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Answer:

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

Step-by-step explanation:

We want to write the equation of a quadratic whose graph passes through (-3, 2), (-1, 0), and (1, 6).

Remember that the standard quadratic function is given by:

[tex]f(x)=ax^2+bx+c[/tex]

Since it passes through the point (-3, 2). This means that when [tex]x=-3[/tex], [tex]f(x)=f(-3)=2[/tex]. Hence:

[tex]f(-3)=2=a(-3)^2+b(-3)+c[/tex]

Simplify:

[tex]2=9a-3b+c[/tex]

Perform the same computations for the coordinates (-1, 0) and (1, 6). Therefore:

[tex]0=a(-1)^2+b(-1)+c \\ \\0=a-b+c[/tex]

And for (1, 6):

[tex]6=a(1)^2+b(1)+c\\\\ 6=a+b+c[/tex]

So, we have a triple system of equations:

[tex]\left\{ \begin{array}{ll} 2=9a-3b+c &\\ 0=a-b+c \\6=a+b+c \end{array} \right.[/tex]

We can solve this using elimination.

Notice that the b term in Equation 2 and 3 are opposites. Hence, let's add them together. This yields:

[tex](0+6)=(a+a)+(-b+b)+(c+c)[/tex]

Compute:

[tex]6=2a+2c[/tex]

Let's divide both sides by 2:

[tex]3=a+c[/tex]

Now, let's eliminate b again but we will use Equation 1 and 2.

Notice that if we multiply Equation 2 by -3, then the b terms will be opposites. So:

[tex]-3(0)=-3(a-b+c)[/tex]

Multiply:

[tex]0=-3a+3b-3c[/tex]

Add this to Equation 1:

[tex](0+2)=(9a-3a)+(-3b+3b)+(c-3c)[/tex]

Compute:

[tex]2=6a-2c[/tex]

Again, we can divide both sides by 2:

[tex]1=3a-c[/tex]

So, we know have two equations with only two variables:

[tex]3=a+c\text{ and } 1=3a-c[/tex]

We can solve for a using elimination since the c term are opposites of each other. Add the two equations together:

[tex](3+1)=(a+3a)+(c-c)[/tex]

Compute:

[tex]4=4a[/tex]

Solve for a:

[tex]a=1[/tex]

So, the value of a is 1.

Using either of the two equations, we can now find c. Let's use the first one. Hence:

[tex]3=a+c[/tex]

Substitute 1 for a and solve for c:

[tex]\begin{aligned} c+(1)&=3 \\c&=2 \end{aligned}[/tex]

So, the value of c is 2.

Finally, using any of the three original equations, solve for b:

We can use Equation 3. Hence:

[tex]6=a+b+c[/tex]

Substitute in known values and solve for b:

[tex]6=(1)+b+(2)\\\\6=3+b\\\\b=3[/tex]

Therefore, a=1, b=3, and c=2.

Hence, our quadratic function is:

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

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[tex]4q = 52[/tex]

Divide sides by 4

[tex] \frac{4q}{4} = \frac{52}{4} \\ [/tex]

Simplification

[tex]q = 13[/tex]

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Answer:

I believe the answer is 20

Step-by-step explanation:

Okie B or D

Maybe C

OK ok ok ok ok ignore that it's probably B? orC

okie nevermind there's lots of bullies and no one even know's I'm autistic people, okie baiiiii

Answer: I don't think the answer is B. -3/5+(-2/8)-4=-5 because B. -3/5+(-2/8)-4 A. (-40)+(-30)+28=-42, C. 130+70+(-37)=163, D. 40+(-58)+160=142. I think A. (-40)+(-30)+28=-42

Answer:

Step-by-step explanation:

x= 0.079

y=-0.169

Answer: x= 0.079

y=-0.169

Step-by-step explanation:

Answer:

Length = [tex]57.5\ \text{inches}[/tex]

Width = [tex]18\ \text{inches}[/tex]

Step-by-step explanation:

The scale of the toy train is [tex]\dfrac{2}{9}[/tex]

So, the dimensions of the toy train is [tex]\dfrac{2}{9}[/tex] times the actual dimensions of the train.

The dimensions of actual train is [tex]\dfrac{1}{\frac{2}{9}}=\frac{9}{2}[/tex] times the toy train's dimensions.

Length

[tex]15\times \dfrac{9}{2}=57.5\ \text{inches}[/tex]

Width

[tex]4\times \dfrac{9}{2}=18\ \text{inches}[/tex]

The length of the railroad car on the long island railroad is 57.5 inches.

The width of the railroad car on the long island railroad is 18 inches.

Answer:-9.5

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

The coefficient is the number that multiply the variable, in this case x.

9514 1404 393

Answer:

  43.2 grams

Step-by-step explanation:

The exponential equation for the decay can be written as ...

  amount remaining = (initial amount)(1 -decay rate)^t

  = 570(1 -0.18)^t

We want to find the amount remaining after 13 minutes. Evaluating this equation for t=13, we have ...

  amount remaining = 570(0.82^13) ≈ 43.2 . . . grams

Answer:

8

Step-by-step explanation:

2 x 2 = 4

4 x 2 = 8

Answer:

8

Step-by-step explanation:

2^3 is the same as 2x2x2 (x is times)

Answer: The number of cups of flour needed for 9 cups of sugar = 12.

Step-by-step explanation:

Equation of direct proportion between two quantities x and y :

[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]

Let x=  the number of cups of flour needed for 9 cups of sugar.

Put [tex]x_1=4,\ y_1=3,\ y_2=9, x_2=x[/tex]

[tex]\dfrac{4}{3}=\dfrac{x}{9}\\\\\Rightarrow\ x=\dfrac{9\times4}{3}\\\\\Rightarrow\ x=12[/tex]

Hence, the number of cups of flour needed for 9 cups of sugar = 12.

Answer:

Step-by-step explanation:

Mary will be twice as old as her brother when the age of her brother is equal to the ... Add this value of 8 to Mary's & her brother's present age. ... In three years time I will be half my brother's age. ... In 4 years, she will be four times as old as her son was 9 years ago

Answer:

Anthony's reasoning is incorrect

Step-by-step explanation:

The expression abc is not made up of three terms because it is just an entity. For the expression to be called a three term expression, each of the variables must be separated using mathematical signs. For example, the expression a + b + c can be referred to as three terms because each variables are separated by a plus sign. In this case they are different entity.

From the above explanation, we can conclude that Anthon's reasoning is incorrect. The expression abc is just one term not three terms.

Answer:

Step-by-step explanation:

Given

As given, sides XW and YZ are parallel and XY = WZ

Since it is isosceles, angles X and W are of same size

Therefore:

Answer:

-273

Step-by-step explanation:

222- (99*5)

222-495

-273

Answer:

-273

(next time if their is options maybe also try and put them, it would help a lot)

Answer: Image #1: C. Distributuve Property Image #2: A. n + 2(7)

Step-by-step explanation: For Image #1, they used the Distributive Property because the number 3 was (distributed) and multiplied to both x and 7. The equation is saying that 3x + 21 = 42, and that we’re trying to solve for x. For Image #2, the answer is A. n + 2(7) because after you solve the expression, the answer would be 14n. When you look at the four options, (A. B. C. D.), letter A. would be the answer because it equals to 14n.

Answer:

about 3141.59 cm^3

Step-by-step explanation:

V of cylinder = (pi)(r^2)(h)

radius = 10 cm

height = 10 cm

V = pi x 10^2 x 10

V = 3141.59 cm cubed

Answer:

-3

Step-by-step explanation:

[tex]\sqrt[3]{-27}[/tex] is -3 and can be proven by doing [tex]-3^{3}[/tex] as -3 x -3 x -3 of itself will give you -27, as [tex]\sqrt[3]{-27}[/tex] is just -27/-3/-3

Answer:

your answer will be c

and distributive property for the second one

Step-by-step explanation:

Answer:

His time in mph is 16.1 mph

Density = mass / volume

Density = 44,800 kg/ 5m^3

Density = 8,960 km/m^3

Answer:

1-75    2-105    3-35

Step-by-step explanation:

1-  180-75-30=75

2-  180-75=105

3-   180-105-40=35

Answer:

b ≥ - 34 / 3

Step-by-step explanation:

Given the inequality :

30b+53≥18b−83

Collect like terms

30b - 18b ≥ - 83 - 53

12b ≥ - 136

Divide both sides by 12

12b / 12 ≥ - 136 / 12

b ≥ - 34 / 3

Hence, b ≥ - 34/3

Answer:

b≥− 34/3

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The sum of all internal angles on a triangle must equal 180°

[tex]28 + 64 + 100 = 192[/tex]

Answer: $5933.04

Step-by-step explanation:

Principal = $5900

Rate = 8%

Time = 7 years

Simple interest = PRT/100

= (5900 × 8% × 7)/100

= (5900 × 0.08 × 7) / 100

= 3304/100

= $33.04

Total amount = Principal + Interest

= $5900 + $33.04

= $5933.04

Answer:

AB and MN

∠B and ∠N  

CB and LN

Step-by-step explanation:

edg

Answer:

8200+1894.40 = $10,094.40

Step-by-step explanation:

The formula we'll use for this is the simple interest formula, or:

I = P x r x t

Where:

P is the principal amount, $8200.00.

r is the interest rate, 4.4% per year, or in decimal form, 4.4/100=0.044.

t is the time involved, 5.5....year(s) time periods.

So, t is 5.5....year time periods.

To find the simple interest, we multiply 8200 × 0.044 × 5.5 to get that:

The interest is: $1984.40  + add to Investment ($8000) and you'll get the answer.

Answer:

125.2 is your answer dear

Answer:

Step-by-step explanation:

2.53 x 105 is 265.65

1.3 x 108​ is 140.4

now, Subtract 2.53 x 105 from 1.3 x 108​

140.4 - 265.65

= -125.25

Hope this helps

plz mark as brainliest!!!!!!

Answer:

Step-by-step explanation:

3.5×4.9

=35/10×49/10

=1715/100

Or 17.15 answer

Answer:

Step-by-step explanation:

3/5 times 4/9. multiply straight across. 3 times 4 is 12. 5 times 9 is 45. your answer is 12/45. but this answer can be simplified if we take out a 3 for each one. so you have 4/15