What is the solution to this system of equations?
3b + 4c = 3
8b+ 5c = 27
2b + 6c = 1

What Is The Solution To This System Of Equations?3b + 4c = 38b+ 5c = 272b + 6c = 1

Answers

Answer 1

Here ya are hope this helps! :]]

What Is The Solution To This System Of Equations?3b + 4c = 38b+ 5c = 272b + 6c = 1

Related Questions

The length of a rectangle is 26 meters and the width is 1 meters. Find the area. Give your answer without units.

Answers

The area of the rectangle is 26 square meters.

Area of a rectangle

From the question, we are to determine the area of the described rectangle.

The area of a rectangle can be determined by the formula

A = l × w

Where A is the area of the rectangle

l is the length of the rectangle

and w is the width of the rectangle

From the given information,

l = 26 meters

w = 1 meter

Thus,

Area = 26 × 1

Area = 26 square meters

Hence, 26 square meters is the area of the rectangle.

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a ball is thrown up vertically. after t seconds, it's height (in feet) is given by the function h (t)=96t-16t^2 . after how long will it reach its maximum height

Answers

The time taken to reaches its maximum height is 3s.

In the question,

It is given that,

Height, h(t) = [tex]96t - 16t^{2}[/tex]

The maximum value of the function is obtained if the first derivative of the function h (t) = 0.

[tex]\frac{dh(t)}{dt} = 96 - 32t = 0[/tex]

⇒ [tex]t = 3[/tex]

So, time taken to reach its max height is 3 seconds.

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Graph the solution to the equations below.
=1/4+2 and =−2−7

Answers

By graphing, the solution of the system of equations is: (-4, 1).

How to Solve a System of Equations by Graphing?

The solution to the system of equations can be solved by graphing both lines of each equation on a coordinate plane, then find the coordinates of the point where both lines intersect each other.

Given the following equations:

y = 1/4x + 2

y = -2x - 7

The graph for y = 1/4x + 2 will intercept the y-axis at 2 and also has a slope of 2. The line for this equation is the red line.

The graph of y = -2x - 7 will also have a slope of -2. Its y-intercept would be -7. The line of the equation is the blue line.

The graph below shows the lines of both equations which intersect at (-4, 1), The solution is, (-4, 1).

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Solve using substitution.

x = –6
x − y = –5

Answers

Put -6 for x

-6 - y = -5

Move -6 to the right

-y = 6 - 5

-y = 1

Divide y by negative and 1 by negative

Answer: y = -1

In a geometric sequence, the difference between each pair of consecutive terms must be the same.

Answers

The given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.

What is a Sequence?

Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -

3, 6, 9, 12, 15

x, x + 2, x + 4, x + 6

Given is the following statement -

"In a geometric sequence, the difference between each pair of consecutive terms must be the same"

The given statement is false as the statement mentioned above is the definition of a arithmetic sequence. In geometric sequence, the ratio of each pair of consecutive terms must be the same. Mathematically -

a[n + 1]/a[n] = r {constant}

Therefore, the given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.

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Convert the height of a person who is 5.2 feet tall to centimeters. Include the inches-centimeter conversion
factor. Use the table given to create conversion factors. Show all conversion factors needed.
Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional
analysis that you learned.

Answers

The height of the 5.2 feet person in centimeters is 158.496 cm.

Explain unit conversion.

A conversion factor must be added, subtracted, multiplied, or divided throughout the multi-step process of unit conversion. Additionally, selecting the appropriate number of significant digits and rounding may be necessary.

Different conversion units are used to quantify various measurements. By definition, unit conversion is the process of converting two measures of the same quantity between distinct units by multiplying or dividing them.

In mathematics, conversion is the process of changing a value's form, such as from millimeters to inches or liters to gallons. Units are used for measurements of length, weight, capacity, temperature, and speed.

Given,

Height of a person = 5.2 feet.

The conversion between inches and centimeters must also be included.

First, convert feet to inches.

1 foot = 12 inches

Converting the given height to inches,

Height = 5.2 × 12

= 62.4 inches

Now, we will convert the height into centimeters,

To convert, we will multiply by 2.54

Height = 62.4 × 2.54

= 158.496 cm

Therefore, the height of the person in centimeters is 158.496 cm

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write an equation in slope-intercept form the table. help fast please
x: -4, 0, 4, 8, 12
y: 5, 6, 7, 8, 9

Answers

The linear equation in the table is written as:

y = (1/4)*x + 6

How to write the linear equation?

The linear equation in slope-intercept form is written as:

y = m*x+ b

Where m is the slope and b is the y-intercept.

We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

m = (y₂ -  y₁)/(x₂ - x₁)

Here we can use the first two points on the table:

(-4, 5) and (0, 6), so the slope is:

m = (6 - 5)/(0 + 4) = 1/4

And because of the point (0, 6) we know that the y-intercept is 6, then the line is:

y = (1/4)*x + 6

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4. Daryll rides a bike 8 miles in 40 minutes. Isabella rides a bike 5 miles in 30
minutes. If they continue to ride at those speeds, who will bike the farthest
in 2 hours? How much father? Show your work.

5 A student sells 5 ears of corn for $2.00 how much will 9 ears cost show your work

6 A market sells 4 oranges for 2.45 how much will 8 oranges cost ? 12 oranges show your work

Answers

Answers
4. Daryl = 24 miles, Isabella = 20 miles
so Daryl bikes the farthest by 4 more miles in 2 hours (120 minutes)

5. $3.60 for 9 ears

6. $4.90 for 8 oranges, $7.35 for 12 oranges
_____________

Step by step

4.
Solve for Daryl
8 miles /40 min = x miles / 120 min.
Find rate 8/40 = .2 miles per minute
.2 x 120 minutes = 24 miles in 120 minutes

Solve for Isabella
5 miles / 30 minutes = x miles / 120 minutes
Find rate 5/30 = 1/6 rate x 120 = 20 miles in 120 minutes

5.
5 ears corn for $2.00
Find rate $2.00/5 = .40 per ear

Multiply .40 x 9 ears = $3.60 for 9 ears

6.

4 oranges for 2.45
Find rate $2.45 / 4 = .6125 per orange

.6125 x 8 oranges = $4.90
.6125 x 12 oranges = $7.35

The curved part of this figures is a semicircle.

What is the best approximation for the area of this figure?

Responses

28+16.25π units²
18 plus 16.25 pi, units²

14+16.25π units²
14 plus 16.25 pi, units²

14+8.125π units²
14 plus 8.125 pi, units²

28+8.125π units²
28 plus 8.125 pi, units²
Coordinate plane with axes labeled x and y. A closed figure is formed by two segments and a semicircle. A segment extends from negative 4 comma negative 2 to negative 4 comma 2. Another segment extends from negative 4 comma 2 to 3 comma 2. A semicircle extends from 3 comma 2 to negative 4 comma negative 2.

Answers

The correct option regarding the area of the figure is given as follows:

14+16.25π units².

How to obtain the area of a figure?

The figure, given with no scale at the end of the answer, is composed by:

A semi-circle.A right-triangle.

The sides of the right-triangle are given as follows:

7, as 3 - (-4) = 7.4, as 2 - (-2) = 4.

The area of a right triangle is given by half the multiplication of the sides, hence:

At = 0.5 x 7 x 4 = 14 units.

The radius of the semicircle is half the hypotenuse of the right triangle, hence, applying the Pythagorean Theorem:

h² = 7² + 4²

h = sqrt(7² + 4²)

r = 0.5sqrt(7² + 4²)

r = 4.03 inches.

The area of a semicircle of radius r is:

As = πr².

Hence:

As = π(4.03)² = 16.25 π.

The total area is obtained as the sum of the areas of each separate part, hence:

A = At + As = 14+16.25π units².

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Answer:

Step-by-step explanation:

14+8.125

C

Could you please help with this.

Answers

Answer:

[tex] \sqrt[2]{15} = 7.5[/tex]

A rectangular patio has a length of 9 2/5 feet and an area of 81 3/8 square feet. What is the width of the patio?

Answers

Step-by-step explanation:

81 3/8 ÷ 9 2/5

81*8+3 = 651

651/8

9 2/5 = 9*5+2=47

47/5

651/8 ÷ 47/5 =

651/8 * 5/47 = 3255/376 =

8.65691489362

Solve the absolute value equation (3x-6)=12.
O a
Ob
Oc
Od
x=6,x=2

x=-6, x=-2
x=6₂x=-2
x=-6₂x=2

Answers

The solution of the absolute value equation |3x - 6| = 12 is x= 6 and x = -2

The absolute value equation is

|3x - 6| = 12

We can write the absolute value equation in two ways

3x - 6 = 12

-(3x - 6) = 12

We have to solve each equation

The first equation is 3x - 6 = 12

3x - 6 = 12

3x = 12+6

3x = 18

x = 18/3

x = 6

The second equation is -(3x - 6) = 12

Apply the distributive property

-3x + 6 = 12

-3x = 12 - 6

-3x = 6

x = 6/-3

x = -2

Hence, the solution of the absolute value equation |3x - 6| = 12 is x= 6 and x = -2

The complete question is:

Solve the absolute value equation |3x - 6| = 12 .

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The cost to rent a frozen yogurt machine is $150 per day plus $25 per hour of use.
Which inequality can be used to determine the maximum number of hours h the
frozen yogurt machine can be used if the rental cost for the day will not exceed $300?

Answers

The inequality that can be used to determine the maximum number of hours h the frozen yogurt machine can be used if the rental cost for the day will not exceed $300 is 150+25h ≤300.

According to the question,

We have the following information:

The cost to rent a frozen yogurt machine is $150 per day plus $25 per hour of use.

And h represents the number of hours.

So, we have the following expression to find the total cost:

150+25h

Now, it is given that the total rental cost should not exceed $300.

So, we have the following inequality:

150+25h ≤300

Hence, the correct option is C.

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During a triathlon, Tasneem swims 1/4 of the total route and cycles 3/5 of the remaining route. She runs the rest of the route. If she runs 3600 m, determine the total distance of the triathlon.

Answers

The total distance of the triathlon is 12000 m.

What is an equation?

Two or more expressions with an equal sign are defined as an equation.

Let the total distance of the triathlon be x.

Tasneem swims 1/4of the total route, therefore, she swims for a distance of S = (1/4)x.

Now the remaining route is,

x - (1/4)x

=3/4x

After swimming, she cycles 3/5 of the remaining route, therefore, she cycles for a distance of C = (3/5)×(3/4)x,

C = (9/20)x

Now, she runs for the rest of the route, therefore, she runs for a distance of R = x - (1/4)x-(9/20)x

Or, R = (20x - 5x - 9x)/20

R = (6x)/20

Given that Tasneem runs 3600 m, therefore, substitute R = 3600 into the above equation,

3600 = (6x)/20

(3600×20)/6 = x

12000 = x

Therefore, the total distance of the triathlon is 12000 m.

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What is the difference between communism and capitalism

Answers

Answers

The primary difference explained in capitalism vs communism is that capitalism is an economic system that allows private ownership and promotes the idea of a free market; in contrast, communism favours collective ownership and restricts the free market with government intervention portraying a planned economy.

Explanation

What is Capitalism?

Capitalism occurs when people are allowed to own and control capital assets, use them according to their self-interest, and earn profit by producing valued goods and services utilizing capital resources. In a capitalist economy, government intervention will be minimal; hence, the production of goods and services is driven by supply and demand. It creates an environment that promotes individualism, innovations, competition, efficient allocation of resources, the efficiency of the private sector, presenting consumers with better choices, and improving living standards. capitalism vs communism.

On the other hand, capitalism is often blamed for favouring the rich. The opponents of the system advocate that in capitalism, the rich get richer and the poor get poorer instigating the unequal distribution of wealth and inequality, creating social division. Moreover, in the wake of producing profit, the capitalist model exploits the workers, and unfair competition can also lead to the emergence of monopolies in specific sections. All these disadvantages communicate the need for the reformation of capitalism.

What is Communism?

Communism ideology aims to establish common ownership and eliminate the private property concept. It simply focuses on replacing private ownership and introducing state-owned organizations, projects, resources, and properties, ensuring economic equality and fairness. Such economies work towards achieving social development, welfare, and the overall development of all the citizens of a nation.

China has long been a significant example of a communist government where the government-controlled major resources, funds, products, and services, but later due to globalization and certain other aspects, has started implementing some elements of capitalism to grow business and take advantage of trade opportunities. Similarly, it has been observed that many nations turn their heads toward capitalism to obtain more opportunities, attain industrialization, and reap the benefits of globalization hence strengthening the capitalism vs communism debate.

Capitalism and communism are inherently contrasting concepts. While capitalism propagates individualism, communism is associated with collectivism. Industrial capitalism was popularised in the 18th century, and modern communism was propagated in the 19th century.

The instances reflecting the conflict based on these ideologies were prevalent from the old times. For example, ideological conflict, and capitalism vs. communism in the Cold War of the 20th century. During the Cold War, the United States and Western European nations were based on capitalism and democracy. In contrast, the Soviet Union was based on communism and dictatorship, and Eastern European nations were under Soviet communist control. Many of the significant events in the Cold War contributed to explaining whether capitalism was better than communism or not.

A quadratic function subtracted from a cubic function is a cubic function? True or False

Add example problem:

Answers

When quadratic function is subtracted from cubic function, the resultant equation is cubic.

So, It is true.

What is function?

Function is defined as, In any equation of two variable, we make change in one  accompanied by second.

For example, [tex]F(x)=2x+1[/tex] when we make changes in x , different values of y will obtain.

what are Quadratic and Cubic function?

Quadratic function in which maximum power of variable is two. Similarly, the function which has maximum power on variable is three is called cubic function.

To solve the given problem, let suppose we have,

Quadratic function:[tex]f(x)=x^{2} +x+1[/tex]

Cubic function: [tex]g(x)= x^{3}+x^{2} +x+1[/tex]

According to question,

Subtract quadratic function from cubic function,we get

[tex]g(x)-f(x)=( x^{3}+x^{2}+x+1)-(x^{2} +x+1 )[/tex]

⇒ [tex]h(x)=x^{3} +1[/tex]

It is a cubic function.

Thus, given statement is True.

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Solve the Inequality and graph the solution set.

-8-8(2x-4)>-5(4x-5)-21

Answers

Answer:

x > -5

Make a number line.  Put a circle on the number line at -5 and then darken an arrow on the number line going to the right of -5

Step-by-step explanation:

-8-8(2x-4) > -5(4x -5) -21  Distribute the -8 and -5

-8 - 16x + 32 > -20x +25 -21  Combine like terms

-16x + 24 > -20x +4  Add 20x to both sides

4x + 24 > 4  Subtract 24 from both sides

4x > -20  Divide both sides by 4

x > -5

Consider Z=x^3-8
A) Find the real root of Z.

B) Write Z as a product of linear terms.

Answers

Using the formula, the real of z is 2 and the linear form of z is [tex](x-2)(x^2+2x+4)[/tex].

In the given question,

The given expression is z=x^3−8

We can given expression as [tex]x^3-8=(x)^3-(2)^3[/tex]...............(1)

We have to find the real root of the z.

We also have to find the z as a product of linear terms.

To solve the given expression using the formula

[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

If we compare equation 1 to the [tex]a^3-b^3[/tex].

After compare we get a=x and b=2

Now the linear form of the given expression is

[tex]z=(x)^3-(2)^2[/tex]

[tex]z=(x-2)(x^2+2x+(2)^2)[/tex]

Simplifying

[tex]z=(x-2)(x^2+2x+4)[/tex]

Now the real root of of z;

x-2=0

x=2

Hence, the real of z is 2 and the linear form of z is [tex](x-2)(x^2+2x+4)[/tex].

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Find the 14th term of the geometric sequence 1,-5,25

Answers

The 14th term of the geometric sequence will be -1220703125.

What is geometric sequence?

The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.

Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.

[tex]1*(-5)^{13}[/tex]The terms are given, 1,-5,25

a = 1

r = -5/1 = -5

The 14th term will be= [tex]ar^{13}[/tex]

= [tex]1*(-5)^{13}[/tex]

= -1220703125

Hence, the 14th term of the geometric sequence will be -1220703125.

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What is 624×8 please answer this

Answers

4,992 is the answer-
-
-
-

Langston wrote an expression with a value of -21. Which of the following expressions could Langston have written?
O-20-(-1)
O-25-4
O-24 +3
O-19+2

Answers

The expression that Langston have written -24 +3.

Expression:

Expression refers the finite combination of symbols that is well-formed according to rules that depend on the context and it consists of numbers, mathematical operations etc.

Given,

Langston wrote an expression with a value of -21.

Here we need to find the expression that could Langston have written.

In order to find the correct expression we have to solve each and every one in the options,

When we take the first expression

-20 - (-1)

Which is equal to

=> -20 + 1

When we simplify it then we get

=> -19

Then the second one is simplified as,

=> -25 - 4 = -29

And the third one given the value of

=> -24 + 3

=> -21

Therefore, this one is the correct expression and this one is taken by Langston.

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The velocity function of a car is given by v(t) = -3t2 + 18t + 9 m/s. Find the acceleration of the car three seconds before it comes to a stop.

A.
a = -6.46 m/s²
B.
a = -2.76 m/s²
C.
a = -0.46 m/s²
D.
a = 2.76 m/s²

Answer: In photo below

You're Welcome :)

Answers

The acceleration of the car three seconds before it comes to a stop is  -2.76 m/s² (Letter B).

Derivative

Derivative indicates the rate of change of a function with respect to a variable. Thus, when you derivate the position function, you find the velocity function. And, when you derivate the velocity function, you find the acceleration function.

In other words, the velocity function represents the first derivative of the position, meanwhile, the acceleration function represents the second derivative of the position.

For derivating an equation, you should apply the rule: [tex](\frac{d}{dx} ) (x^n ) = nx^{n-1}[/tex]. Example: x²= 2x

The car stops when the velocity is equal to zero. Thus, v(t) = -3t² + 18t + 9 =0. Therefore, you  should solve this quadratic function:

Δ=b²-4ac=[tex]18^2-4\left(-3\right)\cdot \:9=324+12*9=324+108=432[/tex]

[tex]t_{1,\:2}=\frac{-18\pm \sqrt{432}}{2\left(-3\right)}\\ \\ t_{1,\:2}=\frac{-18\pm \sqrt{432}}{-6}[/tex]

[tex]t_1=\frac{-18+12\sqrt{3}}{-6}=3-2\sqrt{3}[/tex]

[tex]t_2=\frac{-18-12\sqrt{3}}{-6}=3+2\sqrt{3}[/tex]

Like t is a positive number, you should use [tex]t_2[/tex]. Thus, the value of t that you should apply to find the acceleration of the car three seconds before it comes to a stop is [tex]2\sqrt{3}[/tex].

The acceleration can be found from the derivative of the velocity function. See below.

a(t)= -6t+18 , for t=[tex]2\sqrt{3}[/tex]

a(t)= -6*[tex]2\sqrt{3}[/tex]t+18

a(t)= [tex]-12\sqrt{3}[/tex]t+18

a(t)=-2.76

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Rewrite the equation in standard form from vertex form: y = -4(x - 3)² + 6


The equation of the parabola, in standard form is ______________

Answers

y = -4x²+24x-30 is the standard form of parabola whose equation is  y = -4(x - 3)² + 6

What is Parabola?

Parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

The given equation is y = -4(x - 3)² + 6.

We need to write this equation as standard form of parabola.

the equation of a parabola in  standard form is.

y=ax² +bx+c

The given equation should be expanded y = -4(x - 3)² + 6.

y = -4(x²+9-6x)+6

Now apply distributive property

y = -4x²-36+24x+6

y = -4x²+24x+6-36

y = -4x²+24x-30

Hence y = -4x²+24x-30 is the standard form of parabola whose equation is  y = -4(x - 3)² + 6

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q(x) = -x-2
r(x) = x² + 2
Find the following.
(r∙q)(-5) =
(q∙r)(-5) =

Answers

Answer: 5q-5r               -5q+5r

I need help with this Question.

Answers

Answer:

Step-by-step explanation:

a. 1 hectare = 2.471 acres 

6 hectares x (2.471 acres / 1 hectare)

=14.826 acres

b. prices per acre: 150,000/14.826

=10,117.36 per acre

Classify the following number: -22 Choose all that apply

Answers

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Find the average rate of change.

Answers

The average rate of change = 1.59 ≈ 2

The average rate of change can be calculated by

1) The first one = [tex]\frac{3 + 0}{2}[/tex] = 1.5

2 ) the second can also be solved by ; 8 + 2/ 2 = 5

3 ) the third one will be 20 + 6 / 2 = 13

4) 8.5

5) 12.5

To calculate the average rate of change

we will first add all the distance

Adding all the distance we will get the sum = 3 + 8 + 20 + 10 + 10 = 51

The total time = 2 + 6 + 9 +15 = 32

Thus the average rate of change = 51 / 32 = 1.59

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Please help me simplify

Answers

Answer: [tex]\frac{4\sqrt{x} }{t^2}[/tex]

Step-by-step explanation:

You can start by either applying the exponent to both the numerator and denominator (exponent rule), or make things simpler by dividing first. Doing the latter allows me to show both properties. Since the terms in the fraction are being multiplied, we can divide common terms which will leave us with [tex]\frac{16x}{t^4}[/tex] on the inside. Now that it is simplified, we can apply the exponent. We will end up with 4x^1/2 in the numerator and t^2 in the denominator. If the exponent seems daunting, it is also helpful to know that raising something to the exponent of 1/2 is basically taking the square root of it.

Which graph represents the polynomial function?

Answers

The graph which represents the polynomial function f(x) = x^3 - 2x^2 - 5x + 6 is in option A.

First, let us understand the polynomial function:

A polynomial function is one that uses only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 9y + 6 is a polynomial with an exponent of 1.

We are given:

f(x) = x^3 - 2x^2 - 5x + 6

We know that, when the graph intersects the x-axis, it satisfies the equation that is f(x) = 0 at that point.

Let us check the points one by one;

Option A;

The graph intersects the x-axis at -2, 1, and 3 it should satisfy the equation f(x) = 0.

Let's put x = -2 in f(x), we will get;

f(-2) = -2^3 - 2(-2)^2 - 5(-2) + 6 = -8 - 8 + 10 + 6 = -16 + 16 = 0

f(-2) = 0.

Let's put x = 1 in f(x), we will get;

f(1) = 1^3 - 2(1)^2 - 5(1) + 6 = 1 - 2 - 5 + 6 = 7 - 7 = 0

f(1) = 0.

Let's put x = 3 in f(x), we will get;

f(3) = 3^3 - 2(3)^2 - 5(3) + 6 = 27 - 18 - 15 + 6 = 33 - 33 = 0

f(3) = 0.

So, the points -2, 1, and 3 satisfy the equation f(x).

Thus, the graph which represents the polynomial function f(x) = x^3 - 2x^2 - 5x + 6 is in option A.

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Fine the slope of the line and use rise/run to fill in the blanks

Answers

Answer: Rise is 5 and run is 1 and now that is equal 5

Step-by-step explanation:

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