(a) Let {01, v2} be an orthonormal basis for some two dimensional subspace of R". Define the matrix P= v107 +0207. Prove that P is an orthogonal projector. What is the range of P?

Answer: do i remember how to do this... no

Step-by-step explanation:

Based on the given linear equation of y = - 3/4x + 5, the graph is shown attached.

When given a linear equation, you graph it by coming up with x values and then using the equation to find the corresponding y values.

The linear equation is y = - 3/4x + 5.

If the value x = -1, then y would be:

y = - 3/4x + 5

= -3/4(-1) + 5

= 5.75

If the value x = 0, then y would be:

y = -3/4(0) + 5

= 5

If the value x = 1, then y would be:

= -3/4(1) + 5

= 4.25

If the value x = 2, then y would be:

= -3/4(2) + 5

= 3.5

If the value x = 3, then y would be:

= -3/4(3) + 5

= 2.75

The points would be:
(-1, -5.75) (0, 5) (1, 4.25) (2, 3.5) (3, 2.75)

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Answer:

B. 5.0 × 10⁻¹² moles per liter.

Step-by-step explanation:

In this exercise we have to calculate the pH levels associated with respective hydrogen ion concentration based on the following formula:

\(pH=-\log [H^{+}]\)

Where \([H^{+}]\) is the hydrogen ion concentration, measured in moles per liter.

a) 3.5 × 10⁻¹⁶ moles per liter:

\(pH=-\log [3.5\times 10^{-16}]\)

\(pH \approx 15.456\)

The substance is above the upper bound for alkaline substances.

b) 5.0 × 10⁻¹² moles per liter:

\(pH=-\log [5.0\times 10^{-12}]\)

\(pH \approx 11.301\)

The substance is alkaline.

c) 1.0 × 10⁻⁷ moles per liter:

\(pH=-\log [1.0\times 10^{-7}]\)

\(pH= 7\)

The substance is not acid nor alkaline.

d) 1.1 × 10⁻⁴ moles per liter:

\(pH=-\log [1.1\times 10^{-4}]\)

\(pH \approx 3.959\)

The substance is acid.

Thus, we concluded that correct answer is B.

Answer:

5 * 10^12

Step-by-step explanation:

The true statements regarding the dimensions of △VQK, the transformation of △TZP, are as follows:

△VQK is translated 1 inch down and 1.5 inches to the right compared to △TZP.

The side lengths of △VQK are not equal to the corresponding side lengths of △TZP.

The corresponding angles of △VQK and △TZP are congruent.

△VQK is larger or smaller in size compared to △TZP due to the dilation.

Explanation:

The transformation of △TZP to △VQK involves a translation and a dilation. Firstly, △TZP is translated 1 inch down and 1.5 inches to the right. This means that every point of △TZP is moved 1 inch downwards and 1.5 inches to the right to obtain the corresponding points in △VQK. The translation affects the position of the vertices, but it does not alter the shape or size of the triangle.

Secondly, △TZP is dilated using a scale factor of ⁹⁄₅. This means that every side length of △TZP is multiplied by ⁹⁄₅ to obtain the corresponding side lengths in △VQK. The dilation changes the size of the triangle, making it larger or smaller depending on the scale factor.

Based on these transformations, we can conclude the following true statements:

△VQK is translated 1 inch down and 1.5 inches to the right compared to △TZP.

The side lengths of △VQK are not equal to the corresponding side lengths of △TZP due to the dilation.

The corresponding angles of △VQK and △TZP are congruent, as angles are preserved under both translation and dilation.

△VQK is larger or smaller in size compared to △TZP due to the dilation.

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Answer:

The answer is GV and VD

Step-by-step explanation:

Those are the answers because of the points on the line. Please pick me as brainliest!!  :)

The proportion used to find the value of a is a/18 = 16/a

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Given are three similar triangles, (refer to attached figure to separately see the similar triangles)

We know that, similar triangle have corresponding sides in equal ratio,

Therefore,

a/18 = 16/a

Hence, the proportion used to find the value of a is a/18 = 16/a

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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.

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To solve the inequality 5sin x ≥ -2cos x, we need to use trigonometric identities to simplify it to a form where we can find the solution interval.

Step 1: Simplify the inequality

Use the trigonometric identity: sin^2(x) + cos^2(x) = 1 to transform the inequality from 5sin(x) ≥ -2cos(x) to:

5sin(x) + 2cos(x) ≤ 5

Step 2: Find the critical points

The critical points occur when the left-hand side equals 5, i.e.,

5sin(x) + 2cos(x) = 5

Solve for x:

sin(x) = (5 - 2cos(x)) / 5

Square both sides to eliminate the sin(x) term:

sin^2(x) = (25 - 20cos(x) + 4cos^2(x)) / 25

Apply the trigonometric identity:

1 - cos^2(x) = (25 - 20cos(x) + 4cos^2(x)) / 25

Rearrange and simplify:

5cos^2(x) - 20cos(x) + 20 = 0

cos(x) = (20 ± sqrt(20^2 - 4520)) / (2*5)

cos(x) = 2/5 or cos(x) = 1

Substitute these values of cos(x) into the equation sin(x) = (5 - 2cos(x)) / 5 to find the corresponding values of sin(x):

sin(x) = 3/5 or sin(x) = 0

Therefore, the critical points are x = arcsin(3/5), x = 0, and x = π.

Step 3: Check the endpoints of the interval

Check if the inequality is satisfied at the endpoints of the interval [0, 2π):

At x = 0:

5sin(0) + 2cos(0) = 2 > 0

At x = 2π:

5sin(2π) + 2cos(2π) = -2 < 5

Therefore, the inequality is satisfied at the endpoints.

Step 4: Check the critical points

Check if the inequality is satisfied at the critical points:

At x = arcsin(3/5):

5sin(arcsin(3/5)) + 2cos(arcsin(3/5)) = 5(3/5) + 2(4/5) = 4 > 0

At x = π:

5sin(π) + 2cos(π) = -5 < 5

Therefore, the inequality is satisfied at the critical points.

Step 5: Determine the intervals where the inequality is satisfied

Use the critical points and endpoints to divide the interval [0, 2π) into subintervals where the inequality is either always satisfied or never satisfied.

The critical points divide the interval into three subintervals:

[0, arcsin(3/5)] ∪ [arcsin(3/5), π] ∪ [π, 2π)

For the first subinterval, note that sin(x) is increasing from 0 to 3/5, so 5sin(x) is increasing and 2cos(x) is decreasing.

Therefore, 5sin(x) + 2cos(x) is increasing, and it is always less than or equal to 5 at x = arcsin(3/5). Thus, the inequality is satisfied in the subinterval [0, arcsin(3/5)].

For the first subinterval, note that sin(x) is increasing from 0 to 3/5, so 5sin(x) is increasing and 2cos(x) is decreasing. Therefore, 5sin(x) + 2cos(x) is increasing, and it is always less than or equal to 5 at x = arcsin(3/5). Thus, the inequality is satisfied in the subinterval [0, arcsin(3/5)].

For the second subinterval, note that sin(x) is decreasing from 3/5 to 0, so 5sin(x) is decreasing and 2cos(x) is increasing. Therefore 5sin(x) + 2cos(x) is decreasing, and it is always less than or equal to 5 at x = π. Thus, the inequality is satisfied in the subinterval [arcsin(3/5), π].


For the third subinterval, note that sin(x) is nonpositive, so 5sin(x) is nonpositive, and 2cos(x) is negative. Therefore, 5sin(x) + 2cos(x) is negative in this subinterval, and the inequality is not satisfied.

Thus, the solution interval is [0, arcsin(3/5)] ∪ [arcsin(3/5), π] = [0, 2.532] ∪ [3.751, 2π).

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Answer:

-2 is the slope of the line. (rise over run)

Answer:

14

Step-by-step explanation:

B is the midpoint of AC, in other words it is the halfway point.

So A to B should be equal to B to C

Our expression is:

2x + 9 = 37

Subtract 9

2x = 28

Divide by 2

x = 14

ANSWER

Yes, it can.

EXPLANATION

First of all, let us sort the data according to increasing value:

Time (minutes) 18 20 20 22 22 23 25 30

Duration (minutes) 38 40 42 41 42 44 47 52

As we can already see, the duration of the ride seems to increase as the amount of time after 8 am that she got on the bus.

This means that the Duration of the ride and the time Layne got on the bus have a linear relationship and so, YES, the duration of the ride can be represented as a function of the time Layne got on the bus.

From the data the students for the seventh grade sent more text messages

The two data do not have the same center

By the given histogram the sixth-grade students has a mode of ninety

Mode=90

By the given histogram, For the seventh-grade students has mode of one hundred two

Mode=102

Hence, the seventh grade is higher than the sixth grade.

b. The greater spread:

For the sixth grade:

Spread = 5

For the seventh grade:

Spread = 7

When we compare the sixth grade and seventh grade, the spread is greater for seventh grade

Hence, the spread for the seventh grade is higher

Hence, the students for the seventh grade sent more text messages

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These two histograms show the number of text messages sent in one week by two groups of 100students. The first histogram summarizes data from sixth-grade students. The second histogramsummarizes data from seventh-grade students.2520151051554555 6585 95 105 115 125 135 145text messages sent per week by sixth-grade studentsk

Answer:

(g - 77)

Step-by-step explanation:

Winston has total number of gumdrops = g

He ate gumdrops = 77

To calculate the number of gum drops left with Winston we will subtract the number of gumdrops ate by Winston from total number.

Therefore, expression that represents the gumdrops left with Winston will be,

(g - 77)

Answer: Yes it does.

Step-by-step explanation:

Answer:50

Step-by-step explanation:

3/5 = 3 ÷ 5 = 0.6

30 ÷ 0.6 = 50

otra explicacion:

30/1 ÷ 3/5= 30/1 x 5/3 = 150/3 = 50

(2/3)x = 7 + 2

(2/3)x = 9

2x = 9 × 3

x = 27/2

:. x = 13 1/2

The distance from the point (6, 1, -1) to the plane x - 2y + 2z + 1 = 0 is 1 unit.

To find the distance from a point to a plane, we can use the formula for the distance between a point and a plane.

Let's denote the given point as P(6, 1, -1) and the equation of the plane as Ax + By + Cz + D = 0, where A, B, C, and D are the coefficients of the plane equation.

The formula for the distance (d) between a point (x0, y0, z0) and a plane Ax + By + Cz + D = 0 is:

d = |Ax0 + By0 + Cz0 + D| / √(A² + B² + C²)

In this case, the equation of the plane is x - 2y + 2z + 1 = 0, which can be written as 1x - 2y + 2z + 1 = 0.

Comparing coefficients, we have:

A = 1

B = -2

C = 2

D = 1

Substituting the values into the distance formula, we get:

d = |1(6) + (-2)(1) + 2(-1) + 1| / √(1² + (-2)² + 2²)

= |6 - 2 - 2 + 1| / √(1 + 4 + 4)

= |3| / √(9)

= 3 / 3

= 1

Therefore, the distance from the point (6, 1, -1) to the plane x - 2y + 2z + 1 = 0 is 1 unit.

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To summarize, in this example:
- 20 trees die
- 5 trees are sold for $20 each
- 10 trees grow to be more than 5 ft
- 28 trees taller than 5 ft are sold for $50 each
- 11 trees taller than 5 ft are sold for $30 each
- 17 trees taller than 5 ft remain in the forest

The forest consists of two types of trees: those that are 0–5 ft tall and those that are taller than 5 ft. Each year, there are different percentages of what happens to these trees.
For the 0–5 ft tall trees:
- 40% of them die
- 10% are sold for $20 each
- 30% stay between 0 and 5 ft
- 20% grow to be more than 5 ft
For the trees taller than 5 ft:
- 50% of them are sold for $50 each
- 20% are sold for $30 each
- 30% remain in the forest
To better understand the distribution and changes in the forest, let's consider an example with 100 trees.
In this example, we start with 100 trees, of which:
- 0–5 ft tall trees: 50 trees
- Taller than 5 ft trees: 50 trees
For the 0–5 ft tall trees:
- 40% of them die, so 40% of 50 trees is 20 trees die
- 10% are sold for $20 each, so 10% of 50 trees is 5 trees sold
- 30% stay between 0 and 5 ft, so 30% of 50 trees is 15 trees stay
- 20% grow to be more than 5 ft, so 20% of 50 trees is 10 trees grow
After these changes, we have:
- 0–5 ft tall trees: 15 trees (remaining trees)
- Taller than 5 ft trees: 55 trees (remaining trees + growth)
For the trees taller than 5 ft:
- 50% of them are sold for $50 each, so 50% of 55 trees is 27.5 trees sold (rounding to 28 trees sold)
- 20% are sold for $30 each, so 20% of 55 trees is 11 trees sold
- 30% remain in the forest, so 30% of 55 trees is 16.5 trees remain (rounding to 17 trees remain)
After these changes, we have:
- 0–5 ft tall trees: 15 trees (remaining trees)
- Taller than 5 ft trees: 17 trees (remaining trees)
To summarize, in this example:
- 20 trees die
- 5 trees are sold for $20 each
- 10 trees grow to be more than 5 ft
- 28 trees taller than 5 ft are sold for $50 each
- 11 trees taller than 5 ft are sold for $30 each
- 17 trees taller than 5 ft remain in the forest

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Answer:

thxss for the points love

Step-by-step explanation:

kisses

Answer:

16

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

2x17=34

17x2.5=42.5

1.5x17=25.5

1/2x2x2x1.5=3

34+42.5+25.5+3=105

Answer Po Ba Ay 11.33?

Step-by-step explanation:

Calc

Answer:

20

Step-by-step explanation:

any thing multiplied by a fraction gets divided so you need to reverse it and divide to get the answer

Answer:

20

Step-by-step explanation:

1/2 times 20 = 10

its like the same thing as 10 times 2 = 20

Answer:

Neither are polynomials because polynomials have more than 2 terms

Step-by-step explanation:

Answer: 10 is a polynomial because the power of x is 0, which is a whole number.

Step-by-step explanation: Sorry that's all I got. I hoped that helped you find why 1/4 is not a polynomial.

Answer:

6.75

Step-by-step explanation:

6 is equivalent to 6

3/4 is equivalent to 0.75

Answer:

It is 6.75

Step-by-step explanation:

Can I have brainliest?

Answer:

24°

Step-by-step explanation:

Let's represent the unknown angle with x

So ;

66+x=90

x=90-66

x=24°

Therefore 24° is the missing angle.

Answer:

24°

Step-by-step explanation:

The missing angle is 90-66 = 24°.

The roots of the polynomial functions are

(a) x = -1 or x = -1.2 and x = -0.16

(b) x = -1/7 or x = 2

From the question, we have the following parameters that can be used in our computation:

a) y = (x + 1)(5x² + 7x + 1)

b). y = (7x + 1) (2x - 4)

The roots of the polynomial functions are calculated by setting the functions to 0

So, we have

(x + 1)(5x² + 7x + 1) = 0

(7x + 1) (2x - 4) = 0

Using the zero product property, we have

x + 1 = 0 or 5x² + 7x + 1 = 0 and

7x + 1 = 0 or 2x - 4 = 0

When evaluated, we have

x = -1 or x = -1.2 and x = -0.16

x = -1/7 or x = 2

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Complete question

For each polynomial function below, determine all of the roots.

a) y = (x + 1)(5x² + 7x + 1)

b). y = (7x + 1) (2x - 4)

Answer:

Step-by-step explanation:

The sum of the angles in a triangle is always 180 degrees. Therefore,

2x + 3x + 22 = 180

Simplifying the equation,

5x = 158

Dividing by 5 on both sides,

x = 31.6

To find the actual measures of 2x and 3x, we substitute the value of x:

2x = 2(31.6) = 63.2 degrees

3x = 3(31.6) = 94.8 degrees

Therefore, the actual measures of 2x and 3x are 63.2 degrees and 94.8 degrees, respectively.

The complementary angles will be 65.6° and 24.4°.

What exactly are complementary angles?

Supplementary and complementary angles are defined by the sum of two angles. If the total of two angles is 90 degrees, they are considered to be complimentary angles since they produce a right angle when combined. If the total of two angles is 180 degrees, they are considered to be supplementary angles since they produce a linear angle when combined.

Now,

Let x be a angle then its complementary angle will be 90°-x as sum of complementary angles is equal to 90°.

as given

90°-x-x=18.8°

9--2x=18.8

2x=71.2

x=65.6° and 90-x°=24.4°

hence,

                The complementary angles will be 65.6° and 24.4°.

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The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

9

Step-by-step explanation:

Answer:

X intercept (-40,0)

Y intercept: (0, 15)

Step-by-step explanation:

Where the line meets on the x axis, the coordinate is -40, 0 which is the x intercept and as it is for the y intercept, it meets at 0,15

Answer:

5 6/7 or C option

Step-by-step explanation:

5 6/7 is equal to 5.857 and rounded it is 6

While all the others round to 5

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