Find the solution to the system of
equations.
You can use the interactive graph below to find
the solution.
y = 2x + 3
y = - 3x + 3

Answer:

[tex]C =8t+16\\7\ hours[/tex]

Step-by-step explanation:

Given that, Fixed charge = $16

Per hour charge for renting the bike = $8/hour

To find:

If Matt paid $72 to rent a bike, for how many hours did he rent the bike?

Solution:

Let 't' be the time for which Matt rents the bike.

1 hour charge for the bike rent = $8

't' hour charge for the bike rent = $8 [tex]\times t[/tex]

Total Charge for the bike = Charge for renting the bike for t hours + fixed charge

Let 'C' be the total charge, so the equation becomes:

[tex]C = 8t + 16[/tex]

Given that C is $72, we need to find t:

[tex]72 = 8t+16\\\Rightarrow 8t=72-16\\\Rightarrow 8t=56\\\Rightarrow t = 7\ hours[/tex]

So, he rented the bike for 7 hours.

The equation is: [tex]C = 8t + 16[/tex]

50x30x9x70jssjgsvebdghxhdbgd

Answer:

Step-by-step explanation:

(5 * 10³) * (9*10⁷) = 5*9 * 10³⁺⁷

                          = 45 * 10¹⁰

                          = 4.5 * 10¹¹

(7*10⁵)÷ (2*10²) =

                         [tex]\frac{7}{2}*10^{5-2}\\\\=3.5*10^{3}[/tex]

Answer:

a = -1

b = 1

Step-by-step explanation:

Step 1: Isolate x's

x² + 2x = -2

Step 2: Complete the Square

x² + 2x + 1 = -2 + 1

(x + 1)² = -1

Step 3: Move everything to 1 side

(x + 1)² + 1 = 0

And we have our answer.

Answer:

A=1 and b=1

Step-by-step explanation:

Answer:

[tex] \theta = 51.8^\circ [/tex]   or   [tex] \theta = 308.2^\circ [/tex]

Step-by-step explanation:

[tex] \cos^2 \theta + \cos \theta − 1 = 0 [/tex]

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] \cos \theta = \dfrac{-1 \pm \sqrt{1^2 - 4(1)(-1)}}{2(1)} [/tex]

[tex] \cos \theta = \dfrac{-1 \pm \sqrt{1 + 4}}{2} [/tex]

[tex] \cos \theta = \dfrac{-1 \pm \sqrt{5}}{2} [/tex]

[tex] \cos \theta = 0.61803 [/tex]   or  [tex] \cos \theta = -1.61803 [/tex]

The range of the cos θ function excludes θ = -1.61803, so we discard that solution.

[tex] \theta = 51.8^\circ [/tex]   or   [tex] \theta = 308.2^\circ [/tex]

Answer:

y=-6x+1

Step-by-step explanation:

Step-by-step explanation:

v = 1/3πr²h

1/3×314/100×4×4×7

11,722.666round off

11722.67

formula =v= 3.14×radius×radius ×height ×3

Step-by-step explanation:

pie×radius×squared ×7×3

=117.29

when we round it to the nearest hundredth

its=117.29m squared

Answer:

4(7+3)

Step-by-step explanation:

28 and 12 are both divisible by 4.

28 ÷ 4 = 7

12 ÷ 4 =  3

Answer:

4(7+3)

Step-by-step explanation:

4(7) = 28

4(3)= 12

28+12=28+12

Hope this helps!

Answer:

A: 71,235,000

B: 71,235,00

C: 71,240

Step-by-step explanation: Round by thousands, hundreds and tens.

Answer:

The best option is B: X' = (-7,-4), Y' = (-2,6), Z'=(8, 3).

Step-by-step explanation:

Each vertex can be represented as a vector with regard to origin.

[tex]\vec X = -4\cdot i + 7\cdot j[/tex], [tex]\vec Y = 6\cdot i + 2\cdot j[/tex] and [tex]\vec Z = 3\cdot i -8\cdot j[/tex].

The magnitudes and directions of each vector are, respectively:

X:

[tex]\|\vec X\| = \sqrt{(-4)^{2}+7^{2}}[/tex]

[tex]\|\vec X\| \approx 8.063[/tex]

[tex]\theta_{X} = \tan^{-1}\left(\frac{7}{-4} \right)[/tex]

[tex]\theta_{X} \approx 119.744^{\circ}[/tex]

Y:

[tex]\|\vec Y\| = \sqrt{6^{2}+2^{2}}[/tex]

[tex]\|\vec Y\| \approx 6.325[/tex]

[tex]\theta_{Y} = \tan^{-1}\left(\frac{2}{6} \right)[/tex]

[tex]\theta_{Y} \approx 18.435^{\circ}[/tex]

Z:

[tex]\|\vec Z\| = \sqrt{3^{2}+(-8)^{2}}[/tex]

[tex]\|\vec Z\| \approx 8.544[/tex]

[tex]\theta_{Z} = \tan^{-1}\left(\frac{-8}{3} \right)[/tex]

[tex]\theta_{Z} \approx 290.556^{\circ}[/tex]

Now, the rotation consist is changing the direction of each vector in [tex]\pm 90^{\circ}[/tex], which means the existence of two solutions. That is:

[tex]\vec p = r \cdot [\cos (\theta \pm 90^{\circ})\cdot i + \sin (\theta \pm 90^{\circ})\cdot j][/tex]

Where [tex]r[/tex] and [tex]\theta[/tex] are the magnitude and the original angle of the vector.

Solution I ([tex]+90^{\circ}[/tex])

[tex]\vec p_{X} = 8.063\cdot [\cos (119.744^{\circ}+90^{\circ})\cdot i + \sin (119.744^{\circ}+90^{\circ})\cdot j][/tex]

[tex]\vec p_{X} = -7\cdot i -4\cdot j[/tex]

[tex]\vec p_{Y} = 6.325\cdot [\cos(18.435^{\circ}+90^{\circ})\cdot i+\sin(18.435^{\circ}+90^{\circ})\cdot j][/tex]

[tex]\vec p_{Y} = -2\cdot i +6\cdot j[/tex]

[tex]\vec p_{Z} = 8.544\cdot [\cos(290^{\circ}+90^{\circ})\cdot i +\sin(290^{\circ}+90^{\circ})\cdot j][/tex]

[tex]\vec p_{Z} = 8.029\cdot i +2.922\cdot j[/tex]

Solution II ([tex]-90^{\circ}[/tex])

[tex]\vec p_{X} = 8.063\cdot [\cos (119.744^{\circ}-90^{\circ})\cdot i + \sin (119.744^{\circ}-90^{\circ})\cdot j][/tex]

[tex]\vec p_{X} = 7\cdot i +4\cdot j[/tex]

[tex]\vec p_{Y} = 6.325\cdot [\cos(18.435^{\circ}-90^{\circ})\cdot i+\sin(18.435^{\circ}-90^{\circ})\cdot j][/tex]

[tex]\vec p_{Y} = 2\cdot i -6\cdot j[/tex]

[tex]\vec p_{Z} = 8.544\cdot [\cos(290^{\circ}-90^{\circ})\cdot i +\sin(290^{\circ}-90^{\circ})\cdot j][/tex]

[tex]\vec p_{Z} = -8.029\cdot i -2.922\cdot j[/tex]

The rotated vertices are: i) X' = (-7,-4), Y' = (-2,6), Z'=(8.029, 2.922) or ii) X' = (7,4), Y' = (2,-6), Z' = (-8.029, -2.922). The best option is B: X' = (-7,-4), Y' = (-2,6), Z'=(8, 3).

The answer that line of best fit, how many toys were sold 13 days after the store opened is A.) 195

Step-by-step explanation:

C=2×pi×r

8.61=2pi*×r

8.61÷2pi=13.52 radius

A=pi×r^2

pi×13.52^2=574.25 area

Answer: 450 watches

Step-by-step explanation:

Given the following :

Let Initial number of watches = n

Total number sold in January and February = 342

Total sold in march = 25% of (n - 342) = 0.25(n - 342) = 0.25n - 85.5

Total watches left = 18% of n = 0.18n

Therefore,

Initial number of watches = (watches left + total watches sold)

n = 0.18n + (0.25n - 85.5) + 342

n = 0.18n + 0.25n - 85.5 + 342

n = 0.43n + 256.5

n - 0.43n = 256.5

0.57n = 256.5

n = 256.5 / 0.57

n = 450

n = Initial number of watches = 450

Answer:

on the dive boat deck

Step-by-step explanation:

Answer:

the above is right

Step-by-step explanation:

Answer:

D. Cost

Step-by-step explanation:

In a scatter diagram we have that the x axis corresponds to the explanatory variable or also called the independent variable, since it is the value that is entered in the equation and does not depend on another.

While the y-axis corresponds to the response variable or also called the dependent variable since it is the value of the result of the equation

In this case, the explanatory variable is weight, that is, on the x-axis the weight would go and the cost is the response variable and would go on the y-axis, therefore, the answer is D. Cost

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $120 and a sample of 23 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100. Let 4 year old automobiles be represented by population 1.

State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles.

At a 0.01 level of significance, what is your conclusion? What is the p-value?

Answer:

Null hypotheses = H₀ = σ₁² ≤ σ₂²

Alternative hypotheses = Ha = σ₁² > σ₂²

Test statistic = 1.44

p-value = 0.1954

0.1954 > 0.01

Since the p-value is greater than the given significance level therefore, we cannot reject the null hypothesis.

We can conclude that there is no sufficient evidence to support the claim that the variance in annual repair costs is larger for older automobiles.

Step-by-step explanation:

Let σ₁² denotes the variance of 4 years old automobiles

Let σ₂² denotes the variance of 2 years old automobiles

State the null and alternative hypotheses:

The null hypothesis assumes that the variance in annual repair costs is smaller for older automobiles.

Null hypotheses = H₀ = σ₁² ≤ σ₂²

The alternate hypothesis assumes that the variance in annual repair costs is larger for older automobiles.

Alternative hypotheses = Ha = σ₁² > σ₂²

Test statistic:

The test statistic is given by

Test statistic = σ₁²/σ₂²

Test statistic = 120²/100²

Test statistic = 1.44

p-value:

The degree of freedom corresponding to 4 years old automobiles is given by

df₁ = n - 1  

df₁ = 26 - 1  

df₁ = 25

The degree of freedom corresponding to 2 years old automobiles is given by

df₂ = n - 1  

df₂ = 23 - 1  

df₂ = 22

Using Excel to find out the p-value,  

p-value = FDIST(F-value, df₁, df₂)

p-value = FDIST(1.44, 25, 22)

p-value = 0.1954

Conclusion:

When the p-value is less than the significance level then we reject the Null hypotheses

p-value < α   (reject H₀)

But for the given case,

p-value > α

0.1954 > 0.01

Since the p-value is greater than the given significance level therefore, we cannot reject the null hypothesis.

We can conclude that there is no sufficient evidence to support the claim that the variance in annual repair costs is larger for older automobiles.

Answer:

top one is 3

bottom one is 12

Step-by-step explanation:

In unit time, the distance covered by any object is called speed.

In mathematical term, Speed is express as S=D/T,

where S=speed, D=distance, T= time.

Given that,

Distance covered by  jogging in 0.5 hr = 3 miles.

And distance covered by bike in 1.25 hr = 12 miles.

Since, by jogging,

0.5 hr = 3 miles

⇒1 hr = 6 miles

The Speed of jogging is 6 miles/hr

Since, by bike,

1.25 hr = 12 miles

1 hour = 12/1.25 miles

1 hour = 9.6

The speed of the bike is 9.6 miles/hr.

To know more about Speed on:

https://brainly.com/question/4926312

#SPJ3

Answer:

AngleASZ Is-congruent-to AngleZSB

Step-by-step explanation:

The incenter of a triangle is a point inside a triangle that is equidistant from all the sides of a triangle. The incenter is the point formed by the intersection of all the three angles of the triangle bisected. The lines drawn from the incenter to the sides of the triangle forming right angles to the sides are congruent.

If Point Z is equidistant from the sides of ΔRST, point Z is the incenter of triangle RST. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. This lines are therefore congruent to each other, i.e. ZA = ZB = ZC.. Since the angles of the sides of the triangles are bisected to form the incenter, therefore:

AngleASZ Is-congruent-to AngleZSB

Answer:

AngleASZ Is-congruent-to AngleZSB

Step-by-step explanation:

D is the correct answer

Answer:

become more confident in his faith

Answer:

he will become confident in his faith

Explanation:

the Bible is very open to interpretation and does not always have definite answers. if you are able to form your own ideas and interpretation of the Bible then you'll have a stronger connection to it which will make you more confident in your faith.

Answer:

Circumference

(22÷7)×14.7×2 = 92.4cm

Answer:

16

Step-by-step explanation:

15x = 240 x stands for number of students at 1 table

To solve this we divide by 15 both sides for the "x" to remain alone on one side of the equality sign.

(15/15) x = 240/15

So, x = 16.

Answer:

Here,

The length of an arc of a sector with theta nag radius'r' is:

[tex] \frac{theta}{360} 2\pi \: r[/tex]

CD=?

Radius=7.9 cm

theta=66.4

Length of CD

[tex] \frac{66.4}{360} \times 2 \times \pi \times 7.9 \\ = \frac{66.4}{360} \times 2 \times 3.14 \times 7.9 \\ = 9.1506 \\ = 9.2 \: cm[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

[tex] 3\frac{5}{6} [/tex]

solution,

[tex]5 \frac{3}{4} \div 1 \frac{1}{2} \\ = \frac{5 \times 4 + 3}{4} \div \frac{2 \times 1 + 1}{2} \\ = \frac{20 + 3}{4} \div \frac{2 + 1}{2} \\ = \frac{23}{4} \div \frac{3}{2} \\ = \frac{23}{4} \times \frac{2}{3} \\ = \frac{23}{6} \\ = 3 \frac{5}{6} [/tex]

hope this helps...

Good luck on your assignment..

Answer:

23/6=3 5/6

Step-by-step explanation:

5  3/4=(4*5+3)/4=23/4

1 1/2=(2*1+1)/2=3/2

23/4:3/2=23/4*2/3=23*2/4*3=23/2*3=23/6

Answer:

[tex] P(A)= 0.48, P(B)= ?, P(A \cap B)= 0.21, P(A \cup B) =0.89[/tex]

And for this case we can use the total rule of probability given by:

[tex] P(A \cup B) = P(A) +P(B) -P(A\cap B)[/tex]

And if we solve for [tex] P(B) [/tex] we got:

[tex] P(B)= P(A \cup B) -P(A) +P(A \cap B)[/tex]

And replacing we got:

[tex] P(B) = 0.89 -0.48 +0.21= 0.62[/tex]

Step-by-step explanation:

We have the following probabilities given:

[tex] P(A)= 0.48, P(B)= ?, P(A \cap B)= 0.21, P(A \cup B) =0.89[/tex]

And for this case we can use the total rule of probability given by:

[tex] P(A \cup B) = P(A) +P(B) -P(A\cap B)[/tex]

And if we solve for [tex] P(B) [/tex] we got:

[tex] P(B)= P(A \cup B) -P(A) +P(A \cap B)[/tex]

And replacing we got:

[tex] P(B) = 0.89 -0.48 +0.21= 0.62[/tex]

Answer:

0.62

Step-by-step explanation:

Answer:

  18x +16y +4

Step-by-step explanation:

The area is the product of length and width, so the length is ...

  A = LW

  L = A/W = (72xy +18x)/(9x) = 8y +2

The perimeter is double the sum of length and width:

  P = 2(L +W) = 2(8y +2 +9x)

  P = 18x +16y +4 . . . . the perimeter of the sandbox

Answer:

A

Step-by-step explanation:

If you see - 12a3bc, - 12a divided by 3 will give you - 4a then just put the rest beside them. So the answer will be A.

Answer:

18, 23

Step-by-step explanation:

a. We know that W = 5 and D = 3 so:

P = 3W + D = 3 * 5 + 3 = 18 points

b. We know that P = 50 and D = 14 and that we are solving for W so we get:

50 = 3W + 14

36 = 3W

W = 12 which means the losses are 35 - 12 = 23.

(a) Given:

number of wins = 5

and, number of draws = 3

To find :

Point of the team.

Solution:

P = 3*5 + 3

 = 18

Point of the team = 18

(b)  Given:

number of points = 50

and, number of draws = 14

To find :

Number of games lost by the team.

Solution:

50 = 3*win + 14

3*win = 36

win = 12

Number of games lost by the team = 35 -  12 =23

Answer: x=2

Step-by-step explanation:

7x+1=x+4

7x=x+3

6x=3

x=2

hope it correct :D

Answer: a.) (3x +1)(2x +3)

Step-by-step explanation:

The factors that work to get the middle term, 11x, are 3×3x = 9x and 1×2x=2x. 2x +9x = 11x

Answer:

A

Step-by-step explanation:

the triangles share one angle and they have two equal sides

Answer:

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