Jon and Kristen are both increasing the number of minutes they jog each day, as shown in the tables.

Jon
Day Minutes
0 15
1 17
2 19
3 21
Kristen
Day Minutes
0 22
1 23
2 24
3 25

Which system of linear equations could be used to determine which day they will jog for the same number of minutes, where d represents the day and m represents the number of minutes?

Answer:

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangle

Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.

A system of equations, involving two linear lines has solutions as follows:

In the question, we are informed that Samia created the given tables for a linear system, and concluded that no solution exists for the system.

We are asked to comment on her conclusion.

To check for her conclusion, we calculate the slopes of both the lines to check whether the relations are parallel or not, as, for parallel relations, the slopes are equal.

Slope can be calculated using the formula, m = (y₂ - y₁)/(x₂ - x₁), when (x₁, y₁), and (x₂, y₂) are the points on the line.

Thus, the slope for:-

Relation 1, is m₁ = (22 - 8)/(4 - (-3)) = 14/7 = 2.

Relation 2, is m₂ = (12 - (-2))/(4 - (-3)) = 14/7 = 2.

Since the slope of the two relations is equal, that is, m₁ = m₂, and they are not coinciding with each other, we can say that the two relations are parallel to each other.

Since the two linear relations are parallel to each other, no solution to the system exists. Hence, Samia's conclusion is correct.

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Answer:

Step-by-step explanation:

Total amount in cents (unsimplified): 5N +17(10-N)

Simplified: 170-5N

Answer:

135

Step-by-step explanation:

(n−2) × 180° = sum of the interior angles  where n is the number of sides

There are 6 sides

(6 -2) * 180

4*180

The sum is 720

2x+2x+3x+3x+3x+3x = 720

16x = 720

Divide by 16

16x/16 = 720/16

x = 45

Angle E = 3x= 3(45) = 135

Answer:

Step-by-step explanation:

We have 3 identical pumps working to fill a pool. If it takes them working  together 8 hours to fill the pool, the equation is:

[tex]\frac{1}{x}+\frac{1}{x}+\frac{1}{x}=\frac{1}{8}[/tex] and

[tex]\frac{3}{x}=\frac{1}{8}[/tex] . Cross multiply to get

x = 24, which is the number of hours it will take one pump to do the job all alone. If this be the case, and we have 4 pumps WORKING AT THE SAME TIME, filling the pool will be the number of hours it takes one pump divided by 4.

4 pumps can do the job in 6 hours.

Answer:

48 teachers

Step-by-step explanation:

Here's two solutions:

Solution 1: Build an equation.

Let $T$ be the number of teachers. The number of math teachers is $\frac{3}{8}T$, and the number of non-math teachers is $30$. Since each teacher is either a math teacher or not a math teacher, we have

$$\frac{3}{8}T + 30 = T.$$Multiplying each side of this equation by $8$ gives us

$$3T + 240 = 8T.$$Subtracting $3T$ from each side gives us $240 = 5T$, and dividing both sides by $5$ gives us $48=T$. Therefore, there are $48$ teachers at Naran's school.

Solution 2: Think proportionally.

Since three-eighths of the teachers are math teachers, the other five-eighths are not math teachers. So, these $30$ non-math teachers are five-eighths of the total number of teachers. Therefore, $\dfrac{30}{5} = 6$ teachers are one-eighth of the total. So, there are $6\cdot 8 = \boxed{48}$ teachers in all.

Answer:

Step-by-step explanation:

The rate of change for the interval between x = 2 and x = 6 is simply asking you for the slope of the line that connects these 2 coordinates. If you were in calculus, you could find the instantaneous slope at any point on this parabola, but you're not quite that lucky yet, so we will go about it the only way we can:

by finding the slope. Remember, that slope is the same thing as rate of change.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and filling in:

[tex]m=\frac{14-2}{6-2}=\frac{12}{4}=3[/tex]

Answer:

C x=8

Step-by-step explanation:

Chúc bạn ngày mới tốt lành

Answer:

Roots is a fancy word for zero, which is also another fancy word for the x intercept.

You can factor a quad or use the quadratic equation to get zeros.

In this case, its non-factorable. So you gotta use the quadratic.

Using the quadratic equation you get : x = -2 ± √-1 (√5),

which can be rewritten as x = -2 ± i(√5)

Function was : x^2 + 4x + 9

For quad, I identified the following:

A = 1

B = 4

C = 9

I also added a picture of the formula in the attached.

Answer:

y= -x +2

Step-by-step explanation:

This is a negative slope of one because the line is going down and has a ride over run of 1/1. Then the y intercept is +2 because this line intercepts the y axis at positive 2.

hope it helps!

Answer:

y = -x +2

Step-by-step explanation:

just trust me on this

Answer:

bc=  7

Step-by-step explanation:

Answer:

- 2864

Step-by-step explanation:

Given that,

The number is of 4 digits

All are different

The sum of the 4 digits = 20

Hundred's digit is twice than one's digit

A.T.Q.

Let the unit digit be 4. So, the hundred's digit would be 4 * 2 = 8

Now, we have

_8_4

We know that the sum of four digits is 20. Thus,

_ + 8 + _ + 4 = 20

∵ _ + _ = 20 - 12 = 8

The possible numbers must make a sum of 8. Thus, one possibility can be 2 and 6.

Therefore, the number can be

2864  

( 2 + 8 + 6 + 4 = 20)

Answer:

(4x4) + (6x11) = 82 for area

4+4+10+11+7+6= 42

Step-by-step explanation:

You can calculate this by calculating the two squares separately, and on the bottom line, it is 10, so just subtract 4 to make the rectangle on the right, separate from the square on the left. (for area)

Answer:

Steps shown in picture provided

Answer:

First one: function

Second one: not a function

Step-by-step explanation:

A function is a relationship where each input has it's own unique output. If an input has more than one output then the relationship is not a function

For the first one no x value repeats meaning each input has it's own output therefore it is a function

For the second one the x value 8 has more than 1 output therefore the second one is not a function

Answer:

203 ft.

Step-by-step explanation:

Since we are given the measurements of two sides, we can use trig to find the angle (or our reference angle, we'll call it x) the sides form.

SOH-CAH-TOA

We'll use cosine since the adjacent and hypotenuse were given for our reference angle.

Cos(x) = (adj/hyp)

Cos(x) = (396/445)

[Cos(x)]cos^-1 = (396/445)(cos^-1)

x ≈ 27.1409 (Nearest ten-thousandth)

And now we find the missing side using our now known angle.

SOH-CAH-TOA

Tan(x) = (opp/adj)

Tan(27.1409) = (opp/396)

0.5126 ≈ (opp/396)

(0.5126)(396) ≈ (opp/396)(396)

Opp = 203

Missing Side = 203 ft

Answer:

-21 =x

Step-by-step explanation:

9(3x+3)=10(3x+9)

Distribute

27x +27 = 30x +90

Subtract 27x from each side

27x+27 -27x = 30x-27x +90

27 = 3x+90

Subtract 90 from each side

27-90 = 3x +90-27

-63 = 3x

Divide by 3

-63/3 = 3x/3

-21 =x

Answer:

x = -21

Step-by-step explanation:

9(3x+3) = 10(3x+9)

27x + 27 = 30x + 90

-30x + 27x = 90 - 27

-3x = 63

x = -21

Answer:

A

Step-by-step explanation:

a geometric sequence is where we multiply a factor from element to element.

a1 = $900

a2 = 981 = a1 × f = 900 ×

a3 = 1069.29 = a2 × f = a1 × f × f = s1 × f²

[tex]an = 900 \times {f}^{n - 1} [/tex]

so, now let's try and get f.

remember, 981 = 900 × f

f = 981/900 = 109/100 = 1.09

just to control, we check for s3 :

900 × (1.09)² = 900 × 1.1881 = 1069.29

correct.

so,

a13 = 900 × (1.09)¹² = 2,531.398304

s13 is then the sum of all a1, ..., a13

there is a nice formula for sums of finite sequences

s13 = 900 × (1-f¹³) / (1-f) = 900×(1-(1.09)¹³) / (1-1.09) =

= 900×(1-3.065804612) / (-0.09) =

= 900×(-2.065804612) / (-0.09) = 20,658.04612

.

Answer:

5.25 kg of the mashed potatoes were eaten.

Step-by-step explanation:

(3/4) * 7 = 5.25

I hope this is helpful :)

so, start floor = x

x + 7 - 9 - 4 + 8 - 2 = 14

x = 14

the elevator started on the 14th floor.

to verify: 14 + 7 = 21 - 9 = 12 - 4 = 8 + 8 = 16 - 2 = 14

Answer:

Step-by-step explanation:

please make it a brainliest answer.

Answer: B. θ = 36°

Step-by-step explanation:

Concept:

Here, we need to know the idea of the Law of sines.

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.

The Law of sines: a / sinA = b / sinB = c / sinC

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

a = 10 m

c = 11.2 m

C = 41°

Given formula

a / sinA = c / sinC

Substitute the value into the formula

10 / sinA = 11.1 / sin (41)

Cross-multiply to simplify the equation

sinA × 11.1 = 10 · sin (41)

Divide 11.1 on both sides

sinA × 11.1 / 11.1 = 10 · sin (41) / 11.1

sinA = 10 · sin (41) / 11.1

Apply arcsine or the inverse of sine (basically representing the division of sine)

A = sin⁻¹ (10 · sin (41) / 11.1)

A = 36°

Hope this helps!! :)

Please let me know if you have any questions

Answer:

24 boys & 20 girls

Step-by-step explanation:

Last year:

Number of boys = x

Total number = 45

Number of girls = 45 - x

An increase of 20% is the same as multiplying by 1.2

A decrease of 10% is the same as multiplying by 0.8

This year:

New number of boys: 1.2x

New number of girls: 0.8(45 - x)

New total number = 45 - 1 = 44

1.2x + 0.8(45 - x) = 44

1.2x + 36 - 0.8x = 44

0.4x + 36 = 44

0.4x = 8

x = 20

Last year there were 20 boys and 25 girls.

This year there are 20 * 1.2 = 24 boys

and 44 - 24 = 20 girls

Answer: 24 boys & 20 girls

Answer:

6 minutes

Step-by-step explanation:

20 miles jogs at 1 hour, so for 2 miles,

2/20

= 1/10 hours

= 1/10×60

= 6 minutes

Answered by GAUTHMATH

Answer:

8

Step-by-step explanation:

x=16

x(16)-8=8

Answer:

[tex]\displaystyle lne^4 = 4[/tex]

General Formulas and Concepts:

Algebra II

Natural Logarithms ln and Euler's number e

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle lne^4[/tex]

Step 2: Evaluate

Answer:

√2

Step-by-step explanation:

tan(x) = -1

x = arctan(-1)

x = -π/4

Now since x is between 3π/2 and 2π use use the general form

nπ-π/4

taking n = 2

2×π-π/4

= 7π/4

now tan (7π/4) = -1

so sec (7π/4) = √2

Answered by GAUTHMATH

Answer:

3?

Step-by-step explanation:

A little confused by the question but is it just

1/5 2/5 3/5 4/5

1     2     3     4

so theres 3 in between

The area divided by XYZ is 16/9

i.e. [tex]\frac{A}{[XYZ]} = \frac{16}{9}[/tex]

The given parameters can be represented as:

[tex]r = -\frac{4}{3}[/tex] --- the ratio of dilation

The area of the second triangle is as follows:

[tex]A =r^2 * \triangle XYZ[/tex]

Make [tex]r^2[/tex] as subject

[tex]r^2 = \frac{A}{\triangle XYZ}[/tex]

Substitute value for [tex]r^2[/tex]

[tex](\frac{4}{3})^2 = \frac{A}{\triangle XYZ}[/tex]

[tex]\frac{16}{9} = \frac{A}{\triangle XYZ}[/tex]

Rewrite as:

[tex]\frac{A}{\triangle XYZ} = \frac{16}{9}[/tex]

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Answer:

Step-by-step explanation:

Let each side of triangle XYZ have length s. We therefore have:

s = YZ = YQ + QR + RZ = x + 2y

Since each side of triangle X1 Y2 Z2 is 3/4 the length of the corresponding side of triangle XYZ, we have:

3/4s = X1 Z1 = X1 Q + QP + P Z1 = 2x +y.

The system of equations:

x + 2y = s

2x + y = 3/4s

Multiply the second equation by 2, then subtract the first equation.

3x = 1/2s, so x = 1/6s.

Now we have y = 3/4s-2x = 5/12s.

A/[XYZ] = [XYZ] - 3[YPQ]/[XYZ]

= {[XYZ] - 3[(25)/144] * [XYZ]} / [XYZ]

={23/48* [XYZ]} / [XYZ]

= 23/48