Answer the following questions. Make sure to show all your work. 1. When is it best to solve a system of equations using graphing? 2. When is it best to solve a system of equations using substitution? 3. When it is best to solve a system of equations using elimination? When it is 4. Solve the following system of equations graphically. y=3x+4 y=-2x-5

Answers

Answer 1

Answers

1. Use graphing when you have equations in y intercept form and when you have a graphing calculator or graphing app on line
Example
y = 3x +4
y = -2x -5

2. Substitution works best when you can manipulate your equations so you can have a variable on one side of the equation for substituting into the other equation
y = 3x +4
x = y + 1

3. Elimination works best when one of your variables is a + and a - so they will cancel or eliminate, allowing you to solve for one variable.
Example
2x + 4y = 2
-2x + 2y = 3

4. Solution is ( -1.8, -1.4) and the graph is attached with graphing points

Related Questions

You are investigating having business cards printed for your new game store. A local printing company charges $250 for the cardboard used and an hourly rate for labour of $40.

a. If h is the number of hours of labour required to print the cards, construct an equation for the cost
of the cards, C.

b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give
your answer to the nearest minute.

c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you
get printed with your current budget?

d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?

Answers

Answer:

See below.

Step-by-step explanation:

a. If h is the number of hours of labour required to print the cards, construct an equation for the cost of the cards, C.

C = $250 + ($40/hr)*h

b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give your answer to the nearest minute.

$1000 = $250 + ($40/hr)*h

($40/hr)*h = $750

h = 18.75 hours

(18.75 hours)(60 min/hr) = 1125 minutes

c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you get printed with your current budget?

(18.75 hr)*(1000 cards/hr) = 18,750 cards

d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?

Photocopy Cost for the first 1000 single-sided cards is:

(1000 cards)*($0.15) = $150

Photocopy Cost for the final 17,750 single-sided cards is:

(17,750)*($0.10) = $1,775

Totoal photocopy cost for 18,750 single-sided cards is $1,925. [1775+150]

The cheapest option for 18,750 cards is printing: $1,000

Printing is (1,925 - 1000) $925 cheaper than photocopying.

Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.

Answers

Answer: [tex]\triangle RQP \sim \triangle VPW[/tex]

Step-by-step explanation:

By the corresponding angles theorem, [tex]\angle RPQ \cong \angle VWP[/tex] and [tex]\angle RQP \cong \angle VPW[/tex].

Therefore, [tex]\triangle RQP \sim \triangle VPW[/tex] by AA.

How do I do C?Someone please help asap.

Answers

You have to find the slope of the line. It will give you the conversion rate from inches to centimetres or the other way around.

Looking closely at the graph, or using a ruler as reference, you can estimate that 30 cm ≈ 12 in. In terms of the graph, the line very nearly passes through the point (12, 30). It also passes through the origin, (0, 0), since 0 cm = 0 in exactly.

The slope of the line is then

[tex]\dfrac{30\,\mathrm{cm}-0\,\mathrm{cm}}{12\,\mathrm{in}-0\,\mathrm{in}} = \dfrac{30\,\rm cm}{12\,\rm in} = \dfrac{5\,\rm cm}{2\,\rm in} = 2.5\dfrac{\rm cm}{\rm in}[/tex]

which means that 1 in ≈ 2.5 cm.

So, if Sarah's height is 64 in, we convert this to cm and find her height is (approximately)

[tex]64\,\mathrm{in} \times 2.5\dfrac{\rm cm}{\rm in} = \boxed{160\,\rm cm}[/tex]

Using the sine rule, calculate the length y. Give your answer to 2 s.f.

Answers

Answer:

y = 9.84 mm

Step-by-step explanation:

Sine rule:

Law of sine:

[tex]\sf \boxed{\bf \dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}= \dfrac{c}{Sin \ C}}[/tex]

a = y

A = 31°

b = 17 mm

B = 117°

[tex]\sf \dfrac{y}{Sin \ 31^\circ}=\dfrac{17}{Sin \ 117^\circ}\\\\[/tex]

[tex]\sf y = \dfrac{17}{Sin \ 117^\circ}*Sin \ 31^\circ\\\\ y = \dfrac{17}{0.89}*0.515\\\\y = 9.84 \ mm[/tex]

The equation represents an ellipse. which points are the vertices of the ellipse? (7, 1) and (7, −5) (7, −10) and (7, 6) (10, −2) and (4, −2) (15, −2) and (−1, −2)

Answers

The points which represents the vertices of the given equation are; (15, −2) and (−1, −2).

Which points among the answer choices represents the vertices of the ellipse whose equation is given?

The complete question gives the equation of the ellipse as; (x-7)²/64+(y+2)²/9=1.

Since, It follows from convention that general equation of ellipse with centre as (h, k) takes the form;

(x-h)²/a² +(y-k)²/b² = 1.

Consequently, it follows from observation that the value of a and b in the given equation in the task content is; √64 = 8 and √9 = 3 respectively.

Since, 8 > 3, The vertices of the ellipse are given by; (h±a, k).

The vertices in this scenario are therefore;

(7+8, -2) and (7-8, -2).

= (15, -2) and (-1, -2).

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Chemotherapy in adult highgrade glioma: a systematic review and metaanalysis of individual patient data from 12 randomized trials

Answers

Systemic chemotherapy's impact on survival and recurrence in people with high-grade glioma has not been conclusively studied.

What is Systemic chemotherapy?

Patients undergoing systemic chemotherapy can get their chemotherapy drugs intravenously or orally. The medication may be injected into the body intravenously, or through an IV, or intramuscular, into a muscle (IM).

Some Key features of systemic chemotherapy are-

Background: In order to evaluate the effects of such treatment on survival and recurrence, we conducted a systematic review and meta-analysis.Methods: From 12 randomised controlled studies, information on 3004 patients was incorporated (11 published and one unpublished).Findings: Overall, the findings indicated a significant survival extension associated with chemotherapy, with a hazard ratio of 0.85 (95 percent confidence interval [CI] 0.78–0.91, p0.0001) or a relative reduction in mortality risk of 15%. There was no proof that a patient's age, gender, histology, performance status, or degree of resection affected how chemotherapy worked in any particular way.Interpretation: Further research into pharmacological treatment for malignant tumors is encouraged by this modest but noticeable improvement in survival from chemotherapy.

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3. You recently bought a rolled up poster at a convention and need to fit it in
your luggage. In order to pack it efficiently, we need to know the surface
area of the tube. If the radius measures out to be 0.4 inches and the height
is 25 inches, what is the full surface area? Use 3.14 for .

63.8 in²

1in²

62.8 in²

63.8 in3

Answers

Answer:

A. 63.8 in^2

Step-by-step explanation:

The surface area of a cylinder is given by:

A=2πrh+2πr^2

2πr^2 gives the area of the 2 ends, each with area πr^2.

2πrh gives the suface area of the outside of the cylinder.

r = 0.4 inches

h = 25 inches

Area = 63.8 in^2

Find the missing values

Answers

Answer:

Step-by-step explanation:

5×(-4)=20

5×3=15

5×0.5=2.5

5×5=25

5×0=0

5×(-2)=-10

In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor. Is there a significant difference between the proportions of urban and suburban residents who favor constructing nuclear plants

Answers

The p value for the difference is 0.005.

According to the statement

we have given that the 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor.

And we have to find the difference between them in proportions.

So,

X1 = 74 represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

X2 = 70 represent the number of people suburban residents are in favor

N1 = 100 sample 1 selected

N2 = 125 sample 2 selected

AND

P1 = 0.74 represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

And P2 = 0.56 represent the proportion of suburban residents are in favor And z would represent the statistic (variable of interest)

Pv represent the value for the test (variable of interest)

Here we apply the Z test to find the difference then

Z = (0.74 - 0.56) / (0.64(1-0.64)(1/100+1/125) )^1/2

Now after solving

Z = 2.795.

Now The significance level provided is ,and we can calculate the p value for this test.

Since is a two tailed test the p value would be:

P = (z>2,795)

P = 0.005.

So, The p value for the difference is 0.005.

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If c(x) = 4x − 2 and d(x) = x² + 5x, what is (c.d)(x)?
4x³ + 18x² – 10x
x² + 9x-2
16x² + 4x-6
4x² + 20x-2

Answers

Answer:

[tex]4x^2+20x-2[/tex]

Step-by-step explanation:

To find (c.g)(x) we basically use the function d(x) as your variable, x, and plug it into c(x). So we replace every x in c(x) with the function d(x), [tex]x^{2} +5x[/tex]

c(g(x))=4(x^{2} +5x)-2

c(g(x))4[tex]x^2[/tex]+20x-2

Jeri finds a pile of money with at least $\$200$. If she puts $\$80$ of the pile in her left pocket, gives away $\frac{1}{3}$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $\$200$ of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)

Answers

Solving an inequality, we will see that there is less than $280 in the pile of money.

How much money is originally in the pile?

Let's say that the amount of money is defined by the variable.

First, we know that Jeri keeps $80, so now in the pile we have:

M - $80.

Now she gives one third of that, then the leftover is:

(2/3)*(M - $80) + $80

We know that this is more than:

M - $200

Then we have the inequality:

(2/3)*(M - $80) + $80 > M - $200

And we can solve this for M.

(2/3)*M - (2/3)*$80 + $80 > M - $200

(1/3)*$80 + $200 > M - (2/3)*M

(1/3)*$80 + (1/3)*$200 > (1/3)*M

$280 > M

Then we conclude that there is less than $280 in the pile of money.

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60% of UCLA is girls. What perrcentage are boys
.

Answers

Answer:

40%

Step-by-step explanation:

Percent must be equal to 100, so if 60 are girls, then 40% must be boys.

A landscaping company is covering this trapezoid-shaped yard with grass seed. A trapezoid with base lengths of 6 meters and 7 meters, and height 4 meters. How much area will they need to cover with grass seed

Answers

Area covered with grass seed = 10.4[tex]m^{2}[/tex].

What is trapezoid geometry?

A quadrilateral with one set of parallel opposite sides is referred to as a trapezoid. It can have congruent sides (isosceles) and right angles (a right trapezoid), but neither is necessary.

Area of the trapezoid ={ (a+b)/2} +h

where a and b is base and h is height of the trapezoid geometry.

In the question,

a=6m , b=7m and h=4m.

According to the formula { (a+b)/2} +h.

Area covered with grass seed = {(6+7)/2} + 4

= 10.4[tex]m^{2}[/tex].

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Answer:

Step-by-step explanation:

GOT IT RIGHT`

if m = 2 and n = 5 then find the value of 6m+5n

Answers

Answer:

Step-by-step explanation:

6m+5n

plug in your given values

6(2) + 5(5)

12+25

=37

Answer:

Step-by-step explanation:

6m + 5n

6*2 + 5*5 = 12 + 25

= 37

A line passes through the points ( p , a ) and ( p , − a ) where p and a are real numbers. If p = 0 , what is the y-intercept? Explain your reasoning.

Answers

The y-intercept of the linear function is y = 0.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The y-intercept is given by (0,a) = (0,-a). From this, we have that for it to be a function, a = -a, and the only value that respects this condition is a = 0, hence the y-intercept of the linear function is y = 0.

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Putting the other player's king in check is always a good move. true or false subject: chess

Answers

Putting the other player's king in check is always a good move. true

What is chess?

The policies of chess allow a king to take an opponent's piece whilst in check, so long as that piece isn't always being defended. At the equal time, a king in the test is usually forced to move.The standard regulations of chess, a participant may not make any pass that places or leaves their king in the test. A player may additionally pass the king, seize the threatening piece, or block the check with some other piece. A king cannot look at the opposing king, considering this will vicinity the first king in check as well.

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a set of data has the values 11,14,23 and 16

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The number to add to the set of data is 26

How to determine the new number?

The set of data is given as:

11,14,23 and 16

Let the new number be x

So that

Mean = 18

Mean is calculated as:

Mean = Sum/Count

So, we have:

(11 + 14 + 23 + 16 + x)/5 = 18

Multiply by 5

11 + 14 + 23 + 16 + x = 90

Evaluate the like terms

x = 26

Hence, the number to add is 26

Answers

The equation which represent the interpretation of the scenario is 5 + 2x

Algebra

Number of lawns Homer mowed = 5Additional laws mowed each month = 2Number of months = x

Total laws mowed = Number of lawns Homer mowed + (Additional laws mowed each month × Number of months)

= 5 + (2 × x)

= 5 + 2x

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If you can please explain how you got your answer so I can understand, Thank you!

Answers

Answer:

3 2/5

Step-by-step explanation:

Each slash/mark on the number line is 1/5, meaning that 6 marks away is 3 2/5.

To further explain how I know each mark is 1/5, each question had a denominator of 5, and if you count each mark from 2 1/5 (2 2/5, 2 3/5, 2 4/5, 3, etc) you will eventually land on 4 evenly.

PLEASE ASAP NEEDED SO BADLY PLEASEE PLEASE

Answers

Answer:

[tex]6x^{2} -24x-10[/tex] with remainder -5

Answer:

[tex]6^2-24x-10-\frac{5}{x+4}[/tex]

In other words, [tex]6x^2-24x-10[/tex] is the answer and -5 is the remainder

Step-by-step explanation:

I used long division for this, and I uploaded an image for the steps. The final answer I got was [tex]6x^2-24x-10-\frac{5}{x+4}[/tex]

The difference between two integers is 8 and their product is 65. Assume that the larger of the two numbers is x. Write a quadratic equation in standard form that can be used to determine the value of x. Factor your equation from Part B and determine the possible solutions to your equation. Show your work. Write an expression for the second number.

Answers

A quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0.

The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5.

The value for the second number is 5

Word Problem Leading To Quadratic Equation.

The general formula for quadratic equation in a in standard form is

a[tex]x^{2}[/tex] + bx + c = 0

Given that the difference between two integers is 8

Let the two integers = x and y,

and their product is 65. If the larger of the two numbers is x. Then,

x - y = 8 and xy = 65

Since we are looking for the value of x, make y the subject of formula in the first equation.

y = x - 8

Substitute y in the second equation.

x(x - 8) = 65

[tex]x^{2}[/tex] - 8x - 65 = 0

[tex]x^{2}[/tex] - 13x + 5x - 65 = 0

(x - 13)(x + 5) = 0

x = 13 or -5

We will ignore -5 since x is the larger number.

To get y Substitute x in the second equation.

xy = 65

13y = 65

y = 65/13

y = 5

Therefore, a quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0. The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5. The value for the second number is 5

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Your team decides to erect 8 tent frames that can each hold a tarp to provide shade and cover if needed. The area under each tarp is 25 feet wide and 40 feet long, and the top of the tarp will run the length of your seating area. Your tarp needs a slope of to allow runoff in case of rain. The frame will be 10 feet high around the outside.

How high does the center of the frame need to be?

Answers

The height of the frame is 15 feet.

How to calculate the height?

From the information given, the following can be depicted:

b - 10/a = 2/5

2a = 5b - 50

2a - 5b = -50

Also, slope of AC:

= (b - 10(/(a - 5) = 2/5

2a - 50 = -5b + 50

2a + 5b = 100

Both equations will be solved

The height of the frame will be:

= 5 + 10

= 15 feet

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Please if anyone no math I really need help

Answers

Answer:

Step-by-step explanation:

option a (x-4) translates the graph 4 units right, not down

option b (x)-4 translates the graph 4 units down, not left

option c (x)+4 translates the graph 4 units up, so it is correct

option d (x+4) translates the graph 4 units left, not right

if the number is outside of the parentheses, like (x)+4 or (x)-4, the graph undergoes a vertical translation, and it moves up/down, with + meaning up and - meaning down

if the number is inside of the parentheses, like (x+4) or (x-4), the graph undergoes a horizontal translation, and moves left/right, with - meaning right and + meaning left

HELP PLS PLS!!!! look at pic

Answers

Answer: [tex]\frac{2}{25} +\frac{11}{25}i[/tex]

Step-by-step explanation:

To get the following you have multiply the conjugate. [tex]\frac{(2-i)(3-4i)}{(3+4i)(3-4i)}[/tex]

Cora is wrapping a ribbon around a cylinder-shaped gift box. The box has a diameter of 15 inches and the ribbon is 60 inches long. Cora is able to wrap the ribbon all the way around the box once, and then continue so that the second end of the ribbon passes the first end. What is the central angle formed between the ends of the ribbon? Round your answer to the nearest tenth of a degree.

Answers

The central angle formed between the ends of the ribbon is 98.6°.

How to illustrate the angle?

The circumference will be:

= πd

= 3.14 × 15 = 47.1

Ribbon = 60 - 47.1 = 12.9

Length of arc = x/360 × πd

12.9 = x/360 × 3.14 × 15

x = 98.6°

The angle is 98.6°

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Which term describes the red curve in the figure below?
• A. Hyperbola
B. Circle
C. Parabola
• D. Ellipse

Answers

B. Circle

When a plane intersects a cone and is perpendicular to the height of the cone, then it forms a circle. If the plane intersected the cone at an angle, we would have an ellipse.

A cone has a circular base. So, the answer to your question is B for circle.

In the biblical account, adam lived to be how old?
a. 99
b. 122
c. 545
d. 930

Answers

D is the answer. He lived to be 930 years old.

Select the correct answer. which expression is equivalent to , if x > 0? a. b. c. d.

Answers

The equivalent expression of the expression is 128x^5y^6/2x^7y^5

How to determine the equivalent expression?

The expression is given as:

128x^5y^6/2x^7y^5

Divide 128 by 2

64x^5y^6/x^7y^5

Apply the law of indices

64y^(6-5)/x^(7-5)

Evaluate the differences

64y/x^2

Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5

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Complete question

Select the correct answer. which expression is equivalent to 128x^5y^6/2x^7y^5 , if x > 0 and y > 0

A square metal sheet has the side length of 1 cm. À circular hole of radius 2/5 cm is drilled in the middle of the sheet.
How far the hole is from the edge of the sheet?

Answers

Step-by-step explanation:

PLEASE I NEED HELP ASAP

The question is :
Danielle reflects shape S in the line x = - 1 , and then reflects the new shape in the line y = 2

Zachary reflects shape S in the line y = 2 , and then reflects the new shape in the line x = - 1

Work out the coordinates of the vertex that A maps to after

a) Danielle's two reflections.

b) Zachary's two reflections.
.

Answers

The coordinates of the vertex that A maps to after Daniel's reflections are (3, 4) and the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)

How to determine the coordinates of the vertex that A maps to after the two reflections?

From the given figure, the coordinate of the vertex A is represented as:

A = (-5, 2)

The coordinates of the vertex that A maps to after Daniel's reflections

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A' = (5 - 2, 2)

Evaluate the difference

A' = (3, 2)

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A'' = (3, -2 + 4)

Evaluate the difference

A'' = (3, 4)

Hence, the coordinates of the vertex that A maps to after Daniel's reflections are (3, 4)

The coordinates of the vertex that A maps to after Zachary's reflections

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A' = (-5, -2 + 4)

Evaluate the difference

A' = (-5, 2)

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A'' = (5 - 2, 2)

Evaluate the difference

A'' = (3, 2)

Hence, the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)