write an equation in point-slope form of the line using points D(0,5),E(5,8)

Answer:

r<17

Step-by-step explanation:

Distribute -3 through parentheses --> r + 10 < 6r+9+6 (r + 3)

Take out the oppisities --> r + 10 < 9 + 18

Move constant to the right and change the sign r < 27 -10

Subtract --> r < 17

Answer:

See explanation

Step-by-step explanation:

A triangle PQR has its vertices at points P(1,-1), Q(3,-2) and R(3,-4).

A counterclockwise rotation by angle of 90° about the origin has the rule

[tex](x,y)\rightarrow (-y,x)[/tex]

Hence,

The image triangle is shown in attached diagram.

See the attached picture for the answers:

Final answer:

The scale factor of the dilation that transforms triangle PQR to triangle P'Q'R' does not exist. The coordinates for the reflected triangle P''Q''R'' are P''(-1, 0), Q''(0, -1), and R''(2, -1). Triangle PQR and triangle P''Q''R'' are not congruent.

Explanation:

To find the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R', we can compare the lengths of corresponding sides in the two triangles. The distance between P(4, 0) and P'(1, 0) is 3, the distance between Q(0, -4) and Q'(0, -1) is 3, and the distance between R(-8, -4) and R'(-2, -1) is 6.

Since the lengths of corresponding sides are not equal, the triangles are not similar and there is no scale factor that transforms triangle PQR to triangle P'Q'R'.

To reflect triangle P'Q'R' about the y-axis, we simply change the sign of the x-coordinate for each vertex. The coordinates for the reflected triangle P''Q''R'' are P''(-1, 0), Q''(0, -1), and R''(2, -1).

Triangle PQR and triangle P''Q''R'' are not congruent because their corresponding sides have different lengths.

Answer:

x = -25

Step-by-step explanation:

Solve for x:

(2 x)/5 - 6 = -16

Hint: | Put the fractions in (2 x)/5 - 6 over a common denominator.

Put each term in (2 x)/5 - 6 over the common denominator 5: (2 x)/5 - 6 = (2 x)/5 - 30/5:

(2 x)/5 - 30/5 = -16

Hint: | Combine (2 x)/5 - 30/5 into a single fraction.

(2 x)/5 - 30/5 = (2 x - 30)/5:

(2 x - 30)/5 = -16

Hint: | Multiply both sides by a constant to simplify the equation.

Multiply both sides of (2 x - 30)/5 = -16 by 5:

(5 (2 x - 30))/5 = -16×5

Hint: | Cancel common terms in the numerator and denominator of (5 (2 x - 30))/5.

(5 (2 x - 30))/5 = 5/5×(2 x - 30) = 2 x - 30:

2 x - 30 = -16×5

Hint: | Multiply 5 and -16 together.

5 (-16) = -80:

2 x - 30 = -80

Hint: | Isolate terms with x to the left hand side.

Add 30 to both sides:

2 x + (30 - 30) = 30 - 80

Hint: | Look for the difference of two identical terms.

30 - 30 = 0:

2 x = 30 - 80

Hint: | Evaluate 30 - 80.

30 - 80 = -50:

2 x = -50

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 2 x = -50 by 2:

(2 x)/2 = (-50)/2

Hint: | Any nonzero number divided by itself is one.

2/2 = 1:

x = (-50)/2

Hint: | Reduce (-50)/2 to lowest terms. Start by finding the GCD of -50 and 2.

The gcd of -50 and 2 is 2, so (-50)/2 = (2 (-25))/(2×1) = 2/2×-25 = -25:

Answer:  x = -25

Answer:

x = -25

Step-by-step explanation:

(2/5)x - 6= -16   (add 6 to both sides)

(2/5) x = -16 + 6

(2/5) x = -10  (multiply both sides by 5)

2x = -10 (5)

2x = -50  (divide both sides by 2)

x = -50 / 2

x = -25

The shape moves from its original position, point A, to a point down from A, point B, after the first move. Even after a 90-degree clockwise rotation, because we are considering the shape as a point, it will still be at point B. The final move to the right places the shape at point C. The final position of the shape is at point C.

For the purpose of illustrating this problem, let's assume that the original placement of the shape is at point A. Now, based on the movements described, here are the steps:

The final location of the shape will be at point C, which is down and to the right of the initial position, point A, after a clockwise rotation.

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Answer:

a. [tex]30.36\ cm^2[/tex]

b. [tex]1.6\ cm[/tex]

Step-by-step explanation:

a. You know that the dimensions of Rectangle A are [tex]2\ cm* 3\frac{1}{5}\ cm=2\ cm* 3.2 cm[/tex]

Since Rectangle B’s dimensions are [tex]\frac{3}{5}\ cm[/tex] (which is 0.6 cm) larger than Rectangle A’s dimensions, then the dimensions of Rectangle B are:

[tex](2\ cm+0.6\ cm)( 3.2\ cm+0.6\ cm)=2.6\ cm*3.8\ cm[/tex]

Since Rectangle C’s dimensions are [tex]\frac{3}{5}\ cm[/tex] (which is 0.6 cm) larger than Rectangle B's dimensions, then the dimensions of Rectangle C are:

[tex](2.6\ cm+0.6\ cm)( 3.8\ cm+0.6\ cm)=3.2\ cm*4.4\ cm[/tex]

The find the total area of all three rectangles you must add the products obtained when you multiply their dimensions. Then:

[tex]A_t=(2\ cm* 3.2 cm)+(2.6\ cm*3.8\ cm)+(3.2\ cm*4.4\ cm)\\\\A_t=30.36\ cm^2[/tex]

b. The perimeter of a rectangle can be calculated with this formula:

[tex]P=2l+2w[/tex]

Where "l" is the lenght and "w" is the width.

Knowing the dimensions of each rectangleg, you can calculate the total perimeter as follows:

[tex]P_t=(2)[(2\ cm+ 3.2 cm)+(2.6\ cm+3.8\ cm)+(3.2\ cm+4.4\ cm)]\\\\P_t=38.4\ cm[/tex]

Then, if a 40-cm coil of wire was used to form the rectangles, the amount of wire that is left is:

[tex]40\ cm-38.4\ cm=1.6\ cm[/tex]

Answer:$556.73

Step-by-step explanation:

Watts (1487) multiplied by the hours used daily (24) =35688

Divided by 1000 = 35.68

multiply 35.68 times the number of days (120) = $556.73

Another example:

wattage x hours used ÷ 1000 x price per kWh = $$

1487 x 2880 ÷ 1000 x $0.13 = $556.73

Answer:

$556.7328 is total cost of operating hot tub for 4 months in an outdoor spa.

Step-by-step explanation:

Power drawn by hot tub = 1487 Watts = 1.487 kiloWatt

1 Watt = 0.001 kiloWatt

Utility charges charged by the company = $0.13 / (kiloWatt hour)

Charges in 1 day or 24 hours : (1 day = 24 hours)

$0.13 / (kiloWatt hour) × 1.487 kiloWatt × 24 hours = $4.63944

4 months = 4 × 30 = 120 days (1 month = 30 days)

Total charge for operating hot tub for 4 months or 120 days:

$4.63944 × 120 = $556.7328

Answer:

y=5/4x

Step-by-step explanation:

Final answer:

To divide 5 by 3/7, we multiply 5 by the reciprocal of 3/7 which is 7/3, resulting in 35/3 or 11 2/3.

Explanation:

To calculate 5 divided by 3/7, we invert the fraction 3/7 and multiply by 5. It’s the same as multiplying 5 by the reciprocal of 3/7. The reciprocal of 3/7 is 7/3. Therefore:

5 × 7/3 = 5 × (7 ÷ 3)

5 × 7/3 = (5 × 7) ÷ 3

5 × 7/3 = 35/3

5 × 7/3 is 11 with 2 left over or, in other words, it is 11 2/3.

Remember, when you divide by a fraction, you are essentially calculating how many times that fraction goes into the number. So here, 5 divided by 3/7 is asking how many groups of 3/7 there are in 5, which is why we multiply by the reciprocal.

The median of the given data is 118.

It is required to find the median.

The median is the middle value in a set of data .The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.

Given:

The given date are arranged in ascending order

110 112 114 116 118 120 122 124 126 °F

Total number of the data is 9 which is odd ,so the median is

n+1/2

Where n=number of values in data set

According to given question we have,

Median=n+1/2

Median=9+1/2

Median=5

The 5th term of the number is median of the given data i.e 118.

Therefore, the median of the given data is 118.

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The volume of the given sphere is 32 cm³. Thus, the correct answer is option (A) 32 cm³.

Given that the diameter of the sphere is 4 cm, the radius is half of that or 2 cm.

The formula for the volume of a sphere is:

V = (4/3)πr³

Where r is the radius of the sphere.

Here, r = 2

Substituting these values into the formula, we get:

The volume of a sphere = (4/3) × π × (2)³

The volume of a sphere  = (4/3)π(8)

The volume of a sphere  = 32π/3

Using π = 3.14, we get:

The volume of a sphere  ≈ 33.51 cm³

Therefore, the closest option to the volume of the sphere is 32 cm³.

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Answer:

[tex]\frac{3x+5}{8x-2}[/tex]

Explanation:

The reciprocal of a fraction is when you just "turn it upsidedown". Which means, you take the numerator and the denominator and swap their places. So instead of having the [tex]\frac{numerator}{denominator}  you would change it to \frac{denominator}{numerator}[/tex]

Answer:

(8x - 2) / (3x + 5).

Step-by-step explanation:

Just invert the fraction:

= (8x - 2) / (3x + 5).

Answer:

7) Obtuse, I didn't use a protractor, so I'm estimating about 130 degrees.

8) Straight, all straight lines are equal to 180 degrees.

9) Acute, I estimated about 30-40 degrees, again, no protractor used.

Step-by-step explanation:

Answer:

Alejandro received 6.51 million of votes

Laine received 58% of votes

Step-by-step explanation:

If the ratio of "Laine votes" to "Alejandro votes” was 29:21, then the number of "Laine votes" was 29x and the number of "Alejandro votes” was 21x. In total, 15.5 million votes were cast. So

29x + 21x = 15.5 million

50x = 15.5 million

x = 0.31 million

Then

the number of "Laine votes" [tex]=29\cdot 0.31=8.99[/tex] million

number of "Alejandro votes” [tex]=21\cdot 0.31=6.51[/tex] million

Laine received

[tex]\dfrac{8.99}{15.5}\cdot 100\%=58\%[/tex]

(10v + 45) = 5(2v + 9)

To factor find a number that can go flu shot into the 2 numbers given. In the question you posted, th at number was 5. 5 could go into 10v and 45.

If you need a better explanation just as in the comments.

Happy to help! Please mark as BRAINLIEST! Thanks

Answer:

7 feet and 24 feet

Step-by-step explanation:

In the right triangle, the hypotenuse is 25 feet long. The area of this triangle is 84 square feet.

Let x feet and y feet be the lengths of triangle's legs.

By the Pythagorean theorem,

[tex]x^2+y^2=25^2\\ \\x^2+y^2=625[/tex]

The area of the right triangle is half the product of its legs, thus

[tex]84=\dfrac{1}{2}xy\\ \\xy=168[/tex]

Solve the system of two equations:

[tex]\left\{\begin{array}{l}x^2+y^2=625\\ \\xy=168\end{array}\right.[/tex]

From the second equation:

[tex]x=\dfrac{168}{y}[/tex]

Substitute it into the first equation:

[tex]\left(\dfrac{168}{y}\right)^2+y^2=625\\ \\168^2+y^4=625y^2\\ \\y^4-625y^2+168^2=0\\ \\D=(-625)^2-4\cdot 168^2=(625-2\cdot 168)(625+2\cdot 168)=289\cdot 961=17^2\cdot 31\\ \\\sqrt{D}=17\cdot 31=527\\ \\y^2_{1,2}=\dfrac{-(-625)\pm 527}{2}=49,\ 576\\ \\y_1=7,\ y_2=-7,\ y_3=24,\ y_4=-24[/tex]

The length of the leg cannot be negative, so

[tex]y_1=7\Rightarrow x_1=\dfrac{168}{7}=24\\ \\y_2=24\Rightarrow x_2=\dfrac{168}{24}=7[/tex]

D. The y-intercept is (0,5) of the function 5*(6)ˣ

Given function is f(x) = 5*(6)ˣ

Now we have to choose correct statement from the given options.

Option A: The domain of f(x) is x>0.

Exponential functions are of the form f(x) = a*bˣ

Also the given function is in exponential function.

For any exponential function, domain is the set of real numbers not only x>0,

So this option is false.

Option B : The y-intercept is (0,1).

y-intercept means the value of x is 0.

f(0) = 5*6⁰

⇒ f(0) = 5 ≠ 1

So this option is false.

Option C :  It is always decreasing.

Exponential functions are of the form f(x) = a*bˣ

The function will be increasing, if b>1

Given function is f(x) = 5*(6)ˣ

As 6>1, we can say that the function is increasing function.

So this option is false.

Option D : The y-intercept is (0,5).

y-intercept means the value of x is 0.

f(0) = 5*6⁰

⇒ f(0) = 5

So, the y-intercept is (0, 5).

So this option is true.

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Answer:

−1 1/2

Step-by-step explanation:

i took the test <3

The subtraction of the given expression by the number line is -3/2.

The given expression is:

[tex]-1 \dfrac{1}{3} - \dfrac{1}{6}[/tex]

The improper fraction of [tex]-1 \dfrac{1}{3} =- \dfrac{4}{3}[/tex]

So, the given expression can be written as:

[tex]-\dfrac{4}{3} - \dfrac{1}{6}[/tex]

Since LCM of (3, 6)  = 2

[tex]-\dfrac{4}{3} - \dfrac{1}{6} =\dfrac{-2\times 4 - 1}{6}\\\\ -\dfrac{4}{3} - \dfrac{1}{6} = -\dfrac{9}{6}\\\\ -\dfrac{4}{3} - \dfrac{1}{6} = -\dfrac{3}{2}\\\\[/tex]

Now according to the number

This subtraction will be done, if we add 1/6 toward the left side of the number line.

Hence,

The subtraction:

[tex]-\dfrac{4}{3} - \dfrac{1}{6} = -\dfrac{3}{2}\\\\[/tex]

The procedure by number line is attached below.

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Answer:

[tex]\frac{2}{5},\frac{1}{4},\frac{1}{10},\frac{5}{2},\frac{5}{8},\frac{4}{1},\frac{8}{5},\frac{10}{1}[/tex]

Step-by-step explanation:

Proportions are fractions that can be created using the numbers given. Let's pair each and reduce if possible.

Starting with 2:

2/5

2/8 = 1/4

2/20 = 1/10

Then 5:

5/2

5/8

5/20 = 1/4

Then 8:

8/2 = 4/1

8/5

8/20 = 2/5

Lastly 20:

20/2 = 10/1

20/5 = 4

20/8 = 5/2

So, we can see some are repeating, hence the unique proportions are:

2/5, 1/4, 1/10, 5/2, 5/8, 4/1, 8/5, 10/1

The possible proportions using the numbers 2 5 8 and 20 are:

1. 2:5 = 8:20

2. 2:8 = 5:20

3. 5:20 = 2:8

4. 8:2 = 20:5

5. 20:5 = 8:2

6. 5:2 = 20:8

To create all possible proportions using the numbers 2, 5, 8, and 20, you can set up ratios and see how you can pair these numbers.

A proportion is essentially an equation that states two ratios are equal.

Here are some possible proportions you can create:

1. 2:5 = 8:20

  (This is a direct proportion where both ratios reduce to 2:5.)

2. 2:8 = 5:20

  (Again, this is a direct proportion where both ratios reduce to 1:4.)

3. 5:20 = 2:8

  (This is just another way to write the second proportion.)

4. 8:2 = 20:5

  (This is an inverse proportion where the first ratio is the reciprocal of the second.)

5. 20:5 = 8:2

  (This is just another way to write the fourth proportion.)

6. 5:2 = 20:8

  (This is an inverse proportion where the first ratio is the reciprocal of the second.)

7. 20:8 = 5:2

These are all the possible proportions you can create using the numbers 2, 5, 8, and 20. Note that in each proportion, you can switch the positions of the numbers (e.g., 2:5 = 8:20 is the same as 5:2 = 20:8), but the ratios remain the same.

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1. 612.85

14.42 x 42.5 = $612.85

2. 110.313

612.85 x .18 = $110.313

3. $72.063

110.313 - 38.25 = $72.063

4. %11.75

72.063 / 612.85 = 0.11758

0.11758 x 100 = %11.75

5. 479.861

110.313 x 4.35 = 479.861

Courtney's weekly earnings before taxes are $612.85. After an 18% tax, her earnings are $502.54, which becomes $464.29 after saving $38.25. The paycheck's remaining percentage is 75.76%, and her monthly earnings after taxes average $2,186.05.

Courtney earns $14.42 per hour and works 42.5 hours a week. To calculate her weekly earnings before taxes:

Weekly earnings = Hourly wage times Hours worked per week
Weekly earnings = $14.42 times 42.5
Weekly earnings = $612.85

To find out how much she makes after an 18% tax deduction:

Taxed amount = Weekly earnings times Tax rate
Taxed amount = $612.85 times 0.18
Taxed amount = $110.31

Earnings after tax = Weekly earnings - Taxed amount
Earnings after tax = $612.85 - $110.31
Earnings after tax = $502.54

After Courtney saves $38.25, her disposable weekly income is:

Money left to spend = Earnings after tax - Savings
Money left to spend = $502.54 - $38.25
Money left to spend = $464.29

Now, to calculate the percentage of paycheck left after taxes and savings:

Percentage left = (Money left to spend / Weekly earnings) times 100
Percentage left = ($464.29 / $612.85) times 100
Percentage left = 75.76%

For her monthly earnings after taxes, considering an average of 4.35 weeks per month:

Monthly earnings after taxes = Earnings after tax times Average weeks per month
Monthly earnings after taxes = $502.54 times 4.35
Monthly earnings after taxes = $2,186.05

Answer:

x=−7,1

Step-by-step explanation:

1 Subtract 33 from both sides.

-5|x+3|=-17-3−5∣x+3∣=−17−3

2 Simplify -17-3−17−3 to -20−20.

-5|x+3|=-20−5∣x+3∣=−20

3 Divide both sides by -5−5.

|x+3|=\frac{-20}{-5}∣x+3∣=

​−5

​

​−20

​​  

4 Two negatives make a positive.

|x+3|=\frac{20}{5}∣x+3∣=

​5

​

​20

​​  

5 Simplify \frac{20}{5}

​5

​

​20

​​  to 44.

|x+3|=4∣x+3∣=4

6 Break down the problem into these 2 equations.

x+3=4x+3=4

-(x+3)=4−(x+3)=4

7 Solve the 1st equation: x+3=4x+3=4.

x=1x=1

8 Solve the 2nd equation: -(x+3)=4−(x+3)=4.

x=-7x=−7

9 Collect all solutions.

x=-7,1x=−7,1

Answer:

25

Step-by-step explanation:

The number of orders in which John can wear socks is 5⁵, the correct option is A.

Permutation is the method of arranging all the elements of the set in order, Combination is the selection of elements from the set such that the order of selection does not matter.

John has 5 pairs of different colour socks

The ways in which he can wear the socks if repetition is allowed is 5⁵.

He has 5 choices on day 1, day 2, day 3, day 4 and day 5.

The correct option is

5^5

25

5!

125

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Answer: 2.852 × 10-1

Step-by-step explanation:

7.13 x 10^-3 =  0.00713

0.00713 x 40 = 0.2852

0.2852 = 2.852 × 10-1

Answer:

[tex]\large\boxed{2.852\times10^{-1}}[/tex]

Step-by-step explanation:

[tex]\text{The scientific notation:}\\\\a\times10^k,\ 1\leq a<10,\ k\in\mathbb{Z}\\\\(7.13\times10^{-3})\times40=(7.13\times40)\times10^{-3}=285.2\times10^{-3}\\\\\text{Move the decimal point two places to the left,}\\\text{ increasing the exponent of the power of 10 also by 2}\\\\=2.852\times10^{-3+2}=2.852\times10^{-1}[/tex]

Answer: 461,160 books will be printed.

Step-by-step explanation:

1,512×305=461,160

Answer: [tex]461,160\ books[/tex]

Step-by-step explanation:

 According to the exercise, the number of copies of a book printed in each run is:

[tex]1,512\ copies\ per\ run[/tex]

Then, let be "x" the number of the number of books that will be printed in 305 runs.

In order to calculate the value of "x", you must multiply 1,512 (which is the number of copies of a book printed in each print run) by 305.

Therefore, you get that the number of books that will printed in 305 runs is:

[tex]x=(1,512)(305)\\\\x=461,160\ books[/tex]

Answer:

Scalene and obtuse

Step-by-step explanation:

obtuse cuz 132 is greater than 90

scalene cuz all three sides have different lengths

Final answer:

To find the area of a square when given its perimeter, divide the perimeter by 4 to find the side length and then square this length. Thus, a square with a perimeter of 32 inches has an area of 64 square inches.

Explanation:

If the perimeter of a square is 32 inches, we can calculate the length of one side by dividing the perimeter by 4, because a square has 4 equal sides. So each side is 32 inches ÷ 4, which equals 8 inches.

Once we have the side length, we can calculate the area of the square. The area of a square is determined by squaring its side length (side length × side length). In this case, the area would be 8 inches × 8 inches, which equals 64 square inches.

Therefore, the area of the square with a perimeter of 32 inches is 64 square inches.

Answer:

1.78913×107

Step-by-step explanation:

312·112·512≈1.78913×107

Answer:

b

Step-by-step explanation: