Solve the system of linear equations by graphing. y−x=17 y=4x+2

Answer:

A) 8, 15, 17.

Step-by-step explanation:

Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option  (the hypotenuse) that means that those numbers could be the sides of a right triangle.

The Pythagorean theorem states that: [tex]a^2+b^2=c^2[/tex]

Thus:

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

Option A:

[tex]\sqrt{8^2+15^2}=17[/tex] → 17 = 17 OK!

Option B:

[tex]\sqrt{6^2+8^2}  = 10[/tex] → 10 ≠ 12 NO

Option C:

[tex]\sqrt{9^2+11^2} = [tex]\sqrt{202}[/tex][/tex] → [tex]\sqrt{202}[/tex] ≠ 21 NO

Option D:

[tex]\sqrt{4^2+13^2} = \sqrt{185}[/tex] → [tex]\sqrt{185}[/tex] ≠ 16 NO

Brian should purchase Choice C of fabric

Solution:

Given that Brian wants to purchase a piece of fabric  that is between 49 and 53 inches long

So piece of fabric should be between: 49 and 53 inches

Let us convert feet to inches

[tex]4\frac{3}{4} feet = \frac{4 \times 4 + 3}{4} = \frac{19}{4} feet[/tex]

Now convert to inches

We know that,

1 feet = 12 inches

[tex]\frac{19}{4} feet = \frac{19}{4} \times 12 = 57 inches[/tex]

But this choice is greater than given condition that piece of fabric should be between: 49 and 53 inches

So this is not correct

[tex]4\frac{1}{2} feet = \frac{2 \times 4 + 1}{2} = \frac{9}{2} feet[/tex]

Now convert to inches

[tex]\frac{9}{2} feet = \frac{9}{2} \times 12 inches = 54 inches[/tex]

But this choice is greater than given condition that piece of fabric should be between: 49 and 53 inches

So this is not correct

[tex]4\frac{1}{3} feet = \frac{3 \times 4 + 1}{3} = \frac{13}{3} feet[/tex]

Now convert to inches

[tex]\frac{13}{3} feet = \frac{13}{3} \times 12 inches = 52 inches[/tex]

So this 52 inches lies between 49 and 53 inches

So Brian should purchase Choice C of fabric

Answer:

Step-by-step explanation:

I think it means every data value should be equal to the "mean" to make the standard variation of this set to be zero. Or all data value of the set are equal.

Question:

Ten subtracted from the quotient of a number and 5 is 18. What is the number?

Answer:

140 is the number.

Step-by-step explanation:

Let consider the number as ‘X’

Quotient of a number and 5 can be written as

                         [tex]X \div 5[/tex]

Ten subtracted from the quotient of a number and 5 can be written as

                        [tex](X \div 5) - 10[/tex]

Ten subtracted from the quotient of a number and 5 is 18 can be written as

                        [tex](X \div 5) - 10 = 18[/tex]

By solving the above equation, find ‘X’

                        [tex](X \div 5) = 18 + 10[/tex]

                        [tex]\frac{X}{5} = 28[/tex]

                        [tex]X = 28 \times 5 = 140[/tex]

Answer:

365.35

Step-by-step explanation:

USE A CALCULATOR!!!!

Answer:

The thickness of 1 card  = 0.0025 inches

Step-by-step explanation:

Here, the total number of cards in the stack = 250 cards

The total height of the stack = 5/8 inch = 0.625 in.

[tex]\textrm{Thickness of one card} = \frac{\textrm{The total thickness of the stack}}{\textrm{The total cards in the stack}}[/tex]

[tex]\implies \textrm{Thickness of one card} =\frac{0.625}{250} = 0.0025[/tex]

Hence, the thickness of 1 card  = 0.0025 inches

The valid conclusion based on the provided data is that 15% of students in the sample are below grade level in math, but this does not necessarily indicate the same for all students in grade 6 at HACS.

The question pertains to drawing a valid conclusion from given statistical data about the math proficiency level of students in a specific school.

When it states that 15% of students are below grade level in math, the conclusion can only pertain to the group specified in the data set.

Therefore, the most valid conclusion from the given choices is that 15% of students in the sample are below grade level in math, and we cannot infer the same for the entire grade 6 at High Achievers Charter School (HACS) without further context.

In light of the provided information, one cannot come to any conclusions regarding the math proficiency of students in other grades, nor can one generalize to all students in grade 6 at HACS from a mere sample unless the sample is clearly stated to be the entirety of the grade.

The correct conclusion is B. 15% of all students in grade 6 at HACS are below grade level in math.

To understand why this conclusion is valid, let's analyze the given information and the options provided:

- The school board determined that 15% of the students who took the test were below grade level in math. Since the test was administered to all grade 6 students at HACS, this percentage applies to the entire population of grade 6 students at the school, not just a sample.

Now, let's evaluate the conclusions:

A) 15% of students in the sample are below grade level in math, but we cannot conclude anything about the students in grade 6 at HACS.

- This conclusion is incorrect because the sample includes all grade 6 students at HACS. Therefore, we can generalize the results to the entire population of grade 6 students at the school.

B) 15% of all students in grade 6 at HACS are below grade level in math.

- This conclusion is correct because the test was given to all students in grade 6 at HACS, making the sample representative of the entire population of grade 6 students. Thus, the 15% figure accurately reflects the proportion of grade 6 students at HACS who are below grade level in math.

C) 15% of all students at HACS are below grade level in math.

- This conclusion is incorrect because the test was only administered to grade 6 students. We do not have data on students in other grades at HACS, so we cannot extend the 15% figure to the entire student body of the school.

Answer:

The point lie outside the circle

Step-by-step explanation:

step 1

Find the distance between the center of the circle and the given point

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

(0,0) and (-3,-7)

substitute the values

[tex]d=\sqrt{(-7-0)^{2}+(-3-0)^{2}}[/tex]

[tex]d=\sqrt{58}\ units[/tex]

step 2

Compare the distance with the radius

If d=r ----> the point lie on the circle

If d > r -----> the point lie outside the circle

If d < r -----> the point lie inside the circle

we have

[tex]d=\sqrt{58}\ units[/tex]

[tex]r=\sqrt{53}\ units[/tex]

so

[tex]\sqrt{58}\ units > \sqrt{53}\ units[/tex]

[tex]d > r[/tex]

therefore

The point lie outside the circle

Answer:

C outside the circle

Step-by-step explanation:

khan

Answer:

y <= -8

Step-by-step explanation:

This algebraic expression would read as:

Y is Less than or equal to -8

Answer:

No more than means less than or equal to

y <= -8

Answer:

Step-by-step explanation:

4 cm to 25 miles = 20 cm to x miles

4 / 25 = 20 / x

cross multiply

4x = (25)(20)

4x = 500

x = 500/4

x = 125 miles <=====

Answer:

The correct answer is that the actual distance in miles represented by a line that is 20 cm on map is 125 miles.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Scale on a map: 4 cm = 25 miles

2.  What is the actual distance in miles represented by a line that is 20 cm on map ?

For calculating the distance in miles represented, we will use the following equation:

Actual distance in miles represented = Miles in the scale/Centimeters in the scale * 20

Replacing with the real values:

Actual distance in miles represented = 25/4 * 20 = 25 * 5 = 125

The correct answer is that the actual distance in miles represented by a line that is 20 cm on map is 125 miles.

Answer:

100

Step-by-step explanation:

It will help in the future to memorize your time tables

10*10 is basically 10 plus 10, 10 times but in a easier form

10+10+10+10+10+10+10+10+10+10=100

10+10=20

20+10=30

30+10=40

40+10=50

50+10=60

60+10=70

70+10=80

80+10=90

90+10=100

Answer:

well it would kinda depend on their age,and size,but the average height of an ADULT male is : 5.6 ft

ADULT female:5.2ft

(remember it would depend on their age,but some people might even have medical reasons to be shorter or taller than their original height too. At a age children don't HAVE to be that exact height,but atleast close enough to that height.)

(changes may occur depending on medical reasons,or age too!)

Answer:

?

Step-by-step explanation:

It could be

Answer:

Yes

Step-by-step explanation:

Yes because it is a one-to-one relation. Every x-value maps to a unique value of y.

Answer:

The possible values of v are 6 and -6

Step-by-step explanation:

The opposite operation of an absolute value is to add a ± to the other side, so when we solve for v we get

|v|=6

v=±6

Which is the same as

v=-6 and 6

Answer:

C

Step-by-step explanation:

|6| and |-6| have the same meaning. Both are equal to 6

The answer is C

Work is provided in the image attached.

Answer:

The reflection will be on the point (3, 5).

Step-by-step explanation:

For a given point (x, y) reflection along the line x = k, the co-ordinates will be:

[tex]$ R_{x = k} (x, y) = (2k - x, y) $[/tex].

Here, we have (x, y) = (-1, 5)

Reflection across the line x = 1, we have:

[tex]$ R_{x = 1} (-1, 5) = (2(1) - (-1), 5) $[/tex]

                                  = (3, 5)

Hence, the reflection of the point (-1, 5) would be the point (3, 5).

Answer:

4 workers

Step-by-step explanation:

A group of 9 workers was assigned to paint the walls in a house, which could be completed in 48 hours. Then 1 worker will complete the whole job in [tex]48\times 9=432[/tex] hours.

If 1 worker completes the whole work in 432 hours, then he completes [tex]\dfrac{1}{432}[/tex] of the work per hour.

9 workers complete [tex]9\times\dfrac{1}{432}=\dfrac{1}{48}[/tex] of work per hour and complete [tex]\dfrac{1}{48}\times 8=\dfrac{1}{6}[/tex] of work in 8 hours.

[tex]1-\dfrac{1}{6}=\dfrac{5}{6}[/tex] of work left.

This could be completed by n workers in 72 hours, so

[tex]\dfrac{n}{432} \times 72=\dfrac{5}{6}\\ \\\dfrac{n}{6}=\dfrac{5}{6}\\ \\n=5[/tex]

9 - 5 = 4 workers left the team.

Answer:

So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.

Step-by-step explanation:

We are given a function and we have to find the intervals in which the function has positive value.

y = [tex]x^{2} +12x+27[/tex]

y =(x + 3)(x + 9)

For the function to be positive , y ≥ 0

(x + 3)(x +  9) ≥ 0

Here there are two cases , either both should be positive or both should be negative.

If both are positive,

(x + 3)≥0 and (x + 9)≥0

So, x ≥ -3

If both are negative,

(x + 3)≤0 and (x + 9)≤0

So, x ≤ -9

So the values of x for which the function is positive are x ≥ -3 and x ≤ -9.

The intervals on which the function y = x² + 12x + 27 is positive are

x > -3 and x > -9

For the function given to be positive, it has to be greater than zero.

Since the expression is greater then zero, hence;

x² + 12x + 27 > 0

Factorize the resulting expression

x² + 3x + 9x + 27 > 0

x(x+3) + 9(x+3) > 0

(x+3) (x+9) > 0

x+3 > 0 and x + 9 > 0

x > -3 and x > -9

Hence the intervals on which the function y = x² + 12x + 27 is positive are

x > -3 and x > -9

Learn more here: https://brainly.com/question/17845639

Answer:

i think C

Step-by-step explanation:

Answer:

rate of interest=R=5.5%

Step-by-step explanation:

given principle=P=$1200

simple interest=S.I=$396

time=T=6 years

simple interest=[tex]\frac{P\times R\times T}{100}[/tex]

$396=[tex]\frac{1200\times R\times 6}{100}[/tex]

$396=[tex]72\times R[/tex]

R=[tex]396\div 72[/tex]

R=5.5%

rate of interest=R=5.5% answer

3 small boxes and 6 large boxes were sent to the retailer.

Step-by-step explanation:

Number of books held by small boxes = 30

Number of books held by large boxes = 40

Total books held by boxes = 330

Let,

x represent the number of small boxes

y represent the number of large boxes

According to given statement;

y = 2x     Eqn 1

30x+40y=330    Eqn 2

Putting value of y from Eqn 1 in Eqn 2

[tex]30x+40(2x)=330\\30x+80x=330\\110x=330[/tex]

Dividing both sides by 110

[tex]\frac{110x}{110}=\frac{330}{110}\\x=3[/tex]

Putting x=3 in Eqn 1

[tex]y=2(3)\\y=6[/tex]

3 small boxes and 6 large boxes were sent to the retailer.

Keywords: linear equation, substitution method

Learn more about substitution method at:

#LearnwithBrainly

Answer:

The conversion of 2000 ft per min into miles per hour is 2.268 miles per hour .

Step-by-step explanation:

Given as :

The speed = s = 2000 ft per min

Now, ∵ 5280 feet = 1 miles

so, 1 feet = [tex]\dfrac{1}{5280}[/tex] miles

∴ 2000 feet =  [tex]\dfrac{1}{5280}[/tex] × 2000 miles

i.e 2000 feet = 0.378 miles

Again

∵ 1 minute = [tex]\dfrac{1}{60}[/tex] hour

So, The speed in miles per hour

s = [tex]\dfrac{distance}{time}[/tex]

∴ s = [tex]\frac{0.378}{\frac{1}{60}}[/tex]

i.e s = 2.268 miles per hour

Hence, The conversion of 2000 ft per min into miles per hour is 2.268 miles per hour . answer

To convert 2000 ft./min. to miles per hour, multiply by appropriate conversion factors, and round the result, yielding 22.7 miles per hour.

To convert 2000 ft./min. to miles per hour, follow these steps:

Convert feet to miles: 2000 ft/min x (1 mile/5280 ft) = 0.3788 miles/min

Convert minutes to hours: 0.3788 miles/min x 60 min/hr = 22.73 miles/hr

Rounded to the nearest tenth, 2000 ft/min is 22.7 miles per hour.

Answer:

1.8

Step-by-step explanation:

Do the long division.

Money earned after working for 15 hours and making 8 deliveries is $ 534

Solution:

Given that pizza delivery person earns 30 per hour plus 10.50 for each delivery made

The expression used to find the earnings for him is given as:

30h + 10.50d

Where "h" is the number of hours and "d" is the number of deliveries

We have to find the money earned by him after working for 15 hours and making 8 deliveries

Therefore we get, h = 15 and d = 8

Substitute h = 15 and d = 8 in given expression

Money earned = 30(15) + 10.50(8)

Money earned = 450 + 84 = 534

Thus money earned after working for 15 hours and making 8 deliveries is $ 534

Answer:

(i) 5

(ii) - 1

(iii) - 1

(iv) 0

(v) 1

(vi) 1

Step-by-step explanation:

See the graph attached to this question.

The blue graph shows y = f(x) and the red graph shows y = g(x).

(i) (f + g)(- 3) = f(-3) + g(-3) = 4 + 1 = 5

(ii) (g - f)(- 2) = g(- 2) - f(- 2) = 2 - 3 = - 1

(iii) (fg)(2) = f(2) × g(2) = (- 1) × (1) = - 1

(iv) [tex](\frac{g}{f})(3) = \frac{g(3)}{f(3)} = \frac{0}{- 3} = 0[/tex]

(v) (fog)(1) = f[g(1)] = f(1) = 1

(vi) (gog)(- 1) = g[g(-1)] = g(2) = 1  (Answer)

After using the graph with the values of f and g we find the values as follows:

(i) (f+g)(-3) = 5

(ii) (g-f)(-2) = -1

(iii) (fg) (2) = -1

(iv) (g/f) (3) = 0

(v) (f o g) (1) = 1

(vi) (g o g)(-1) = 1

i) ( f +g ) (-3)

= ( f (-3) + g(-3) )

Values we got from the graph are:

f(-3) = 4

g(-3) = 1

After substituting these values in the given equation we get

( f + g) (-3) = 5

ii) ( g - f ) (-2)

= ( g(-2) - f(-2) )

Values we got from the graph are:

g(-2) = 2

f(-2) = 3

After substituting these values in the given equation we get

( g - f ) (-2) = - 1

iii) ( fg) (2)

= ( f(2) g(2))

Values we got from the graph are:

f(2) = -1

g(2) = 1

After substituting these values in the given equation we get

( fg)(2) = -1

iv) (g/f) (3)

( g(3) / f(3) )

Values we got from the graph are:

g(3) = 0

f(3) = - 3

After substituting these values in the given equation we get

( g / f ) (3) = 0

v) ( f o g ) (1)

= ( f(1) o g(1) )

Values we got from the graph are:

g(1) = 1

f(1) = 1

After substituting these values in the given equation we get

( f o g ) (1) = 1

vi) ( g o g ) (-1)

= ( g(-1) o g(-1) )

Values we got from the graph are:

g(-1) = 2

g(2) = 1

After substituting these values in the given equation we get

( g o g ) (-1) = 1

Answer:

$150.

Step-by-step explanation:

$250 - 0.20 *250 = $200.

Final price = 200 - 0.25*200

= $150.

Answer:

  [tex]32\text{ for }x=0.\overline{40}[/tex]

Step-by-step explanation:

It looks like you want the sum of digits of the product ...

  [tex]x = (0.\overline{6})(0.\overline{60})=\dfrac{2}{3}\cdot\dfrac{20}{33}=\dfrac{40}{99}=0.\overline{40}[/tex]

Since the decimal fraction starts off with 4 and has an even number of repeating digits, there will be 8 4's and 7 0's in the sum of the first 15 decimal digits:

  sum = 8×4 +7×0 = 32

The sum of the first 15 digits after the decimal point is 32.

Answer:

x=-19/5

Step-by-step explanation:

-3x=2x+19

-3x-2x=19

-5x=19

x=19/-5

Answer:

get x to one side by subtracting 2x from 2x+19

new equation:

-3x-2x=19

-5x=19

divide both sides by -5

x=-19/5

or x=-3 4/5

Answer:

The last system is that one with exactly one solution:

–2x + 7y = –5  

2x + 7y = –9

Step-by-step explanation:

We can easily check the number of solutions that each system has in this problem, since the equations contain most of them combinations of terms in y and in x that can be easily cancelled out via simple term by term addition.

Going through them system by system, and adding term by term the equations which are in standard form we get:

(1) –5x – 10y = 24  

      5x + 10y = 16  

---------------------------

     0x  +  0y   = 40  which sates a mathematical absurd: "0 = 40", and therefore there are no x and y solution values that could verify such. This also means that the lines represented by the system do NOT intersect (they are parallel lines)

(2)  3x + 4y = –7  

   –3x – 4y = 7  

   --------------------

    0x   + 0y  = 0 which gives that zero equals zero, which any pair (x, y) belonging to any of the two equations can verify, so an infinite number of solutions (the lines in the system overlap)

(3) –12x + 8y = 16  

      12x – 8y = 16  

      -------------------

       0x  +  0y   = 32 which sates a mathematical absurd: "0 = 2", and therefore there are no x and y solution values that could verify such. This also means that the lines represented by the system do NOT intersect (they are parallel lines)

(4)  –2x + 7y = –5  

        2x + 7y = –9

      ---------------------

        0x + 14y = -14

This is the only system that shows solution. It allows us first to solve for "y" in the resultant equation: 14 y = -14 giving us the value y = -14/14 = -1

and then using it the unique value for x can be determined:

        2x + 7y = –9

        2x + 7 (-1) = -9

        2x -7 = -9

        2x = -9 + 7

        2x = -2

          x = -2/2 = -1

Therefore, the pair (-1, -1) is the unique solution to the system

Answer:

Step-by-step explanation:

Trust me guys. The guy above me has a full explanation, but if you are just looking for a simple answer, then I gotchu

Answer:

y=3x+6

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

y-y1=m(x-x1)

y-0=3(x-(-2))

y-0=3(x+2)

y=3x+6+0

y=3x+6