The graph represents a quadratic function. Write an equation of the function in standard form.

Answer:

y = -2x + 9

Step-by-step explanation:

The equation of the new line is the same as that of this given line, EXCEPT that the constant will be different.

Start with y = mx + b; substitute 1 for y, 4 for x and -2 for m:

1 = -2(4) + b

Then b = 9, and y = -2x + 9

Answer:

U (7,1)

T (10,1)

V (7,9)

S (10,9)

Step-by-step explanation:

The image of the rectangle STUV after a reflection over the line y= –x is attached below.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The coordinates of the points in the graph are S(-9,-10) , T(-1,-110) , U(-1,-7) , V(-9,-7)

We have to graph the image of the rectangle STUV after a reflection over the line y= –x

The points obtained after graphing ate,

U (7,1)

T (10,1)

V (7,9)

S (10,9)

Thus, the image of the rectangle STUV after a reflection over the line y= –x is attached below.

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ2

Answer:

They used 7 vans and 2 cars.

Step-by-step explanation:

With 7 vans, they can hold 91 students and with 2 cars, the can hold 6 students. 91+6=97 students.

Answer: Food surpluses led to population growth.

Step-by-step explanation:

Food surpluses led to population growth.

The equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is 3x + 2y + z = 8.

We need a point b and a vector v along the line in order to characterize it. We might alternatively begin with the two points a and b and use the formula v = ab.
A point Q and a vector n perpendicular to the plane are required in order to describe a plane. Later on, we'll look at how to get n from various types of information, such as the positions of three points on a plane.

A plane is a flat, endlessly long, two-dimensional surface. A plane is a point with zero dimensions, a line with one dimension, and space with three dimensions in two dimensions. The picture below that is attached shows the answer.

Here is another question with an answer similar to this about equation of the plane: https://brainly.com/question/27190150

#SPJ4

Question correction:

Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0

Answer:

The value of n = 4 and  

The value of x = \(\frac{5}{3}\)

Step-by-step explanation:

Method I:

As given, 12x -20=n (3x-5)      .........(1)

Firstly , take 12x - 20

As 12x - 20 can be written as 4(3x - 5)

∴ equation (1) becomes

4(3x - 5) = n (3x-5)

Divide the equation by (3x-5) , we get

4 = n

Method II:

As given, 12x -20=n (3x-5)

⇒12x - 20 = 3nx - 5n

⇒12x - 3nx = 20 - 5n

⇒3x(4 - n) = 5( 4 - n)

Divide the equation by (4-n) , we get

3x = 5

⇒ x = \(\frac{5}{3}\)

∴ we get

n = 4 and  x = \(\frac{5}{3}\)

Now, check that value of n and x satisfies the equation or not

12(\(\frac{5}{3}\)) - 20 = 4( 3(\(\frac{5}{3}\)) - 5)

⇒4(5) - 20 = 4(5 - 5)

⇒20 - 20 = 4(0)

⇒ 0 = 0

Hence , we get

The values of x and n satisfies the equation

so, we get

n = 4 and  x = \(\frac{5}{3}\)

Answer:

B

Step-by-step explanation:

Fip numbers and change both signs when reflecting over y=-x

Answer:

C

Step-by-step explanation:

The three options that are true about the equation of the circle are:

B) The center of the circle lies on the x-axis

A) The radius of the circle is 3 units.

E) The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The standard equation of a circle is expressed as:

x² + y² + 2gx + 2fy + c = 0

Where:

Center is (-g, -f)

radius = √g²+f²-C

Given a circle whose equation is x² + y² - 2x - 8 = 0

Get the Centre of the circle:

2gx = -2x

2g = -2

g = -1

Similarly, 2fy = 0

f = 0

Centre = (-(-1), 0) = (1, 0)

This shows that the center of the circle lies on the x-axis

r = radius = √g² + f² - C

radius = √1² + 0² - (-8)

radius =√9 = 3 units

The radius of the circle is 3 units.

For the circle x² + y² = 9, the radius is expressed as:

r² = 9

r = 3 units

Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Read more about Equation of a Circle at: https://brainly.com/question/1559324

#SPJ1

Answer:

1/10, 0.1, 10%

3/4, 0.75, 75% of 1

1/5, 0.2, 20%

Step-by-step explanation:

i hope this helped : )

The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

Learn more about acceleration

brainly.com/question/12550364

#SPJ11

Answer:

Y = 4x - 2

Step-by-step explanation:

Use the given slope and point to substitute into the point-slope formula

Answer:B

62ç=32-86

62c=-54

C=0.87

The maximum volume square candy box to be cut out is 2.88 inches.

If the size of the squares to also be cut out is x, then

A rectangular box's volume is provided by length x width x height.

V = (25 - 2x)(14 - 2x)x = x(350 - 78x + 4x²)

V = 350x - 78x² + 4x³

For the maximum volume of the candy box.

dV/ dt = 0

Differentiate the volume with respect to time.

dV/ dt = 350 - 156x + 12x².

Then,

350 - 156x + 12x² = 0

Solve the above quadratic equation by the quadratic formula and find the roots as-

x = 10.12  and 2.88

However, the size of a square cut out cannot be 10.12 because 10.12 inches cannot be cut from both sides of a 14-inch width.

As a result, the maximum volume square to be cut out is 2.88 inches.

To know more about the maximum volume, here

https://brainly.com/question/17219343

#SPJ4

The coordinates of the point which is an outlier would be ( 14, 13).

The correlation between the 13 British towns is Linear.

The number of hours of sunshine for the British town with the maximum of 17.4 degrees Celsius is 13 hours of sunshine.

The coordinates of the outlier would be ( 14, 13). This is because, that point on the graph is far from the other points and does not follow their correlation.

The rest of the towns seem to be increasing in the same direction so they are linear.

The number of hours of sunshine in the British town with the maximum temperature of 17.4 degrees Celsius, based on the line of best fit drawn, would be 13 hours of sunshine.

Find out more on hours of sunshine at https://brainly.com/question/12334715

#SPJ1

Full question is:

The scatter graph shows the maximum temperature and the numbers of hours of sunshine in 13 British towns in one day.

A line of best fit has also been drawn.

One of the points in an outliner.

a) Write down the coordinates of this point. (1)

b) For all the other points write down the type of correlation in just one word. (1)

On the same day, in another British town, the maximum temperature was 17.4C.

c) Estimate the number of hours of sunshine in this town on this day. (2)

Answer:

6(4x + 2y)

Step-by-step explanation:

24x = 2 * 2 * 2 * 3 * x

18y = 2 * 3* 3 * y

Common factors = 2 * 3 = 6

24x + 18y = (6*4x) + (6*2y)   {6 is common in both terms}

               = 6*(4x + 2y)

Extra people required is 50.

Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Question 1 :

Number of associates = 30

Number of direct workers = 30 - 2 = 28

You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.

Direct rate = 150 units per hour

Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week

                                                            = 37.5 hours per week

Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units

28 people produce 5625 units in a week

Let x people produce 10,000 + 5625 = 15,625 units in a week

Using proportion,

28 : 5625 = x : 15,625

28 / 5625 = x / 15,625

x = (28 × 15,625) / 5625 = 77.78 ≈ 78

Extra people required = 78 - 28 = 50

Question 2 :

Number of sandwiches made in 10 minutes = 1

Number of sandwiches made in 10 hours = 60

5 workers are there. one worker makes 60/5 = 12 sandwiches

But Deli want number of sandwiches in 10 hours = 75

One worker should make 75/5 = 15 sandwiches instead of 12.

Number of sandwiches made in 8 minutes should be 1.

So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.

Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.

Learn more about Proportion here :

https://brainly.com/question/26974513

#SPJ1

Answer:

0.44237 units

Step-by-step explanation:

Given

\(v(t) = e^t*sin(e^t)\)

\(0 \le t \le \frac{\pi}{2}\)

Required

The distance traveled in this interval

We have:

\(v(t) = e^t*sin(e^t)\)

The distance is calculated as:

\(d(t) = \int\limits^a_b {v(t)} \, dt\)

So, we have:

\(d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(e^t)} \, dt\)

Let:

\(u = e^t\)

Differentiate

\(\frac{du}{dt} = e^t\)

So:

\(dt = e^{-t} du\)

So, we have:

\(d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(e^t)} \, dt\)

\(d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(u)} \, e^{-t} du\)

Rewrite as:

\(d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t* e^{-t}*sin(u)} \, du\)

\(d(t) = \int\limits^{\frac{\pi}{2}}_0 {sin(u)} \, du\)

Integrate:

\(d(t) = -\cos(u)|\limits^{\frac{\pi}{2}}_0\)

Substitute \(u = e^t\)

\(d(t) = -\cos(e^t)|\limits^{\frac{\pi}{2}}_0\)

Split

\(d(t) = -\cos(e^\frac{\pi}{2}) - [-\cos(e^0)]\)

\(d(t) = -\cos(e^\frac{\pi}{2}) +\cos(e^0)\)

\(d(t) = -0.09793 + 0.5403\)

\(d(t) = 0.44237\)

The distance traveled in this interval is: 0.44237 units

dt =

d(t) = \int\limits^2_0 {e^t*sin(e^t)} \, dt

With linear inequalities in two variables, you still have y=mx+b and it still tells you the same thing.

The inequality portion adds two additional layers on top of the y=mx+b line.

If the inequality is > or <, then you draw the line as a dashed line.

If the inequality is ≥ or ≤, then you draw the line as a solid line.

The difference is that points on the > or < line do NOT make the inquality true, while points on the ≥ or ≤ line do.

The other piece is that all the points on one side of the line will also make the inequality true.

If you have "y>mx+b" or "y≥mx+b", then you shade above the line.

If you have "y<mx+b" or "y≤mx+b", then you shade below the line.

So there are three parts:

1. Where is the line?  

2. Is the line solid or dashed?

3. Do you shade above or below the line?

The three graphs are attached.

Answer:

C

Step-by-step explanation:

If you add 1,000 to a number 10 times, it will only increase the number by 10,000, not multiply the number by 1,000.

Answer: The correct answer is b

Step-by-step explanation:

25% off $30 is 22.50 and then when you add 7%ax it turns out to be 24.08

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(2 \times \frac{1}{2} hour = 1hour \\ \)

\(2 \times \frac{3}{4} mile = \frac{6}{4} mile = \frac{3}{2} miles \\ \)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

1.50 miles or 1 and 1/2

Step-by-step explanation:

Answer:

35 feet

Step-by-step explanation:

if 1 inch = 5 feet

if the scale drawing is 7 inches, the width of the deck = 7 x 5 = 35 feet

Answer:

A confidence interval is made from a sample to estimate the truth for a population.

A confidence interval is a statistical interval that is found from analyzing sample data to justify a larger statement about a great group of people or things. Common confidence intervals are 95% and 99%.

For point 4. Since -4 is less than zero, that is

then to find f(-4) replace x = -4 into x², like this

For point 5. Since 3 is in the interval

then

Finally, for point 6. Since 12 is greater than 3, that is

then to find f(12) replace x = 12 into 4-x, like this

Answer:

the answer is C

Step-by-step explanation:

hope this helps

Answer:

\(x^{18}\)

Step-by-step explanation:

When one exponent is being raised by another exponent, you can multiply them. The base remains the same.

3 * 6 = 18

Answer:

When a number is written using a whole number plus a portion of one, with the portion separated from the whole number by a dot, is called a mixed fraction.

Step-by-step explanation:

A fraction is a number that is obtained by dividing an integer into equal parts and is expressed as:

\(\frac{numerator}{denominator}\)

An improper fraction is a fraction in which the numerator, that is, the top number, is greater than or equal to the denominator, that is, the bottom number.  In contrast, in proper fractions, the numerator is less than the denominator.

Improper fractions can be represented as mixed fractions. A mixed fraction represents a whole number and a proper fraction, in other words, it corresponds to the sum of a whole part plus a fractional part.   In summary, mixed fractions are made up of an integer part and a fractional part.

So, when a number is written using a whole number plus a portion of one, with the portion separated from the whole number by a dot, is called a mixed fraction.

The end behavior of each function is defined as follows:

1. \(\sqrt{6x}\): as x -> ∞, f(x) -> ∞.

2. \(\sqrt{x - 5} - 6\): as x -> ∞, f(x) -> ∞.

3. \(-3\sqrt{x + 3} + 7\): as x -> ∞, f(x) -> -∞.

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

The functions in this problem are all variations of the square root function, which is defined only for non-negative numbers, and thus only the limit when x goes to infinity has to be considered.

As x goes to infinity, the square root goes to infinity, which already define the end behavior for items 1 and 2.

For item 3, the negative leading coefficient means that the function is reflected over the x-axis, assuming a negative value, and thus the end behavior is that the function goes to negative infinity.

More can be learned about the end behavior of a function at brainly.com/question/1365136

#SPJ1