Write a quadratic equation with each pair of values as roots.5-10.

9514 1404 393

Answer:

  yes

Step-by-step explanation:

The number has a finite number of digits, so is rational.

__

Additional comment

It would also be rational if it had an infinite number of digits with the decimal fraction ending in a finite-length portion that repeats.

Answer:

f(x)=x²-3x-10

Step-by-step explanation:

\(f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5\)

therefore the zeros of the equation are x₁=-2,x₂=5

The answer option that matches the graph I drew include the following: D. graph D.

In Mathematics, the following rules are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph:

In this context, we can logically deduce that the most appropriate graph to represent the solution to the given inequality y ≤ - 2x is graph D because the solid boundary lines must be shaded below.

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Answer:

14 is +1

15 is -9

Step-by-step explanation:

For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

A right triangle, right-angled triangle, or more formally an orthogonal triangle—previously known as a rectangled triangle—is a triangle with one angle that is a right angle (i.e., a 90-degree angle), meaning that two of its sides are perpendicular. The foundation of trigonometry is the relationship between the sides and other angles of a right triangle.

The hypotenuse is the side that faces the right angle (side c in the figure). Legs are the sides that are next to the right angle (or catheti, singular: cathetus). Side a can be thought of as the side that is adjacent to angle B and opposite to (or opposite) angle A, whereas side b is the side that is adjacent to angle A and opposite to angle B.

Given a right triangle with base = 8 and an angle = 24°

Using angle sum property of triangle

24 + 90 + angle L = 180

L = 66°

Using Sohcahtoa

Tangent: tan(θ) = Opposite / Adjacent

tan(24°) = LK/8

0.445 = LK/8

LH = 8 × 0.445

LK = 3.56

LM = \(\sqrt{MK^2 + LK^2}\)

LM = \(\sqrt{8^2 + 3.56^2}\)

LM = 8.75

Thus, For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

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Answer:

64 people

Step-by-step explanation:

if 1/4 of a bus is 16, do 16x4 and u will get 64

Answer:

to find the ammount of twine left we subtract (twine used) from (total twine) or (total twine)-(twine used)=ammount left

so he must cut 42 legnths of rope  each legnth is 4.75 and this is taken from a

total legnth of 240 so

240-42(4.75)=amount left

42 trimes 4.75=199.5

240-199.5=40.5 left

Step-by-step explanation:

Answer:

True the product of a number and its reciprocal is equal to one.

Step-by-step explanation:

let the number be X

Now the reciprocal will be 1/X

And when we multiply them

X ×1 /X = 1

To find the minimum score required for an A grade, we need to determine the cutoff point that corresponds to the top 13% of scores.

Given that the scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5, we can use the standard normal distribution to calculate the cutoff point. Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the top 13% is approximately 1.04. To find the corresponding raw score, we can use the formula:

x = μ + (z * σ)

where x is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we have:

x = 69.5 + (1.04 * 9.5) ≈ 79.58

Rounding this to the nearest whole number, the minimum score required for an A grade would be 80. Therefore, a student would need to score at least 80 on the test to achieve an A grade according to the professor's grading scheme.

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The interest rate is 10.89%

1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..

The size of the nominal money supply in the new short-run equilibrium is 121.07.

2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.

Real exchange rate will remain unchanged.

3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.

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Answer:

A linear function can be written in the slope intercept form or a point slope form of a line. Where a table is given for values representing the function, the ordered pairs will represent points on the line.The gradient of the line is a ratio of rise to run from the table values.In slope intercept form, the gradient and initial value of the function are indicated.

For example in a function f(x)=mx+b , m is the gradient of the line and b is the y-intercept value of the function.

To find the slope, m, you divide the difference between y-values by the difference in corresponding x-values of any two points on the line.

A decreasing linear function has a negative slope; if m<0 then f(x)=mx+c is decreasing

An increasing linear function has a positive slope where m>0.

Step-by-step explanation:

Answer:

OG slope is 1, perpendicular slope is -1

Step-by-step explanation:

rise over run is 1/1, perpendicular slopes are the reciprocoal, or opposite slope, so -1

Answer:

(a) To find the inverse of the function f(x), we interchange x and y and solve for y. The inverse function is f^(-1)(x) = (x + 1) / 3.

(b) The domain of f(x) is the set of all real numbers since there are no restrictions on the input x. The range is also the set of all real numbers since f(x) can take any real value. The horizontal asymptote is y = 3, as x approaches positive or negative infinity, f(x) approaches 3.

(c) The domain of f^(-1)(x) is the set of all real numbers since there are no restrictions on the input x. The range is also the set of all real numbers since f^(-1)(x) can take any real value. There are no vertical asymptotes in either f(x) or f^(-1)(x).

Step-by-step explanation:

(a) To find the inverse of a function, we interchange the roles of x and y and solve for y. For the function f(x) = 3(x + 2) - 1, we can write it as y = 3(x + 2) - 1 and solve for x. Interchanging x and y, we get x = 3(y + 2) - 1. Solving for y, we have y = (x + 1) / 3, which gives us the inverse function f^(-1)(x) = (x + 1) / 3.

(b) The domain of f(x) is the set of all real numbers because there are no restrictions on the input x. For any value of x, we can evaluate f(x). The range of f(x) is also the set of all real numbers because f(x) can take any real value depending on the input x. The horizontal asymptote of f(x) is y = 3, which means that as x approaches positive or negative infinity, the value of f(x) approaches 3.

(c) The domain of the inverse function f^(-1)(x) is also the set of all real numbers since there are no restrictions on the input x. Similarly, the range of f^(-1)(x) is the set of all real numbers because f^(-1)(x) can take any real value depending on the input x. There are no vertical asymptotes in either f(x) or f^(-1)(x) since they are both linear functions.

In summary, the inverse function of f(x) is f^(-1)(x) = (x + 1) / 3. The domain and range of both f(x) and f^(-1)(x) are the set of all real numbers, and there are no vertical asymptotes in either function. The horizontal asymptote of f(x) is y = 3.

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- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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Answer:

15 white cubes

Step-by-step explanation:

Given

\(White\ Cubes = -1\)

\(Black\ Cubes = +1\)

\(Number\ of\ Black\ Cubes = 15\)

Required

Determine the number of white cubes needed to represent 0

To solve this question, we make use of the following equation.

\(Black\ Cubes +White\ Cubes = 0\)

If there are 15 black cubes, the the 15 black cubes is worth: +1 * 15

Substitute +1 * 15 for the Black Cubes

\(+1 * 15 +White\ Cubes =0\)

\(+15 +White\ Cubes =0\)

Collect Like Terms

\(White\ Cubes = 0 - 15\)

\(White\ Cubes = - 15\)

Recall that 1 white cube is worth -1

So, the number of white cubes is:

\(Number = \frac{-15}{-1}\)

\(Number = 15\)

Hence, the student needs 15 white cubes

Answer: it will

Step-by-step explanation:

your welcome

Probability for the number of correct answers  is fewer than 4 is 0.3993.

The probability that the number x of correct answers is fewer than 4 can be found using the binomial probability formula:

P(X = x) = (n choose x) * p^x * (1-p)^(n-x)

Where n is the number of trials, x is the number of successes, and p is the probability of success.

For this problem, n = 8, p = 0.45, and we want to find P(X < 4).

To find P(X < 4), we need to find the probability of 0, 1, 2, and 3 correct answers and add them together:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula, we can find each of these probabilities:

P(X = 0) = (8 choose 0) * 0.45^0 * (1-0.45)^(8-0) = 0.0059
P(X = 1) = (8 choose 1) * 0.45^1 * (1-0.45)^(8-1) = 0.0416
P(X = 2) = (8 choose 2) * 0.45^2 * (1-0.45)^(8-2) = 0.1275
P(X = 3) = (8 choose 3) * 0.45^3 * (1-0.45)^(8-3) = 0.2243

Adding these probabilities together, we get:

P(X < 4) = 0.0059 + 0.0416 + 0.1275 + 0.2243 = 0.3993

Therefore, the probability that the number x of correct answers is fewer than 4 is 0.3993.

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The most important cell in your body is the red blood cell.

Cells are the fundamental components of life. Every item you observe contains cells. Organelles are structures found inside cells that allow the cell to function.

Red blood cells are the most frequent form of blood cell and the vertebrate's primary mechanism of distributing oxygen to bodily tissues via blood flow through the circulatory system.

Blood cell activity is essential to life, from delivering oxygen throughout the body to battling infection. Bone marrow is responsible for the production of blood cells. Red blood cells, white blood cells, and platelets are the three major types of blood cells.

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To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

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It examines the marketing and advertising environment, specifies the goals of the media campaign, and explains how a company can judge whether a campaign was successful.

Important attribute 1 essential brand recall characteristic 2 The message's mental availability is high.

Consumers should be able to relate the brand to the creative for an ad to successfully achieve business results (brand recall). The most effective advertisements also clearly deliver a message that viewers may recall in critical moments (mental availability).

The most effective advertising campaigns are frequently those that effectively define the brand's value to their target audience, either intrinsically or extrinsically.

People don't want to think about what you're trying to teach them. As a result, make certain that your message is clear and does not cause confusion.

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Answer:

\(x=33^{\circ}\)

Step-by-step explanation:

First off, your drawing is kinda inaccurate, because the \(124^{\circ}\) looks like a right angle, but as you drew it yourself it doesn't matter too much.

We know that the sum of the angles of a triangle will always equal \(180^{\circ}\), so we have that \(23+124+x=180\).

Combining like terms on the left side gives \(147+x=180\).

Subtracting \(147\) from both sides gives \(x=33\).

So, \(\boxed{x=33^{\circ}}\) and we're done!

Answer:

33°

Step-by-step explanation:

1. All angles in any triangle add up to 180°, so 23° + 124° + x° = 180.

2. Now, let's solve that equation we just wrote!

Step 1: Combine like terms

Step 2: Subtract 147 from both sides.

Therefore, x = 33°!

Answer:

94594945

Step-by-step explanation:

First we need 1105 of 450450450 we get this by multiply it by 1.10 we'll get 495495495 then we add that to his score  of the first month to get 94594945

Answer: 945

Step-by-step explanation: since he is reading 10% MORE you would find the percentage of 450 PLUS 10%

110/100= 1.1

1.1 * 450= 495

495 + 450= 945

Hopefully this makes sense

Answer: Macy will travel a distance of 226.20 feet if she swims around the pool 4 times.

Step-by-step explanation:

C = πd, where d is the diameter of the circle

C = πd = π(18 feet) = 56.55 feet (rounded to two decimal places)

If Macy swims around the pool 4 times, she will travel a total distance of:

4 × C = 4 × 56.55 feet = 226.20 feet (rounded to two decimal places)

Answer:

She traveled approximately 226.08 feet.

Step-by-step explanation:

c = 2\(\pi r\)  Since she swims the pool 4 times, we will multiply this by 4

c = 4(2)\(\pi r\)

c = 8(3.14)(9)  If the diameter is 18, then the radius is 9.  I used 3.14 for \(\pi\)

c = 226.08

Helping in the name of Jesus.

Answer:

No.

Step-by-step explanation:

Line XY will be tangent to Circle W when XY is perpendicular to the radius XW. We can test if it is perpendicular by using Pythagoras theorem as it only works on right angled triangle. If the angle WXY is 90 degrees (XY ⊥ WX) then the theorem should work.

\((XY)^2=(WX)^2+(XY)^2\\R.H.S = 66^2+54^2 = 7272\\L.H.S = 87^2 = 7569\\R.H.S \neq L.H.S\)

Thus the angle is not 90 degrees since the Pythagoras theorem doesn't work thus the line is not tangent since it is not at 90 degrees with the radius WX.

Answer:

not a tangent

Step-by-step explanation:

if XY is a tangent to the circle then ∠ WXY = 90°

using converse of Pythagoras' identity.

if the square of the longest side is equal to the sum of the squares on the other 2 sides , then the triangle is right.

longest side is WY

WY² = 87² = 7569

WX² + XY² = 66² + 54² = 4356 + 2916 = 7272

since WY² ≠ WX² + XY² , then Δ WXY is not right

then XY is not a tangent to the circle

Answer:

I cant answer everything but I know that there are 8 cups in a liter

Step-by-step explanation:

Answer:

B,D

Step-by-step explanation:

As a point estimator for, we utilise x-bar (sample mean) (mu, population mean)

The average value in mathematics is the middle number, which is calculated by dividing the total number of numbers by the sum of all the numbers. A set of data's average is calculated by adding up all the values and dividing the result by the total number of values.

We use the x-bar (sample mean) as a point estimator for (mu, population mean). As long as the sample is random, this estimator's impartial long-run distribution is centred at (mu).

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Complete question -

Answer:

1000

Step-by-step explanation: