a ladder 7.5m long rests against a wall . the botton of ladder is 2.1m from the wall . calculate how far the ladder reaches up the wall.
PLEASE SOLVE THIS QUESTION!!​

Answer:

The right answer is A

Step-by-step explanation:

The value of the exponential equation is y = 3ˣ and the graph is plotted

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

y = 3ˣ   be equation (1)

Now , the y intercept of the equation is when x = 0

So , when x = 0

y = 3⁰

y = 1

Now , when y₁ = 3^1.2

The value of y₁ = 3.7

Therefore , the y intercept of the equation is 1 and the graph is plotted

Hence , the exponential equation is y = 3ˣ

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Answer: y=2x-1

Step-by-step explanation:

Equation of a line that passes through (a,b) and have slope m is given by :-

\((y-b)=m(x-a)\)   [point slope form]

Given, Point = (4,7)  , m= 2

Equation in point slope form :   \((y-7)=2(x-4)\)

To write in slope intercept form (y=mx+c) , we need to simplify it

\(y-7= 2x-8\\\\\Rightarrow\ y-2x=-8+7\\\\\Rightarrow\ y-2x=-1\\\\\Rightarrow\ y=2x-1\)

Hence,  y=2x-1

An expression for x in terms of a and b is y = b - 2x and an expression for y in terms of a and b is y = 2a - b.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A system of equations x + y = a and 2x + y = b.

Now,

x + y = a.

x = a - y and y = a - x.

2x + y = b.

2x = b - y.

x = (b - y)/2.

y = b - 2x.

An expression for x in terms of a and b is,

x + y = a

x + b - 2x = a.

- x = a - b.

x = b - a.

An expression for y in terms of a and b is,

2(a - y) + y = b.

2a - 2y + y = b.

2a - y = b.

- y = b - 2a.

y = 2a - b.

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Given

Procedure

The value of side TS is,

⇒ TS = 28

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Additionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK

LY = HJ,

so, LY = 14

And, 42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

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The time is 1.81

Distance = 250 miles

Rate= 138.0861

Time= Distance/rate

= 250/138.0861

= 1.81

Hence the time is 1.81

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The points (-8,0) & (-8,6)

To find the distance between then

Apply the distance formulae for coordinates:

Substitute the coordinates:

So, Icecream is 6 units away from the sprinkles

Answer : 6 unit

The subgroup of S4 that is isomorphic to Z2 is {e, (1 2)(3 4)}.

Plant food is indeed dung or a mix of nitrates that are also given to soil to make it fruitful. Plant fertilizers are available in a variety of formats in the market, including water-soluble plant fertilizer, sustained-release crop fertilizer, and many others. Natural organic food is the best option for fertilizing.

Therefore, the final answer is "2nd Choice".

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The probability of rolling a sum from 2 to 12 on 2 dices is 100%

Given the data,

The two dice should be rolled.

Now, there are 36 possibilities that might occur while rolling two normal six-sided dice. The reason for this is that when rolling two dice, the total number of outcomes is the product of the numbers of outcomes for each die, and each die has six potential outcomes (numbers 1 through 6).

The resultant 36 results are as follows:

1-1, 1-2, 1-3, 1-4, 1-5, 1-6

2-1, 2-2, 2-3, 2-4, 2-5, 2-6

3-1, 3-2, 3-3, 3-4, 3-5, 3-6

4-1, 4-2, 4-3, 4-4, 4-5, 4-6

5-1, 5-2, 5-3, 5-4, 5-5, 5-6

6-1, 6-2, 6-3, 6-4, 6-5, 6-6

When using two dice, there are a total of 36 possibilities that might occur.

As a result, the results' total ranges from 2 to 12.

Hence , the probability is 100 %

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Answer:

i dnt know

Step-by-step explanation:

Answer:

m<1 = 75

m<2 = 55

m<3 = 55

Step-by-step explanation:

Well <1 + 50° is vertical to 125 so do this

<1 + 50 = 125 (subtract 50 on both sides)

<1 = 75

Now <1 + <2 + 50° = 180

We know what <1 is so..

75 + <2 + 50 = 180 (collect like terms)

125 + <2 = 180 (subtract 125 on both sides)

<2 = 55

Since <2 and <3 are vertical that means they equal the same so

<3 = 55

Hope this helps ya! Keep smiling!

Answer:

\(x=2\)

Step-by-step explanation:

We are given:

\(\displaystyle \frac{w^{-x+4}}{w^{-3}}=w^{2x+1}\)

First, by the quotient property:

\(w^{(-x+4)-(-3)}=w^{2x+1}\)

Since they both have the same base, their exponents must be equivalent:

\((-x+4)-(-3)=2x+1\)

Solve for x. Simplify:

\(-x+7=2x+1\)

Therefore:

\(3x=6\Rightarrow x=2\)

Answer:

x=2

Step-by-step explanation:

:]

Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

Answer:

12

Step-by-step explanation:

8x1+8x0.5

8+4

12

12$ is the total cost

so the idea being, we have a system of equations of two variables and 4 equations, each one rendering a line, for this case these aren't equations per se, they're INEquations, so pretty much the function will be the same for an equation but we'll use > or < instead of =, but fairly the function is basically the same, the behaviour differs a bit.

we have a line passing through (-6,0) and (0,8), side one

we have a line passing through the x-axis and -6, namely (-6,0) and the y-axis and -4, namely (0,-4), side two

we have a line passing through (0,-4) and (6,4), side three

now, side four is simply the line connecting one and three.

the intersection of all four lines looks like the one in the picture below, so what are those lines with their shading producing that quadrilateral?

well, we have two points for all four, and that's all we need to get the equation of a line, once we get the equation, with its shading like that in the picture, we'll make it an inequality.

\((\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{8 -0}{0 +6} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = \cfrac{4}{3} ( x +6) \\\\\\ y=\cfrac{4}{3}x+8\hspace{5em}\stackrel{\textit{side one} }{\boxed{y < \cfrac{4}{3}x+8}}\)

\(\rule{34em}{0.25pt}\\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{-4 -0}{0 +6} \implies \cfrac{ -4 }{ 6 } \implies - \cfrac{2}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = - \cfrac{2}{3} ( x +6) \\\\\\ y=-\cfrac{2}{3}x-4\hspace{5em}\stackrel{\textit{side two} }{\boxed{y > -\cfrac{2}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{0}}} \implies \cfrac{4 +4}{6 -0} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{0}) \implies y +4 = \cfrac{4}{3} ( x -0) \\\\\\ y=\cfrac{4}{3}x-4\hspace{5em}\stackrel{ \textit{side three} }{\boxed{y > \cfrac{4}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\((\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{6}}} \implies \cfrac{ 4 }{ -6 } \implies - \cfrac{2}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{6}) \\\\\\ y=-\cfrac{2}{3}x+8\hspace{5em}\stackrel{ \textit{side four} }{\boxed{y < -\cfrac{2}{3}x+8}}\)

now, we can make that quadrilateral a trapezoid by simply moving one point for "side four", say we change the point (0 , 8) and in essence slide it down over the line to  (-3 , 4).  Notice, all we did was slide it down the line of side one, that means the equation for side one never changed and thus its inequality is the same function.

now, with the new points for side for of (-3,4) and (6,4), let's rewrite its inequality

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{4 -4}{6 +3} \implies \cfrac{ 0 }{ 9 } \implies 0\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ 0}(x-\stackrel{x_1}{(-3)}) \implies y -4 = 0 ( x +3) \\\\\\ y=4\hspace{5em}\stackrel{ \textit{side four changed} }{\boxed{y < 4}}\)

The value of the variable 'x' in logarithmic expression is: 2

What is logarithm?

In mathematics, the term logarithmic expression can be explained as the exponent or the power which is raised on the base value of the logarithmic expression.

According to the question, the given logarithmic expression are as follows:

\(log_{1/2}x = -1\)

Using standard logarithmic property, we get

x = (1/2)^-1

⇒x = 2

Hence, the logarithmic value of the variable 'x' is: 2

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Answer:

B, No solution

Step-by-step explanation:

If two lines are graphed, the point they intersect is the solution. However, if the slope is the same, they will never intersect

In the first and second equation, the slopes are both 3 so they will never intersect.

The radius of the circle, marked p on the diagram, is approximately 5.8 cm.

Radius is a term used in geometry to describe the distance from the center of a circle to any point on the circumference. It is a line segment that has its two endpoints at the center of the circle and at any point on the circumference.

The area of a sector is equal to the fraction of the circle's area that the sector occupies multiplied by the area of the entire circle.
Therefore, the area of the sector is equal to (θ/360) × πr^2.
Since the area of the sector is given as 85 cm^2, we can rearrange the equation to get:
85 = (θ/360) × πr^2
Rearranging further, we get:
r^2 = (85 × 360)/(πθ)
Taking the square root of both sides, we get:
r = √((85 × 360)/(πθ))
Since the angle θ is not given, we cannot solve for r. However, we can approximate the angle θ to be equal to 360° since the sector occupies the entire circle.
Therefore, the radius of the circle is equal to:
r = √((85 × 360)/(π × 360))
r = √(85/π)
r ≈ 5.8 cm
Therefore, the radius of the circle, marked p on the diagram, is approximately 5.8 cm.

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Answer:

x=-5

Step-by-step explanation:

Divide by 5 on both sides and you get x=-5

Hope this helps mark brainliest if correct

Answer:

Step-by-step explanation:

Given the following simplified expressions:

4√3, 3 3√2, 2 3√3, 3√5

It's radical equivalent is :

4√3 = √4² * √3 = √16 * √3 = √16*3 = √48

3 3√2 = 3 * √3² * √2 = √9 * √2 = √9*2 = 3√18

2 3√3 = 2 * √3² * √3 = √9 * √3 = √9*3 = 2√27

3√5 = √3² * √5 = √9 * √5 = √9*5 = √45

Answer:

answer attached

Step-by-step explanation:

hope this helps!

Answer:

It took Adele's brother 37.45 + 2.10 = 39.55 seconds to run the race.

Answer:

There’s two options for each. Look below.

Step-by-step explanation:

Savings: there is no risk of losing any money put into this account

              interest income is the only way to earn money in this type

‘investment: this account may generate income from a variety of sourses.

                  If no deposits or withdrawals are made, money held in this acct..

Answer:

log12=log(2.2.3)

=log2+log2+log3

=0.30103+0.30103+0.47712

=0.60206+0.47712

=1.07918

a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.

a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:

Industry Average Salary = 96% of Firm B's Average Salary

= 0.96 * $58,000

= $55,680

b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:

Firm A's Average Salary = 93% of Industry Average Salary

= 0.93 * $55,680

= $51,718.40

c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:

Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100

= ($58,000 / $51,718.40) * 100

≈ 112.27%

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The percent of the increase, rounded to the nearest tenth of a percent, concerning the sales of boxes of cookies that Molly sold last month and this month, is 11.5%.

The percentage increase can be determined by finding the difference or the amount of increase in sales.

This difference is divided by the previous month's sales and multiplied by 100.

The total number of boxes of cookies Molly's Scout Troop sold last month = 148

The total number sold this month = 165

The increase = 17 (165 - 148)

Percentage increase = 11.5% (17 ÷ 148 x 100)

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Answer:

14

7/8of 160=140

140×10=1400

1400÷100=14

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

The mean of the sampling distribution of the sample proportions is 0.62 and the standard deviation is 0.0485.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

62% of the households have cable tv.

This means that \(p = 0.62\)

Sample of 100.

This means that \(n = 100\)

What is the mean and standard deviation of the sampling distribution of the sample proportions?

\(\mu = p = 0.62\)

\(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.62*0.38}{100}} = 0.0485\)

The mean of the sampling distribution of the sample proportions is 0.62 and the standard deviation is 0.0485.