Factor form of x^2-x-30

Answer:

4 units

Step-by-step explanation:

The distance from x=-5 to x=-1 on the line y=4 is -1-(-5) = -1+5 = 4 units.

_____

It might help to plot the points on a graph and count the grid squares between them.

Answer:

4 units

Step-by-step explanation:

on edge

Answer:

A''(7, 5)

Step-by-step explanation:

Reflection over the line x=L is the transformation ...

(x, y) ⇒ (2L-x, y)

For L=-5, this is ...

(x, y) ⇒ (-10 -x, y)

Then, translation over the line x=2 gives ...

(x, y) ⇒ (2·2 -(-10 -x), y) = (14+x, y)

So, the point (-7, 5) is translated to (14-7, 5) = (7, 5).

Answer:

y-5=3x+2

Step-by-step explanation:

1) to make up the equation through the given two points:

[tex]\frac{x+8}{-6+8}= \frac{y+1}{5+1}; \ => \ y=3x+24[/tex]

2) to change that equation according to the condition:

y-5=3x+24-5; ⇔ y-5=3x+19.

P.S. the way suggested above is not the shortest one.

Answer:  [tex]sin\ 2x=-\dfrac{240}{289}\qquad cos\ 2x=\dfrac{161}{289}\qquad tan\ 2x=-\dfrac{240}{161}[/tex]

Step-by-step explanation:

[tex]cos\ x=\dfrac{15}{17}\quad and\quad csc\ x<0\implies sin\ x=-\dfrac{8}{17}\ and\ tan\ 2x=-\dfrac{8}{15}\\\\sin\ 2x=2(sin\ x\cdot cos\ x)\\\\.\qquad =2\bigg(\dfrac{-8}{17}\cdot \dfrac{15}{17}\bigg)\\\\\\.\qquad =2\bigg(\dfrac{-120}{289}\bigg)\\\\\\.\qquad=\large\boxed{-\dfrac{240}{289}}[/tex]

[tex]cos\ 2x=cos^2\ x-sin^2\ x\\\\.\qquad=\bigg(\dfrac{15}{17}\bigg)^2-\bigg(\dfrac{-8}{17}\bigg)^2\\\\\\.\qquad=\dfrac{225}{289}-\dfrac{64}{289}\\\\\\.\qquad=\large\boxed{\dfrac{161}{289}}[/tex]

[tex]tan\ 2x=\dfrac{sin\ 2x}{cos\ 2x}\\\\\\.\qquad=\large\boxed{-\dfrac{240}{161}}[/tex]

The trigonometry values are:[tex]\mathbf{sin(2x) = -\frac{240}{289}}[/tex], [tex]\mathbf{cos(2x) =\frac{161}{289}}[/tex] and [tex]\mathbf{tan(2x)= -\frac{240}{161}}\\[/tex]

The given parameter is:

[tex]\mathbf{cos(x) = \frac{15}{17}}[/tex]

If csc(x) is less than 0, then sin(x) is less than 0.

Using the following trigonometry ratio,

[tex]\mathbf{sin^2(x) +cos^2(x) = 1}[/tex]

Substitute [tex]\mathbf{cos(x) = \frac{15}{17}}[/tex]

[tex]\mathbf{sin^2(x) +(\frac{15}{17})^2 = 1}[/tex]

Expand

[tex]\mathbf{sin^2(x) +\frac{225}{289} = 1}[/tex]

Collect like terms

[tex]\mathbf{sin^2(x) = 1 -\frac{225}{289}}[/tex]

Take LCM

[tex]\mathbf{sin^2(x) = \frac{289-225}{289}}[/tex]

[tex]\mathbf{sin^2(x) = \frac{64}{289}}[/tex]

Take square roots

[tex]\mathbf{sin(x) = \pm\frac{8}{17}}[/tex]

Recall that, the sine of the angles is negative.

So, we have:

[tex]\mathbf{sin(x) = -\frac{8}{17}}[/tex]

sin(2x) is then calculated as:

[tex]\mathbf{sin(2x) = 2sin(x)cos(x)}[/tex]

This gives

[tex]\mathbf{sin(2x) = 2 \times \frac{-8}{17} \times \frac{15}{17}}[/tex]

[tex]\mathbf{sin(2x) = -\frac{240}{289}}[/tex]

cos(2x) is then calculated as:

[tex]\mathbf{cos(2x) =cos^2(x) - sin^2(x)}[/tex]

This gives

[tex]\mathbf{cos(2x) =(\frac{15}{17})^2 - \frac{64}{289}}[/tex]

[tex]\mathbf{cos(2x) =\frac{225}{289} - \frac{64}{289}}[/tex]

Take LCM

[tex]\mathbf{cos(2x) =\frac{225 - 64}{289}}[/tex]

[tex]\mathbf{cos(2x) =\frac{161}{289}}[/tex]

Lastly, tan(2x) is calculated using:

[tex]\mathbf{tan(2x)= \frac{sin(2x)}{cos(2x)}}[/tex]

So, we have:

[tex]\mathbf{tan(2x)= \frac{-240/289}{161/289}}[/tex]

[tex]\mathbf{tan(2x)= -\frac{240}{161}}\\[/tex]

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Answer:

7

Step-by-step explanation:

Add them and hen divide by how many numbers there are

Negative exponents work like this: you have to consider the multiplicative inverse of the positive exponent.

So you have

[tex] y={-3} = \dfrac{1}{y^3},\quad x^{-5} = \dfrac{1}{x^5}[/tex]

The third expression already contains positive exponents only, you don't have to do anything.

Answer:

5 seconds

Step-by-step explanation:

The relationship between "d" and "the ground" is not described. If we assume that "d" is distance above the ground, then the rock will hit the ground when d=0. This gives rise to the quadratic equation ...

-t^2 +4t +5 = 0

-(t -5)(t +1) = 0

t = 5 or t = -1 are solutions. Only the positive solution is useful.

The rock will hit the ground after 5 seconds.

Answer: 2.3

Step-by-step explanation:

 The triangle shown in the image attached is a right triangle.

Therefore, you can calculate the missing lenght of the triangle (x), by applying the proccedure shown below:

- Apply [tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

- Substitute values.

- Solve for the missing side x.

Therefore, you obtain the following result:

[tex]tan\alpha=\frac{opposite}{adjacent}\\tan(25)=\frac{x}{5}\\x=5*tan(25)\\x=2.3[/tex]

Answer:

The value of x = 2.3 units to the nearest tenth

Step-by-step explanation:

* The triangle is right angle triangle

- We can use one of the trigonometry functions to find the value of x

∵ The measure of the one of the acute angle is 25°

∵ The length of the adjacent side of the angle is 5 units

∵ The length of the opposite side of the angle is x

- because we have opposite and adjacent of the given angle

∴ We will use the tan function

∵ tanФ = opposite to Ф/adjacent to Ф

∴ tan25 = x/5 ⇒ by using cross-multiplication

∴ x = 5 × tan25 = 2.33 ≅ 2.3

∴ The value of x = 2.3 units to the nearest tenth

put it on negative three

Answer:

Draw an open circle at -4 and shade in the line to the left of -4.

Step-by-step explanation:

x < -4 means that the number is to the left of -4 on the number line.

To graph the inequality, draw an open circle at -4 to show that the number cannot be -4.

However, the number can be anywhere to the left of -4, so you shade in that part of the line.

Answer:

ΔXOY ≅ ΔZOW ⇒ proved down

Step-by-step explanation:

* Lets study some facts on the circle

- If two chords equidistant from the center of the circles,

 then they are equal in length

* the meaning of equidistant is the perpendicular distances

 from the center of the circle to the chords are equal in length

* Lets check this fact in our problem

∵ XY and WZ are two chords in circle O

∵ OT ⊥ XY

- OT is the perpendicular distance from the center to the chord XY

∵ OU ⊥ WZ

- OU is the perpendicular distance from the center to the chord WZ

∵ OT ≅ OU

- The two chords equidistant from the center of the circle

∴ The two chords are equal in length

∴ XY ≅ WZ

* Now in the two triangles XOY and ZOW , to prove that

 they are congruent we must find one of these cases:

1- SSS ⇒ the 3 sides of the 1st triangle equal the corresponding

               sides in the 2nd triangle

2- SAS ⇒ the two sides and the including angle between them

                in the 1st triangle equal to the corresponding sides and

                including angle in the 2nd triangle

3- AAS ⇒ the two angles and one side in the 1st triangle equal the

                corresponding angles and side in the 2nd triangle

* Lets check we will use which case

- In the two triangles XOY and ZOW

∵ XY = ZW ⇒ proved

∵ OX = OZ ⇒ radii

∵ OY = OW ⇒ radii

* This is the first case SSS

∴ ΔXOY ≅ ΔZOW

Answer: Darren’s range is 20 points.

Step-by-step explanation: A range is the difference between the highest score and the lowest score. With the lowest score being 280 and the highest score being 300, the difference is 20 points for the range.

Answer: 14 gallons

Step-by-step explanation:

Let's call the total gallons Abdul's tank can hold x.

Then, based on the information given in the problem, you can write the following expression:

[tex]\frac{1}{5}x+7=\frac{7}{10}x[/tex]

Therefore, when you solve for x, you obtain the following result:

[tex]\frac{1}{5}x+7=\frac{7}{10}x\\\\\frac{1}{5}x-\frac{7}{10}x=-7\\\\-\frac{1}{2}x=-7\\\\-x=(-7)(2)\\x=14[/tex]

Abdul's tank can hold 14 gallons of gas. This is determined by establishing that 7 gallons brought the tank level from 1/5 to 7/10 full and calculating that 7 gallons is equivalent to half the tank's total capacity.

When solving for how many gallons Abdul's tank can hold, we need to create an equation based on what we know from the problem.

Originally, the gas tank is 1/5 full. After adding 7 gallons of gas, it is 7/10 full. The difference between 7/10 and 1/5 (which is the same as 2/10) gives us the amount of gas that was added to reach 7/10 full from 1/5 full. Therefore, 7/10 - 2/10 equals 5/10 or 1/2. This means the 7 gallons added filled up half of the tank's capacity.

If 7 gallons represent 1/2 of the tank's capacity, then the full capacity (C) can be found by doubling the 7 gallons:

Therefore, Abdul's tank can hold 14 gallons.

Answer:

[tex]f^{-1}(x)=(+/-)\sqrt{4-x}[/tex]

Step-by-step explanation:

we have

[tex]f(x)=4-x^{2}[/tex]

Let

y=f(x)

[tex]y=4-x^{2}[/tex]

Exchange the variables x for y and y for x

[tex]x=4-y^{2}[/tex]

Isolate the variable y

[tex]y^{2}=4-x[/tex]

square root both sides

[tex]y=(+/-)\sqrt{4-x}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=(+/-)\sqrt{4-x}[/tex] -----> inverse function

Answer:

f⁻¹(x) = ±√x-4

Step-by-step explanation:

We have given  a function.

f(x) = 4-x²

We have to find the inverse of given function.

Putting y = f(x) in given equation, we have

y  = 4-x²

Adding -4 to both sides of equation, we have

y-4 = 4-x²-4

y-4 = -x²

x² = 4-y

Taking square root to both sides of above equation, we have

x = ±√4-y

Putting x = f⁻¹(y) , we have

f⁻¹(y) = ±√4-y

Replacing y by x, we have

f⁻¹(x) = ±√x-4 which is the answer.

Hey there!

The correct answer is D. Nine Hundred Thousand

This is the place it’s in => 900,000

Hope this helps you!

God bless ❤️

Brainliest would be appreciated!

xXxGolferGirlxXx

Answer:4

Step-by-step explanation:4/5 / 1/10= 4/5*10/1=20/5=4

4/5 divided by1/10 equals 4/5 times 10/1 which is 40/5=8

Answer:

1/2 inch

Step-by-step explanation:

The area of a rectangle is the product of its length and width. So, the length and width of the photo will give a product of 24 when they are multiplied together.

One set of factors of 24 is 4 and 6, each of which is 1 unit less than the 5 and 7 dimensions of the paper on which the photo is printed. Hence a 1/2-inch border all around will result in a printed photo that is 4x6 on a 5x7 piece of paper.

___

If you want to write and solve equations, you can let b represent the border width. Then the photo area is ...

(5 -2b)(7 -2b) = 24

35 -24b +4b^2 = 24

4b^2 -24b +11 = 0

(2b -1)(2b -11) = 0

Solutions to this quadratic are b = 1/2, b = 11/2. The only viable solution is b = 1/2.

The border is 1/2 inch wide.

Answer:

28.8 ft

Step-by-step explanation:

SOH CAH TOA reminds you that ...

Tan = Opposite/Adjacent

The height to the top of the antenna is opposite the angle of elevation, and the distance to the building is adjacent. So, we have ...

tan(58°) = (160 ft +antenna height)/(118 ft)

(118 ft)·tan(58°) = 160 ft + antenna height . . . . . . . multiply by 118 ft

188.8 ft - 160 ft = antenna height = 28.8 ft . . . . . . subtract 160 ft, evaluate

The height of the antenna is 28.8 ft above the top of the building. (The total height of building + antenna is 188.8 ft.)

The problem can be solved using trigonometry. The tangent of the angle of elevation equals the total height (building plus antenna) divided by the distance from the point to the base of the building. Subtract the building's height from the total height to get the antenna's height.

To find the height of the antenna, we need to solve a right triangle problem using trigonometry. We know that the building is 160 Ft tall, and the angle of elevation to the top of the antenna is 58 degrees from a point 118 Ft from the base of the building. This forms a right triangle, with the building's height as one side, the horizontal distance of 118 Ft as another, and the antenna height as the hypotenuse. We can use the tangent of the angle to calculate the height of the antenna:

tangent(58) = opposite/adjacent

Here, 'opposite' represents the antenna's total height above the ground and 'adjacent' the distance from the point to the base of the building. So:

tangent(58) = total height / 118

To find the total height, we rearrange the formula:

total height = tangent(58) * 118

But remember the total height includes the building's height, so we subtract that to get the antenna's height:

antenna's height = total height - height of the building

Which, after substituting the known values, gives us the antenna's height.

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I guess you mean

[tex]\sec^6x(\sec x\tan x)-\sec^4x(\sec x\tan x)=\sec^5x\tan^3x[/tex]

On the left side, we have a common factor of [tex]\sec^4x(\sec x\tan x)=\sec^5x\tan x[/tex], so that

[tex]\sec^6x(\sec x\tan x)-\sec^4x(\sec x\tan x)=\sec^5x\tan x(\sec^2x-1)[/tex]

Recall that

[tex]\sec^2x=1+\tan^2x[/tex]

from which it follows that

[tex]\sec^5x\tan x(\sec^2x-1)=\sec^5x\tan x\tan^2x=\sec^5x\tan^3x[/tex]

Answer: [tex](x+10)^2+(y+6)^2=121[/tex]

Step-by-step explanation:

The equation of a circle in the general form is:

 [tex]ax^{2}+by^2+cx+dy+e=0[/tex]

The equaton of  a circle in standard form is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where the center is at (h, k) and r is the radius

To write the equation of a circle from general form to standard form, you must complete the squaare, as you can see below:

1- Given the equation in general form:

[tex]x^{2}+y^2+20x+12y+15=0[/tex]

2- Complete the square:

-Group the like terms and move the constant to the other side.

- Complete the square on the left side of the equation.

- Add the same value to the other side.

Then you obtain:

[tex](x^{2}+20x)+(y^2+12y)=-15\\(x^2+20x+(\frac{20}{2})^2)+(y^2+12y+(\frac{12}{2})^2)=-15+(\frac{20}{2})^2+(\frac{12}{2})^2\\\\(x+10)^2+(y+6)^2=-15+100+36\\(x+10)^2+(y+6)^2=121[/tex]

Answer:  overspending $50 per month

Step-by-step explanation:

Income (Money In):           Expenses (Money out):

              $800                   Rent = $400

                                          Food = $200

                                          Gas   = $100

                                  Insurance = $ 50

                                      Phone = $100  

TOTAL = $800             TOTAL = $850

Jessie has more money out than money in so she is overspending

by $850 - $800 =  $ 50

Answer:

158

Step-by-step explanation:

Hey there!

503 - 345 = 158

Therefore, the answer is 158

Hope this helps you!

God bless ❤️

xXxGolferGirlxXx

Answer:

The vale of 6 is 'Thousands'

Answer:

Place value of 6 is thousand and tens.

Step-by-step explanation:

6560   is the number where 6 has 2 place value

(1) at thousands

(2) at tens .

6,560 = 6000+500+60

          = 6x1000 +5x100+6x10

              Here we can see that 6 is at two places

              thousand and tens

all are corespondent to each lateral line

Answer:

73.19

Step-by-step explanation:

4 * (1/2)* (6.5) * (5.63)

Answer:

-5 2/3 points per minute

Step-by-step explanation:

change / time = (-85 points)/(15 minutes) = -17/3 points/minute = -5 2/3 points/minute

the next number can be 34 as the sequence goes in difference of 1,2,3,4,5,6,5,2,1,1so I think it will continue with sequence 1

The value of the next number is 34

A sequence is defined as an arrangement of numbers in a particular order. On the other hand, a series is defined as the sum of the elements of a sequence.

There are two types of sequence, the arithmetic sequence and geometry sequence.

Example of arithmetic sequence is 2,4,6 ,8, 10... and we get the next number by adding 2. Also

Example of geometry sequence is 2,4,8,16,32... we get the next number by multiplying 2.

From the sequence above the next number will be 34 because the last three number has a common difference of 1.

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Answer:

  D. A table of values represents points that lie on the graph of a linear function.

Step-by-step explanation:

A table of values can represent any relation, not necessarily a linear function. Statement D is not always true.

Statement D, 'A table of values represents points that lie on the graph of a linear function,' is not always true. A table of values could represent various types of functions or data sets. All other statements are correct for a linear function.

Let's analyze each of the given statements to identify which one is not always true:

Therefore, the correct answer is D. A table of values represents points that lie on the graph of a linear function.

Answer with explanation:

1.→Answer Written by Jack is Incorrect.

[tex]m^n=\text{exponent}\\\\\frac{x^a}{x^b}=x^{a-b}\\\\x^a \times x^b=x^{a+b}[/tex]

Error:Instead of subtracting powers,jack has added powers of same exponent.

Correct Solution:

    [tex]=\frac{54\times x^9 \times y^8}{6\times x^3 \times y^4}\\\\ \text{Here ,correct answer should be}=9\times x^{9-3} \times y^{8-4}\\\\=9 x^6 y^4[/tex]

2.Initial Amount, a=78,000

Rate =3 %=0.03

Error: Rate percent should be divided by 100, to get the value of b.

So, b= 0.03

Correct Solution:

Exponential growth is given by

  [tex]y=a\times b^x\\\\y=78,000\times (0.03)^x[/tex]

3.The Expression is

[tex]m^2-13 m -30\\\\a=1, b= -13,c= -30\\\\ac=-30\\\\b=-13= -15 +2,as -15 \times 2 = -30\\\\\text{Equivalent expression}=(m-15)(m+2)[/tex]

Option A: (m-15)(m+2)  

[tex]4.\rightarrow x^n=(x^3) \times (x^{-17})\\\\=\text{using law of indices},x^a\times x^b=x^{a+b}\\\\x^n=x^{3-17}\\\\x^n=x^{-14}\\\\n=-14[/tex]  

The equivalent of an expression is the other form of the expression.

The equivalent expression is: [tex]\mathbf{x^{-14}}[/tex]

The expression is given as:

[tex]\mathbf{(x^3)(x^{-17})}[/tex]

Remove brackets

[tex]\mathbf{(x^3)(x^{-17}) = x^3 \times x^{-17}}[/tex]

Apply law of indices

[tex]\mathbf{(x^3)(x^{-17}) = x^{3-17}}[/tex]

[tex]\mathbf{(x^3)(x^{-17}) = x^{-14}}[/tex]

Hence, the equivalent expression is: [tex]\mathbf{x^{-14}}[/tex]

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Answer:

Step-by-step explanation:

With the variables defined as above, the total amount spent is ...

  x + y = 56 . . . . . the amount spent on accessories and clothes

When the amount spent on accessories is subtracted from the amount spent on clothes, the result is $18, so we can write another equation that says this:

  y - x = 18

Both equations can be rearranged to put y alone on the left. In the first case, we add -x to both sides of the equation. In the second case, we add x to both sides of the equation.

Answer:

B.) (x+3, y-7)

Step-by-step explanation:

x-coordinates increase farther to the right of the y-axis. Increasing the x-coordinate of a point by 3 will move the point 3 units to the right.

y-coordinates increase farther above the x-axis. Decreasing the y-coordinate of a point by 7 will move the point 7 units down.

To translate a point (x, y) 3 units right and 7 units down, the new coordinates need to be ....

(x +3, y-7) . . . . . . . . matches selection B