Solve the system of equations.
y = 7x + 43
y = 2x + 13
a. (-6, 1)
b. (6, -1)
C. (6, 1)
d No solution
Please select the best answer from the choices provided
A
B
Ο Ο Ο Ο
С

The slope of the equation c=450+28g represents the increase in cost per additional guest.

Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2). The letter "m" is frequently used to signify slope.

We can see that the preceding equation is in the slope-intercept format, where m denotes the line's slope and b is its y-intercept or starting point.

In this case, the slope is 28 dollars per additional guest. This means that for every additional guest, the cost of the banquet increases by $28.

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Answer:

              \(\bold{a_1=7\,,\quad a_2=2\,,\quad a_3=-3}\)

Step-by-step explanation:

                                      \(a_n=12-5n\\\\\\a_1=12-5\cdot1=12-5=7\\\\a_2=12-5\cdot2=12-10=2\\\\a_3=12-5\cdot3=12-15=-3\)

Answer:

13 feet

Step-by-step explanation:

if we assume the angle on the ground to the truck is a ninety degree angle

Answer:

6x+3x×12-30

9x×do 30-12

then multiple it and there is the ans

Answer:

11 units

Step-by-step explanation:

To find the distance between the two points, you can use the distance formula, which is derived from the Pythagorean theorem. The formula is:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the distance between the two points (3, 5) and (3, -6):

Distance = √((3 - 3)^2 + (-6 - 5)^2)

= √(0^2 + (-11)^2)

= √(0 + 121)

= √121

= 11

Therefore, the distance between the two points is 11 units.

Principal =P = $18,000

time = T = 10 years

(a) Simple interest

SI = P x R x T

Where:

R = simple interest in decimal form = 5/100= 0.05

SI = 18,000 x 0.05 x 10 = $9,000

Value of investment = 18,000 + 9,000 = $27,000

(b) compounded monthly

A = P (1 + r/n )^nt

Where:

A= future amount

n = number of compounding periods per unit t = 12

A= 18,000 (1 + 0.05/12)^12*10

A= $29,646.17

Answer:

the answer would be c

Step-by-step explanation:

The amount of pounds of pumpkin made in 30minutes is 96 pounds

Fractions are written as a ratio of two integers.

If Michael makes 16/5 pounds of pumpkin pie filling per minute, then;

16/5 pounds of pumpkin = 1 minutes

In order to determine the amount made in half an hour (30 mins)

x = 30mins

Take the ratios

16/5x = 1/30
5x = 480

x = 480/5

x = 96

Hence the amount of pounds of pumpkin made in 30minutes is 96 pounds

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Answer:-6r+5

Step-by-step explanation:you just combine like terms and add or the positive 5

Answer:

-6r+5

Step-by-step explanation:

(combine like terms)

-4r - 2r = -6r

Using the formula for the perimeter and area of the circle, The circumference is \(6 \pi\) km and area is \(9\pi km^{2}\).

A circle is a spherical shape without boundaries or edges. A circle is a closed, curved object with two dimensions in geometry.

The formula for perimeter is:

P= \(2\pi r\)

A=\(\pi r^{2}\)

radius = 3km

Circumference =  perimeter = \(2*\pi *3\)

=\(6 \pi\) km

Area = \(\pi * 3^{2}\)

=\(9\pi km^{2}\)

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Answer:

$51.2

Step-by-step explanation:

If you subtract 64 to 20% then you end up with $51.2

Using the range to compare the variability of data sets is a rather insensitive measure of data variance is the correct answer.

In this question,

The range tells you the spread of your data from the lowest to the highest value in the distribution. The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest.

Data variability also known as spread or dispersion, refers to how spread out a set of data is. Variability gives users a way to describe how much data sets vary and allows users to use statistics to compare their data to other sets of data.

Thus the disadvantage of using range is that it does not measure the spread of the majority of values in a data set, it only measures the spread between highest and lowest values.  

The options are a) It is a rather insensitive measure of data variance, b) It is hard to compute, c) It is a sensitive measure of data variance, d) It does not have any variance.

Hence we can conclude that using the range to compare the variability of data sets is a rather insensitive measure of data variance.

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The equation of slope-intercept form for the line is,

⇒ y = 1/2x - 8

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Slope = 1/2

y - intercept = - 8

We know that;

The equation of slope-intercept form for the line is,

y = mx + b

Where, m is slope and y - intercept of the line.

Substitute all the values we get;

y = mx + b

y = 1/2x - 8

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The prove of ∠1 equal to ∠2 is shown below.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

⇒ AB = AC, AD = AE and DC = EB

Now,

In ΔDBC and ΔEBC;

⇒ DC = EB   (Given)   ..(i)

Since,  AB = AC

So, the ΔABC is a isosceles triangle.

Hence, ∠DBC = ∠ ECB   ..(ii)

Here,  AB = AC and AD = AE

So, BD = EC   ..(iii)

Hence, By the condition (i), (ii) and (iii);

By SAS condition,

⇒ ΔDBC ≅ ΔEBC

Hence, We get;

⇒ ∠1 = ∠2

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Answer:

\(Area = 6.5p\)

Step-by-step explanation:

Given

\(Area\ of\ Old = p\)

\(Area\ of\ New = 6.5 * Area\ of\ Old\)

Required

Write an expression for the area of new post office

From the question, we have the following:

\(Area\ of\ Old = p\)

and

\(Area\ of\ New = 6.5 * Area\ of\ Old\)

Substitute p for Area of Old in the second equation

\(Area\ of\ New = 6.5 * p\)

\(Area\ of\ New = 6.5 p\)

Hence, the expression is:

\(Area = 6.5p\)

Answer:

∠ ADB = 59°

Step-by-step explanation:

The vertices of a rectangle are right angles, then

∠ ADB + 31° = 90° ( subtract 31° from both sides )

∠ ADB = 59°

Costo de opcion 1: y = 0.05x + 20

Costo de opcion 2: y = 0.20x + 5

500 (250 cada uno) mensajes en opcion 1: y = 0.05(500) + 20 = 25 + 20 = 45

500 (250 cada uno) mensajes en opcion 2: y = 0.20(500) + 5 = 100 + 5 = 105

Como cada quien paga la mitad:

Pago en opcion 1: 45/2 = $22.50

Pago en opcion 2: 105/2 = $52.50

Respuesta:

Pago en opcion 1: $22.50

Pago en opcion 2: $52.50

Answer:  31.4 meters

Work Shown:

\(C = 2\pi r\\\\C \approx 2*3.14*5\\\\C \approx 31.4\\\\\)

The quadratic equation that represents the solution is F: p(x) = x² - 49.

The term "quadratic" refers to functions where the highest degree of the variable (in this example, x) is 2. A quadratic function's graph is a parabola, which, depending on the sign of the leading coefficient a, can either have a "U" shape or an inverted "U" shape.

Algebra, geometry, physics, engineering, and many other branches of mathematics and science all depend on quadratic functions. They are used to simulate a wide range of phenomena, including population dynamics, projectile motion, and optimisation issues.

Given that the solution of the quadratic function are x = -7 and x = 7 thus we have:

p(x) = (x + 7)(x - 7)

Solving the parentheses we have:

p(x) = x² - 7x + 7x - 49

Cancelling the same terms with opposite sign we have:

p(x) = x² - 49

Hence, the quadratic equation that represents the solution is F: p(x) = x² - 49.

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Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{x = 15 °}}}}}\)

Step-by-step explanation:

\( \sf{x + 30 ° + 100 ° + 3x - 10 ° = 180 °}\)

( Sum of angle in straight line )

Collect like terms

⇒\( \sf{4x + 30 ° + 100 ° - 10 ° = 180 °}\)

Calculate the sum or difference

⇒\( \sf{4x + 120 ° = 180 °} \)

Move 120 to right hand side hand change it's sign

⇒\( \sf{4x = 180 ° - 120 °}\)

Subtract 120 from 180

⇒\( \sf{4x = 60 ° }\)

Divide both sides of the equation by 4

⇒\( \sf{ \frac{4x}{4} = \frac{60}{4} }\)

Calculate

⇒\( \sf{x = 15  °}\)

Hope I helped!

Best regards!!

Answer:

si

Step-by-step explanation:

no

freememeskids

Answer: (x−3)(3x−8)

Step-by-step explanation:(x−3)(3x−8)

Apply the distributive property by multiplying each term of x−3 by each term of 3x−8.

3x

2

−8x−9x+24

Combine −8x and −9x to get −17x.

3x

2

−17x+24

Using the order of operations, the expression can be simplified as  

9 + 1.34 + 62.88 = 73.22

The order of operations instructs us on how to solve steps in multi-step expressions. Any operations contained within parenthesis or brackets are first solved. After that, we handle any exponents. Third, we perform all division and multiplication operations from left to right. Fourth, all addition and subtraction problems are solved from left to right.

Remember PEMDAS when simplifying multi-step expressions, i.e.:

P (Parentheses)

E (Exponents, Powers and Square Roots)

MD (Multiplication and Division, left-to-right)

AS (Addition and Subtraction, left-to-right)

The expression given in the problem is:  9 + 1.34 + 1 2 (3.50 +1.74)

Apply the above operation order:

Step 1: solve the addition inside the parenthesis

9 + 1.34 + 1 2 (3.50 +1.74)  =  9 + 1.34 + 1 2 (5.24)

Step 2: Multiply the result by 12

9 + 1.34 + 1 2 (5.24) = 9 + 1.34 + 62.88

Step 3: Apply addition from left to right

9 + 1.34 + 62.88 = 73.22

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Answer:

6π

Step-by-step explanation:

First we need to find the circumference of the circle. We know that the radius is 4 and the formula is πd or 2πr

Leaving it in terms of pi, the circumference is 8π

Now we need to find the length of the arc.

Since the missing part of the circle is labeled with a right angle, we know that it's exactly 1/4 of the whole circle. That means the arc we need to find is 3/4 of the circumference.

3/4 of 8π is 6π

Answer:

Step-by-step explanation:

\( \frac{20}{x} = 4\)

\( = > 20 = 4x\)

\( = > x = \frac{20}{4} \)

=> x = 5 (Ans)

Answer:

In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.

Step-by-step explanation:

The range of the given trigonometric equation is -1≤y≤1. Therefore, option D is the correct answer.

The given trigonometric equation is y=cosx.

Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,∞),{x|x∈R}

Range: [−1,1],{y|−1≤y≤1}

Therefore, option D is the correct answer.

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