7. The parabola shown has the form y = ax2 + bx + c.
a. What is the axis of symmetry? x=
b. Look at the width of the parabola to find a.
c. Use the formula x = to find b.
2a
d. What is the equation of the parabola?

Answer:

140 degrees

Step-by-step explanation:

first start by making the given angles equal each other because they are congruent.

2x+28=6x+4

Subtract 4 on both sides

2x+24=6x

subtract 2x on both sides

24=4x

divide both sides by 4 to get x

24/4=4x/4

6=x

next to find the actual number of the angle, plug 6 back into either one of the equations. Im gonna use the first one.

2x + 28

2(6) + 28

12+28= 40

Now that we have the number, we already know that a full circle is 360 degrees so half a circle is 180.

Take 40 and subtract from 180

180-40= 140

Well, m∠1 and m∠3 are congruent by the Vertical Angle Congruent Theorem (VACT). This means that because the angles are opposite of each other, their angles are the same because they are formed by the same two intersecting lines.

Because of this, we can set m∠1 and m∠3 equal to each other:

m∠1 = m∠3

(2x + 28) = (6x + 4)

2x + 28 = 6x + 4

-4x + 28 = 4

-4x = -24

-x = -6

x = 6

Knowing that x equals 6, we can use this to find m∠2. By the Supplementary Angles Theorem (SAT), angles that are on the same line add up to equal 180°. To use the SAT, we need to plug x in to find m∠1 or m∠3, because they are both the same:

x = 6

m∠1 = (2x + 28)

m∠1 = 2(6) + 28

m∠1 = 12 + 28

m∠1 = 40°

m∠3 also equals 40°.

Now that we have the value for ∠1 (or ∠3), we can use the SAT:

m∠2 + m∠3 = 180 ← You could also use m∠1, because they both equal the same!

m∠2 + 40 = 180

m∠2 = 140°

So, the measure of ∠2 is 140°.

If you have any questions, feel free to ask! :)

Answer:

150 Miles

Step-by-step explanation:

Let's say it takes x time to get there.

X x 30=(8 - 6) x 50 (The distance is the same)

30X=400 - 50X=7 X=5 hours.

So the distance is 5 x 30=150 miles.

Answer:

The correct answer is 39 units.

Parameter is the sum of the lengths of all sides of a polygon. The sides of the polygon are PT, TS, SR, RQ, and QP. To get the length of a side, we use the distance formula:

d =

Each vertex in the polygon has its corresponding points:

P (-2,11)

T (8, 7)

S (1, 7)

R (2, 0)

Q (-4,5)

So to get the length of side PT, we use the distance formula and the vertices of side PT:

P  = (-2, 11)

T  = (8, 7)

The length of PT is

The same procedure is done for the other 4 sides and the following are the answers:

TS =

SR =

RQ =

QP =

And by adding all the sides, you get the perimeter:

By rounding off, the answer is 39 units.

Step-by-step explanation:

Given:

The length of first ribbon is, 7 10/27 yards.

The length of second ribbon is, 7 3/4 yards.

The length of third ribbon is, 14 5/9 yards.

The objective is to find the total length of the yard.

The total length of the yard can be calculated as,

To provide the final numerical answer, the exact values of f(x1), f(x2), f(x3), and f(x4) need to be calculated using a calculator or numerical approximation techniques.

To approximate the integral of the function f(x) = x · 2^x over the interval [0, 4], we can use the midpoint rule with four equal-width subintervals. The midpoint rule estimates the integral by evaluating the function at the midpoint of each subinterval and multiplying it by the width of the subinterval.

To apply the midpoint rule, we divide the interval [0, 4] into four equal-width subintervals. The width of each subinterval is (4-0)/4 = 1.

The midpoints of the subintervals are located at x = 0.5, 1.5, 2.5, and 3.5. Let's denote these midpoints as x1, x2, x3, and x4, respectively.

For each subinterval, we evaluate the function f(x) = x · 2^x at the corresponding midpoint and multiply it by the width of the subinterval:

I ≈ Δx [f(x1) + f(x2) + f(x3) + f(x4)]

Now, let's calculate the values of f(x) at each midpoint:

f(x1) = 0.5 · 2^(0.5) = 0.5 · sqrt(2)

f(x2) = 1.5 · 2^(1.5)

f(x3) = 2.5 · 2^(2.5)

f(x4) = 3.5 · 2^(3.5)

Finally, we substitute these values into the midpoint rule formula:

I ≈ 1 [f(x1) + f(x2) + f(x3) + f(x4)]

Replace the values of f(x) at each midpoint and simplify to find the approximate value of the integral.

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Answer:

0.85 gallons

Step-by-step explanation:

4.675(gallons) dived by 5.5(hours). Hope it helps

Answer: ok

Step-by-step explanation: ok

Answer:

i would say 10

Step-by-step explanation:

A piecewise function is a function that is defined by different equations or formulas on different intervals or pieces of its domain. In other words, a piecewise function is a function that consists of multiple functions "stitched" together.

When looking at the line graph, it is clear that there is a error because the scales don't begin at 0.

An example of a chart that shows data trends over time or other continuous periods is a line graph. The x-axis represents time or another continuous variable, while the y-axis represents the value of the data. It consists of a sequence of data points connected by a line.

The visualisation of trends and patterns in data, such as variations in temperature, stock prices, or sales numbers over time, is frequently done using line graphs. Due to the ability to draw many lines in a variety of colors and patterns, they are particularly helpful for comparing different data series on the same graph.

When looking at the line graph, it is clear that there is a flaw because the scales don't begin at 0.

It presents information that is incongruous, as if it were saying that the highest hour on Friday is 7, but that it is precisely 1 to 7, making it equivalent to 6.

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Heritability is a statistic that refers to the proportion of variance in a group of individuals that can be accounted for by genetic variance.

These are differences in cells of organisms as a result of genetic differences or environmental factors.

Plomin et al. (2019) coined Heritability as being a statistics which talks about the level of variance in a group of organisms.

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Optimal maintenance interval will be 2.68 weeks.

Ratio = Preventive cost / Breakdown cost

Preventive cost = $ 800

Breakdown cost = $ 1200

Ratio = 800/1200

= 0.6666 or 0.67

Probability = 0.67

Z score for 0.67 = 0.44

OPTIMAL MAINTENANCE LEVEL IS GIVEN BY :

= (Z score * Standard Deviation) + Mean

= (0.44 * 0.41 ) + 2.5

= 2.68 weeks

Hence 2.68 weeks is the optimal maintenance interval.

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Answer:

4/5 of the wall

Step-by-step explanation:

In 1/4 of an hour, 1/5 of the wall is painted. That means that

in 4/4 of an hour (which is an hour), 4/5 of the wall is painted.

4/5 is your answer

The inverse Laplace transform of Y(s), we get:

y(t) = tsin(5t) + 3/5(1-e^(3-5t))*u(t-3)

Taking the Laplace transform of the differential equation y''+25y=g(t), where y(0)=0 and y'(0)=0, we get:

s^2Y(s)-sy(0)-y'(0) + 25Y(s) = G(s)

s^2Y(s) + 25Y(s) = G(s)

Y(s) = G(s) / (s^2 + 25)

Substituting the given piecewise function for g(t), we get:

G(s) = L{g(t)} = L{t} + L{3u(t-3)}

G(s) = 1/s^2 + 3e^(-3s)/s

Substituting G(s) into the Laplace transform of y(t), we get:

Y(s) = [1/s^2 + 3e^(-3s)/s] / (s^2 + 25)

Y(s) = (1/s^2) / (s^2 + 25) + (3e^(-3s)/s) / (s^2 + 25)

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Step-by-step explanation:

you know that you can change and reform any equation by doing the same operation to everything on the left and on the right side of the "=" sign ?

that way you can change the appearance of terms and the locations of variables or constants without changing the expressed balance.

this is like in a 2-bowl scale, where you can add or remove the same weight on both sides to keep the scale in balance.

and that is the principle, when we transform equations.

4.

V = RI

we want to have "I" alone on one side. so, what do we need to do ? a division by "R", of course.

again, it has to happen on both sides of the "scale" ...

V/R = I

I = 50/2.5 = 20 A (or amps)

5.

the area of a circle is

A = pi × r²

with r being the radius.

now, r should stand alone (and is the result of the other values). so, what do we need to do ?

well, first we divide both sides by pi :

A/pi = r²

and now ? how do we get r from r² ? we pull the square root (sqrt()) ! again, as always, both sides :

r = sqrt(A/pi)

r = sqrt(100/pi) = sqrt(31.83098862...) =

= 5.641895835... ≈ 5.64 mm

Answer:

Ohm's Law

\(V=RI\)

where:

Part (a)

Given equation:

\(\implies V=RI\)

Divide both sides by R:

\(\implies \dfrac{V}{R}=\dfrac{RI}{R}\)

Cancel the common factor:

\(\implies \dfrac{V}{R}=\dfrac{ \diagup\!\!\!\!\!R\:I}{\diagup\!\!\!\!\!R}\)

Therefore:

\(\implies I=\dfrac{V}{R}\)

Part (b)  

Given:

Substitute the given values into the formula and solve for I:

\(\implies I=\dfrac{V}{R}\)

\(\implies I=\dfrac{50}{2.5}\)

\(\implies I=20\:\:\sf A\)

\(\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}\)

Part (a)

Given formula:

\(\implies A=\pi r^2\)

Divide both sides by \(\pi\):

\(\implies \dfrac{A}{\pi}=\dfrac{\pi r^2}{\pi}\)

Cancel the common factor:

\(\implies \dfrac{A}{\pi}=\dfrac{\diagup\!\!\!\!\!\pi r^2}{\diagup\!\!\!\!\!\pi}\)

\(\implies r^2=\dfrac{A}{\pi}\)

Square root both sides:

\(\implies \sqrt{r^2}=\sqrt{\dfrac{A}{\pi}}\)

\(\implies r=\sqrt{\dfrac{A}{\pi}}\)

Part (b)

Given:

Substitute the given value into the formula and solve for r:

\(\implies r=\sqrt{\dfrac{A}{\pi}}\)

\(\implies r=\sqrt{\dfrac{100}{\pi}}\)

\(\implies r=5.64\:\:\sf mm \:(2 \:dp)\)

Given data:

The expression for the equation of the line is 6x-8y=40.

The given equation can be written as,

6x-8y=40

8y=6x-40

y=6x/8-40/8

=3x/4-5

Thus, the slope intercept form is y=3x/4-5.

Answer:

no

Step-by-step explanation:

Answer:

Ya what's up??

Step-by-step explanation:

You have to double 1 and 50 to get 2 and 100

1:50 = 2:100

1x2=2

50x2=100

So the statement, if she studied for 2 hours, she would have gotten 100%,  makes sense

Hope this helps!

Answer: 32a^5b^3√b

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors assuming positive real numbers

Answer:

can you show a picture or a more simplified version?

The ratio of the length and the width of the bigger rectangle, l:w = 6:5.

The ratio is the relational representation of two familiar quantities.

The ratio of two quantities a and b is written as a:b, read as "a is to b", and functions as a/b.

In the question, we are asked to determine the ratio l:w, given that each of the smaller rectangles is congruent to each other.

We assume the length of each smaller rectangle to be x, and its width to be w.

Now, from the diagram, we can say that 3x = 4y, as the length of the bigger rectangle is covered by 3 lengths of smaller rectangles or 4 widths of the smaller rectangles.

From this, we can say that x = (4/3)y.

Now, the length of the bigger rectangle l covers 3 lengths of the smaller rectangles.

So, we can say that l = 3x.

Also, the width of the bigger rectangle w covers 2 widths and 1 length of the smaller rectangles.

So, we can say that w = 2y + x.

Thus, the ratio l:w = l/w, can be written as:

3x/(2y + x).

Substituting x = (4/3)y, we get:

= 3(4/3)y/(2y + (4/3)y)

= 4y/((10/3)y)

= 12/10 = 6/5 = 6:5.

Thus, the ratio of the length and the width of the bigger rectangle, l:w = 6:5.

The provided question is inappropriate.

The correct question is:

"Ten boxes are packed tightly in a crate. From above, the packed crate looks like the attachment provided.

The visible faces of the boxes are all congruent rectangles (that means the ten small rectangles in the diagram are the same shape and size). The top of the crate is l inches long by w inches wide, where l ≥ w (as shown above). What is the ratio l:w in simplified form?"

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Answer:

I had my child look for the patterns. We found the answer of 4.5. I had her add another 1.5 which gave us the number 6 in the chart to show proof to her.

Answer:

The answer is 4.5

Step-by-step explanation:

Hope this helps you/everyone :)

In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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Answer:

Step-by-step explanation:

(5x )4 +(5x )3 = (10x)12

The equilibrium price and quantity for each pair of demand and supply functions are as follows:

a. Q = 10 - 2P

To find the equilibrium, we set the quantity demanded equal to the quantity supplied:

10 - 2P = P

By solving this equation, we can determine the equilibrium price and quantity. Simplifying the equation, we get:

10 = 3P

P = 10/3 ≈ 3.33

Substituting the equilibrium price back into the demand or supply function, we can find the equilibrium quantity:

Q = 10 - 2(10/3) = 10/3 ≈ 3.33

Therefore, the equilibrium price is approximately $3.33, and the equilibrium quantity is also approximately 3.33 units.

b. Q = 1640 - 30P

Setting the quantity demanded equal to the quantity supplied:

1640 - 30P = P

Simplifying the equation, we have:

1640 = 31P

P = 1640/31 ≈ 52.90

Substituting the equilibrium price back into the demand or supply function:

Q = 1640 - 30(1640/31) ≈ 51.61

Hence, the equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In summary, for the demand and supply functions given:

a. The equilibrium price is approximately $3.33, and the equilibrium quantity is approximately 3.33 units.

b. The equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In the first paragraph, we summarize the steps taken to determine the equilibrium price and quantity for each pair of demand and supply functions. We set the quantity demanded equal to the quantity supplied and solve the resulting equations to find the equilibrium price. Substituting the equilibrium price back into either the demand or supply function allows us to calculate the equilibrium quantity.

In the second paragraph, we provide the specific calculations for each pair of functions. For example, in case a, we set Q = 10 - 2P equal to P and solve for P, which gives us P ≈ 3.33. Substituting this value into the demand or supply function, we find the equilibrium quantity to be approximately 3.33 units. We follow a similar process for case b, setting Q = 1640 - 30P equal to P, solving for P to find P ≈ 52.90, and substituting this value back into the function to determine the equilibrium quantity of approximately 51.61 units.

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Answer:

The correct answer is C

Step-by-step explanation:

Just trust the process

Answer:

9560

Step-by-step explanation:

Use a calculator or do long division.

You can also divide by 2 twice.

38240/2 = 19120

19120/2 = 9560

Answer: 9560

Answer:

9560

Step-by-step explanation:

30000÷4=7500

8000÷4=2000

200÷4=50

40÷4=10

0÷4=0

7,500+2,000+50+10+0=9,500+60=9,560

Answer:

Do you what the graph?

Step-by-step explanation:

‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎‏‏‎ ‎

Answer:

66

Step-by-step explanation:

45+17+4

Answer:

66

Step-by-step explanation:

Following the x-axis on the chart, labeled Mother's age (in years), add all the values that happened after age 40 (45 + 17 + 4 = 66)

For the principal $400 is invested at an interest rate of 4.5% per year, the final amount of the investment at the end of 14 years compounded interest

a) $750

b) $746.

c) $748.

d) $751.

We know that in compound interest, interest is calculated in different methods. We will use the following formula: \(A=P(1 + \frac{r}{n})^{nt}\)

To calculate the final amount continuously, we will use the following formula, \(A = Pe ^{rt}\)

Where, P = the initial amount.

Now, we have Initial invested amount, P= $400

Rate of interest, r = 4.5 % = 0.045

Time, t = 14 years.

Let us assume that the final amount will be equal to A.

a) When the interest is compounded annually then the number of times interest is calculated in a year is, n = 12

By using the formula of compound interest, we have: \(A=400(1+ \frac{0.045}{12})¹⁴\) ≈750

b.) When the interest is compounded semiannually then the number of times interest is calculated in a year is, n = 2

By using the formula of compound interest, \(A= 400(1 + \frac{0.045}{2})²⁸\) ≈746.

c) When the interest is compounded quarterly then the number of times interest is calculated in a year is, n = 4

By using the formula of compound interest,\(A = 400(1 + \frac{0.045}{4})⁵⁶\) ≈748.

d) When the interest is compounded continuously then we will use continuous compound interest formula. By using the formula of continuous compound interest, \(A= 400e^{0.045×14 }\)≈ 751. Hence, required value is 751.

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Answer:

for 6 weeks 15 + 15 + 15 + 15 + 15 + 15 = 90

for 10 weeks = 150

for 14 weeks = 210

Step-by-step explanation:

i did 15 because they said tripling it every week so 5 x 3 = 15 for 1 week now 15 x 6 = 90 and so on...

hope this helps

Answer:

It's the third one,

Step-by-step explanation:

the only one with the dot in the negatives