One side of a square is 3 centimeters long. What is its area?

Answer:

a) The radius of the lake to be r=10 units.

b) [tex]14\sqrt{5}[/tex] units

Step-by-step explanation:

The lake has equation: [tex]x^2+y^2=100[/tex]

We can rewrite this as [tex]x^2+y^2=10^2[/tex]

Comparing this to  [tex]x^2+y^2=r^2[/tex]

We have the radius of the lake to be r=10 units.

b)  The bridge is represented by the function  y −x = 2

This is the same as y=x+2

We substitute this into the equation of the circle to get:

[tex]x^2+(x+2)^2=100[/tex]

[tex]x^2+x^2+4x+4-100=0[/tex]

[tex]2x^2+4x-96=0[/tex]

[tex]x^2+2x-48=0[/tex]

[tex](x+8)(x-6)=0[/tex]

[tex]x=-8,x=6[/tex]

When x=8, y=2(8)+2=18

When x=-6, y=2(-6)+2=-10

The length of the bridge is the distance between the points (8,18) and (-6,-10)

[tex]=\sqrt{(8--6)^2+(18--10)^2}[/tex]

[tex]=\sqrt{196+784}[/tex]

[tex]=\sqrt{196+784}[/tex]

[tex]=\sqrt{980}[/tex]

[tex]=14\sqrt{5}[/tex]

Answer:

D = 15

Step-by-step explanation:

|-10|+|5|=10+5=15

|-10|=10

|5|=5

Answer:

D)15

Step-by-step explanation:

| | these cancel out the negative in the ten making it a positive

so it would be 10+5

which is 15

Answer:

B.$675 and $1,775

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

e2020 exam

A.

If you multiply the original equation by 3 you get -45x+3y=54, which is the exact same as A, therefore they have infinite solutions.

Answer: g(x)=12x^2+8

Step-by-step explanation:

original function f(x)=3x^2+2

Now to stretch function vertically and rename to g(x) we just multiply the function by 4;

g(x)=4(3x^2+2)=12x^2+8

Any questions feel free to ask. Thanks

The equation of the function f(x) after stretching is g(x) = 12x² + 8.

A function is a law that relates a dependent and an independent variable.

The function given is

F(x) =  3x²+2

For when a function is vertically stretched

F'(x) = k .F(x)

k >1

here it is given that k = 4

The equation becomes

g(x) = 4( 3x²+2 )

g(x) = 12x² + 8

Therefore , The equation of the function f(x) after stretching is g(x) = 12x² + 8.

To know more about Function

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The unit rate, or the number of acres the workers can plant in one day, is calculated by dividing the total number of acres (3/5) by the number of days worked (5/6). The result is 18/25 acres per day, or approximately 0.72 acres per day.

In this example, we need to find out how many acres the workers plant in one day, also known as the unit rate.

To calculate this, we divide the total amount of acres (3/5) by the total number of days taken (5/6).

So the formula would be: (3/5) ÷ (5/6) = (3/5)*(6/5) = 18/25.

So, the unit rate in acres per day for the group of workers is 18/25 acres/day, which means they plant approximately 0.72 acres per day.

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Answer:

B

Step-by-step explanation:

C = R/1.8 - 273

C + 273 = R/1.8

1.8 * (C + 273) = R

1.8 can also be read as the fraction 9/5.

9/5 * (C + 273) = R

Thus your answer is B. Hope I helped!

So, if you add it all up it would be...

1.8 which could also be in the fraction form of 9/5 and 9/5 would be basically C.

So, even though C has 5/9 in the front that wouldn't be the case. It would be the one in parentheses we would be focusing on. So, the answer all together would be C.

I Hope this helps! c:

Answer: [tex]x=15[/tex]

Step-by-step explanation:

You can observe in the exercise that the equation you need to solve is:

[tex]x-5=10[/tex]

You need to find the value of the variable "x" of this equation. To do this, you need to remember the Addition Property of equality, which states that:

[tex]If\ a=b\ then\ a+c=b+c[/tex]

Knowing this, to solve for the variable "x", you must add 5 to both sides of the equation. Therefore, you get this result:

[tex]x-5+5=10+5\\x=15[/tex]

This relation is a function because a function, in fact this is a linear function. We have that:

[tex]\left[\begin{array}{cc}x & y\\2 & 3\\4 & 4\\6 & 5\\8 & 6\end{array}\right][/tex]

As you can see below, all the points have been plotted an this is a linear function. Therefore, with two points we can get the equation, so:

[tex]The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_{1},y_{1}) \ is:\\ \\ y-y_{1}=m(x-x_{1}) \\ \\ \\ y-3=\frac{4-3}{4-2}(x-2) \\ \\ \\ y-3=\frac{1}{2}(x-2) \\ \\ y=\frac{1}{2}x-1+3 \\ \\ y=\frac{1}{2}x+2 \\ \\ \\ Where: \\ \\ (x_{1},y_{1})=(2,3) \\ \\ (x_{2},y_{2})=(4,4)[/tex]

Finally, the equation is:

[tex]\boxed{y=\frac{1}{2}x+2}[/tex]

Answer:

y=0.5x +2

Step-by-step explanation:

Answer:

that the are both have a right angle. And that the are both cones.

Step-by-step explanation:

Answer:

3 : 5

Step-by-step explanation:

The ratio can be determined using the radii or the heights of the 2 cones

radii  6 : 10 = 3 : 5 ← in simplest form

height 9 : 15 = 3 : 5 ← in simplest form

Answer:

A rectangular prism and a cube.

Step-by-step explanation:

A rectangular prism when sliced by a plane can have a square facing up, meaning that a square will be produced. A cube has all square faces and when cut horizontally will produce a square.

Answer:

The equation would be:

[tex]x^2+y^2=169[/tex]

In the attachment!!!

Hope this helps!!!

[tex]Sofia[/tex]

Answer:

[tex]\large\boxed{Q1.\ q(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ q(2)=\dfrac{9}{2}}\\\boxed{Q2.\ t(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ t(0)=\dfrac{7}{2}}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{We have}\\\\q(-1)=3\to(-1,\ 3)\\q(3)=5\to(3,\ 5)[/tex]

[tex]\text{Calculate the slope:}\\\\m=\dfrac{5-3}{3-(-1)}=\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}\\\\\text{We have the equation:}\\\\y=\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the point (-1, 3) to the equation:}\\\\3=\dfrac{1}{2}(-1)+b\\\\3=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}[/tex]

[tex]q(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\q(2)-\text{put x = 2 to the equation:}\\\\q(2)=\dfrac{1}{2}(2)+\dfrac{7}{2}=\dfrac{2}{2}+\dfrac{7}{2}=\dfrac{9}{2}[/tex]

[tex]t(-4)=3\to(-4,\ 3)\\t(4)=4\to(4,\ 4)\\\\m=\dfrac{4-3}{4-(-4)}=\dfrac{1}{8}\\\\y=\dfrac{1}{8}x+b\\\\\text{put the coordinates of the point (4,\ 4):}\\\\4=\dfrac{1}{8}(4)+b\\\\4=\dfrac{1}{2}+b\qquad\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}\\\\t(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\t(0)=\dfrac{1}{2}(0)+\dfrac{7}{2}=0+\dfrac{7}{2}=\dfrac{7}{2}[/tex]

The equality that is graphed on the line is 2(m-3)+7>11 (A).

The correct inequality graphed on the number line is option C: [tex]\(2(m-3)-7 \leq 11\)[/tex].

To determine the correct inequality graphed on the number line, let's analyze the highlighted region (5 to 10) and compare it with the given options.

The highlighted region indicates values greater than 5. Now, testing each option:

A. [tex]\(2(m-3)+7 \geq 11\)[/tex]:

[tex]\[2(m-3)+7 \geq 11\][/tex]

[tex]\[2m - 6 + 7 \geq 11\][/tex]

[tex]\[2m + 1 \geq 11\][/tex]

[tex]\[2m \geq 10\][/tex]

[tex]\[m \geq 5\][/tex]

B. [tex]\(2(m+3)+7 \geq 11\)[/tex]:

[tex]\[2(m+3)+7 \geq 11\][/tex]

[tex]\[2m + 6 + 7 \geq 11\][/tex]

[tex]\[2m + 13 \geq 11\][/tex]

[tex]\[2m \geq -2\][/tex]

[tex]\[m \geq -1\][/tex]

C. [tex]\(2(m-3)-7 \leq 11\)[/tex]:

[tex]\[2(m-3)-7 \leq 11\][/tex]

[tex]\[2m - 6 - 7 \leq 11\][/tex]

[tex]\[2m - 13 \leq 11\][/tex]

[tex]\[2m \leq 24\][/tex]

[tex]\[m \leq 12\][/tex]

D. [tex]\(2(m+3)-7 \leq 11\)[/tex]:

[tex]\[2(m+3)-7 \leq 11\][/tex]

[tex]\[2m + 6 - 7 \leq 11\][/tex]

[tex]\[2m - 1 \leq 11\][/tex]

[tex]\[2m \leq 12\][/tex]

[tex]\[m \leq 6\][/tex]

Therefore, the correct inequality graphed on the number line is option C: [tex]\(2(m-3)-7 \leq 11\)[/tex].

Answer:

Not enough information

Step-by-step explanation:

To determine which inequality is true, compare the absolute values of the given numbers. The correct answer is B, |-8| < |-5|.

To determine which inequality is true, we need to compare the absolute values of the given numbers. Absolute value is the distance of a number from zero on the number line. In this case:

Therefore, the correct answer is B, |-8| < |-5|.

[tex]f(x) = |x-4|+3 \\ \\ \text{We have no existential conditions: }\\ \Rightarrow D = \mathbb{R}\\ \\ |x-4|\geq 0~~\big|+3 \Rightarrow |x-4|+3 \geq 3 \Rightarrow f(x) \geq 3 \\ \\ \Rightarrow \text{The range of the function is }[3,+\infty)[/tex]

ANSWER

Domain:

All real numbers

Range:

[tex]y \geqslant 3[/tex]

EXPLANATION

The given function is

[tex]f(x) = |x - 4| + 3[/tex]

This is the function obtained by the shifting the base absolute value function to the right by 4 units and up by 3 units.

The vertex of this function is at:

(4,3)

The domain is all real numbers because there is no x-value that will make the function undefined.

The least y-value on this graph is 3.

The graph opens up forever.

The range is [3,∞) or y≥3

Answer:

Part a) The width of parking lot is 87m.

Part b) The length of rectangular pool is 94 m

Step-by-step explanation:

a) The area of parking lot Area= 8439 m^2

Length of Parking Lot = Length = 97 m

Width of Parking Lot = Width= ?

Area of rectangle = Length * Width

Putting the values,and finding width,

8439 = 97 * Width

=> Width = 8439/97

=> Width = 87 m

So, The width of parking lot is 87m.

b) Perimeter of rectangular pool = Perimeter= 344 m

Width of rectangular pool = Width = 78 m

Length of rectangular pool = Length = ?

The formula for perimeter is:

Perimeter = 2*(Length + Width)

Putting values in the formula:

344 = 2*(Length + 78)

344/2 = Length + 78

172 = Length + 78

=> Length = 172 - 78

Length = 94 m

So, the length of rectangular pool is 94 m.

ANSWER

[tex]m + 23[/tex]

EXPLANATION

The given expression is

[tex]m - 13 + 42 - 6[/tex]

We regroup the numerical parts to get;

[tex]m + 42 - 6 - 13[/tex]

Now let us simplify the negative numbers.

[tex]m + 42 - 19[/tex]

We now subtract 19 from 42 to get;

[tex]m + 23[/tex]

We can't simplify further

Hence the simplest form is:

[tex]m + 23[/tex]

Answer:

  Look for the same entry in both (all) tables.

Step-by-step explanation:

We assume here that the system of equations consists of two equations in two variables. If there are more equations in more variables, the general approach is the same.

A "solution" to a system of equations is a set of variable values that satisfies all equations of the system simultaneously. A table for one equation will generally list sets of variable values that satisfy that equation. When the same set of values appears in the table for each of the equations, then that set of values is the solution.

__

Example

The attachment shows tables for two equations:

Highlighted are the table entries that are the same for both equations. This is the solution to the system of equations. (x, y) = (3, 6) satisfies both equations:

ANSWER

No, because there is no common ratio

EXPLANATION

The given sequence is

-1, 1, 4, 8

If this sequence is geometric, then there should be a common ratio among the consecutive terms.

[tex] \frac{1}{ - 1} \ne \frac{4}{1} \ne \frac{8}{4} [/tex]

Hence the sequence

-1, 1, 4, 8

is not a geometric sequence.

Answer:

The sequence is not a geometric sequence

Step-by-step explanation:

In a geometric sequence you find the following term multiplying the current by a fixed quantity called the common ratio.

To prove if a sequence is geometric we need to check if the ratio is consistent across the sequence. To check for the ratio we use the formula:

[tex]r=\frac{a_n}{a_{n-1}}[/tex]

were

[tex]r[/tex] is the ratio

[tex]a_n[/tex] is the current term  

[tex]a_{n-1}[/tex] is the previous term

Let's star with 1, so [tex]a_n=1[/tex] and [tex]a_{n-1}=-1[/tex]

[tex]r=\frac{a_n}{a_{n-1}}[/tex]

[tex]r=\frac{1}{-1}[/tex]

[tex]r=-1[/tex].

Now let's check 4 and 1, so [tex]a_n=4[/tex] and [tex]a_{n-1}=1[/tex]

[tex]r=\frac{a_n}{a_{n-1}}[/tex]

[tex]r=\frac{4}{1}[/tex]

[tex]r=4[/tex]

Since the ratios between two pair of numbers are different, we can conclude that the sequence is not geometric.

Answer:

68

Step-by-step explanation:

Let x be the measure of one of the angles of the triangle

Two of the angles have the same measure, so another angle is x

The third is 12 degrees more, x+12

The sum of the three angles of a triangle is 180

x+x+x+12 = 180

Combine like terms

3x+12 = 180

Subtract 12 from each side

3x+12-12 = 180-12

3x = 168

Divide by 3

3x/3 = 168/3

x = 56

x=56

x=56

x+12 = 56+12 = 68

The largest angle is 68

ANSWER

271 pre-sale tickets were sold.

EXPLANATION

Let p represent the number of pre-sale tickets and t represent the number of tickets sold.

According to the question,a total of 800 pre-sale tickets and tickets were sold .

This implies that,

[tex]p + t = 800[/tex]

Also the number of tickets sold is 13 less than twice the number of pre-sale tickets.

This gives another equation:

[tex]t = 2p - 13[/tex]

We substitute, the second equation into the first equation to obtain:

[tex]p + 2p - 13 = 800[/tex]

This implies that;

[tex]3p = 813[/tex]

Divide both sides by 3

[tex]p = \frac{813}{3} = 271[/tex]

Hence 271 pre-sale tickets were sold.

By setting up an algebraic equation and denoting pre-sale tickets as x, we discover that 271 pre-sale tickets were sold for the football city championship game.

To solve the problem of how many pre-sale tickets were sold for the football city championship game, we can set up an algebraic equation. Let's denote the number of pre-sale tickets as x. According to the question, the number of tickets sold at the gate is thirteen less than twice the number of pre-sale tickets, which we can express as 2x - 13. We are given that the total number of tickets sold is 800.

So, we set up the equation:

x + (2x - 13) = 800

Combining like terms, we get:

3x - 13 = 800

Adding 13 to both sides:

3x = 813

Then we divide both sides by 3 to find the value of x:

x = 813 / 3

x = 271

Therefore, 271 pre-sale tickets were sold.

The answer is 1/5

Step-by-step explanation:

You have the probability of getting 1/5 correct.

For this case, we have by definition, the calculation of probabilities:

[tex]probability = \frac {number\ of \favorable\ cases} {number\ of\ possible\ cases}[/tex]

We have 5 possible answers, and we have only one favorable case, that is, only one correct option among the 5 possible answers.

So, we have:

[tex]Probability = \frac {1} {5} = 0.2[/tex]

Answer:

0.2

Answer:

Use desmos.com/calculator. It is a graphing calculator that can do many things

Step-by-step explanation:

say thanks and vote

  10,000

x 10,000

________

100,000,000

Answer:

100,000,000

Step-by-step explanation:

Answer:

[tex]\boxed{4}[/tex]

Step-by-step explanation:

When you reflect a point (x, y) across the x-axis, the x-coordinate remains the same, but the y-coordinate gets the opposite sign.

Thus,  the y-coordinate becomes [tex]\boxed{\textbf{4}}[/tex].

7/9 is going to be the greatest since it is the only positive number and the. it’s going to be -4/5 and then the least is going to be -1/14.

-1/14 , -4/5 , 7/9

The numbers -1/14, 7/9, -4/5 arranged from least to greatest are -4/5, -1/14, 7/9. This is found by converting fractions to decimals for easier comparison and then arranging them in order.

To go about solving this, we first consider each number's location on the number line. The numbers closer to the left are smaller than those on the right. Given the numbers -1/14, 7/9, and -4/5, we can start by converting each fraction to a decimal for easier comparison.

-1/14 equals approximately -0.0714, 7/9 equals approximately 0.7777, and -4/5 equals -0.8. Therefore, from smallest to largest, these numbers can be arranged as -0.8, -0.0714, 0.7777. Converting these back to fractions gives us the desired result: -4/5, -1/14, 7/9.

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The graph of the function f(x) = cos(2x) + 1 is added as an attachment

Sketching the graph of the function

From the question, we have the following parameters that can be used in our computation:

f(x) = cos(2x) + 1

The above function is a cosine function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

Your answer would be A = 444.72 Or 445