find the area of right-andled triangled whose sight-angled
making side are 3cm and 4cm​

Here are all of the answers to these four questions:

1. log2^64=6, or 2 to the power of 6=64.

2. log11^121=2, or 11²=121.

3. log8^512=3, or 8³=512.

4. log4^1/16=-2, or 4 to the negative second (-2) power.

I hope that this answered your question.

Yeah, so the answer is 6, 2, 3, and -2.

Answer:

24 + 30 = 54 pancakes flipped in 2 minutes :)

Step-by-step explanation:

damon = 5 pancakes in 20 seconds

we do 20 x 3 and 5 x 3 to find how many pancakes he can flip in a minute

15 pancakes and a minute, we then multiply them by 2 to get the amount for 2 minutes

30 pancakes flipped in 2 minutes

Hailey = 2 pancakes in 10 seconds. to make it an equal amount of pancakes per second with damon, i will multiply them by 2 to have 4 pancakes in 20 seconds

we will then do 4 x 3 and 20 x 3 to find out how many pancakes per minute

then we multiply by 2 for 2 minutes

Answer:

54

Step-by-step explanation:

2 minutes=120 seconds

Damon=120 divide 20=6

6x5=30

Hailey=120 divide 10=12

12x2=24

24+30=54

Hope this helps! Thanks.

Answer:

630 and 90 respectively

Step-by-step explanation:

Let the speed of wind be x and the plane speed be y

ATQ, (y+x)*3=2160 and (y-x)*4=2160. Solving it, we will get x=90 and y=630

The speed of the plane in still air is 630 miles per hour and the speed of the wind is 90 miles per hour.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

An airplane takes 3 hours to travel a distance of 2160 miles with the wind. The return trip takes 4 hours against the wind.

Let 'x' be the speed of the plane and 'y' be the speed of the wind. Then the equations are given as,

x + y = (2160 / 3)

x + y = 720                  ...1

x - y = (2160 / 4)

x - y = 540                  ...2

Add equations 1 and 2, then we have

2x = 720 + 540

x = 1260 / 2

x = 630 miles per hour

Then the value of 'y' is calculated as,

630 + y = 720

y = 90 miles per hour

The speed of the plane in still air is 630 miles per hour and the speed of the wind is 90 miles per hour.

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[tex]3x=x+10[/tex]

We tripple something and get 10 more than something.

Put the x-es on the left and non x-es to the right,

[tex]2x=10[/tex]

Divide both sides by 2,

[tex]x=5[/tex]

Et Viòla.

Hope this helps :)

When a number is tripled, its value increases by 10 then the original number is 5.

Let's call the original number "x". According to the problem, when this number is tripled, its value increases by 10. Mathematically, we can represent this as an equation:

3x = x + 10

Now, we can solve for "x" step by step:

1. Subtract "x" from both sides of the equation:

  3x - x = 10

2. Simplify the left side:

  2x = 10

3. Divide both sides by 2 to solve for "x":

  x = 10 / 2

  x = 5

So, the original number "x" is 5.

In other words, if you take a number, triple it (multiply by 3), and then increase the result by 10, you would end up with the value 5. This can be verified by checking:

3 * 5 = 15

15 + 10 = 25

The equation 3x = x + 10 represents the relationship between the original number and its tripled value with an increase of 10. Solving this equation helps us find the original value that satisfies the given condition.

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Answer:

A = 22.5 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 1/2(5)(9)

A = 45/2

A = 22.5 cm^2

[tex]\begin{gathered} {\underline{\boxed{ \rm {\red{Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: base \: \times \: height}}}}}\end{gathered}[/tex]

[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: 5 \: cm \: \times \: 9 \: cm[/tex]

[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{1}{2} \: \times \: 45 \: cm[/tex]

[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \frac{45 \: {cm}^{2} }{2} \: \\ [/tex]

[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: \cancel\frac{45}{2} \: \: ^{22.5 \: {cm}^{2} } \: \\ [/tex]

[tex]\bf \longrightarrow \:Area \: \: of \: \: triangle \: = \: 22.5 \: {cm}^{2} [/tex]

Hence , the area of triangle is 22.5 cm²

Answer:

(a) 31

(b) 32

Step-by-step explanation:

We will do (b) first since it will help us do (a).

(b)

There are [tex]n(A)=5[/tex] elements in [tex]A[/tex]. Using the formula for the number of subsets of a given (finite) set, the number of subsets of [tex]A[/tex] is

[tex]2^{n(A)}=2^5=32[/tex]

(a)

A subset of [tex]A[/tex] is called proper if it does not equal [tex]A[/tex]. The only subset of [tex]A[/tex] that is not proper is [tex]A[/tex] itself, so simply subtract 1 from the number of subsets to get the number of proper subsets, which is

[tex]32-1=31[/tex]

Answer:

348 km³

Step-by-step explanation:

Volume = base area×height

base area = 5.8×12/2 = 34.8 km²

volume = 34.8×10 = 348 km³

Answer:

yip that's all

Step-by-step explanation:

not more than 276 means less or equal to 276,

46 × y ≤ 276

y ≤ 6

Answer:

46y<276

Step-by-step explanation:

no more than means less than or equal to.

Answer:

C is the answer

C) 48pi in^2

Answer:

15

Step-by-step explanation:

5:22=15:66, simply multiply 3 in the right hand side

Answer:

15

Step-by-step explanation:

5 : 22 = x : 66

Product of means = product of extremes

22*x = 66*5

[tex]x = \frac{66*5}{22}[/tex]

x = 3 * 5 = 15

Answer:

y = -8x+19

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = -8x+b

Substitute the point into the equation

3 = -8(2)+b

3 = -16+b

Add 16 to each side

3+16 = b

19 = b

y = -8x+19

Step-by-step explanation:

to find the equation of this line you use the equation of the slope intercept which is y-y1= m (x-x1)

y-3=-8(x-2)

y-3=-8x+16

y=-8x+16+3

y=-8x+19

I hope this helps

Answer:

[tex]x=129[/tex] °

Step-by-step explanation:

A secant is a line that intersects a circle in two places. The secants interior angle theorem states that when two secants intersect a circle inside a circle, the measure of any one of the angles formed is equal to half of the sum of the two intersecting arcs. Therefore, one can apply this theorem here:

[tex]x=\frac{204+54}{2}[/tex]

Simplify,

[tex]x=\frac{204+54}{2}[/tex]

[tex]x=\frac{258}{2}[/tex]

[tex]x=129[/tex]

Answer:

hsv s deutsche ki bhar ke dekhte hai mera gham na

Answer:

b.  e^9.45 = x

see last example and this explains whole numbers and decimals.

Step-by-step explanation:

Another example we can Solve  100=20e^2t .

Solution

100 = 20e^2t

5 = 20e ^2t

in 5 = 2t

Therefore  t = in5/ 2

Step 1 was ; Divide by the coefficient of the power

Step 2 was ; Take ln of both sides. Use the fact that ln(x) and ex are inverse functions

Step 3 was; Divide by the coefficient of t

Another example;

Solve  e^2x−e^x = 56 .

Solution

Analysis

When we plan to use factoring to solve a problem, we always get zero on one side of the equation, because zero has the unique property that when a product is zero, one or both of the factors must be zero. We reject the equation  e^x=−7  because a positive number never equals a negative number. The solution  ln(−7)  is not a real number, and in the real number system this solution is rejected as an extraneous solution.

Another example is;

Solve  e^2x=e^x+2 .

Answer

Q&A: Does every logarithmic equation have a solution?

No. Keep in mind that we can only apply the logarithm to a positive number. Always check for extraneous solutions.

Last example determines decimals ;

Solve  lnx =3 .

Solution

lnx^x=3=e^3

Use the definition of the natural logarithm

Graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to  20 . In other words  e^3≈20 . A calculator gives a better approximation:  e^3≈20.0855 .

The graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to  20 . In other words  e^3≈20 . A calculator gives a better approximation:  e^3≈20.0855 .

It shows values of graphs of  y=lnx  and  y=3  cross at the point  (e^3,3) , which is approximately  (20.0855,3) .

See graph below.

Answer:

its B. 636 to 1404

Step-by-step explanation:

Using the Empirical Rule, about 95% of the scores lie between values 636 to 1404. The correct option is c.

The standard deviation of a set of values is a measure of its variation or dispersion. The square root of the variance, which is the average of the squared differences from the mean, is used to calculate it.

According to the Empirical Rule, approximately 68% of the data for a normal distribution fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

In this case, the mean SAT score is 1020, with a standard deviation of 192. As a result, roughly 95% of the scores fall within two standard deviations of the mean, or between

(1020 - 2(192)) and (1020 + 2(192)).

Calculating, we get:

Lower bound: 1020 - 2(192) = 636

Upper bound: 1020 + 2(192) = 1404

Therefore, the answer is (b) 636 to 1404.

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Answer:

150

Step-by-step explanation:

Increase = New Number - Original Number.

divide the increase by the original number and multiply the answer by 100.

Hi, I'm happy to help!

Parallel means that two lines are lined up in the same directions and will never intersect even if they were extended forever in directions.

Let's look at the first option of AB, and AD. We can see that both lines intersect at point A, so AB and AD are not parallel.

For the next option of CD and BE, we can see that both lines don't intersect and won't ever even if the lines were extended. So, CD and BE are parallel.

For the third option, we have BC and DE. These lines don't intersect and aren't in line to ever do so. Therefore, BC and DE and parallel.

The last option is AD and BC. These two lines will never meet, but, they aren't line up in the same directions. AD is traveling upwards while BC isn't. Think about being able to make a road out of the two lines, it would never work. AD and BC are not parallel.

To sum it up: You should select the 2nd and 3rd options because those lines are parallel.

I hope this was helpful, keep learning! :D

The cost of one barrel of gasoline given the total amount made from all the barrels sold is $20.

A pie chart is a graph that displays information using a circle. The circle is divided into sections which represent a numerical proportion. The sum of percentages in a pie chart is 100%.

The first step is to determine the number of barrel of gasoline.

Number of barrels of gasoline = percentage of gasoline x number of barrels

34% x 60 million

0.34 x 60 million = 20.4 barrels

The second step is to divide the total amount generated from the sales by the number of barrels.

Cost of one barrel of gasoline = 408 million / 20.4 million = $20

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Answer:  Choice C

[tex]\frac{2x+3}{x+2}[/tex]

===============================================

Work Shown:

[tex]h(x) = f(x) \div g(x)\\\\h(x) = \frac{f(x)}{g(x)}\\\\h(x) = \frac{2x^2-x-6}{x^2-4}\\\\h(x) = \frac{(x-2)(2x+3)}{(x-2)(x+2)}\\\\h(x) = \frac{2x+3}{x+2}\\\\[/tex]

Optional Extra Info:

Keep in mind that [tex]x \ne 2[/tex] and [tex]x \ne -2[/tex] to avoid division by zero errors. We can plug in x = 2 just fine into the simplified version of h(x), but we always need to go back to the original.

Answer:

sum is 2(a² + b²)

Step-by-step explanation:

[tex] {(a - b)}^{2} + {(a + b)}^{2} \\ = ( {a}^{2} - 2ab + {b}^{2} ) + ( {a}^{2} + 2ab + {b}^{2} ) \\ = 2 {a}^{2} + 2 {b}^{2} \\ = 2( {a}^{2} + {b}^{2} )[/tex]

Answer:Each of the points and the y-intercept of their perpendicular bisectors

Step-by-step explanation:

Where AB and CD are parallel lines:

the y-intercept of line AB is -56/5

the equation of line CD is: y = 7/5x - 2

If two lines are parallel, they will have the same slope (m) value in their equation, y = mx + b (slope-intercept form).

Find the slope of AB:

Slope of AB (m) = change in y / change in x = (7 - 0)/(3 - 8) = 7/5

To find the y-intercept (b) of AB, substitute (x, y) = (8, 0) and m = 7/5 into y = mx + b

0 = 7/5(8) + b

0 - 56/5 = b

b = -56/5 (y-intercept of AB)

AB is parallel to CD, so, CD will have the same slope of 7/5.

To find the equation of CD, substitute m = 7/5 and (a, b) = (5, 5) into y - b = m(x - a)

y - 5 = 7/5(x - 5)

y - 5 = 7/5x - 7

y = 7/5x - 7 + 5

y = 7/5x - 2 (equation of line CD)

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Answer:

Hello,

Step-by-step explanation:

Roots are -2 and 4

y=k*(x+2)(x-4)

Vertex = (1,-9) is a point of the parabola

-9=k*(1+2)(1-4) ==> k=1

Equation of the parabola is y=(x+2)(x-4)

But you don' t have given the graphs !!!!

The graph show a parabola with a vertex that has Roots are -2 and 4.

A parabola is a U-shaped curve this is drawn for a quadratic function,

f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.

Given that,

The vertex of (1,-9) and solutions of (-2,0) and (4,0).

y = k*(x+2)(x-4)

Vertex = (1,-9) is a point of the parabola

-9 = k*(1+2)(1-4)

Substitute the value of k = 1 in the equation,

The equation of the parabola is y = (x+2)(x-4).

The graph show a parabola with a vertex that has Roots are -2 and 4.

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Answer:

what's is the question anyway

Let

[tex]I(m) = \displaystyle \int_0^\pi x\sin^m(x)\,\mathrm dx[/tex]

Integrate by parts, taking

u = x   ==>   du = dx

dv = sinᵐ (x) dx   ==>   v = ∫ sinᵐ (x) dx

so that

[tex]I(m) = \displaystyle uv\bigg|_{x=0}^{x=\pi} - \int_0^\pi v\,\mathrm du = -\int_0^\pi \sin^m(x)\,\mathrm dx[/tex]

There is a well-known power reduction formula for this integral. If you want to derive it for yourself, consider the cases where m is even or where m is odd.

If m is even, then m = 2k for some integer k, and we have

[tex]\sin^m(x) = \sin^{2k}(x) = \left(\sin^2(x)\right)^k = \left(\dfrac{1-\cos(2x)}2\right)^k[/tex]

Expand the binomial, then use the half-angle identity

[tex]\cos^2(x)=\dfrac{1+\cos(2x)}2[/tex]

as needed. The resulting integral can get messy for large m (or k).

If m is odd, then m = 2k + 1 for some integer k, and so

[tex]\sin^m(x) = \sin(x)\sin^{2k}(x) = \sin(x)\left(\sin^2(x)\right)^k = \sin(x)\left(1-\cos^2(x)\right)^k[/tex]

and then substitute u = cos(x) and du = -sin(x) dx, so that

[tex]I(2k+1) = \displaystyle -\int_0^\pi\sin(x)\left(1-\cos^2(x)\right)^k = \int_1^{-1}(1-u^2)^k\,\mathrm du = -\int_{-1}^1(1-u^2)^k\,\mathrm du[/tex]

Expand the binomial, and so on.

Answer:

Oh no I am sorry! If you want answers to be done the real way let me know

Answer:I'm so sorry for you but congrats you did get the answer right it's just the test I guess

Step-by-step explanation: