Find the value of x.

Answer:

\(3(10p + 3z + 12) = 3(10 \times 3 + 3 \times 6 + 12) \\ 3(30 + 18 + 12) \\ 3(60) \\ = 180\)

The above formula is used to find the distance betweent two points on the coordinate plane

let x1 = -5

let y1 = 8

let x2 = 9

let y2 = -2

inputing the following values in the above equation

\(\begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_8(x)-\log_8(7)=\log_8\left( \cfrac{5}{7} \right)\implies \log_8(\stackrel{x }{5})-\log_8(7)=\log_8\left( \cfrac{5}{7} \right)\)

Answer:

75% of 124 is 93.

Step-by-step explanation:

I hoped this helped ^^

The period of the frequency factor b that is given in the diagram above would be = 0.2 sec.

The frequency of a water wave is defined as the number of times the wave completes a cycle within a given period of time. While the period is the time it takes for the completion of a cycle.

The dot the represents the frequency factor b is the green dot on the wave table. Therefore the period as traced from the graph= 0.2 sec.

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Answer:

\((a)\ P(White) = \frac{1}{2}\)

(b) 10 additional white balls

(c) 10 additional black balls

Step-by-step explanation:

Given

\(White = 5\)

\(Black =3\)

\(Red = 2\)

Solving (a): P(White)

This is calculated as:

\(P(White) = \frac{White}{Total}\)

\(P(White) = \frac{5}{5+3+2}\)

\(P(White) = \frac{5}{10}\)

\(P(White) = \frac{1}{2}\)

Solving (b): Additional white balls, if \(P(White) = \frac{3}{4}\)

Let the additional white balls be x

So:

\(P(White) = \frac{White+x}{Total+x}\)

This gives:

\(\frac{3}{4} = \frac{5+x}{10+x}\)

Cross multiply

\(30+3x = 20 + 4x\)

Collect like terms

\(4x - 3x = 30 - 20\)

\(x = 10\)

Hence, 10 additional white balls must be added

Solving (c): Additional black balls, if \(P(White) = \frac{1}{4}\)

Let the additional black balls be x

So:

\(P(White) = \frac{White}{Total+x}\)

So, we have:

\(\frac{1}{4} = \frac{5}{10+x}\)

Cross multiply

\(10+x = 5 * 4\)

\(10+x = 20\)

Collect like terms

\(x = 20 -10\)

\(x = 10\)

Hence, 10 additional black balls must be added

Answer:

Step-by-step explanation:

when a fraction divide a number the number is in denominator to multiple it this number gets multipled into denominator of a particular fraction.

11/12*4

11/48

= 0.22

Answer:

Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)

Step-by-step explanation:

As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.

11^2 + 5^2 = AC^2

121 + 25 = AC^2

146 = AC^2

sqrt(146) = AC^2

Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)

Answer: 32 + 8 = 40 × 2 = (80) is the correct answer.

Step-by-step equation:

Cami is wrong 34 is not the correct answer. She made the mistake in her multiplying.

What mistake did Cami make when evaluating the expression? Cami divided instead of multiplying.  

What is the correct answer? The correct answer is 48. Notice that you first multiply first 8 x 2 and then add 32. Recall that you always multiply and then add.

Answer:

0.905

Step-by-step explanation:

1 - 0.095 = 0.905

Answer:

Step completed incorrectly:  2

Correct Answer: y = -4x + 22

Step-by-step explanation:

The graph is a straight line through points M(4, -1) and N(8, 0).  Point Q is located at (6, -2).

To calculate the slope of the line, substitute the points into the slope formula:

\(\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}\)

Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.

If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.

The negative reciprocal of 1/4 is -4.

Therefore, the slope of the perpendicular line is -4.

So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.

Corrected work

\(\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}\)

\(\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4\)

\(\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}\)

\(\textsf{Step 4:} \quad y+2=-4x+24\)

\(\textsf{Step 5:} \quad y+2-2=-4x+24-2\)

\(\textsf{Step 6:} \quad y=-4x+22\)

Therefore, step 2 has been completed incorrectly.

The correct answer is y = -4x + 22.

From the table, the probability of getting exactly 1 girl is 0.018.

The problem is looking for getting 1 or fewer girls, so we should also consider when the number of girls is 0.

The probability of NOT getting a girl is 0.001.

Take the sum of both probabilities.

0.018 + 0.001 = 0.019

The answer is 0.019

Answer:

y = 4

28?

Step-by-step explanation:

this could be wrong, if so, I am sorry

The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.

The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.

When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.

To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.

For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.

In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.

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Let's raise i to various powers starting with 0,1,2,3...

i^0 = 1

i^1 = i

i^2 = ( sqrt(-1) )^2 = -1

i^3 = i^2*i = -1*i = -i

i^4 = (i^2)^2 = (-1)^2 = 1

i^5 = i^4*i = 1*i = i

i^6 = i^5*i = i*i = i^2 = -1

We see that the pattern repeats itself after 4 iterations. The four items to memorize are

i^0 = 1

i^1 = i

i^2 = -1

i^3 = -i

It bounces back and forth between 1 and i, alternating in sign as well. This could be one way to memorize the pattern.

To figure out something like i^25, we simply divide the exponent 25 over 4 to get the remainder. In this case, the remainder of 25/4 is 1 since 24/4 = 6, and 25 is one higher than 24.

This means i^25 = i^1 = i

Likewise,

i^5689 = i^1 = i

because 5689/4 = 1422 remainder 1. The quotient doesn't play a role at all so you can ignore it entirely

Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given two triangles, Where the base of these triangles are same

And also given that the two angles are the same.

Since,

Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).

Thus, the third angle is also equal

From AAS:

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,

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Answer:150?

Step-by-step explanation:

Answer: 47/40 miles or 1 and 7/40 miles

Step-by-step explanation:

      We will add these two fractions together by finding common denominators.

3/8 + 4/5 = 15/40 + 32/40 = 47/40 = 1 and 7/40 miles.

Answer:

Step-by-step explanation:

greater than or equal to

A) The value of x in log₄(x² - 12x + 48) = 2, is x = 4 OR x = 8

B) The value of x in 27^(4x-6) =(1/9)^(2x-7), is x = 2

From the question, we are to solve the given equations

The given equation is log₄(x² - 12x + 48) = 2

From one of the laws of logarithm, we have that

logₐ x = n ⇒ x = aⁿ

Thus,

log₄(x² - 12x + 48) = 2 becomes

(x² - 12x + 48) = 4²

x² - 12x + 48 = 16

x² - 12x + 48 - 16 = 0

x² - 12x + 32 = 0

Solve the quadratic equation

x² - 12x + 32 = 0

x² - 8x - 4x + 32 = 0

x(x - 8) -4(x - 8) = 0

(x - 4)(x - 8) = 0

x - 4 = 0 OR x - 8 = 0

x = 4 OR x = 8

B) 27^(4x-6) =(1/9)^(2x-7)

Solve for x

27^(4x-6) =(1/9)^(2x-7)

Express the bases in index form

3^3(4x-6) =(3)^-2(2x-7)

Equate the powers

3(4x - 6) = -2(2x - 7)

12x - 18 = -4x + 14

12x + 4x = 14 + 18

16x = 32

Divide both sides by 16

16x/16 = 32/16

x = 2

Hence, the value of x is 2

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Answer:

$163.68

Explanation:

136.40 times 20% or 0.2 = 27.28

27.28 +136.40 = $163.68

Answer: The answer is C (or the third option)

Step-by-step explanation: The formula for finding the measure of interior hexagon angles is ( n − 2) × 180 °. This means that C is the correct answer

Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

Answer:

The answer is B!

Step-by-step explanation:

I hope this helps! Have a great rest of your day!

well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years

\(~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}\)

\(A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}\)

\(A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}\)

The true statement about the graphs:

Their slopes will be different from the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x).

The correct answer is an option (C)

First we draw a graph of function f(x) = -x + 3.

Find the graph in attached figure.

the x-intercept of f(x) is:

0 = -x + 3

i.e., x-intercept = (3, 0)

Then, three graphs of k(-x + 3) are drawn, for k = -1, -2, -3.

Let g(x) = -1(-x + 3)

The x-intercept of g(x) would be,

0 = -1(-x + 3)

i.e., x-intercept = (3, 0)

Let h(x) = -2(-x + 3)

The x-intercept of h(x) would be,

0 = -2(-x + 3)

2x = 6

i.e., x-intercept = (3, 0)

Let t(x) = -3(-x + 3)

The x-intercept of t(x) would be,

0 = -3(-x + 3)

3x = 9

i.e., x-intercept = (3, 0)

the graph of functions g(x), h(x) and t(x) is shown below.

We can observe that the x-intercept is same for all graphs but the slopes are different.

Therefore, the correct answer is an option (C)

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The ratio of the lengths of and is 1: 1

PQ parallel to RS

PR and PS; perpendicular to PQ and RS.

Perpendicular lines are lines that intersect at a 90 degrees angle. Parallel lines are lines that are always the same distance apart.

FOR parallel lines, the perpendicular line joining then is always the same; here the 4 angles formed are all 90°

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The number gives the exact value of three and seven fifteenths is (b) three and forty six hundredths with the six repeating

The number is given as:

Three and seven fifteenths

This can be represented as:

Three + seven fifteenths

Express seven fifteenths as 7/15

Three + 7/15

Express Three as 3

3 + 7/15

Evaluate the quotient 7/15

3 + 0.466...

Evaluate the sum

3 .466...

This can be rewritten as:

three and forty six hundredths with the six repeating

Hence, the number gives the exact value of three and seven fifteenths is (b) three and forty six hundredths with the six repeating

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Answer: b

Step-by-step explanation: i took the test

The indefinite integral of  ∫(2ti+j+8k)dt is  t²i +tj+8tk+c.

Given the expression is ∫(2ti+j+8k)dt

The indefinite integrals, also known as the derivatives of functions, are integrals that can be computed using the process of differentiation in reverse.

Further approaches for resolving indefinite integrals include integration by parts, substitution, integration of partial fractions, and integration of inverse trigonometric functions.

now, ∫(2ti+j+8k)dt

= 2t²/2 i + tj +8tk

= t²i +tj+8tk+c

hence we get the indefinite integral as  t²i +tj+8tk+c

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8/21 of the lawn still needs to be mowed.

To compare fractions, we need a common denominator. The least common multiple of 7 and 3 is 21.

Miss Lianto's fraction: (2/7) x (3/3) = 6/21

Son's fraction: (1/3) x (7/7) = 7/21

To calculate how much of the lawn still needs to be mowed, we can subtract the combined fractions mowed from the total:

Combined fractions mowed: 6/21 + 7/21 = 13/21

So, Remaining fraction: 1 - 13/21 = 8/21

Therefore, 8/21 of the lawn still needs to be mowed.

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