a number has 2,5 and 7 as its prime factors. what are the four smallest values it and take​

Answers

Answer 1

Answer:

  70, 140, 280, 350

Step-by-step explanation:

Obviously, it must have the factors 2, 5, 7 as a minimum, so the smallest value is 2×5×7 = 70.

Any of these primes can be added to the product. In increasing order, the smallest additional factors will be 2, 4, 5, 7, 8, 10, ...

So, the four smallest numbers with prime factors of 2, 5, and 7 are ...

  70 = 2·5·7

  140 = 2²·5·7

  280 = 2³·5·7

  350 = 2·5²·7


Related Questions

Two buildings are 12m apart on the same horizontal level. From the top of the taller building, the angle of depression of the bottom of the shorter building is 48degrees and from the bottom, the angle of of elevation of the top of the shorter building is 36 degrees. Calculate the difference in the heights of the buildings

Answers

Answer:

4.61 m

Step-by-step explanation:

The angle of depression of the bottom of the shorter building from the top of the taller building = 48° equals the angle of elevation of the top of the taller building from the bottom of the shorter building

Using trig ratios

tan48° = H/d where H = height of taller building and d = their distance apart = 12 m

H = dtan48° = 12tan48° = 13.33 m

Also, the angle of elevation of the top of the shorter building from the bottom of the taller building is 36°

Using trig ratios

tan36° = h/d where h = height of shorter building

h =dtan36° = 12tan36° = 8.72 m

Now, the difference in height of the buildings is thus H - h = 13.33 m - 8.72 m = 4.61 m

The value of 1.8/(0.4×0.3) is

Answers

Answer:

15

Step-by-step explanation:

1.8 over 0.4 multiply 0.3

Answer: 15

Step-by-step explanation:

 1.8/(0.4×0.3)

=1.8/0.12

=15

Hope this helps!! :)

find the area of a trapezium which has a height 20 cm and its parallel sides are 7 cm and 8 cm long​

Answers

Answer:

150cm²

Step-by-step explanation:

area of trapezium=1/2h(a+b)

=1/2×20(7+8)

=10(15)

=150 cm²

Answer:

The area of the trapezium is

150 cm²

Step-by-step explanation:

The area of a trapezium is given by

[tex]Area = \frac{1}{2} (a + b) \times h[/tex]

where

h is the height

a and b are the parallel sides of the trapezium

From the question

h = 20cm

a = 7cm

b = 8 cm

Substitute the values into the above formula

We have

[tex]Area = \frac{1}{2} (7 + 8) \times 20[/tex][tex]Area = \frac{1}{2} \times 15 \times 20[/tex][tex]Area = 15 \times 10[/tex]

We have the final answer as

Area = 150 cm²

Hope this helps you

PLEASE HELP
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square.

Answers

Answer:

perimeter is  4 sqrt(29) + 4pi  cm

area is 40 + 8pi cm^2

Step-by-step explanation:

We have a semicircle and a triangle

First the semicircle with diameter 8

A = 1/2 pi r^2 for a semicircle

r = d/2 = 8/2 =4

A = 1/2 pi ( 4)^2

  =1/2 pi *16

  = 8pi

Now the triangle with base 8 and height 10

A = 1/2 bh

  =1/2 8*10

  = 40

Add the areas together

A = 40 + 8pi cm^2

Now the perimeter

We have 1/2 of the circumference

1/2 C =1/2 pi *d

         = 1/2 pi 8

        = 4pi

Now we need to find the length of the hypotenuse of the right triangles

using the pythagorean theorem

a^2+b^2 = c^2

The base is 4 ( 1/2 of the diameter) and the height is 10

4^2 + 10 ^2 = c^2

16 + 100 = c^2

116 = c^2

sqrt(116) = c

2 sqrt(29) = c

Each hypotenuse is the same so we have

hypotenuse + hypotenuse + 1/2 circumference

2 sqrt(29) + 2 sqrt(29) + 4 pi

4 sqrt(29) + 4pi  cm

Step-by-step explanation:

First we need to deal with the half circle. The radius of this circle is 4, because the diameter is 8. The formula for the circumference of a circle is 2piR.

2pi4 so the perimeter for the half circle would be 8pi/2.

The area of that half circle would be piR^2 so 16pi/2.

Now moving on the triangle part, we need to find the hypotenuse side of AC. We will use the pythagoram theorem. 4^2+10^2=C^2

16+100=C^2

116=C^2

C=sqrt(116)

making the perimeter of this triangle 2×sqrt(116)

The area of this triangle is 8×10=80, than divided by 2 which is equal to 40.

We than just need to add up the perimeters and areas for both the half circle and triangle.

The area would be equal to 8pi+40

The perimeter would be equal to 4pi+4(sqrt(29))

Add this matrix to find the answer.

Answers

Answer:

[tex]\huge\boxed{Option \ 2:\left[\begin{array}{ccc}6&1\\1&5\end{array}\right]}[/tex]

Step-by-step explanation:

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

Adding both the corresponding elements

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

[tex]\left[\begin{array}{ccc}6&1\\1&5\end{array}\right][/tex]

determine if the equation is a linear equation -x + 3y^2=18

Answers

Answer:

No

Step-by-step explanation:

Linear equations must have no squares, roots, cubes, or any powers. If the graph has an asymptote or any restrictions, it is not a linear function.

A linear function will only appear in either point-slope form or slope-intercept form. These forms will not have square roots or powers in them.

-x + 3y² = 18

We know here that this is not a linear function. But we can try to write it in slope-intercept form:

3y² = x + 18

y² = x/3 + 6

y = √(x/3 + 6)

We can see from here that our graph is a square root function and has a restricted domain (no negative numbers).

Alternatively, we can graph the equation to see if it is a constant line (linear equation) or not. When we do so, we see that it is definitely not a linear function:

Solve for x. A. 19 B. 17 C. 15 D. 11

Answers

Answer:

B. 17

Step-by-step explanation:

By the property of intersecting secants outside of a circle, we have:

7 (7 + x) = 8 (13 + 8)

49 +7x = 8*21

7x = 168 - 49

7x = 119

x = 119/7

x = 17

Matthew has 170 tiles he can use for this project. Identify the largest patio design that he can make. Show or explain your reasoning.

Answers

Answer:

Design 12

Step-by-step explanation:

See the attached for missing part of the question

As we see each design comprises of entrance and exit - each one tile and:

Design 1 has 1 row and 3 columns,Design 2 has 2 rows and 4 columns,Design 3 has 3 rows and 5 columns.

So design x has x rows and two more columns according the pattern we observe.

The number of tiles of design x is:

x by (x + 2) and 2 more tiles

We can put it as equation to get 170 tiles and solve for x:

x(x+2) + 2 = 170x² + 2x - 168 = 0x² - 12x + 14x - 168 = 0x(x - 12) + 14(x - 12) = 0(x + 14)(x - 12) = 0x = - 14 (discarded as negative root)x = 12 (the solution)

So this is a design 12

It has 12 rows, 14 columns, 1 entrance and 1 exit tiles, the total number is

12*14 + 2 = 170 tiles

asap!!
~~~~~~
A line passes through point (–6, –1) and is parallel to the equation y = –2x – 5. What's the equation of the line?

Question 25 options:

y = –2x – 13

y = 12{"version":"1.1","math":"\(\frac{1}{2}\)"}x + 3

y = –12{"version":"1.1","math":"\(\frac{1}{2}\)"}x – 1

y = 2x + 5

click on picture for a, b, c ,or d

Answers

Answer:

y=−2x−13.

Step-by-step explanation:

The equation of the line in the slope-intercept form is y=−2x−5.

The slope of the parallel line is the same: m=−2.

So, the equation of the parallel line is y=−2x+a.

To find a, we use the fact that the line should pass through the given point: −1=(−2)⋅(−6)+a.

Thus, a=−13.

Therefore, the equation of the line is y=−2x−13.

Joey's pizza sells large cheese pizzas for $12.00. Each additional topping costs $0.50. Basketball Boosters bought 12 large pizzas, each with 3 toppings. There are 8 slices per pizza. How much does it cost per slice? Round to the nearest cent.

Answers

Answer:

169 cent

Step-by-step explanation:

Given the following :

Cost of large pizza = $12

Cost of additional topping = $0.5

Number of large pizza purchased = 12

topping per large pizza = 3

Amount paid for each pizza :

(cost of pizza) + (3 * cost of topping)

($12) + (3*$0.5)

($12 + $1.5) = $13.5

Total cost of pizza:

Number of pizzas bought * cost per pizza

12 * $13.5 = $162

Number of slices per pizza = 8

Total slices = 12 * 8 = 96 slices of pizza

Cost per slice :

Total cost / total slices

$162 / 96 = $1.6875

= $1.69 = 169 cent

if the Diameter of a cicle is 28cm calculate the perimeter

Answers

Answer:

Simple. 28pi

// pi is [tex]\pi[/tex].

Which is 88.0 by rounding tenth

Step-by-step explanation:

Please pick me brainliest.

Hope it helps!

Answer:

88 cm

Step-by-step explanation:

Perimeter = πd

= (22/7)× 28

= 88 cm

Can anyone help idk how to do it

Answers

Answer:

Carl can type 450 words in 5 minutes at that rate.

Step-by-step explanation:

Every two minutes, carl can type 180 words. To find out how many words he can type in 1 minute, all we have to to is divide 180 by 2 to get 90wpm (words per minute)

if we multiply 90wpm by 5 Minutes, we get 450 words per minute

Answer: 450 words in 5 minutes

Step by step:
2+2=4
180+180=360
180/2=90
4+1=5
360+90=450

If you want to add or subtract fractions, what is the first thing you need to do?​

Answers

Answer:

take lowest common factor

Step-by-step explanation:

Answer:

Find the least common denominator for both fractions and set up the fractions so they can both contain that same denominator.

Step-by-step explanation:

For example, let's say you want to add the fractions [tex]\frac{3}{4}[/tex] and [tex]\frac{2}{7}[/tex].

First, you will want to find the least common demoninator.  Write out the multiples for both denominators originally given, in this case 4 and 7.  Let's go up to 4*10 and 7*10:

4: 4,8,12,16,20,24,28,32,36,40

7: 7,14,21,28,35,42,49,56,63,70

Se which number in both sets is the first number to be the same in both sets.  That will be your least common denominator.  In this case, the least comon denominator is 28.

To set the fractions right, you would need to multiply the first fraction, 3/4, by 7/7: [tex]\frac{3}{4}*\frac{7}{7}=\frac{21}{28}[/tex]

Then, you would need to multiply the second fraction, 2/7, by 4/4: [tex]\frac{2}{7}*\frac{4}{4}=\frac{8}{28}[/tex]

Now, since both fractions have a common deonminator now, you can add them togther and simplify afterwards if you need to:

[tex]\frac{21}{28}+\frac{8}{28}=\frac{29}{28}=1\frac{1}{28}[/tex]

And that's it.

La madre de rosita se ha comprado una mascarilla por un valor de 1 25 dolares al mismo tiempo se ha comprado un paquete de jabones de 2 00 dolares y luego compra un gel de alcohol en 3 00 dolares después de pagar le queda 7 65 dolares que debemos saber que tengo que hacer para obtener el resultaron

Answers

Answer:

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos es de $13.90

Step-by-step explanation:

La información dada son;

El valor de la máscara = $ 1.25

El valor del paquete de jabones = $ 2.00

El valor del gel de alcohol = $ 3.00

La cantidad que le quedaba después de pagar = $ 7.65

Por lo tanto, tenemos;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = La cantidad que le quedaba después de pagar + El valor del gel de alcohol + El valor del paquete de jabones + El valor de la mascarilla

Por lo tanto;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = $ 7.65 + $ 3.00 + $ 2.00 + $ 1.25 = $ 13.90.

I NEED HELP WITH THIS QUESTION PLEASE ? :(

Answers

Answer:

x=42

Step-by-step explanation:

Mai is putting money into a checking account.Let Y represent the total amount of money in the account (dollars)Let X represent the number of weeks Mai has been adding money suppose that x and y are related by the equation 550+40x =y what is the change per week in the amount of money in the account ?

Answers

Answer:

The answer is $40.

Step-by-step explanation:

According to the equation given in the question, we can assume that 550 is constant and was there when Mai started saving into a checking account.

Then as x gets increased by 1 each week, the amount of change in the account per week is $40.

I hope this answer helps.

A survey of 100 people found that 35 people exercise in
the morning, 45 people exercise in the afternoon, and 20
people exercise at night. Tara claims that 35:55, 45:80,
and 20:65 are possible ratios from this data. Jim claims
that 35:100, 45:100, and 20:100 are possible ratios from
this data. Who is correct? Explain.​

Answers

Answer:

Jim's claim is correct

Step-by-step explanation:

Total survey=100 people

Morning exercise=35 people

Afternoon exercise=45 people

Night exercise=20 people

Morning exercise : Total survey

=35 : 100

Afternoon exercise : Total survey

=45 : 100

Night exercise : Total survey

=20 : 100

Jim's claim is correct because in finding the ratio, one has to relate it with the total people involved in the survey.

Tara's claim however seems to relate one variable with two other variables

Example:

35 : 55

Morning exercise : (morning exercise + night exercise)

35 : (35+20)

35 : 55

Answer:

Sample Response: Jim is correct because 35:100, 45:100, and 20:100 are part-to-whole comparisons. There are other possible part-to-part ratios from the data.

If a person invests $290 at 6% annual interest, find the approximate value of the investment at the end of 15 years. A. $450 B. $2030 C. $695 D. $707

Answers

Answer:

[tex]\large \boxed{\sf \bf \ \ C. \ \$ 695 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

At the beginning, we have $290.

After 1 year, we get 290 + 6% * 290 = 290 (1+0.06)= 290 * 1.06

After n years, we get [tex]290\cdot 1.06^n[/tex]

So after 15 years, we get.

[tex]290\cdot 1.06^{15}=695.0018...[/tex]

Thank you

The inverse of the function graphed below is a function.
A. True
B. False

Answers

Answer:

B. False

Step-by-step explanation:

We are given a graph of a function. Shown graph represents a function because there is only unique value of y for each unique value of x.

So, it would pass the vertical line test.

All the vertical lines on the graph would cross the graph at only single point (unique) point.

But if we draw the inverse function graph, each of (x,y) coordinate would switch to (y,x) and the graph would flip to right side.

And if we draw any vertical line on the graph, it could cut the graph at two or more points.

Therefore, it would not pass the vertical line test and it would not be a graph of a function.

The inverse of the function graphed below is not a function as it fails to pass the horizontal test. Hence, B. False is the right option.

What is a function?

A function is a relation between a dependent and an independent variable, say y and x respectively, written as y = f(x). Any such relationship will be called a function if and only if, there is only one value of y corresponding to every x.

We check for a graphed relation to be a function using the vertical test.

When is the inverse of a function also a function?

The inverse of a function, say y = f(x), is given as x = f⁻¹(y), is also a function when f⁻¹(y) passes the vertical test, or simply y = f(x) passes the horizontal test.

What are vertical and horizontal tests?Vertical test: In the test, vertical lines are taken parallel to the y-axis, and the number of the intersection of the given graph of the relation to this line is tested. If the intersections on every vertical line ≤ 1, then the given relation passes the test, and it is a function.Horizontal test: In the test, horizontal lines are taken parallel to the x-axis, and the number of the intersection of the given graph of the relation to this line is tested. If the intersections on every horizontal line ≤ 1, then the given relation passes the test, and its inverse is a function.

How to solve the given question?

In the question, we are asked to tell whether the inverse of the given function graphed is also a function or not.

To check if the inverse is a function, we perform the horizontal test.

The given graph fails to pass the horizontal test, as for almost every line, the graph intersects two times to the line.

For example, the horizontal line y = 5, the graph intersects at two points.

Thus, the inverse of the function graphed below is not a function as it fails to pass the horizontal test. Hence, B. False is the right option.

Learn more about functions and inverse of functions at

https://brainly.com/question/3831584

#SPJ2

If 24, x, and 6 form the first three terms of an arithmetic sequence
then which of the following is the value of x?
(1) 12
(3) 20
(2) 15
(4) 42

Answers

Answer:  15

===============================================

Work Shown:

d = common difference

p = first term = 24

q = second term = a+d = 24+d

r = third term = q+d = 24+d+d = 24+2d = 6

------------

Solve for d

24+2d = 6

2d = 6-24

2d = -18

d = -18/2

d = -9

We add -9 to each term to get the next term. This is the same as subtracting 9 from each term to get the next term.

------------

First term = 24

Second term = 24-9 = 15

Third term = 15-9 = 6

We get the sequence 24, 15, 6

Please Help. Will Mark Brainliest Answer. A container of juice is taken from the refrigerator and poured into a pitcher. The temperature of the juice will warm to room temperature over time. The temperature of the juice can be modeled by the following function: f(t)=72−32(2.718)−0.06t, where t is measured in minutes after the juice is taken out of the refrigerator. Use the drop-down menus to complete the explanation of how the function models the juice warming over time. Dropdown possible answers: When t = 0, the temperature of the juice is -0.06, 0, 2.718, 32, 40, 72 degrees. As time increases, -32(2.718)^-0.06t gets close and closer to -0.06, 0, 2.718, 32, 40, 72. So, f(t) gets close and closer to -0.06, 0, 2.718, 32, 40, 72.

Answers

Answer:

When t= 0

f(t)= 40 degrees

The value of −32(2.718)^−0.06t approach 0 as t increases

If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72

Step-by-step explanation:

The temperature of the juice can be modeled by the following function: f(t)=72−32(2.718)−0.06t, where t is measured in minutes after the juice is taken out of the refrigerator.

f(t)=72−32(2.718)^−0.06t

When t= 0

f(t)=72−32(2.718)^−0.06(0)

f(t)=72−32(2.718)^(0)

f(t)=72−32(1)

f(t)=72−32

f(t)= 40 degrees

As t increases −32(2.718)^−0.06t

Let t= 1

=−32(2.718)^−0.06(1)

= −32(2.718)^−0.06

= -30.14

Let t = 2

=−32(2.718)^−0.06(2)

=−32(2.718)^−0.12

=−32(0.8869)

= -28.38

The value of −32(2.718)^−0.06t approach 0 as t increases

If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72

When t = 0, the temperature of the juice is 40°.

                    As time increases, [tex]-32(2.718)^{-0.06\times 0}[/tex] gets closer and closer to 0.

                    So, f(t) gets close to 72°

    Function representing the temperature of of the juice at any time 't' is,

[tex]f(t)=72-32(2.718)^{-0.06t}[/tex]

1). If t = 0,

  [tex]f(0)=72-32(2.718)^{-0.06\times 0}[/tex]

          [tex]=72-32(1)[/tex]

          [tex]=40[/tex] degrees

2). If [tex]t\rightarrow \infty[/tex],

    [tex]-\frac{1}{32(2.718)^{0.06t}} \rightarrow 0[/tex]  

[As denominator of the fraction becomes larger and larger with the increase in the value of t, value of fraction gets smaller and smaller]

3). if [tex]t\rightarrow \infty[/tex], [tex]f(t)\rightarrow 72[/tex]

  Therefore, when t = 0, the temperature of the juice is 40°.

                    As time increases, [tex]-32(2.718)^{-0.06\times 0}[/tex] gets closer and closer to 0.

                    So, f(t) gets close to 72°.

Learn more,

https://brainly.com/question/10283950

(x+3)(x-5)=(x+3)(x−5)=

Answers

Answer:

All real numbers are solutions. 0=0

Step-by-step explanation:

(x+3)(x−5)=(x+3)(x−5)

Step 1: Simplify both sides of the equation.

x2−2x−15=x2−2x−15

Step 2: Subtract x^2 from both sides.

x2−2x−15−x2=x2−2x−15−x2

−2x−15=−2x−15

Step 3: Add 2x to both sides.

−2x−15+2x=−2x−15+2x

−15=−15

Step 4: Add 15 to both sides.

−15+15=−15+15

0=0

All real numbers are solutions.

i need help please :(

Answers

Answer:

The answer is option 1.

Step-by-step explanation:

You have to apply Indices Law :

[tex] \frac{ {a}^{m} }{ {a}^{n} } ⇒ {a}^{m - n} [/tex]

So for this question,

[tex] \frac{ {7}^{ - 3} }{ {7}^{ - 5} } = {7}^{ - 3 - ( - 5)} = {7}^{ - 3 + 5} = {7}^{2} [/tex]

Answer :

7²

[tex] \frac{ {7}^{ - 3} }{ {7}^{ - 5} } = \\ {7}^{ - 3 - ( - 5)} = \\ {7}^{ - 3 + 5} = {?}^{2} [/tex]

24. Three minus four times a number is equal to ten times a number plus ten.
25. Four times the quantity of three times c plus 5 is equal to 8.
26. Six less than two thirds of a number is negative ten. Find the number.
27. Twenty-nine is thirteen added to four times a number. What is the number.

Answers

Answer:

(24) 3 - 4b = 10c + 10

(25) 4(3c+5) = 8

(26) - 6

(27) 4

Step-by-step explanation:

These questions require that words are translated into equations and then may be solved.

(24)  Three minus four times a number is equal to ten times a number plus ten.

let the first number be b.

(a)Three minus four times a number ... can be represented as:

3 - (4 x b) = 3 - 4b

(b) ...ten times a number plus 10

let the other number be c. Therefore we have;

(10 x c) + 10 = 10c + 10

Now, three minus four times a number is equal to ten times a number plus ten means that expressions in (a) and (b) above are equal. i.e

3 - 4b = 10c + 10

(25) Four times the quantity of three times c plus 5 is equal to 8.

(a) four times the quantity of three times c plus 5 can be represented as

4 x (3 x c + 5) = 4(3c + 5)

(b) ... is equal to 8. This means that the expression in (a) is equal to 8.

4(3c + 5) = 8

(26) Six less than two thirds of a number is negative ten. Find the number.

(a) six less than can be represented as:

- 6

(b) two thirds of a number can be represented as

([tex]\frac{2}{3}[/tex])x           [where x is the number]

(c) six less than two thirds of a number can thus be written as;

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

(d) ... is negative 10 means that the expression is (c) above is equal to -10. i.e

([tex]\frac{2}{3}[/tex])x - 6 = -10

(e) Find the number.

The number can be found by solving for x in the expression in (d) above.

([tex]\frac{2}{3}[/tex])x - 6 = -10         [multiply through by 3]

2x - 18 = -30        [collect like terms]

2x = -30 + 18

2x = -12               [divide both sides by 2]

x = - 6

Therefore, the number is -6

(27) Twenty-nine is thirteen added to four times a number. What is the number.

(a) ... thirteen added to four times a number can be written as:

13 + 4b         [where the number is b]

(b) Twenty-nine is thirteen added to four times a number means that the 29 is equal to the expression in (a) above. i.e

29 = 13 + 4b

(c) Find the number.

The number can be found by solving for b in the expression in (b) above. i.e

29 = 13 + 4b        [collect like terms]

4b = 29 - 13

4b = 16                [divide both sides by 4]

b = 4

Therefore, the number is 4.

when simplifying the expression y=(2x(x-3)(x-3))/(x-1)(x-3) do all of the x-3 s get cancelled or just one in the numerator and one in the denominator?​

Answers

Answer:

Just one of the ones in the numerator and the one in the denominator

Step-by-step explanation:

Find the slope of the line passing through the points (-9, -3) and (7,-7).
DI
DD
Undefined
$
?

Answers

Answer:

-1/4

Step-by-step explanation:

Slope = y/x - y1/x1

=> -7/7 - (-3/-9)

=> -7 +3 / 7+9

=> -4/16

=> -1/4

The slope for the given coordinates of points is -1/4.

What is the slope of straight line?

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.

The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The given points are (-9, -3) and (7,-7).

The general expression to find the slope for two points (x₁, y₁) and (x₂, y₂) is given as,

m = (y₁ - y₂)/(x₁ - x₂)

Plug (x₁, y₁) = (-9, -3) and (x₂, y₂) = (7, -7) to get,

⇒ m = (-3 + 7)/(-9 - 7)

⇒ -1/4

Hence, the slope is obtained as -1/4.

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WILL CHOOSE BRAINLIEST Let Events A & B be described as follows: P(A) = watching a movie P(B) = going out to dinner The probability that a person will watch a movie is 62% and the probability of going out to dinner is 46%. The probability of watching a movie and going out to dinner is 28.52% Are watching a movie and going out to dinner independent events? Group of answer choices No, because the P(A)P(B) ≠ P(A and B). Yes, because the P(A)P(B) = P(A and B). No, because the P(A) + P(B) ≠ P(A and B). Yes, because the P(A) + P(B) is greater than 100%.

Answers

Answer:

Yes, because the P(A)P(B) = P(A and B)

Step-by-step explanation:

Independent Events are events that occurs simultaneously i.e they occur at the same time. This means that the occurrence of one does not affect the other. If A and B are two events, for the to be independent then;

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

Given: P(A) = watching a movie = 62% = 0.62

P(B) = going out to dinner = 46% = 0.46

The probability of watching a movie and going out to dinner will be

P(A and B)

P(A and B) = 0.62×0.46

P(A and B) = 0.2852

P(A and B) = 28.52%

Since the probability of watching a movie and going out to dinner is 28.52% which tallies with the question, hence it can be concluded that watching a movie and going out to dinner are independent events.

The surface area, A, of a cylinder of radius, r, and height, h, can be found with the equation above. Which of the following correctly shows the cylinder's height in terms of its radius and surface area?

Answers

Step-by-step explanation:

If r and h are the radius and height of the cylinder, then its surface area A is given by :

[tex]A=2\pi r^2+2\pi rh[/tex] ....(1)

We need to find the cylinder's height in terms of its radius and surface area. Subtracting [tex]2\pi rh[/tex] on both sides, we get :

[tex]A-2\pi r^2=2\pi rh+2\pi r^2-2\pi r^2\\\\A-2\pi r^2=2\pi rh[/tex]

Dividing both sides by [tex]2\pi r[/tex]. So,

[tex]\dfrac{A-2\pi r^2}{2\pi r}=\dfrac{2\pi rh}{2\pi r}\\\\h=\dfrac{A-2\pi r^2}{2\pi r}[/tex]

Hence, this is the required solution.


Rearrange the equation below to identify the variables a, b and c.
0 = 4x – 5x2​

Answers

Answer:

a = -5x

b = 4

c = 0

Step-by-step explanation:

binomial equation is written in form of

[tex]ax^2 + bx + c = 0[/tex]

given equation

[tex]0 = 4x - 5x^2[/tex]

rearranging it we have

[tex]0 = - 5x^2 + 4x + 0[/tex]

comparing this equation with [tex]ax^2 + bx + c = 0[/tex]

comparing coefficient of variables  with same power.

a = -5x

b = 4

c = 0

If you're good at exact values of trig ratios pea shell me with 13a

Answers

It is an equilateral triangle so its angles are equal 60°. From the definition, we know that:

[tex]\sin60^\circ=\dfrac{h}{4}[/tex]

and

[tex]\sin60^\circ=\dfrac{\sqrt{3}}{2}[/tex]

so

[tex]\dfrac{\sqrt{3}}{2}=\dfrac{h}{4}\quad \Big|\cdot4\\\\\\h=\dfrac{4\cdot\sqrt{3}}{2}\\\\\boxed{h=2\sqrt{3}}\\[/tex]

Answer:

h = √12

Step-by-step explanation:

use the Pythagorean

h² = 4² - 2²

h² = 16 - 4

h = √12

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