What is the point-slope form of a line that has a slope of 5 and passes through the point (3, –4)?

Your answer is the third option, x = -2 and x=6

We can see this because the solutions of x^2/2 - 8 = 2x - 2 are going to be where the lines y = x^2/2 - 8 and y = 2x - 2, because this is where the two equations are equal to each other.

Therefore, we can just look on the graph at where the two lines intersect, and see that it happens when x = -2 and x = 6.

I hope this helps!

Answer:

x=-2 and x=6

Step-by-step explanation:

The solution to a graph would be where the two lines intersect. When you look at the graph you plot where they connect

(-2, -6), (6, 10)

The x value is the very first variable in an ordered pair. Therefore, the solution to this graph would be x=-2 and x=6.

Answer:

(2,0) was already given so (-1,0) is the other one.

Step-by-step explanation:

So we are asked to use the quadratic formula.

To find the x-intercepts (if they exist) is use:

[tex]\text{ If } y=ax^2+bx+c \text{ then the } x-\text{intercepts are } (\frac{-b \pm \sqrt{b^2-4ac}}{2a},0)[/tex].

Let's start:

Compare the following equations to determine the values for [tex]a,b, \text{ and }c [/tex]:

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

[tex]y=4x^2-4x-8[/tex]

So

[tex]a=4[/tex]

[tex]b=-4[/tex]

[tex]c=-8[/tex]

We are now ready to enter into our formula:

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

[tex]x=\frac{4 \pm \sqrt{(-4)^2-4(4)(-8)}}{2(4)}[/tex]

[tex]x=\frac{4 \pm \sqrt{16+16(8)}}{8}[/tex]

[tex]x=\frac{4 \pm \sqrt{16(1+8)}}{8}[/tex]

[tex]x=\frac{4 \pm \sqrt{16}\sqrt{1+8}}{8}[/tex]

[tex]x=\frac{4 \pm 4\sqrt{9}}{8}[/tex]

[tex]x=\frac{ 4 \pm 4(3)}{8}[/tex]

[tex]x=\frac{4 \pm 12}{8}[/tex]

[tex]x=\frac{4(1\pm 3)}{8}[/tex]

[tex]x=\frac{1(1\pm 3)}{2}[/tex]

[tex]x=\frac{1 \pm 3}{2}[/tex]

[tex]x=\frac{1+3}{2} \text{ or } \frac{1-3}{2}[/tex]

[tex]x=\frac{4}{2} \text{ or } \frac{-2}{2}[/tex]

[tex]x=2 \text{ or } -1[/tex]

So the x-intercepts are (2,0) and (-1,0).

(2,0) was already given so (-1,0) is the other one.

Answer:

34 bottles per person per week

Step-by-step explanation:

1) identify info: The cycling tour has 340 bottles of water for each week.there are 10 people on the tour.

2) compile info: 340 bottles for 10 people per week

3) calculate: bottles per person = 340/10 = 34 bottles per person each week

The question asks to figure out how many bottles of water each person on a cycling tour gets per week. By dividing the total bottles of water (340) by the number of people (10), we find that each person receives 34 bottles of water per week.

The question is asking us to determine how many bottles of water each person on the cycling tour gets per week. This involves division in mathematics as we are dividing the total number of water bottles by the number of people.

To solve such problems, we start with the total amount given, which is 340 bottles of water here. Then, we divide this total by the number of individuals, which is 10 people in this case. So, the calculation becomes 340 bottles ÷ 10 people.

This calculation gives us 34 bottles. Hence, each person on the cycling tour gets 34 bottles of water per week.

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Answer:3 hours

Step-by-step explanation:

i did it one edg

5)

[tex]\bf \begin{array}{|cc|cccc|ll} \cline{1-6} sodas&x&\underline{24}&28&\underline{32}&36\\ \cline{1-6} cost&y&\underline{18}&21&\underline{24}&27\\ \cline{1-6} \end{array}~\hspace{9em} (\stackrel{x_1}{24}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{32}~,~\stackrel{y_2}{24}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{24-18}{32-24}\implies \cfrac{6}{8}\implies \cfrac{3}{4}[/tex]

6)

[tex]\bf \begin{array}{|cc|cc|ll} \cline{1-4} year&x&0&12\\ \cline{1-4} \$&y&720&1080\\ \cline{1-4} \end{array}~\hspace{10em} (\stackrel{x_1}{0}~,~\stackrel{y_1}{720})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{1080}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1080-720}{12-0}\implies \cfrac{360}{12}\implies \cfrac{30}{1}\implies 30[/tex]

7)

slope as you should already know is rise/run, or how much something moves in relation something else, namely how much the y-axis go up as the x-axis moves sideways, one moves, the other follows, but the increments will be different, sometimes the same, but usually different.

the y-intercept means, when the graph of the equation touches or intercepts the y-axis, and when that happens x = 0, or the horizontal distance is at bay.

for the slope on  6), 30 or 30/1 means, for every 1 year(x) passed, the worth(y) increased by 30, or jumped by 30 units, so as the x-axis moved 1, the y-axis moved 30.  After 12 years 30 * 12 = 360, and we add the initial 720 and we end up with 1080.

the y-intercept, well, as aforementioned is when x = 0, is year 0.

Answer:

Top:

The rate change is 4.

Bottom:

The rate change is 3.

Step-by-step explanation:

24+4= 28     28+4=32  (and)  32+4=36

18+3=21  21+3=24    (and)  24+3=27

I will get back to you on the rest>

Hope this helped tho! :3

Answer:

D

Step-by-step explanation:

Formula

Volume = pi*r^2*h

Givens

r = x

h = 3x

Volume= 242

Solution

242 = pi * x^2 * 3x

242 = 3.14 * 3x^3                    Divide by pi

242/3.14 = 3.14 * 3x^3 / 3.14   Do the division

77 = 3x^3                                 Divide by 3

77/3 = 3x^3 /3

25.69 = x^3                              Take the cube root of both sides.

2.95  = x

The height of the cylinder is 3 times that of the radius of the circle (x)

The answer is 8.85. I suppose the closest answer is 8.

Answer:

I think that the answer is A.

Answer:

No options is correct.    

Step-by-step explanation:

Given : The product of -4 and 3.

To find : Which expression could be used to determine the product ?

Solution :

The product of -4 and 3 is [tex]-4\times 3=-12[/tex]

To know which expression we solve each options and get whose result is same as ours,

A) [tex](-4)(3)\times (-4)(\frac{1}{4})[/tex]

Solve,

[tex](-4)(3)\times (-4)(\frac{1}{4})= -12\times -1=12[/tex]

B) [tex](-4)(3)+(-4)(\frac{1}{4})[/tex]

Solve,

[tex](-4)(3)+(-4)(\frac{1}{4})= -12+(-1)=-13[/tex]

C) [tex](3)(-4)\times (3)(\frac{1}{4})[/tex]

Solve,

[tex](3)(-4)\times (3)(\frac{1}{4})=-12\times\frac{3}{4}=-9[/tex]

D) [tex](3)(-4)+(3)(\frac{1}{4})[/tex]

Solve,

[tex](3)(-4)+(3)(\frac{1}{4})=-12+\frac{3}{4}=-11.25[/tex]

From the given options, No options will get the product.

Answer:

the cost of rib eye steak dinner = $22.47

the cost of grilled salmon dinners= $10.57 .....

Step-by-step explanation:

Let x be the rib eye steak dinner.

Let y be the grilled salmon dinner.

According to the first given statement:

12x+27y= $554.98    (equation 1)

According to the second statement:

26x+9y=$584.36      ( equation 2)

Lets take a look at the 1st equation:

12x+27y= $554.98

12x=$554.98- 27y

x=$554.98- 27y/12

Now substitute the value of x in 2nd equation:

26x+9y=$584.36

26($554.98- 27y/12)+9y=$584.36

26(554.98- 27y)+9y=584.36*12

14429.48-702y=7012.32

-702y=7012.32-14429.48

-702y= -7417.16

y= 7417.16/702

y=$10.57

Now substitute the value of y in equation 1:

12x+27y= $554.98

12x+27(10.57)=554.98

12x+285.39 = 554.98

Move the constant to the R.H.S

12x=554.98-285.39

12x=269.59

Divide both the terms by 12

12x/12=269.59/12

x=$22.47

Thus the cost of rib eye steak dinner = $22.47

the cost of grilled salmon dinners= $10.57 .....

Answer: 28 km

Step-by-step explanation: For the first 25 minutes, he drove 60 km/h. Since there is 60 minutes in an hour, we know that he drove 25 km. The rest of the journey is 15 minutes. 15 minutes is 1/4 of an hour, so get 1/4 of 12 km/h. This would be 3 km. Add 25 km and 3 km. The distance between the 2 malls is 28 km.

The feline expanded in weight compared with the canine's underlying weight which is steady with the data given.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Let c be the feline's unique weight. Let c* be the feline's new weight.

Let d be the canine's unique weight. The d* be the canine's new weight.

The equation is given as,

c = 1.2 c

d = .9 d

c = d

The other equation is given as,

p = (d - c)/d = 1 - c/d

We know that the given condition,

c = d = 0.9 d

Then the equation is written as,

p = 1 - 0.9d/d

p = 1 - 0.9

p = 0.1 or 10%.

Hence, toward the beginning, the rate contrast compared with the canine was,

q = (d - c)/d = 1 - 0.75 = 0.25 or 25%.

That is, the feline weighed not exactly like the canine toward the beginning. Since p < q, the feline expanded in weight compared with the canine's underlying weight — which is steady with the data given.

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if the circle has a diameter of 25.2, its radius is half that or 12.6.

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=12.6\\ \theta =168 \end{cases}\implies s=\cfrac{\pi (168)(12.6)}{180} \\\\\\ s=11.76\pi \implies \implies \stackrel{\pi =3.14~\hfill }{s=36.9264}\implies \stackrel{\textit{rounded up}}{s=36.93}[/tex]

Answer:

x = -3 or x = 2

Step-by-step explanation:

It is given a quadratic equation,

(x + 3)(x - 2) = 0

To find the solution of given equation

Let  (x + 3)(x - 2) 0

⇒ either (x + 3) = 0 or (x - 2) = 0

If (x + 3) = 0 then  x = -3

If (x - 2) = 0 then x = 2

Therefore the solution of given equation are

x = -3 or x = 2

D) two parabolas one facing down with a vertex at 0, 3 and one facing up with a vertex at 0, negative 3

First of all, let's rewrite the equations in a mathematical language:

[tex]y=\frac{3}{4}x^2-3[/tex]

Since the leading coefficient, the number that accompanies [tex]x^2[/tex] is positive, that is, its value is 3/4, then the parabola opens upward. On the other hand, the vertex can be found as:

[tex](h,k)=\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right) \\ \\ a=3/4 \\ b=0 \\ c=-3 \\ \\ h=-\frac{0}{2(3/4)}=0 \\ \\ k=f(0)=\frac{3}{4}(0)^2-3=-3 \\ \\ \\ \boxed{Vertex \rightarrow (h,k)=0,-3}[/tex]

[tex]y=-\frac{3}{4}x^2+3[/tex]

Since the leading coefficient is negative, that is, its value is -3/4, then the parabola opens downward. Similarly the vertex can be found as:

[tex](h,k)=\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right) \\ \\ a=-3/4 \\ b=0 \\ c=3 \\ \\ h=-\frac{0}{2(-3/4)}=0 \\ \\ k=f(0)=-\frac{3}{4}(0)^2+3=3 \\ \\ \\ \boxed{Vertex \rightarrow (h,k)=0,3}[/tex]

Both graph are shown below and you can see that the conclusion of our problem is correct.

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Answer:

I think the answer is d

Step-by-step explanation:

since the graph is a lot bigger than the females, but the box thing is in about the same spot as the females ( you know what i mean), but i'm not 100% sure, but i think its the safest answer

Answer:

[tex]\large\boxed{3^\frac{2}{3}}[/tex]

Step-by-step explanation:

[tex]Use\\\\\sqrt[n]{a^m}=a^\frac{m}{n}\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}\\\\\bigg(\sqrt[4]{9^{15}}\cdot\sqrt{3^3}\bigg)^\frac{2}{27}=\bigg(\sqrt[4]{(3^2)^{15}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(\sqrt[4]{3^{2\cdot15}}\cdot3^{\frac{3}{2}}\bigg)^\frac{2}{27}\\\\=\bigg(3^{\frac{30}{4}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(3^{\frac{15}{2}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(3^{\frac{15}{2}+\frac{3}{2}}\bigg)^\frac{2}{27}[/tex]

[tex]=\bigg(3^{\frac{18}{2}}\bigg)^\frac{2}{27}=\bigg(3^9\bigg)^\frac{2}{27}=3^{9\cdot\frac{2}{27}}=3^\frac{2}{3}[/tex]

Answer:

6

Step-by-step explanation:

You can see how f(x) is now f(8), this implies you have to replace any x's you see with an 8.

So f(8) = 2(8-5) = 2(3) = 6

Answer:

B+

Step-by-step explanation:

Grades earned in five subjects are;

A,C+,A-,B- and B+

Remaining subject is biology

Total number of subjects will be=6

3.2 gpa as a percentile =86

For her to maintain 3.2 gpa total sum of percentile in the 6 subjects should be at least

6×86=516

Emily total sum of subjects in percentile is 93+77+90+80+87=427

Find the difference , 516-427=89

89 is grade B+

Emily should earn a grade of B+ to keep her 3.2 gpa

Answer: Choice C

x represents time and x is positive; y value is 45 times more than the x value

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

Explanation:

The inequality y > 45x is the same as y > 45*x

We have y greater than 45*x meaning that y is 45 times more than the x value.

As an example, if x = 2, then 45*x = 45*2 = 90 meaning that y must be larger than 90 if you picked x = 2. In this scenario, x = 2 means that if you traveled for 2 hours then you must have gone more than 90 miles in total distance.

Answer:

A: radius of the sphere

Step-by-step explanation:

The formula for surface area is A = 4πr^2

With r being the radius and A the surface area.

For volume it is

V= (4/3)πr^3

to determine the surface area and volume of sphere A: the radius of the sphere is required.

The formula for surface area is A = 4πr^2

With r being the radius and A the surface area.

For volume it is

V= (4/3)πr^3

The radius is half the diameter, so we use the equation r = D / 2. This is the same method used to calculate the radius from the diameter of a circle. If you have a sphere with a diameter of 16 cm, divide 16/2 to find the radius to make it 8 cm. If the diameter is 42, the radius is 21.

A sphere is defined as a set of all points in distant 3D Euclidean space. ("Radius") From a specific point ("center"). Twice the radius is called the diameter, and the pair of points on the sphere on the opposite side of the diameter is called the antipodes.

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AnswerB. because x is in denominator

Step-by-step explanation:

Answer:

[tex]6\leq W\leq 8[/tex]

[tex]8\leq L\leq 10[/tex]

Step-by-step explanation:

Let the length of the rug be = L

Let the width of the rug be = W

Area =[tex]L\times W[/tex]

The length is 2 feet more than the width, so [tex]L=W+2[/tex]

Area = [tex](W+2)\times W[/tex]

= [tex]W^{2} +2W[/tex]

Now given is that the area of rug to be no smaller that 48 square feet and no bigger than 80 square feet.

This can be modeled as:

[tex]48\leq W^{2} +2W\leq 80[/tex]

Solving it separately:

[tex]48\leq W^{2} +2W[/tex]

=> [tex]0\leq W^{2}+2W \leq -48[/tex]

=> [tex]6\leq W[/tex]

[tex]W^{2} +2W-80\leq 0[/tex]

=> [tex]W\leq 8[/tex]

We have the following result:

[tex]6\leq W\leq 8[/tex]

And length will be :

[tex]6+2\leq L\leq 8+2[/tex]

[tex]8\leq L\leq 10[/tex]

Answer:  The required co-ordinates of the point are (9, 0).

Step-by-step explanation:  We are given to find the co-ordinates of the point that is [tex]\dfrac{3}{5}[/tex] of the way from A(-9,3) to B(21, -2).

Let K be the required point. Then, we mus have

[tex]AK:AB=3:5\\\\\Rightarrow \dfrac{AK}{AK+BK}=\dfrac{3}{5}\\\\\\\Rightarrow 5AK=3AK+3BK\\\\\Rightarrow 2AK=3BK\\\\\Rightarrow AK:BK=3:2.[/tex]

We know that

the co-ordinates of a point that divides the line joining the points (a, b) and (c, d) in the ratio m : n are given by

[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{2}\right).[/tex]

For the given division, m : n = 3 : 2.

Therefore, the co-ordinates of the point K are

[tex]\left(\dfrac{3\times21+2\times(-9)}{3+2},\dfrac{3\times(-2)+2\times3}{3+2}\right)\\\\\\=\left(\dfrac{63-18}{5},\dfrac{-6+6}{5}\right)\\\\=\left(\dfrac{45}{5},\dfrac{0}{5}\right)\\\\=(9,0).[/tex]

Thus, the required co-ordinates of the point are (9, 0).

Building and solving an equation, it is found that the coordinates are: (9,0).

C is 3/5 of the way from A to B, thus:

[tex]C - A = \frac{3}{5}(B - A)[/tex]

This is used to find both the x-coordinate and the y-coordinate of C.

First, the x-coordinate, considering [tex]C = x, A = -9, B = 21[/tex].

[tex]C - A = \frac{3}{5}(B - A)[/tex]

[tex]x + 9 = \frac{3}{5}(21 + 9)[/tex]

[tex]x = 18 - 9[/tex]

[tex]x = 9[/tex]

Then, the y-coordinate, considering [tex]C = y, A = 3, B = -2[/tex].

[tex]C - A = \frac{3}{5}(B - A)[/tex]

[tex]y - 3 = \frac{3}{5}(-2 - 3)[/tex]

[tex]y = -3 + 3[/tex]

[tex]y = 0[/tex]

Thus, the coordinates are (9,0).

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Answer:

[tex]\boxed{\text{1. y + 5 = -4(x - 3); \qquad 2. y - 8 = x + 1}}[/tex]

Step-by-step explanation:

Question 1

The point-slope formula for a straight line is

y – y₁ = m(x – x₁)

x₁ = 3; y₁ = -5; m = -4  

Substitute the values

[tex]\boxed{\textbf{y + 5 = -4(x - 3)}}[/tex]

The diagram shows the graph of equation 1 (red) with slope -4 passing through (3,-5).

Question 2

x₁ = -1; y₁ = 8; m = 1  

Substitute the values

[tex]\boxed{\textbf{y - 8 = x + 1}}[/tex]

The diagram shows the graph of equation 2 (green) with slope 1 passing through (-1,8).

Step-by-step explanation:

The sum of the product of a and b and the number c:i

[tex]a\cdot b+c=ab+c[/tex]

The sum of the product of a and b and the number c, written as a mathematical expression, is ab + c.

The question is asking for the sum of the product of a and b and the number c. In mathematical terms, this can be written as an expression: ab + c. This expression first calculates the product of a and b (represented by 'ab') then adds the number c to this product.

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Answer:

4 ropes.

Step-by-step explanation:

There are 100 cms in a meter.

So 10 meters = 10* 100

= 1000 cms.

1000 / 210 = 4  ropes with  160 cms remaining.

Answer:

3x³ - 13x² + 7x - 12

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

x(3x² - x + 3) - 4(3x² - x + 3) ← distribute both parenthesis

= 3x³ - x² + 3x - 12x² + 4x - 12 ← collect like terms

= 3x³ - 13x² + 7x - 12

Answer:

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

Step-by-step explanation:

we know that

2 is a zero of multiplicity 3 of the polynomial

so

we have that

x=2  is a solution of the polynomial

A factor of the polynomial is

[tex](x-2)^{3}[/tex] ----> is elevated to the cube because is a multiplicity 3

and the other solution is x=-2

since the polynomial  is fifth degree, x=-2 must have a multiplicity 2

so

the other factor of the polynomial is  

[tex](x+2)^{2}[/tex] ----> is squared because is a multiplicity 2

therefore

The polynomial is equal to multiply the factors by the leading coefficient

so

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

The polynomial function based on the given properties: zeros at 2 (with multiplicity 3) and -2 (with multiplicity 1), leading coefficient of 2, is f(x) = 2(x - 2)³(x + 2).

To construct a polynomial with given zeros and multiplicities, we need to set up a product of binomial factors based on the zeros, with each binomial factor raised to the power of its respective multiplicity. The resulting polynomial is the given function f(x).

For the given properties, the roots are 2 and -2. The root 2 has multiplicity 3 and the root -2 has multiplicity 1. Also, the leading coefficient is 2. So, we can set up the polynomial function as follows:

f(x) = 2(x - 2)3(x + 2)

This represents a fifth degree polynomial function that has the zeros and multiplicities listed, with the leading coefficient of 2.

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Answer:

[tex]\large\boxed{4x^4\sqrt[3]{2x^2}}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{2x^5}\cdot\sqrt[3]{64x^9}\qquad\text{use}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\=\sqrt[3]{2}\cdot\sqrt[3]{64}\cdot\sqrt[3]{x^5x^9}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt[3]2\cdot4\cdot\sqrt[3]{x^2x^3x^9}\\\\=4\sqrt[3]2\cdot\sqrt[3]{x^2x^{12}}\\\\=4\sqrt[3]2\cdot\sqrt[3]{x^2x^{4\cdot3}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=4\sqrt[3]2\cdot\sqrt{x^2(x^4)^3}\\\\=4\sqrt[3]2\cdot\sqrt[3]{x^2}\cdot\sqrt[3]{(x^4)^3}\qquad\text{use}\ \sqrt[n]{a^n}=a\\\\=4\sqrt[3]{2x^2}\cdot x^4\\\\=4x^4\sqrt[3]{2x^2}[/tex]

Answer: it's c to put it simply

Step-by-step explanation:

Answer:

75 yd^2.

Step-by-step explanation:

If the width = x yards, the length will be 3x yards.

The perimeter = 2 * length + 2 * width

= 2* 3x + 2*x = 40

6x + 2x = 40

8x = 40

x = 5

So the width is 5 and the length is 15 yards.

The area = 5 * 15 = 75 yd^2.

Answer:

75

Step-by-step explanation:

x=breadth

3x=length

perimeter=2(x+3x)=8x

40=8x

x=5

length=15

breadth=5

area=15*5=75