Show that (2.1) is a solution of the system of equations.
Substitute (2, 1) into x + 3y = 5 to get -
Simplify the equation to get -
Substitute (2, 1) into y = -x+ 3 to get -
Simplify the equation to get -

Show That (2.1) Is A Solution Of The System Of Equations.Substitute (2, 1) Into X + 3y = 5 To Get -Simplify

Answers

Answer 1

Answer:

Substitute (2, 1) into x + 3y = 5 to get  2 + 3(1) = 5

Simplify the equation to get 5 = 5 is true

Substitute (2, 1) into y = –x + 3 to get 1 = -(2) + 3

Simplify the equation to get 1 = 1 is true

Step-by-step explanation: well i am doing it right now and i got it right


Related Questions

Humberto deposited $50 in a new account at his bank. The bank pays 5.3% annual simple interest on this account. Humberto makes no additional deposits or withdrawals. How much money will be in his account at the end of 5.5 years?

Answers

Answer:

$58.415

Step-by-step explanation:

Initial value: 50 dollars

Independent variable: 5.3%

Dependent variable: Y

This equation can be written in slope intercept form:

[tex]y=mx+b[/tex]

[tex]y= 1.53x+50[/tex]

x= the number of years

[tex]y= 1.53(5.5)+50[/tex]

[tex]y=8.415+ 50[/tex]

[tex]y= 58.415[/tex]

State the slope and y-intercept of the graph of the equation y = 3x + 2

The slope is _________.

The y-intercept is ____________-

Answers

Slope 3
Intercept is 2

A company is designing a new cylindrical water bottle. The volume of the bottle will be 187 cmcubed. The height of the water bottle is 7.3 cm. What is the radius of the water​ bottle? Use 3.14 for pi.

Answers

Answer:

2.86cm

Step-by-step explanation:

Step 1:

Data obtained from the question. This includes the following:

Volume (V) = 187cm3

Height (h) = 7.3cm

Pi (π) = 3.14

Radius (r) =..?

Step 2:

Determination of the radius of the cylindrical water bottle.

The radius of the cylindrical water bottle can be obtained as follow:

V = πr^2h

187 = 3.14 x r^2 x 7.3

Divide both side by 3.14 x 7.3

r^2 = 187 / (3.14 x 7.3)

Take the square root of both side

r = √[187 / (3.14 x 7.3)]

r = 2.86cm

Therefore, the radius of the cylindrical water bottle is 2.86cm

Find the smallest number to be Find the smallest number to be added to 2345 to get the nearest perfect square.

Answers

Answer:

48^2 =2304 < 2345 < 2401 = 49^2

=> Smallest number should be: 2401 - 2345 = 56

Hope this helps!

:)

Answer:

56

Step-by-step explanation:

sqrt(2345) = 48.425...

Nearest integer is 49

So, the nearest perfect is 49²

49² = 2401

To be added:

2401 - 2345

56

If the point (a,1) lies on the line y = 3x - 5, what is the value of a?

Answers

Answer:

a = 2

Step-by-step explanation:

Note that a point uses (x , y).

y = 1

x = a

Plug in 1 for y in the equation, and a for x:

y = 3x - 5

1 = 3a - 5

Isolate the variable, a. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First add 5 to both sides:

1 (+5) = 3a - 5 (+5)

1 + 5 = 3a

6 = 3a

Next, divide 3 from both sides:

(6)/3 = (3a)/3

a = 6/3

a = 2

2 is your value for a.

~

Sandy was given this function. f(x)=3x2−24+1/3 She used the method of completing the square to rewrite the function. In this second step of her process, r and s are real numbers. f(x)=3(x2−8x+r)+1/3+s What are the values of r and s? Enter your answers in the boxes.

Answers

Answer:

[tex]r = 16[/tex], [tex]s = -48[/tex]

Step-by-step explanation:

The values of [tex]r[/tex] and [tex]s[/tex] can be found with the help of algebraic manipulation on the second-order polynomial described on statement:

[tex]f(x) = 3\cdot x^{2} - 24\cdot x + \frac{1}{3}[/tex]

[tex]f(x) = 3\cdot (x^{2} - 8\cdot x) + \frac{1}{3}[/tex]

[tex]f(x) = 3\cdot (x^{2} - 8\cdot x + 16 - 16) + \frac{1}{3}[/tex]

[tex]f(x) = 3\cdot (x^{2}-8\cdot x + 16) + \frac{1}{3} - 48[/tex]

By comparing each expression, the results are presented below:

[tex]r = 16[/tex], [tex]s = -48[/tex]

Find the exact value of sin 300°.

Answers

Answer:

-0.86602540378 or -√3/2

The probability that Shruti succeeds at any given free-throw is 80%, percent. She was curious how many free-throws she can expect to succeed in a sample of 12 free-throws.


She simulated 25 samples of 12 free-throws where each free-throw had a 0.8, point, 8 probability of being a success.


Shruti counted how many free-throws were successes in each simulated sample. Here are her results:


Use her results to estimate the probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

Give your answer as either a fraction or a decimal.

Answers

Answer:

0.5584 probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either she makes it, or she does not. The probability of making a free throw is independent of other free throws. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that Shruti succeeds at any given free-throw is 80%, percent.

This means that [tex]p = 0.8[/tex]

Sample of 12 free throws:

This means that [tex]n = 12[/tex]

Use her results to estimate the probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 10) = C_{12,10}.(0.8)^{10}.(0.2)^{2} = 0.2835[/tex]

[tex]P(X = 11) = C_{12,11}.(0.8)^{11}.(0.2)^{1} = 0.2062[/tex]

[tex]P(X = 12) = C_{12,12}.(0.8)^{12}.(0.2)^{0} = 0.0687[/tex]

[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) = 0.2835 + 0.2062 + 0.0687 = 0.5584[/tex]

0.5584 probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

Answer:0.8

Step-by-step explanation:in 5 of the 25 stimulated trials, scrutiny continued federal than 10 successes

Which statement about the angle measure is true

Answers

Answer:

D

Step-by-step explanation:

each angle of the triangle is 95° and the second angle has to be in alphabetical order

The true statement is ∠BAC + ∠ABC = 95°

What is an angle?

An angle is a figure formed by two rays or lines that share a common endpoint, called the vertex.

Angles can lie in a plane or be formed by the intersection of two planes or two curves. A reflex angle is an angle that is greater than 180 degrees but less than 360 degrees.

Given is a figure, we need to find the correct answer from the option,

We know that,

The sum of two opposite interior angles of a triangle is equal to the measurement of the exterior angle.

Therefore,

∠BAC + ∠ABC = ∠ACD

∠BAC + ∠ABC = 95°

Hence, the true statement is ∠BAC + ∠ABC = 95°

Learn more about angles, click;

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Reduce the following mixed number 2 2/8

Answers

Answer:

2 1/4

Step-by-step explanation:

2 2/8

The top and bottom of the fraction can be divided by 2

2 1/4

if anyone know probability stuff pls help w this!!

Answers

Answer:

A - 9/34

B - 7/34

Step-by-step explanation:

A girl grabs a lollipop - 9/34 (Event A)

A boy grabs a fruit chew - 7/34 (Event B)

Because there are 34 possibilities in total....

Thanks!

i need the missing blanks .

Answers

Answer:

K, (-3.5,-5), E, (3.5, 3)

Step-by-step explanation:

The function f(x)=200/x + 10 models the cost per student of a field trip when x students go on the trip. How is the parent function f(x)=1/x transformed to create the function f(x)=200/x + 10

Answers

Answer:

Step-by-step explanation:

We need to explain the transformations applied to 1/x to get f(x). We get f by following the following steps.

1. Multiply 1/x by 200 to get the function 200/x. This represents taking the graph of 1/x and expanding it vertically by a factor of 200.

2. Sum 10 units to 200/x. This represents a vertical shift of 10 units to the graph of 200/x.

Find the surface area of a right cone that has a diameter of 11.2 feet and a height of 9.2 feet. Round your answer to the nearest hundredth.

Answers

Answer:

S=288ft^2

Step-by-step explanation:

d=11.2ft, h=9.2ft

r=d/2=11.2/2=5.6

e=√r^2+h^2=√5.6^2+9.2^2

e=10.77ft

s=πr^2+πre

s=π(5.6)^2+π(5.6) (10.77)

s=91.67π

s≈288ft^2

If the slant height of the cone is 10.77 feet and the radius of the base circle is 5.6 feet. Then the surface area of the cone is 189.48 square feet.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The height of the cone is 9.2 feet and the diameter is 11.2 feet. Then the radius will be

r = d/2

r = 11.2/2

r = 5.6

Then the slant height of the cone will be

[tex]l = \sqrt{5.6^2 + 9.2}\\\\l = 10.77 \ \rm ft[/tex]

Then the surface area of the cone will be

[tex]\rm Surface \ area = \pi rl\\\\Surface \ area = \pi \times 5.6 \times 10.77\\\\Surface \ area = 189.48 \ ft^2[/tex]

More about the geometry link is given below.

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2x² - x-6=0 resuelve

Answers

Answer:

x = -3/2          x=2

Step-by-step explanation:

2x² - x-6=0

Factor

(2x     ) (x      ) =0

6 = 2*3

2*-2 +3 = -1

(2x  +3   ) (x  -2    ) =0

2x+3 =0      x-2 =0

2x = -3            x=2

x = -3/2          x=2

The line plot shows the number of bags of grapes,grouped by weight, to the nearest 1/8 pound. How many bags of grapes had a weight of 3/8 pound or less

Answers

Answer:

2.25 pounds

Step-by-step explanation:

The diagram showing the weight of bags with grapes is shown in the attached file below.

From the diagram; number of  bags of grapes that had a weight of [tex]\dfrac{3}{8}[/tex] pounds or less is:

[tex]\dfrac{3}{8}[/tex] pounds  = 3

[tex]\dfrac{1}{4}[/tex] pounds = 4

[tex]\dfrac{1}{8}[/tex] pounds = 1

Thus; the total is = 3+4+1 = 8

However, The total weight of the grapes in the bag that had a weight of  [tex]\dfrac{3}{8}[/tex] pounds or less is :

= [tex]\dfrac{3}{8}(3) + \dfrac{1}{4}(4) + \dfrac{1}{8}(1)[/tex]

= [tex]\dfrac{9}{8} + 1 + \dfrac{1}{8}[/tex]

= [tex]\dfrac{9+8+1}{8}[/tex]

= [tex]\dfrac{18}{8}[/tex]

= 2.25 pounds

easy geometric shapes question!

Answers

Answer:

Cylinder

Step-by-step explanation:

The given geometric shape is of a cylinder.

Answer:

Cylinder

Step-by-step explanation:

The shape will make a cylinder if put together.

Which reason best describes why you can divide any number by 10 by moving the decimal point one place to the left?

1.Dividing a number by 10 is the same as subtracting the number ten times.

2. Dividing by 10 is the same as removing a zero.

3. Moving the decimal point left makes the number smaller.

4. Moving the decimal point one place to the left makes the number 1/10 of its original value.

Answers

4 is the answer

The next best is 3

two integers that multiply to 18 and add to -11

Answers

Answer:

-9 and 2

Step-by-step explanation:

Isaiah was given a gift card for a coffee shop. Each morning, Isaiah uses the card to buy one cup of coffee. Each cup of coffee costs $2.50 and after buying 16 cups of coffee, the card had a $5 remaining balance. Write an equation for A(x),A(x), representing the amount money remaining on the card after buying xx cups of coffee.

Answers

Answer:

$45-$2.50xx

Step-by-step explanation:

Let first of all determine the original amount on the gift card as follows

amount utilized=$2.50*16=$40

balance left after utilizing $40=$5

original amount on the gift card=amount utilized+balance left=$40+$5=$45

if xx cups of coffee is purchased ,the amount utilized would be xx*$2.50

i.e $2.50xx

The equation for the amount left would total amount on the gift card minus the $2.50xx

equation for amount remaining =$45-$2.50xx

If the questioner has duplicated x,which means he or she meant just x

equation of the amount remaining would=$45-$2.50x

What is 13 - 4 x = 1 - x?

Answers

Answer:

x=4

Step-by-step explanation

Answer:

x = 4

Explanation:                                                                                                                  

You start with a penny which doubles each day for 30 days. How much money would you have after 30 days?



Answers

Answer:

$5,368,709.12

Step-by-step explanation:

Kono Dio Da!!

Answer:

5368709.12

Step-by-step explanation:

i just did this earlier

What is the mean and median of 25,50,58,54,55

Answers

Answer:

median = 58

mean= 48.4

Step-by-step explanation:

to find the mean you add all of the numbers and divide it by 5 in this case

the mean is 48.2
the median is 54

100 POINTS!!!!!! the following stem and leaf plot shows the number of hours that mrs. dixon's students spent on their pre calc work last week. what is the mean absolute deviation for the data

Answers

Answer:

11.2467

Step-by-step explanation:

First we need to find the mean

Add up all the data and divide by number of points)

(6+7+8+10+12+13+14+17+17+17+18+19+21+23+24+24+25+27+31+31+32+36+36+39+41+45+45+46+49+50)/30

261/10

26.1

Then to find the mean absolute deviation take each value and find the absolute value from the mean and sum it and then divide by the number of points

((26.1 -6)+(26.1-7)+(26.1-8)+(26.1-10)+(26.1-12)+(26.1-13)+(26.1-14)+(26.1-17)+(26.1-17)+(26.1-17)+(26.1-18)+(26.1-19)+(26.1-21)+(26.1-23)+(26.1-24)+(26.1-24)+(26.1-25)+(27-26.1)+(31-26.1)+(31-26.1)+(32-26.1)+(36-26.1)+(36-26.1)+(39-26.1)+(41-26.1)+(45-26.1)+(45-26.1)+(46-26.1)+(49-26.1)+(50-26.1))/30

11.2467

Answer:

11 16/75

Step-by-step explanation:

Find the mean: sum/n

783/30

26.1

Find individual |x - 26.1| and add them:

|6-26.1| + |7-26.1| + ...... + |50-26.1|

= 20.1 + 19.1 + .... + 23.9

= 336.4

M.A.D = 336.4/30

11 16/75

A sample space consists of 80 separate events that are equally likely. What is the probability of each? A sample space consists of 80 separate events that are equally likely. What is the probability of each?

Answers

Answer:

1/80

Step-by-step explanation:

The probability of selecting each of the event in the sample space is; 1/80

How to Find the Probability?

We are given;

Sample Space = 80 separate events

Now, we are told that each event is equally likely to be selected.

Thus;

Probability of selecting each event = 1/80

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Construct a histogram to display for each given data set.

The data for the circumferences of the pumpkins in the Jeffiers' family pumpkin crop are 22.1, 35.6, 15.8, 36.9, 40.0, 28.5, 38.4, 20.4, 25.8, 34.1, 39.9, 42.2, 24.3, 22.7, 19.8, 27.9, 22.2, 34.3, 40.4, 20.6, 38.2, and 18.1. Use 10 sx < 20 as the first interval.

Answers

Answer:

See attachement

Step-by-step explanation:

The interval 0-20 on vertical axis will be skipped on paper graph and graph will start from 20.

please help quickly !

Answers

Answer:

75-52.5 =x

Step-by-step explanation:

We know that the total amount they eat is 75

They eat 52.5 is acacia leaves.  The rest is other types of leaves

75 - 52.5 = other types of leaves

75-52.5 =x

Which is the correct way to model the equation-+8 = 7x+(-8) using algebra tiles?
1 positive x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 positive unit tiles on the right side
8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side
1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side
8 positive x-tiles and 1 negative unit tile on the left side; 8 negative X-tiles and 7 positive unit tiles on the right side
VX

Answers

Answer:

Step-by-step explanation:

1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side

Answer:

the answer is c

Step-by-step explanation:

how do you write 2x - 2y = 8 in slope-intercept form ?

Answers

Answer:

y=x-4

Step-by-step explanation:

The general scaffold for the slope intercept form is y=mx+b, where m is the slope and b is the y intercept. You can rearrange the equation that you are given like this:

2x-2y=8

-2y=-2x+8

y=x-4

Hope this helps!

Answer:

Rearrange the equation so that it is written in slope intercept form:

y=mx+b.

2x+2y=8.

2y=−2x+8.

y=−x+4.

3x-2y=2 in slope intercept form

Answers

Answer:

y= - 3/2x + 1

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