Could someone help me with this math problem?

Final Answer:

The direct distance from point A to point B, considering a straight path through the pond, is 80 meters. This is obtained by applying the Pythagorean theorem to the right-angled triangle formed by walking 23 meters and then 57 meters along the edges of the pond. Subtracting the initial 23 meters provides the actual direct distance.

Step-by-step explanation:

In this scenario, we can apply the Pythagorean theorem to find the direct distance from point A to point B. Let's denote the sides of the right-angled triangle formed by walking along the edges of the pond as follows: the first leg (along one edge) is \(a = 23\) meters, the second leg (along the other edge) is [tex]\(b = 57\)[/tex] meters, and the hypotenuse (direct distance from A to B, walking through the pond) is (c). According to the Pythagorean theorem, [tex]\(c^2 = a^2 + b^2\).[/tex]

Substituting the given values, we get [tex]\(c^2 = 23^2 + 57^2\).[/tex] Calculating this gives [tex]\(c^2 = 529 + 3249\)[/tex], resulting in [tex]\(c^2 = 3778\)[/tex]. Taking the square root of both sides gives [tex]\(c ≈ \sqrt{3778} ≈ 61.47\)[/tex]. Therefore, the direct distance from point A to point B, walking through the pond, is approximately 61.47 meters.

However, since the question asks for the distance considering walking straight through the pond, we need to add the lengths of both sides of the pond. Thus, [tex]\(61.47 + 23 + 57 = 80\)[/tex]. Therefore, the final answer is 80 meters. This approach considers the direct path, incorporating the lengths of the edges and the hypotenuse, providing the most accurate measurement for the distance from point A to point B.

Answer:

[tex]\large\boxed{V=99\pi}[/tex]

Step-by-step explanation:

The formula of a volume of a cylinder:

[tex]V=\pi r^2H[/tex]

r - radius

H - height

We have 2r = 6 → r = 3, H = 11.

Substitute:

[tex]V=\pi(3^2)(11)=99\pi[/tex]

Answer:

{ x ∈ R | x ≥  9 }

Step-by-step explanation:

we have

[tex]2x-7 \geq 11[/tex]

solve for x

Adds 7 both sides

[tex]2x\geq 11+7[/tex]

[tex]2x\geq 18[/tex]

Divide by 2 both sides

[tex]x\geq 18/2[/tex]

[tex]x\geq 9[/tex]

The solution is the interval -----> [9,∞)

In set builder notation

{ x ∈ R | x ≥  9 }

All real numbers greater than or equal to 9

Answer:

The equations represent circles that result in the same graph.

Step-by-step explanation:

we have

[tex]-10x^{2}-10y^{2}=-300[/tex]

Divide by -10 both sides

[tex]x^{2}+y^{2}=30[/tex] -----> equation A

This is the equation of a circle centered at origin with radius [tex]r=\sqrt{30} \ units[/tex]

and

[tex]5x^{2}+5y^{2}=150[/tex]

Divide by 5 both sides

[tex]x^{2}+y^{2}=30[/tex] -----> equation B

This is the equation of a circle centered at origin with radius [tex]r=\sqrt{30} \ units[/tex]

equation A and equation B are equal

therefore

The system has infinite solutions, because the equations represent circles that result in the same graph.

Answer:

2¹⁵x¹⁵ (2nd option)

Step-by-step explanation:

When you expand (2x+10y)¹⁵ you would get:

32,768x¹⁵ + 2,457,600x¹⁴y + 86,016,000x¹³y² + 1,863,680,000x¹²y³+

27,955,200,000x¹¹y⁴+307,507,200,000x¹⁰y⁵ + 307,507,200,000x¹⁰y⁵ + ... so on and so forth.

Since you are not interested in anything else but the first term, observe that the first term is:

32,768x¹⁵

That is equal to: 2¹⁵x¹⁵

What happened there is you need to distribute the exponent to the coefficient of the term as well, so you need to distribute it to 2 as well.

Answer:

D.5/6 and 10/12​

Step-by-step explanation:

A.3 1/2 and 4 4/4  

    3 1/2 and 4+1

     3 1/2  and 5

not equal

B.3/2and 2/3

  2/2 + 1/2   and 2/3

   1 1/2 and 2/3

  not equal

C.6/7and 1 5/7

  6/7  and  1 5/7

   not equal

D.5/6 and 10/12​

  5/6*2/2 and 10/12

   10/12 and 10/12

  equal

Answer: 595 Dollars

Step-by-step explanation:

16 1/2 times 18 1/2 = 305.25

one square yard = nine feet

305 devided by nine 33.9166667 (round to 34)

34 times 17.50 = 595

Answer:

$593

Step-by-step explanation:

We have been that a customer wants to buy carpet for a room that is 16 1/2 feet by 18 1/2 feet in size.

First of all, we will find area of carpet by multiplying both side lengths as:

[tex]\text{Area of carpet}=16\frac{1}{2}\text{ ft}\times 18\frac{1}{2}\text{ ft}[/tex]

Convert mixed fraction into improper fraction:

[tex]16\frac{1}{2}\Rightarrow \frac{16\times2+1}{2}=\frac{32+1}{2}=\frac{33}{2}[/tex]

[tex]18\frac{1}{2}\Rightarrow \frac{18\times2+1}{2}=\frac{36+1}{2}=\frac{37}{2}[/tex]

[tex]\text{Area of carpet}=\frac{33}{2}\text{ ft}\times \frac{37}{2}\text{ ft}[/tex]

[tex]\text{Area of carpet}=\frac{1221}{4}\text{ ft}^2[/tex]

[tex]\text{Area of carpet}=305.25\text{ ft}^2[/tex]

1 square feet equals 0.111 square yards.

[tex]305.25\text{ ft}^2=305.25*0.1111\text{ yards}^2[/tex]

To find the cost to carpet the room, we will multiply area of carpet by cost $17.50 per square yards.

[tex]305.25\times 0.1111\text{ yards}^2\times\frac{\$17.50}{\text{ yard}^2}[/tex]

[tex]305.25\times 0.1111\times\$17.50[/tex]

[tex]\$593.4823125\approx \$593[/tex]

Therefore, the cost to carpet the room would be $593.

Answer:

[tex]b/a\ hours[/tex]

Step-by-step explanation:

we know that

Betsy can clean a/b of the house in an hour

The whole house (100%) correspond to the number 1

so

using proportion

Find out how long will it take her to clean the whole house

[tex]\frac{(a/b)}{1}=\frac{1}{x} \\ \\x=1/(a/b)\\ \\x=b/a\ hours[/tex]

Answer: [tex]x=1[/tex]

Step-by-step explanation:

In order to find the value of "x", it is important to remember that:

[tex]Tangent\ chord\ angle=\frac{1}{2}(Intercepted\ arc)[/tex]

 We can identify in the figure that:

[tex]Tangent\ chord\ angle=(43x)\°\\\\Intercepted\ arc=AB[/tex]

Then:

[tex]43x=\frac{1}{2}AB[/tex]

Solving for AB:

[tex]2(43x)=AB\\\\AB=86x[/tex]

Now, since there are 360° in a circle, we know that:

[tex]AB+(272x+2)=360[/tex]

Then we can substitute [tex]AB=86x[/tex] into [tex]AB+(272x+2)=360\°[/tex] and solve for "x". This is:

[tex](86x)+(272x+2)=360\\\\358x=360-2\\\\x=\frac{358}{358}\\\\x=1[/tex]

Answer:

=5.1 units

Step-by-step explanation:

To use the sine rule to find the length of c we first need to find the angle at C.

C=180-(13+12)

C=180-25

C=155°

a/Sin A=c/Sin C

Calculating for the value of c using the sine rule:

12/Sin 13=c/Sin 155

c=12 sin 155

=5.07 units

Thus to 1 decimal places, the value of c is 5.1 units.

Final answer:

The cost of 2.50 pounds of bananas is 1.50 dollars.

Explanation:

To find the cost of 2.50 pounds of bananas, we need to multiply the weight of the bananas by the cost per pound. In this case, the cost per pound is 60 cents.In the store, bananas cost 60 cents per pound, and the cost in dollars for x pounds of bananas is given by the equation 0.6x. To find the cost of 2.50 pounds of bananas, you simply substitute x with 2.50 in the equation: 0.6 times 2.50.  So, we multiply 2.50 pounds by 0.60 dollars per pound:

2.50 pounds x 0.60 dollars/pound = 1.50 dollars.

Therefore, the cost of 2.50 pounds of bananas is 1.50 dollars.

Answer:

1. C) 5.50x + 10

2. 54

Step-by-step explanation:

1. C) 5.50x + 10

You have a static fee of $10 which does not need to be attached to a variable as it will not change. You also have a fee of $5.50, which may be charged depending on the amount of classes. Since this is dependent on something, it includes a variable.

Therefore, your terms are:

5.5x

10

Simply add them together for your equation.

[tex]5.5x+10[/tex]

2. 54

To solve, simply plug in 8 to your equation which you created in part 1. This is possible because x stands for the amount of classes and, as the question tells us, 8 is the amount of classes.

[tex]5.5(8)+10\\44+10\\54[/tex]

Answer:

Step-by-step explanation:

[tex]10^.^7^5=10^l^o^g^(^x^)\\=10^.^7^5=x\\=10^\frac{3}{4}=\sqrt[4]{10^3} =\sqrt[4]{1000} =5.6=x[/tex]

To solve the equation 0.75 = log(x), we exponentiate both sides with base 10, resulting in x = 10^0.75. The calculated value of x to the nearest hundredth is approximately 5.62.

To solve the equation 0.75 = log(x), we need to understand that the logarithm function here is the common logarithm, which means it has a base of 10. The equation essentially states that 10 raised to the power of 0.75 equals x. To find x, we simply need to perform the inverse operation of taking the logarithm, which in this case is exponentiation.

We use the fact that if logb(a) = c, then bc = a, where b is the base, a is the result, and c is the exponent. Therefore, we can rewrite our original equation as:

x = 100.75

Using a calculator, we can find that:

x ≈ 5.62

This is the value of x, rounded to the nearest hundredth, as the question requested.

Answer:

y = -2x/3 + 6

Step-by-step explanation:

y = mx+b

m = y2-y1/x2-x1

m = 2 - 6/6 - 0

m= -4/6 = -2/3

b = y-intercept = 6

Answer:

Arc length = (30/360)(2π)(14)

= (7/3)π cm = about 7.33 cm

Answer:

My man above in Correct

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The least common multiple of 4 and 6 is what we are looking for

4,8 ,12,16,20

6,12,18

The smallest number is 12

Answer:

f(x)=x-3

Step-by-step explanation:

You are given x-y=3 and you want to rewrite in function notation with x being the independent. That means we need to solve for y so y can depend on x.

x-y=3

Subtract x on both sides:

 -y=-x+3

Multiply both sides by -1:

  y=x -3

So function notation would be f(x)=x-3

The function notation of the equation x - y = 3, with x as the independent variable, is f(x) = x - 3.

The equation x - y = 3 is in standard form. To express this equation in function notation with x as the independent variable, we need to solve for y in terms of x. By moving y to the other side of the equation and 3 to the opposite side, we get y = x - 3. In function notation, where y is usually replaced by the function f(x), the equation becomes f(x) = x - 3.

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Answer:

Part 1) The rate of change is [tex]2,000\ \$/year[/tex]

Part 2) The equation of the line into slope intercept form is [tex]y=2,000x+73,000[/tex]

Part 3) Tom's salary would be [tex]\$93,000[/tex] in ten years

Step-by-step explanation:

Let

x ------> the number of years worked

y -----> Tom's salary amount in dollars

we have the points

A(1, 75,000) and B(4,81,000)

step 1

Find the rate of change (slope)

The slope is equal to

[tex]m=(81,000-75,000)/(4-1)=2,000\ \$/year[/tex]

step 2

Find the equation of the line into slope-intercept form

we know that

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

we have that

[tex]m=2,000\ \$/year[/tex]

point A(1, 75,000)

substitute

[tex]75,000=(2,000)(1)+b[/tex]

[tex]b=75,000-2,000=73,000[/tex]

The equation of the line is

[tex]y=2,000x+73,000[/tex]

step 3

What will Tom's salary be in ten years?

For x=10 years

Substitute in the linear equation

[tex]y=2,000(10)+73,000=\$93,000[/tex]

Answer:

The increment in salary is $1500 each year. The slope intercept form is [tex]y=1500x+75000[/tex] and the salary in 10 years will be $90000.

Step-by-step explanation:

Consider the provided information.

The starting is $75,000 per year.

Let x is the number of years worked and y is Tom's salary amount in dollars.

When he has 0 yr of experience, his salary is $75000 per year.

it can be written as (0,75000).

His salary will probably be $81,000 in four years.

It can be written as (4,81000).

STEP 1:

Find the rate of change by using the formula slope=[tex]m=\frac{rise}{run}[/tex].

Determine the rise by subtracting 75000 from 81000.

Rise = 81000 - 75000 = 6000

Now determine the run by subtracting 0 from 4.

Run = 4 - 0 = 4

Substitute the respective values in the above formula.

[tex]slope=m=\frac{6000}{4}\\slope=m=1500[/tex]

Therefore, the rate of change, or the salary increase per year is $1500.

STEP 2:

Write the slope intercept form by using the formula:

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute m = 1500 and [tex](x_1,y_1)=(0,75000)[/tex] on the above formula.

[tex](y-75000)=1500(x-0)\\y-75000=1500x\\y=1500x+75000[/tex]

Thus, the slope intercept form is [tex]y=1500x+75000[/tex].

STEP 3:

The salary in 10 years. can be calculated as:

Substitute the value of x = 10 in [tex]y=1500x+75000[/tex].

[tex]y=1500(10)+75000\\y=15000+75000\\y=90000[/tex]

Hence, the salary in 10 years will be $90000.

Answer:

5y - 4x = 5. This gives you your points with a slope of 4/5

Answer:

[tex]y=\frac{4}{5}x+1[/tex]

Step-by-step explanation:

We are given the slope, and the y-intercept. So we can use the slope-intercept equation. Which is as follows:

[tex]y=mx+b[/tex]

where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the value of [tex]y[/tex] when [tex]x=0[/tex]).

The information that we have is that the slope of the line is:

[tex]m=\frac{4}{5}[/tex]

and that the line crosses the y-axis at (0, 1).

From this point we can find the y-intercept [tex]b[/tex], because b is the value of [tex]y[/tex] when [tex]x=0[/tex].

And since the line passes through (0, 1) when [tex]x = 0[/tex], [tex]y =1[/tex]. Thus, the y-intercept is:

[tex]b=1[/tex]

substituting the values of the slope and the y-intercept into the equation:

[tex]y=mx+b\\y=\frac{4}{5}x+1[/tex]

the answer is:   [tex]y=\frac{4}{5}x+1[/tex]

Answer:

[tex]\log_3(a)=n[/tex] has exponential form [tex]3^n=a[/tex].

[tex]\log(3a)=n[/tex] has exponential form [tex]10^{n}=3a[/tex].

Please let me know if neither of my interpretations of your problem/question is correct.  That is I can either assume you wrote [tex]\log_3(a)=n[/tex]  or [tex]\log(3a)=n[/tex].

If something else was intended, please let me know. Thanks kindly.

Step-by-step explanation:

Let's assume: [tex]\log_3(a)=n[/tex].

The base is 3.

The exponent is n. (Just remember the logarithm is the exponent.)

So we have [tex]3^n=a[/tex]

In general these forms are equivalent:

[tex]log_b(a)=y \text{ is equivalent to } b^y=a[/tex].

[tex]\log(3a)=n[/tex] is the same as [tex]\log_{10}(3a)=n[/tex]

The base is 10 (if you don't see a base and log is written).

The exponent is n.

So we have [tex]10^n=3a[/tex].

To transform the logarithmic function log3 a = n into an exponential form, we apply the rule that if logb a = n, then b^n = a. Therefore, the exponential form is 3^n = a.

The student's question is about transforming a logarithmic equation into an exponential form. This is a common request in mathematics, particularly in algebra and precalculus.

The given equation is log3 a = n. The exponential form of a logarithmic equation is based on this relationship: If logba = n, then the exponential form is bn = a. Applying this rule to the provided equation gives 3n = a as the exponential form.

This transformation is based on the definition of logarithms, which are the inverses of exponential functions. The logarithm of a number to a particular base is the exponent to which the base must be raised to get that number. So in this case, n is the power you need to raise 3 to in order to get a.

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Answer:

The correct answer is last option 3√2 units

Step-by-step explanation:

From the figure we can see that two small  right angled triangle.

These two triangle combined to form a large right angled triangle.

To find the value of x

Consider the small triangle with hypotenuse x and one side 3 units.

The angles of this triangle be 45°, 45° and 90°, then the sides are in the ratio 1 : 1 : √2

Therefore we can write,

3 : 3 : x = 1 : 1 : √2

x = 3√2

The correct answer is last option 3√2 units

Answer:

x = 38

Step-by-step explanation:

Add 13 to both sides, to isolate x:  x = 38

We verify this solution using substitution (not subtraction):

Is 38 - 13 = 25 true?  Yes, it is.

Answer:

X-13=25

get coefficient X by itself by adding 13 to both sides

X=-13+13=25+13

X=38

Answer: [tex]\frac{3}{8}x-\frac{41}{5}[/tex] or  [tex]\frac{3}{8}x-8\ \frac{1}{5}[/tex]

Step-by-step explanation:

Given the following expression:

[tex]\frac{3}{4}(\frac{1}{2}x-12)+\frac{4}{5}[/tex]

You can follow these steps in order to simplify it:

1.  You need to apply Distributive property:

[tex]=\frac{3}{8}x-9+\frac{4}{5}[/tex]

2. And now you must add the like terms. Then:

[tex]=\frac{3}{8}x-\frac{41}{5}[/tex]

Therefore you get the following answer:

[tex]\frac{3}{8}x-\frac{41}{5}[/tex] or  [tex]\frac{3}{8}x-8\ \frac{1}{5}[/tex]

Answer:

B

Step-by-step explanation:

Look for an expression with (x - 5 ) as this will give zero when x = 5, that is

x - 5 = 5 - 5 = 0

The only expression with a factor of (x - 5 ) is B

Answer: people who have had Pedro’s perfect pizza delivered to their house in the last month

Step-by-step explanation:

I guessed and got lucky lol

In total, there are 200 students from North Beach.

Of those 200 students, 110 attended the game.

Because it is only asking for the probability that a student from North Beach attended, the answer would be 110 / 200, or 0.55.

Therefore, the answer would be C.

Hope this helps! :)

Answer:

0.314

Step-by-step explanation:

Given:

total number of students=350

total number of students that attented= 170

students that attended from North beach =110

probability that a student attended the game, given that the student is from North Beach= 110/350

                    =0.314 !

Answer:

D

Step-by-step explanation:

Reminder:  A function returns ONLY ONE y value for each input value.  

We immediately discard possible answer A, since 2 points have input 1 with different outputs.

Same for B:  discard this.

Same for C:  discard this.

D is a function.  All of the inputs are unique (no duplication).

Answer:

A

n=27, n+2=29, n+4=31

The correct option is A: n + n + 2 + n + 4 = 87; n -27, n + 2 - 29, n + 4 - 31.

Let's denote the three consecutive odd integers as n, n + 2, and n + 4. The sum of these integers is given as 87.

The correct equation to represent this situation is:

n + (n + 2) + (n + 4) = 87

Now let's solve for n:

3n + 6 = 87

Subtract 6 from both sides:

3n = 81

Divide both sides by 3:

n = 27

n + (n + 2) + (n + 4) = 87

27 + 29 + 31 = 87

The three consecutive odd integers are 27, 29, and 31.

Answer:

[tex]\large\boxed{x=-\dfrac{8}{3}\ or\ x=\dfrac{7}{2}}[/tex]

Step-by-step explanation:

[tex]6x^2-5x=56\qquad\text{subtract 56 from both sides}\\\\6x^2-5x-56=0\\\\6x^2+16x-21x-56=0\\\\2x(3x+8)-7(3x+8)=0\\\\(3x+8)(2x-7)=0\iff 3x+8=0\ \vee\ 2x-7=0\\\\3x+8=0\qquad\text{subtract 8 from both sides}\\3x=-8\qquad\text{divide both sides by 3}\\\boxed{x=-\dfrac{8}{3}}\\\\2x-7=0\qquad\text{add 7 to both sides}\\2x=7\qquad\text{divide both sides by 2}\\\boxed{x=\dfrac{7}{2}}[/tex]