Please please help me!!
solve the system of equations by the substitution method.
{ 21x + 7y = 41
{ -3x = y + 6

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution is __ ( type an ordered pair. Simplify your answer.)
B. There are infinitely many solutions.
C. There is no solution.

Answers

Answer 1

Answer:

C. There is no solution.

Step-by-step explanation:

Similarly to the previous question, you want to substitute one of these equations into the other:

21x + 7y = 41

-3x = y + 6

But first, you need to isolate for a variable. I'm going to isolate for y in the second equation to avoid fractions.

-3x = y + 6

y = -3x - 6

Now that I've done that, I can now plug it into the first equation to solve for x:

21x + 7(-3x - 6) = 41

21x + -21x - 42 = 41

0x = 41

0 ≠ 41

Since 0 ≠ 41, these lines are parallel, which means that there are no solutions.


Related Questions

48=16 p what Is p ? Please help

Answers

Answer:

p = 3

Step-by-step explanation:

48 = 16p

divide both sides by 16

3 = p


four hundred thirty-seven
ten-thousandths in decimal form

Answers

Answer:

0.0437

Step-by-step explanation:

I can't really explain this one

Answer:

.0437

Step-by-step explanation:

the 4 is in the hundreds spot, the 37 is in the thousands and ten thousandths

A magazine survey of a five-year period considered 100 featured actors. The
table to the right shows the "worst" ten actors, in terms of how much their
films returned per dollar that the actor earned.

Answers

The set of actors with at least a return of $7.50 are {H, J, K}

What are the set of actors?

The actors that would be included in this set include actors that earn an amount equal to $7.50 or an amount greater than $7.50.

A set can be described as a collection of objects whose elements are fixed and cannot be changed. Thus, elements in this set would include those who earn more than or equal to $7.50.

To write a set in a roster form, the elements in the set are written in a row within curly brackets or braces - { }. The elements in the set are then separated by commas.

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When using the quotient rule of exponents, you must _____
coefficients and _____
the exponents.

Answers

Answer:

When multiplying exponents of the same base, add the exponents. When dividing exponents of the same base, subtract the exponents. When raising a power to a power, multiply the powers.

Step-by-step explanation:

What is the base when the expression (-1.5)2 • (3.2)5 is written as a single power of 5?

Answers

we can rewrite:

(-1.5)²*(3.2)⁵ = 3.76⁵

The new base of the expression is 3.76

What is the new base of the expression?

Here we have the expression:

(-1.5)²*(3.2)⁵

And we want to write this as a single expression with a power of 5.

First we can rewrite:

(-1.5)² = x⁵

x = (-1.5)^(2/5)

Then the new base of the expression will be:

x*3.2

(-1.5)^(2/5)*3.2 = 3.76

Then we can rewrite:

(-1.5)²*(3.2)⁵ = 3.76⁵

The new base of the expression is 3.76

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25% discount for AED 4000

Answers

Answer:

The 25% discount on AED 4000 will be: 1000 AED

Step-by-step explanation:

Given

The amount = 4000Discount = 25%

In order to determine a 25% discount on the amount AED 4000, all we need means is to multiply 25/100 or (0.25) by 4000.

i.e

Discount amount = 25% of 4000

                             = 25/100 × 4000

                             = 0.25 × 4000

                             = 1000 AED

Thus, the 25% discount on AED 4000 will be: 1000 AED

The indefinite integral of ((6e^4x)(e^arctan(3e^4x)))/(1+9e^8x)

Answers

Answer:

[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{e^\big{arctan(3e^{4x})}}{2} + C[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Integration

Integrals[Indefinite Integrals] Integration Constant C

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

U-Substitution

U-Solve

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx[/tex]

Step 2: Integrate Pt. 1

[Integrand] Rewrite:                                                                                       [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \int {\frac{6e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]:                 [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = 6\int {\frac{e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex]

Step 3: integrate Pt. 2

Set variables for u-substitution.

Set u:                                                                                                             [tex]\displaystyle u = 4x[/tex][u] Differentiate [Basic Power Rule, Multiplied Constant]:                         [tex]\displaystyle du = 4 \ dx[/tex]

Step 4: Integrate Pt. 3

[Integral] Rewrite [Integration Property - Multiplied Constant]:                 [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{4e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex][Integral] U-Substitution:                                                                               [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(3e^u) + u}}{1 + 9e^\big{2u}}} \, du[/tex]

Step 5: Integrate Pt. 4

Set variables for u-substitution #2.

Set v:                                                                                                               [tex]\displaystyle v = 9e^{2u} + 1[/tex] [v] Differentiate [Exponential Differentiation, Chain Rule]:                       [tex]\displaystyle dv = 18e^{2u} \ du[/tex][v] U-Solve:                                                                                                    [tex]\displaystyle u = ln \Big( \frac{\sqrt{v - 1}}{3} \Big)[/tex][dv] U-Solve:                                                                                                   [tex]\displaystyle du = \frac{e^{-2u}}{18} \ dv[/tex][U-Solve] Rewrite u:                                                                                       [tex]\displaystyle e^u = \frac{\sqrt{v - 1}}{3}[/tex]

Step 6: Integrate Pt. 5

[Integral] U-Solve:                                                                                              [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(3(\frac{\sqrt{v - 1}}{3})) + ln(\frac{\sqrt{v - 1}}{3})}}{1 + 9(\frac{\sqrt{v - 1}}{3})^2} \frac{1}{18e^{2u}}\, dv[/tex][Integral] Simplify:                                                                                              [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{\sqrt{v - 1}e^\big{arctan(\sqrt{v - 1})}}{3[1 + v - 1]} \frac{1}{18(\frac{\sqrt{v - 1}}{3})^2}\, dv[/tex][Integral] Simplify:                                                                                         [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{\sqrt{v - 1}e^\big{arctan(\sqrt{v - 1})}}{3v} \frac{1}{2(v - 1)}\, dv[/tex][Integral] Simplify:                                                                                         [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(\sqrt{v - 1})}}{6v\sqrt{v - 1}} \, dv[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]:                 [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{1}{4}\int {\frac{e^\big{arctan(\sqrt{v - 1})}}{v\sqrt{v - 1}} \, dv[/tex]

Step 7: Integrate Pt. 6

Set variables for u-substitution #3.

Set z:                                                                                                               [tex]\displaystyle z = arctan(\sqrt{v - 1})[/tex][z] Differentiate [Arctrig Differentiation, Chain Rule]:                                 [tex]\displaystyle dz = \frac{1}{2v\sqrt{v - 1}} \ dv[/tex]

See attachment for rest of work (would not fit entire answer in answering box).


Find the percent of decrease. Round the percent to the neares
amount of decrease: 20 pounds
original amount: 80 pounds

Answers

Answer:

75% decrease

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/algebra/percentage-decrease-calculator.php?v_1=80&v_2=20&action=solve


Kamama is making a quilt. She started with a hexagon that she loves. If Kamama wants the rest of her hexagons to be congruent, which transformations can
she use?
Please choose all of the transformations that she can use to create a congruent image.
Fun fact: Kamama is a Cherokee name meaning Butterfly.
Reflection
Translation
Dilation
Rotation

Answers

Based on the fact that Kamama wants her hexagons to be congruent, the transformations that she can use are:

ReflectionTranslationRotationWhat transformations give congruent shapes?

In order to have congruent shapes, there are three transformations that can be used.

Firstly, it is important to note that congruent shapes have the same size and the same shape. They are identical except for their orientation which may be different.

A reflection would create a congruent shape that would have the same size and angles but the orientation should be different. This is the same as a rotation. A translation will often result in congruent shapes that also have the same orientation. This means that Kanama can use any of these transformations.

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Please show me the work!

Answers

Answer:

9/2π cm/s

Step-by-step explanation:

Volume of the spherical balloon V= 4/3πr³

Rate of change of volume dV/dt = dV/dr * dr/dt

dV/dr = 3(4/3πr²)

dV/dr = 4πr²

dV/dr = 4π(2)²

dV/dr = 16π

If V = 72cm²/s

72 = 16π*dr/dt

dr/dt = 72/16π

dr/dt = 9/2π cm/s

Hence the radius is changing at  9/2π cm/s

If a bass drum has a diameter of 3 feet, which of these represents C, the circumference of the drum?

Answers

Answer:

9.42

Step-by-step explanation:

C= 2 times pie times radius

2. Complete the truth table for the statement S ^ P.
S P S ^ P T T T F F T F F

Answers

Answer:

Step-by-step explanation:

Pleaseee help me on this question

Answers

Answer:

B

Step-by-step explanation:

For every 1 liter of water, 0.07 kilograms of salt must be added. They are asking for 0.5 liters of water, which is half of 1 liter. So therefore, they need half of 0.07 kilograms of salt, which is 0.035 kilograms

Answer:

0.035 kg.

Step-by-step explanation:

0.5 liter is 1/2 liter

0.07kilograms / 2 = 0.035kg

after eating La Huerta your subtotal was 25.72$ you want to leave a 15% tip. 15% as a decimal is

Answers

15% as a decimal is 0.15

.The values of x and y vary directly, and mul
when x = 48, y = 36. Find the value of x when
y = 18

Answers

Step-by-step explanation:

In the general scenario we find thaf x exceeds y by 12. If they vary directly it means even though the values x and y change they will always have the constant different 12

x=y+12

:. x=18+12

x=30

I HOPE THIS HELPS

What is the value of x in the equation 2x +3y = 36, when y=6?
O9
O 27
O 36

Answers

Answer:

x=9

Step-by-step explanation:

Substitution and solving

[tex]2x+3y=36\\2x+3(6)=36\\2x+18=36\\2x+18-18=36-18\\36/2=2x/2\\x=9[/tex]

your answer is 9.
explanation: when plugging in 6 to 3y you get 18. 3(6)=18. from there you have 2x+18=36. subtract 18 on both sides. 36-18. you get 18. then divide 18 by 2 and you get 9.

Need help pls help thanks

Answers

Answer:

your right

Step-by-step explanation:

Find the slope of the line from the table.
X
1
4
7
10
у
7
5
3
1
1

Answers

the slope would be ten ❤️

Please help!!
How do you do this?

Write a system of inequalities to describe the
shaded region.

Answers

Answer:

In Explanation.

Step-by-step explanation:

In situations like this, you want to first find the equations of the individual lines.

Let's start with the left one.

It has a negative slope of 2 while it has a y-intercept of 1

y=-2x+1

is the equation.

The other line has a slope of 3/2.

The y-intercept is not visible, so we need to use point slope form.

I chose (2,-3)

y+3=3/2(x-2)

Simplify.

y=3x/2-3-3

y=3x/2-6

so we have

y=-2x+1

and

y=[tex]\frac{3x}{2}[/tex]-6

Since both lines are solid, the signs are ≥ or ≤

The shadings intersect above both lines so the individual shadings also have to be above the line.

That means the equation is less than the "y".

y≥-2x+1

y≥[tex]\frac{3x}{2}[/tex]-6

Write the equation for line L in point-slope form and slope-intercept form
L is perpendicular to y=2x

Answers

The equation of the line in slope intercept form is y = - 1 / 2 x - 5

The equation of the line in point slope form is (y + 4) = - 1 / 2 (x + 2)

How to represent equation in slope intercept form and point slope form?

The equation in a slope intercept form is represented as follows:

y = mx + b

where

m = slopeb = y-intercept

Therefore, let's find the equation of the line L in slope intercept form.

The line L is perpendicular to y = 2x

Hence,

m₁m₂ = -1

2m₂ = -1

m₂ = -1 / 2

Therefore,

y = - 1 / 2 x + b

let's find b using (-2, -4)

-4 = - 1 / 2 (-2) + b

b = -4 - 1

b = -5

Hence, the equation of the line in slope intercept form is as follows:

y = - 1 / 2 x - 5

The equation of the line in point slope form is represented as follows:

(y - y₁) = m(x - x₁)

where

m = slopex₁ and y₁ are the coordinates

Therefore, using (-2, -4),

(y + 4) = - 1 / 2 (x + 2)

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Help help help ! :)

Which equation’s line is steeper and explain how you know

Answers

The equation's line that is steeper is y = 3x + 7

Slope of a line

From the question, we are to determine which of the given equations' line is steeper

The given equations are

y = 3x + 7

and

y = (1/2)x + 9

First, we will compare the equations to the form of an equation of a straight line

The equation of a straight line is of the form

y = mx + c

Where m is the slope

and c is the y intercept

Thus,

The slope of the equation, y = 3x + 7, is 3

and

The slope of the equation, y = (1/2)x + 9, is 1/2

NOTE: The higher the slope of a line, the steeper the line

Hence, the equation's line that is steeper is y = 3x + 7

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what is the result if you decrease the sum of 78.932 and 721.832 by 389.823 pls

Answers

Answer:

410.941

Step-by-step explanation:

Some one please help

I have attached the question

Answers

Answer:

a number question's answer is a power 2. and is c power 1

Answer

A) a2
B) c

Explaining

can anyone help me ?

Answers

Answer: i think u got it write its that one

Step-by-step explanation:

The cost of a gallon of orange juice is $3,50, What is the maximum number of containers you can buy for $15

Answers

23 is the maximum since 350 divided by 23

Beinggreat78, you are ~Summoned~

Answers

Answer:

B.

Step-by-step explanation:

0.32 > 0.304 > 0.03

Work and answers are provided in the screenshot attached! :)

The area of the figure is
square units.

Answers

Answer:

80 square units

Step-by-step explanation:

The figure given can be decomposed to have two trapezoids of equal dimensions and a rectangle.

Area of the figure = (2*area of a trapezoid) + (area of a rectangle)

Area of the 2 trapezoids:

Area of the two trapezoid = 2(½(a + b)*h)

Where,

a = 2 + 6 + 2 = 10 units

b = 6 units

h = 2 units

Plug in the values:

Area of the two trapezoid = 2(½(10 + 6)*2)

= 2(½(16)*2)

Area = 32 units²

Area of the rectangle:

Area = length × width

Length = 8 units

Width = 6 units

Area = 8 × 6 = 48 units²

✔️Area of the figure = 32 + 48 = 80 units²

Find the area of a rectangle with a length of 17 centimeters and a width of 6 centimeters.

Answers

Answer:

102 cm ²

Step-by-step explanation:

At age 30 you deposit $150 at the end of each month into an IRA that pays 4% interest compounded monthly. In the previous question, we found that the value of the annuity at age 65 would be $137,059.64. How much interest did you earn?

Answers

According to the given statement the interest that we earn is

=  $74,059 . 64

What Is an Annuity's Present Value?

The present value of an annuity seems to be the current worth of future annuity payments based on a predetermined rate of return, as well as discount rate. The higher the discount rate, the smaller the annuity's present value.

According to the given data:

monthly payment is 150

at the age = 30

interest rate = 4

till age of = 65

At age 65, the annuity would be worth $137,059.64.

We only need to determine the amount of interest. = ?

 for monthly payments, we need to take n, which equals 12 points now total interest. determined by future value. Substitute minus p m t multiplied by n multiplied by t for all values now.

the amount of interest   =  deposited amount x year x no of year invested

                                       = 150 x 12x(65-30)

           present value     = 63000

At age 65, the annuity would be worth $137,059.64.

We know that the interest is  = balance - capital

                                                 = 137,059.64 - 63000

                                                 = $74,059 . 64

According to the given statement the interest that we earn is

=  $74,059 . 64

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How many 3-digit number can you write with only 4 and 7?

Answers

Answer:

8 numbers

Step-by-step explanation:

447

477

474

774

744

747

777

444

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