Which expression is equivalent to

Answer:

y=|x|-0.5

Step-by-step explanation:

downward is represented outside of the abolsute value.

Answer:

|x|-0.5

Step-by-step explanation:

its correct

Answer:

1/5^9

Step-by-step explanation:

X^n / X^m = (X)^n-m

5^(-6-3)

5^-9

1/5^9

Best regards

For this case we have that by definition of power properties:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, we have the following expression:

[tex]\frac {5 ^ {- 6}} {5 ^ 3}[/tex]

It can be rewritten as:

[tex]\frac {1} {5 ^ 6 * 5 ^ 3}[/tex]

By definition of power properties we have:

[tex]a ^ m * a ^ n = a ^ {m + n}[/tex]

So:

[tex]\frac {1} {5 ^ 6 * 5 ^ 3} = \frac {1} {5 ^ 9}[/tex]

Answer:

Option A

Answer:

Step-by-step explanation:

If the side of a triangle inscribed in a circle is a diameter, then it is a right triangle.

Use the Pythagorean theorem:

d - diameter

[tex]d^2=8^2+6^2\\\\d^2=64+36\\\\d^2=100\to d=\sqrt{100}\\\\d=10[/tex]

The nth term of the sequence can be expressed as:

[tex]T_n = -4n + 23[/tex]

Since term to term rule is to take away 4, thus when we go back in sequence, the rule will be to add 4 term to term.

Thus:

Second term = 4 + third term = 4 + 11 = 15

First term = 4 + second term = 15 + 4 = 19

Since the given sequence has a constant difference of -4 between each adjacent terms, thus it is an arithmetic progression with d = -4

The nth term of an arithmetic progression with difference d is given by:

[tex]T_n = T_1 + (n-1) \times d[/tex]

Since d = -4 and first term is 19, thus we have:

[tex]T_n = 19 + (n-1) \times (-4) = -4n + 23\\T_n = -4n + 23[/tex]

Thus, the nth term of the sequence can be expressed as:

[tex]T_n = -4n + 23[/tex]

Learn more about arithmetic progression here:

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The expression for the nth term of the given sequence is 23 - 4n. Starting from the third term which is 11, we find the first term and use the common difference to write the formula.

The student is dealing with a linear sequence and is asked to write an expression for the nth term of the sequence based on the term-to-term rule 'take away 4'. To find the nth term of this arithmetic sequence, we need to use the structure of arithmetic sequences, which follow the pattern a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference between terms. Because we know that the third term is 11, we can backtrack to find the first term by adding 4 twice (since we have been taking 4 away to move forward in the sequence). Therefore, the first term a_1 is 11 + 4 + 4 = 19. Given the common difference is -4 (since we are taking away 4 each time), our nth term expression is a_n = 19 + (n - 1)(-4) or simplified a_n = 23 - 4n.

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Answer:

(0 , 0) , (18 , 0) , (18 , -18) , (0 , -18) ⇒ the second answer

Step-by-step explanation:

∵ The vertices of the rectangles are:

  (0 , 0) , (0 , 6) , (6 , 6) , (6 , 0)

∵ 3 × [tex]\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right][/tex] × R

∴ That is mean The rectangle rotate 270° around the origin

  (270° anti-clockwise or 90° clockwise)

  and enlargement by scale factor 3

Answer:

(0 , 0) , (18 , 0) , (18 , -18) , (0 , -18) ⇒ the second answer

Step-by-step explanation:

Mathhhh

Answer: Christina weighs 98 pounds.

Step-by-step explanation: The formula to solve this problem is x + 17 + x = 179, where x equals Sarah’s weight.

X + 17 + x = 179

First you need to combine the x values:

2x + 17 = 179

Next, subtract 17 from both sides:

2x = 162

Finally, divide both sides by 2:

X = 81

Sarah’s weight is 81 pounds and Christina weighs 17 pounds more, which is 98 pounds. You can double check your work by adding both of their weights (98 + 81) to make sure that your answer is correct.

Final answer:

By setting up a system of equations with the given information, we can solve for Christina's weight. Christina weighs 125 pounds.

Explanation:

To determine how much Christina weighs, we can set up an equation based on the information given. Let's define Sarah's weight as 's' and Christina's weight as 'c'. According to the question, Christina weighs 17 pounds more than twice Sarah's weight. So we can write the equation as:

c = 2s + 17

The combined weight of Christina and Sarah on the freight scale is 179 pounds. We represent this with another equation:

c + s = 179

Now we have a system of two equations:

Substituting the expression for 'c' from the first equation into the second equation gives us:

(2s + 17) + s = 179

Combining like terms, we have:

3s + 17 = 179

Moving 17 to the other side by subtracting 17 from both sides:

3s = 179 - 17

3s = 162

Dividing both sides by 3 to find Sarah's weight:

s = 162 / 3

s = 54

Now that we know Sarah weighs 54 pounds, we can find Christina's weight using the first equation:

c = 2(54) + 17

c = 108 + 17

c = 125

So, Christina weighs 125 pounds.

Answer:

1. 121 π  unit²

2. 143°

3. 151 unit²

Step-by-step explanation:

1.

Area of a circle is given by the formula  A = πr²

where

A is the area,

r is the radius of the circle

From the given diagram, we can see that the radius is 11, hence the area will be:

[tex]A=\pi r^2\\A=\pi (11)^2\\A=121\pi[/tex]

The answer is  [tex]121\pi[/tex] units^2

2.

The unshaded secctor and the shaded sector equals the circle. We know that circle is 360°. The unshaded sector has an angle of 217°. So the shaded part will be 360 - 217 = 143°

The measure of the central angle of the shaded sector is 143°

3.

Area of a sector is given by the formula  [tex]A=\frac{\theta}{360}*\pi r^2[/tex]

Where

[tex]\theta[/tex] is the central angle of the sector (in our case it is 143°)

r is the radius (which is 11)

Plugging in all the info into the formula we have:

[tex]A=\frac{\theta}{360}*\pi r^2\\A=\frac{143}{360}*\pi (11)^2\\A=150.99[/tex]

rounding to the nearest whole number, it is 151 units^2

Answer:

4y^(2)+14y+31

Step-by-step explanation:

First you need to do (y+7)(y+7)

y^2+7y+7y+49

y^2+14y+49

Add it all together

y^2+14y+49+3y^2-15

4y^(2)+14y+31

Answer: 450 miles

Step-by-step explanation:

3 inches / 1 inch = 3 times 150 miles = 450 miles

Answer:

[tex]\large\boxed{\ln e^A=A}[/tex]

Step-by-step explanation:

[tex]Use\\\\\log_ab^n=n\log_ab\\\\\log_aa=1\\\\\ln a=\log_e a\to\ln e=1\\====================================\\\\\ln e^A=A\ln e=A(1)=A[/tex][/tex]

Answer:

[tex]\large\boxed{x=\pm5i}[/tex]

Step-by-step explanation:

[tex]i=\sqrt{-1}\to i^2=-1\\==========================\\\\x^2+25=0\qquad\text{subtract 25 from both sides}\\\\x^2=-25\to x=\pm\sqrt{-25}\\\\x=\pm\sqrt{(-1)(25)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x=\pm\sqrt{-1}\cdot\sqrt{25}\\\\x=\pm i\cdot5\\\\x=\pm5i[/tex]

Answer: Answer is D

Answer:

(2,-4)

Step-by-step explanation:

it is a minimum because as you can see the lowest is at the point of (2,-4)

Answer:

(2,-4)

Step-by-step explanation:

➷ First find the number of scans produced per second

To do this, multiply the number of scans by 30:

525 x 30 = 15750

So, there are 15750 scans produced per second

You need the value for 30 seconds, so multiply by 30 again

15750 x 30 = 472500

Your answer would be 472500

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

case 1) [tex]z=10[/tex]

case 2) [tex]z=5/32[/tex]

Step-by-step explanation:

case 1) we know that

Using proportion

[tex]\frac{1}{z}=\frac{(4/5)}{8}[/tex]

solve for z

[tex]\frac{1}{z}=\frac{(4/5)}{8}\\ \\z(4/5)=8\\ \\z=8*5/4\\ \\z=10[/tex]

case 2) we know that

Using proportion

[tex]\frac{1}{z}=\frac{4}{5/8}[/tex]

solve for z

[tex]\frac{1}{z}=\frac{4}{5/8}\\ \\4z=5/8\\ \\z=5/32[/tex]

Answer:

2x - y = 13

Step-by-step explanation:

To write the equation of a line use the formula [tex]y - y_1 = m(x-x_1)[/tex].

Substitute m = 2 and (4,-5).

[tex]y --5 = 2(x-4)\\y + 5 = 2(x - 4)\\y + 5 = 2x - 8\\y = 2x -13\\-2x + y = -13\\2x - y = 13[/tex]

Answer:

45

Step-by-step explanation:

Decreasing by 25% means that there is 25% less of last years amount or 0.25x less. It also means that this year there is only 75% of what was last year actually in the lake or 0.75x. Since last year, there were 60 fish, this means this year there is 0.75(60) = 45. This year has 45 fish.

Answer:

45

Step-by-step explanation:

Answer:

Q(20,10)

Step-by-step explanation:

If point T (6,3) is a point 3/10 of the way from P(0,0) to Q(x,y), then

[tex]\overrightarrow {PT}=\dfrac{3}{10}\overrightarrow {PQ}.[/tex]

Find the coordinates of the vectors [tex]\overrightarrow {PT},\ \overrightarrow {PQ}:[/tex]

[tex]\overrightarrow {PT}=(6-0,3-0)=(6,3);\\ \\\overrightarrow {PQ}=(x-0,y-0)=(x,y).[/tex]

Thus,

[tex](6,3)=\dfrac{3}{10}(x,y),\\ \\(x,y)=\dfrac{10}{3}(6,3)=(20,10).[/tex]

Answer:

m=-13

Step-by-step explanation:

What you do is you minus 45 from each side to get.

m=-13 as your answer.

Answer: -13

Step-by-step explanation:

Subtract 45 from 32 u get -13 = m

Final answer:

For every 5 orange fish in the fish tank, there are 4 blue fish since the number of orange fish is 1 1/4 times the number of blue fish.

Explanation:

In the fish tank scenario where the number of orange fish is 1 1/4 times the number of blue fish, for every 5 orange fish, we need to determine the corresponding number of blue fish. To find this, we can set up a ratio where the number of blue fish (let's call it B) multiplied by 1 1/4 must equal 5 (since 1 1/4 times B is the number of orange fish). So, B * 1 1/4 = 5. This equation can be simplified to B * 5/4 = 5, and by further simplification, we find B = 5 / (5/4) which is equal to B = 4. Therefore, for every 5 orange fish, there would be 4 blue fish in the tank. Hence, if you drag blue fish to represent the number of blue fish, there should be 4 of them for every 5 orange fish.

Answer:

$791

Step-by-step explanation:

Find the equation of the line passing thru  (30, 1,181) and (44, 1,363),   The y-intercept of this equation will answer this question:  it represents the annual golf pass.

Moving from (30, 1,181) to (44, 1,363), we see x increasing by 14 from 30 to 44 and y increasing by  182   from 1181 to 1363.

Thus, the slope of this line is m = rise / run = 182 / 14 = 13.

Subst. the knowns (30, 1,181) and m = 13 into the standard equation for a straight line in slope-intercept form, y = mx + b, we get:

1181 = 13(30) + b.  Then 1181 - 390 = 791.

The flat fee is $791, payable at the beginning of each year.

Answer:

The answer is $760

Step-by-step explanation:

First, find the rate of change, or slope, from the two given points.

Next, find the equation for the linear model using the slope and a point.

The initial value is the value of y when x equals 0.

In this case, the initial value is the flat fee for the annual golf pass.

Therefore, the flat fee for the annual golf pass is $760.

Let x be the unknown number. One fifth of this number is x/5, one fourth of this number is x/4. So, we have

[tex]\dfrac{x}{4}-\dfrac{x}{5} = \dfrac{5x-4x}{20} = \dfrac{x}{20}[/tex]

We know that this difference equals 9, so we have

[tex]\dfrac{x}{20}=9[/tex]

Multiply both sides by 20 to get

[tex]x=180[/tex]

The break ended at 4pm when he was at 15 km.

The ride ended at 6pm when he was at 45 km.

From 4 to 6pm he rode 45 - 15 = 30 km.

Answer: it would be 30 kilometer

Step-by-step explanation:

45-15=30

Answer:

Step-by-step explanation:

Convert the equation to the slope-intercept form (y = mx + b):

[tex]2x+5y=-10[/tex]        subtract 2x from both sides

[tex]5y=-2x-10[/tex]       divide both sides by 5

[tex]y=\-\dfrac{2}{5}x-2[/tex]

Put x = 0 to the equation of a line:

[tex]y=-\dfrac{2}{5}(0)-2=-0-2=-2\to(0,\ -2)[/tex]

The lines c and d passes through that's point.

Put x = 5 to the equation of a line:

[tex]y=-\dfrac{2}{5}(5)-2=-2-2=-4\to(5,\ -4)[/tex]

The line d passes through that point.

Answer:

Tasha made a mistake in Step 4

Step-by-step explanation:

She made a mistake in step 4

When rewriting the value for  4^(-4)

She needed to write

(1/256) =   4^(-4)

Instead, she wrote

(1/256) =   -1/4^(-4)

-1/4^(-4) = -256 ≠ (1/256)

Answer:

The answer is D

Step-by-step explanation:

We know that a triangle adds up to 180 degrees.

Solve for x:

Combine like terms.

2x + 3x - 10 + 50 = 180

Subtract 40 on both sides.

5x + 40 = 180

      -40    -40

Divide both sides by 5.

5x = 140

----    ----

5        5

And you get a solution of:

x = 28

Check:

Substitute 28 into x and multiply 28 by the number outside of the parentheses.

2(28) + 3(28) - 10 + 50 = 180

Add/Subtract from left to right.

56 + 84 - 10 + 50 = 180

Add them together.

140 + 40 = 180

And you get 180!

180 = 180

Final answer:

The probability of Robert eating two mint sticks consecutively from a bag of candy is 3/95, which is found by multiplying the individual probabilities of selecting a mint stick on the first and second draw.

Explanation:

The question involves calculating the probability that the first two pieces of candy Robert eats are both mint sticks. To find this probability, follow a step-by-step process to consider all possible outcomes.

Step 1: Probability of first mint stick

Initially, Robert has 20 pieces of candy with 4 being mint sticks. So, the probability of picking a mint stick first is:

4 mint sticks / 20 total pieces = 1/5 or 0.20.

Step 2: Probability of second mint stick

After eating one mint stick, there remain 3 mint sticks out of 19 total pieces. Thus, the probability now becomes:

3 mint sticks / 19 total pieces = 3/19.

Step 3: Combined probability

To find the probability of both events happening consecutively, multiply the separate probabilities:

(1/5) * (3/19) = 3/95, which simplifies to 0.0316, or about 3.16% chance.

Therefore, the correct answer is C. 3/95.

Answer:

20cm or A

Step-by-step explanation:

pythagorean theorem

25^2=15^2+b^2

625=225+b^2

b^2=400

b=20

A because it is the number in between 15 and 25 because the line is shorter

Answer:

An angle showing a turn through 1/8 of a circle is smaller

Step-by-step explanation:

we know that

A complete circle represent 360°

so

An angle showing a turn through 1/8 of a circle is

[tex](360\°)*(\frac{1}{8})=45\°[/tex]

An angle showing a turn through 1/3 of a circle is

[tex](360\°)*(\frac{1}{3})=120\°[/tex]

therefore

An angle showing a turn through 1/8 of a circle is smaller

Answer:

1/8 is smaller because it equals 45 degrees

1/3 is bigger because it equals 120 degees

Answer:

less 13 gallons equals 52 quarts

Step-by-step explanation:

Equal to. There are 4 quarts in 1 gallon. So 16x4=64

Answer:

A

Step-by-step explanation:

Since we can see that the figure is congruent but just flipped over x = 0, we are just reflecting it across the y=axis.

Answer:

A

Reflection across the y-axis.