Hi can u help me with 6th Grade math questions 13,14,15,16

Answer:A

Step-by-step explanation:

The principal amount of $5,000 deposited for 8 years with simple interest gives amount $7,880 at the annual interest of 7.2%.

Total amount 'A' in the Macy account after 8 years = $7,880

Time 't' = 8 years

Principal amount 'P' = $5,000

Let 'r' be the rate of interest given in saving account with annual simple interest.

Simple interest = Amount - Principal

                         = $7,880 - $5,000

                         = $2,880

Simple interest = ( P × r × t ) / 100

Substitute the value we get,

⇒ $2,880 = ( 5,000 × r × 8 ) / 100

⇒ r = ( 2,880 × 100 ) / ( 5,000 × 8 )

⇒ r = 7.2%

Therefore, the annual interest rate for the given amount as per simple interest is equal to 7.2%.

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Answer:

12000

Step-by-step explanation:

4500:12=470

425:125=100

1000×12=12000

Step-by-step explanation:

So to start

Perpendicular lines are lines that form 90 degree angles when they meet.

Parallel lines will never touch, no matter how far they go.

So

Top left

A vertical line and a horizontal line

This would be perpendicular

Lines that intersect to form right angles

As mentioned above this would be perpendicular

Two nonvertical lines that have a product of -1 for their slopes.

Parallel lines always have the same slope, so this goes for parallel.

Equations that can be written in slope intercept form

This would be both as all lines can be written in this form

Non vertical lines that have the same slope and different y-intercepts

As they have the same slope this would make it parallel

You can determine the relationship between two lines by comparing their slopes and y-intercepts.

This is both as this is a way to compare all lines

Lines in the same plane never intersect

This would be parallel

Slopes are opposite reciprocals

This is perpendicular as the slopes of perpendicular lines are reciprocals

Vertical lines that have different x-intercepts

This would be parallel

Sorry this is a lot

Hope this helped though :)

The solution for this equation system is x= 29, y=53, (29, 53).

[tex](1)y=3x-34\\ \\(2)y=2x-5[/tex]

[tex](2x-5)=3x-34\\\\2x-5=3x-34[/tex]

[tex]2x-5+5=3x-34+5\\ \\2x=3x-29[/tex]

[tex]2x-3x=3x-29-3x\\ \\-1x=-29\\ \\-x=-29[/tex]

[tex]-x(-1)=-29(-1)\\ \\x=29[/tex]

To find a value of "y", use the calculated value of "x" (29), and substitute in any of the two equations to find the value of "y". For this solution, we're going to use equation 2.

[tex]y=2(29)-5\\ \\y=58-5\\ \\y=53[/tex]

On step 6 we proved that the value of "x=29" returns a value of "53" when evaluating with equation 2. Now, if equation 1 returns the same "y" value when evaluating "x=29", then the calculated values of both "x" and "y" are correct. Let's verify!

[tex]y=3(29)-34\\ \\y=87-34\\ \\y=53[/tex]

Both of the equations return the same value of "y" (53) when evaluated with "x=29". Therefore, the solution for this equation system is x= 29, y=53, (29, 53).

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The quantity of has he had left in his car after taking both friends home would be = 4.76gallons

The total amount of gas in gallons in his car = 6 gallons

The amount of gas he used to take one of his friends home = 1.04 gallons.

The second friend he used a total of = 1/5 = 0.2 gallons.

The total amount of gas he uses = 1.04+0.2 = 1.24 gallons.

Then the amount of gas remaining = 6 - 1.24 = 4.76gallons.

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Answer: For every one who is annoyed with the dude aboves answer the correct answer is: D 4.56

Step-by-step explanation:

The plane is travelling at a speed of 424.26 mph.

Velocity of an object is the speed of the object with a given direction. Therefore velocity is a vector quantity and speed is a scalar quantity.

Given that,

A plane is traveling Northeast.

If the plane is travelling northeast, then the angle that the plane makes with the horizontal component will be 45°.

The eastern component of it's velocity is 300 mph.

Vector v can be represented as v cos (θ) i + v sin(θ) j.

Here v cos (θ) is the eastern component and v sin(θ) is the northern component.

v cos (θ) = 300

v cos(45°) = 300

v = 300 / cos(45°)

  = 300 / (1/√2)

  = 424.26 mph

Hence the speed of the plane is 424.26 mph.

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Since triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15), the scale factor used is: A. 5.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Scale factor = -15/-3

Scale factor = 5.

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Answer: its 5

Step-by-step explanation: I did it in a test and got it right

The length and the width are 21cm and 16cm respectively.

The formula for calculating the perimeter of a rectangle is expressed as;

P = 2(l +w)

Given that;

But we have that;

Length = 5 + w

Substitute the value

74 = 2(5 + w + w)

collect like terms

74=2 (5 + 2w)

expand the bracket

64 = 4w

Make 'w' the subject of formula

w = 16cm

Then, length = 5 + 16 = 21cm

Hence, the values are 16cm and 21cm

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The simplified expression is equal to 2/3.

        2m⁰ * n⁶ / (3n⁵)

       2 * n⁶ / (3n⁵)

        2 * n / (3n) = 2/3

So the simplified expression is equal to 2/3.

The rules of arithmetic and exponentiation that I used to simplify the expression are general mathematical principles that are applicable to many mathematical problems. However, the specific techniques for simplifying an expression will depend on the particular expression and the context in which it is being used.

For example, there might be additional rules or simplification techniques that are specific to a particular field of mathematics, such as algebra, calculus, or geometry. In these cases, it's important to understand the specific rules and techniques that apply to the problem at hand in order to simplify an expression effectively.

In general, the goal of simplifying an expression is to make it easier to understand and manipulate mathematically, either for further calculations or for understanding the relationships between the variables involved.

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The distance around the track along its outer edge is  238 + 100 x π metres and the area of the track is  1250 x π  + 2380 square metres.

The racetrack is divided by two parallel sections and two semi-circular endpoints. The two parallel segments are 119 metres long, and the track is 10 metres wide. The inner length of the two parallel sections is 70 metres.

To calculate the distance around the track's outer edge, multiply the lengths of the two parallel segments by the diameter of the two semi-circular ends. C = 2 x π x r, where r is the radius of the semi-circle, may be used to compute the circumference of each semi-circular end.

The radius of each semi-circle is calculated by subtracting the track width (10 metres) from half the inner distance between the two parallel sections (70 metres / 2 = 35 metres). So, the radius of each semi-circle is 35 metres - 10 metres = 25 metres.

As a result, the circumference of each semi-circle is 2 x π x 25 = 50 x π  metres. As a result, the circumference of the track along its outside border is 119 metres + 119 metres + 50 x π  metres + 50 x π  metres = 238 + 100 x π metres.

To calculate the area of the track, first calculate the areas of the two semi-circular ends and the two parallel segments, then add them. A = π[tex]r^{2}[/tex], where r is the radius of the semi-circle, may be used to compute the area of each semi-circular end.

Each semi-circle has an area of π x [tex]25^2[/tex] = 625 x π  square metres. The size of the two parallel lengths is 1190 square metres (119 metres x 10 metres). The track's total area(A) = 625 x π  + 625 x π  + 1190 + 1190

A= 1250 x π  + 2380 square metres.

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Answer:

3.1.1) There are four terms in this expression.

3.1.2) The coefficient of x^3 is 0.5.

3.1.3) The constant term is 8.

3.1.4) The degree of the expression is 5.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Multiplication is often referred to as repeated addition because what the multiplication problem is telling you is that you have a certain number of groups of something, all containing a specific number. Confused yet? Here's an example.

You have 3 bags of candy, and each bag contains 5 pieces of candy. How many pieces of candy do you have?

There are two ways to solve this problem. The first is by adding up the pieces of candy:

5 + 5 + 5 = 15

The other way to solve this problem is to use multiplication, because you have 3 groups of candy with 5 pieces of candy in each bag.

3 * 5 = 15

The answer to this multiplication problem is the product, which in this case is 15.

Here's another example. The classroom has 8 rows of chairs and each row has 7 chairs in it. How many chairs are there?

Again, you could add:

7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56

Or, you can find the product by multiplying:

7 * 8 = 56

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CORRECT QUESTION FORMAT IS GIVEN BELOW -----

Q. What is the Product in Math?

"Every linear transformation is a matrix transformation." This is false. Not all linear transformations are matrix transformations, even if all matrix transformations are linear transformations.

A point, line, or geometric object can be changed in four different ways that are all referred to as transformations. The Pre-Image refers to the object's initial shape, and the Image, after transformation, refers to the object's ultimate shape and location.

Bring out the pattern blocks, tangrams, and geoboards for another low-prep, high-engagement method of teaching geometric transformations. Students can produce an original design and then hand it off to a partner so that they can add a reflection, rotation, or translation to it.

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The median weight of the players on the football team is approximately 160 lbs.

The box plot provides a visual summary of the data which shows the distribution of the weights of the players on the football team. The box plot consists of a box and two "whiskers" which represent the upper and lower quartiles of the data. The box is bounded by the upper quartile and lower quartile and the two whiskers represent the highest and lowest values in the data set, excluding any outliers. The median weight of the players is represented by the line in the middle of the box, which is approximately 160 lbs. The box plot is a useful tool for summarizing the data and provides a quick and easy way to visualize the distribution of the players' weights. The median weight of 160 lbs gives us an idea of the average weight of the players, which can be used to determine the overall strength of the team.

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The complete question is

a high school has 40 players on the football team. the summary of the players' weights is given in the box plot. what is the median weight of the players and find lbs.

The number of bacteria after 3 months is 7500.

The equation is y = 60,000 x [tex]0.5^3[/tex].

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

Number of bacteria initially = 60,000

After one month,

The number of bacteria = 30,000

This means,

60,000 - 30,000 = 30,000

The percentage decreased.

= 30,000 / 60,000 x 100

= 1/2 x 100

= 50%

Now,

The equation for the number of bacteria after x months.

y = 60,000 x [tex]0.5^x[/tex]

For x = 3,

y = 60,000 x [tex]0.5^3[/tex]

y = 60,000 x 0.125

y = 7500

Thus,

The number of bacteria after 3 months is 7500.

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Answer:

-3(x+0.5)^2-181/4 (if I calculated correctly)

Step-by-step explanation:

f(x)=-3x^2-3x-46

=-3(x^2+x+46/3)

=-3(x+0.5)^2-(0.5)^2+46/3

=-3(x+0.5)^2+181/12

=-3(x+0.5)^2-181/4

Answer: 174 miles

Step-by-step explanation: 14.5 (14 1/2) times 12 is 174

The value of m for which the equation will have two equal solutions is given as follows:

m = -2.5.

A quadratic equation is modeled by the rule presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:

For this problem, the discriminant is given as follows:

Δ = 2m + 5 (it is the term that goes inside the root during the solution).

Hence, to have two equal solutions, the condition is:

Δ = 0.

Hence:

2m + 5 = 0

2m = -5

m = -5/2

m = -2.5.

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Answer:

[tex]t=14.7[/tex]

Step-by-step explanation:

In the equation: [tex]t-9.25=5.45[/tex] we need to get [tex]t[/tex] by itself. To do that, we need to add [tex]9.25[/tex] from one side to the other. We do this because on the side where [tex]t[/tex] is, [tex]9.25[/tex] is being subtracted and we have to do the opposite of that. So:

[tex]t-9.25=5.45[/tex]

  [tex]+9.25[/tex]     [tex]+9.25[/tex]

In this case, we got [tex]t[/tex] by itself. The new equation is:

[tex]t=14.7[/tex]

The length of the arc is 42.98 inches, so the correct option is A.

For an arc defined by an angle θ on a circle of radius r the length of the arc is given by:

L = (θ/360°)*2*pi*r

Where pi = 3.1416

Here we know that:

r = 10.26 inches

θ = 240°

Then we can replace that in the formula above, we will get:

L = (240°/360°)*2*3.1416*10.26 in

L = 42.98 inches

The correct option is A.

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The rate of exponential decay is 0.19.

f(x) = 202.5x is the equivalent function.

The correct option is A.

An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.

The exponential decay function:

Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.

Given:

The function f(x) = 500(1 − 0.19 )ˣ/2,

models the price of a share of stock over time.

Compared to the definition,

we get,

The rate of exponential decay is 0.19.

When x = 0,

Then f(x) = 202.5x

Therefore, f(x) = 202.5x is the equivalent function.

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The number 7 will be placed in the middle circle.

To place the numbers 2, 6, 7, 8, and 9 in the circles so that the sums across and down are equal, you can use the following method:

1. Place the median number (7) in the middle circle.

2. Place the two smallest numbers (2 and 6) on either side of the median number.

3. Place the two largest numbers (8 and 9) in the top and bottom circles.

Here is a list of them. Each group of three numbers makes up a side of the triangle. Of course, within a side you can replace round numbers that are not on a corner, but that does not really give any new solutions.

So, the final arrangement would be:

6 2 7

9 8 7

6 2 7

Therefore, the number 7 will be placed in the middle circle.

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The length of MN is roughly 13.89 units.

The polygonal shape of a triangle has three sides and three corners. It is one of the fundamental geometric shapes. Triangle ABC is a symbol for a triangle with vertices A, B, and C. When three points are not collinear, unique triangles and planes are found using Euclidean geometry.

Triangle JKL and triangle MNO are comparable, thus we can use the aspect ratio to determine the appropriate side lengths.

MN is 'x' in length. Then, it appears as follows:

JK/MN = 26/x, and KL/NO = 19/x

We can use their ratio to get x because we are aware of the lengths of JK and KL. We obtain: using the first ratio.

26/x = 58/26

x=26*26/58

x = 26^2/58

x = 13.89 (rounded to nearest integer)

Therefore, MN is approximately 13.89 units long. 

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The probability of randomly selecting a girl from Ms. Garcia's class is 5/9.

Which means that for every 5 students in the class, 4 of them are boys and 5 of them are girls.

To calculate the probability of selecting a girl from the class, we need to divide the number of girls by the total number of students:

Number of girls: 5 students

Total number of students: 4 students + 5 students = 9 students

Probability of selecting a girl: 5 students / 9 students = 5/9

So the probability of randomly selecting a girl from Ms. Garcia's class is 5/9.

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Answer:

8b + 4 = 6

Step-by-step explanation:

8b + 4 = 6

It didn't say you have to solve for b, but just in case...

8b = 6 - 4 = 2

b = 2/8 = 1/4

Answer:

Let's first convert 1/6 mile into minutes by multiplying the distance by the number of minutes per mile:

1/6 mile * (1 minute/1/6 mile) = 6 minutes/mile

Next, let's convert the 7/9 minutes into miles:

7/9 minutes * (1/6 mile/minute) = 7/9 * 1/6 mile = 7/54 miles

Now that we have the distance and time in the same units, we can calculate Ed's speed as:

Speed = Distance / Time = 7/54 miles / 7/9 minutes = 7/54 miles / (7/9 * 1 minute) = 7/54 miles / (7/9) minutes = 7/54 miles / (7/9) = 54/7 miles/minute

So, Ed's speed is 54/7 miles per minute.

Step-by-step explanation:

The length of the side x is 60.

Pythagorean Theorem is a mathematical statement that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c^2 = a^2 + b^2

Let the unknown side in the first triangle be a

We know that;

a^2 = 55^2 - 25^2

a= 49

Then again;

x^2 = 35^2 + 49^2

x = 60

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