a) 4
If the perimeter of this figure is 62 what is the value of x?
A.) 4
B.) -4
C.) -7
D.) 7

A graph that represent the quadratic equation y = -x² + 4x + 21 is shown in the image attached below.

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a downward parabola because the coefficient of x² is negative and the value of "a" is lesser than zero (0).

Since the leading coefficient (value of a) in the given quadratic function y = -x² + 4x + 21 is negative 1, we can logically deduce that the parabola would open downward and the solution would be represented by the following x-intercepts (zeros or roots);

Ordered pair = (-3, 0)

Ordered pair = (0, 7)

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use sin

sin(50) = x/6

sin(50) x 6 = x

x = ~4.5963

Answer: \(4\frac{2}{3} in;\)  \(5\frac{2}{3} in;\)  \(6\frac{2}{3} in\)

Answer:

  (5 +√5) and (-√5 -5)

Step-by-step explanation:

Given two roots of the 4th-degree polynomial with integer coefficients are (5-√5) and (√5-5), you want to know the other two roots.

The other two roots are the conjugates of the given roots. That is, the signs of the √5 term will change:

  (5 +√5) and (-√5 -5)

__

Additional comment

The polynomial is x⁴ -60x² +400.

The average number of intersections the traffic engineer would need for each type of traffic signal to reject the null hypothesis at the 0.01 level of significance with a power of 0.90 is six

To test the effectiveness of these signals, the engineer must reject the null hypothesis, which states that there is no significant difference in the mean delays between the three types of signals. The engineer wants to reject the null hypothesis at the 0.01 level of significance with a power of 0.9. In other words, they want to be 90% sure that they can detect a significant difference if it exists.

Using the data provided in the study, the engineer can calculate the sample size needed for each type of signal. They need at least five intersections for pretimed signals, six intersections for semi-actuated signals, and four intersections for fully actuated signals to reject the null hypothesis at the desired level of significance with a power of 0.9.

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Answer:

82.1

Step-by-step explanation:

a triangle will always be 180° so you add the numbers you have already and subtract them from the total

41.2 + 56.7 =97.9

180-97.9= 82.1

Answer:

1 gallon = 16 cups

3 cups per person

32 people

32x3=96/16=6

she needs 6 gallons

Answer:

\( M(6, 6) \)

Step-by-step explanation:

Given:

Endpoints of a line segment, T(6, 3) and U(6, 9)

Required:

Midpoint, M, of line segment TU

✍️Solution:

Apply the midpoint formula, which is given as: \( M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) \).

Let:

\( T(6, 3) = (x_1, y_1) \)

\( U(6, 9) = (x_2, y_2) \)

Plug in the values into the formula

\( M(\frac{6 + 6}{2}, \frac{3 + 9}{2}) \)

\( M(\frac{12}{2}, \frac{12}{2}) \)

\( M(6, 6) \)

Coordinates of the midpoint, M, of line segment TU is \( (6, 6) \)

The eigenvalues in terms of α are (7 + sqrt(49 - 16α)) / 4 and (7 - sqrt(49 - 16α)) / 4, in increasing order. There are no critical values.

The given coefficient matrix is [[7/4, 3/4], [α, 7/4]]. To find the eigenvalues, we need to solve the characteristic equation det(A - λI) = 0, where A is the coefficient matrix, I is the identity matrix, and λ is the eigenvalue.

Expanding the determinant, we get:(7/4 - λ)(7/4 - λ) - (3/4)(α) = 0

Simplifying and rearranging, we get: λ^2 - (7/2)λ + (49/16) - (3/4)α = 0

Using the quadratic formula, we get: λ = (7 ± sqrt(49 - 16α)) / 4

Therefore, the eigenvalues in terms of α are (7 + sqrt(49 - 16α)) / 4 and (7 - sqrt(49 - 16α)) / 4, in increasing order.

To find the critical values of α where the qualitative nature of the phase portrait changes, we need to examine the sign of the eigenvalues. If both eigenvalues are real and have the same sign, the phase portrait consists of either a stable node or a stable spiral. If both eigenvalues are real and have opposite signs, the phase portrait consists of either a saddle or an unstable node. If both eigenvalues are complex conjugates with positive real part, the phase portrait consists of a stable focus, and if both eigenvalues are complex conjugates with negative real part, the phase portrait consists of an unstable focus.

From part a), we know that the eigenvalues are (7 + sqrt(49 - 16α)) / 4 and (7 - sqrt(49 - 16α)) / 4. To determine the critical values of α where the nature of the phase portrait changes, we need to set each eigenvalue equal to zero and solve for α.

Setting (7 + sqrt(49 - 16α)) / 4 = 0, we get sqrt(49 - 16α) = -7, which is not possible since the square root of a real number is always non-negative. Therefore, there are no critical values of α where the nature of the phase portrait changes. Alternatively, we can examine the sign of the discriminant, which is 49 - 16α. If the discriminant is positive, the eigenvalues are real and have opposite signs, indicating a saddle or an unstable node. If the discriminant is zero, one of the eigenvalues is zero, indicating a degenerate case. If the discriminant is negative, the eigenvalues are complex conjugates with non-zero real part, indicating a stable focus or a stable spiral. In this case, the discriminant is always positive or zero, since α can take any value. Therefore, there are no critical values of α where the nature of the phase portrait changes.

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Answer:

20.4

Step-by-step explanation:

Answer:

42, 56, 70

Step-by-step explanation:

A right triangle must always have a ratio of side lengths that allow it to connect fully.

Answer:

x = 0.5

x-0.5=0

10x - 5 = 0

2x - 1 = 0

y=1/10

y - 1/10 = 0

10y - 1 = 0

Given: In Δ ABC and ΔAEC,

AB=BC and AD=CD

i) In ΔADB and CBD, we have

AD = DC        [given]

AB=BC           [given]

DB= DB           [given]

⇒ ΔADB ≅ΔCDB   [By SSS congruence rule]

⇒ ∠ADB ≅∠CDB       ...(i)           [Corresponding parts of congruent triangles are congruent]

Since AC is a straight line,

∠ADB+∠CDB = 180°   [Linear pair]

⇒∠ADB+∠ADB=180°   [from (i)]

⇒2 ∠ADB=180°  

⇒∠ADB=90°  =∠CDB

Also ∠ADB+∠ADE=180°   [Linear pair]

⇒∠ADE=180°-∠ADB  = 180°-90°

⇒∠ADE=90°, i.e. ∠ADE is a right triangle.

Similarly, ∠CDB+∠CDE=180°

⇒∠CDE=90°

ii) Now, in ΔADE and CDE

AD= CD   [given]

ED=ED   [Common]

∠ADE= ∠CDE = 90°

⇒ΔADE ≅ CDE   [By SAS congruence rule ]

⇒AE=EC   [Corresponding parts of congruent triangles are congruent]

Hence proved.

This relationship between AT-1 and A-I be used to determine information about matrix X by option (A) and (C).

(A) Since the two matrices are equal, the nonzero vector x must be a constant multiple of the nonzero vector v and (C) Since the two matrices are inverses, if either (AT-x=0 or (A-AI)v=0 has at least one nontrivial solution, then all of the statements of the Invertible Matrix Theorem are true for both matrices.

Therefore, if A is an eigenvalue of A, then λ must be an eigenvalue of AT, and vice versa. This can be seen by comparing the equation (A-λI)x=0 with the equation (AT-λI)v=0. If x is an eigenvector of A with eigenvalue λ, then it follows that v=x is an eigenvector of AT with eigenvalue λ. And if v is an eigenvector of AT with eigenvalue λ, then it follows that x=v is an eigenvector of A with eigenvalue λ.

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Answer:

13

Step-by-step explanation:

w^2 = -2^2 = 4

-v = -1*-8 = 8

Put it together: w^2-v+1 --> 4+8+1 = 13

I hope this can help you out some

Data set (ii) because it has two entries that are far from the mean. the deviations from the mean are smaller,

The sample standard deviation measures the dispersion or spread of data points in a data set. To determine which data set has the greatest sample standard deviation, we need to consider the distribution of values relative to the mean.

In data set (ii), which has two entries that are far from the mean, the presence of these outliers can significantly increase the sample standard deviation. Outliers are data points that deviate significantly from the majority of the data, and their inclusion in a data set can inflate the standard deviation.

This is because the standard deviation calculates the average distance between each data point and the mean, and outliers contribute to larger distances.

Data set (i), on the other hand, having more entries that are close to the mean, suggests a more concentrated or clustered distribution of values.

When data points are closer to the mean, the deviations from the mean are smaller, resulting in a smaller standard deviation compared to a data set with outliers.

Data set (iii), with more entries that are farther away from the mean, may also have a higher sample standard deviation. However, without specific information about the magnitude of these deviations and the overall distribution of values,

we cannot definitively conclude that data set (iii) has the greatest standard deviation. Therefore, based on the information provided, the data set (ii) with two entries that are far from the mean is likely to have the greatest sample standard deviation.

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The area of triangle OPQ is 44 square units.

How to find the area of tringle?

There are different ways to find the area of a triangle, depending on the information given. Here are a few common methods:

There are different methods to find the area of a triangle, but one common method is to use the coordinates of its vertices and the distance formula. The distance formula is

d = √((x2-x1)^2 + (y2-y1)^2)

We can use the distance formula to find the lengths of the sides of the triangle OPQ, which are:

OP = √((8-3)^2 + (3-4)^2) = √((5)^2 + (-1)^2) = √(25+1) = √26

OQ = √((4-3)^2 + (8-4)^2) = √((1)^2 + (4)^2) = √(1+16) = √17

PQ = √((4-8)^2 + (8-3)^2) = √((-4)^2 + (5)^2) = √(16+25) = √41

Once we have the lengths of the sides of the triangle, we can use the Heron's formula to find its area:

s = (OP + OQ + PQ)/2

Area = √(s(s-OP)(s-OQ)(s-PQ))

s = (√26 + √17 + √41)/2 = (√44)/2 = 4√11

Area = √(4√11(4√11-√26)(4√11-√17)(4√11-√41))

Area = √(4√11 * √(44-26) * √(44-17) * √(44-41))

Area = √(4√11 * √18 * √27 * √3)

Area = √(4√11 * 3√2 * 3√3 * √3)

Area = 4*11 = 44 square units

Hence, the area of triangle OPQ is 44 square units.

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Answer:

bhi

Step-by-step explanation:

hf

Answer:

ok

Step-by-step explanation:

The rate of change of y with respect to x is given by dy/dx = xy - (3/2)x²y.

To find the rate of change of y with respect to x, we need to differentiate the given equation. The rate of change can be determined by taking the derivative of both sides of the equation with respect to x.

First, let's differentiate each term separately using the rules of differentiation.

Differentiating x²y with respect to x gives us 2xy using the product rule.

To differentiate 5, we know that a constant has a derivative of 0.

Differentiating 2ln(y) with respect to x requires the chain rule. The derivative of ln(y) with respect to y is 1/y, and then we multiply by dy/dx. So, the derivative of 2ln(y) is 2/y * dy/dx.

Differentiating x³ gives us 3x² using the power rule.

Now, we can rewrite the equation with its derivatives:

2xy - 2/y * dy/dx = 3x²

To solve for dy/dx, we can isolate it on one side of the equation. Rearranging the equation, we get:

2xy = 2/y * dy/dx + 3x²

To isolate dy/dx, we move the term 2/y * dy/dx to the other side:

2xy - 2/y * dy/dx = 3x²

2xy = 2/y * dy/dx + 3x²

2/y * dy/dx = 2xy - 3x²

Now, we can solve for dy/dx by multiplying both sides by y/2:

dy/dx = (2xy - 3x²) * (y/2)

Simplifying further, we have:

dy/dx = xy - (3/2)x²y

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Answer:

5/4 and then 5/3

Step-by-step explanation:

The measures of central tendency for the given data set are:

- Mean: 59.85

- Median: 61.5

- Mode: None

To determine the three measures of central tendency for the given data set, we can calculate the mean, median, and mode.

a) Mean:

The mean, also known as the average, is calculated by summing up all the values in the data set and dividing it by the total number of values. In this case, we add up all the final grades and divide by the total number of grades:

92 + 48 + 59 + 62 + 66 + 98 + 70 + 70 + 55 + 63 + 70 + 97 + 61 + 53 + 56 + 64 + 46 + 69 + 58 + 64 = 1197

The total number of grades is 20.

Mean = 1197 / 20 = 59.85

Therefore, the mean of the final grades is approximately 59.85.

b) Median:

The median is the middle value in a sorted list of data. To find the median, we first need to sort the grades in ascending order:

2, 46, 48, 53, 55, 56, 58, 59, 61, 62, 63, 64, 64, 66, 69, 70, 70, 92, 97, 98

Since the total number of grades is even (20), we take the average of the two middle values:

Median = (61 + 62) / 2 = 61.5

Therefore, the median of the final grades is 61.5.

c) Mode:

The mode is the value that appears most frequently in the data set. In this case, there is no value that appears more than once. Therefore, there is no mode for the final grades.

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Answer:

88 i think so

Step-by-step explanation:

Answer:

is there a graph for this

Step-by-step explanation:

i need a grapg or to know what they wanted to know

Answer: 0.95k + 3.15

Step-by-step explanation:

0.95k is because each of k kilometers costs $0.95.  + 3.15 is because it costs 3.15 as a flat rate regardless of distance

Hope it helps <3

Answer:

.95k+3.15

Step-by-step explanation:

To write an expression you need a variable (k). I look at the directions and I see that the length of the trip is 'k' kilometers. So I pay the flat fee of 3.15 ONE TIME. Then I pay $0.95 for every kilometer I go, so the expression is

->   .95k+3.15