Find the minimum distance between the point (-5,1) and the line x = -2​

Answer:

2,4

Step-by-step explanation:

This question is quite simple. First you need to find the factors of 8. Then you need to see which factors of positive 8 can add up to make -6. The factors are -4 and -2. Then expand. Now you have the equation x^2-4x-2x+8. Now group it.

(x^2-4x) +(-2x+8)

Then take out the X from the first group and the -2 from the second. We want the values in the brackets to be the same.

Now you have

x(x-4)-2(x-4)

Take the x and the -2x and make it a group. Now you have (x-4)(x-2)

Set x-4 equal to zero. x-4=0 Now solve it like a regular equation. Add four to both sides. Now you have x=4

Do the same thing with (x-2) and you get x=2

4 and 2 are your solutions

Answer:

x = 4 and x = 2

Step-by-step explanation:

The easiest way to find the roots is by converting the function into its factored form. This can be determined by asking the question:

What two numbers have a product 8 and a sum of -6?

These two values are -4 and -2.

-4 x -2 = 8

-4 + (-2) = -6

These two numbers are used in the factored form of the equation. You can prove the accuracy of the factored form by re-expanding it (multiply all the terms in the first parentheses by the terms in the second parentheses). The factored form looks like this:

(x - 4)(x - 2)

The roots are the values that make the expression equal 0. This can be done by setting each parentheses equal to 0 and solving for "x".

x - 4 = 0                              x - 2 = 0

x = 4                                    x = 2

Therefore, the roots of the function x² - 6x + 8 are x = 4 and x = 2.

The surface area of the solid will be A=327.5 square inches and the lateral surface area will be A= 377.5 square inches.

The space occupied by any figure in the two-dimensional space is called an area. The area can be rectangular circular triangular types.

Here we have the figure made up by the two pyramids and one rectangular box. So we will find the surface area of the pyramid then the rectangular box and again the pyramid and will add all of them.

The Lateral surface area will be calculated as:-

A=2W√(w÷2)²+(h)²+w²

A=2x5√(5÷2)²+(3)²+5x5

A=152.5 +25

A=177.5 square inch

Area of lower pyramid= (1÷2)xbxh+w²

A=(1÷2)x5x7.5 + 25 =75+25= 100

Area of the rectangular box= 4(w²)=4(5x5)=100

So total lateral surface area will be =100+100+177.5=377.5 square inch

(2)The surface area will be calculated as:-

A=2W√(w÷2)²+(h)²

A=2x5√(5÷2)²+(3)²

A=152.5 square inches

Area of lower pyramid= (1÷2)xbxh

A=(1÷2)x5x7.5  =75 square inches

Area of the rectangular box= 4(w²)=4(5x5)=100

So total surface area will be =100+75+152.5=327.5 square inch

Hence the surface area of the solid will be A=327.5 square inches and the lateral surface area will be A= 377.5 square inches.

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Answer:

1.9

Step-by-step explanation:

r=C/2π

r-12.1/2π=1.9257...

Answer:

1.9 mm

Step-by-step explanation:

Circumference of circle = 2πr

             2πr = 12.1 mm

     [tex]\sf 2* \dfrac{22}{7}*r= 12.1\\\\[/tex]

                  [tex]\sf r = \dfrac{12.1*7}{2*22}\\\\[/tex]

                     = 1.925

                 [tex]\sf \boxed{radius =1.9 \ mm }[/tex]

The correct classification for the angle JML is an acute angle.

What is an acute angle?

An acute angle has a measure, or it's smaller, than a right angle.

Therefore, the acute angle is the small angle which is less than 90°

let's find the measure of ∠JML

Hence,

∠JML = ∠JMK + ∠KML

∠KML = 180 - 132 = 48 degrees.

Therefore,

∠JML = 41 + 48 = 89 degrees.

Therefore, the correct classification for the angle JML is an acute angle.

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Answer:

The slope of the line is 3 and the y-intercept is (3/2) three-halves.

Step-by-step explanation:

The data provided is:

X     Y

-1.0     -1.5

-0.5     0.0

0.0     1.5

0.5     3.0

The slope of the linear function is denoted by, b and the intercept is denoted by, a.

The formula to compute the slope and intercept are:

Compute the values required in Excel.

Compute the slope and intercept as follows:

Thus, the slope of the line is 3 and the y-intercept is (3/2) three-halves.

Answer:

I forgot to change pi into 3.14

Step-by-step explanation:

the awnser enlarges, preserves, scale reduces

Using the transformation of an exponent to a power, the formula that is equivalent to f is given by:

[tex]440\sqrt[12]{2^{10}}[/tex]

It happens according to the following rule:

[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]

In this problem, the rule for f is given by:

[tex]440(2)^{\frac{10}{12}}[/tex]

Hence, applying the rule, the equivalent formula is given by:

[tex]440\sqrt[12]{2^{10}}[/tex]

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Answer:

C

Step-by-step explanation:

Answer:

The answer is 18 pounds per bucket.

In this question, we are given the expression that relates the pounds of lobster to the number of buckets:

[tex]\displaystyle \frac{\text{450 pounds}}{\text{25 buckets}}[/tex]

This fraction is presented to give a proportion of pounds of lobster to the number of buckets these lobsters inhabit.

To solve this problem, we need to know exactly how this rate will work.

A rate is the same thing as a fraction, percentage, or decimal. All of these forms are convertible between one another.

For instance, if we took 25%, we know that by dividing this by 100, we receive a decimal form (0.25) or a fractional form (1/4).

We can apply the same principle here.

Part I - Set up the Rate

To solve, set up the rate:

[tex]\displaystyle \frac{450 \ \text{pounds}}{25 \ \text{buckets}}[/tex]

Part II - Find the GCF

Then, find the Greatest Common Factor (GCF) of the two digits:

Check for common factors between the two trees:

Since 25 is the greatest of the three factors, it is the GCF.

Part III - Apply the GCF

Divide both the numerator and the denominator by 25:

[tex]\displaystyle \frac{450}{25} = 18[/tex]

[tex]\displaystyle \frac{25}{25} = 1[/tex]

Part IV - Simplify

Set up the new fraction:

[tex]\displaystyle \frac{18}{1}[/tex]

Anything divided by 1 does not change:

[tex]\displaystyle \frac{18}{1} = 18[/tex]

Since we got 18 an answer, this means that there are 18 pounds of lobster per bucket.

The rule is a translation rule, and another way of writing the rule t -8, 4(x, y) is (x - 8, y + 4)

The rule is given as:

t -8, 4(x, y)

The above rule means that:

A translation of 8 units right and 4 units up.

This is represented as:

(x - 8, y + 4)

Hence, another way of writing the rule t -8, 4(x, y) is (x - 8, y + 4)

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Answer:

C: (x, y) → (x – 8, y + 4)

Step-by-step explanation:

Step 1 Divide all terms by a (the coefficient of x2). Step 2 Move the number term (c/a) to the right side of the equation. Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.

The graph of f(x) = -x² + 2x + 1 and g(x) = 2ˣ, have the same y-intercept of (0, 1)

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

Given the polynomial function f(x) = -x² + 2x + 1 and an exponential function g(x) = 2ˣ

From the graph of f(x) = -x² + 2x + 1 and g(x) = 2ˣ, have the same y-intercept of (0, 1)

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Step-by-step explanation: To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Step-by-step explanation:

Mean :

13 + 25 + 7 + 28 + 42 + 7 + 15 + 23 + 1 + 17.

= 178

178 ÷ 10

= 17.8

Median =

13, 25, 7, 28, (42, 7,) 15, 23, 1, 17

= 42 + 17

= 59 ÷ 2

= 29.5

Range :

42 - 1

= 41

Hope it helps :))

Answer:

Mean- 17.8 Median- 16 Mode- 17.8

Step-by-step explanation:

1. Put the numbers in ascending order.

1, 7, 7, 13, 15, 17, 23, 25, 28, 42

2. Look for the median. The median is the number located in the middle of a set of numbers. In this case, the median is going to be between 15 and 17 because they are both in the middle. This means that the median will be 16.

1, 7, 7, 13, 15, 17, 23, 25, 28, 42

3. Find the mode. The mode is the number you see the most in a set of numbers. In this case, there are two 7's so 7 is the mode of this set.

1, 7, 7, 13, 15, 17, 23, 25, 28, 42

4. Find the mean. The mean is the overall average of a set of numbers. To find the average, find the sum of all the numbers in the set and divide it by the number of integers there are. In this case, there are ten integers, so we'll find the sum (178) and divide it by 10 to get a mean of 17.8.

[tex]\frac{1+7+7+13+15+17+23+25+28+42}{10}[/tex] = 17.8

5. Find the range. The range is basically the difference between the lowest and highest values in a set of numbers. The lowest number is 1 and the highest is 42. So, we'll subtract the two to get a range of 41.

1, 7, 7, 13, 15, 17, 23, 25, 28, 42

42 - 1 = 41

Answer:

See below

Step-by-step explanation:

There are two feasible ways to place the turtle eggs.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's calculate the circumference ~

[tex]\qquad \sf  \dashrightarrow \: c = \pi d[/tex]

where,

now, plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: c = 3.14 \times 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: c = 12.56 \: \: m[/tex]

The circumference of the given circle.

[tex]c = 2 {\pi}r[/tex]

[tex]c = 2 \times 3.14 \times r[/tex]

[tex]c = 2 \times 3.14\times 2[/tex]

[tex]c = 12.56 \: m[/tex]

Hence, the circumference of the given circle is 12.56 meters.

Answer:

135 cars; 205 SUVs

Step-by-step explanation:

Let c = number of cars sold.

Let s = number of SUVs sold.

s = c + 70

c + s = 340

Substitute s in the second equation with c + 70 and solve for c.

c + s = 340

c + c + 70 = 340

2c = 270

c = 135

s = c + 70

s = 135 + 70

s = 205

Answer: 135 cars; 205 SUVs

Answer:

I wouldn't say this is entirely correct, but I think it's 45%.

Step-by-step explanation:

If you started with $90 and it was reduced 20%, than 25% MORE, the final percentage that was lowered would be the 20% and 25% added together.

The answer is 45%.

(Please do tell me if I got this wrong!!)

The original price reduced to 60%.

A percentage is a ratio or number that can be expressed as a fraction of 100. Additionally, it is denoted by the symbol "%."

On September 1, a dress was priced at $90. On October 1, the price was reduced by 20%.

That means,

the price is now = $90 - (90 x 20 /100) = $72

On November 1, the price was further reduced by 25% of the October 1 price.

The price is now = $72 - ( 72 x 25 / 100) = $54

To find the percentage of original price;

The percentage of original price

= 5400 / 90

= 60%

Therefore, the final price is 60% of the original price.

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Answer:

B

Step-by-step explanation:

Everyone eats whereas not everyone would enjoy being at the other options

The graph of function y = 2x - 4 is shown in figure.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Equation of line is,

⇒ y = 2x - 4

Now, WE know that;

Standard form of equation of line is,

y = mx + c

Where, m is slope and c is y - intercept.

Here, Function is,

y = 2x - 4

Hence, y - intercept = - 4

Thus, The graph of function y = 2x - 4 is shown in figure with y - intercept (0, - 4).

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Answer:

-9

Step-by-step explanation:

use an equation to solve this

consecutive means in succession, one after the other

since they're odd, both numbers have to be odd

let x be the first number

x+x+2=-20

+2 because if you only +1, one of the numbers would be even

2x+2=-20

-2. -2

2x=-22

x=-11

the smaller would be -9 since we are adding x and x+2 together

Answer:

600 inches

The volume of the box is 600 because if we take the formula and substitute the numbers given, you are left with 600 inches.

Step-by-step explanation:

V = lwh

l = 10

W = 5

H = 12

10 × 5 × 12 = 600

Quadratic equations are equations that has a leading degree of 2. The value of x from the given quadratic equation is 2 or -12

Quadratic equations are equations that has a leading degree of 2

GIven the quadratic equation expressed as x^2 + 10x + 12 = 36

Rewrite

x^2 + 10x - 36 + 12 = 0

x^2 + 10x - 24 = 0

Factorize

x^2 + 12x -2x - 24 = 0
x(x+12) -2(x+12) = 0
x - 2 = 0 and x = -12

x =2 or -12

Hence the value of x from the given quadratic equation is 2 or -12

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Answer:

A on edge 23'

Step-by-step explanation:

because i said so

Answer: Its D

Step-by-step explanation:

Check the picture below.

so hmmm let's get the whole area of the rectangle, and then get the areas of those 3 triangles and subtract their area from that of the rectangle's, what's leftover is what we didn't subtract, namely, the white triangle.

[tex]\stackrel{\textit{\huge Areas}}{\stackrel{rectangle}{(3)(4)}~~ - ~~\stackrel{green~triangle}{\cfrac{1}{2}(2)(3)}~~ - ~~\stackrel{pink~triangle}{\cfrac{1}{2}(2)(2)}~~ - ~~\stackrel{yellow~triangle}{\cfrac{1}{2}(4)(1)}} \\\\\\ 12~~ - ~~3~~ - ~~2~~ - ~~2\implies 5[/tex]

Answer:

The average strand of hair is 25.4μm

Step-by-step explanation:

Diameter of dime is 2.985×10² times of diameter of human hair.

The correct option is B.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given,

Diameter of dime = 17.91mm

Diameter of human hair = 6.0×10⁻²mm

Ratio of diameter of dime to diameter of human hair = 17.91/6.0×10⁻²

                                                                                        = 2.985×10²

Hence, 2.985×10² times of diameter of human hair is diameter of dime.

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Answer: 256 miles

Step-by-step explanation:

if 1 1/4 inches = 80 miles, then 1/4 inch = 16 miles (there are five 1/4 in 1 1/4 inches, so 80/5 = 16)

there are sixteen 1/4 inches in 4 inches, and we know that each 1/4 inch is equal to 16 miles, so 16*16 = 256

Un dominio razonable para la función  f(d)  en el periodo de tiempo estudiado es:

Dominio de  f(d)  =  d  ∈  [0, 7]

Mientras que el intercepto con el eje f(d) ocurre en el valor 11 mm y representa el valor del radio del alga cuando se inició el experimento en el tiempo cero.

Explicación paso a paso:

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function?

De acuerdo con la gráfica anexa y el significado de las variables involucradas,  el dominio razonable para la función  f(d)  en el periodo de tiempo estudiado es:

Step-by-step explanation:

so, that means we want to find the time t (days) after which N = No/2

because "half-life" means the amount of time until half of the substance has disappeared (or transformed into something else).

so, we have

No/2 = No × e^(-0.1481×t)

No = 2× No × e^(-0.1481×t)

1 = 2×e^(‐0.1481×t)

1/2 = 0.5 = e^(-0.1481×t)

ln(0.5) = -0.1481×t

t = ln(0.5)/-0.1481 = 4.680264555... ≈ 4.7 days

Answer:

See below.

Step-by-step explanation:

The side of the square is k.

The area of the square is k².

The diameter of the circle is k.

For a circle, radius = diameter/2.

The radius of the circle is k/2.

Formula for area of circle: A = πr².

Here, the radius, r, is k/2.

The area of the circle is π(k/2)² = (πk²)/4

The shaded area is the difference between the area of the square and the area of the circle.

shaded area = k² - (πk²)/4

We are told that the shaded area = A

A = k² - (πk²)/4

Multiply both sides of the equation above by 4.

4A = 4k² - πk²