The equation:
2x + 4 = -8 + 5x
-3x
Step 1 and 2:
Add or Subtract
(use the inverse
operation)
Step 3:
Multiply or
Divide
(use the inverse
operation)
Final Answer:

Answer:

= 70f - 9g

Step-by-step explanation:

1. Remove parentheses

2. Multiply the numbers

3. Multiply the numbers

Answer:

-1

Step-by-step explanation:

Answer:

1,177.5cm^3 of candle wax will be required.

Step-by-step explanation:

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Answer:

= 5 (-2y+3) / -y+3

Step-by-step explanation:

If you need more help, you can look at this website called "symbolab".

Calculating the volume of a cylinder the radius is squared,

If the radius was 8 when 8 is squared you get 64

If the radius is multiplied by 1/2 the radius would become 4, 4 squared is 16

16 / 64 = 1/4

The volume would be 1/4 the original volume, so it would be 4 times smaller.

Final answer:

Halving the diameter of a cylinder makes its volume four times smaller, because the volume depends on the square of the radius, and reducing the diameter by half means the radius is also halved.

Explanation:

When the diameter of a cylinder is multiplied by 1/2, the radius of the cylinder is also reduced to half its original size. To understand the impact on the volume, we examine the volume formula for a cylinder: V = (pi = 3.1416) times r^2 times h, where V is the volume, r is the radius, and h is the height. If both the diameter and radius are reduced by half, the volume of the cylinder will be reduced by a factor of 1/2^2 for the radius squared part of the formula.

Volume is directly proportional to the square of the radius, so taking the original volume formula V =
times (original radius)^2 times h and then applying the radius reduction, we get the new volume V' =
times (1/2 times original radius)^2 times h = 1/4 times original volume. Therefore, the volume of the cylinder becomes four times smaller when the diameter (and thus radius) is halved.

Answer:

The distance from the ground to the top of the ladder the building is touched is 16 feet.

Step-by-step explanation:

Given:

A ladder that is 20 feet tall is leaning against a building.Samuel measures that the base of the ladder touches the ground 12 feet from the base of the building.

Now, to find the distance from base of the building to the top of the ladder where building is touched.

Here, to understand the situation below is the figure attached:

Now, to get the distance from the ground to the top of the ladder where the building is touched we use pythagorean theorem:

[tex]AB^2+BC^2=AC^2\\\\AB^2+12^2=20^2\\\\AB^2+144=400\\\\Subtracting\ both\ sides\ by\ 144\ we\ get:\\\\AB^2=256\\\\Using\ square\ root\ on\ both\ sides\ we\ get:\\\\AB=16\ feet.[/tex]

Therefore, the distance from the ground to the top of the ladder the building is touched is 16 feet.

Answer:

The required vector parametric equation is given as:

r(t) = <3cost, 3sint>

For 0 ≤ t ≤ 2π

Step-by-step explanation:

Given that

f(x, y) = <2y, -sin(y)>

Since C is a cirlce centered at the origin (0, 0), with radius r = 3, it takes the form

(x - 0)² + (y - 0)² = r²

Which is

x² + y² = 9

Because

cos²β + sin²β = 1

and we want to find a vector parametric equations r(t) for the circle C that starts at the point (3, 0), we can write

x = 3cosβ

y = 3sinβ

So that

x² + y² = 3²cos²β + 3²sin²β

= 9(cos²β + sin²β) = 9

That is

x² + y² = 9

The vector parametric equation r(t) is therefore given as

r(t) = <x(t), y(t)>

= <3cost, 3sint>

For 0 ≤ t ≤ 2π

The vector parametric equation for the circle C that starts at the point (3,0) and travels around the circle once counterclockwise for 0≤t≤2π is:

[tex]r(t) = <3cost, 3sint>[/tex]

We have

[tex]f(x, y) = <2y, -sin(y)>[/tex]

As C is a circle centered at the origin (0, 0), with radius r = 3,

So, equation is:

[tex](x - 0)^2 + (y - 0)^2 = r^2[/tex]

[tex]x^2+ y^2 = 9[/tex]

 As, cos²β + sin²β = 1

 Take ,

x = 3cosβ

y = 3sinβ

Then

[tex]x^2 + y^2 = 3^2cos^2\beta + 3^2sin^2\beta\\= 9(cos^2\beta + sin^2\beta) \\= 9\\x^2 + y^2 = 9[/tex]

The vector parametric equation r(t) is therefore given as

[tex]r(t) = <x(t), y(t)>[/tex]

[tex]= <3cost, 3sint>[/tex]

For 0 ≤ t ≤ 2π

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Answer:

(24*10)+50=290

Step-by-step explanation:

a) The equation for the amount of money Autumn makes is y = 10x , where x is the number of bracelets she sells and y is the total amount

b) The amount Autumn makes is $ 290

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

a)

Let the number of bracelets Autumn sells be = x

Let the cost of one bracelet be = $ 10

Now , the equation will be

So , the cost of x number of bracelets y = number of bracelets x cost of one bracelet

The cost of x number of bracelets y = 10x

So , the equation is y = 10x

b)

The equation is y = 10x

The cost of 5 bracelets = 10 x 5

                                       = $ 50

Now , the cost of 24 bracelets = 24 x 10

                                                  = $ 240

So , the total amount Autumn makes = cost of 5 bracelets + cost of 24 bracelets

The total amount Autumn makes = 240 + 50

                                                       = $ 290

Hence ,

a) The equation for the amount of money Autumn makes is y = 10x , where x is the number of bracelets she sells and y is the total amount

b) The amount Autumn makes is $ 290

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Answer:

Hence the function only :

Secx and Cosx functions are symmetric about y-axis

And remaining functions are not symmetric about y-axis.

Step-by-step explanation:

Given:

Six circular function as :

y= sinx ,y=cosx , y=tanx,  y= cotx ,y=secx  y=cosecx

To Find:

Which functions are symmetric about the y-axis

Solution:

The function is said to be symmetric about the y-axis is given by

f(x)=f(-x)

Now

1)For y=sinx  i.e. f(x)=sinx

So put x=-x

f(-x)=sin(-x)

=-sinx

Hence f(x)≠f(-x)

This function is not symmetric about y-axis

2)For y=cosx ,i.e. f(x)=cosx

put  x=-x

f(-x)=cos(-x)...............(as value for x and -x cos value remain the same )

=cosx

hence f(x)=f(-x)

This function is symmetric to the y-axis

3)For y=tanx     i.e   f(x)=tanx

put  x=-x

f(-x)=tan(-x)

=-tanx

Hence f(x)≠f(-x)

This function is not symmetric about y-axis

4)For y=cotx  i.e.  f(x)=cotx

Using above observation,

f(x)≠f(-x)

This is not symmetric about y-axis

5)For y=secx  i.e f(x)=secx

f(x)=f(-x)

This function is symmetric about y-axis.

6) for y=cosecx

f(x)≠f(-x)

This function is not symmetric about y-axis

Answer:

y = x + 2

Step-by-step explanation:

It looks like its adding 2 everytime.

y = x + 2

Answer:

16 ^3/4 = 8

Step-by-step explanation:

distribute the exponential fraction.

Answer:

The correct options are 1, 3, and 5

Step-by-step explanation:

Answer:

Sum of the interior angles of a regular polygon is given by = (n-2)180°

where n is the no. of sides.

In the above figure, n= 10

Therefore, sum of the interior angles = (10-2)×180°

= 8×180°

= 1440°

Measure of each angle = 1440/10= 144°

Therefore, 10x+4=144

=> 10x= 140

=> x= 14

For the given figure the value of x is 14

Given  a regular polygon

A regular polygon is a polygon which has all sides equal and each side  subtends equal interior angle at the center.

According to the figure

We are given a regular polygon with 10 sides

The angle subtended  at the center is given as

(10x + 4)°

[tex]\rm The\; Sum \; of \; Interior\; angles = \bold {(n-2) \times 180\textdegree} ......(1) \\Where n = Number \; of \; sides \;of\; a \;polygon[/tex]

The Sum of interior angles =  ( 10-2) [tex]\times 180\textdegree[/tex]= 1440°

So the angle subtended by one side at the center is given as follows

1440°/ 10 = 144°

Since the angle subtended at the center = 144° = (10x + 4)°

so by solving this we can get

140 = 10x

x = 14  

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Answer:

It's a 19 percent increase.

Step-by-step explanation:

Divide 97/120, then multiply it by 100. After that, you can subtract the answer by 100. The answer will be negative, so make it positive.

Answer:

a = -2  b = 6  c = -3

x = -6 +- sq root (6^2 -4 * -2 *-3) / 2 * -2

x1 = [-6 + sq root (36 - 24)] / -4

x1 = [-6 + sq root (36 - 24)] / -4

x1 = (-6 + sq root (12) ) / -4

x1 = (-6 + 3.4641016151 ) / -4

x1 = -2.5358983849  / -4

x1 = 0.6339745962

x2 = (-6 - sq root (12) ) / -4

x2 = (-6 - sq root (12) ) / -4

x2= (-6 - 3.4641016151 ) / -4

x2 = - 9.4641016151 / -4

x2 = 2.3660254038

Step-by-step explanation:

Answer:

If you're asking about which graph would be better, you can show it by a histogram best.

Step-by-step explanation:

Sorry if this is not your question if not I misunderstood, but a line graph is to measure the changes between data, while histograms measure a single measurement for each subject matter. So the best graph to display this info would be through a histogram

Answer: 280

Step-by-step explanation:

??/500=7/100

7x500/100

35/500=7/100

35x8=280

I think this is the answer.

Answer:

$859.09

Step-by-step explanation:

Answer:

The correct option is;

d. 24.2 to 25.6

Step-by-step explanation:

Here we have a sample with unknown population standard deviation, we therefore apply the student t distribution at 64 - 1 degrees of freedom

Therefore, we have

[tex]CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex]

Where:

[tex]\bar x[/tex] = Mean = 25

σ = Standard deviation = 2

n = Sample size = 64

t = T value at 98% = [tex]\pm 2.387[/tex]

Which gives

[tex]CI=25\pm t_{63}\frac{2}{\sqrt{64}}[/tex]

That is the value is from

24.40325 to 25.59675 which gives,by rounding to one decimal place, is

24.4 to 25.6.

The 98% confidence interval for the true average age of all students at the university, given a sample mean age of 25, standard deviation of 2, and a sample size of 64, is approximately option (d) 24.4 to 25.6 years.

The 98% confidence interval for the true average age of all students in the university can be calculated using the sample mean, the sample standard deviation, and the size of the sample. Since the population standard deviation is unknown and the sample size is less than 30, we use the t-distribution to find the critical value (t).

First, we find the t-score corresponding to a 98% confidence level with 63 degrees of freedom (n-1 = 64-1). Using a t-distribution table or calculator, the t-score is approximately 2.390.

Next, we calculate the margin of error (ME) using the formula:
ME = t * (s/√n)
where s is the sample standard deviation and n is the sample size. Plugging in our numbers:
ME = 2.390 * (2/√64) = 0.5975

Finally, we add and subtract this margin of error from the sample mean to find the confidence interval:
CI = mean ± ME
CI = 25 ± 0.5975
CI = (25 - 0.5975, 25 + 0.5975)
CI = (24.4025, 25.5975)

Therefore, the 98% confidence interval for the true average age is approximately 24.4 to 25.6 years.

The side length, s, of the resulting polyhedron is (20√3)/3 cm.

To find the value of s, the side length of the resulting polyhedron, we can analyze the original cube's corners and the pyramids that Donatello slices off. Each corner of the cube contributes one-eighth of a pyramid to the polyhedron. These pyramids are similar, and their base is an equilateral triangle with side length s/2, and the height is s/2.

Considering one of these pyramids, we can use the Pythagorean theorem to find its slant height (the side length of the original cube):

(s/2)^2 + (s/2)^2 + (s/2)^2 = 10^2

Simplifying:

3/4 * s^2 = 100

Now, solve for s:

s^2 = (4/3) * 100

s^2 = 400/3

s = √(400/3)

s = 20/√3

To rationalize the denominator, multiply by (√3/√3):

s = (20/√3) * (√3/√3)

s = (20√3)/3

So, the side length s of the resulting polyhedron is (20√3)/3 cm.

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The side length of the resulting polyhedron after slicing off corner pyramids is  [tex]\( \frac{10}{3} \).[/tex]

Of course, here's the solution in LaTeX:

To find the side length ( s ), we can break down the process step by step:

1. Start with a cube of side length ( 10 ).

2. Slice off a pyramid from each corner.

Since all the edges of the resulting polyhedron have the same length, let's find the side length of the pyramid. Consider one of the corner pyramids:

- It has a square base, with side length ( x , which is also equal to the side length of the cube.

- It has four congruent triangular faces.

If we draw a cross-section through the pyramid and the cube, we'll see that the cross-section of the pyramid is an isosceles right triangle with legs of length ( x ).

Given this, we can use Pythagoras' theorem to find the height of the pyramid. The hypotenuse of the right triangle is ( x ), and the legs are each  x ). So, we have:

[tex]\[ x^2 = x^2 + x^2 + h^2 \][/tex]

Solving for \( h \), the height of the pyramid, we get:

[tex]\[ h = \sqrt{x^2 - x^2} = \sqrt{x^2 - \left(\frac{x}{\sqrt{2}}\right)^2} \]\[ h = \sqrt{x^2 - \frac{x^2}{2}} = \sqrt{\frac{x^2}{2}} = \frac{x}{\sqrt{2}} \][/tex]

Now, we know that the height of the pyramid is [tex]\( \frac{x}{\sqrt{2}} \).[/tex]

When we remove the corner pyramid, the remaining shape is a pentagonal pyramid with a square base. This means the side length of the square base of the remaining polyhedron is [tex]\( 10 - 2x \).[/tex]

The height of this pentagonal pyramid is the same as the height of the corner pyramid, which is  [tex]\( \frac{x}{\sqrt{2}} \).[/tex]

So, we can set up an equation for the height of the remaining pyramid:

[tex]\[ 10 - 2x = \sqrt{2} \cdot \frac{x}{\sqrt{2}} \]\[ 10 - 2x = x \][/tex]

Solving for \( x \):

[tex]\[ 10 = 3x \]\[ x = \frac{10}{3} \][/tex]

So, the side length  [tex]\( s \) of the polyhedron after slicing off the corner pyramids is \( \boxed{\frac{10}{3}} \).[/tex]

Answer:

C. d = 10t + 10

Step-by-step explanation:

If d represents the distance, you know that the equation on the other side has to have +10 included in it because this was stated in the problem (he has traveled 10 miles). C is the only option with +10, but if you'd like a further explanation on the 10t part... by the end of his trip, he has traveled 30 miles total.  Subtract the 10 he initially traveled before arriving at the gas station, and he has traveled 20 miles in two hours. 20 (miles) / 2 (hours) = 10, so after the gas station, he traveled at an average speed of 10 mph. We now know that he traveled 10 miles, plus another 10 miles for every additional hour (t) he travels after that. This gives us d = 10t + 10.

Answer:

r=7

Step-by-step explanation:

-30=12-6r

We move all terms to the left:

-30-(12-6r)=0

We add all the numbers together, and all the variables

-(-6r+12)-30=0

We get rid of parentheses

6r-12-30=0

We add all the numbers together, and all the variables

6r-42=0

We move all terms containing r to the left, all other terms to the right

6r=42

r=42/6

r=7

Answer:

-3 = r OR r = -3

Step-by-step explanation:

-30 = 12 - 6r

30+12 = -18   12+12 = (cancels out left with just 6r)

-18/6r = -3

-3 = r

Hope this helped :)

Answer:

its 4xy and 12x

( options B and C)

hope that helped :)

Answer:

its 4xy and 12x

Step-by-step explanation:

Answer:

X = 76*4

= 304 cups of food

Step-by-step explanation:

Given:

So Let X is the number of cups of food that elephants eat per day, we have the equation:

X = 76*4

= 304 cups of food

Hope it will find you well.

Answer:

b because it cost u more for a certain distance

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

It's correct answer is A.

Answer:

A represents the connector of X and Y.

Step-by-step explanation:

Answer:

result if 3 would be 3 I think I hope it helps have a good day

Answer:

7/11

Step-by-step explanation: