solve the following problem below

Answer:

y=4x-16

Step-by-step explanation:

We want to find the equation of the line in the form y=mx+c, where m is the slope and c is the y-intercept.

If the lines are parallel, their slopes will be the same. The slope of y=4x+1 is 4.

Our equation is now y=4x+c. Sub in point P to get c:

4=4(5)+c

4=20+c

c=-16

Therefore our equation is y=4x-16

Answer:

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r

here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

The graph that shows the solution set for the system y ≥ -2, x < 2 is illustrated below.

First, we graph y ≥ -2. This inequality represents all the points above or on the line y = -2. To graph this, we draw a horizontal line at y = -2 and shade in all the points above this line.

Next, we graph x < 2. This inequality represents all the points to the left of the line x = 2. To graph this, we draw a vertical line at x = 2 and shade in all the points to the left of this line.

The solution set of the system is the region that satisfies both inequalities simultaneously. Since the region that satisfies both inequalities is the shaded region above the line y = -2 and to the left of the line x = 2, we select the graph that shows this shaded region.

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Answer: 28/5    or 5.6

Step-by-step explanation:

5(x-1) = 23        Distribute on the left side

5x - 5 = 23        Add 5 to both sides

    +5      +5

5x = 28       Divide both sides by 5

x = 28/5

Answer:

x = 28/5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

5(x - 1) = 23

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 23 does indeed equal 23.

∴ x = 28/5 is the solution to the equation.

the cost of 145 refrigerators is $16954.82 and fixed cost rate per refrigerator is $116.92

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

A company manufactures small refrigerators. The total cost to manufacture 57 refrigerators is $6665.

manufacture 1 refrigerator is $6665/57 = $116.92

So to make 145 refrigerators the money will spent is $116.92*145= $16954.82

The fixed cost arte per refrigerator is $116.92

Hencve the cost of 145 refrigerators is $16954.82 and the fixed cost rate per refrigerator is $116.92

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Answer:

C. \(cos^2A -sin^2A\)

Step-by-step explanation:

Given:

\(cos2A\)

To find:

The given expression is equivalent to:

A. \(sin^2A-cos^2A\)

B. \(sin^2A+cos^2A\)

C. \(cos^2A -sin^2A\)

D. \(cosA-sinA\)

Solution/Proof:

First of all, let us have a look at the compound angle formula for \(cos(X+Y)\).

Compound angle means in which there is sum of two angles given.

In the above we are having X+Y i.e. sum of two angles X and Y. So it is compound angle.

The compound angle formula for cosine is given as:

\(\bold{cos(X+Y)=cosXcosY-sinXsinY}\)

Here, let us put X = Y = A

\(cos(A+A)=cosAcosA-sinAsinA\\\Rightarrow \bold{cos(2A)=cos^2A-sin^2A}\)

So, cos2A is equivalent to \(cos^2A -sin^2A\).

Correct answer is:

Option C. \(cos^2A -sin^2A\)

The probability she pulls out a purple piece of candy would be 0.22.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is Sam's fathers collection.

We can write the equations for upstream and downstream as -

x - y = 7/2

x + y = 21/10

Solving the equations graphically -

{x} = 2.8

{y} = 0.7
In still water, the speed would be -

S = 3 - 0.7

S = 2.3 Km/h

Distance peddled upstream -

D = 2.8 x 3.5 = 9.8 Km

Therefore, the speed in still water would be 2.3 Km/h and the distance peddled upstream would be 9.8 Km.

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Answer:

8x-28+15c

Step-by-step explanation:

we can multiply, so we have 8x-28+15c.

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equations are given below.

6x = 52 - 2y

6x + 2y = 52

3x + y = 26                   ...1

5x + 7y = 70

(5/7)x + y = 10              ...2

Subtraction equation 2 from equation 1, then we have

3x - (5/7)x = 26 - 10

(16/7)x = 16

x = 7

Then the value of 'y' is given as,

3(7) + y = 26

21 + y = 26

y = 5

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

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Answer:

$3.47

Step-by-step explanation:

$4.88 + d = $8.35

-4.88. -4.88

d = $3.47

$3.47 more money Ilana need to buy a new scrapbook that costs $8.35.

Two or more expressions with an Equal sign is called as Equation.

Given,

Ilana needs d more dollars to buy a new scrapbook that costs $8.35.

She has $4.88.

The given equation is  $4.88+d=$8.35

We need to find value of d to find how much money ilana needs.

The given equation is four point eight eight plus d equal to eight point three five.

$4.88+d=$8.35

Let us separate d

Subtract 4.88 on both sides

$4.88+d-$4.88=$8.35-$4.88

d=$3.47

Hence $3.47 more money Ilana need to buy a new scrapbook that costs $8.35.

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a. The center of the circle is (-2, -1).

b. The radius of the circle is √136.

c. The equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.

a. To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

In this case, the endpoints of the diameter are P(-7, -4) and Q(3, 2).Applying the midpoint formula:

Midpoint = ((-7 + 3)/2, (-4 + 2)/2)

= (-4/2, -2/2)

= (-2, -1)

Therefore, the center of the circle is at the coordinates (-2, -1).

b. To find the radius of the circle, we can use the distance formula, which calculates the distance between two points (x1, y1) and (x2, y2). The radius of the circle is half the length of the diameter, which is the distance between points P and Q.

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

Using the distance formula:

Distance = √[(3 - (-7))^2 + (2 - (-4))^2]

= √\([(3 + 7)^2 + (2 + 4)^2]\)

= √\([10^2 + 6^2\)]

= √[100 + 36]

= √136

Therefore, the radius of the circle is √136.

c. The equation for a circle with center (h, k) and radius r is given by:

\((x - h)^2 + (y - k)^2 = r^2\)

In this case, the center of the circle is (-2, -1), and the radius is √136. Substituting these values into the equation:

\((x - (-2))^2 + (y - (-1))^2\) = (√\(136)^2\)

\((x + 2)^2 + (y + 1)^2 = 136\)

Therefore, the equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.

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The estimate of 179% of 41 by rounding is about 73.19.

To find this estimate, first convert the percentage to a decimal by dividing it by 100: 179/100 = 1.79. Then, multiply this decimal by 41: 1.79 * 41 = 73.39.

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Answer:

x=12

Step by step explanation:

Let's solve your equation step-by-step.

2x+3=x+15

Step 1: Subtract x from both sides.

2x+3−x=x+15−x

x+3=15

Step 2: Subtract 3 from both sides.

x+3−3=15−3

x=12

=>x=12

The explanatory variable is the clients while the response variable is change in duration.

A causal relationship is said to exist between variables whereby the occurrence of an event is as a result of another event.

In a causal relationship between variables, a value may represent explanatory variable while another value may represent a response variable.

An explanatory variable is the variable where observation of changes are being made such as the clients while the response variable are the outcome of the observation such as the duration of the run by each client.

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The mean for the data items in the given frequency distribution is 4.152

To find the mean of the data items in the frequency distribution, we need to use the formula:

Mean = (Sum of (xi * fi)) / (Sum of fi)

where xi is the midpoint of the class interval and fi is the corresponding frequency.

So, we have

Mean = (3 + 12 + 15 + 20 + 20 + 30 + 21 + 16)/(3 + 6 + 5 + 5 + 4 + 5 + 3 + 2)

Evaluate

Mean = 4.152

Hence, the mean is 4.152

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Answer:

tan(θ)= dn/de

θ=arctan(dn/de)

Step-by-step explanation:

Answer:

The list price would be $420.

Answer:

\(Length = 25cm\)

Step-by-step explanation:

Given

Brass Shape: Square

\(Density = 4.2g/cm^3\)

\(Mass = 1.05kg\)

\(Height = 4mm\)

Required

Determine the length of the plate

First, we need to calculate the Volume of the Brass using

\(Density = \frac{Mass}{Volume}\)

Make Volume the subject of formula

\(Volume = \frac{Mass}{Density}\)

Substitute 1.05kg for Mass and 4.2g/cm³ for Density

\(Volume = \frac{1,05\ kg}{4.2\ g/cm^3}\)

Convert 1.05 kg to grams

\(Volume = \frac{1.05 * 1000\ kg}{4.2\ g/cm^3}\)

\(Volume = \frac{1050 \ kg}{4.2\ g/cm^3}\)

\(Volume = \frac{1050 \ kg}{4.2\ g/cm^3}\)

\(Volume = 250cm^3\)

Next is to determine the Area of the brass;

\(Volume = Height * Area\)

Substitute 250cm³ for Volume and 4mm for Height

\(250cm^3 = 4mm * Area\)

Convert mm to cm

\(250cm^3 = 4 * 0.1cm * Area\)

\(250cm^3 = 0.4cm * Area\)

Divide both sides by 0.4cm

\(\frac{250cm^3}{0.4cm} = \frac{0.4cm * Area}{0.4cm}\)

\(\frac{250cm^3}{0.4cm} =Area\)

\(625cm^2 = Area\)

\(Area = 625cm^2\)

Lastly, we'll calculate the length of the brass

Since the brass is square based;

\(Area = Length^2\)

Substitute 625cm² for Area

\(625cm^2 = Length^2\)

Take square root of both sides

\(\sqrt{625cm^2} = Length\)

\(25cm = Length\)

\(Length = 25cm\)

Hence, the length of the square brass is 25cm

Answer:

\(\cos(x) \approx 0.82\)

Step-by-step explanation:

Cosine is defined as:

adjacent / hypotenuse.

We can determine that 18 is the side adjacent to x, and that 22 is the triangle's hypotenuse.

Putting these values into the definition of cosine:

\(\cos(x) = \dfrac{\text{adj}}{\text{hyp}}\)

\(\cos(x) = \dfrac{18}{22}\)

\(\cos(x) \approx 0.82\)

Answer:

cos x= adjacent/hypotenus

cos x= 18/22

cos x=0.8182

x=35.09⁰

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

Do Y divided by X.

Step-by-step explanation:

This is normally what I do so hope I helped.

Answer:

Area- (4x+3)(3x-1)

Area- (12x^2 + 9x-4x-3)

Area- (12x^2 +5x-3)

Area- 12x^2 + 5x - 3

Let  me know if this helps!

Answer:

18 weeks

Step-by-step explanation:

250 - 70 = 180

180/10 = 18 weeks

Answer:

18 Weeks

Step-by-step explanation:

The least amount of weeks that Irene must work in order to buy the bike is 18. To find your answer, subtract $70 from $250. You will get $180. This is the amount of money that Irene still needs to earn. If she saves her money for 18 weeks, she will have her $180. This is because $180 divided by $10 is 18.

The equivalent expression for five eighths raised to the negative first power times forty-two hundredths raised to the second power is option B

(5/8)^-1 × (0.42)^2

= {1 ÷ (5/8)¹} × 0.42²

= {1 × (8/5)¹} × 0.42²

= (8/5)¹ × 0.42²

Therefore, the equivalent expression is eight fifths raised to the first power times the quantity one over forty-two hundredths raised to the second power

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Answer:

(1.6) (0.42)^2 C

Step-by-step explanation:

I had originally put B, but my teacher explained and said its C.

the first part of b is correct where it says 8/5, bc you need to flip it in order to not have a negative exponent (you cant have a negative exponent as an answer) but 0.42 is correct and iit does not need to be fliped, since there is no (8/5)(0.42)^2 option, you need to make the 8/5 into a decimal, it becomes 1.6 and so the answer is C

Answer:

It won't let me see the picture

Step-by-step explanation:

Answer:

2/8 = 1/4

hope this helps

please give me a good rate