state the gradient of the line y= 5-5x

The units digit of 23^23 is 7. This is found using the power cycle of 3 (the units digit of the base number), which is 3, 9, 7, 1 and the remainder when the exponent 23 is divided by the length of this power cycle (4).

To find the units digit of 2323, one needs to understand a pattern in power cycles. For any number, the units digit will repeat in a certain cycle when the number is raised to higher powers. For number 3, every fourth power goes back to the value 1. Thus, the cycle for the number 3 is 3, 9, 7, 1.

Here’s how the calculation works:

https://brainly.com/question/17038912

#SPJ2

Answer:

coordinate of point A is (a,b)

coordinate of point C is (2c,d)

slope of AD and BC =[tex]\frac{b}{a-c}[/tex]

Step-by-step explanation:

According to midpoint formula

If we have points P [tex](x_{1} ,y_{1} )[/tex] and Q [tex](x_{2} ,y_{2} )[/tex]

then the coordinate (x,y) of mid point of line PQ is given by

[tex]x=\frac{x_{1} +x_{2} }{2}[/tex] and [tex]y=\frac{y_{1} +y_{2} }{2}[/tex]

now from the given diagram A is the mid point of line joining  R(0,0) and S(2a,2b)

Using midpoint formula, coordinates of point A is given by

[tex]x=\frac{0+2a}{2}= a[/tex] and [tex]y=\frac{0+2b}{2} =b[/tex]

so we have

coordinate of point A is (a,b)

Also C is the midpoint of line joining T (2c,2d) and V(2c,0)

coordinate of point C is given by

[tex]x= \frac{2c+2c}{2} =2c[/tex] and [tex]y=\frac{2d+0}{2} =d[/tex]

so we have

coordinate of point C is (2c,d)

it is given that coordinate of point B is (a+c, b+d) and coordinate of D is (c,0)

If we have points P [tex](x_{1} ,y_{1} )[/tex] and Q [tex](x_{2} ,y_{2} )[/tex]

then the slope of PQ =[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1}  }[/tex]

hence slope of AD= [tex]\frac{0-b }{c-a} [/tex]

                                 =[tex]\frac{-b}{c-a}[/tex]

                                  =[tex]\frac{-b}{-(a-c)}[/tex]

                                  =[tex]\frac{b}{a-c}[/tex]

and slope of BC  =[tex]\frac{d-(b+d)}{2c-(a+c)}[/tex]

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

                             =[tex]\frac{-b}{c-a}[/tex]

                              =[tex]\frac{b}{a-c}[/tex]

so we have

slope of AD and BC =[tex]\frac{b}{a-c}[/tex]

Answer:

Co-ordinates of A are ( a, b )

Co-ordinates of C are ( 2c, d )

Slope of line segments AD and BC is [tex]\frac{-b}{c-a}[/tex]

Step-by-step explanation:

We know that, the co-ordinates of the mid-point of a line segment having end points (x,y) and [tex](x_{1} , y_{1} )[/tex] is [tex](\frac{x+x_{1} }{2} , \frac{y+y_{1} }{2} )[/tex]

Now as 'A' is the mid-point of the line segment RS having end points (0,0) and (2a,2b).

The co-ordinates of A will be ( [tex]\frac{0+2a}{2}[/tex], [tex]\frac{0+2a}{2}[/tex] ) i.e [tex]( a, b )[/tex]

Now as 'C' is the mid-point of the line segment TV having end points (2c,2d) and (2c,0).

The co-ordinates of C will be ( [tex]\frac{2c+2c}{2}[/tex], [tex]\frac{2d+0}{2}[/tex] ) i.e. [tex]( \frac{4c}{2} , \frac{2d}{2})[/tex] i.e. [tex]( 2c, d )[/tex].

Further, we need to find the slope of line segments AD and BC.

AD has end points [tex]( a, b )[/tex] and [tex]( c, 0 )[/tex]. Then the slope of AD will be [tex]\frac{0-b}{c-a}[/tex] i.e [tex]\frac{-b}{c-a}[/tex]

Similarly, BC has end points [tex]( a+c, b+d )[/tex] and [tex]( 2c, d )[/tex]. Then the slope of BC will be [tex]\frac{d-b-d}{2c-a-c}[/tex] i.e [tex]\frac{-b}{c-a}[/tex]

Hence, the slope of AD and BC is [tex]\frac{-b}{c-a}[/tex].

Answer:

3000 gallons of 12 percent is required

Step-by-step explanation:

We can use the formula

percentage * amount + percentage * amount =  percentage*total amount

We have 9 percent and 15 percent wine that we are mixing to get 12 percent wine.

We are adding g gallons and 3000 gallons to get a total of (g+3000) gallons

Substituting this information in

.09 *g + .15 * 3000 = .12 (g+3000)

Distribute

.09g +450 = .12g+360

Subtract .9g from each side

.09g-.09g +450 = .12g-0.09g+360

450 = .03g + 360

Subtract 360 from each side

450-360 = .03g

90 =.03g

Divide each side by .03

90/.03 = .03g/03

3000 = g

Answer:

C. (5, -3)

Step-by-step explanation:

4x + 3y = 11

x - y = 8  (multiply by 3) --> 3x - 3y = 24

4x + 3y = 11

3x - 3y = 24

---------------------add

7x = 35

 x = 5

5 - y = 8

y = 5 - 8

y = -3

(5, -3)

Answer:

C. (5, -3)

Step-by-step explanation:

Rewrite the first equation.

Multiply the second equation by 3 and write it under the first equation.

4x + 3y = 11

3x - 3y = 24

Now add the equations.

7x        = 35

Divide both sides by 7.

x = 5

Substitute 5 for x in the original first equation:

4(5) + 3y = 11

20 + 3y = 11

3y = -9

y = -3

Solution: (5, -3)

The sales tax that should be paid in dollars on the new price is $22

Order of Operations in Mathematics follow this following rule :

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem !

Given:

Initial Price = $550

Sales Tax = 3%

Percentage of Price Increase = 33¹/₃ %

Unknown:

Final Sales Tax = ?

Solution:

[tex]\texttt{Final Price} = \texttt{Initial Price} \times (100\% + \texttt{Percentage of Price Increase} )[/tex]

[tex]\texttt{Final Price} = \$550 \times (100\% + 33\frac{1}{3}\% )[/tex]

[tex]\texttt{Final Price} = \$550 \times (100\% + \frac{100}{3}\% )[/tex]

[tex]\texttt{Final Price} = \$550 \times (\frac{300}{3}\% + \frac{100}{3}\% )[/tex]

[tex]\texttt{Final Price} = \$550 \times (\frac{400}{3}\%)[/tex]

[tex]\texttt{Final Price} = \$550 \times (\frac{4}{3})[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{Final Sales Tax} = 3\% \times \texttt{Final Price}[/tex]

[tex]\texttt{Final Sales Tax} = 3\% \times \$550 \times (\frac{4}{3})[/tex]

[tex]\texttt{Final Sales Tax} = \frac{3}{100} \times (\frac{4}{3}) \times \$550[/tex]

[tex]\texttt{Final Sales Tax} = \frac{4}{100} \times \$550[/tex]

[tex]\texttt{Final Sales Tax} = 4 \times \$5.5[/tex]

[tex]\texttt{Final Sales Tax} = \$22[/tex]

[tex]\texttt{ }[/tex]

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces

The sales tax should be paid in dollars on the new price is [tex]\boxed{\$ 22}.[/tex]

Further Explanation:

Given:

The listed price of furniture is [tex]\$550.[/tex]

The sales tax is of [tex]3\%[/tex] on the listed price.

The price is increased by [tex]33\dfrac{1}{3}\%.[/tex]

Calculation:

The increased price of the furniture can be obtained as follows,

[tex]\begin{aligned}{\text{Increased price}} &= 550 + \left( {33\frac{1}{3}\%  \times 550} \right)\\&= 550 + \left( {\frac{{33.34}}{{100}} \times 550} \right)\\&= 550 + 0.3333 \times 550\\&= 550 + 183.32\\&= 733.32\\\end{aligned}[/tex]

The new price of the furniture is [tex]\$ 733.32.[/tex]

The sales tax is of [tex]3\%[/tex] on the listed price.

The sales tax can be obtained as follows,

[tex]\begin{aligned}{\text{Sales tax}} &= 3\% {\text{ of new price}}\\&= \frac{3}{{100}} \times 733.32\\&= \$ 22\\\end{aligned}[/tex]

The sales tax should be paid in dollars on the new price is [tex]\boxed{\$ 22}.[/tex]

Learn more:

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Investment and return

Keywords: May, 2018, store, furniture, listed, price, listed price, $550, sales, sales tax, 3%, tax on listed price, next month, price increased, increased price, month[tex], 33 1/3%[/tex], paid, dollars, new price.

Answer:

It would be C

Step-by-step explanation:

The number is between integers, so it can't be an integer or a whole number. It's written as a ratio of two integers, so it's a rational number and not irrational.

Answer:

C.

Step-by-step explanation:

because if -6 is a rotational number it should also be able to be translated into a fraction form

Answer:

The first car

Step-by-step explanation:

183/3 = 61mph

Answer:

183/3 or Option A

Step-by-step explanation:

Edge 2021

thats where i got the correct answer plus i took the test

So for this, I will be completing the square to solve for x. Firstly, add 10 and subtract 30x on both sides of the equation:

[tex]x^2-30x=10[/tex]

Next, we want to make the left side of the equation a perfect square. To find the constant of this soon-to-be perfect square, divide the x coefficient by 2 and square the quotient. Once you get that result, add it to both sides of the equation:

[tex]30\div 2 = 15\\15^2=225\\\\x^2-30x+225=235[/tex]

Now, factor the left side:

[tex](x-15)^2=235[/tex]

Next, square root both sides:

[tex]x-15=\pm\ \sqrt{235}[/tex]

Now, add 15 to both sides of the equation:

[tex]x=15\pm \sqrt{235}[/tex]

This is the exact solution. To find the approximate solution, solve the left side twice -- once with the plus sign, once with the minus sign:

[tex]x=30.33,-0.33[/tex]

In short:

[tex]x^2-10=30x\qquad\text{subtract 30x from both sides}\\\\x^2-30x-10=0\\\\\text{Use the quadratic formula}\\\\ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a},\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\text{We have}\ a=1,\ b=-30,\ c=-10\\\\\text{Substitute.}\\\\b^2-4ac\to(-30)^2-4(1)(-10)=900+40=940\\\\\sqrt{b^2-4ac}=\sqrt{940}=\sqrt{4\cdot235}=\sqrt4\cdot\sqrt{235}=2\sqrt{235}\\\\x_1=\dfrac{-(-30)-2\sqrt{235}}{2(1)}=\dfrac{30-2\sqrt{235}}{2}=15-\sqrt{235}\\\\x_2=\dfrac{-(-30)+2\sqrt{235}}{2(1)}=\dfrac{30+2\sqrt{235}}{2}=15+\sqrt{235}[/tex]

[tex]Answer:\ \boxed{x=15-\sqrt{235}\ and\ x=15+\sqrt{235}}[/tex]

Answer:

D. The graph contains the point (4, -10)

Step-by-step explanation:    

We have been given an equation of a function: [tex]y=4x-10[/tex]. We are asked to find which of the given statements are not true about our given function.

A. The slope of the line can be written as 4/1.  

We can see from our given equation that slope is 4 we can write 4 as 4/1 as it will not change value of 4, therefore, option A is true.

B. The graph crosses the y-axis 10 units below the origin.  

Since we know that b represents y-intercept, where line crosses y-axis. y-intercept for our given equation is -10, which means that our given line crosses y-axis at -10 (10 units below the origin), therefore, option B is true.

C. The line has a constant rate of change.

We can see that slope of line is 4 which means with each increase in x, y will increase by 4 units, which remains constant, therefore, option C is true indeed.

D. The graph contains the point (4, -10)

Since we know that y-intercept is -10, which occurs at x equals 0, therefore, the graph does not contain the point (4,-10) and option D is not true.

I will get in 2:16.

Now it is given that I clock out or I got out when the time was 1 hour 46 minutes.

And I have 30 minutes to go in.

So after 30 minutes, the time will be :

   1 hour +  46 minutes

+                 30  minutes  

   1 hour  +  76 minutes

Now we know that 60 minutes = 1 hour

So the time will be 2 hours and 16 minutes.

Therefore, the time at which I will get in after 30 minutes is 2:16

Learn more :

https://brainly.com/question/11780640

Answer:

x=2

Step-by-step explanation:

32x ÷ 4 = 16

32x = 64

x = 2

Answer:

x = - 3.5

Step-by-step explanation:

32 * ( x + 4 ) = 16  

x + 4 = 16 / 32  

x + 4 = 0.5  

x = 0.5 - 4  

x = - 3.5

Answer:

2 miles

Step-by-step explanation:

convert 3/4 into 6/8. With this you have a ratio of 6/8 miles to 3/8 hours. Meaning 2/8 mile is equal to 1/8 of an hour. With this you can find that Jacie can swim 2 miles in a hour

Jacie can swim 2 miles in one hour, based on her speed of swimming 3/4 of a mile in 3/8 of an hour.

The student has asked how far Jacie can swim in one hour if she can swim 3/4 of a mile in 3/8 of an hour. To find out how far she can swim in one hour, we need to calculate her swimming speed and then use that speed to determine the distance she can cover in one full hour.

First, we determine Jacie's speed by dividing the distance by the time:

Speed = Distance / Time

Speed = (3/4) mile / (3/8) hour = 2 miles per hour

Now that we know Jacie swims at a speed of 2 miles per hour, we can find out the distance she swims in one hour simply by considering the speed:

Distance in one hour = Speed / Time

Distance in one hour = 2 miles per hour / 1 hour = 2 miles

Therefore, Jacie can swim 2 miles in one hour.

Answer:

13 Miles

Step-by-step explanation:

This problem could be solved using the Pythagorean theorem.

a² + b² = c²

a = 12    b = 5

12² + 5² = 169

√169 = 13

Therefore, you are 13 miles away from your house!

Answer:

43.452

Step-by-step explanation:

284 times .153 = 43.452

GEMDAS!

1:

3 - 7 x 5 + 2 x 4

3 - 35 + 2 x 4

3 - 35 + 8

3 - 27

-24

2:

7 - 2 x 5 + 9 x 3

7 - 10 + 9 x 3

7 - 10 + 27

7 + 17

24

3:

2 - 8x + 3x When x = 5

2 - 8(5) + 3(5)

2 - 40 + 15

2 - 25

-23

4:

4 - 2x + 5x when x= 4

4 - 2(4) + 5(4)

4 - 8 + 20

4 + 12

16

5:

z ÷ 2 - 4z + 3(z - 3) when z = 8

8 ÷ 2 - 4(8) + 3(8 - 3)

8 ÷ 2 - 32 + 24 - 9

4 - 32 + 24 - 9

4 - 8 - 9

-13

I might've did #5 incorrect.... Really really sorry...

Answer:

The interest on a yearly investment start building interest - at the end of the first period.

Step-by-step explanation:

In an ordinary annuity, the interest on a yearly investment start building interest - at the end of the first period.

An ordinary annuity is a series of payments, where all the payments are of the same amount and are paid at the same intervals of time. The interest is calculated at the end of first period.

Answer:

(x-10)(x+10)

Step-by-step explanation:

Here, the given expression,

[tex]x^2-100[/tex]

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

By using the identity [tex]a^2-b^2=(a+b)(a-b)[/tex]

[tex]=(x+10)(x-10)[/tex]

[tex]=(x-10)(x+10)[/tex]   ( By the commutative property )

Since, further factorization is not possible,

Hence, the factors of [tex]x^2-100[/tex] are,

[tex](x-10)(x+10)[/tex]

Second option is correct.

Answer:

Eight

Step-by-step explanation:

We have two conditions:

(1)           C + D  = 12

(2)      2C + 3D = 32          Subtract D from each side of Equation (1)

                    C = 12 - D     Multiply both sides by 5

2(12 – D) + 3D = 32          Remove parentheses

24 – 2D + 3D = 32          Combine like terms

           24 + D = 32           Subtract D from each side

                   D = 8

Philip bought eight DVDs.

Answer:

Step-by-step explanation:

Pru, Piper, Phoebe ratio 5:3:4vadded = 12

What this means is Pru has 5/12 of the total amount, Piper has 3/12 of the total amount, and Phoebe has 4/12 of the total amount of spices.

pru = piper + 24

5/12x = 3/12x + 24

5/12x - 3/12x = 24

2/12x = 24

x = 24 / (1/6)

x = 24 * 6

x = 144 spices in total

Pru has : 5/12(144) = 720/12 = 60 spices

Piper has : 3/12(144) = 432/12 = 36 spices

Phoebe has : 4/12(144) = 576/12 = 48 spices

I hope this can help.

Answer:

48

Step-by-step explanation:

Pru, Piper, and Phoebe share spices in the ratio 5:3:4

5+3+4=12

So Pru has 5/12 share of spices, Piper has 3/12 share of spices, and Phoebe has 4/12 share of spices.

If Pru has 24 more spices than Piper, (5/12 - 3/12)=2/12 share of spices =24

Total spices = 24x12/2 = 144

Phoebe has 4/12x144 = 48 spices

Answer:

$0.24

Step-by-step explanation:

1.49 - 1.25 = 0.24

Answer:

$0.24

Step-by-step explanation:

Answer:

Answer:  3240 = 2^3×3^4×5

Factor the following integer:

3240

The last digit of 3240 is 0, which means it is even. Therefore 3240 is divisible by 2:

3240 = 2 1620:

3240 = 2×1620

The last digit of 1620 is 0, which means it is even. Therefore 1620 is divisible by 2:

1620 = 2 810:

3240 = 2×2×810

The last digit of 810 is 0, which means it is even. Therefore 810 is divisible by 2:

810 = 2 405:

3240 = 2×2×2×405

405 is not divisible by 2 since 405 is odd and 2 is even:

3240 = 2×2×2×405 (405 is not divisible by 2)

The sum of the digits of 405 is 4 + 0 + 5 = 9, which is divisible by 3. This means 405 is divisible by 3:

405 = 3 135:

3240 = 2×2×2×3×135 (135 is not divisible by 2 since 405 is not)

The sum of the digits of 135 is 1 + 3 + 5 = 9, which is divisible by 3. This means 135 is divisible by 3:

135 = 3 45:

3240 = 2×2×2×3×3×45 (45 is not divisible by 2 since 135 is not)

The sum of the digits of 45 is 4 + 5 = 9, which is divisible by 3. This means 45 is divisible by 3:

45 = 3 15:

3240 = 2×2×2×3×3×3×15 (15 is not divisible by 2 since 45 is not)

The sum of the digits of 15 is 1 + 5 = 6, which is divisible by 3. This means 15 is divisible by 3:

15 = 3 5:

3240 = 2×2×2×3×3×3×3×5 (5 is not divisible by 2 since 15 is not)

Divide 3 into 5:

| 1 | (quotient)

3 | 5 |  

- | 3 |  

| 2 | (remainder)

5 is not divisible by 3:

3240 = 2×2×2×3×3×3×3×5 (5 is not divisible by 2 or 3)

No primes less than 5 divide into it. Therefore 5 is prime:

3240 = 2×2×2×3×3×3×3×5

There are 3 copies of 2, 4 copies of 3 and 1 copy of 5 in the product:

Answer:  3240 = 2^3×3^4×5

3,240 =

= 324 × 10 =

= 4 × 81 × 10 =

= 2^2 × 3^4 × 2 × 5 =

Answer:

When you have large numbers to divide,

draw a tableau for long division on the side.

Write the steps that will be your guide,

D, M, S, B and R – Abide by to long divide!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

56 packs

Step-by-step explanation:

just divide

Answer:

associative property of multiplication

Step-by-step explanation:

edge 2021

Answer:

If he sells $2500 worth of merchandise, his salary is $800.

Step-by-step explanation:

You can find a function that gives you his salary as a function of the sales.

You have two points: (100, 500) and (700, 575).

y = mx + b

m = (575 - 500)/(700 - 100) = 75/600 = 0.125

Now use point (100, 500) to find b.

y = mx + b

500 = 0.125(100) + b

500 = 12.5 + b

b = 487.5

y = 0.125x + 487.5

If he sells $2500, then x = 2500.

y = 0.125x + 487.5

y = 0.125(2500) + 487.5

y = 800

If he sells $2500 worth of merchandise, his salary is $800.

Answer:

Your answer is (A) $.06/mi

Step-by-step explanation:

Answer:

option D

Step-by-step explanation:

[tex]f(x) = x^2 + 5x + 6[/tex]

[tex]g(x)= \frac{1}{x+3}[/tex]

(fog)(x) = f(g(x))

Plug in g(x) in f(x)

We plug in 1/x+3 in the place of x  in f(x)

[tex]f(g(x))= f(\frac{1}{x+3})= (\frac{1}{x+3})^2 + 5(\frac{1}{x+3}) + 6[/tex]

To simplify it we take LCD

LCD is (x+3)(x+3)

[tex]\frac{1}{(x+3)(x+3)}+5\frac{1*(x+3)}{(x+3)(x+3)}+\frac{6(x+3)(x+3)}{(x+3)(x+3)}[/tex]

[tex]\frac{1}{x^2+6x+9}+\frac{(5x+15)}{x^2+6x+9}+\frac{6x^2+36x+54}{x^2+6x+9}[/tex]

All the denominators are same so we combine the numerators

[tex]\frac{1+5x+15+6x^2+36x+54}{x^2+6x+9}[/tex]

[tex]\frac{6x^2+41x+70}{x^2+6x+9}[/tex]

Option D is correct

Answer:

The correct option choice is D. 6x^2 + 41x + 70 / x^2 +6x + 9

Final answer:

Each rectangle can be divided into 8 equal parts, allowing [tex]\frac{3}{4}[/tex] and [tex]\frac{5}{8}[/tex] to be expressed with the same denominator for comparison.

Explanation:

To determine how many parts each rectangle can be divided, we need to find a common denominator that allows us to express [tex]\frac{3}{4}[/tex] and [tex]\frac{5}{8}[/tex] using the same size parts. The smallest number that both denominators 4 and 8 can divide into without a remainder is 8. Therefore, the first rectangle can be divided into 8 equal parts, with 6 of those parts being shaded (since [tex]\frac{3}{4}[/tex] is equivalent to [tex]\frac{6}{8}[/tex]). The second rectangle is already divided into 8 equal parts with 5 of those parts being shaded.