PLZZ HELP!!!!!!
Solve the equation, justify each step with an algebraic property: -2 = x + 28 *

x = -26, Subtraction Property of Equality
x = -30, Addition Property of Equality
x = -14, Division Property of Equality
x = -30, Subtraction Property of Equality

(a) sin⁻¹(-1/2) = -π/6, (b) sin⁻¹(3√2) does not have a solution in the interval [-π/2,π/2]. (c) sin⁻¹(-3√2) does not have a solution in the interval [-π/2,π/2].

(a) The inverse sine function sin⁻¹(x) returns the angle whose sine is x. In this case, we want to find the angle whose sine is -1/2. Since the sine function is negative in the third quadrant and the range of sin⁻¹(x) is [-π/2,π/2], the angle we are looking for is in the fourth quadrant.

Therefore, we use the reference angle π/6 and add a negative sign to get -π/6 as our final answer.

(b)  The inverse sine function sin⁻¹(x) returns the angle whose sine is x. In this case, we want to find the angle whose sine is 3√2. However, since the range of the sine function is [-1,1], there is no angle whose sine is greater than 1.

Therefore, this expression does not have a solution in the interval [-π/2,π/2].

(c)  The inverse sine function sin⁻¹(x) returns the angle whose sine is x. In this case, we want to find the angle whose sine is -3√2. However, since the range of the sine function is [-1,1], there is no angle whose sine is less than -1.

Therefore, this expression does not have a solution in the interval [-π/2,π/2].

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Answer:

x = -3 or x = -5

Step-by-step explanation:

x (x -2 ) = -5

x = -5 or x = -5+2

x = -3

The probability of the event occuring is 29/51

When we talk about probability, we are essentially trying to measure the likelihood of an event occurring. One way to do this is by using the ratio of the number of favorable outcomes to the total number of outcomes.

In this case, the odds for a certain event are given as 29 to 22. This means that for every 29 favorable outcomes, there are 22 unfavorable outcomes. So, the total number of outcomes can be calculated as the sum of the favorable and unfavorable outcomes, which is 29 + 22 = 51.

To calculate the probability of the event occurring, we need to divide the number of favorable outcomes by the total number of outcomes. In this case, the number of favorable outcomes is 29, so the probability can be calculated as:

Probability = 29 / 51

This can be simplified by dividing both the numerator and denominator by the greatest common factor, which is 1 in this case. So the final answer is:

Probability = 29/51

This means that if we were to repeat the event many times, we would expect the event to occur approximately 29/51 or 56.86% of the time.

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Answer:

The number of paperclips decreased by 12.5%

Step-by-step explanation:

72-63=9

9/72 = .125 or 12.5%

Answer:

Step-by-step explanation:

To get percentage change, we use the formula:

Percentage change =

Here,

the new value is the later value of 63 and the old value is the first value of 72

Plugging in the values in the formula gives us:

Percentage change =

The percent change is 12.5% (we can also say that it is a decrease of 12.5% since negative)

You are more likely to win by playing regular defense.

The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.

Assume out of 100 reviewed games, there were 50 regular defense games and 50 prevent defense games. And out of 50 regular defense games, 38 were won, 12 were lost.

And out of 50 prevent defense game, 29 were won, 21 were lost.

Probability to win the game by playing regular defense is:

P(win | regular) = 38/50 = 0.76

Probability to win the game by playing prevent defense is:

P(win | prevent) = 29/50 = 0.58

Since the probability of winning by regular defense game is more than prevent defense game (0.76 > 0.58),

Hence, you are more likely to win by playing regular defense.

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Answer:

74-21=d or d+21=74

Step-by-step explanation:

Answer:d+21=74 and if you want to solve it would be

get d by itself so minus 21 on both sides 21-21 is

d= 74-21 is 53

so d=53

Step-by-step explanation:

Answer: m = -1 , b = -8

Step-by-step explanation:

y=mx+c

m = gradient of the line / slope of the line

c = y intercept

-x=-1x so the gradient is -1

-8 = y intercept

Answer:

19/20 cups

Step-by-step explanation:

Add the amounts together

1/4 + 7/10

Get a common denominator of 20

1/4 *5/5   + 7/10 *2/2

5/20 + 14/20

19/20

Answer:

19/20

Step-by-step explanation:

find a common denominator then do the same with the numerator then add.

After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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Answer:

m = undef

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define

Point (3, 2)

Point (3, -2)

Step 2: Find slope m

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer:

the answer is D.

Step-by-step explanation:

this is because if you distribute 0.4 times 0.3 you get 0.12.

then you are left with 0.12+1 which means both shops charge the same price.

The quantity of more flour that she needs to add would be = 3/4

A fraction is defined as the representation of the part of a whole data in a form of numerator and denominator.

The quantity of flour Ryan needs for baking = 3¼

The quantity of flour she has already added = 2½

The remaining amount that she needs to add;

= 3¼-2½

= 3/4

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Answer:

Step-by-step explanation:

Given sequence:

a)

The terms can be rewritten as:

b)

Sum of the first n terms:

Sum of the first 40 terms:

Answer:

Step-by-step explanation:

A is certainly true. If you put 30 into your calculator, you get factions for the cube root and square root. True

B is true. 5^2 = 25 Twenty five is made up of 2 fives.

C is a perfect cube. 10 * 10  * 10 = 1000. But it is not a perfect square. False.

D 64 is a perfect cube. (It is also a perfect square).

E false 16 is a perfect square. It is not a perfect cube

True Statements

A B D

Answer:

33+ 110x

Step-by-step explanation:

open the bracket.

hope it helps!!!

Step-by-step explanation:

one side.

as each tile is guaranteed an equilateral triangle, all sides are equally long. measuring 1 side clarifies therefore the overall size of the tile.

the angles are the same in any case, as every equilateral triangle (no matter its size) has only angles of 60°.

so, if any side has the same length as the side lengths of the other triangles, then the checked triangle is congruent with the others.

Answer:nunya

Step-by-step explanation:

The difference between the level of real GDP per capita in the United States and real GDP per capita in Bolivia will shrink over time. The correct option is (b)

Real GDP per capita is a measure of the standard of living in a country, and it depends on the growth rate of real GDP and the population growth rate.

In this scenario, the United States has a higher initial level of real GDP per capita, and it is growing at a faster rate than Bolivia.

Over time, the difference in real GDP per capita between the two countries will shrink because the growth rate of real GDP per capita in the United States is not high enough to offset the initial gap in real GDP per capita between the two countries.

Option (a) is incorrect because the difference in real GDP per capita between the two countries will not always be 1.9%. It will depend on the initial gap and the growth rates of the two countries.

Option (c) is incorrect because if real GDP per capita in the United States is growing at a faster rate than in Bolivia, then the gap between the two countries should shrink over time, not increase.

Option (d) is incorrect because the difference in real GDP per capita between the two countries is not a fixed amount, but rather a percentage difference that will change over time.

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Answer:

y = 45/2

Step-by-step explanation:

Given:

y = 4x - 1 1/2

find the value of y when x=6

y = 4x - 1 1/2

Substitute x = 6 into the equation

y = 4(6) - 1 1/2

y = 24 - 1 1/2

** 1 1/2 = 3/2

y = 24 - 3/2

y = (48-3) / 2

y = 45/2

y = 45/2 when x = 6

Answer:

528 cm squared

Step-by-step explanation:

A parallelogram (slanted shape at the bottom) is essentially the same area as a rectangle.

Therefore, both shapes have the same measurements.

Multiply the length and height of the rectangle to get its area: 22cm×12cm =264cm squared

Since the area of the rectangle corresponds geometrically to the area of the parallelogram, just multiply the area of the rectangle (264cm squared), by 2.

So 264×2, = 528cm squared

Ta da...

Answer:

120

Step-by-step explanation:

white : blue : green

5        :4          :1

48 are blue

48/4 = 12

Multiply each by 12

white : blue : green

5*12   4*12     1*12

60        48        12

Add the numbers together to get the total

60+48+12

120

Taner will only need to run 3 km this week to complete his 6 km running goal.

If we require a definition, we may start by saying that fractional numbers are numbers that symbolize one or possibly more portions of a unit that has been subdivided into equal parts.

Given that, Taner's overall running goal is 6 km (including last week and this week)

So,

Taner's 2-week goal is 6 kilometres.

Now,

Taner's goal for the week is 3 kilometres = (6/2).

As the Taner completed 3 km of running last week. Taner can achieve his objective this week by running just 3 miles.

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Answer:

Step-by-step explanation:

it will ride at 45 miles because if you know every 2 hours she rides 18 miles and your trying to see how many in 5 hours you just do 18 + 18 +9 because half of 18 is 9 and you get 45.

An electric circuit is a closed course that consists of all of the additives linked to finish the go with the drift of modern-day.

The circuit underneath is composed of:

A battery as a supply of direct modern-day which materials electricity within side the circuit for modern-day to go with the drift. Direct modern-day affords uni-directional modern-day. Here it has cells. Here 4 cells are linked in collection for the battery.

Two bulbs A and B linked in parallel connection. Each bulb has been parallel connected with a voltmeter.

A voltmeter measures the voltage throughout the element that it's miles linked with. It is continually linked in parallel with the additives.

Main circuit has an ammeter in collection with the battery and connection of bulb.

An ammeter measures the modern-day flowing within side the circuit. It is continually linked in collection.

Therefore, an electric circuit is a closed course that consists of all of the additives linked to finish the go with the drift of modern-day.

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Step-by-step explanation:

g(x) is also called y. the functional result value for an input value x is shown in the y direction above or below that x value on the x axis.

so, when it says g(x) = c, the solution is to find the values of x for which b the function g delivers c as result.

now, we look at the graphic.

for example, g(x) = 0 (c = 0) has actually 3 solutions, as the function crosses the x-axis (and that means y or g(x) = 0) 3 times. so, there are 3 different values of x that create g(x) = 0.

but we are looking for a c that has only one solution (one value of x to create that result).

c = 1 ?

let's imagine a horizontal line through y = 1.

we see, it cuts the function also 3 times. 3 solutions.

c = -1 ?

a similar horizontal line through y = -1 cuts the function also 3 times. 3 solutions

but c = 3 !

a horizontal line through y = 3 stays above all the waves of the function and then cuts the function only one time at the very right. 1 solution !

and that is therefore our answer.

Answer:

Step-by-step explanation:

I am assuming that by "interior" angle you do not mean the central angle.

This is a 10-sided polygon, a decagon. That means that there are 10 triangles that can extend from the center, with their sides being equal to the radii of the decagon. If we extract one of these triangles we can find what the interior angle is. The vertex angle measures 360/10 which is 36.

Split this triangle in half from the vertex to the base, creating a right triangle. The vertex angle is also split in half, making this angle (the vertex angle is the one at the top of the triangle) 18 degrees. We already know that one angle inside this right triangle is 90 (definition of a right triangle) and to find the other one, we apply the Triangle Angle-Sum Theorem:

180 - 18 - 90 = 72 degrees. That is the measure of the base angle that is NOT the right angle, obviously.