What is a point-slope equation of the line with the slope -13 that goes through the point (5,7)?

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Answer:

B) 5.4 cm 2

Step-by-step explanation:

A==1/2 bh

5.4*2=10.8

10.8/2=5.4

Answer: X+5

Step-by-step explanation:

When you take out the 9 it should be 9(x+5) and when you take out the 9x on the bottom it gives you (x+5)+20 therefore x+5 is your GCF.

I hope this helps :)

The greatest common factor (GCF) of the numerator 9x+45 and the denominator x^2 +9x+20 of the provided rational expression is x+5.

The greatest common factor (GCF) is found by factoring both the numerator and the denominator and then identifying the largest factor that appears in both. For the provided rational expression 9x+45 over x2 +9x+20, let's factor both parts:

Comparing both factored forms, we can see that x+5 appears in both the numerator and the denominator, and it is the largest factor common to both. Therefore, the GCF of the numerator and the denominator is x+5.

Answer:

87n+6*55n

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

2(15) - 3(4)

= 30 - 12

= 18

Answer:

Frequency = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

We are given the following function and we are to find its frequency:

[tex]f (x) = 3 cos (\pi x) -2[/tex]

We know that the standard form of cosine function is [tex]y=Acos (Bx)+c[/tex]

where [tex]A[/tex] is the amplitude, [tex]B=\frac{2\pi}{\text{Period}}[/tex] while [tex]c[/tex] is the mid line.

Frequency is given by:

[tex]F=\frac{1}{P}[/tex] where [tex]F[/tex] is frequency and [tex]P[/tex] is the period.

Finding period by comparing the given function:

[tex]y=3cos(\pi x)-2[/tex]

[tex]Period - B = \pi[/tex]

Substituting B to get:

[tex]\pi =\frac{2\pi}{\text{Period}}[/tex]

[tex]\text{Period}=\frac{2\pi}{\pi}=2[/tex]

So, Period = 2.

Since frequency is [tex]\frac{1}{P}[/tex], therefore

Frequency = [tex]\frac{1}{2}[/tex]

The frequency is T / (2π).

To find the frequency of the function f(x) = 3 cos(T x) – 2, start by recognizing the standard form of a cosine function, which is f(x) = A cos(Bx + C) + D. Here, A, B, C, and D are constants with specific roles.

        f = ω / (2π)

        f = T / (2π)

Therefore, the frequency of the function f(x) = 3 cos(Tx) – 2 is T / (2π).

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{4}{ h},\stackrel{1}{ k})\qquad \qquad radius=\stackrel{2}{ r} \\\\\\ (x-4)^2+(y-1)^2=2^2\implies (x-4)^2+(y-1)^2=4[/tex]

Answer:

The airplane gains speed when it takes off. Then it begins to lose speed at the same rate. The plane then stays at the same speed the rest of the time.

Answer:

$0.20

Step-by-step explanation:

A dozen of pencils = $2.40

1 pencil = $2.40 ÷ 12 = $0.20

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ALSO, DO HAVE A GREAT DAY ;)

The unit price per pencil is determined by dividing the total cost of the pencils ($2.40) by the total number of pencils (12), giving a result of $0.20 per pencil.

To find the unit price per pencil, you would divide the total cost by the total number of items.

In this case, the total cost is $2.40 and there are twelve pencils, so the calculation is $2.40 ÷ 12.

This will give you the unit price per pencil.

Using the numbers provided, $2.40 (the total cost) divided by 12 (the total number of pencils) equals $0.20.

So, the unit price of a pencil is $0.20.

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Answer:

The page numbers are 36 and 37.

Step-by-step explanation:

n + (n + 1) = 73

2n + 1 = 73

n = (73 - 1)/2

= 72/2 = 36

Follow below steps:

The sum of the page numbers on the facing pages of a book is 73. To solve this, we need to establish that facing pages in a book are always one number apart. If we call one page number x, then the other page number is x+1 because page numbers are consecutive.

Now, we can create the equation x + (x+1) = 73 to find the value of x. Solving this equation, we get:

2x + 1 = 73

2x = 73 - 1

2x = 72

x = 72 / 2

x = 36

Since x is the lower of the two page numbers, then the pages are 36 and 37.

Answer:

x=-2 x=-8

Step-by-step explanation:

x2 + 10x + 16 = 0

(x + 2)(x + 8) = 0

x + 2 = 0 or x + 8 = 0

x = and x =

x=-2 x=-8

Answer:

.0075 (hope this help; let me know if not)

Step-by-step explanation:

The operation is + and the signs of the numbers are opposite so we have to subtract. The bigger number has positive sign in front if so we do 1.2-1.125=1.200-1.125

I'm going to line up

1.200

-1.125

---------

If you have 200 and you take about 125... 75 should beleft

so

1.200

-1.125

---------

0.075

Answer:

Slope = -3

Step-by-step explanation:

Slope of a straight line graph is given by; change in y ÷ change in x

Slope = [tex]\frac{-3 - 6}{2 - -1}[/tex] = [tex]\frac{-9}{3}[/tex] = -3

[tex]\text{Hey there!}[/tex]

[tex]\text{The formula should look like: m =\ }\bf{\frac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\text{y}_2=-3\\\\\text{y}_1=6\\\\\text{x}_2=2\\\\\text{x}_1=-1[/tex]

[tex]\frac{-3-6}{2-(-1)}[/tex]

[tex]\text{-3 - 6 = -9}[/tex]

[tex]\frac{-9}{2-(-1)}[/tex]

[tex]\text{2-(-1)=2 + 1 = 3}[/tex]

[tex]\frac{-9}{3}=-9\div3=-3[/tex]

[tex]\boxed{\boxed{\text{Thus your answer/ slope is: -3}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

[tex]\large\boxed{\dfrac{V_{cone}}{V_{prism}}=\dfrac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a cone:}\ V_{cone}=\dfrac{1}{3}B_cH_c\\\\B_c-base\ area\ of\ a\ cone\\H_c-height\ of\ a\ cone\\\\\text{The formula of a volume of a prism:}\ V_{prism}=B_pH_p\\\\B_p-base\ area\ of\ a\ prism\\H_p-height\ of\ a\ prism\\\\\text{The cone and the prism have the same base area and height.}\\\text{Therefore}\\\\V_{cone}=\dfrac{1}{3}BH\ \text{and}\ V_{prism}=BH\\\\\text{The ratio of the volume of the cone to the volume of the prism:}[/tex]

[tex]\dfrac{V_{cone}}{V_{prism}}=\dfrac{\frac{1}{3}BH}{BH}=\dfrac{1}{3}[/tex]

Answer:

See the image attached for answer

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), hence

F(- 1, 9) → F'(- 1, - 9)

G(- 2, 1) → G'(- 2, - 1)

H(- 7, 4) → H'(- 7, - 4)

The second option is the best representation of the question.

Fractions represent equal parts of a whole or a collection.

Explanation:

The whole quantity = 1

Divide this whole by 4 and separate it into four equal parts of 1 / 4

Combine two of these four parts to make 1 / 2

Hence, the second option is the best representation of the given question.

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Answer:

cos46°

Step-by-step explanation:

Using the co function identity

sin x° = cos(90 - x)°, hence

sin44° = cos(90 - 44)° = cos46°

Answer:  The correct option is (b) cos 46°.

Step-by-step explanation:  Given that when solving for x, the sine of 44º is used.

We are to select the other angle and trigonometric function that could be used to solve for x.

We know that,

the sine of any acute angle is equal to the cosine of its complement.

That is,

if y denotes the measure of any acute angle, then we have

[tex]\sin y=\cos(90^\circ-y).[/tex]

Therefore, if y = 44°, then we get

[tex]\sin 44^\circ=\cos(90^\circ-44^\circ)=\cos 46^\circ.[/tex]

Thus, the other angle and the  trigonometric function that could be used to solve for x is cos 46°.

Option (b) is CORRECT.

Answer:

The fraction = 9/35

To find the fraction, calculate the sum of 5 1/3 and 6 1/3, which is 35/3, then divide the final product, 3, by this sum. The fraction that when multiplied by the sum equals 3 is 9/35.

The question asks us to find the fraction when the product of the fraction and the sum of 5 1/3 and 6 1/3 is 3.

First, let's calculate the sum of 5 1/3 and 6 1/3:

5 1/3 can be written as (5*3 + 1)/3 = 16/3.

6 1/3 can be written as (6*3 + 1)/3 = 19/3.

Adding these fractions, we get (16/3) + (19/3) = (35/3).

So, we have the equation:

Fraction  imes (35/3) = 3

To find the unknown fraction, we divide both sides by 35/3:

Fraction = 3 / (35/3) = 3  imes (3/35) = 9/35

Therefore, the fraction we are looking for is 9/35.

[tex]\displaystyle\\\sum_{n=2}^6\dfrac{(n-1)!}{2}=\dfrac{(2-1)!}{2}+\dfrac{(3-1)!}{2}+\dfrac{(4-1)!}{2}+\dfrac{(5-1)!}{2}+\dfrac{(6-1)!}{2}=\\\\=\dfrac{1}{2}+\dfrac{2}{2}+\dfrac{6}{2}+\dfrac{24}{2}+\dfrac{120}{2}=0.5+1+3+12+60=76.5[/tex]

Answer:

D. 76.5

Step-by-step explanation:

The summation sign means that it is the sum of the expression for all values of n upto 6.

n = 2 below the summation sign means that n starts from 2.

∑(n-1)!/2 from n= 2 to n=6

= (2-1)!/2 + (3-1)!/2 + (4-1)!/2 + (5-1)!/2 + (6-1)!/2

= 1!/2 + 2!/2 + 3!/2 + 4!/2 + 5!/2

= 1/2 + 2*1/2 + 3*2/2 + 4*3*2/2 + 5*4*3*2/2

= 1/2 + 2/2 + 6/2 + 24/2 + 120/2

= 0.5 + 1 + 3 + 12 + 60

= 76.5

To find out the difference between her highest score and lowest score, we can deduct the amount of highest score by lowest score.

Her highest score: 135

Her lowest score: 98

Her highest score is higher than the lowest score by:

135 - 98

=37

Therefore, her highest score is 38 more than her Lowest score.

Hope it helps!

Answer: Inconsistent.

Step-by-step explanation:

The  equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Solve for "y" in each equation:

Equation 1

[tex] x=-5-y\\\\y=-x-5[/tex]

Equation 2

[tex]4+y=-x+3\\\\y=-x+3-4\\\\y=-x-1[/tex]

You can notice that the slope of the Equation 1 is:

[tex]m_1=-1[/tex]

And the slope of the Equation 2 is:

[tex]m_2=-1[/tex]

Observe that [tex]m_1=m_2[/tex], then you can conclude that the lines are parallel and the System of equations has No solution.

When there is no solution the classification  of the system of equations is: "Inconsistent".

Answer:

B and C

Step-by-step explanation:

The denominator of the rational expression cannot be zero as this would make it undefined.

Equating the denominator to zero and solving gives the values that x cannot be.

solve

3x² - 75 = 0 ( add 75 to both sides )

3x² = 75 ( divide both sides by 3 )

x² = 25 ( take the square root of both sides )

x = ± [tex]\sqrt{25}[/tex] = ± 5 → B and C

Answer:

12.75 oz

Step-by-step explanation:

1 gallon is equivalent to 64 oz.

Writing and solving an equation of ratios, we get:

 1.5 oz       1 gal

----------- = ------------

     x          8.5 gal

Here we must cross-multiply to solve for x.

x(1 gal) = (1.5 oz)(8.5 gal) = 12.75 oz

Thus, x = 12.75 oz of cleaning product must be added to 8.5 gal of water to create the desired solution.

To make an all-purpose cleaner, you need 12.75 ounces of cleaner for 8.5 gallons of water.

This is determined by multiplying the ratio of 1.5 ounces per gallon by 8.5 gallons.

follow these steps:

Therefore, 12.75 ounces of cleaner will be added to 8.5 gallons of water.

Answer:

two ten-thousandths

Step-by-step explanation:

You would write 0.0002 as two ten-thousandths. However some people say it the easy way, zero point zero zero zero two.

Hope this helps!

Answer:

It would be 2 ten thousandths.

Step-by-step explanation:

It goes tenths, hundredths, thousands, 10 thousands in order as you move right 1 place value.  

Answer:

slope = [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 2) and (x₂, y₂ ) = (3, 4)

m = [tex]\frac{4-2}{3+2}[/tex] = [tex]\frac{2}{5}[/tex]

The value of (5.3x 10^4) (4.2x10^3) in scientific notation Option C 2.226 times 10^8

5.3×10^4  × 4.2 × 10^3

We multiply the numbers out front

5.3× 4.2 = 22.26

We add the exponents

10^(4+3) = 10^7

22.26×10^7

But we are not done yet because The number out front has to be between 1 and less than 10

Move the decimal 1 place to the left and add 1 to the exponent

2.226 × 10 ^(7+1)

=2.226×10^8.

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.

Scientific Notation is the expression of a number n in the form a∗10b. where a is an integer such that 1≤|a|<10. and b is an integer too. Multiplication: To multiply numbers in scientific notation, multiply the decimal numbers.

The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10. b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number.

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[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{7}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8-7]^2+[-9-(-1)]^2}\implies d=\sqrt{(-8-7)^2+(-9+1)^2} \\\\\\ d=\sqrt{225+64}\implies d=\sqrt{289}\implies d=17[/tex]

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

According to the data we have:

[tex](x_ {1}, y_ {1}) :( 7, -1)\\(x_ {2}, y_ {2}): (- 8, -9)[/tex]

Substituting:

[tex]d = \sqrt {(- 8-7) ^ 2 + (- 9 - (- 1)) ^ 2}\\d = \sqrt {(- 15) ^ 2 + (- 9 + 1) ^ 2}\\d = \sqrt {(- 15) ^ 2 + (- 8) ^ 2}\\d = \sqrt {225 + 64}\\d = \sqrt {289}\\d = 17[/tex]

Thus, the difference or distance between the points is 17

Answer:

[tex]d = 17[/tex]

Answer:

150.6 ft^9

Step-by-step explanation:

The easisest way to solve this problem is to convert everything to the same unit

1 cu yd = (27 cu ft)

1 cu in = (0,000578704 cu ft)

The expression is

6cu yd* 9cu ft * 134cu in + 1cu yd* 12cu ft* 200cu in

=  6(27 cu ft) * 9cu ft * 134(0,000578704 cu ft) + 1(27 cu ft)* 12cu ft* 200(0,000578704 cu ft)

Please see attached image below

The answer is

150.6 ft^9

Answer:

x = 0; x = 5

Step-by-step explanation:

2x² = 10x

2x² - 10x = 0

2x(x - 5) = 0

x = 0; x = 5

Answer:

The values of x for which it is true that  [tex]2x^2=10x[/tex]  are:

[tex]x = 0[/tex] and [tex]x = 5[/tex]

Step-by-step explanation:

We have the following equation

[tex]2x^2=10x[/tex]

To solve the equation subtract 10x on both sides of the equation

[tex]2x^2-10x=10x-10x[/tex]

[tex]2x^2-10x=0[/tex]

Now take the variable x as a common factor

[tex]2x(x-5)=0[/tex]

Then the equation is equal to 0 when x = 0 or when x = 5

[tex]x = 0[/tex] and [tex]x = 5[/tex]

Answer:

B.2 1/41

Step-by-step explanation:

In a perfect square trinomial of the form ax+bx+c where a, b and c are constants, the value of (b/2)²=ac

In the provided equation the value of a=1, b=-3 c=?

Therefore, (-3/2)²=c since a-the coefficient of x²=1 and 1×c=c

c=2.25= 2 1/4

Thus the trinomial x² - 3x + 2 1/4 is a perfect square.