How many distinct factors does 75 have?

Answer:

c=1`8h

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\underline{+\left\{\begin{array}{ccc}5x+3y=13\\-5x-12y=23\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-9y=36\qquad\text{divide both sides by (-9)}\\.\qquad y=-4\\\\\text{put the value of y to the first equation:}\\\\5x+3(-4)=13\\5x-12=13\qquad\text{add 12 to both sides}\\5x=25\qquad\text{divide both sides by 5}\\x=5[/tex]

Originally there are 6 cats

5 run away so take 5 away from 6:

6 - 5 = 1

This means there is only one cat left, but now 10 more cats came:

1 + 10 = 11

There are 11 cats

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

11.

Step-by-step explanation:

6 - 5 + 10

= 11.

Answer:

7 pages

Step-by-step explanation:

this is because 2 times 3 equals 6 and plus one equals 7

Final answer:

Ashlee starts with 1 page of notes and will take 3 pages of notes for each hour of class she attends. After attending 2 hours of class, she will have a total of 7 pages of notes in her notebook.

Explanation:

The question involves solving a simple algebraic equation to find the total number of pages of notes Ashlee will have after attending 2 hours of class. Ashlee starts with 1 page of notes and takes 3 pages of notes for each hour of class. To find the total number of pages of notes, we can use the equation:

Total pages = Initial pages + (Pages per hour × Number of hours)

Substituting the given values into the equation:

Total pages = 1 + (3 × 2) = 1 + 6 = 7 pages

Therefore, Ashlee will have 7 pages of notes in her notebook after attending 2 hours of class.

Answer:

See below

Step-by-step explanation:

I don't know if this helps you, but I wanted to get you an answer as quickly as I could in case you needed it really soon.  This is what a graph of this function would look like.  Choose the answer that looks like this one.

I really hope this helps!

The graph for the given function is plotted. The graph of a function is represented by y = f(x).

The given function is f(x) = x² + 4x - 1

Consider x values as {-5, -4, -3, -2, -1, 0, 1, 2}

Substituting these values in the function for finding y-values

When x = -5

y = f(-5) = (-5)² + 4(-5) -1 = 4

∴ (-5, 4)

When x = -4

y = f(-4) = (-4)² + 4(-4) -1 = -1

∴ (-4, -1)

When x = -3

y = f(-3) = (-3)² + 4(-3) -1 = -4

∴ (-3, -4)

When x = -2

y = f(-2) = (-2)² + 4(-2) -1 = -5

∴ (-2, -5)

When x = -1

y = f(-1) = (-1)² + 4(-1) -1 = -4

∴ (-1, -4)

When x = 0

y = f(0) = 0 + 4(0) -1 = -1

∴ (0, -1)

When x = 1

y = f(1) = 1² + 4(1) -1 = 4

∴ (1, 4)

When x = 2

y = f(2) = 2² +4(2) -1 = 11

∴ (2, 11)

Plotting these points in the graph and connecting them gives a curve (parabola).

Checking for the vertex:

f(x) = a(x - h)² + k

⇒ x² + 4x - 1

⇒ (x - (-2))² -5

So, the vertex is (h, k) = (-2, -5).

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The augmented matrix for this system is

[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\4&1&5&30\\3&-1&-1&4\end{array}\right][/tex]

Subtract row 1 from row 2, and subtract 3(row 1) from 4(row 3):

[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\0&4&4&8\\0&5&-7&-50\end{array}\right][/tex]

Multiply row 2 by 1/4:

[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\0&1&1&2\\0&5&-7&-50\end{array}\right][/tex]

Subtract 5(row 2) from row 3:

[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\0&1&1&2\\0&0&-12&-60\end{array}\right][/tex]

Multiply row 3 by -1/12:

[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\0&1&1&2\\0&0&1&5\end{array}\right][/tex]

While this isn't exactly RREF, you can already solve the system quite easily:

[tex]\boxed{z=5}[/tex]

[tex]y+z=2\implies\boxed{y=-3}[/tex]

[tex]4x-3y+z=22\implies4x=8\implies\boxed{x=2}[/tex]

We can confirm this solution by continuing with the row reduction. Subtract row 3 from row 2:

[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\0&1&0&-3\\0&0&1&5\end{array}\right][/tex]

Subtract -3(row 2) and row 3 from row 1:

[tex]\left[\begin{array}{ccc|c}4&0&0&8\\0&1&0&-3\\0&0&1&5\end{array}\right][/tex]

Finally, multiply row 1 by 1/4:

[tex]\left[\begin{array}{ccc|c}1&0&0&2\\0&1&0&-3\\0&0&1&5\end{array}\right][/tex]

and we end up with [tex]\boxed{(x,y,z)=(2,-3,5)}[/tex], as before.

Final answer:

To solve for x, y, and z, the given system of equations is represented as an augmented matrix, then reduced to its reduced row-echelon form through row operations, from which the solutions can be directly obtained.

Explanation:

To solve the system of equations by finding the reduced row-echelon form of the augmented matrix, we first write the system as an augmented matrix:

[ 4 -3  1 | 22 ]
[ 4  1  5 | 30 ]
[ 3 -1 -1 |  4 ]
Next, we perform row operations to convert the matrix to its reduced row-echelon form. Once we have the reduced form, we can directly read off the solutions for the variables x, y, and z.

These row operations usually involve scaling rows, adding and subtracting rows, and swapping rows to systematically bring the matrix into the desired form. The final reduced row-echelon form should look like:

[ 1 0 0 | x ]
[ 0 1 0 | y ]
[ 0 0 1 | z ]

Where x, y, and z are the solutions to the original equations. At this stage, each row corresponds to an equation of the form x=..., y=..., z=..., making it straightforward to determine the values of the variables.

Answer:

The translation is left 4 units

Step-by-step explanation:

we know that

[tex]y=2(x-15)^{2}+3[/tex]

Is a vertical parabola open upward with vertex at (15,3)

[tex]y=2(x-11)^{2}+3[/tex]

Is a vertical parabola open upward with vertex at (11,3)

so

The rule of the  translation of (15,3) ----> (11,3) is equal to

(x,y) ----> (x-4,y)

That means ----> The translation is left 4 units

Answer:

x=(c-b)/3

Step-by-step explanation:

we have

3x+b=c

Solve for x

That means -----> Clear variable x

Subtract b both sides

3x+b-b=c-b

3x=c-b

Divide by 3 both sides

x=(c-b)/3

Answer:

B,C,D,E

Step-by-step explanation:

The similarity statement that describe the relationship is similarities by (AAA)

Similar triangles have corresponding angles equal and proportional sides. Their shapes are identical, but sizes may differ.

For two triangles to be similar, the corresponding angles must be equal, and the ratio of the corresponding sides must be equal.

From the diagram, The similarity statement that describe the relationship is similarities by (AAA)

angle R =angle Z

angle S = angle X

angle P = angle Y.

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[tex](-4qr)(-4qr)(-4qr)(-4qr)=(-4qr)^4=256q^4r^4[/tex]

To rewrite the expression (-4qr)(-4qr)(-4qr)(-4qr) using the properties of exponents, we can rewrite it as (-4qr)^4 = 256q^4r^4.

To rewrite the given expression (-4qr)(-4qr)(-4qr)(-4qr) using the properties of exponents, we need to understand that multiplying the same base with different exponents is equivalent to adding the exponents. In this case, the base is (-4qr) and the exponents are 1 for each occurrence. So, we can rewrite the expression as:

(-4qr)4 = -44q4r4 = 256q4r4

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Answer:

2n

Step-by-step explanation:

2n = 2*n

36n = 2*3*2*3 n

They both have 2*n in common, so the greatest common factor is 2n

Answer:

length=72

width=63

Step-by-step explanation:

Let us start by supposing the following:

w=w

l=9+w

2l+2w=p(perimeter)

2(9+w)+2*w=270

    2w+2w+18=270

            4w+18=270

                   4w=252

                     w=63

                      l=72

We used the perimeter formula, 2l+2w=P(perimeter)

Final answer:

To calculate the dimensions of the rectangle, we use the perimeter formula P=2l+2w. After setting up an equation with the given perimeter and relationship between length and width, we find the width to be 63 cm and the length to be 72 cm.

Explanation:

The problem states that the length of a rectangle is 9 cm more than its width and that the perimeter is 270 cm. To find the dimensions of the rectangle, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Let's denote the width of the rectangle as w cm. Then the length would be w + 9 cm. We can substitute these expressions into the perimeter formula to obtain:
270 = 2(w + 9) + 2w

Simplify and solve for w:
270 = 2w + 18 + 2w
270 = 4w + 18
252 = 4w
w = 63 cm

Now that we have the width, we can find the length:
l = w + 9 = 63 + 9 = 72 cm

Therefore, the width is 63 cm, and the length is 72 cm.

Answer:

option 4

Step-by-step explanation:

Given

[tex]\frac{3}{5}[/tex] × [tex]\frac{2}{3}[/tex]

Cancel the 3's on the numerator/denominator of the fractions, leaving

= [tex]\frac{1}{5}[/tex] × [tex]\frac{2}{1}[/tex] = [tex]\frac{2}{5}[/tex] ← in simplest form

The product of 3/5 x 2/3, in simplest form, is 2/5 after multiplication and reduction.

In order to answer your question about the product of 3/5 x 2/3, you need to multiply the two fractions. To do this, you multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. So, for this problem, you would multiply 3 by 2 to get 6, and 5 by 3 to get 15. Therefore, 3/5 x 2/3 = 6/15. However, to put it in simplest form, you should always reduce the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common factor, which in this case is 3. Therefore, 6/15 reduces to 2/5.

Answer:

D

Step-by-step explanation:

Using the section formula

x = [tex]\frac{5(-8)+8(7)}{5+8}[/tex] = [tex]\frac{-40+56}{13}[/tex] = [tex]\frac{16}{13}[/tex] ≈ 1.2

y = [tex]\frac{5(-9)+8(-2)}{5+8}[/tex] = [tex]\frac{-45-16}{13}[/tex] = [tex]\frac{-61}{13}[/tex] ≈ - 4.7

Coordinates are (1.2, - 4.7 ) → D

Answer:

I've done this question before and the answer is really weird. its 3/8

Answer:2.5 cups of flour in each loaf of raisin bread

Step-by-step explanation:

The pretzel uses 2.5 cups of flour so the remaining flour is 10(12.5-2.5)

Since there are four loaves and 10 cups of flour left

Therefore one loaf has 10/4 or 2.5 cups of flour

Answer:

Four times the amount of flour for the raisin bread plus 2.5 cups equals 12.5 cups total. The equation is 4x + 2.5 = 12.5. First, I subtract 2.5 from both sides, and then I divide both sides by 4. Each loaf contains 2.5 cups of flour.

--

Brianna Edwards

e d g e n u i t y things

Thanks in advance

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The equation that will be used to find t is:

                [tex]3(2-t)+1.5t=5[/tex]

Total distance that is traveled by Amir is: 5 miles.

and the total time taken by him is: 2 hours.

On the first part of the hike, Amir averaged 3 miles per hour.

Let t denote the time he spent hiking during the second i.e. difficult part of the hike.

( Since, the total time was 2 hours)

Also, we know that:

[tex]Distance=Speed\times Time[/tex]

Hence, distance traveled in first part of hike is:

[tex]Distance=3\times (2-t)[/tex]

Since the total distance traveled by him is 5 miles.

It is given that his speed decreased to 1.5 miles per hour.

Now, we know that:

[tex]Time=\dfrac{Distance}{Speed}[/tex]

Hence, time spent by him in second part of hike is:

[tex]t=\dfrac{5-3(2-t)}{1.5}\\\\i.e.\\\\1.5t=5-3(2-t)\\\\i.e.\\\\3(2-t)+1.5t=5[/tex]

Answer:

x^2 +3

Step-by-step explanation:

f(x) = 2x^2 + 2

g(x) = x^2 - 1

(f - g)(x) = 2x^2 + 2 -( x^2 - 1)

     Distribute the minus sign

              2x^2 +2 -x^2 +1

              x^2 +3

[tex](f-g)(x)=2x^2+2-(x^2-1)=2x^2+2-x^2+1=x^2+3[/tex]

Answer:

0.21

Step-by-step explanation:

If A and B are independent, then:

P(A and B) = P(A) × P(B)

Given P(A) = 0.3 and P(B) = 0.7:

P(A and B) = 0.3 × 0.7

P(A and B) = 0.21

Answer:

P(A and B) = 0.21

Step-by-step explanation:

Two events are said to be independent when the occurrence of event 1 does not affect the occurrence of event 2

Given two probabilities A and B whose probabilities are given as follows

P(A) = 0.3, P(B)  = 0.7

P(A and B) is calculated as follows;

P(A and B) is calculated by multiplying both probabilities together

P(A and B) = P(A) * P(B)

P(A and B) = 0.3 * 0.7

P(A and B) = 0.21

Hence, P(A and B) = 0.21

Answer:

bottom left graph

Step-by-step explanation:

A proportional relationship is linear, represented by a straight line graph passing through the origin.

The graph on the bottom left is straight line passing through the origin.

Answer:

$ (7t+872)

Step-by-step explanation:

Earning for 1 hour as a tutor= $15

Earnings for 1 hour as a waitress= $8

Total hours worked in the month combined jobs= 109 hrs

Number of hours worked as tutor for the month= t

Find the number of hours worked as waitress for the month= 109-t  hours

Total amount earned that month = amount earned as a tutor+ amount earned as a waitress

Amount earned as a tutor=  $15 × t = $15t

Amount earned as a waitress= $8× (109-t)= $ (872-8t)

Total amount earned combined= $ 15t + $ (872-8t)

                                                    =$ ( 15t-8t +872)

                                                    = $ (7t+872)

Final answer:

Rachel's total earnings from both jobs can be expressed as the sum of her hourly rates multiplied by the hours worked in each job, which gives the equation: Total Earnings = 15t + 8(109 - t), where t is the number of hours she worked as a tutor.

Explanation:

To write an expression for the combined total dollar amount Rachel earned this month through her two jobs, we can start by indicating that she earns $15 an hour for tutoring and $8 an hour as a waitress. Given that t represents the number of hours she worked as a tutor, we can calculate her earnings from tutoring as 15t. If the total number of hours worked is 109, then the remaining number of hours worked as a waitress would be 109 - t. Her earnings from working as a waitress would thus be 8(109 - t).

Adding these two amounts together gives us the expression for Rachel's total earnings:
Total Earnings = 15t + 8(109 - t)

Answer:

5

Step-by-step explanation:

85 * 18 / 18 * 17

18 cancels out.

85/17

= 5

Your answer for this question is 5

1.) When you divide 85/18 by 17/18, the first step you want to take is switch the reciprocal.

[tex]\frac{85}{18}[/tex]÷[tex]\frac{17}{18}[/tex]=

[tex]\frac{85}{18}[/tex]×[tex]\frac{18}{17}[/tex]

2.) When you switch the reciprocal, you then division sign is changed to times.

[tex]\frac{85}{18}[/tex]×[tex]\frac{18}{17}[/tex]

3.) Now you simply multiply

[tex]\frac{85}{18}[/tex]×[tex]\frac{18}{17}[/tex]=[tex]\frac{1530}{306}[/tex]

4.) Last step, you divide

[tex]\frac{1530}{306}[/tex] = 5

Hope This Helps.

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Answer:

x=1

Step-by-step explanation:

-5 - (15x-1) = 2(7x-16) -x

Distribute the negative sign

-5-15x+1 = 2(7x-16)-x

Distribute the 2

-5-15x+1 = 14x -32-x

Combine like terms

-4-15x = 13x-32

Add 15x to each side

-4-15x+15x = 13x+15x-32

-4 = 28x-32

Add 32 to each side

-4+32 = 28x-32+32

28 = 28x

Divide each side by 28

28/28 = 28x/28

1 =x

Answer:

x = 10

Step-by-step explanation:

Make x the subject

2x - 8 = 12

2x = 12 + 8

2x = 20

x = 20/2

x = 10

!!

Answer:

None

Step-by-step explanation:

y<2x - 4

Substitute points to determine if they are a solution

(-1,1)

1<2(-1) - 4

1 < -2-4

1 < -6  False  not a solution

(1,-1)

-1<2(1) - 4

-1 < 2-4

-1 < -2  False  not a solution

(3,2)

2<2(3) - 4

2 < 6-4

2 < 2  False  not a solution

(2,3)

3<2(2) - 4

3 < 4-4

3 < 0  False  not a solution

Step-by-step explanation:

6b < 42 or 4b + 12 > 8

6b < 42

= 6b/6 < 42/6

= b < 7

4b + 12 > 8

=4b - 12 + 12 < -12+8

= 4b > - 12 + 8

= 4b > -4

= 4b/4 = -4/4

b > -1

so

7 > b > -1

The solution of the compound inequality 6b < 42 or 4b + 12 > 8 is   -1 < b < 42.

The inequality represent the relationship between two expression, it can represent by  < is less than > is greater than.

The inequality is;

[tex]\rm 6b < 42\\\\\dfrac{6b}{6} < \dfrac{42}{6}\\\\b < 7[/tex]

The solution of the inequality  6b < 42 is b < 7.

The inequality is;

[tex]\rm 4b + 12 > 8\\\\4b+12-12 > 8-12\\\\4b > -4\\\\\dfrac{4b}{b} > \dfrac{-4}{4}\\\\b > -1[/tex]

The solution of the inequality  4b + 12 > 8  is b > -1.

So combining both conditions, the compound equality will be:

-1 < b < 42

It depicts b is greater than -1 and smaller than 42.

Hence, the solution of the compound inequality 6b < 42 or 4b + 12 > 8 is   -1 < b < 42.

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Answer: 279.4 centimeters hope this helped

Step-by-step explanation: 110 x 2.54 = 279.4

Answer:

60000/4 pr 15000

Step-by-step explanation:

Rate of change = change in population / change in time

80000 - 20000 = 60000

January to April is 4 months

so the rate of change will be 60000/4 or 15000

Answer: -4

Step-by-step explanation:

Solve 2x+7=-1

2x. =-8

x. =-4

Answer:

-4

Step-by-step explanation:

To find the value you have to substitute x for -1. because f(x) = -1.

-2x + 7 = -1

-7= -7

-2x =-8

÷-2

x=-4

Hope it helps!

Answer:

2) -81t² +16

Step-by-step explanation:

(9t -4)(-9t -4) = (9t x -9t) + (9t x -4) + (-4 x -9t) + (-4 x -4)

                     = -81t² - 36t + 36t + 16

                     = -81t² + 16

Answer:

- 81t² + 16

Step-by-step explanation:

Simply expand the equation by factoring

(9t-4)(-9t-4)    factor out negative sign

= -(9t - 4) (9t +4)

= -(9t + 4) (9t - 4)      recall a² - b² = (a+b) (a-b)

= - [ (9t)² - 4²]

= - ( 81t² - 16)

= - 81t² + 16