dollar amount and usually less than $25. Different insurance companies have varying co-pay amounts for different services, such as doctor visits and prescriptions.

Isaiah will pay $20 for a visit to the doctor, as stated in the policy document. The $50 premium is payable to the insurance company every month to maintain the insurance coverage.  

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Answer:

Step-by-step explanation:

20=v+9-16

So first, we combine like terms

20=v-7

Then we want to add 7 on each side

20=v-7

+7      +7

Then we are left with

27=v

Step-by-step explanation:

Subtract the numbers

20=v+9-16 =20=v-7

Add 7 to both sides

20=v-7

20+7=v-7+7

Then simplify P.S if you dont know how to comment on the answer

ANSWER v=27

Answer:

For the first equation, it is "True for one value of x."

For the second equation, it is "True for no value of x."

For the third equation, it is "True for all values of x."

Step-by-step explanation:

Just solve the equation and check the numbers:

If both numbers are the same, it is "true for all values of x"

If there is a variable and a number, it is "true for one value of x"

If there are two numbers and they are different, it is "true for no values of x"

Hope this helps!

Please give brainliest

We need to check whether the given equations are true for all values of [tex]x[/tex] , one value of [tex]x[/tex] , or no values of [tex]x[/tex] .

The equations are ,

solve this equation for x ,

[tex]\longrightarrow 3x +9=-4.5x+20\\[/tex]

[tex]\longrightarrow 3x+4.5x =20-9\\[/tex]

[tex]\longrightarrow 7.5x =11\\[/tex]

[tex]\longrightarrow \underline{\underline{x =\dfrac{11}{7.5}}}[/tex]

Hence the equation is true for one value of x .

solve out for x ,

[tex]\longrightarrow 9x +27=9x-12\\ [/tex]

[tex]\longrightarrow 9x -9x =-27-12\\ [/tex]

[tex]\longrightarrow 0 = -39[/tex]

This can never to true , so the equation is true for no values of x .

solve out for x ,

[tex]\longrightarrow 8x+12=12+8x \\[/tex]

[tex]\longrightarrow 12-12=8x-8x\\[/tex]

[tex]\longrightarrow 0=0 [/tex]

Hence this equation is true for all values of x .

And we are done!

Answer: Row: 9 Column: 9

Step-by-step explanation:

Carol wants a square garden that means the amount of plants must be square, which it is so the square root of 81 is 9 so the square is 9 by 9

The subtraction between the functions f(x) = 4 · x - 8 and g(x) = - 3 · x + 1 is equal to (f - g) (x) = 7 · x - 9.

Herein we find f(x) and g(x) defined as linear functions and we are asked to find the subtraction between two functions, which is defined below:

(f - g)(x) = f(x) - g(x)

If we know that f(x) = 4 · x - 8 and g(x) = - 3 · x + 1, then the result of the subtraction of the two functions is:

(f - g) (x) = f(x) - g(x)

(f - g) (x) = (4 · x - 8) - (- 3 · x + 1)

(f - g) (x) = 7 · x - 9

The subtraction between the two functions is (f - g) (x) = 7 · x - 9.

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He rented the pressure washer for 4 hours, given that the total bill was $86.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let x = total number of hours he rented the pressure washer

The total bill, which was $86, includes the flat fee of $50 plus $9 per hour of use.

Hence, the equation will be 50 + 9x = 86.

Solve for x.

50 + 9x = 86

9x = 86 - 50

9x = 36

x = 4

total number of hours he rented the pressure washer = 4

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Phil lives in a state where his tax rate does not change when his income changes. This is an example of a proportional or flat tax.

Tax is defined as the official way individuals contribute to their state revenue through the compulsory deduction of some amount of money from their monthly income.

There are two types of tax which include the following:

Proportional or flat tax: This is defined as the type of tax that is being paid by individuals from different class in the society whereby all are expected to pay tax with the same rate irrespective of the income.

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The solutions to the equation [tex]2x^{2} +3x=-8\\[/tex] are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex] respectively.

What is a quadratic equation?

A second-degree algebraic equation is a quadratic equation in x.

[tex]ax^{2} +bx+c=0[/tex] is the quadratic equation in standard form, where a and b are the coefficients, x is the variable, and c is the constant term.

To find the root value of x, [tex]x= \frac{-b}{2a}[/tex] ± [tex]\frac{\sqrt{b^{2} -4ac} }{2a}[/tex]

Given, [tex]2x^{2} +3x=-8\\[/tex]

or, [tex]2x^{2} +3x+8=0[/tex]

Comparing the equation [tex]2x^{2} +3x+8=0[/tex] with the equation  [tex]ax^{2} +bx+c=0[/tex] , we get

[tex]a=2, b=3, c=8[/tex]

Then, [tex]x= \frac{-3}{2*2}[/tex] ± [tex]\frac{\sqrt{3^{2} -4*2*8} }{2*2}[/tex]

or,  [tex]x= \frac{-3}{4}[/tex] ± [tex]\frac{i\sqrt{55} }{4}[/tex]

Taking '+' sign, we get [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex]  and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex]

Therefore, the solutions of the given equation are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex].

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Answer:

B is correct: also if u add C and D together there both different and if u added B and A correctly u would have got B as your answer.

Step-by-step explanation:

Answer:

4.73

Step-by-step explanation:

10% is 10

so, you have to multiple 3×.10=.30

3-.30=2.70

2.70×.75 because 7.5% is .75

that is 2.0250 and then you have to add 2.0250 with 2.70 that is 4.7250 and if you round it. It is 4.73

Hope that works

The leading coefficients and parabolic equations, considering the vertices, are given as follows:

1. a = 7/4, y = 7/4(x - 4)² - 1.

2. a = -2, y = -2(x + 1)² + 2.

The equation of a parabola with vertex given by (h,k) is presented as follows:

y = a(x - h)² + k.

In which a is the leading coeffiicent.

For item 1, the coordinates of the vertex is given as follows:

(4,-1).

Hence:

h = 4, k = -1, and the equation is:

y = a(x - 4)² - 1.

When x = 6, y = 6, hence the leading coefficient is calculated as follows:

6 = a(6 - 4)² - 1

4a = 7

a = 7/4.

Thus the equation is:

y = 7/4(x - 4)² - 1.

For item 2, the vertex is:

(-1,2).

Hence:

y = a(x + 1)² + 2.

When x = 0, y = 0, hence the leading coefficient is calculated as follows:

0 = a(0 + 1)² + 2

a = -2.

Hence the equation is:

y = -2(x + 1)² + 2.

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The solution to the points are:

This is the point where the curve or curves of the graph changes direction.

In this case, the turning point in the vertex

The graph has its vertex at (1, -3.2)

This means that

Turning point = (1, -3.2)

This is the point where the curve or curves of the graph touches the x-axis i.e. f(x) = 0

In this case, the points are: (-1, 0) and (3, 0)

This means that

The roots are (-1, 0) and (3, 0)

This is the point where the curve or curves of the graph passes through x = 2.5

In this case, the points are: (2.5, -1.4)

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The tank with the smallest surface area has dimensions of 6ft.

s = 12ft and h = 6ft.

A(s) = s² + 4 × (V ÷ s)

The rectangular tank has a capacity of 864 feet.

Let the square base's long sides be.

Let h represent the tank's height.

Let A represent the tank's whole area.

A = (Base Area) + (4 × Lateral Area)

Lateral Area = s × h

Lateral Area = s × (V ÷ s²)

Lateral Area = (V ÷ s)

Base Area = s²

Compared to the objective function,

A(s) = s² + 4 × (V ÷ s)

A(s) = s² + 4 × (864 ÷ s)

The area function's derivative,

A'(s) = 2s - (3456 ÷ s²)

The smallest surface area is now.

A'(s) = 0

2s - (3456 ÷ s²) = 0

2 × [tex]s^{3}[/tex] = 3456

[tex]s^{3}[/tex] = 3456

s = [tex]\sqrt[3]{3456}[/tex]

s = 12ft

The volume is,

V = s² × h

864 = 12² × h

h = 6ft

As a result, the tank's height is 6 feet, and the square base's long sides measure 12 feet.

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The question is -

A rectangular tank with a square​ base, an open​ top, and a volume of 864 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function.

The measure of angle 11x+1 is 100°.

According to the question,

We have the following information:

We have a figure where two parallel lines are divided by a line. We know that the vertically opposite angles are equal. And when two parallel lines are cut by another line then the alternate interior opposite angles are equal.

Now, we have 10x+10 as the alternate opposite interior angle to 11x+1.

So, we have the following expression:

10x+10 = 11x+1

11x-10x = 10-1

x = 9

Putting the value of x in 11x+1:

11*9+1

99+1

100°

Hence, the measure of angle 11x+1 is 100°.

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The required addition of the given fraction is given as 7/6.

Given that, a mixed fraction is given 1 1 /6 we have to determine the simplified fraction.

Fraction is defined as the number of compositions that constitutes the Whole.

Here,
Given fraction = 1 1 /6
This fraction is written as 1 + 1/6
Simplifying the fraction by multiplying the one with 6 and adding the product to the 1 in the numerator,
= [1×6 + 1]/6
= 7/6

Thus, the required addition of the given fraction is given as 7/6.

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Answer:

.444....

Step-by-step explanation:

4 out of 9 is   4/9      or   4 ÷ 9 = .444...

Answer

12

Step-by-step explanation:

click on square root

click on 144

then your answer will pop out below your equation

The slope Using the formula will be h = -100t + 4000

This is a linear function because for every 5 seconds that pass, the height of the plane drops 500 feet, or -500 to be exact. So that's the slope of the line.

If we look at the table we can determine where the graph goes through the h axis. The h axis is the y axis, and the t axis is the x axis. So where the graph goes through the h axis is also the y-intercept.

If your teacher is any good at all, he/she would make sure that you understand beyond a shadow of a doubt that the y-intercept exists where x = 0. Looking at the table, where x (t) is 0, y (h) is 4000 feet.

Writing the linear equation then is super easy. In the form y = mx + b, we already know both the slope (-100) and the y-intercept (4000), so we fill in accordingly:

h = -100t + 4000 which appears to be choice a.

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The loan amount at the end of 2 years is Rs. 12,127 .

In the given question we have, amount Rs. 11500 is borrowed by investor at the interest rate of 6% per annum.

compund interest is defined as the addition of interest to the principal of loan.

principal (P) = 11500

If interest is compunded quarterly then time(t) = 3 years = 12 , rate ( r%) = 6/4% = 2/3 %

Using the formula of Amount ,

Amount = P( 1 + r / 100) ᵗ

= 11500( 1 + 2/ 300)⁸

= 12127.83 ~ 12128

compound interest = Amount - principal =

12128- 11500 = Rs. 628

So, An investor has to pay total Rs. 12128 at the end of 2- year.

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