What are the different ways to write multiplication in math

Answer:

Step-by-step explanation:

Problem 1

g(-23) = 3

g(0) = 5

2 = g(10)

1 = g(34)

Problem 2

No, because g(x) = f(-x).  For g(x) to inverse of f(x), g(f(x)) = x

Problem 3

tan(50) = 1.19

Height of statue = 250*1.19 - 150

= 147.9 ft

Problem 4

cosθ = 9/12

θ = 41.41 deg.

Answer:

Step-by-step explanation:

g(x) is inverse of f(x)

so g(f(x))=x

g(-23)=3

g(0)=5

g(10)=2

g((34)=1

no, it is an inverse

4 inverse fn, g(r(x))=x

but here g(x)=r(-x)

so g(r(x))=r(-r(x)) n NOT =x

pedestal + statue = 250*tan(50degree) = 297.94

statue ht = 297.94-150 = 147.94 ft

cos(theta) = 9/12

theta = 41.41 deg.

Answer:

x = \(\frac{4}{5}\), y = \(\frac{1}{5}\)

Step-by-step explanation:

Express as 2 equations, that is

x + y = 1 → (1)

- x + 9y = 1 → (2)

Add the 2 equations term by term to eliminate x, that is

10y = 2 ( divide both sides by 10 )

y = \(\frac{2}{10}\) = \(\frac{1}{5}\)

Substitute this value into (1) and solve for x

x + \(\frac{1}{5}\) = 1 ( subtract \(\frac{1}{5}\) from both sides )

y = \(\frac{5}{5}\) - \(\frac{1}{5}\) = \(\frac{4}{5}\)

Answer:

-147

Step-by-step explanation:

We can solve this by plugging in p = 5 and q=−2 and then evaluating using PEMDAS which tells us the order we do the math in by operation

Remember,

PEMDAS means

Parenthesis

Exponents

Multiplication and Division ( perform going left to right )

Addition and Subtraction ( perform going left to right )

-3(p-q)²

==> plug in p = 5 and q = -2

-3(5-(-2))²

==> remove parenthesis on -2

-3(5 + 2)²

==> do the operations inside of the parenthesis

-3(7)²

==> do the exponents

-3(49)

==> multiply -3 and 49

=-147

Answer:70

Step-by-step explanation:

a. Constant speed, C =  0. 19 miles/minutes

b. The fraction representing her constant speed is  1/x miles/minutes

c. The time it takes her to drive exactly 1 mile is 5. 38 minutes

The formula for calculating constant speed is expressed as;

Constant speed = total distance covered/ total time taken

From the information given, we have that;

Now, substitute the values into the formula

Constant speed = 1. 3 / 7

Divide the values

Constant speed = 0. 19 miles/minutes

When distance 1 mile, time taken = x minutes

Constant speed = 1/x miles/minutes

If 1. 3 miles = 7 minutes

Then, 1 mile = x

cross multiply

x = 7/1. 3

x = 5. 38 minutes

Hence, the constant speed is 0. 19 miles/minutes

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Answer:

-5+√2 and -5-√2

Step-by-step explanation:

With the quadratic formula:

\(\displaystyle x^2 + 10x + 25 = 2\\\\x^2+10x+23=0\\\\x=\frac{-10\pm\sqrt{10^2-4(1)(23)}}{2(1)}=\frac{-10\pm\sqrt{100-92}}{2}=\frac{-10\pm\sqrt{8}}{2}=\frac{-10\pm2\sqrt{2}}{2}=-5\pm\sqrt{2}\)

We can also complete the square (which is faster):

\(x^2+10x+25=2\\(x+5)^2=2\\x+5=\pm\sqrt{2}\\x=-5\pm\sqrt{2}\)

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

-3

Step-by-step explanation:

Hey there!

Equation:

m - n

Solving:

m - n

= 4 - 7

Start at 4 and go up 7 spaces to your left/right

= -3

Therefore, your answer should be: -3

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

Answer:

Give the other guy brainliest he earns it

Step-by-step explanation:

Answer:

\(x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}\)

Step-by-step explanation:

Given trigonometric equation:

\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

To solve the equation for x in the given interval [0, 2π), first rewrite the equation in terms of sin x and cos x using the following trigonometric identities:

\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric identities}\\\\$\tan \left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos \theta}{\sin \theta}$\\\\\\$\csc \theta = \dfrac{1}{\sin \theta}$\\ \end{minipage}}\)

Therefore:

              \(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

\(\implies 2 \left(\dfrac{1-\cos x}{\sin x}\right)- \dfrac{1}{\sin x}=0\)

  \(\implies \dfrac{2(1-\cos x)}{\sin x}- \dfrac{1}{\sin x}=0\)

\(\textsf{Apply the fraction rule:\;\;$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$}\)

\(\dfrac{2(1-\cos x)-1}{\sin x}=0\)

Simplify the numerator:

\(\dfrac{1-2\cos x}{\sin x}=0\)

Multiply both sides of the equation by sin x:

\(1-2 \cos x=0\)

Add 2 cos x to both sides of the equation:

\(1=2\cos x\)

Divide both sides of the equation by 2:

\(\cos x=\dfrac{1}{2}\)

Now solve for x.

From inspection of the attached unit circle, we can see that the values of x for which cos x = 1/2 are π/3 and 5π/3. As the cosine function is a periodic function with a period of 2π:

\(x=\dfrac{\pi}{3} +2n\pi,\; x=\dfrac{5\pi}{3} +2n\pi \qquad \textsf{(where $n$ is an integer)}\)

Therefore, the values of x in the given interval [0, 2π), are:

\(\boxed{x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}}\)

Answer:

C=0.15y+7.89

Step-by-step explanation:

The linear equation represents the cost C of a movie ticket y is C=0.15y+7.89. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We define a linear equation. Equations of degree 1 are linear equations. It is the straight line's equation. A linear equation with parameters a and b equal to zero has the conventional form ax+by+c = 0.

When two linear expressions are equal, there is a linear equation in one variable. Or, to put it another way, a graph would be one method of solving this equation.

Given ,

Average price of movie ticket =$7.89

Increased average tickets =$0.15

So Simplifying the equation is

C=0.15y+7.89

Therefore The linear equation represents the cost C of a movie ticket y is C=0.15y+7.89.

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The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

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The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.

An equation is an expression that shows the relationship between two or more variables and numbers.

Inequality is an expression that shows the non equal comparison of two or more numbers and variables

The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.

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The graphs of f(x) and g(x) are transformed function from the function y = x^2 and the solution of the set of inequalities is (±1.581, -0.5)

The complete question is in the attached image (the first graph)

From the graph, we have:

f(x) = x^2 - 3 and g(x) = -x^2 + 2

To derive y ≤  x^2 - 3, we simply change the equality sign in the function f(x) to less than or equal to.

To derive y > -x^2 + 2, we simply change the equality sign in the function g(x) to greater than

The inequalities of the graphs become

y ≤ x^2 - 3 and y > -x^2 + 2

From the graph of the above inequalities (see attachment 2), we can see that the curves of the inequalities intersect at (±1.581, -0.5)

Hence, the solution of the set of inequalities is (±1.581, -0.5)

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Answer:  The swimming pool holds 59,840 gallons of water.

Step-by-step explanation:

Multiply 7.48 times 8000

The volume of the trapezoidal ditch is 486000 in³. The volume of the half-cylinder ditch is 457812 in³. Therefore, the trapezoidal ditch holds a greater volume of water

Given:

Two flood control ditches; one is a trapezoidal ditch and the other a half cylinder

To find:

the volume of the two ditches and compare which has a greater volume of water

To determine the shape with higher volume, we need to find the volume of each of the ditches

The volume of the trapezoidal ditch is greater than the volume of the half-cylinder

The volume of the trapezoidal ditch is 486000 in³. The volume of the half-cylinder ditch is 457812 in³. Therefore, the trapezoidal ditch holds a greater volume of water

If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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Answer:

20

Step-by-step explanation:

first of all, let's layout the facts:

Tracy has a total of 35 students

3/7 of those students are ten y/o

and the rest (4/7) are nine y/o

to work out how many students are nine we are going to first work out how many students are ten.

to work out how many students are ten we are going to take the fraction, and think of it as to parts, the top and the bottom.

with the bottom number, 7, we are going to divide that by our total, 35.

35 / 7 = 5

now with our top number, 3, we are going to multiply that by the answer we just received, 5.

5 x 3 = 15

this means that 15 of the students are ten years old.

now since the REMAINDER of the students are nine we are going to subtract our ten year olds from the total number of students like this:

35 (total students) - 15 (ten year olds) = 20 (nine year olds)

which gives us our final answer, 20.

Answer:

20 nine year olds

Step-by-step explanation:

To find how many students are nine year olds, we have to find the fraction of how many nine year olds.

Since 3/7 of them are ten year olds, then the remaining of that fraction is the fraction of nine year olds.

7/7 - 3/7 = 4/7

To find the number of nine year olds, you divide the fraction of nine year olds by the total amount of students

4 x 35 = 140

7 x 1 = 7

140/7 = 20

There are 20 nine year olds in Tracy's class.

Answer:

102.2 miles

Step-by-step explanation:

First, convert the minutes to hours:

101.5/60

= 1.69 hours

Multiply this by 60.4 to find how many miles it covered:

= 102.2 miles

Answer:

46.8 cm²

Step-by-step explanation:

The diagonal of the square has length \(\sqrt{6^2+10^2}=2\sqrt{34}\). Therefore, the radius of the circle is \(\sqrt{34}\), meaning the area is \(\pi(\sqrt{34})^2 \approx 34(3.14)=106.76\).

The area of the rectangle is \((6)(10)=60\) cm².

Subtracting the areas, the answer is 46.76 cm², which is 46.8 cm² to the nearest tenth.

Answer:

\(12\frac{2}{3}\)

Step-by-step explanation:

Answer:

254,000

Step-by-step explanation:

What is 25.4 x 10 to the 4th power?

Translate:

25.4 * 10⁴

25.4 * 10,000

Here, we will be moving the decimal four times to the right:

25.4 * 10,000

254,000

Note: if you're not sure, you can always use a calculator to double check :)

Hope this helps!

The distance traveled by the center of the wheel (from time t = 0 seconds to time t = 3 seconds) starting from rest that has an angular acceleration of 6 rad/s² is 13.5 meters

Angular motion can be described the motion of a body around a circular path or a curved path around a fixed axis.

Radius of the wheel, r = 0.5 meters

The wheel rolls starting from rest without sliding on the horizontal surface

Constant angular acceleration of the wheel = 6 rad/s²

The angle rotation, θ, of the wheel can be found by the formula;

θ = θ₀ + ω₀·t + (1/2)·α·t²

Where;

θ = Rotation of the wheel

θ₀ = Initial angular rotation of the wheel = 0 (The wheel is initially at rest)

ω₀ = The angular velocity of the wheel at the start = 0 (The wheel starts from rest)

α = The angular acceleration of the wheel = 6 rad/s²

Therefore;

θ = 0 + 0 + 0.5 × 6 × 3² = 27

The angle turned by the wheel = 27 radians

The linear displacement of the, d = r·θ

Therefore;

The distance traveled by the wheel, r·θ = 0.5 m × 27 rad = 13.5 m

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Complete question; To find the the distance traveled by the center of the wheel from t = 0 seconds to t = 3 seconds

Answer:

6:22

9:33

12:44

Step-by-step explanation:

Answer:

15:55

Step-by-step explanation:

3x5 equals 15 and 11x5 is 55

Answer: C-$0.15

Step-by-step explanation:

Answer: A line of best fit is a straight line that is the best approximation of the given data. It can be represented by the equation: y = mx + b, where m is the slope (the rate of change) of the line and b is the y-intercept (the point where the line crosses the y-axis)

To find the equation for the line of best fit for a set of data, we can use the least squares method. It involves finding the slope (m) and y-intercept (b) that minimize the difference between the predicted values of y and the actual values of y.

To find the slope, we use this formula:

m = (N∑(xy) - (∑x)(∑y)) / (N∑(x^2) - (∑x)^2)

Where N is the number of data points, x is the independent variable, y is the dependent variable, ∑ denotes the sum of all the values.

To find the y-intercept, we use this formula:

b = (∑y - m(∑x))/N

After applying the formula:

m = (5*(731) - (58)(96)) / (5*(198) - (58)^2)

m = 0.957

b = (96 - 0.957*58)/5

b = -6.836

So, the equation for the line of best fit for the given data is:

y = 0.957x - 6.836

Rounded to three decimal places, the slope and y-intercept are:

m = 0.957 and b = -6.836

So the equation for the line of best fit for the given data is: y = 0.957x - 6.836.

This equation represents the line of best fit for the given data, meaning that it is the line that most closely approximates the data.

Step-by-step explanation:

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

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