Find the gradient of the line segment joining of
(1, 1) and (3, 5)

Answer:

[tex]\huge\boxed{\sf x - 3 }[/tex]

Step-by-step explanation:

Let the certain number be x

So,

Sum is to add so we'll use the sign +

= x + (-3)

We know that + and - makes - because - sign will flip the + sign and make it negative, So:

= x - 3

[tex]\rule[225]{225}{2}[/tex]

Solution: c-3

[tex]\searrow[/tex]

Detailed explanation:

[tex]\searrow[/tex]

This problem tells us to convert the verbal phrase (in words) "the sum of a certain number and -3" into an algebraic expression, which is written in numbers.

Let's start by taking a look at our problem.

"the sum of a certain number and -3". We can first write this "certain number" as one letter (any letter you want). Let it be c.

Our expression already looks a little easier: "the sum of c and -3".

Now, the word "sum" tells us to add. So we should add c and -3.

[tex]--\mapsto\boldsymbol{c+-3}[/tex]

Which is the exact same thing as [tex]\boldsymbol{c-3}[/tex].

Voila! There's our answer.

______________________

Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

_______________________

Answer:

45 dollars for going over 2GB

Step-by-step explanation:

If he pays 25 dollars every month and he goes over 2 GB then he’ll have to pay 20 dollars extra since every GB over cost 10 dollars. The equation is 25+10+10 which equals 45.

An expression is a mixture of terms that are combined by using operations such as subtraction, addition, multiplication, and division. 

The amount when 2 GB is used over the limit in a month is $45.

An expression is a mixture of terms that are combined by using operations such as subtraction, addition, multiplication, and division. 

Example: 2x + 3x2  is an expression.

We have,

Cost of data plan with 2 GB = $25

Cost of one GB = $10

The equation that can be used to find the amount to pay when using x GB over the limit in a month:

= 25 + 10x

The amount when 2 GB is used over the limit in a month:

= 25 + 10 x 2

= 25 + 20

= $45

Thus,

The amount when 2 GB is used over the limit in a month is $45.

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Using the graph attached, If g(x) = 2f(x-1), the graph of the function will be:  g(x) = x - 7.

Using the graph, the function is:

f(x-1) =1/2 (x-1) - 3

f(x-1) = 1/2x - 1/2 - 3/1

f(x-1) = 1/2x - 7/2

So:

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

g(x) = 2 (1/2x - 7/2)

g(x) = x - 7

Therefore,:

At  x = 0,  y = -7

y = 0, x = -7

Thus, Using the graph attached, If g(x) = 2f(x-1), the graph of the function will be:  g(x) = x - 7.

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Got it right on Plato/Edmentum UωU <3

Answer+Step-by-step explanation:

[tex]f^{-1}\left( x\right) =\frac{1}{7} x^{2}+3 \ ,\text{where}\ x\geq 0[/tex]

Answer:

1

Even degree: the start and the end of the graph goes either both up or down (1 and 4)

positive leading coefficient: right side of the graph is going up (1 and 2)

Answer:

11 + 5√5

Step-by-step explanation:

6 + 3√5 +2√5 + 5

11 + 5√5

root n * root n = n , which is why there is a 5 at the end

Answer:

the answer is 11+5√5

Step-by-step explanation:

Answer:

$26

Step-by-step explanation:

Let blueberry pies = x and lemon pies = y.

4x + 13y = 230

4x + 2y = 76

Using elimination, we see that 11y = 154. Therefore, y = 14.

4x + 2(14) = 76

4x + 28 = 76

4x = 48

x = 12

x + y = 12 + 14 = 26.

$26 is your answer.

Answer:

Step-by-step explanation:

Let B be the price of a blueberry pie.  Let L be the price of a lemon meringue pie.

We are told that Shreya makes a total of $76 by selling 4 blueberry and 2 lemon meringue pies.  This can be made into an equation:

Shreya:  4B + 2L = $76

We also learn that Shanice is doing particularly well:

Shanice:  4B + 13L = $320

We want to determine the prices for each type of pie, B and L.  We have two equations and two unknowns.  That means we should be able to find the answers by substitution.

Rearrange Shreya's equation to isolate B:

Shreya:  4B + 2L = $76

               4B   = $76 - 2L

                 B = ($76-2L)/4

Now use this definition of B in Shanice's equation:

Shanice:  4B + 13L = $320

                4( ($76-2L)/4) + 13L = $320

                     ($76-2L) + 13L = $320

            11L = 244

                L = $22.18

Use L = $22.18 in either equation and solve for B:

4B + 2L = $76

4B + 2*($22.18) = $76

4B = $31.64

B = $7.91

---

Blueberry pies are $7.91 each.

Lemon meringue pies are $22.18 each

=========

CHECK:  Do these prices provide the correct sales for each person?

            Price($/pie)        Shreya     Shanice

Blueberry          7.91               4            4

Lemon Mer.    22.18                2           13

Blueberry Sales ($)                    31.64        31.64

Lemon Mer. Sales ($)               44.3       288.36

Total Sales                              $76        $320

YES - These prices account for each person's sales.

Answer:

10√7

Step-by-step explanation:

you can simplify the second radical and break it up into

√4 * √7 which then simplifies to 2√7 which you then multiply by 3. 4√7 + 3(2√7) which becomes 4√7 + 6√7 and then you just add the numbers Infront to get 10√7

The number of primes less than 190 using the principle of inclusion-exclusion are 42

The principle of inclusion-exclusion is known as a counting technique that computes the number of elements satisfying at least one of several properties and guaranteeing that the numbers are not counted twice.

Prime numbers are numbers only divisible by 1 and itself.

Prime numbers less than 190 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181

They are 42 in number

Therefore, the number of primes less than 190 using the principle of inclusion-exclusion are 42

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:y-6 = 3(x + 2) [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Equation of line in point - slope form :

[tex]\qquad \tt \rightarrow \:y-y_1 = m(x - x_1)[/tex]

Here :

[tex]\qquad \tt \rightarrow \:y - 6 = 3(x - ( - 2))[/tex]

[tex]\qquad \tt \rightarrow \:y - 6 = 3(x + 2)[/tex]

Answer:

6.6 cm and 14.6 cm

Step-by-step explanation:

(a)

the length of arc AB is calculated as

AB = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{95}{360}[/tex]

     = 2π × 4 × [tex]\frac{95}{360}[/tex]

     = 8π × [tex]\frac{95}{360}[/tex]

     = [tex]\frac{8\pi (95)}{360}[/tex]

     ≈ 6.6 cm ( to the nearest tenth )

(b)

the perimeter (P) of sector AOB is

P = r + r + AB = 4 + 4 + 6.6 = 14.6 cm

Step-by-step explanation:

3.

the circumference of a circle is

2×pi×r

r = 4 cm

so, we know, the full circle circumference is

2×pi×4 = 8×pi = 25.13274123... cm

a.

the arc length of AB is the part of the whole circumference that corresponds to 95° out of the full 360° of a whole circle.

arc AB = 8×pi × 95/360 = pi × 95/45 = pi × 19/9 =

= 6.632251158... cm

b.

the perimeter of OAB (the "pie slice") is then the arc AB plus 2 radius lengths (from the end points on the arc to the center of the circle) :

pi × 19/9 + 2×4 = pi×19/9 + 8 = 14.632251158... cm

Answer:

First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct

Step-by-step explanation:

This question deals with Slope of a line.

Slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

For first climbing equipment rise = 6 feet, run(horizontal) = 4 feet

Thus, slope =  6/4 = 3/2 ≈ 1.5

For second climbing equipment rise = 10 feet, run(horizontal) = 6 feet

Thus, slope=   10/6 = 5/3 ≈ 1.66

Thus,

Slope of first climbing equipment = 3/2 < slope of second climbing equipment = 5/3

Thus, First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: a_{33} = 1\degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

In a matrix, [tex] \sf a_{ij} [/tex] represents an element in " i " th row and " j " th column.

Henceforth, element [tex] \sf a_{33} [/tex] represents element in 3rd row and 3rd column.

[tex]\qquad \tt \rightarrow \:a_{33} = 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

20%

Step-by-step explanation:

Half of 2 = 1

Half of 1.6 = 0.8

1 - 0.8 = 0.2

0.2 × 100 = 20%

If a plane including pints p,q, and r cuts through the cube, the shape that will be gotten is a triangle.

A triangle is a polygon with three edges and three vertices. The sum of the internal angles of a triangle is equal to 180 degrees.

In this case, when a plane including pints p,q, and r cuts through the cube, the shape that will be gotten is a triangle.

The diagram is attached.

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Answer:

(f + g)(x) = 6x³ - 3x² + 7x - 8  

Step-by-step explanation:

Another way of writing (f + g)(x) is f(x) + g(x). So, this question is asking you to combine both of the functions.

f(x) + g(x)                                          

(4x² + 7x - 3) + (6x³ - 7x² - 5)                      <----- Insert functions

-3x² + 7x - 3 + 6x³ - 5                                 <----- Combine 4x² and -7x²

-3x² + 7x - 8 + 6x³                                       <----- Combine -3 and -5

6x³ - 3x² + 7x - 8                                       <----- Rearrange

The linear measure of arc vw as described in the task content is; 46.89in.

It follows from the task content that the radius of the circle with center p is given as pv = 32in. and the angle subtended by the arc is; 84.

On this note, the measure of arc vw is;

= (84/360) × 2 × 3.14 × 32

= 46.89 inches.

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Answer: True: The graph of y=3x²-3 opens up

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (0,−3)(0,-3)

Focus: (0,−35/12)

Axis of Symmetry: x=0

Directrix: y=−37/12

X={-2, -1, 0, 1, 2}

Y={9, 0, -3, 0, 9

Step-by-step explanation:

Answer:

Period = 4 units

Step-by-step explanation:

Standard form of a tangent function:

[tex]f(x)=\sf A \tan(B(x+C))+D[/tex]

The tangent function has a vertical asymptote whenever cos(x) = 0

The tangent function does not have an amplitude because it has no maximum or minimum value.

Given function:

[tex]y=\tan \left(\dfrac{\pi}{4}\left(x-\dfrac{\pi}{3}\right)\right)[/tex]

Therefore:

Answer: 4 units

Step-by-step explanation:

Answer:

[tex]\frac{XM}{4y}=u[/tex]

Step-by-step explanation:

First, multiply both sides by M.

X M = 4uy

Now, divide both sides by 4y.

[tex]\frac{XM}{4y} =\frac{4uy}{4y}[/tex]

Therefore,

[tex]\frac{XM}{4y}=u[/tex]

Answer:

[tex]\fbox {r = 34}[/tex]

Step-by-step explanation:

Finding IQ and RJ by tangent rule :

⇒ IQ = QK = 10

⇒ KR = RJ = 8

Finding PJ :

⇒ PJ = 32 - 8

⇒ PJ = 24

∴ But PJ = PI (by tangent rule)

⇒ PI = 24

Finding r :

⇒ PI + IQ

⇒ 24 + 10

⇒ r = 34

Answer:

false

Step-by-step explanation:

so D(2) is equal to how much money he has after 2 years while D(7) is after 7 years. since he earns 3% interest each year he will have more money after 7 years than 2 years

Answer:

[tex] log_{b}(x) - log_{b}(y) [/tex]

Answer:

the first equation could be something along the lines of [tex]y=3x^{2}[/tex] then the second is [tex]y=3x^{2} -3\\[/tex]

Step-by-step explanation:

this is how shifting works

Answer: A. The function has two distinct real zeros.

Answer:

C. The function has four distinct real zeros.

Step-by-step explanation:

The function intersects y=0 at x=1/2, 4, and 6 twice. It has two solutions at 6 twice as it is a behavior of polynomial or rational functions

Answer: [tex]2x^2+2x-4-\frac{4}{x+1}[/tex]

Not a factor because there is a remainder.

Step-by-step explanation:

Let's use synthetic division to solve this..

-1  ║ 2 | 4 | -2 | -8

   ║    | -2| -2 |  4

   ║ 2 | 2|  -4 |  -4

[tex]2x^2+2x-4-\frac{4}{x+1}[/tex]

PS: if anyone knows a better way to do a synthetic division chart please let me know.

Answer:

Step-by-step explanation:

We got two shapes in the given figure,on the right we got a rectangle and on the left we have a square.

Area of rectangle:-

Area of square :-

Total area :-

Answer:

Step-by-step explanation:

you have two rectangles, the bigest has the base of 6cm and the height of 4cm, the area is 6 * 4 = 24cm ^ 2, the other rectangle has the base of 6 - 4 = 2 and the height of 5 - 4 = 1, 2*1=2.

we add the dimensions and we have the area of ​​the complete figure 24 + 2 =

26 cm ^ 2