9. x is directly proportional to y. When x = 4, y = 9. Write an equation
for y in terms of x.

Answer:

i would say transitive which is what u put because well i would say translate because it translates n2 different parts of the letter

Step-by-step explanation:

Answer:

a. D = R \ {13}

b. D = [-9;+∞)

D = R \ { [tex]\frac{-1}{2}[/tex] }

Step-by-step explanation:

a. 13 - x ≠ 0

 x ≠ 13

D = R \ {13}

b. 9 + x ≥ 0

x ≥ -9

D = [-9;+∞)

c. 2x + 1 ≠ 0

x ≠ [tex]\frac{-1}{2}[/tex]

D = R \ { [tex]\frac{-1}{2}[/tex] }

Answer:

Part A)

Approximately 318.1318 meters.

Part B)

Approximately 137.7551 meters.

Step-by-step explanation:

The path of a projectile is given by the equation:

[tex]\displaystyle y = \sqrt{3} x -\frac{49x^2}{9000}[/tex]

Part A)

The range of the projectile will be given by the difference between its starting point and landing point. In other words, its two zeros.

Let y = 0 and solve for x:

[tex]\displaystyle 0 = \sqrt{3}x - \frac{49x^2}{9000}[/tex]

Factor:

[tex]\displaystyle 0 = x\left(\sqrt{3} - \frac{49x}{9000}\right)[/tex]

Zero Product Property:

[tex]\displaystyle x = 0 \text{ or } \sqrt{3} - \frac{49x}{9000} = 0[/tex]

Solve for each case:

[tex]\displaystyle x = 0 \text{ or } x = \frac{9000\sqrt{3}}{49}\approx 318.1318[/tex]

Hence, the range of the projectile is approximately (318.1318 - 0) or 318.1318 meters.

Part B)

Since the equation is a quadratic, the maximum height is given by its vertex. Recall that the vertex of a quadratic is given by:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = -49/9000 and b = √3.

Find the x-coordinate of the vertex:

[tex]\displaystyle x = - \frac{(\sqrt{3})}{2\left(\dfrac{-49}{9000}\right)} = \frac{4500\sqrt{3}}{49}[/tex]

Then the maximum height will be:

[tex]\displaystyle \displaystyle \begin{aligned} y\left(\frac{4500\sqrt{3}}{49}\right) &=\sqrt{3} \left(\frac{4500\sqrt{3}}{49}\right) -\frac{49\left(\dfrac{4500\sqrt{3}}{49}\right)^2}{9000} \\ \\ &= \frac{13500}{49} -\frac{6750}{49}\\ \\ &=\frac{6750}{49}\\ \\ &\approx 137.7551\text{ meters}\end{aligned}[/tex]

The maximum height reached by the projectile will be 137.7551 meters.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{3t + 4y + 5t}[/tex]

[tex]\huge\textsf{COMBINE the LIKE TERMS}[/tex]

[tex]\huge\text{(3t + 5t) + 4y}[/tex]

[tex]\huge\text{= 8t + 4y}[/tex]

[tex]\huge\text{Answer: \textsf{8t + 4y}}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

8t + 4y

Step-by-step explanation:

First, we have to combine LIKE TERMS giving us (3t + 5t) + 4y.

We know that 3 + 5 = 8 so 3t + 5t must be 8t.

We still have the 4y left over so we get 8t + 4y. We cannot simplify this expression anymore

So, the answer is [tex]8t + 4y[/tex] as our answer.

(Hope this helped you!)

Answer: x= 1.4 or x=7/5

Step-by-step explanation:

2(5x)=14

Divide both sides by 2

5x=7

divide again this time both sides by 5 to solve for x

x=7/5 or 1.4 as a decimal

Answer:

Umm, I believe your only correct answer for your equation above would be -1.

Step-by-step explanation:

Using the PEDMAS method:

-2 - 3= -5

= -5 - (-4)

-(-4) = 4

= -5 + 4

-5 + 4 = -1

So, your answer would be -1. Hope this helps!

Answer:

the answer is 500!!

Step-by-step explanation:

10 x 50=500

Answer:

500

Step-by-step explanation:

50*10=500

50 into 10 equals 500

Answer:

option c (-2,1)

Step-by-step explanation:

hope it helps u

Answer:

hi,

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}a&=&3*\vec{i}-4\vec{j}\\b&=&2*\vec{i}-5\vec{j}\\c&=&\lambda*\vec{i}+\mu*\vec{j}\\\end{array}\right.\\\\\\\lambda*c=2a+3b\\=2*(3*\vec{i}-4\vec{j})+3*(2*\vec{i}-5\vec{j})\\=12*\vec{i}-23\vec{j}\\=\lambda*(\lambda*\vec{i}+\mu*\vec{j})\\\\\\\left\{\begin{array}{ccc}\lambda^2&=&12\\\lambda*\mu&=&-23\end{array}\right.\\\\\\\left\{\begin{array}{ccc}\lambda&=&2\sqrt{3}\\\mu&=&\dfrac{-23*\sqrt{3} }{6} \\\end{array}\right.\\[/tex]

Answer: 36π

Step-by-step explanation:

Answer:

0.825

Step-by-step explanation:

In order to make the denominator 100, we must multiply both the numerator and denominator by 2.5

33*2.5 = 66 + 16.5 = 82.5

33/40 = 82.5/100

Now we solve, 82.5/100 = 0.825

Answer:

He was 45 in present day. But 12 years ago, he was 33.

Step-by-step explanation:

12+3=15

15•3=45 (you multipply because if you use 1/3 you would have to divide 45 by 3.)

Hello :D

Ruto is currently 12 years old. In 3 years he will be 15. 1/3 is 15. 3/3 would be 45 years old. 45 - 12 = 33

Answer:

17°

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

x=17

Step-by-step explanation:

The angles add to 180

6x-20 + 6x-4 = 180

Combine like terms

12x -24 =180

Add 24 to each side

12x = 180+24

12x = 204

12x/12 = 204/12

x =17

Answer:

(1,-3)

(2,0)

(3,5)

(4,12)

(0,-4)

(-1,-3)

(-2,0)

Answer:

$495

Step-by-step explanation:

This is because  Gross income is the total amount without taxes or deductions  

So all you have to do is 11x45 which gives you 495.

[tex] \frac{3 {a}^{2} - 9a}{ {a}^{2} - 9} = \frac{3a(a - 3)}{(a + 3)(a - 3)} = \frac{3a}{a + 3} [/tex]

[tex] \frac{ {y}^{2} - 3yz -4 {z}^{2} }{3 {y}^{2} - 12yz } = \frac{(y + z)(y - 4z)}{3y(y - 4z)} = \frac{y + z}{3y} [/tex]

[tex] \frac{ {d}^{2} + 4d + 4}{ {d}^{2} + 2d} = \frac{(d + 2)(d + 2)}{d(d + 2)} = \frac{d + 2}{d} [/tex]

[tex] \frac{5f - 15}{3 {f}^{2} - 13f + 12} = \frac{5(f - 3)}{(3f - 4)(f - 3)} = \frac{5}{3f - 4} [/tex]

I hope I helped you^_^

Answer:

30x + 28

Step-by-step explanation:

To evaluate (f ￮ g)(x), substitute x = g(x) into f(x) , that is

f(g(x))

= f(- 6x - 6)

= - 5(- 6x - 6) - 2 ← distribute parenthesis and simplify

= 30x + 30 - 2

= 30x + 28

Answer:

I can't answer the B question, but I can answer the A question. First, you need to add 1/3, 1/4, and 5/8 by converting them into having the same denominators (24 is the best) and then subtracting them by 24/24 or the number of your choosing. That's how you find out how much he saves.

Step-by-step explanation:

Answer:

I)

[tex]2a + 2b = -10\text{ or } 2a + 2b = 10[/tex]

II)

[tex]2a - 2b = -2 \text{ or } 2a-2b= 2[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaytstyle a^2 + b^2 = 13 \text{ and } ab= 6[/tex]

I)

Recall the perfect square trinomial pattern:

[tex]\displaystyle (a+b)^2 = a^2 + 2ab + b^2[/tex]

Rewrite:

[tex]\displaystyle (a+b)^2 = (a^2 + b^2) + (2ab)[/tex]

Substitute:

[tex]\displaystyle (a+b)^2 = (13) + (12)[/tex]

Evaluate:

[tex]\displaystyle (a + b)^2 = 25[/tex]

Take the square root of both sides:

[tex]\displaystyle a + b = \pm\sqrt{25} = \pm5[/tex]

Hence:

[tex]\displaystyle 2a + 2b = \pm 10[/tex]

Therefore:

[tex]\displaystyle 2a + 2b = -10 \text{ or } 2a + 2b = 10[/tex]

II)

Likewise:

[tex]\displaystyle (a-b)^2 = a^2 - 2ab + b^2[/tex]

Substitute:

[tex]\displaystyle (a-b)^2 = (13) -(12)[/tex]

Solve:

[tex]\displaystyle \begin{aligned} (a-b)^2 &= 1 \\ a-b &= \pm \sqrt{1} \\ a-b &= \pm 1\\ 2a - 2b &= \pm 2\end{aligned}[/tex]

In conclusion:

[tex]2a - 2b = -2 \text{ or } 2a-2b= 2[/tex]

The best approximation of the cost for an additional square foot of living space for homes in this neighborhood is a decrease of $0.125 thousand, or $125, for every one additional square foot of living space.

Since we are looking for an approximation of the cost for an additional square foot of living space, we need to find the slope of the line of best fit for the given scatterplot. The slope of the line represents the change in the cost of the house for every one unit increase in the living space, which in this case is one square foot.

From the scatterplot, we can see that as the living space increases, the cost of the house also increases, indicating a positive linear relationship. We can also see that there is a line of best fit that closely approximates this relationship.

To find the slope of the line of best fit, we can choose any two points on the line and calculate the change in the y-coordinate (the cost) divided by the change in the x-coordinate (the living space). One way to do this is to choose the two points where the line intersects the y-axis and the x-axis. From the scatterplot, we can estimate these points to be approximately (0, 200) and (1600, 0), respectively.

Using these two points, the slope of the line of best fit is:

slope = (change in y) / (change in x)

slope = (200 - 0) / (0 - 1600)

slope = -0.125

Therefore, the best approximation of the cost for an additional square foot of living space for homes in this neighborhood is a decrease of $0.125 thousand, or $125, for every one additional square foot of living space.

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Answer:

find the area of each side of the shapes and add make sure it's in square centimeters

Answer:

-3

Step-by-step explanation:

move the constant to the other side and get

X = 2 - 5

and X = -3

The proportional formula for b is 3/2 in terms of t.

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Answer:

Yes.

Step-by-step explanation:

We want to determine if (x + 1) is a factor of the polynomial:

[tex]x^4 + 2x^3 + 2x^2 - 2x -3[/tex]

According to the Factor Theorem, if a binomial in the form (x - a) is a factor of a polynomial P(x), then P(a) must equal zero.

Our binomial factor is (x + 1) or (x - (-1)). Hence, a = -1.

Let our polynomial be P(x). Find P(-1):

[tex]\displaystyle\begin{aligned} P(-1) &= (-1)^4 + 2(-1)^3 +2(-1)^2 -2(-1) -3 \\&=0\end{aligned}[/tex]

Therefore, since the resulting value is indeed zero, (x + 1) is indeed a factor of the given polynomial.

In conclusion: yes.

Answer:

Is this a story hmm mm i think

3/8 is smaller than 3/5.

3/8 is smaller than 3/5

Find the LCD of both fractions:

Multiples of 8:

8, 16, 24, 32, 40, 48, 56, 64, 72, …

Multiples of 5:

5, 10, 15, 20, 25, 30, 35, 40, 45, …

40 is the LCD of denominators 5 and 8.

Multiply both denominators by a number that makes it 40, multiply that same number by each numerator:

3/8:

3 x 5 = 15

8 x 5 = 40

15/40

3/5:

3 x 8 = 24

5 x 8 = 40

24/40

15/40 < 24/40

Hope this helps

Answer:

2x+x+2=5x-10

3x+2=5x-10

-3x -3x

2=2x-10

+10 +10

12=2x

2x/2=x 12/2=6

x=6

QR=x+2

6+2=8

QR=8

The value of x is 6 and the value of QR will be 8 units.

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that the value of x and QR if Q is between P and R.

PQ=2x

QR=x + 2

PR= 5x -10

The value of x will be calculated as below:-

2x+x+2=5x-10

3x+2=5x-10

2=2x-10

12=2x

x = 12 / 2

x =6

The value of QR will be calculated as below:-

QR=x+2

6+2=8

Therefore, the value of x is 6 and the value of QR will be 8 units.

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Answer:

342.30.

Step-by-step explanation:

The third decimal place is 6 so we round up  the previous 2 dec places by 1

29 -->> 30 so it is 342.30.

(We round up if the next decimal  place is 5 6 7 8 or 9)