What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x3−1 ?

Answer:

x = 7,  y = 28

Step-by-step explanation:

We're given that ABCD is a rectangle, so we know that all sides opposite from each others are equal in length. This also means that each part of the criss-cross-X thing inside the rectangle are equal in length to each others as well. (AE = BE = DE = CE).

AC = 100 from the given picture, which means half of that from AE would be 50. Since DE is the same length as AE, we can set x²+1 = 50 and solve for x. We get x = 7.

To solve for y, we know that opposite sides of a rectangle are of the same length. So AD = BC.

The question already gave us the equation for those sides so we just need to set them equal to each other.

2y + 5 = 3y - 23

sovle for it and you get y = 28.

Answer:

Option b) 36 over 25 is correct

That is given expression is equivalent to [tex]\frac{36}{25}[/tex]

Step-by-step explanation:

Given expression can be written as below:

[tex](\frac{7\times 3\times 2}{7\times 5})^2\times \frac{7^0}{5^{-3}}\times 5^{-9}[/tex]

To find the value of given expression:

[tex](\frac{7\times 3\times 2}{7\times 5})^2\times \frac{7^0}{5^{-3}}\times 5^{-9}=(\frac{6}{5})^2\times (\frac{1}{5^{-3}})^3\times \frac{1}{5^9}[/tex]

[tex]=(\frac{6}{5})^2\times (5^3)^3\times \frac{1}{5^9}[/tex]

[tex]=\frac{36}{25}\times 5^9\times \frac{1}{5^9}[/tex]

[tex]=\frac{36}{25}[/tex]

Therefore [tex](\frac{7\times 3\times 2}{7\times 5})^2\times \frac{7^0}{5^{-3}}\times 5^{-9}=\frac{36}{25}[/tex]

Option b) 36 over 25 is correct

That is given expression is equivalent to [tex]\frac{36}{25}[/tex]

Answer:

36/25 is the answer

Answer:

    31415 92653

Step-by-step explanation:

The result of the integral is π. The first 30 digits of π are ...

  3.14159 26535 89793 23846 26433 8327 ...

_____

Pi is a transcendental number. Not only is it irrational, but it is not the root of any polynomial with rational real coefficients. It is not a repeating decimal.

Answer:

x = [tex]\frac{5b-2d}{a-2c}[/tex]

Step-by-step explanation:

Given

ax + 2d = 2cx + 5b (subtract 2d from both sides )

ax = 2cx + 5b - 2d ( subtract 2cx from both sides )

ax - 2cx = 5b - 2d ← factor out x from each term on the left side

x(a - 2c) = 5b - 2d ← divide both sides by (a - 2c)

x = [tex]\frac{5b-2d}{a-2c}[/tex]

The value of x is x = (5b - 2d )/(a - 2c)

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

ax + 2d = 2cx + 5b

Now subtract 2d from both sides;

ax = 2cx + 5b - 2d

Then subtract 2cx from both sides;

ax - 2cx = 5b - 2d

Now factor out x from each term on the left side

x(a - 2c) = 5b - 2d

Now divide both sides by (a - 2c)

x = (5b - 2d )/(a - 2c)

To know more about an expression follow;

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#SPJ3

The distance between the points (10, -11) and (-1, -5) is approximately 12.5 units.

The distance between two points can be found using the Distance Formula.

The formula is:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the given points (10, -11) and (-1, -5), we can plug the values into the formula:

distance = sqrt((-1 - 10)^2 + (-5 - (-11))^2)

distance = sqrt((-11)^2 + (6)^2)

distance = sqrt(121 + 36)

distance = sqrt(157)

To the nearest tenth, the distance is approximately 12.5 units.

The solutions for ‘x’ in the given equation are – 3  and  - 7

Step-by-step explanation:

Given equation:

                   [tex]x^{2} + 10 x + 21 = 0[/tex]

To find the ‘x’ value, try to factor, because in this case it works, it's fast. By using factor method, we get

                    (x + 3) (x + 7) = 0  (adding both value we get 10 and multiply as 21 as in equation and check with signs also while factoring)

                     x = - 3, -7

Verify above values by multiply both terms,

                     (x + 3) (x + 7) = 0

                [tex]x^{2} + 7 x + 3 x + 21 = 0[/tex]

                [tex]x^{2} + 10 x + 21 = 0[/tex] (so values obtained from factor method are correct)

Or, can use quadratic formula, for [tex]a x^{2} + b x + c=0[/tex], the solutions are given by:

                      [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

In the given equation, a = 1, b = 10, c = 21, apply these in above formula

                     [tex]x=\frac{-10 \pm \sqrt{10^{2}-(4 \times 1 \times 21)}}{2(1)}=\frac{-10 \pm \sqrt{100-84}}{2}[/tex]

                     [tex]x=\frac{-10 \pm \sqrt{16}}{2}=\frac{-10 \pm 4}{2}[/tex]

So,

When  [tex]x=\frac{-10+4}{2}=\frac{-6}{2}=-3[/tex]

When [tex]x=\frac{-10-4}{2}=\frac{-14}{2}=-7[/tex]

Hence, the values for ‘x’ are - 3 and - 7

Answer:I got it right on quiz

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Use exponent laws

1/3^-3 = 3^3 = 27

Answer:

D

Step-by-step explanation:

An operation of two real numbers is defined by the rule

[tex]a\bigotimes b=b^a+2ab[/tex]

Calculate [tex]2\bigotimes (1\bigotimes 3).[/tex] First evaluate the expression in brackets:

[tex]1\bigotimes 3=1^3+2\cdot 1\cdot 3=1+6=7[/tex]

Now,

[tex]2\bigotimes (1\bigotimes 3)=2\bigotimes 7=2^7+2\cdot 2\cdot 7=128+28=156[/tex]

Final answer:

The digit in the hundredths place of the number 9.014 is 1. Significant figures and rounding concepts determine that if the digit in the thousandths place is 5 or greater, the hundredths place digit is rounded up.

Explanation:

The digit in the hundredths place of the number 9.014 is 1. When dealing with decimal numbers, the first place to the right of the decimal point is the tenths place, the second place is the hundredths place, and so on. In the context of significant figures and rounding, if we need to round a number to the hundredths position, and the digit in the thousandths place (the third position to the right of the decimal) is 5 or greater, we round the hundredths digit up.

For example, if the calculator answer is 921.996 and we need to round to the hundredths place, we look at the thousandths place digit. Since it is greater than 5, we round up, changing the answer to 922.00.

Answer:

1) p > or =3

2)7< or = r

3)a<0

4) 3< x

Step-by-step explanation:

follow on the attached picture

Answer:

5 red, 7 blue and 8 yellow

Step-by-step explanation:

Just make a ratio and simplify

Red : Blue : Yellow

25 : 35 : 40

All divisible by 5

5 : 7 : 8

These dont have a common factor so this is the simplest ratio

Therefore the minimum drops Ava can add to a gallon of white paint to have that ratio are 5 red drops, 7 blue drops and 8 yellow drops.

Answer:

Except k=7, any real number for k would cause the system of equations to have no solution.

Step-by-step explanation:

In general a system of equations can be represented as ax+by=c and dx+ey=f. In order this system of equations to have NO SOLUTIONS a/d=b/a≠c/f. In our example a=6, b=4, c=14, d=3, e=2 and f=k. To apply the formula above, 6/3=4/2≠14/k. Hence k≠7. It can be concluded that except k=7, any real number for k would cause the system of equations to have no solutions.

Just for information, if k=7 the system will have infinitely many solutions.

The error in Percy's statement is that, the system of equations would have infinite many solutions when k = 7

The system of equations is given as:

6x + 4y = 14,

3x + 2y = k

Multiply the second equation by 2

[tex]3x + 2y = k \to 6x + 4y = 2k[/tex]

Subtract the new equation, from the first equation

[tex]6x - 6x + 4y - 4y =14 -2k[/tex]

[tex]0=14 -2k[/tex]

Collect like terms

[tex]2k = 14[/tex]

Solve for k

[tex]k = 7[/tex]

The above means that:

The system of equations would have infinite many solutions when k = 7

Read more about system of equations at:

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Answer:

You have to subtract 1.01 from 4.12 because it says how much it rained on Tuesday.

Step-by-step explanation:

The equation says that it rained 4.12 inches on Monday and 1.01 less on Tuesday.

So to write in number form = 4.12 - 1.01 = 3.11

So your answer is 3.11 inches.

It rained 3.11 inches on Tuesday.

Hope this helps!

Answer:

Store used 7.5 pounds of gummy candy, 2.5 pounds of jelly beans, and 3 pounds of hard candy.

Step-by-step explanation:

Let the amount of gummy candy be 'x'.

Let the amount of jelly beans be 'y'.

Let the amount of hard candy 'z'.

Now Given:

Sue is buying 13 pound of mixture.

So we can say that;

[tex]x+y+z =13[/tex]

But Given:

The mixture calls for three times as many gummy candy pieces as jelly beans.

[tex]x=3y[/tex]

Substituting the value of x in above equation we get;

[tex]3y+y+z=13\\\\4y +z =13 \ \ \ \ \ equation \ 1[/tex]

Also Given:

cost of gummy candy = $1.20

cost of jelly beans = $2.00

cost of hard candy = $2.60

Total Cost of mixture  = $21.80

Now Total Cost of mixture is equal to cost of gummy candy multiplied amount of gummy candy plus cost of jelly bean multiplied amount of jelly bean plus cost of hard candy multiplied amount of hard candy.

framing in equation form we get;

[tex]1.2x+2y+2.6z=21.80[/tex]

But  [tex]x=3y[/tex]

So [tex]1.2(3y)+2y+2.6z=21.80\\\\3.6y+2y+2.6z=21.80\\\\5.6y+2.6z=21.80[/tex]

Now Multiplying by both side by 10 we get;

[tex]10(5.6y+2.6z)=21.80\times 10\\\\10\times5.6y + 10\times2.6z =218\\\\56y+26z=218 \ \ \ \ \ equation \ 2[/tex]

Now Multiplying equation 1 by 14 we get;

[tex]14(4y +z) =13\times14\\\\14\times4y +14z =182\\\\56y+14z=182[/tex]

Now Subtracting equation 3 from equation 2 we get;

[tex](56y+26z) - (56y+14z) =218-182\\\\56y +26z-56y-14z=36\\\\12z=36\\\\z=\frac{36}{12} = 3 \ pounds[/tex]

Now Substituting value of z in equation 1 we get;

[tex]4y+z=13\\\\4y+3=13\\\\4y=13-3\\\\4y = 10\\\\y=\frac{10}{4} = 2.5 \ pounds[/tex]

Now also;

[tex]x= 3y\\\\x =3\times2.5 =7.5 \ pounds[/tex]

Hence Store used 7.5 pounds of gummy candy, 2.5 pounds of jelly beans, and 3 pounds of hard candy.

Answer:

14 sq. ft [tex](14 ft^{2})[/tex]

Step-by-step explanation:

First, we know that the area of a circle is [tex]\\ A_{circle} =\pi * r^{2}[/tex], where r is the radius of the circle, and [tex]\pi[/tex] is the ratio of the length of a circle's circumference to its diameter, that is, [tex]\pi[/tex]=3.1415926535 ... . But we have here a semicircle.

So, the area of a semicircle is [tex]\\ A_{semicircle} = \frac{1}{2} (\pi * r^{2})[/tex].

We also know that 1 feet = 12 inches, so 36 inches are:

[tex]\\ \frac{1ft}{12inches} * 36 inches = 3 ft[/tex]

Then, the area of the semicircular window is:

[tex]\\ A_{semicircular-window} = \frac{1}{2} (\pi * 3^{2})[/tex] ≈ 14.1372.

Well, rounding the answer to the nearest square foot, we have that the semicircular window allows light through an area of 14 sq. ft [tex] (14 ft^{2})[/tex].

Answer:

1/3

Step-by-step explanation:

(8/15)   -   (1/5)

change 1/5 to 3/15 (which is equivalent to 1/5)

(8/15) - (3/15) = (5/15)

Simplify

(5/15) = (1/3)

Answer:

1/3

Step-by-step explanation:

8/15-1/5=8/15-3/15=5/15=1/3

The price of 1 youth ticket is $ 22

Solution:

Let "y" be the price of 1 youth ticket

Let "a" be the price of 1 adult ticket

To find: price of 1 youth ticket

Brianna's family spent $134 on 2 adult tickets and 3 youth tickets at an amusement park

So we can frame a equation as:

2 adult tickets x price of 1 adult ticket + 3 youth tickets x price of 1 youth ticket = 134

[tex]2 \times a + 3 \times y = 134[/tex]

2a + 3y = 134 ---- eqn 1

Max's family spent $146 on 3 adults tickets and 2 youth tickets

So we can frame a equation as:

3 adult tickets x price of 1 adult ticket + 2 youth tickets x price of 1 youth ticket = 146

[tex]3 \times a + 2 \times y = 146[/tex]

3a + 2y = 146 ----- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "y"

Multiply eqn 1 by 3

6a + 9y = 402 ---- eqn 3

Multiply eqn 2 by 2

6a + 4y = 292 ----- eqn 4

Subtract eqn 4 from eqn 3

6a + 9y = 402

6a + 4y = 292

( - ) -------------------

5y = 110

y = 22

Thus the price of 1 youth ticket is $ 22

Answer:

Horizontal line or the technical name: Zero slope.

Step-by-step explanation:

When graphed, the line comes out horizontally, and horizontal lines are called zero slopes.

Step-by-step explanation:

a - any real number

This is the equation of the horizontal line passing through the points in the form (x, a), where x is any real number.

A slope of a horizontal line is equal 0.

It's a horizontal line passing through the points in the form (x, 7).

Look at the picture.

Answer:

b. m can be any positive real number.

Step-by-step explanation:

The value of m can be any positive real number. The correct answer is option b) m can be any positive real number.

Step 1

To determine the value of m that makes the ranges of [tex]\( f(x) = m^x \)[/tex] and [tex]\( g(x) = x^m \)[/tex] the same, we need to analyze the ranges of both functions.

Analyzing [tex]\( f(x) = m^x \)[/tex] :

- If [tex]\( m > 0 \)[/tex], [tex]\( m^x \)[/tex] is an exponential function.

 - For [tex]\( m > 1 \)[/tex], [tex]\( f(x) = m^x \)[/tex] increases and its range is [tex]\( (0, \infty) \)[/tex].

 - For [tex]\( 0 < m < 1 \)[/tex], [tex]\( f(x) = m^x \)[/tex] decreases and its range is also [tex]\( (0, \infty) \)[/tex].

Step 2

Analyzing [tex]\( g(x) = x^m \)[/tex] :

- The range of [tex]\( x^m \)[/tex] depends on whether m is positive or negative:

 - For positive m :

   - When [tex]\( m = 1 \)[/tex], [tex]\( g(x) = x \)[/tex], the range is all real numbers, [tex]\( \mathbb{R} \)[/tex].

   - When [tex]\( m > 1 \)[/tex] or [tex]\( 0 < m < 1 \)[/tex], the function is defined for [tex]\( x > 0 \)[/tex] and its range is [tex]\( (0, \infty) \)[/tex] .

 - For negative m :

   - The function [tex]\( x^m \)[/tex] is undefined for [tex]\( x = 0 \)[/tex] and for negative x, and thus its range is [tex]\( (0, \infty) \)[/tex].

Both [tex]\( f(x) = m^x \)[/tex] and [tex]\( g(x) = x^m \)[/tex] have the range [tex]\( (0, \infty) \)[/tex] for any positive [tex]\( m \)[/tex], but for any negative m, [tex]\( g(x) \)[/tex] is undefined at zero and for negative x.

The value of m can be any positive real number (option b).

Complete question : If the range of f(x) = ^mx and the range of g(x) = m ^ x are the same, which statement is true about the value of m?

a) m can only equal 1.

b) m can be any positive real number.

c) m can be any negative real number.

d) m can be any real number.

42+n/6

Step-by-step explanation:

Answer:

q  =  − 1 \6

Step-by-step explanation:

q  =  − 0.1 6 ¯  6

Answer:

40

Step-by-step explanation:

Evaluate g(- 3) then use the value obtained to evaluate h(x)

g(- 3) = 2(- 3) = - 6, then

h(- 6) = (- 6)² + 4 = 36 + 4 = 40

Turn both into improper fractions.

6 1/3 = 19/3

4 1/9 = 37/9

Find common denominators

19/3 = 57/9

37/9

Subtract.

57/9 - 37/9 = 20/9

Turn back into a mixed number.

20/9 = 2 2/9

Best of Luck!

Answer:

2 2/9

Step-by-step explanation:

Cuz yeah

Answer:

Margaret O'Connor has the highest votes.. 12,926.

Leonard Hansen has the least votes.. 12,409

Final answer:

Margaret O'Connor received the most votes with 12,926, while Leonard Hansen received the least with 12,409. Margaret would win in a plurality election, but a runoff would be needed in a majority election as no candidate won over 50% of the votes.

Explanation:

In the results of an election for mayor, which candidate received the most votes and which received the least?

Margaret O'Connor received the most votes with a total of 12,926. Leonard Hansen received the least number of votes, totaling 12,409. If this were a plurality election, Margaret O'Connor would be declared the winner since she has more votes than any other candidate. In a majority election, a runoff would likely be necessary because no single candidate received more than 50% of the votes.

Answer:

∠CPB is an acute angle.

Step-by-step explanation:

Firstly, lets go over what an acute angle is. An acute angle is any angle that is less than 90°.

In the problem, we are told that ∠APE is a right angle. This means that it is 90°.

As ∠APE and ∠BPD are vertical angles, they must have the same measure. This means that ∠BPD is also 90°

As ∠BPD has the line PC in the middle of it, this angle could be split into ∠CPB and ∠CPD. These two angles must add up to be the same as ∠BPD, which is 90°. As these two angles must add to be 90° they must be less than 90°. This means that both ∠CPB and ∠CPD are acute angles.

As ∠CPD is not one of the options for the question, ∠CPB is the only correct answer.

Acute angles measure less than 90°. Among the options, only C) Angle CPB fulfills this condition. It's the only angle clearly smaller than a right angle in the image.

An acute angle is an angle that measures less than 90 degrees. In the image you sent, only one of the angles measures less than 90 degrees.

-angle APE is a right angle, which measures exactly 90 degrees.

-angle CPE and angle APC are both obtuse angles, which measure more than 90 degrees but less than 180 degrees.

-angle CPB is the only angle that measures less than 90 degrees, so it is the only acute angle.

Therefore, the answer is C) Angle CPB.

Answer:

20

Step-by-step explanation:

120x=100*24

x= 100*24/120

Answer:

[tex]x^2=3x(x-2)[/tex]

Step-by-step explanation:

Let length of square be "x"

According to problem,

Length of Rectangle is 3 times, so

Length of Rectangle = 3x

Also,

Width of rectangle is 2 units less than length of square, so

Width of Rectangle = x - 2

Now, area of square is  Side * Side

and

area of rectangle = length * width

Hence,

Area of Square = [tex]x^2[/tex]

Area of Rectangle = [tex](3x)(x-2)[/tex]

If they are equal, we can write:

[tex]x^2=3x(x-2)[/tex]

Answer:

Step-by-step explanation:

Answer:

b = 6.7cm

Step-by-step explanation:

The law of sines is:

[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex] OR [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

Each section represents an angle (capital) and its opposite side (lowercase). When you use it, only use two sections at a time. You may have one missing piece of information when using it. Use the formula that puts the missing information in the numerator (top).

This problem:

We are given one set of information, 8cm and 55°. This can be "a" and "A" (not labelled).

We need angle B to find side b.

Since we are given two of the three angles in the triangle, and the sum of all interior angles of any triangle is 180°, we can find the missing angle.

∠B = 180° - (∠A + ∠C)

∠B = 180° - (55° + 82°)

∠B = 43°

Use the law of sines with sections "A" and "B", with the lowercase letters in the top.

[tex]\frac{a}{sinA} =\frac{b}{sinB}[/tex]  Substitute known measurements

[tex]\frac{8cm}{sin(55)} =\frac{b}{sin(43)}[/tex]  Rearrange to isolate "b"

[tex]b = \frac{8cm}{sin(55)}X{sin(43)}[/tex]  Solve, degree mode on calculator

[tex]b = 6.660...cm[/tex] Exact answer

[tex]b = 6.7cm[/tex] Rounded to nearest tenth

Therefore side b is 6.7cm.

6 goes into 49 8 times with a remainder of 1.

Answer:

A convenience sample is used. The sample could be biased because it limits the population to listeners of that radio station at a certain time. Callers may be more likely to have a strong opinion on the issue.

Answer:

A convenience sample is used. The sample could be biased because it limits the population to listeners of that radio station at a certain time. Callers may be more likely to have a strong opinion on the issue.

Step-by-step explanation:

It limits population to listeners of that radio station at only a particular time