2. MGSE9-12.A.REI. 1 Which step in solving this equation is justified by the Distributive Property? Consider the sequence of steps to solve the equation: 6v + 3(v – 5) = 4v - (2v + 1) Given = 6v + 3(v — 5) = 4v - (2v + 1) Step 1 = 6 + 3x – 15 = 4y - (2v + 1) Step 2 => 6v + 3v – 15 = 4v – 2y = 1 Step 3 9v – 15 = 4y – 2y - 1 Step 4 => 9v - 15 -- 2v + 4y = 1 Step 5 =9v = 15 = 2y + 1 Step 6 3 7v - 15 =-1 Step 7 3 Tv = 14 Step 8 = v= 2 a. Step 1 b. Step 7 C. Step 5 d. Step 2

The other side of the triangle by using Pythagoras theorem is 15 cm.

Given that,

The triangle has an hypothesis 25cm, adjacent is 20 cm and opposite is x cm.

We have to find the other side by using Pythagorean theorem.

The hypotenuse of a triangle, which has a straight angle of 90 degrees, has a square that, according to the Pythagoras theorem, equals the sum of the squares of the other two sides.

c²=a²+b²

25²=20²+x²

625=400+x²

x²=625-400

x²=225

Square root on both sides.

x=√225

x=15.

Therefore, The other side of the triangle by using Pythagoras theorem is 15 cm.

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80 percent of games 32 games is 40 games.

You just multiply a decimal figure by 100 to convert it to a percentage, such as 0.57. In other words, 0.57 x 100 Equals 57. In percentage terms, 0.57 is equivalent to 57%. 0.03 x 100 = 3% is another illustration.

Assume G to be the total number of games.

Given the information below:

The number equals 80%

Finished: 32 games

To track down the elusive amount of games:

You must calculate the total number of games that result from multiplying 32 games by an 80 percent proportion in this task. G would then be multiplied by the percentage and converted into 32 games.

For the contests:

80/100×G = 32

G = 32/0.8

G = 40games.

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x represents the cost of each bottle of juice. Given that he bought a pack containing 6 bottles of juice, the cost of the 6 pack juice bottles would be $6x

Given that the total cost of a bag of popcorn which costs $2.11 and a 6-pack of juice bottles is $11.41, it means that

2.11 + 6x = 11.41

6x = 11.41 - 2.11

6x = 9.3

x = 9.3/6

x = 1.55

The cost of each bottle of juice is $1.55

The total weight in ounces of the two identical nail boxes is 336 ounces.

Jason bought two identical boxes of nails.  One box weighs 168 ounces.

The total weight in ounces of the nails that Jason bought can be calculated as follows:

The boxes of nails are identical. Therefore, they have the same weight. The weight of the two boxes is the sum of the weight of the boxes.

Hence,

total weight of the boxes = 168 + 168

total weight of the boxes = 336 ounces

Therefore, the total weight is 336 ounces.

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The Required Sample size is 138 . Yes, this number of IQ test Score is a fairly large number.

In the given statements we have , An IQ test is designed such that

the mean of adults ( X bar ) = 100

standard deviations (σ ) = 18

Estimate the mean iq score of statistics students such that the confidence level is 95%

We know the value of Z score for given confidence level 95% is 1.96 .

Margin of error in IQ test = 3

we shall calculate the sample size here.

Using the Margin of error formula,

M.E = Z( √σ ²/n )

where, Z--> z score value

σ --> standard deviations

n ---> sample size

putting all the values in this formula we get ,

3 = 1.96 (√(18)²/n )

=> 3/1.96 = √324/n => (1.5306)² = 324/n

=> n = 324/ 2.342 = 138.29

Hence, the required Sample size is 138 .

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Complete question:

An IQ test is designed so that the mean is 100 and the standard deviation is 18 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 3 IQ points of the true mean. Assume that σ =18 and determine the required sample size using technology.

Then determine if this is a reasonable sample size for a real world calculation.

The graph of g(X) = -(x+3)⁴ compares to the parent function of f(x) = x⁴ got shifted 3 units to left and reflected over x-axis.

Translation means shifting , rescaling and reflecting parents function.

Shifting the graph means to move the graph to new location

Scaling means changing it shape

and Reflecting means a mirror image of parent function across either x-axis or y-axis.

here, If we draw graph of both the function you'll see

The parent function f(x) = x⁴ have center as (0,0)

where as Center of function g(x) = -(x+3)⁴ is (-3,0)

means g(x) = -(x+3)⁴ is moves towards the left by 3 units

and also the graph is in downwards which means it has also reflected across x-axis

Hence , the g(x) = -(x+3)⁴ is shifted 3 units to the left and reflected over the x-axis compare to parent function.

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Answer:

x = 10

Step-by-step explanation:

y = - 8 is a horizontal line parallel to the x- axis

A line perpendicular to it will therefore be a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (10, - 20 ) with x- coordinate 10 , then

x = 10 ← equation of perpendicular line

The distance from D to the base AB is 6 cm

If ΔACB is an isosceles triangle, then ∠A ≅ ∠B and AC ≅ CB

Since ∠C = 120° and ∠A + ∠B + ∠C = 180°, then ∠A = 30° and ∠B = 30°

Next, look at ΔADB.  ∠A + ∠D + ∠B = 180°, so ∠A + 90° + 30° = 180° ⇒ ∠A = 30°

Now look at ΔADC.  Since ∠A = 30° in ΔACB, and ∠A = 60° in ΔADB, then ∠A = 30° in ΔADC per angle addition postulate.

Now that we have shown that ΔADB and ΔADC are 30-60-90 triangles, we can use that formula to calculate the side lengths.

CD = 4 cm (given) so AC = 2(4 cm) = 8 cm

Since AC ≅ BC, then BC = 8 cm. Therefore, BD = 4 + 8 = 12 by segment addition postulate.

Lastly, look at ΔBHD.  Since ∠B = 30° and ∠H = 90°, then ∠D = 60°. So, ΔBHD is also a 30-60-90 triangle.

BD = 12 cm, so HD =  = 6 cm

Therefore, the distance from D to the base AB is 6 cm

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(x means multiplication)

21/7=3, so he gets the deal 3 times. 2x3=6, so he gets 6 bonus books, leading to a total of 27 books.

Given:

The cardboard costs 0.05 per square inch

And the surface area = 286

So, the total cost is the product of the surface area and the cost per square in.

Total cost =

So, the answer will be Total cost = $14.30

Answer: Not equal to.

Step-by-step explanation: you don't get the same answer to the problem for both.

Answer: 2.5, 5.3

Step-by-step explanation:

[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]

The distance covered by him in one hour is 4 miles.

What is distance and time?

Distance of a point from a line is the length of the shortest line segment from the point to the line. This will also be perpendicular to the line.

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.

Given

a person walked 2/5 miles in each 1/10 hour

that is miles = 2/5 = 0.4 miles.

Now time is given as 1/10 hours,

one hour contains 60 minutes.

0.4 = 1/10(60)

0.4 miles = 6 minutes.

1 hour = 0.4 (60)/6

1 hour =  4 miles.

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In the ratio of 2:6 , Lacey will get 6 cards and Martha will get 18 cards

Total number of cards = 24

Let Lacey gets "x" numbers of cards and Martha gets "y" numbers of cards

Ratio of cards given to Lacey to Martha = 2:6

x:y = 2:6

and we also know that total cards are 24

x + y = 24

x = 24 - y

putting value of x in the ratio,

[tex]\frac{24 - y}{y} = \frac{2}{6}\\[/tex]

cross multiplication,

6(24 - y) = 2y

144 - 6y = 2y

8y = 144

y = 18

Substituting value of y ,

x = 24 - 18

x = 6

Hence , Lacey will get 6 cards and Martha will get 18 cards.

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Answer

The remaining board piece will be 3 (7/8) feet long

Explanation

Mia's board is 15 (1/2) feet long.

He cut three pieces off the board with each board measuring 3 (7/8) feet long.

The key to this is to first convert the values given in mixed fractions as improper fractions.

3 (7/8) = (31/8)

15 (1/2) = (31/2)

Then, the three pieces each had a length of 3 (7/8)

1 piece = 3 (7/8) feet = (31/8) feet

3 pieces = 3 × (31/8) = (93/8) feet

So, taking this out of 15 (1/2) long board will leave

[15 (1/2)] - (93/8)

= (31/2) - (93/8)

To do that, we need to take the LCM of these two denominators

The remaining board piece will be

(31/8) = 3 (7/8) feet long

Hope this Helps!!!

Let's label the diagram with the information provided. The diagram would look like:

This is labeled as x.

With respect to angle alpha, the side x is opposite and the antenna is the side adjacent.

Thus, we need the trig ratio tan to solve for "x". Shown below:

Answer: 58.23 feet

This is labeled as y.

With respect to angle beta, the side y is opposite and the antenna is the side adjacent.

Thus, we need the trig ratio tan to solve for "y". Shown below:

Answer: 77.97 feet

The distance between Anchor 1 and Anchor 2 is "x + y". We already found x and y. Let's do the sum:

Answer: 136.2 feet

The smallest a and b values such that 41a = 14b. The smallest value is a = 0.34.

Given,

41a = 14b

a = 14b/41

Simplifying,

41a = 14b divide both side by 41

41a/41 = 14b/41b

= 41a/14

b is = 2.92

and the a is,

a = 14b/41 = 0.34

Hence the lowest value is a = 0.34

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Using the given ratio, we will see that we can define the proportions to find that:

Sandra gets 12 marshmallows.

Peter gets 18 marshmallows.

We know that Sandra and Peter share a packet of 30 marshmallow eggs in the ratio of 2:3.

We can find the fractions for each person by doing the following steps:

So if we add the two values in the ratio we get 2 + 3 = 5

The ratio is:

Sandra:Peter = 2:3

Then we can write the fractions as:

The fraction of the total number of eggs that Sandra gets is 2/5

The fraction of the total number of eggs that Peter gets is 3/5

Now remember that the total number of marshmallow eggs is 30, then the number that Sandra gets is:

S = (2/5)*30 = 12

And the number that Peter gets is:

S = (3/5)*30 = 18

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The value of unknown variable [x] is x = 36 x 10⁻⁴

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have a proportional relationship of the form -

y₁/x₁ = y₂/x₂

We can write it as -

x = (5.1 x 10⁴ x 12)/(1.7 x 10⁸)

x = 36 x 10⁻⁴

Therefore, the value of unknown variable [x] is x = 36 x 10⁻⁴

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In 5040 different ways, 7 runners can places 1 through 4 be determined if in a race there are 7 runners. trophies for the race are awarded to the runners finishing in places 1 through 4.

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations. Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation could be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!

Given,

Ways 7 runners can places 1 through 4 be determined:

By using permutation:

7!

7 ×6 × 5 ×4×3×2×1

5040

In 5040 different ways, 7 runners can places 1 through 4 be determined if in a race there are 7 runners. trophies for the race are awarded to the runners finishing in places 1 through 4.

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Answer:

price - savings

= $60 - $15

= $45

grandma's bonus =

hence, $45 + x = $60

Collect like terms

60 - 45 =

X = $15

Answer:0.56

Step-by-step explanation:

You simply divide 14 by 25

so 14÷25 or 14/25

put that in a calculator and it comes out to 0.56

Answer:0.56

Step-by-step explanation:

if you make the 25 into 100 which is x4 and 14x4= 56

so it will be 56/100 which is 0.56

Answer:

The slope is 5.

Explanation:

In the slope-intercept form of an equation

m is the slope, and b is the y-intercept of the equation.

Now in our case,

therefore, the slope is 5 and the y-intercept is -3.

The required perimeter is 11x +11

In relation to mathematics, the concepts "area" and "perimeter" are crucial. Any field shape, whether asymmetrical or symmetrical, applies to this. It is measured from the object's edge to its perimeter. Like the yard that is fenced in at your home. The distance around anything is called its perimeter. The fence is 200 feet long for a yard that is 50 feet by 50 feet.

A measurement of an object's interior space is its area. An area is the size you must be in order to begin a lawn in the same yard. Units of squared distance are used in the area. There must be 2500 square feet of grass for a 50 ft by 50 ft.

The perimeter can be calculated by simply adding all the given expression;

= 7x - 13 + x + 29 + 3x + 5

bringing the like terms together

= 7x + x + 3x + 16 + 11

= 11x + 11

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1.The multiplied answer for the given numbers 2.5 and 3.15 is 7.875. Option 4 is correct.

2. Her investment is 578.85, Option-C is correct.

Given that,

There is a question in the picture that is

The numbers 2.5×3.15

We have to find the multiplied answer.

Mathematicians use multiplication to calculate the product of two or more numbers. It is a basic mathematical procedure that is widely used in daily life. When we need to combine groups of similar sizes, we utilize multiplication.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Multiplying the numbers makes it simpler to add the same number repeatedly.

=2.5×3.15

=7.875

Therefore, the multiplied answer for the given numbers 2.5 and 3.15 is 7.875. Option 4 is correct.

2. We have she has invest $500 at 5% annual compound interest. After 3 years, what is her investment.

500×5%

25

Next 525×5%

551.50

Next

578.85

Therefore, her investment is 578.85, Option-C is correct.

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Answer:

61.56%

Explanation:

Let the first American = A

• P(A goes) = 0.62

• P(A does not) = 0.38

Let the second American = B

• P(B goes) = 0.62

• P(B does not) = 0.38

The probability that one or both of the people chosen does not go on vacation each year

=P(A goes and B does not) or P(A does not and B does) or P(both do not)

Therefore, the probability that one or both of the people chosen does not go on vacation each year is 61.56%.

Function 1 has a greater rate of change: false.

Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x in function 2, which represents a line that is passing through the points (2, 0) and (8, 6):

Rate of change, m = (6 - 0)/(8 - 2)

Rate of change, m = 6/4

Rate of change, m = 1.5 or 3/2.

From function 1 (y = -x + 6), we can logically deduce that the rate of change is equal to -1.

In conclusion, the rate of change of function 2 (m = 1.5) is greater than the rate of change of function 1 (m = -1).

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Notice that the all estimations for each graph are correct.

Given the function

First I'll rewrite it in terms of y

Next is to determine the values of y (range) for the given values of x

Now you can graph it: