Write the coordinates of the vertices after a reflection over the line y=–x.

Answer:

x intercept is 7.5

y intercept is -3

Step-by-step explanation:

let me know if you need more help

He drove 828 miles on the first day.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.

Let x = distance Pete traveled on the second day

If on the first day, he traveled 1.5 times as far as he did the second day, then

distance Pete traveled on the first day = 1.5x

If Pete traveled 1,380 miles in two days, the the sum of the distance he traveled in two days is equal to 1380.

x + 1.5x = 1380

Simplify the equation and solve for the value of x.

x + 1.5x = 1380

2.5x = 1380

x = 552

distance Pete traveled on the second day = 552 miles

distance Pete traveled on the first day = 1.5(552) = 828miles

Therefore, he drove 828 miles on the first day.

The problem seems incomplete. The question must be

"Pete traveled 1,380 miles in two days. The first day, he traveled 1.5 times as far as he did the second day. How many miles did he drive on the first day?"

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An HL triangle is a type of triangle with two sides of equal length and one side that is longer than the other two sides. The triangle has an acute angle between the two equal sides, and an obtuse angle between the longest side and one of the equal sides.

An HL triangle can be described as an isosceles triangle with one side longer than the other two. The sides that are of equal length form an acute angle, while the longest side forms an obtuse angle with one of the equal sides. The longest side of the HL triangle is typically referred to as the hypotenuse, while the two equal sides are referred to as the legs. The hypotenuse is always the longest side, and the two legs are always of equal length.

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Answer:

y = -1/2x+3

Step-by-step explanation:

We have y = 2x-9

This is in slope intercept form

y = mx+b  where m is the slope

The slope is 2

We want a line that is perpendicular

Perpendicular lines have slopes that are negative reciprocals

The slope is -1/2

The equation of the new line is

y = -1/2x+b

Substituting the point into the equation

5 = -1/2(-4)+b

5 = 2+b

5 -2=b

3=b

y = -1/2x+3

Answer:

y = -1/2x + 3

Step-by-step explanation:

We know that if two lines are perpendicular to each other the multiplication of the slopes of those 2 lines equals -1.

m₁ × m₂ = -1

Given that, the slope of one line is 2 (m₁). Now, let us find the slope of the other line (m₂) using the above formula.

2 × m₂ = -1

2m₂ = -1

Divide both sides by 2.

m₂ = -1/2

And now let us find the value of the y-intercept ( c in the formula y = mx + c) using the given coordinate.

( -4 , 5 )⇒ ( x , y ).

Let us find it now.

y = mx + c

5 = -1/2x × -4 + c

5 = 2 + c

5 - 2 = c

3 = c

And now let us write the equation for the new line.

y = m x + c

y = -1/2x + 3

The perimeter of the figure is 48 meters

From the question, we have the following parameters that can be used in our computation:

Shape = rectangle

length = 10 meters

width = 14 meters

The perimeter of the figure is then calculated as

Perimeter = 2 * (length + width)

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 * (10 + 14)

Evaluate

Perimeter = 48

Hence, the perimeter is 48 meters

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Answer:

y = [tex]\frac{-8}{3}[/tex] x + [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

The slope is the change in y over the change in x.

[tex]\frac{0-8}{1 - -2}[/tex] = [tex]\frac{-8}{1+2}[/tex] = [tex]\frac{-8}{3}[/tex]

The slope (m) is [tex]\frac{-8}{3}[/tex]

Use the slope and one of the points to find the y intercept

I will use the point (1,0)

x = 1

y = 0

m = [tex]\frac{-8}{3}[/tex]

y = mx + b  Substitute in what you know and solve for b

0 = [tex]\frac{-8}{3}[/tex](1) + b

0 = [tex]\frac{-8}{3}[/tex] + b  Add [tex]\frac{8}{3}[/tex] to both sides

[tex]\frac{8}{3}[/tex] = b

The y-intercept (b) is [tex]\frac{8}{3}[/tex]

y = mx + b

y = [tex]\frac{-8}{3}[/tex] x + [tex]\frac{8}{3}[/tex]

Answer:

Original: 0.24958333333... | Rounded Up: 0.25

Step-by-step explanation:

unit price = total price divided by quantity
5.99 divided by 24 = 0.24958333333...
We can round this to 0.25

The polynomial 6x³ + x² - 2x + 15 divided by 2x + 3 will give a quotient of 3x² - 4x + 5 and a remainder of zero, which makes option a correct.

The long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder

We shall divide the polynomial 6x³ + x² - 2x + 15 by 2x + 3 as follows;

x³ divided by 2x equals 3x²

2x + 3 multiplied by 3x² equals 6x³ + 9x²

subtract 6x³ + 9x² from 6x³ + x² - 2x + 15 will result to -8x² - 2x + 15

-8x² divided by 2x equals -4x

2x + 3 multiplied by -4x equals -8x² - 12x

subtract -8x² - 12x from -8x² - 2x + 15 will result to 10x + 15

10x divided by 2x equals 5

2x + 3 multiplied by 5 equals 10x + 15

subtract 10x + 15 from 10x + 15 will result to a remainder of 0

Therefore by the long division method, 6x³ + x² - 2x + 15 divided by 2x + 3 gives a quotient 3x² - 4x + 5 and a remainder of 0.

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The depth of the water is increasing at 0.167 ft/min.

In this problem, we are given the radius of the conical tank (12 feet), the height of the tank (26 feet) and the rate at which water is flowing into the tank (20 ft3/min). To calculate the rate of the water's increase in depth, we need to first calculate the volume of the tank.

The volume of a conical tank can be calculated using the formula V = 13r2h, where r is the radius and h is the height. Using this formula, we can calculate the volume of the tank to be 13(12)2(26) = 7584 ft3.

Next, we need to calculate the rate at which the depth of the water is increasing. This can be done by dividing the rate at which water is flowing into the tank (20 ft3/min) by the volume of the tank (7584 ft3). This gives us a rate of 0.0026 ft3/min. To get the rate at which the depth is increasing, we need to divide this number by the area of the tank's base (113 ft2). This gives us a rate of 0.167 ft.

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The equation for the graph is y = 20x + 50, where the rate of change is 20 and the initial value is 50.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given graph shows the relationship between the number of cubic yards of mulch ordered and the total cost of the mulch delivered,

x-axis shows the cubic yards and y-axis shows cost,

A. to find the constant rate of change,

from graph, we find that x₁ = 0 and x₂ = 5

y₁ = 50 and y₂ = 150

constant rate of change  = (y₂ - y₁)/(x₂ - x₁)

rate of change  = (150 - 50)/(5 - 0)

rate of change  = 100/5 = 20

the constant rate represents the slope of the line,

for equation of line y = mx + c

here m = slope of the line or constant rate of change.

2. to find the initial value,

the initial value represents the y-intercept or the value of constant for equation y = mx + c,

where c is the initial value

we have  m = 20 x = 0 and  y = 50

50 = 20(0) + c

c = 50

the equation for the graph is y = 20x + 50

Hence the rate of change is 20 and the initial value is 50.

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Answer:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

C : is the hypotenuse

A and B are two sides

[tex] {6}^{2} + \: {x}^{2} = {15}^{2} \\ {15}^{2} - {6}^{2} = 189 \\ \sqrt{189} = 3 \sqrt{21} [/tex]

The ratio if the dimensions are expressed in inches instead of feet is 1/16.

Ratio is defined as the relationship between two quantities. It can be expressed as a to b, a : b, or a / b.

Meanwhile, proportion is defined as the equality between two ratios.

a / b = c / d

If the ratio of the numerical value of the perimeter to the numerical value of the area, expressed in feet, is 3/4, then converting each component to inches will give its ratio, expressed in inches.

perimeter / area

= 3 feet / 4 feet²

= 3 feet(12 inches / 1 foot) / 4 feet²(12 inches / 1 foot)(12 inches / 1 foot)

= 36 inches / 576 inches²

Simplifying the ratio by dividing both by 36.

36 / 576 = 1 / 16

Hence, the ratio will become 1/16.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 4000\left(1+\frac{0.04}{4}\right)^{4\cdot 10}\implies A=4000(1.01)^{40} \implies A \approx 5955.45[/tex]

Answer:

$5955.45

Step-by-step explanation:

We can use the formula to find the sum of the money, when we calculate the amount of money according to compound interest.

Before we getting ready to solve the sum, we have to keep these points in our mind.

Formula to find the sum of money after compound interest is:

[tex]\sf S = X ( 1 + r )^n[/tex]

Here,

S = Sum of money

X = Amount of money deposited

r = Interest rate

n = Time ( in years )

Let us solve it now.

[tex]\sf S = X ( 1 + r )^n\\\\\sf S = 4000 ( 1 + \frac{4}{100}*\frac{1}{4} )^4^0\\\\\sf S = 4000 ( 1 + \frac{4}{400} )^4^0\\\\\sf S = 4000 ( 1 + 0.01 )^4^0\\\\\sf S = 4000 ( 1.01 )^4^0\\\\\sf S = 5955.45[/tex]

The mean of the distribution is 61.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given, the median and mode of a dataset are 45 and 13 respectively

They have given that the median of the distribution is 45

They have given that the mode of distribution is 13

To find the mean of the distribution, let's consider

The relationship between the mean, mode, and the median is given by

Mode = 3 Median - 2 Mean

Mean = (3* 45 - 13)/2

Mean = 122/2

Mean = 61

Therefore, the mean of a distribution if its median and mode are 45 and 13 respectively is 61.

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The solution to the inequality expression 1/4|x + 1| ≥ 4 is (b) x ≤ -17 or x ≥ 15

From the question, we have the following parameters that can be used in our computation:

1/4|x + 1| ≥ 4

Multiply through the inequality by 4

So, we have the following representation

|x + 1| ≥ 16

Remove the absolute bracket

-16 ≥ x + 1 ≥ 16

Subtract 1 from all sides

-17 ≥ x ≥ 15

So, we have

x ≤ -17 or x ≥ 15

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Answer:

x=15

Step-by-step explanation:

x/3+x/5=8

Both multipling 15:  15(x/3+x/5)=15*8

5x+3x=120

     8x=120

      x=15

The principal sum refers to the amount payable in one sum in the case of accidental death and, in some cases, accidental dismemberment.

The amount paid in the case of accident or medical insurance in the event that the insured person dies, loses a limb, or loses sight is known to be as principal sum. It means that the principal sum amount is the maximum amount paid to the insured person for all injuries resulting from the accident.

Thus, the principal sum is the amount insured to be paid by the company to the beneficiary in the case of the insured individual's accidental death as well as in the loss of limb or sight.

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Answer:

f2 + 5 when f = 3 is 11.

Step-by-step explanation:

So let's start by replacing f with 3:

3(2) + 5 =

When we have a variable right next to another number, we multiply. Some examples of this are 2x or 5y or 10000t, or even 0.001j.

Therefore, we multiply the 3 and 2 together, which gets us 6:

6 + 5 =

And 6 plus 5 equals 11

6 + 5 = 11, final answer.

Answer:

B.  x <= -17 or x >= 15

Step-by-step explanation:

To solve this inequality, we need to split the absolute value expression into two separate cases, one for each possible sign of the expression within the absolute value bars.

For the case where the expression within the absolute value bars is positive, we can remove the absolute value bars and solve the resulting inequality as follows:

1/4(x+1) >= 4

(x+1) >= 16

x >= 15

For the case where the expression within the absolute value bars is negative, we can again remove the absolute value bars and solve the resulting inequality as follows:

-1/4(x+1) >= 4

-(x+1) >= 16

x <= -17

Combining these two cases, we get that the solution to the inequality is:

x <= -17 or x >= 15

So, the correct answer is B.

Answer:

Isha Chawla the viewer's attention to detail and the game name is the viewer's of the viewer's the viewer's of math and science and time of year for you are interested please contact me homework for the same to the viewer's attention to the seller if

If j(x) = 5^(x - 3), using laws of exponents to solve the given expression [j(x + h) - j(x)]/h gives; [j(x + h) - j(x)]/h =  [(5^(x - 3))(5^(h) - 1)]/h

We are given the function as;

j(x) = 5^(x - 3)

Now, we want to solve the expression;

[j(x + h) - j(x)]/h

This gives us;

j(x + h) = 5^(x - 3 + h)

Thus, our expression is now;

[j(x + h) - j(x)]/h = [5^(x - 3 + h) - 5^(x - 3)]/h

Now, according to laws of exponents, we know that;

y³ × y² = y³ ⁺ ²

Thus;

5^(x - 3 + h) = 5^(x - 3) × 5^h

Therefore;

[5^(x - 3 + h) - 5^(x - 3)]/h = [(5^(x - 3))(5^(h) - 1)]/h

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The equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Violet's birthday is C = 24 - 4t

Number of chocolate violet eats each night = 4

Number of chocolate originally in the box = 24

Number of chocolate remaining = C

Number of days after violet birthday = t

Number of chocolate remaining = Number of chocolate originally in the box - (Number of chocolate violet eats each night × Number of days after violet birthday)

C = 24 - (4 × t)

C = 24 - 4t

In conclusion, the equation which represents violet's remaining chocolate after her birthday is C = 24 - 4t

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Answer: x = 4

Step-by-step explanation: (4x+9)−6.

Subtract 6 from 9 to get 3.

d/dx (4x+3)

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^n

 is nax^n-1.

4x^1-1

Subtract 1 from 1.

4x^0

For any term t, t×1=t and 1t=t.

x = 4

​

Answer:

1.6 oz

Step-by-step explanation:

8 oz to spread into 5 bowls = 8/5

8/5=1.6

Answer:1.6

Step-by-step explanation: First your going to divide 8/5 but do it like this-8.0 divided by 5= 1.6 so that gonna be your answer. Hope it was helping you.

The perimeter of the shape is approximately 20.57 inches.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

The shape consists of two shapes; a square and 2 semi-circles

Perimeter of square = 4L

where L = 2 inches

Perimeter = 4(2)

Perimeter = 8 inches

Perimeter of Semi-circle = [tex]\pi r}[/tex]

where [tex]\pi = 3.142[/tex]

r = 2 inches

Perimeter of Semi-circle = 3.142 x 2

Perimeter of Semi-circle = 6.284 inches

Perimeter of shape = Perimeter of square + 2 x Perimeter of Semi-circle

Perimeter of shape = 8 inches + 2 x  6.284 inches

Perimeter of shape = 8 inches + 12.568 inches

Perimeter of shape = 20.568 inches

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Answer:

lol.

Step-by-step explanation:

Refer to the image attached. Please rate, and let me know if you have any questions. Thanks!

[tex]\begin{array}{ll|ll} 21!\implies &21\cdot 20\cdot 19\cdot 18\cdot 17.....\\&\\ &21\cdot 20\cdot 19! \end{array} \begin{array}{llll} 20!\implies &20\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15.....\\\\ & 20\cdot 19! \end{array} \\\\[-0.35em] ~\dotfill\\\\ (21\cdot 20\cdot 19!)-(20\cdot 19!)\implies (21\cdot 20\cdot c)-(20\cdot c) \\\\\\ 420c-20c\implies \text{\LARGE 400c}[/tex]

Answer:

Below

Step-by-step explanation:

Here is the point-slope form of this line to start:

y-3 = -4 ( x-1)      which can be re-arranged to

y = -4x +7            which is y = mx + b form ( slope -intercept from)

or

4x + y = 7      sometimes called 'standard form'

When proved, the total surface area of the solid is π/4 r(11r - 2l)

The Solid comprise a cone mounted on top of a hemisphere. The total surface area of the object is given as follows

Total surface area = Total surface area of cone -total surface area of the hemisphere.

This implies that TSA = 1/2πr(1/2r +l) -3πr²

πr/2(r+2l)/2 -3πr²

This implies that the expression will be (πr² +2πrl)/4 - 3πr²

⇒(πr² +2πrl - 12πr²)/4

Conclusively, the expression finally gives π/4 r (11r - 2l)

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