Please help I’ll mark you as brainliest if correct!

The equation of the parabola for the given points is y = -3x² + 7x + 1

Equation of the parabola

The standard form of the equation of a parabola is expressed as

y = f(x) = ax² + bx + c

where a, b, and c are constants and a ≠ 0.

Given,

Here we have the points (0, 1), (1, 5), (2, 3).

Now, we have to find the equation of the parabola.

Here we are given three coordinates (0, 1), (1, 5), and (2, 3) which lie on the parabola and which means that it satisfies the parabolic equation.

In order to find the values of a, b and c we need to formulate three equations using the three given points.

Since for the three unknowns a, b, and c, we will require three equations.

For that we have to take the Point (0,1) i.e. x = 0 and y = 1

Substituting the values of x and y in the standard parabola equation, then we get,

1 = a(0)² + b(0) + c

1 = 0 +  0 + c

c = 1 -------------------(1)

Next, we have to take the Point (1, 5) i.e. x = 1 and y = 5

Substituting the values of x and y in the standard parabola equation, then we get,

5 = a(1)² + b(1) + c

5 = a +  b + c

It can be written as,

a + b + c = 5 -----------------------------(2)

Finally, we have to take the Point (2, 3) i.e. x = 2 and y = 3

Substituting the values of x and y in the standard parabola equation, then we get,

3 = a(2)² + b(2) + c

3 = 4a +  2b + c

It can be written as,

4a + 2b + c = 3 -----------------------------(2)

Apply the value of c as 1 in equation (2), then we get,

a + b + 1 = 5

a + b = 4 ---------------------(4)

Similarly, apply the value of c on the equation (3), then we get,

4a + 2b + 1 = 3

4a + 2b = 2

Divide the equation by 2 on both sides, then we get,

2a + b = 1 --------------------(5)

Subtract equation (5) from equation (4),

(2a - a) +(b - b) = 1 - 4

a = -3

Apply the value of a in the equation (4) to get the value of b,

(-3) + b = 4

b = 7

Therefore, the equation of the parabola is

y = -3x² + 7x + 1

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There are countless possibilities for shapes that are similar but not congruent to shape 1, as long as they maintain the same proportions and shape.

There are many shapes that are similar but not congruent to shape 1. Similar shapes have the same shape, but their sizes may be different. In contrast, congruent shapes have the same shape and size.

One example of a similar shape to shape 1 is a rectangle that is twice as long and half as wide. Another example could be a square that is three times larger in area than shape 1.

A parallelogram that has the same base as shape 1 but is three times as tall is also similar but not congruent.

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Answer:

0

Step-by-step explanation:

Step 1:

- 4k + 1 = 1 + k + 3k     Equation

Step 2:

- 4k + 1 = 1 + 4k     Add

Step 3:

1 = 1 + 8k       Add 4k on both sides

Step 4:

0 = 8k     Subtract 1 on both sides

Answer:

k = 0

Hope This Helps :)

Answer:

Step-by-step explanation:

Part A:

Let's assume that the velocity of the runner changes linearly over time. We can use the slope-intercept form of a linear equation, y = mx + b, to describe the velocity of the runner at different times. In this case, the y-axis represents the velocity in km/h and the x-axis represents time in hours. We can define:

y = velocity of the runner in km/h

x = time in hours

The velocity of the runner changes by -2/3 km/h for every hour that passes. This gives us a slope of -2/3. We can use the point-slope form of a linear equation to find the equation of the line:

y - 5 = -2/3(x - 1)

Simplifying this equation, we get:

3y - 15 = -2x + 2

Rearranging to standard form, we get:

2x + 3y = 17

So the equation in two variables in standard form that can be used to describe the velocity of the runner at different times is 2x + 3y = 17.

Part B:

To graph the equation obtained in Part A for the first 5 hours, we can simply plot points for different values of x and y. For example, we can use x = 0, 1, 2, 3, 4, and 5 to find the corresponding values of y using the equation 2x + 3y = 17. Then we can plot these points on a graph and connect them with a straight line.

Here are the values of y for different values of x:

x = 0, y = 17/3

x = 1, y = 5

x = 2, y = 13/3

x = 3, y = 3

x = 4, y = 7/3

x = 5, y = 1

Plotting these points and connecting them with a straight line, we get the graph of the equation 2x + 3y = 17 for the first 5 hours:

|

6.0 -| .

| .

5.5 -| .

| .

5.0 -| .

|.

4.5 -|

|

4.0 -| .

| .

3.5 -| .

| .

3.0 -| .

|.

2.5 -|

|

2.0 -| .

| .

1.5 -| .

| .

1.0 -|.

|

0.5 -|

|

--------------

0 1 2 3 4 5

The y-intercept of the line is 17/3, which represents the initial velocity of the runner at time 0. The slope of the line is -2/3, which represents the rate of change of the velocity over time.

Answer: CLICK THANKS IF YOU LIKE MY ANSWER. HAVE A GOOD DAY SIR/MAAM #KEEPSAFE

Part A:

Let v be the velocity of the runner in km/h and let t be the time elapsed in hours. We can use the two given data points to form a system of two equations:

v = 5 when t = 1

v = 3 when t = 3

To find the equation in standard form, we can first use point-slope form:

v - 5 = m(t - 1) (using the point (1, 5))

v - 3 = m(t - 3) (using the point (3, 3))

Simplifying both equations:

v - 5 = m(t - 1)

v - 3 = m(t - 3)

v = mt + (5 - m)

v = mt + (3m - 3)

Setting the right-hand sides equal to each other:

mt + (5 - m) = mt + (3m - 3)

Simplifying and rearranging:

-m = -2

m = 2

Substituting m = 2 into one of the equations above:

v = 2t + 3

This is the equation in two variables in standard form that describes the velocity of the runner at different times.

Part B:

To graph the equation v = 2t + 3 for the first 5 hours, we can plot points for different values of t and then connect them with a line. For example:

When t = 0, v = 3, so the point (0, 3) is on the line.

When t = 1, v = 5, so the point (1, 5) is on the line.

When t = 2, v = 7, so the point (2, 7) is on the line.

When t = 3, v = 9, so the point (3, 9) is on the line.

When t = 4, v = 11, so the point (4, 11) is on the line.

When t = 5, v = 13, so the point (5, 13) is on the line.

Plotting these points on a coordinate plane and connecting them with a line, we get the graph of the equation v = 2t + 3 for the first 5 hours:

    |

 15 +-------*

    |       |

 13 +           *

    |           |

 11 +               *

    |               |

  9 +                   *

    |                   |

  7 +                       *

    |                       |

  5 +                           *

    |                           |

  3 +---------------*-----------*

    0   1   2   3   4   5   6   7

The x-axis represents time (t) in hours, and the y-axis represents velocity (v) in km/h. The line starts at (0, 3) and has a slope of 2, indicating that the velocity is increasing by 2 km/h for every hour that passes.

Step-by-step explanation:

Answer:

0.07

Step-by-step explanation:

Answer:

0.07

Between 6 and 8, it is the only whole number in-between.

Answer:

A.10,4

B.5,10

C.5,5

D4,4

Step-by-step explanation:

KERE ON LERNER?

Answer:

$20 after the applied coupon

Step-by-step explanation:

The required sale price of the shirt after getting  1/3 off is $20.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
A $30 shirt is marked, "Get 1/3 off.
The sale price of the shirt,
= 30 - 1 / 3×30
= 30 - 10
= $ 20

Thus, the required sale price of the shirt after getting  1/3 off is $20.

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Answer:

hi

Step-by-step explanation:

Answer:

x=-9, x=1/4

Step-by-step explanation:

Split it into x+9=0 and 4x-1=0.

x+9=0; x=-9

4x-1=0; 4x=1; x=1/4

The total price of the vehicle would be $18,192.88.

The total deferred price of the car would be $11,191.60.

The length of the financing agreement is 68 months .

The total deferred price after the payments was $19,601.84.

The monthly payments would be $516.92.

Subtotal = Base price + Options + Destination charges

Subtotal = $14,500 + $982 + $592 = $16,074

Dealer preparation = 5% of subtotal

Dealer preparation = 0.05 x $16,074 = $803.70

Sales tax = 7% of subtotal

Sales tax = 0.07 x $16,074 = $1,125.18

Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee

Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88

Tax = 8% of selling price = 0.08 x $8,850 = $708

Tag fee = $130

Title fee = $35

Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223

Annual interest rate = 9.5%

Number of years financed = 3

Total finance charges = $8,223 x 0.095 x 3 = $2,341.595

Total financed amount = $8,223 + $2,341.595 = $10,564.595

Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615

Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595

Total deferred price = $28,000

Down payment = $2,100

Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900

Monthly payments = $380

Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16

The financing agreement is approximately 68 months long.

Sticker price = $19,200

Discount = 6% of sticker price = 0.06 x $19,200 = $1,152

Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048

Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84

Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84

Using the formula for monthly payments on a loan:

P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)

= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92

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The key features of this quadratic relation y = -3x² - 24x - 36 include;

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped.

Since the leading coefficient (value of a) in the given quadratic function y = -3x² - 24x - 36 is negative 16, we can logically deduce that the parabola would open downward and the x-intercept (roots) is given by the ordered pair (-6, 0) and (-2, 0).

When x = 0, the y-intercept can be determined as follows;

y = -3x² - 24x - 36

y = -3(0)² - 24(0) - 36

y = -36

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-24)/2(-3)

Axis of symmetry, Xmax = -4

For the vertex, we have:

y(-4) = -3x² - 24x - 36

y(-4) = -3(-4)² - 24(-4) - 36

y(-4) = 12

In conclusion, the quadratic function has a maximum value at 12.

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Answer:

33L of 32%

15L of 16%

Step-by-step explanation:

x is the amount of 32% the remainder is 16%, together they make 48 of 27%

32x + 16(48 - x) = 27(48)

distribute

32x + 768 - 16x = 1,296

combine like terms

16x = 528

Divide both sides by 16

x = 33L of 32%

48 - x = 15L of 16%

The confidence interval based on the given values (x = 45, n = 96, Confidence level = 95%.

The confidence level (95%), sample size (n = 96), and sample mean (x = 45), we can calculate the margin of error and the confidence interval. Here's how:

1. Margin of Error:

The margin of error represents the maximum expected difference between the true population parameter and the sample estimate. It depends on the confidence level and the standard deviation (which we don't have in this case).

Since the standard deviation is unknown, we can use the t-distribution to estimate it. With a sample size of n = 96, the degrees of freedom are (n - 1) = 95. Considering a 95% confidence level, the critical value for a two-tailed test is approximately 1.984 (referencing a t-distribution table or calculator).

The margin of error (E) can be calculated using the following formula:

E = critical value * (standard deviation / sqrt(n))

However, since we don't have the standard deviation, we can't compute the margin of error in this case.

2. Confidence Interval:

The confidence interval represents a range of values within which the true population parameter is likely to fall.

The confidence interval can be calculated using the formula:

CI = x ± (critical value * standard deviation / sqrt(n))

The confidence interval based on the given values (x = 45, n = 96, confidence level = 95%.

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Answer:the third triangle

Step-by-step explanation:

Answer:

0.30a + 0.50 (4+a) = 3.60

Step-by-step explanation:

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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The statement fourth "The population is all text messages she sent and the sample is the 50 text messages she randomly selected" is correct.

Simple random sampling is a sampling strategy in which every item in the population has an equal probability of being chosen for the sample.

We have:

A student would like to know what proportion of the text messages she sends is to her best friend.

The number of sample methods she selects =  50 text messages

As the sample consists of the 50 texts she randomly chose from the population of all the texts she sent.

Thus, the statement fourth "The population is all text messages she sent and the sample is the 50 text messages she randomly selected" is correct.

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Answer:

Adult=58

Step-by-step explanation:

c=child, a=adult

6.4c+9.7a=1145 equation 1

c+a=149 equation 2

a=149-c modified equation 2 to isolate a

6.4c+9.7(149-c)=1145 substitute value of a from equation 1 into equation 2

6.4c+1445.3-9.7c=1145

-3.3c=-300.3

c=91

solve for a

c+a=149

91+a=149

a=58

Check answer:

6.4c+9.7a=1145

6.4(91)+9.7(58)=1145

582.40+562.60=1145

1145=1145

Answer:

A)

\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)

B)

\(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)

C)

= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)

D)

= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)

Step-by-step explanation:

A) How many ways can you put all Jellybeans in a row

Total number of Jellybeans = 80

The first jellybeans = 20 yellow , second is 20 orange jellybeans , third is 20 red jellybeans , fourth is 20 green jellybeans

Therefore the number of ways the Jellybeans can be put in a row is :

\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)

B) How many ways are there to select a handful of 20 jellybeans

lets assume:

yellow jellybeans = a , orange jellybeans = b , red jellybeans = c , green jellybeans = d

a + b + c + d = 20

This is the number Non-negative integer solutions

= \(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)

C) This is also the number of Non-negative integer solutions but in this case the value of C ≥ 3

hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red

= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)

D) In this case the value of C ≥ 3 and B ≤ 2

Hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red and at most 2 orange

= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)

The function can be defined as  price = 6x

It will cost $150 to buy 25 reams of paper.

The domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.

The range of the function is all non-negative real numbers, since the price cannot be negative.

Fir 25 items, price = 6(25) = $150

It will cost $150 to buy 25 reams of paper.

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Answer:

A. 70.69 is the correct answer.

Step-by-step explanation:

Given:

Two lines:

\(3x - 4y + 5 = 0 \\2x + 3y -1 = 0\)

To find:

Angle between the two lines = ?

Solution:

Acute Angle between two lines can be found by using the below formula:

\(tan \theta = |\dfrac{(m_1 - m_2)}{ (1 + m_1m_2)}|\)

Where \(\theta\) is the acute angle between two lines.

\(m_1, m_2\) are the slopes of two lines.

Slope of a line represented by \(ax+by+c=0\) is given as:

\(m = -\dfrac{a}{b }\)

So,

\(m_1 = -\dfrac{3}{- 4} = \dfrac{3}{4}\)

\(m_2 = -\dfrac{2}{ 3}\)

Putting the values in the formula:

\(tan \theta = |\dfrac{(\dfrac{3}{4}- (-\dfrac{2}{3}))}{ (1 + \dfrac{3}{4}\times (-\dfrac{2}{3 }))}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{3}{4}+\dfrac{2}{3}}{ (1 -\dfrac{1}{2})}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{17}{12}}{ \dfrac{1}{2}}|\\\Rightarrow tan \theta = \dfrac{17}{6}\\\Rightarrow \theta = tan^{-1}(\frac{17}{6})\\\Rightarrow \theta = \bold{70.69^\circ}\)

So, correct answer is A. 70.69

Answer:

3/4

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

What we have to realize is that RS + ST = RT. Since we know the value of all, let's substitute inside the equation.

\(23 - 2x + 9x - 5 = 39\)

Now let's try and solve for x by isolating the variable on one side.

Combine like terms:

\(7x + 18 = 39\)

Subtract 18 from both sides:

\(7x = 21\)

Divide both sides by 7:

\(x = 3\)

Now that we know the value of x, we can substitute it back into the equation for RS, \(23-2x\).

\(23-2(3)\\\\23-6\\17\)

Hope this helped!

Answer:

Answer: The value of x- 2y is a. \(\pm 3\).

Step-by-step explanation:

Given:  x and y are two positive real numbers such that \(x^2+4y^2=17\)   and \(xy= 2\) .

Consider \((x-2y)^2=x^2-2(x)(2y)+(2y)^2\ \ \ [(a+b)^2=(a^2-2ab+b^2)]\)

\(=x^2-4xy+4y^2\)

\(=x^2+4y^2-4(xy)\)

Put  \(x^2+4y^2=17\)   and \(xy= 2\) , we get

\((x-2y)^2=17-4(2)=17-8=9\)

\(\Rightarrow\ (x-2y)^2=9\)

Taking square root on both sides , we get'

\(x-2y= \pm3\)

Hence, the value of x- 2y is a. \(\pm 3\).

Answer:

x=67
y=67
z=113

Step-by-step explanation:

Because this is a rhombus, that means that angle 113 and z are correlating, and angle y and x correlate. This is a four-sided shape, so the total of all four angles will add up to 360.

113 and z are correlating, so z is 113.

To find the other two, we first need to find out how much angle measurement is left. To do this, we will subtract angle 113 and z from 360 (our total).

This gives us 134 degrees left.

Now, since x and y are equal to each other, that means that their measurements will be exactly half of the remainder we just found.

So taking 134 and dividing it by 2, we get our final two measurements for x and y, 67 degrees each.

Answer:

x = 67

y = 67

z = 113

Work:

There are a total of 360 degrees in a rhombus and a straight line is 180 degrees. You also know that opposite angles in a rhombus are equal.

If z is opposite 113, then z = 113.

Then to find x, 180 - 113 = 67.

If x is 67 then y is 67 since they are opposite angles.

Answer:

10000000000000

Step-by-step explanation:

I do not know how to explain