Solve the system of equations 3x + y = 3 and 7x + 2y = 1.
1. Solve for the variable y in the first equation:
y=3 - 3x
2. Substitute the value for y into the second equation: 7x + 2(3 - 3x) = 1
3. Solve forx:
X=

With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.

So, in the given situation:

TR and WY are as follows:
TR/WU

24/2

2/1

Similarly,

TS/WV

2/1

7/x

7/3.5

Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

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Answer:

$54.00

Step-by-step explanation:

area of balcony= length * width

area= 3*9

area= 27 sq.feet

cost of 1 sq.feet=$2.00

cost of 27 sq.feet= $2.00*27

cost of 27 sq.feet= $54.00

Answer:

Step-by-step explanation:

This is a reflection over a horizontal line.

Let's find the line by calculating the difference of the y-coordinates of corresponding points:

The middle line is:

The actual answers are A and C.

im taking the assignment right now lol. ♥

Answer:  Correct Answer is 1,3  or A /C

Step-by-step explanation:

1: 2.54 cm/1 in

3: 1 meter/100 cm

The amount of solution A and B required are 60 and 90 ounces respectively.

Creating simultaneous equations for the problem:

Mass of solution A = a

Mass of solution B = b

a + b = 150 _____(1)

0.65a + 0.90b = 150×0.80

0.65a + 0.90b = 120 __(2)

From (1)

a = 150-b ____(3)

substitute (3) into (2)

0.65(150-b) + 0.90b = 120

97.5 - 0.65b + 0.90b = 120

0.25b = 120-97.5

0.25b = 22.5

b = 22.5/0.25

b = 90

a = 150 - b

a = 150 - 90

a = 60

Therefore , 60 ounces of solution A and 90 ounces of solution B is required.

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Answer: $175

Step-by-step explanation:

$7.00 x 15 = $105.00

$105.00 / 3 hours = $35/hr.

$35 x 5 = $175

Mrs. Lovewell needs your help trying to determine where to get the best value for candy to buy to pass out to trick or treaters for Halloween. M & M are her favorite so she looked for all value packs containing M&Ms and other types of candy. Belower are the prices she found for each company:

Amazon: 23.98 for 365 pieces of candy

Walmart: 9.94 for 55 pieces of candy

Target: 15.99 for 150 pieces of candy

Sams: 16.42 for 115 pieces of candy

Dollar general: 10.00 form 100

In order to prove to me what is the best you need to:

Find the Constant of Proportionality for each and show the math for how you found it

Turn each constant of proportionality into an equation

Create a table for each one showing how much 50, 100, 150, 200, and 250 pieces of candy would cost from each store.

This means you will need 5 total tables

Create a graph plotting the numbers for the table

You will plot all 5 stores on the same graph

Make each line a different color to better be able to differentiate

Present a claim for which store would be best, and use your C.O.P as evidence to support.

Answer:

0

Step-by-step explanation:

1. First, we should know the slope-intercept form of any equation: y = mx + b.

2. In the equation y = -2/3(x), it appears that the variables we can see are y, m, and x. However, the y-intercept, b, is still there with the value of 0.

Therefore, the y-intercept is 0.

Answer:

The first one is infinite solutions, Second one is no solution

Step-by-step explanation:

1) 12+4x=4x+12

4x=4x

Infinite Solutions

2) 32x-4=19+32x

-4=19

No Solution

Answer:

15.6

Step-by-step explanation:

complementary angles sum up to 90

90-74.4=15.6

therefore the measure of it's complementary angle is 15.6

The transformation of graph f (x) = x and h (x) = x - 4 is a translation 4 units to the left

The term transformation is used in mathematics to refer to the movements made by objects.

Translation refers to a type of transformation that involve a linear movement.

Movements as seen in translation includes

up

down

left

right

The y coordinate governs movements in the vertical direction that are up and down.

While the x coordinate controls the horizontal movement in the left and right directions.

The movement as described in the graphs f(x) and h(x) is translation 4 units to the left

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Answer:

X intercept (-13,0)

y intercept (0,13/3)

Step-by-step explanation:

slope intercept form

y=1/3x+13/3

Answer:

\(\frac{dP}{dt} \ =\ \frac{1}{5}P\)

Step-by-step explanation:

Given

Variation: Directly Proportional

Insects = 10 million when Rate = 2 million

i.e. \(P = 10\ million\) when \(\frac{dP}{dt} = 2\ million\)

Required

Determine the differential equation for the scenario

The variation can be represented as:

\(\frac{dP}{dt} \ \alpha\ P\)

Which means that the rate at which the insects increase with time is directly proportional to the number of insects

Convert to equation

\(\frac{dP}{dt} \ =\ k * P\)

\(\frac{dP}{dt} \ =\ kP\)

Substitute values for \(\frac{dP}{dt}\) and P

\(2\ million = k * 10\ million\)

Make k the subject

\(k = \frac{2\ million}{10\ million}\)

\(k = \frac{2}{10}\)

\(k = \frac{1}{5}\)

Substitute \(\frac{1}{5}\) for k in \(\frac{dP}{dt} \ =\ k * P\)

\(\frac{dP}{dt} \ =\ \frac{1}{5}* P\)

\(\frac{dP}{dt} \ =\ \frac{1}{5}P\)

Answer:

right triangles

Step-by-step explanation:

Answer:

c.92,598

Step-by-step explanation:

20000 + 20000/1.04 + 20000/(1.04^2) + 20000/(1.04^3) + 20000/(1.04^4)

= 20000 + 19230.77 + 18491.12 + 17779.73 + 17096.08

= 92597.7

= 92,598

Answer:

3 15/17  days

Step-by-step explanation:

let the amount of work done to roof the whole house by x

Time taken by homeowner to roof his house = 11 days

In 11 days homeowner can do x work

in 1 day homeowner can do x/11 work

Time taken by professional to roof the house = 6 days

In 6 days professional can do x work

in 1 day professional can do x/6  work

In 1 day total work done, if both professional and homeowner work together

= x/6 + x/11 = (11x + 6x)/11*6 =  17x/66

17x/66 work is done by both in 1 day

we have to calculate total work done by both , to find this we multiply both side by 66/17 to eliminate it from term containing x(which is the total work done to roof the house)

17x/66 *(66/17)work is done by both in 66/17  days

x work is is done by both in 3 15/17  days.

Hence, it will take  3 15/17  days to roof the house,  if the homeowner helps the roofer.

Answer:

The 80% confidence interval for the population proportion of disks which are defective is (0.059, 0.079).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

Suppose a sample of 1067 floppy disks is drawn. Of these disks, 74 were defective.

This means that \(n = 1067, \pi = \frac{74}{1067} = 0.069\)

80% confidence level

So \(\alpha = 0.2\), z is the value of Z that has a pvalue of \(1 - \frac{0.2}{2} = 0.9\), so \(Z = 1.28\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.069 - 1.28\sqrt{\frac{0.069*0.931}{1067}} = 0.059\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.069 + 1.28\sqrt{\frac{0.069*0.931}{1067}} = 0.079\)

The 80% confidence interval for the population proportion of disks which are defective is (0.059, 0.079).

Answer:

The apple pies sell for a price is 0.64

there are 24 hours in 1 day, so 1 hour alone will be 1/24 of a day.

there are 60 minutes in 1 hour, now, how much is 45 mins of 60 minutes, namely 45/60 = 3/4, so 45 mins is 3/4 of an hour.

so 45 minus is 3/4 of that 1/24 of a day, or namely

\(\cfrac{\stackrel{1}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{4}\cdot \cfrac{1}{\underset{8}{~~\begin{matrix} 24 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{1}{32}\)

Answer:

Triangles in Geometry

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

The area of a parallelogram is

A = bh where b is the base and h is the height

140 = b*10

Divide each side by 10

140/10 = 10b/10

14 = b

Answer:

The listener is approximately 71.414 feet far from the whisperer.

Step-by-step explanation:

We must remember that two fundamental variables for every ellipse are the major semiaxis (\(a\)) and the minor semiaxis (\(b\)). The major semiaxis equals a half of the length of the whispering gallery, whereas the minor semiaxis equals a half of the width of the whispering gallery. These are:

\(a = 46\,ft\) and \(b = 29\,ft\)

The distance between both whisperers (\(d\)), measured in feet, is two times the distance between center and any of the foci (\(c\)), measured in feet, whose valued is obtained by using this Pythagorean identity:

\(d = 2\cdot c\)

\(c = \sqrt{a^{2}-b^{2}}\)

If \(a = 46\,ft\) and \(b = 29\,ft\), then:

\(c = \sqrt{(46\,ft)^{2}-(29\,ft)^{2}}\)

\(c \approx 35.707\,ft\)

\(d = 2\cdot (35.707\,ft)\)

\(d = 71.414\,ft\)

The listener is approximately 71.414 feet far from the whisperer.

Answer:

1 cm and 18 cm

2 cm and 9 cm

3 cm and 6 cm

Step-by-step explanation:

We need to find the factors of 18
which are; 1,18; 2,9; 3,6
So therefore we'd pick:
1 cm and 18 cm

2 cm and 9 cm

3 cm and 6 cm

Answer:

{x!=0, sqrt((1764 x^20)/(36 x^4))} = {x!=0, 7 sqrt(x^16)} thus: 7x^16

Step-by-step explanation:

The equation that represents the total cost that Debra paid is: C = 5N

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Information about the problem:

The function that models the situation is the following:

C = 5N

Where:

Number of notebooks = N

Cost of each notebook = $5

Total cost = C

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Correctly written question:

Debra purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Debra paid.

There is no whole number by which you can multiply or divide 16087 to make it a perfect square.

To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.

In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.

To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.

A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.

Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.

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Step-by-step explanation:

70 to 85 % of his maximum

Maximum is estimated to be 220 - age  = 220 - 42 = 178

70% of this is 125

85 % is 89  151  

I believe I would go with the third choice  116-160 bpm

The best estimate of the solution to the system of linear equations is the point are (x,y) will be (0.76, 4.30).

A linear equation in two variables is one that is written in the form axe + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Given:

as x,y are variables,

-3x + y = 2 ..............(1)

- 4x + 7y = 1 ...........(2)

We know that,

The solution of the system of linear equations is the intersection point of both graphs

Multiply equation (1) by 7 on both sides and then subtract it from eq (2)

- 4x + 7y = 1 ...........(2)

-21x + 7y = 14 ..............(1)

⇒- 17 x = -13

⇒ 17 x = 13

⇒ x =\(\frac{13}{17}\)

⇒ x = 0.76

Now on putting value of x  = 0.76 in eq (1) we get

- 3x + y = 2 ............ (1)

⇒- 3(0.76) + y = 2

⇒y = 4.30

The best estimate of the solution to the system of linear equations is the point (x,y) will be (0.76, 4.30).

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