Question 6
Which is the graph of y=-x-3?
Graph B
Graph C
Graph A

Answer:

The solutions to the system of equations are [tex]y=4,\:x=5[/tex].

Step-by-step explanation:

To solve the system [tex]\begin{bmatrix}4x+5y=40\\ 6x+3y=42\end{bmatrix}[/tex]

First,

[tex]\mathrm{Multiply\:}4x+5y=40\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x+15y=120\\\\\mathrm{Multiply\:}6x+3y=42\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:12x+6y=84[/tex]

[tex]\begin{bmatrix}12x+15y=120\\ 12x+6y=84\end{bmatrix}[/tex]

Subtract the first equation from the second equation

[tex]12x+6y=84\\\underline{-12x-15y=-120}\\-9y=-36[/tex]

Solve [tex]-9y=-36[/tex] for y:

[tex]\frac{-9y}{-9}=\frac{-36}{-9}\\y=4[/tex]

For [tex]12x+15y=12[/tex] plug in [tex]y=4[/tex] and solve for x

[tex]12x+15\cdot \:4=120\\12x=60\\x=5[/tex]

The solutions to the system of equations are:

[tex]y=4,\:x=5[/tex]

Answer:

  6

Step-by-step explanation:

Because you are familiar with your times tables, you know that ...

  30 = 6·5

  42 = 6·7

The greatest common factor is 6.

Answer:

[tex]8.182X10^8 $pounds[/tex]

a=8.182 and b=8

Step-by-step explanation:

Weight of the Empire State Building =[tex]7.3X 10^8[/tex] pounds.

Weight of the One World Trade Center building= 88,200,000 pounds.

=[tex]8.82 X 10^7[/tex]

The addition of the two:

[tex]=7.3X 10^8+8.82 X 10^7\\$To make it easier to add, express both as powers of 8\\=7.3X 10^8+0.882 X 10^8\\=(7.3+0.882)X10^8\\=8.182X10^8 $ pounds[/tex]

Comparing with the form: [tex]aX10^b[/tex]

a=8.182 and b=8

Answer:

Step-by-step explanation:

A general equation of a hyperbola is

 x^2     y^2

-------- - ------- = 1   (This applies only when the center of the hyperbola

 a^2     b^2                               is at (0, 0)  ).

You must compare the given equations to this standard form to identify which represents the hyperbola shown, and also you must share the illustration of the hyperbola.

The equation represents the hyperbola shown in the graph is  (y - 1)² / 9 - (x + 4)² / 4  = 1

A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

Given that, a graph, showing hyperbola, we need to find the equation,

We have the general equation for up - down facing hyperbola as

(y - k)² / b²- (x - h)² / a²  = 1.

Let's start listing the properties of this graph -

Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1).

Therefore, (h, k) = (- 4,1).

This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference.

Therefore, a = 3.

That gives asymptotes. Now remember that it will be in the form

y = ± b / a.

We already know a = 3, so we have to find b.

Looking at this graph we can say that another point besides (- 4,1) that lies on the "dotted line" is (- 2, - 2).

Calculating the slope of the dotted line would be as follows,

Given: (- 4,1) and (- 2, - 2)

Slope = - 2 + 4 / - 2 - 1 = 2 / 3

We have the equation y = 2 / 3x.

Therefore, b = 2.

Let's substitute to equation...

h = - 4, k = 1, b = 2, a = 3

(y - 1)² / (3)²- (x + 4)² / (2)²  = 1

(y - 1)² / 9 - (x + 4)² / 4  = 1

Hence, the equation represents the hyperbola shown in the graph is  (y - 1)² / 9 - (x + 4)² / 4  = 1

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The complete question is attached

Answer:

I also belive for Part A the second one is the answer because it equals 120 Part B is 120 pints! Good Luck! And I hope this Helps!

Answer:

B

Step-by-step explanation:

Answer:

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Step-by-step explanation:

x < 7

Answer: [tex]1\frac{1}{2} *9=\frac{3}{2}*9=\frac{27}{2}=13\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:             27

                        -------  

                           2

Step-by-step explanation:

Step-by-step explanation:

-2a + 2a + 7 = 8

Solving like terms

7 = 8

= 8 - 7 = 1

Has one solution

Answer:69°43'

Step-by-step explanation:

Complementary angles add up to 90

Let them complement be y

y+20°17`=90°

Collect like terms

y=90-20°17' 20°17'=1217/60

y=90-1217/60

y=(60x90 -1 x 1217)/60

y=(5400-1217)/60

y=4183/60

y=69°43'

Answer:

[tex]45\pi$ square inches[/tex]

Step-by-step explanation:

The radius, r of the expanding circle of oil is modeled by the function:

[tex]r=3\sqrt{s}[/tex] , where s is time in seconds.

When s=5

Radius [tex]r(5)=3\sqrt{5}$ inches[/tex]

Area of a circle [tex]=\pi r^2[/tex]

Therefore, the area of the oil spill when s=5 seconds

[tex]=\pi* (3\sqrt{5})^2\\=45\pi$ square inches[/tex]

The area of the spill when s=5 seconds is 45pi square inches.

Answer:

228 of them are made from wool, but there is no enough information to determine how many would he has in stock.

Step-by-step explanation:

Mr Ollivander's stuffed bear shop has 456 bears in stock, and exactly half of them are made from wool, this means that 1/2 of 456 are made from wool

1/2 of 456 = 1/2 × 456 = 456/2 = 228.

That is 228 of them are made from wool.

However, nothing tells us that this is all he has in his stock. There is no information available to determine how many would he has in stock.

Answer:

The area of the quadrilateral ABCD is 114 square units

Step-by-step explanation:

We must calculate the area of each triangle and then add these areas so we calculate the area of the quadrilateral ABCD

First for the BAD right triangle:

AD = sqrt [BD ^ 2 - AB ^ 2]

AD = sqrt [15 ^ 2 - 12 ^ 2]

AD = sqrt [225-144]

AD = sqrt [81]

AD = 9

The area of a triangle is half the product of the base times the height, that is:

A1 = AB * AD / 2 = 12 * 9/2 = 54

Then for the second triangle in the right triangle BDC:

DC = sqrt [BC ^ 2 - BD ^ 2]

DC = sqrt [17 ^ 2 - 15 ^ 2]

DC = sqrt [289 - 225]

DC = sqrt [64] = 8

We calculate the area

A2 = DC * BD / 2 = 8 * 15/2 = 60

The total area then is:

AT = A1 + A2

AT = 54 + 60 = 114

Which means that the area of the quadrilateral ABCD is 114 square units

Answer:

-7x⁹

Step-by-step explanation:

[tex]\sqrt{49x^{18}} = \sqrt{(7^2)(x^9)^2} =\sqrt{(7x^{9})^2} = |7x^9|[/tex]

Since  x < 0 ,then |7x⁹| = -7x⁹

Answer:

Total textbook cost of tuition fees per month will be $ 2,356 and 25 cents

Step-by-step explanation:

To solve the exercise, we will first define the total cost per quarter.

cost of 1 credit hour = $ 601

then we solve the following:

cost of 15 credit hours = $ 601 * 15 = $ 9015

textbooks = $ 410

then we solve the following:

total cost = 9015 + 410 = $ 9425

total cost for 3 quarters = 3 * $ 9425 = $ 28275 for 12 months

we calculate as follows

Total textbook cost of tuition fees per month will be

$ 28,275 / 12 = $ 2,356 and 25 cents

Answer:

x-intercept: -13/6

y-intercept: 13

General Formulas and Concepts:

Algebra I

Equality Properties

Coordinate Planes

Slope-Intercept Form: y = mx + b

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

y = 6x + 13

Step 2: Find y-intercept

Compare given equation to slope-intercept form.

y = 6x + 13 ↔ y = mx + b

Slope m = 6

y-intercept b = 13

Step 3: Find x-intercept

Substitute y = 0.

Answer:

x = -3

y = -3

Step-by-step explanation:

To solve this system of equations, you can use the elimination method, which is to have one of the variables match, but be the opposite sign of the other:

- x + y = 0

4x - 3y = -3

The easier one to match is the 1st equation, and to make it match oppositely, you multiply the whole equation by 4:

4(-x + y = 0)

-4x + 4y = 0

4x - 3y = -3

-4x and 4x cancel each other out:

4y = 0

-3y = -3

_______

y = -3

Then plug in -3 for y, into one of the equations:

- x + y = 0

- x - 3 = 0

Add 3 to both sides:

- x = 3

Divide both sides by -1:

x = -3

The meaning of each parameter is given as follows:

Then the yearly percent increase is of:

4%.

C(3) represents the cost in 2015, which was of $33,746.

a) The expression to represent the cost in 2007 is of: C(-5).

b) The cost was of: $24,658.

An exponential function is defined as follows:

y = ab^x.

In which:

For this problem, the function is defined as follows:

y = 30000(1.04)^x.

In which:

C(3) represents the cost in 2015 and is obtained as follows:

C(3) = 30000(1.04)^3 = $33,746.

C(-5) represents the cost in 2007 and is obtained as follows:

C(-5) = 30000(1.04)^(-5) = $24,658.

(as 2007 was five years before 2012).

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Answer:

Black Line     y = 3 + 2x ,     y = 2x +3

Red Line       y = -2 - .5x.     y = -.5x -2

vice versa

Step-by-step explanation:

For the black line, the lines intersects y at coordinate (0,3) and that would be b. To find the slope, use the equation rise / run. It rises 4 and runs 2. Putting this into an equation 4/2, it would be 2 as the constant. In other words, it would be 2x. Therefore, the function for the black line is y = 3 + 2x

For the red line, using the same explanation from the black line, the line intersects y at -2, and the slope would be -.5x, since it runs downwards 2 and runs 4, and since it runs downwards, a negative sign would be necessary in front of the slope.

Answer:

18.333

Step-by-step explanation:

Answer:3

Step-by-step explanation:

edg

Answer:

The point of estimate for the true difference would be:

[tex] 186-171= 15[/tex]

And the confidence interval is given by:

[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]

[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] \bar X_1 = 186[/tex] the sample mean for the first sample

[tex] \bar X_2 = 171[/tex] the sample mean for the second sample

[tex]s_1 =33[/tex] the sample deviation for the first sample

[tex]s_2 =23[/tex] the sample deviation for the second sample

[tex]n_1 = 8[/tex] the sample size for the first group

[tex]n_2 = 7[/tex] the sample size for the second group

The confidence interval for the true difference is given by:

[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]

We can find the degrees of freedom are given:

[tex] df = n_1 +n_2 -2 =8+7-2= 13[/tex]

The confidence level is given by 90% so then the significance would be [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex] we can find the critical value with the degrees of freedom given and we got:

[tex] t_{\alpha/2}= \pm 1.77[/tex]

The point of estimate for the true difference would be:

[tex] 186-171= 15[/tex]

And replacing into the formula for the confidence interval we got:

[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]

[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]

Answer:

1/1 x 7/1 x 1/12

Is there any options?

Step-by-step explanation:

Answer:6/8 adding 1/4

Step-by-step explanation: Because im right probably

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

I think its A

Step-by-step explanation:

Answer:

2x³ - 17x² + 13x + 11

Step-by-step explanation:

(2x + 1)(x² - 9x + 11)      Distribute the 2x then the 1

2x³ - 18x² + 22x + x² - 9x + 11       Combine like terms

2x³ - 17x² + 13x + 11

If this answer is correct, please make me Brainliest!

Answer:

6.14125(0.15) = 0.9211875 (below 1)

6.14125 - 0.92118 = 5.22007

Step-by-step explanation:

Given data

1. 10(.15)=1.5

2. 10-1.5=8.5

3. 8.5 (.15)=1.275

4. 8.5-1.275=7.225

continuation the sequence

5)    7.225 (0.15) = 1.08375

6)    7.225 -  1.08375 = 6.14125

7)   6.14125(0.15) = 0.9211875   (below -one)

8 ) 6.14125 - 0.9211875 = 5.2200625 (get number 5)

9)   5.2200625(0.15) = 0.783009

10) 5.2200625 - 0.783009 = 4.4370532

Answer:

10 x 17.1 = 171

Step-by-step explanation:

10 x 17.1 = 17.1

Answer:

The theoretical probability of drawing a red marble is 1/3.

Step-by-step explanation:

1. Add all of the marbles together to get total marbles. 16 + 12 + 8 = 36.

2. Create a fraction, with numerator being favorable outcomes and denominator being total possible outcomes. In this case it would be 12/36.

3. Since it is asking for a reduced fraction, simplify 12/36 to 1/3.