erite an equation and solve for x if the area of the rectangle is 55 square units

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The cost of one ticket in Virginia is $8

A System of Linear Equations is when we have two or more linear equations working together.

Given that, 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77, Also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91.

To find the cost of a ticket in Virginia we will establish a system of linear equations and then solve them,

Let V represents the cost in Virginia that of in Maryland be M

Therefore,

4v+5m = 77.......(i)

8v+3m = 91........(ii)

Multiplying the equation eq(i) by 2 and subtracting eq(ii) from eq(i) [Elimination]

(8v+10m = 154)  - (8v+3m = 91)

7m = 63

m = 9

Put m = 9 in eq(i)

4v+5(9) = 77

4v = 77-45

4v = 32

v = 8

Hence, Each ticket in Virginia and Maryland costs $8 and $9 respectively.

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The population standard deviation of the data is 111.

1. Find the mean of the data:

Mean = (314 + 158 + 482 + 284 + 310 + 281) / 6 = 1029 / 6 = 171.5

2. Find the difference between each data point and the mean:

Feb: (314 - 171.5) = 142.5

Mar: (158 - 171.5) = -13.5

Apr: (482 - 171.5) = 310.5

May: (284 - 171.5) = 112.5

Jun: (310 - 171.5) = 138.5

Jul: (281 - 171.5) = 109.5

3. Square each of the differences:

Feb: (142.5)^2 = 20,312.5

Mar: (-13.5)^2 = 182.25

Apr: (310.5)^2 = 95,822.25

May: (112.5)^2 = 12,656.25

Jun: (138.5)^2 = 19,082.25

Jul: (109.5)^2 = 11,982.25

4. Sum all of the squared differences:

20,312.5 + 182.25 + 95,822.25 + 12,656.25 + 19,082.25 + 11,982.25 = 149,047.5

5. Divide the sum of the squared differences by the number of data points minus one:

149,047.5 / (6 - 1) = 149,047.5 / 5 = 29,809.5

Square root of 29,809.5 = 111 (rounded to the nearest integer)

Therefore, the population standard deviation of the data is 111.

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Answer: d = √(5² + 9²) = √106, or approximately 10.3 units.

Answer:

y=3x-10

Step-by-step explanation:

first, we need to find the slope of line s, as that will determine the slope of line t

the formula for the slope calculated from 2 points is (y2-y1)/(x2-x1)

we can label the points for (3,4) and (2,1)

x1=3

y1=4

x2=2

y2=1

substitute into the formula:

m=(y2-y1)/(x2-x1)

m=(1-4)/(2-3)

m=-3/-1

m=3/1

m=3

the slope of line s is 3

as said above, parallel lines have the same slope, but different y intercepts.

that means that line t will have the same slope as line s (3).

typically, lines are written in the form y=mx+b, where m is the slope and b is the y intercept

here's what is line t so far:

y=3x+b

we need to find b

because the line passes through the point (4,2), we can use it to solve for b

plug 4 in as x and 2 as y

2=3(4)+b

2=12+b

-10=b

so that means that b is -10

therefore the equation for line t is y=3x-10

Hope this helps! Good luck on your assignment!

Answer:

5.5

Step-by-step explanation:

180/3 =60 (60/1 hr)

330/60 =5.5

Total interest earned = 68

Total amount collected = 1268

Simple interest is a way to figure out how much interest will be paid on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the following year's principal to compute interest, the principal amount under simple interest remains constant.

Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest.

Since nothiong mentioned the interest is considered simple

Total amount = 1200 (principal)

Time = 1 year 5 month = [tex]1\frac{5}{12} = \frac{17}{12}[/tex]

rate = 4 %

Total interest earned = [tex]\frac{1200 * 4 * \frac{17}{12} }{100}[/tex] = 68

Total amount generated = 1200 + 68 = 1268.

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Answer:

(8,-2)

Step-by-step explanation:

Answer:

-3.3

Step-by-step explanation:

-2.3 - (4.5-3.5)

-2.3 - (1.)

-3.3

Answer:

Jo turned around and walked back to the starting point

8 km/hr

Step-by-step explanation:

4 km/one-half hr = 8 km/hr

Step-by-step explanation:

A)

If we look at the graph at 10 mins its evident that there has been some movement meaning Joes has moved 1km (as we can see in the graph) away from the starting point.

B)

For the last 30 mins of the graph we can see some changes.

so Joe started at 30 mins and ended at 60mins so there is a difference of 30 mins. In those 30 mins Joe moved from 0km to 4km. Meaning that Joe moved at 4km in 30 mins.

We are going to work this out in KPH. Since we have 30 mins and the unit we are using to measure his speed is measured in hours, we need to double it along with the kilometres he moved so it stays fair and constant. so we will have 8km and 60 min (1 hour). Therefore Joe moved at 8kph.

Hope this helps

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A:

f(x) = -x² + 4x - 10

f(2) = -(2)² + 4(2) - 10

f(2) = -4 + 8 - 10

f(2) = 4 - 10

f(2) = -6

Part B:

g(x) = 5x + 1

g(6) = 5(6) + 1

g(6) = 30 + 1

g(6) = 31

Part C:

f(x) = -x² + 4x - 10

f(-1) = -(-1)² + 4(-1) - 10

f(-1) = -1 - 4 - 10

f(-1) = -5 - 10

f(-1) = -15

Part D:

g(x) = 5x + 1

16 = 5x + 1

15 = 5x

3 = x

x = 3

Answer: Brady made 72 shots

Step-by-step explanation:

Number of shots taken on his pop- a- shot basketball hoop=80

Percentage of shots made into the basket=90%

Number of shots made into the basket= 90% x 80

= 90/100 x 80

= 72

Area of the middle rectangular section = length x width = 35 x 20 = 700 square cm.

The radius of the circular sections is 25 cm

Area of a full circle is pi x r^2 = 3.14 x 25^2 = 1962.5 square cm.

There are two quarter circles which is 1/2 of a circle. The area of those would be 1962.5/2 = 981.25 square cm.

Total area of the figure = 700 + 981.25 = 1681.25 square cm

The steps to solve two polynomial equations are given below.

What is polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

x^2 + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

Apply the Zero Factor Property to an Equation Solving.

ZERO. FACTOR, write the equation with one side equal to zero. the expression by a factor.

PROPERTY. Solve the equation by setting each factor to zero.

Check by adding substitutes to the initial equation.

Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero once it has reached zero. The original equations' solutions are the solutions to the resulting equations. Factoring cannot always be used to solve polynomial equations.

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The required point that satisfies each system of equation is (12, -1). Option B is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

To equations are given as,
y = -1/3x + 3 - - - - (1)
y = -3/4x + 8 -- - - - (2)

From equation 1 and 2
-1/3x + 3 = -3/4x + 8
3/4x - 1/3x = 8 - 3
9x - 4x / 12 = 5
5x = 60
x = 12

Now, to evaluate the y ordinate put the above x in equation 1
y = -1/3(12) + 3
y = -4 + 3
y = -1

Thus, the required point that satisfies each system of equation is (12, -1). Option B is correct.

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Solutions refers to the answer to the problem, Real Solutions are realistic and practical whereas ideal solutions are the best cases for the solutions.

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

Ideal Solutions - Best cases, Usually not possible.

Real Solutions - Practical and possible to attain.

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Answer: obtuse

Step-by-step explanation:

Answer:

637 in^3

Step-by-step explanation:

V=(BxH)/2

V=((13x7) x 14)/2

V=(91x14)/2

V=1274/2

V=637 in^3

Answer:

the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.

Step-by-step explanation:

The expression 23x² + 6x + 7 is in the form of a quadratic equation. A quadratic equation is an equation in the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. In this case, the coefficients of the x², x, and the constant term are a = 23, b = 6, c = 7.

One way to factor a quadratic equation is by using the factoring by grouping method, where we group the terms in pairs and factor out the greatest common factor (GCF) from each group.

Here is one way to factor this equation:

23x² + 6x + 7 = (23x² + 6x) + 7

= (23x² + 6x) + 7

= (23x² + 6x + 6x) + 7

= (23x² + 12x) + 7

= (23x(x) + 3x(4)) + 7

= (23x(x+4) + 7)

= (x+4)(23x + 7)

So the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.

It's important to note that the above expression factors into a product of two binomials and not two factors of 23x² + 6x + 7

You can also use Quadratic formula to solve the above expression if this method seems confusing.

Answer:

10 and 24units

Step-by-step explanation:

Pythagoras' Theorem applies to right angle triangles with the formula:

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

where c is the longest side, with a and b the shorter ones (interchangable)

With the parameters given from the question and the formula given as well, we can find the value of x and therefore the side lengths.

By Pythagoras' Theorem,

[tex] {26}^{2} = ( {5x)}^{2} + ( {12x)}^{2} \\ 676 = 25 {x}^{2} + 144 {x}^{2} \\ 169 {x}^{2} = 676 \\ {x}^{2} = 676 \div 169 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ = 2[/tex]

Now we can find the side lengths.

[tex]5x = 5(2) = 10units \\ 12x = 12(2) = 24units[/tex]

Therefore the side lengths are 10 and 24 units.

ok um 213=89Step-by-step explanation:ummmmmmmmmm

Answer:

[tex] \sf \rightarrowtail \: \frac{x}{4} = \frac{2}{5} \\ \sf \rightarrowtail \: 4 \times 2 = 5x \\ \sf \rightarrowtail \: 5x = 8 \\ \sf \rightarrowtail \: \boxed{ \bf \: x = \frac{8}{5} }[/tex]

Answer:

first graph is a function

Step-by-step explanation:

9514 1404 393

Answer:

  total purchase price: $27,722.01

Step-by-step explanation:

The price of the car plus tax is ...

  $25,625 × (1 +7.5%) = $27,546.88

Adding license and title charges brings the total to ...

  $27,546.88 +175.13 = $27,722.01 . . . total purchase price

_____

Additional comment

10% of that, or $2,772.20, will be the required down payment, leaving a balance due of $24,949.81. The payments on a 36-month loan at 9% will be $793.40, for a total loan cost of $28,562.30. Then the full cost of the car, including financing, is $31,334.50. The cost of the financing is $3,612.49.

Answer:

D) 5x+15

Step-by-step explanation:

5×x+5×3

5x+15

plz mark as brainliest

Answer: first u have to find the perimiter for each side

Step-by-step explanation:

the answer is 100 d z

Answer:

100π sq. ft

Step-by-step explanation:

Given,

Radius ( r ) = 10 ft

To find : Area ( circle ) = ?

Formula : -

Area ( circle ) = π r^2

Area ( circle )

= π x 10^2

= π x 100

= 100π sq. ft

Answer:

area of circle : πr^2

                      = π(10)^2

                      = 314.1592654

                      ≈ 314.16 cm2

The correct answer is "C" - a decrease in personal income tax is most likely to result in an increase in consumer demand.

Taxes are compulsory payments made by a government organization, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools.

A value-added tax, often referred to as a goods and services tax in some nations, is a kind of tax that is imposed gradually. At every stage of manufacture, distribution, or sale to the final customer, it is added to the cost of a good or service.

There is an increase in consumer demand when personal income taxes are cut because people have more money that they can spend on products and services.

On the other hand, a rise in personal income taxes would reduce the amount of disposable money that consumers have, which will result in a drop in demand from consumers.

In a similar vein, a rise in company tax would result in higher business costs and lower profits, both of which would reduce consumer demand. Conversely, a drop in corporate tax would not directly influence consumer spending.

So the correct answer is C.

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