What is the equation of the line that passes through (4, -1) and (-2, 3)?

a.) 2 x + 3 y - 5 = 0
b.) -2 x + 3 y - 5 = 0
c.) 2 x - 3 y - 5 = 0

Answer:

3 3/4 hour

Step-by-step explanation:

(3/4) ÷ (1/5) = (3*5) / (4*1)

= 15/4 hour

15/4 = 12/4 + 3/4 = 3 + 3/4 hour

= 3 3/4 hour

Add 8 to both sides.

Add 7 and 8 to get 15.

Divide both sides by 3.

Divide 15 by 3 to get 5.

Subtract 9 from both sides.

Subtract 9 from −15 to get −24.

Divide both sides by 8.

Divide −24 entre 8 para obtener −3.

Swap the sides so that all the terms of the variables are on the left side.

Add 13 to both sides.

Add 8 and 13 to get 21.

Divide both sides by 3.

Divide 21 by 3 to get 7.

Subtract 22 from both sides.

Subtract 22 from 4 to get −18.

Divide both sides by 6.

Divide −18 entre 6 para obtener −3.

Swap the sides so that all the terms of the variables are on the left side.

Subtract 51 from both sides.

Subtract 51 from 84 to get 33.

Divide both sides by 11.

Divide 33 by 11 to get 3.

Solution 1 :-

>> 3k - 8 = 7

>> 3k = 7 + 8

>> 3k = 15

>> k = 15 / 3

>> k = 5

Solution 2 :-

>> 8b + 9 = -15

>> 8b = -15 - 9

>> 8b = -24

>> b = -24 / 8

>> b = -3

Solution 3 :-

>> 8 = 3x - 13

>> 3x = 13 + 8

>> 3x = 21

>> x = 21 / 3

>> x = 7

Solution 4 :-

>> 6p + 22 = 4

>> 6p = 4 - 22

>> 6p = -18

>> p = -18 / 6

>> p = -3

Solution 5 :-

>> 84 = 51 + 11c

>> 11c = 84 - 51

>> 11c = 33

>> c = 33 / 11

>> c = 3

It is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).

To find the domain and range:

Therefore, it is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).

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The complete question is given below:

What are the domain and range of g of x equals the square root of the quantity x plus 4?

(A) D: [4, ∞) and R: [0, ∞)

(B) D: (–4, ∞) and R: (–∞, 0)

(C) D: [–4, ∞) and R: [0, ∞)

(D) D: (4, ∞) and R: (–∞, 0)

Answer:

10, 8

Step-by-step explanation:

l + w = 18

l*w = 80

8 and 10 works

Answer:

Below in bold,

Step-by-step explanation:

a. There's is only one card that fits this description so

Probability = 1/52.

b. There are 2 black Kings so

Probability = 2/52 = 1/26.

c. There are 2 of these - 7 of diamonds and 7 of hearts

so

Probability = 2/52 = 1/26.

d.  There 13 diamonds and 13 hearts so

Probability = 26/52 = 1/2.

e.  There  26 black cards

Probability = 26/52 = 1/2.

Answer:

71

Step-by-step explanation:

Answer:

Step-by-step explanation:

Movie A: 267 students

Movie B: 217 students

Movie C: 233 students

Movie D: 183 students

Answer: [tex]\displaystyle\\\frac{x^3}{y^7}[/tex].

Step-by-step explanation:

[tex]\displaystyle\\x^3y^{-7}=\frac{x^3}{y^7} .[/tex]

Answer:

x = 12

Step-by-step explanation:

1 + 7x = 5x + 25 ( subtract 5x from both sides )

1 + 2x = 25 ( subtract 1 from both sides )

2x = 24 ( divide both sides by 2 )

x = 12

Answer:

12

Step-by-step explanation:

Start by subtracting both sides by 5x:

[tex]1+7x-5x=25\\1+2x=25[/tex]

Subtract 1 from both sides

[tex]2x=24[/tex]

Divide both sides by 2

[tex]x=12[/tex]

[tex]1+7(12)=5(12)+25\\1+84=60+25\\85=85[/tex]

Therefore x = 12

Answer:

13. Two real solutions.

14. No real solutions.

Step-by-step explanation:

Given quadratic equations:

13. [tex]x^2+7x+10=0[/tex]

14. [tex]4x^2-3x+4=0[/tex]

[tex]{\large \textsf{Quadratic Formula: }} x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]

What is the discriminant?

The discriminant (Δ) is b² - 4ac, which is under the square root in the quadratic formula. It is used to determine the number of real solutions (roots) of a quadratic:

13. x² + 7x + 10 = 0

[tex]\implies a=\textsf{1},b=\textsf{7},c=\textsf{10}[/tex]

Find the discriminant value.

[tex]\implies \Delta = b^2 - 4ac[/tex]

[tex]\implies \Delta=(7)^2 - 4(1)(10)[/tex]

[tex]\implies \Delta=49 - 40[/tex]

[tex]\implies \Delta=9[/tex]

As [tex]9[/tex] > 0, this quadratic has two real solutions.

14. 4x² - 3x + 4 = 0

[tex]\implies a=\textsf{4},b=\textsf{-3},c=\textsf{4}[/tex]

Find the discriminant value.

[tex]\implies \Delta = b^2 - 4ac[/tex]

[tex]\implies \Delta = (-3)^2 - 4(4)(4)[/tex]

[tex]\implies \Delta = 9 - 64[/tex]

[tex]\implies \Delta = -55[/tex]

As [tex]-55[/tex] < 0, this quadratic has no real solutions.

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80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible. This can be obtained by converting the given statements into algebraic equation.

Here in the question it is given that,

that is each day the athlete spends 80 min.

So we can write that,

400 min is the time spent by the athlete

400 min  = number of days × time spent by the athlete in one day

400 min  = d × 80

⇒ 80d = 400  

Hence 80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible.

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Considering the angle of the arc, it is found that the value of x is of x = 12º.

It is twice the inside angle.

In this problem, the angle of the arc is of 102º, hence the inside angle is of 51º, which means that we can solve for x as follows:

4x + 3 = 51

4x = 48

x = 12º.

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Answer:

y=1

Step-by-step explanation:

Since you already found x,

We will only be needing one equation to find y..

I will take equation two: 3(2)+2y=8

Step Two: 6+2y=8 (then you minus 6 on each side)

Step Three: 2y=2 (divide)

y=1

The extremum of f(x,y) is subject to the given constraint, There is a global minimum (x,y,z.) (4,2,-8).

An instance of a constraint is the fact that there are only so many hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. one which restricts, limits, or regulates; a test.

A constraint is something that limits or controls what you may do. Their decision to abandon the ride turned into made due to economic constraints. Water shortages in the location could be the main constraint on development. Synonyms: limit, drawback, scale back, rein more Synonyms of constraint.

predicament or restriction. repression of herbal emotions and impulses: to exercise constraint. unnatural restraint in manner, communique, and many others.; embarrassment. Something that constrains.

By lagranier multi plur

of = hog

(2x, is, 22>= 25-47

8x=42

10x + 2 = 42

2

28

2x=4, 4= 2

=2

722 (4)

(4.9,2) = (4.2-8)

(4,2-8)= 84

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The missing length indicated on the right triangle is 120 units

To start with:

The missing length in the right triangle can be represented with the variable x

Next, we have the following equivalent ratio from the given triangle

64 : x = x : 289 - 64

Express the ratio as a fraction

64/x = x/(289 - 64)

Evaluate the difference on the right-hand side

64/x = x/225

Cross multiply in the above equation

x * x = 64 * 225

This gives

x^2 = 64 * 225

Take the square root of x^2 (do not approximate)

x = 64 * 225

Take the square root of 64 and 225 (do not approximate)

x = 64 * 225

Evaluate the product of 8 and 5

x = 120

Based on the given parameters, the missing length indicated on the right triangle is 120 units

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The volume of the 0.3% concentration of sodium fluoride required to mix with 100mL of a strong toothpaste with a 1.1% concentration of sodium fluoride to create a blend with a 0.8% concentration of sodium fluoride is 60 mL.

Mixtures refers to substances which are composed of two or more substances physically combined together.

The 1.1% concentration of sodium fluoride will form a mixture with the 0.3% concentration sodium fluoride.

Let the volume of the 0.3 % concentration toothpaste required be x.

Final volume of toothpaste = (100 + x) mL

Amount of mixture = 0.8 * (100 + x)

100 ml * 1.1 + x * 0.3 = 0.8 * (100 + x)

solving for x

110 + 0.3x = 80 + 0.8x

110 - 80 = 0.8x - 0.3x

30 = 0.5x

x = 60

Therefore, 60 mL of the 0.3% concentration of sodium fluoride is required.

In conclusion, the volume of the weaker solution of the sodium fluoride solution required is obtained from the method of mixtures.

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When [tex]y\ge0[/tex] (above and on the [tex]x[/tex]-axis), we have [tex]|y|=y[/tex]. The parabola [tex]x=y^2[/tex] intersects with [tex]x=-|y|+12[/tex] in this region when

[tex]y^2 = -y + 12 \implies y^2 + y - 12 = (y-3)(y+4) = 0 \implies y=3[/tex]

On the other hand, when [tex]y<0[/tex] (below the [tex]x[/tex]-axis, we have [tex]|y|=-y[/tex], and so the curves intersect when

[tex]y^2 = -(-y) + 12 \implies y^2 - y - 12 = (y - 4)(y+3) = 0 \implies y=-3[/tex]

The area between the curves is then given by the definite integral,

[tex]\displaystyle \int_{-3}^3 (-|y| + 12) - y^2 \, dy[/tex]

The integrand is symmetric about the [tex]x[/tex]-axis, so the integral is equivalent to

[tex]\displaystyle 2\int_0^3 12 - y - y^2 \, dy = 2 \left(12y - \frac{y^2}2 - \frac{y^3}3\right)\bigg|_0^3 = \boxed{45}[/tex]

Answer:

To find the biggest 4-digit number which is a perfect square, we have to take the square of biggest 2-digit number. ∴ The biggest 4-digit number which is a perfect square = 9801.

Step-by-step explanation:

Answer:

9801

Step-by-step explanation:

well we know 100 squared is the first 5 digit square number so it must be 99 squared, which is 9801

Answer:

x = 8

Step-by-step explanation:

→ Add 16 to both sides

x = 8

The correct solution for the given expression [tex]-16+x = -8 \\[/tex]  is [tex]x[/tex] is equal to [tex]8[/tex].

Given expression:

[tex]-16+x =- 8 \\[/tex]

To solve for [tex]x[/tex], Rearrange the equation or isolate [tex]x[/tex] terms on one side of the expression.

Add [tex]8[/tex] on both side of the equation:

[tex]-16+x+8=-8+8[/tex]

Simplify:

[tex]x-8 = 0[/tex]

Isolate [tex]x[/tex] on one side:

[tex]x= 8[/tex]

The correct value of [tex]x[/tex] is [tex]8[/tex].

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Answer:

-4

Step-by-step explanation:

We are going to substitute 0 in for x and solve for y.  

-2(0)+ 8y = -32  Anything times zero is zero

0 + 8 y = -32  Anything plus zero is itself.

8y = -32 Divide both sides by 8

y = -4

Solving a system of equations, we conclude that the value of x is 28.

Here we have the quadratic number pattern:

6, 15, x, 45, ...

First, we have that:

15 - 6 = 9

So 9 is the first difference.

Then we will have:

x = 15 + 9 + a

(where a is the second difference, constant of the sequence).

And:

45 = x + 9 + a + a

Then we have a system of equations:

x = 15 + 9 + a

45 = x + 9 + a + a

We can isolate a on the first equation:

a = x - 24

We can replace that in the other equation:

45 = x + 9 + 2a

45 = x + 9 + 2*(x - 24)

Now we can solve that for x:

45 - 9 = x + 2*(x - 24)

36 = 3x - 48

36 + 48 = 3x

84 = 3x

84/3 = x = 28

The value of x is 28.

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The estimated standard error for the sample is 6

Given,

Sample size, n = 36

Sample variance, [tex]s^{2}[/tex] = 1296

Standard deviation, s = √1296

                                   = 36

Standard error, SE = [tex]\frac{s}{\sqrt{n} }[/tex]

                              = [tex]\frac{36}{\sqrt{36} }[/tex]

                              = [tex]\frac{36}{6}[/tex]

                              = 6

Concept

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Answer:

D) subtract 6 from the previous term

Step-by-step explanation:

27-6=21, 21-6=15, 15-6=9, and 9-6=3

Answer:

No real solutions.

Step-by-step explanation:

To solve this, we need to use Quadratic Formula.

Quadratic Formula:

[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ [/tex]

in the form of:

[tex]a {x}^{2} + bx + c[/tex]

Given information from the question, we can deduce:

a = -1

b = -2

c = 5

Let's substitute these values into the formula.

[tex]x = \frac{ - ( - 2) + - \sqrt{ {( - 2)}^{2} - 4( - 1)( -5)} }{2( - 1)} \\ = no \: real \: solutions[/tex]

if you punch these into the calculator.

Answer:

  (a)  (f +g)(x) = √(x-2) +√(x)

Step-by-step explanation:

The sum of two functions is the sum of their definitions.

  (f +g)(x) = f(x) +g(x)

  (f +g)(x) = √(x -2) +√(x)

Note: the radicals can only be combined if they can be reduced to a form that has the same expression under the radical. Here, that is not the case, so there is no way to simplify the sum.

The option that describes the end behavior of the graph of the square root function with coordinates (-3, 0), (0, 3), (2, 4), and (5, 5), is the option;

C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.

The given coordinates on the graph are;

(-3, 0), (0, 3), (2, 4), and (5, 5)

The coordinates of the starting point of the graph = (-3, 0)

Shape of the graph = Extends from point (-3, 0), upwards and to the right

Therefore;

As the x-value increases, the y-value increases and vice versa, with, x increasing faster than y.

However, given that the graph is for a square root function, the correct option is option C;

C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.

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Answer:

b

Step-by-step explanation:

B

First symmetrically cut the pentagon to get 5 pieces. (So that you will get the idea that this polygon is divided into 5 triangles)

Then find the area of one of the triangles:

Area of Triangle = [tex]\frac{1}{2} bh[/tex]

A = [tex]\frac{1}{2}[/tex] × 4 × 10

A = 20 m²

To find the area of the whole pentagon shape:

A = 20 × 5 = 100 m²

Hope it helps!