Consider the system of equations.
x-3y = 9
1/5 x - 2y = -1
Which number can be multiplied by the second equation to eliminate the x-variable when the equations are added
together?

Answer:

34

Step-by-step explanation:

Answer:  ¹/₂( x² - 10y² + 10xy - xy )

Step-by-step explanation:

From the diagram area of the triangle = ¹/₂ ˣ base ˣ height

where the base = x + 10y and the height = x - y

Therefore putting these into the formula above

Area  =   ¹/₂ [( x + 10y )( x -y )]

         =   ¹/₂( x² - xy + 10xy - 10y²)units²

         = ¹/₂( x² - 10y² + 10xy - xy )

Answer:

Step-by-step explanation:

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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The Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.

Volume can be defined as the total quantity of a substance that a container can hold at a given period of time. Also, the volume of a container is measured in:

Based on the information provided in the table above, we can infer and logically deduce that the Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.

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Applying the tangent to a circle theorem and the two tangents theorem, the value of WY is: 6 units.

The tangent to a circle theorem states that if a line is tangent to a circle, then it will be perpendicular to the radius of the circle.

The two tangents theorem states that two tangents that intersect at a point outside a circle are equal in length.

Applying the tangent to a circle theorem, ΔWXO would be a right triangle. Therefore, apply Pythagorean theorem to find XW given the following:

OX=3.2

OW = 6.8

Applying the pythagroean theorem, we would have:

XW = √(OW² - OX²)

Substitute

XW = √(6.8² - 3.2²)

XW = 6

Based on the two tangents theorem, XW = WY. Therefore,

WY = 6.

In summary, applying the tangent to a circle theorem and the two tangents theorem, the value of WY is: 6 units.

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Answer:

No, this is not a function because this would not pass the vertical line test in which only one y point can be on one x axis not two. As you can see, on (0,3) and (0,(-2)) are on the same x axis. So, not a function.

Answer:

i. The horizontal component of the ball = 15.8

ii. The vertical component of the ball = 11.2

Step-by-step explanation:

A thrown ball is an example of a projectile, whose motion can be explained with respect to both horizontal and vertical components.

Horizontal component of the ball = U Cos θ

Vertical component of the ball = U Sin θ

where U is the initial velocity of the ball, and θ is the angle of projection.

Thus for the given question,

U = 70 km/hr (19.44 m/s)

θ = 35°

So that;

i. The horizontal component of the ball = 19.44 Cos 35°

                                               = 19.44 x 0.8192

                                               = 15.785

The horizontal component of the ball = 15.8.

ii. The vertical component of the ball = 19.44 Sin 35°

                                                = 19.44 x 0.5736

                                                = 11.151

The vertical component of the ball = 11.2

Answer:

i think it is 62.5

Step-by-step explanation:

Answer:

0.016

Step-by-step explanation:

In order to determine the quotient between 3,477 and 5, divide the numbers in standard form:

695.4

5 l 3,477

-30

477

-45

27

-25

20

-20

0

Hence, the quotient between 3,477 and 5 is 695.4

The total area of all six sides that will be painted on the wooden cube is 96 square centimeters.

First, we need to understand that each cube has six faces or sides, which are all squares of the same size. When we paint the cube, we will be painting all six sides of it. Therefore, we need to find the total area of all six sides that will be painted.

To calculate the area of each side, we need to know the length of the side. You mentioned that the wooden blocks are cubes, so each side will have the same length. Let's say the length of each side is 4 cm.

Now, we can calculate the area of one side of the cube by squaring the length of the side. In this case, the area of one side will be:

Area of one side = (length of side)²

= (4 cm)²

= 16 cm²

Since there are six sides to each cube, we can find the total area of all six sides by multiplying the area of one side by six:

Total painted area = 6 x Area of one side

= 6 x 16 cm²

= 96 cm²

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Answer:

the answer is 4

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Answer:  Triangle 4

The red triangle (that's unlabled) is reflected over the vertical line x = 6 to produce triangle 4.

The ordering of cube root of fifty-eight, thirty-two over seven, square root of twenty-eight from greatest to least will be B. thirty-two over seven, square root of twenty-eight, cube root of fifty-eight

The cube root of 58 is approximately 4. It should be noted that thirty two over seven will give a value of 4.57 and the square root of 28 will be 5.29.

Therefore, the ordering of cube root of fifty-eight, thirty-two over seven, square root of twenty-eight from greatest to least will be B. thirty-two over seven, square root of twenty-eight, cube root of fifty-eight.

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Answer:A

Step-by-step explanation:

Answer: all real numbers

Step-by-step explanation:

you can plug in any number for x and get back a corresponding y value. So the domain is all real numbers.

Answer:

8 years

Step-by-step explanation:

Observe the side lengths

Here

Now we know

that bigger side has bigger opposite angle

\(\\ \tt\hookrightarrow <H ><J ><I\)

Answer:

Observe the side lengths

Here

JI>JH>IH

Now we know

that bigger side has bigger opposite angle

Step-by-step explanation:

The final velocity of the parameters is 13.5m/s

In this question, the given parameters are represented as

Formula: v = u + at

Initial velocity = 3m/s

Acceleration = 1.5m/s²

Time = 7 seconds

When these parameters are represented using their required notation, we have the following representations

u = 3m/s

a = 1.5m/s²

t = 7 s

Next, we substitute the above parameters in the above equation

So, we have the following representation

v = 3 + 1.5 * 7

Evaluate the products

This gives

v = 3 + 10.5

Evaluate the sum

So, we have the following representation

v = 13.5

The notation v represents the final velocity

Hence, the final velocity is 13.5m/s

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7) ∠EFG = 88 degree

8) DC and AB are parallel to each other.

AE and AB are perpendicular to each other

CG and AB are perpendicular to each other.

9) ∠ACD = 102 degree

What do you mean by co interior angle?

Co-interior angles, or consecutive interior angles, are two angles on the same side of a transverse line. Co interior angles are interior angles that add up to 180 degrees. This means that the sum of the two interior angles on the same side of the horizontal side are complementary.

7) Given :

∠EFG = 32 degree

∠GFH = 56 degree

∠EFG = ∠EFG + ∠GFH = 32 + 56 = 88 degree

Therefore, ∠EFG = 88 degree

8) DC and AB are parallel to each other.

AE and AB are perpendicular to each other

CG and AB are perpendicular to each other.

9) As AB and CD are parallel to each other therefore , ∠BAC and ∠ACD are cointerior angle and sum of co interior angles is 180 degree.

6x + 6 + 9x - 6 = 180

15x = 180

x = 180/15 = 12

∠ACD = (9x - 6) degree = 9(12) - 6 = 108 - 6 = 102

Therefore, ∠ACD = 102 degree

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A probability value equal to or smaller than 0.05 would indicate that Gaurav's null hypothesis should be rejected at the 5% significance level.

In hypothesis testing, the significance level, denoted as alpha (α), is the predetermined threshold used to determine whether to reject the null hypothesis.

Gaurav has specified a 5% significance level, which means he wants to control the probability of making a Type I error (rejecting the null hypothesis when it is true) at 5% or less.

If Gaurav were to conduct a test and calculate the p-value, he would compare it to the significance level of 0.05.

The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.

If the p-value is less than or equal to the significance level (p ≤ α), it indicates that the observed difference is unlikely to occur by chance alone under the assumption of the null hypothesis.

Gaurav would reject the null hypothesis and conclude that there is a significant difference between the average amount of medication his patients are taking and the national average.

Conversely, if the p-value is greater than the significance level (p > α), it suggests that the observed difference could reasonably occur by chance, and Gaurav would fail to reject the null hypothesis.

This would imply that there is no significant difference between the average medication amounts of Gaurav's patients and the national average.

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The height of the stump is 3 ft.

The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.

In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:

h(0) = -16(0)² + 64(0) + 3

Since any term multiplied by zero is zero, we can simplify further:

h(0) = 0 + 0 + 3

Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.

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Answer:

$2.50/pound

Step-by-step explanation:

Because if its $5for 2 pounds divide by 5 by 2 to see how much 1 pound costs

Answer:

Shelter b has 320 beds that are occupied

Step-by-step explanation:

500/5=100

90x5=450 beds in shelter A

450/15=30

30x16=480

480/3=160

160x2=320

Answer:

first odd number be x = - 73

second odd number be x + 2 = (- 73 + 2) = - 71

third odd number be x + 4 = (- 73 + 4) = - 69

Step-by-step explanation:

let the first odd number be x

second odd number be x + 2

third odd number be x + 4

Now, three consecutive odd integers whose sum is - 213.

i.e.,

(x) + (x + 2) + (x + 4) = - 213

Then,

(x) + (x + 2) + (x + 4) = - 213

x + x + 2 + x + 4 = - 213

3x + 6 = - 213

3x = - 213 - 6

3x = - 219

x = - 219/3

x = - 73

Thus, The value of x is - 73

Here,

first odd number be x = - 73

second odd number be x + 2 = (- 73 + 2) = - 71

third odd number be x + 4 = (- 73 + 4) = - 69

So

(x) + (x + 2) + (x + 4) = - 213

(- 73) + (- 73 + 2) + (- 73 + 4) = - 213

(- 73) + (- 71) + (- 69) = - 213

- 73 - 71 - 69 = - 213

- 213 = - 213

Hence, L.H.S = R.H.S

-TheUnknownScientist

Answer:

the weight of 1 textbook is 2 pounds

the weight of 1 game is about 0.5 pounds

Step-by-step explanation:

1/2 of 2 = 0.5 pounds

0.5 times 8 (games) = 4

22 - 4 = 18

18 divided by 9 (textbooks) = 2 pounds

Answer:

Each game is 0.5 pounds and each textbook is 2 pounds.

Step-by-step explanation:

If x represents games and y represents textbooks you can use the equation

6x + 9y = 21

we know that if the box was 21 pounds and she adds two games and it's now 22 pounds that each game is 0.5 pounds so x = 0.5

after plugging in the x value the equation is:

3 + 9y = 21

Combine like terms and it's 9y = 18

Divide 18 by 9 and you get:

Y= 2

Hope this helps! Good luck on your test.