Which of the following combinations of side lengths will form a triangle with vertices X, Y, and Z?
A. XY = 19 mm, YZ = 11 mm, XZ = 29 mm
В. XY = 19 mm, YZ = 11 mm, XZ = 31 mm
C. XY = 19 mm, YZ = 10 mm, XZ = 30 mm
D. XY = 20 mm, YZ = 11 mm, XZ = 32 mm

Answer:

Number of students = 441 Students

Step-by-step explanation:

Given:

Percent of women = 40%

Percent of women = 35.5%

Total number of people = 1,800

Find:

Number of students

Computation:

Percent of student = 100% - 35.5% - 40%

Percent of student = 24.5%

Number of students = 1,800 x Percent of student

Number of students = 1,800 x 24.5%

Number of students = 441 Students

Answer:

Step-by-step explanation:

it would be "c" because the question asks for the number that makes the inequality true

4x≤ x+3

the graph in c is saying that every number that is 1 or less than 1 makes the inequality true. so lets take -7 as an example

4 x -7=-28

-28+3=-25

-25 is greater than -28 so the inequality is true. the reason why graph d doesnt work is because if we plug in 2 into the equation, then 4x =8 and x+3=5

5 is not greater than 8 so it doesnt work

Answer:

-2<=y<=-7

Step-by-step explanation:

Answer:

The answer is "0.45385".

Step-by-step explanation:

The time is taken to reach the coast \(= \frac{\sqrt{(2^2 + x^2)}}{4}\)

The  time is taken to reach Q after reaching the coast \(= \frac{\sqrt{(1 + (3-x)^2)}}{4}\)

Total time, \(T= \frac{\sqrt{(1 + (3-x)^2)}}{4}+ \frac{\sqrt{(1 + (3-x)^2)}}{4}\)

This has to be minimum,

\(\to \frac{dt}{dx} = 0\)

\(\to \frac{\sqrt{(2^2 + x^2)}}{2} + \frac{\sqrt{1 + (3-x)^2}}{3}\\\\ \frac{x}{4}\sqrt{(4+x^2)} + \frac{(x-3)}{(4\sqrt{(x^2-6x+10)}} = 0\\\\\frac{x^2}{16} \times (4+x^2) = \frac{(x-3)^2}{16 \times (x^2-6x+10)}\\\\x^2(4+x^2) = \frac{(x-3)^2}{(x^2-6x+10)}\\\\4x^2+x^4 = \frac{ x^2+9-6x}{(x^2-6x+10)}\\\\ 4x^2+x^4(x^2-6x+10) = x^2+9-6x\\\\4x^4-24x^3+40x^2+x^6-6x^5+10x^4= x^2+9-6x\\\\x^6-6x^5+ 14x^4-24x^3+39x^2+6x-9=0\\\\\)

x=0.45385

Answer: Angle ABD is 39°

Step-by-step explanation:

Angle CBA is 90° (given by "box" on the corner of the right triangle)

Angle CBD is given as 51°

Subtract:

90° - 51° = 39°

Answer:

C=25.13274 ft

Step-by-step explanation:

Circumference=2*pi*r

C=2*pi*4

C=25.13274 ft

Answer:

Option A is the right answer mate...

Answer:

  B.  A point

Step-by-step explanation:

You want a description of the intersection between a plane and a cone given that the plane is parallel to the base and passes through the vertex of the cone.

The vertex of a cone is a single point. If a plane passes through that, but does not intersect the base of the cone, it will not intersect anywhere else.

The intersection is one point.

__

Additional comment

Figure f in the attachment illustrates this case.

9514 1404 393

Answer:

  171° (angle) and 9° (supplement)

Step-by-step explanation:

If 'a' represents the measure of the angle then ...

  a = 19(180 -a) . . . . . the angle is 19 times its supplement

  20a = 19(180) . . . . add 19a

  a = 19(9) . . . . . . . . divide by 20

  a = 171 . . . degrees (the angle)

  180-a = 9 . . . degrees (the supplement)

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

The inequality shown on the number line is -3<p<2

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.

Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Based on the information, the inequality shown on the number line is -3<p<2

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Answer:

Step-by-step explanation:

You have all correct choices.

We can use the given values and work out the equation:

The function for this situation is:

Answer:

2(2)^t

Step-by-step explanation:

PLATO

Answer:

Point C will be at (3,1), Point B will be at (7,1) and Point A will be at (7,5)

Step-by-step explanation:

Answer:

\( \frac{(6x + 7)}{(2x)} - \frac{3}{ {x}^{2} } \\ = \frac{x(6x + 7) - 6}{2 {x}^{2} } \\ = \frac{ {6x}^{2} + 7x - 6}{2 {x}^{2} } \\ = 3 + \frac{7}{2x} - \frac{3}{ {x}^{2} } \)

Answer:

3

Step-by-step explanation:

The answer is three because u need to simply the fractions

Answer:

Step-by-step explanation:

This number line says that  we can take all values of x that are less than or equal to 2. That is, the solution is

                                  \(x\leq 2\)

NOTE: if the circle at 2 were not filled in then that would mean x<2 (2 would not be an accepted value of x)

Answer:

-7333/4400

Step-by-step explanation:

Given:

Sol:

Graph of the inverse of tan(x) is:

So the value is:

Answer:

Two signs

When adding positive numbers, count to the right.

When adding negative numbers, count to the left.

When subtracting positive numbers, count to the left.

When subtracting negative numbers, count to the right.

Step-by-step explanation:

Answer:

12.5%

Step-by-step explanation:

105 over 120 is the fraction that he got so you subtract 105 from 120 to get how much he missed. 120-105=15

He miscalculated by 15 cm out of the total of 120, 15/ 120

15/120=5/40=2.5/20 multiply the top and bottom by 5 to get the percentage out of 100. 2.5 times 5 =12.5, so he miscalculated by 12.5%

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer:

No

Step-by-step explanation:

10 is not less than 6, so 10 < r when r=6 is not true.

Answer:

0.9772 = 97.72% probability that the grade of a randomly selected students score is more than 60.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average grade for an exam is 74, and the standard deviation is 7.

This means that \(\mu = 74, \sigma = 7\)

What is the probability that the grade of a randomly selected students score is more than 60?

This is 1 subtracted by the pvalue of Z when X = 60. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{60 - 74}{7}\)

\(Z = -2\)

\(Z = -2\) has a pvalue of 0.0228

1 - 0.0228 = 0.9772

0.9772 = 97.72% probability that the grade of a randomly selected students score is more than 60.

The age of the person who entered the room is 19

The given parameters are:

Mean is calculated as:

Mean = Sum/Count

For the five people, we have

Sum/5 = 37

Multiply by 5

Sum = 185

For the five people, we have

Sum/6 = 34

Multiply by 6

Sum = 204

Let the last person be x

So, we have

x + 185 = 204

Subtract 185

x = 19

Hence, the age of the person who entered the room is 19

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Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.