5 Rewrite in simplified exponential notation: (79-4) (798)

Answer:

  x = 10

Step-by-step explanation:

You want the value of x in triangle RST with angle bisector UT dividing RS into parts RU=3x and US=x+2, while RT=40 and ST=16.

The angle bisector divides the sides of the triangle proportionally;

  3x/40 = (x +2)/16

  6x = 5x +10 . . . . . . . multiply by 80

  x = 10 . . . . . . . . . subtract 5x

The value of x is 10.

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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:

60

Step-by-step explanation:

The area of the rectangle will be 60 square units. The correct option is C.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

In the given image we need to calculate the two sides of the rectangle by using the Pythagorean theorem.

DG=√( 2²+6²) = √40

ED = √(9² + 3²) = √90

The area of the rectangle will be calculated as:-

Area = L x W

Area = DG x ED

Area = √40 x √90 = √3600

Area = 60 square units.

Therefore, the area of the rectangle will be 60 square units. The correct option is C.

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Answer:

the answer would be c

Step-by-step explanation:

the answer would be c because its a fraction

Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

Answer:

i thinnk A

Step-by-step explanation:

Answer:

2.65 pounds/week

Step-by-step explanation:

(13 1/4) / 5

13.25 / 5

= 2.65 pounds/week

Answer:

2.65 lbs per week

Step-by-step explanation:

13.25 is how many pounds

5 weeks is the length of time

pounds/length of time

13.25/5 = 2.65

2.65 lbs per week

Explanation:

Most states (but not all) require liability insurance at minimum. This covers injury and property damage to the person you accidently hit. It likely does not cover you personally so you'd need other insurance for that.

States like Iowa, New Hampshire, and Ohio offer exemptions from insurance if you can show you are responsible with money. Meaning that if you have a steady income and are smart with money, then you likely would be able to pay off any future accident without needing insurance. Though the damages might get wildly expensive, so a liability policy isn't always a bad thing.

The number of times the students on your floor order pizza in a week, population.

A population is a complete set of individuals or objects that share common characteristics. It is an entire group of people, animals, plants, or objects that can be studied. A population can also be a group of people living in a certain geographical area.

A sample is a subset of a population. It is a smaller group of individuals or objects drawn from the population that are used to make inferences about the population as a whole.

A sample is used in statistical analysis to estimate population characteristics, such as mean, median, and variance. The accuracy of the estimates depends on the size and representativeness of the sample.

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The complete question is:

Determine whether the statement describes a population or a sample. The number of times the students on your floor order pizza in a week, ___.

\((3-2)^2+(7+5)(3-2)=(3-2)(3-2)+(7+5)(3-2)=(3-2)(3-2+7+5)=1*13=13\)

Answer:

In a room of just 23 people there's a 50-50 chance of at least two people having the same birthday. In a room of 75 there's a 99.9% chance of at least two people matching. Put down the calculator and pitchfork, I don't speak heresy.

Step-by-step explanation:

Answer:

6600 is the answer

Step-by-step explanation:

The maximum revenue possible in this situation is 15625/A dollars, where A is the coefficient in the quadratic equation.

To find the maximum revenue possible in this situation, we can use the concept of vertex or the vertex form of a quadratic equation.

The revenue equation is given by R = -Ax^2 + 250x, where A is a constant coefficient.

The maximum revenue occurs at the vertex of the parabolic curve represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -A and b = 250. Plugging in these values, we get:

x = -250 / (2 * (-A))

= 125 / A

To find the maximum revenue, we substitute this value of x into the revenue equation:

R = -A * (125 / A)^2 + 250 * (125 / A)

= -A * (15625 / A^2) + (31250 / A)

= -15625 / A + 31250 / A

= 15625 / A

The maximum revenue is given by 15625 / A. The value of A is not specified in the question, so we cannot determine the exact maximum revenue without knowing the value of A. However, we can say that the maximum revenue increases as A decreases.

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They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞.

The correct option is D.

From the given points, we can write an exponential function in the form of f(x) = abˣ, where a and b are constants.

Using the point (-4, 9): 9 = ab⁻⁴

Using the point (0, 1): 1 = ab⁰ = a

Using the point (1, 0): 0 = ab¹

Using the point (5, -2): -2 = ab⁵

Solving these equations, we get a = 1 and b = 1/3. So, the function f(x) = 1(1/3)ˣ = (1/3)ˣ.

For function g(x), we can see that as x approaches -∞, g(x) approaches ∞ , and as x approaches ∞, g(x) approaches 0.

This is because as x gets more negative, 24 times 2⁻ˣ becomes a larger positive number, and as x gets larger, 2ˣ becomes a larger positive number causing the product to approach zero.

Therefore, the two functions have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞, making option D the correct answer.

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Answer; put the question again l cant see it

Step-by-step explanation:

Check the picture below.

\(\stackrel{\textit{\LARGE Areas}}{\stackrel{\textit{front and back}}{2(5\cdot 7)}~~ + ~~\stackrel{\textit{left and right}}{2(4\cdot 7)}~~ + ~~\stackrel{\textit{top and bottom}}{2(4\cdot 5)}}\)

The expression which represents the total surface area of the prism is 2 (7 × 4) + 2 (7 × 5) + 2 (4 × 5).

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Given is a rectangular prism.

There are six faces for the rectangular prism.

Each pair of sides are identical.

Total surface area = (7 × 4) + (7 × 4) + (7 × 5) + (7 × 5) + (4 × 5) + (4 × 5)

                               = 2 (7 × 4) + 2 (7 × 5) + 2 (4 × 5)

Hence the total surface area is 2 (7 × 4) + 2 (7 × 5) + 2 (4 × 5).

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let's firstly convert the mixed fraction to improper fraction and proceed from there.

\(\stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9}{4}\div \left(\cfrac{3}{8}\div \cfrac{1}{2} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{8}\cdot \cfrac{2}{1} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{4} \right) \\\\\\ \cfrac{9}{4}\cdot \left(\cfrac{4}{3} \right)\implies \cfrac{9}{3}\cdot \cfrac{4}{4}\implies 3\cdot 1\implies \text{\LARGE 3}\)

Two-variable linear equations have a line as their graph, which is why they are referred to as linear equations. Plotting (x1,y1) and (x2,y2), then creating a line that connects the two.

\($\frac{d}{d x}\left(-(x-2)^2+1\right)$\)

Domain of \($-(x-2)^2+1:\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$\)

Range of \($-(x-2)^2+1:\left[\begin{array}{cc}\text { Solution: } & f(x) \leq 1 \\ \text { Interval Notation: } & (-\infty, 1]\end{array}\right]$\)

Interception zones on the axis \($-(x-2)^2+1: \quad X$\) Intercepts: \($(3,0),(1,0), Y$\)Intercepts: (0,-3) .

Vertex of \($-(x-2)^2+1: \quad$\) Maximum (2,1) .

The graph of the equation y=2x+1 shows a straight line, or it is a linear equation. When the value of x rises, eventually the value of y rises by twice the rise in x plus one. With a ruler and the specified amount as the starting point, draw a vertical line. From the line across to the -axis, create a horizontal line using a ruler. Look at the value on the -axis.

There are three fundamental ways to graph linear functions. The initial method involves charting points and then tracing a line through them. The second is by using the slope and y-intercept. The identity function f(x)=x is transformed as the third method.

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The length of side AB is about 5.87 units.

The triangle ABC is a right angle triangle. A right angle triangle is a triangle that has one of its angles as 90 degrees.

Therefore, let's find the length AB in the right triangle.

Using trigonometric ratios,

cos 33 = adjacent / hypotenuse

Therefore,

Adjacent side = AB

hypotenuse side = 7 units

cos 33° = AB / 7

cross multiply

AB = 7 cos 33

AB = 7 × 0.83867056794

AB = 5.87069397562

AB = 5.87 units

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Hey there!

I believe this would be your answer: \(\frac{a^2+ab+b^2} {a+b}\)

Hope this helps!

Have a great day!

The midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

To find the point with the position vector 1/3(a+b+c), we can use the fact that the position vector of a point that divides a line segment in a given ratio can be found by taking the weighted average of the position vectors of the endpoints.

Given that D, E, and F are the midpoints of line segments BC, AC, and AB, respectively, we know that:

D = (B + C) / 2

E = (A + C) / 2

F = (A + B) / 2

To find the point with the position vector 1/3(a+b+c), we can substitute a = 3F - 2D - E into the equation:

1/3(a + b + c) = 1/3((3F - 2D - E) + b + c)

Expanding the equation further:

1/3(a + b + c) = 1/3(3F - 2D - E + b + c)

= (F - (2/3)D - (1/3)E) + (1/3)(b + c)

Therefore, the point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

Substituting the midpoints:

P = (A + B) / 2 - (2/3)((B + C) / 2) - (1/3)((A + C) / 2) + (1/3)(b + c)

= (A + B - 2B - 2C - A - C + b + c) / 2 + (1/3)(b + c)

= (b + c - B - C) / 2 + (1/3)(b + c)

Therefore, the midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

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Answer:

Make the -4 exponent in the denominator positive.

The expression of 602.16 dam in decimeters can be written as 60216 decimeter.

The concept that will be used in the calculation is conversion. to perform this conversion, it is important to note that 1 Decimeter (dm) is equal to 0.01 dekameter (dam).

Then, if 1dm = 0.01 dam

               Xdm     = 602.16 dam

Where x is the value in decimeter.

Then we can cross multiply as :

X= (602.16 dam * 1dm)/ 0.01 dam

= 60216 decimeter.

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Answer:

It should be C.

Step-by-step explanation:

Answer:

it is the first bubble the one you have already selected

Answer:

all real values of x where x < -1

The correct statement is all real values of x where x < -1.

Option A is the correct answer.

We have,

To determine the values for which the graph of the function

f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.

Let's consider the factors individually:

(x - 3): This factor is positive for x > 3 and negative for x < 3.

(x + 1): This factor is positive for x > -1 and negative for x < -1.

To determine the overall sign of the function, we need to consider the signs of both factors together.

When both factors are positive or both factors are negative, the function is positive.

When the factors have opposite signs, the function is negative.

From the above analysis, we can conclude the following:

When x > 3, both factors are positive, so the function is positive.

When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.

When x < -1, both factors are negative, so the function is positive again.

Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).

Thus,

The correct statement is all real values of x where x < -1.

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Answer:

YU = 4.82.  angle STR = 23°

Step-by-step explanation:

7) Angle between U and V = 72°, since angles on a straight line add up to 180°. so angle UV = 180 - 108 = 72°.

similarly, angle YU = 180 - 85 - 72 = 23°.

length of circumference of full circle = π X diameter = π (2r)

= 2πr (radius = half of diameter).

circumference = 2π(12) = 24π.

there are 360° in full circle.

remember that angle YU = 23°.

length YU = (23/360) X 24π

= (23π)/15

= 4.817

= 4.82 to nearest one hundredth.

8) triangle RST sits inside of half the circle, ie in the semicircle.

angle RST = 90° because the angle in a semicircle =  90°.

there are 180° in a full triangle.

since angle RST = 90°, angle STR must be less than 180 - 90.

angle STR < 90°. so STR must be 23°.

the container needs to have a volume of  0.01514 cubic meters to hold 205 kg of mercury.

Volume is the measure of the amount of three-dimensional space enclosed by an object or space. It is typically expressed in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).

The density of mercury is approximately 13,534 kg/m³.

We can use the formula:

Volume = mass/density

To find the volume of mercury that has a mass of 205 kg:

Volume = 205 kg / 13,534 kg/m³

Volume ≈ 0.01514 m³

Therefore, the container needs to have a volume of approximately 0.01514 cubic meters to hold 205 kg of mercury.

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The complete question is:

What volume should a container have to hold 205 kg of mercury?

There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.

To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.

Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.

Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.

To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.

Therefore, there will be 12 slices of pizza left over.

To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.

If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.

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