Solve the system of equations
−5x−3y=−28 and x+2y=0 by combining the equations

So

Hence

Option A

Answer:

Option A

Step-by-step explanation:

y=4x+10

So

Put x ax 12°C

Hence

y=4(12)+10

y=48+10

y=58

Answer:

Mean = 3.125 ≈ 3.13

Step-by-step explanation:

Mean = Sum of numbers =  1 + 2 + 3 + 4 + 2 + 6 + 3 + 4 = 25 = 3.125≈3.13

           Amount of number                     8                             8

The total cost when 881 minutes is used is $477.50.

a + 480b = 277 equation 1

a + 990b = 532 equation 2

Where:

Subtract equation 1 from equation 2

510b = 255

b = 255 / 510

b = $0.50

In order to determine the flat fee, substitute for b in equation 1

a + 480(0.5) = 277

a + 240 = 277

a = 277 - 240

a = $37

Total cost = flat fee + (variable cost x number of minutes spoken)

$37 + (881 x 0.5) = $477.50

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Answer:

6 m²

Step-by-step explanation:

Original area :

12 × 14 = 168 m²

New area :

(12-3) × (14+4) =  

9 × 18 = 162 m²

168 - 162 = 6

Area would change by 6 m²

Probability that the first candy selected is taffy and the second candy is caramel is 0.144.

The data missing in the question is

A box has 18 candies in it: 3 are peppermint, 4 are caramel, and 11 are taffy.

Probability can be defined as the study of likelihood of an event to happen.

It has a range of 0 to 1.

Probability is the ratio of the expected outcomes / total coutcome.

Total outcomes = 18

The probability that the first candy is taffy is 11/18

Now as there is no replacement , the total outcomes can be 17

The probability that the second candy is caramel is 4/17

Probability that the first candy selected is taffy and the second candy is caramel =  (11/18)(4/17)

= 0.144

Therefore the Probability is 0.144

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Answer:

They both have an infinite number of solutions.

Step-by-step explanation:

Given system of equations:

a) 2x + 4y = 15

b) 6x + 12y = 45

Slope-intercept form: y = mx + b

where:

Rewrite both equations into slope-intercept form:

a) 2x + 4y = 15

⇒ 2x + 4y = 15 [subtract 2x from both sides]

⇒ 2x - 2x + 4y = 15 - 2x

⇒ 4y = - 2x + 15 [divide both sides by 4]

⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

b) 6x + 12y = 45

⇒ 6x + 12y = 45 [subtract 6x from both sides]

⇒ 6x - 6x + 12y = 45 - 6x

⇒ 12y = - 6x + 45 [divide both sides by 12]

⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

New equations:

[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.

System of equations can have the following:

No Solution: the same slope (both lines will be parallel)

One Solution: different slopes and different y-intercepts

Infinitely Many Solutions: the same slope and y-intercept

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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.

Equation #1

Subtract 2x from both sides

Divide both sides by 4

Equation #2

Subtract 6x from both sides

Divide both sides by 12

Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other.  Therefore, there are infinite solutions as they will always continue on top of each other.

Answer:

[tex]\frac{1}{102}[/tex]

Step-by-step explanation:

1) Negative Power Rule: [tex]x}^{-a}=\frac{1}{{x}^{a}}[/tex].

[tex]\frac{1}{3}\div 34[/tex]

2) Use this rule: [tex]a\div \frac{b}{c}=a\times \frac{c}{b}[/tex].

[tex]\frac{1}{3}\times \frac{1}{34}[/tex]

3)  Use this rule: [tex]\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}[/tex].

[tex]\frac{1\times 1}{3\times 34}[/tex]

4) Simplify [tex]1\times 1[/tex] to [tex]1[/tex].

[tex]\frac{1}{3\times 34}[/tex]

5) Simplify  [tex]3\times 34[/tex] to [tex]102[/tex] .

[tex]\frac{1}{102}[/tex]

Answer:

Normally,in calculating the amount of space an object occupies...the volume method is require due to 3 dimensional rule,vice versa an area

Answer: 29, 31, 37, 41, 43, 47, 53.

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

the units of measure must be the same, so

2m = 2 × 100 cm = 200 cm

then

[tex]\frac{40}{200}[/tex] × 100%

= 0.2 × 100%

= 20%

Answer:

20%

Step-by-step explanation:

Answer:

Step-by-step explanation:

#a

pattern 0 will include 4 reds in square

Because it's independent of pattern no

#b

Figure 1 has 4+4=8

Figure 2=4+8+2=14

Figure 3=4+12+3=19

The pattern n rule is

So for 13th n

#c

attached

#d

Already given in c

The answers to the question are

The median of the data set is gotten by arranging the values in order

3, 4, 5, 5, 7, 8

The median can be gotten by

5 + 5 / 2

= 10/2

Median = 5

This is the value under which 25 percent of the data are found in the group of data. The lower quartile is 4.

This is the point from which 75 percent of the data is found when it is in ascending order. The upper quartile is 7.

The lowest value in the data set is 3

The highest value in the data set is 8

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The probability that the student was NOT a female that got a "C" is 15 / 32.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C =  15 / 32.

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Answer:

35,000

Step-by-step explanation:

^4 means 4 zeros

10^4 = 10,000

3.5 times 10,000 =

35,000

9880 different possibilities are there in Sally's new combination option second 9880 is correct.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

Total unique numbers consists in a Sally locker = 3

From the digits 0 to 39

Total numbers = 40

Apply combination formula:

= C(40, 3)

= 40!/(3!37!)

= 9880

Thus, 9880 different possibilities are there in Sally's new combination option second 9880 is correct.

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a. A critical point at x = 25 would mean f'(25) = 0 or doesn't exist. We have derivative

[tex]f(x) = x - k \sqrt x \implies f'(x) = 1 - \dfrac k{2\sqrt x}[/tex]

so that

[tex]f'(25) = 1 - \dfrac k{2\sqrt{25}} = 1 - \dfrac k{10} = 0 \implies \boxed{k=10}[/tex]

b. Taking the second derivative, we get

[tex]f''(x) = \dfrac k{4 x^{3/2}} = \dfrac5{2 x^{3/2}}[/tex]

At x = 25, the second derivative has a positive sign,

[tex]f''(25) = \dfrac 5{2 \times 25^{3/2}} = \dfrac 5{2\times5^3} = \dfrac1{50} > 0[/tex]

which means f(x) is concave upward around x = 25, so this critical point is a local minimum.

Answer:

y = 2/3

Step-by-step explanation:

Assuming you are looking for "y":

15 * ( y - 4 ) - 2 * (y - 9 ) + 5 * (y + 6) = 0

15y - 60 - 2y + 18 + 5y + 30 = 0

15y - 2y + 5y -60 + 18 + 30 = 0

18y = 60 - 18 - 30

18y = 12

y = 12/18

y = 2/3

The equation of the scatter plot is (a) y = 100x + 2

The line of best fit of the scatter plot passes through the points

(x,y) = (0,2) and (1,102)

Start by calculating the slope using:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{102 - 2}{1 - 0}[/tex]

m = 100

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 100(x -0) + 2

Evaluate

y = 100x + 2

Hence, the equation of the scatter plot is (a) y = 100x + 2

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When Leonardo and his wife file married filing jointly in 2021, the average tax rate will be 15.63 percent

In the question above, Leonardo's taxable income = $80,000

Theresa's taxable income = $15,000

Total taxable income for both of them will be:

$ 80,000 + $ 50,000 = $ 130,000

When you make use of the Schedule Y-1,

The amount of the tax on total income shall be said as:

Tax liability = $9,086 + (($130,000 - $78,950) * 22%)

= $9,086 +($51,050 * 22%)

= $9,086 + $11,231

= $ 20,317

To get the Effective tax rate, it will be:

= tax liability / Total taxable income Effective tax rate

= [tex]\frac{20,317}{30000}[/tex]  that is also written as $20,317/ $130,000

So, the  average tax rate is = 15.63%

Therefore, the average tax rate will be = 15.63 percent

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The computation of the index shows that the value of 9 × 10² will be 900.

From the information given, we are told to calculate the value of 9 × 10². This will be calculated thus:

= 9 × 10²

Note that 10² simply means that you've to multiply 10 twice. This will be:

= 10 × 10 = 100

Therefore, 9 × 10² will be:

= 9 × 100

= 900

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Answer:

The answer is in Step.

Step-by-step explanation:

Domain: (- inf, + inf)

Range: (- inf, 3]
Increasing: (- inf , 0)

Decreasing: (0 , + inf)
Positive: (- 1 , 1 )
Negative: (- inf , -1) , (1 , + inf)

Maximum: (0,3) or just 3.

Minimum: None.
x-int: -1, 1
y-int: 3

The point R is the point which is not coplanar with points C, D and E.

We need to find the point which is not coplanar with points C, D and E.

The points that lie on the same plane are called coplanar points.

In the given figure there are five planes which are as follows:

BCUD, BRAE, BRAC, BTDE, ACUDE

Now, points C,D and E lie in plane ACUDE.

In the plane ACUDE points A, C, U, D, E and S lies.

From the options point, R is not lining in the same plane as C, D and E lies.

Therefore, the point R is the point which is not coplanar with points C, D and E.

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Answer:

Adults = 448

Students = 888

Step-by-step explanation:

Write equations with info given

A = Adult tickets

S = Student tickets

5A+1S=3,128

A+S=1336

Subtract equations from each other

4A=1792

Solve for A

A=448

Plug A into second equitation

448+S=1336

Solve for S

S=888

Step-by-step explanation:

12 . The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations..