85m+16m+43m=85m+43m+16m is an example of what mathematical property?

Answer: 1/2

Step-by-step explanation:

y=1/2x-3

Answer:

C, D

Step-by-step explanation:

We can solve this graphically and analytically.

Graphically, looking at the attached image below, if we graph the two inequalities and plot the points, you can find the points which are solutions by finding the points in the overlapping area.

This obviously excludes A as it only appears in \(y \geq x+2\)

C is included as y \(\geq x+2\) includes the point on the line.

D is obviously a solution.

B is however not a solution because is lies on the line \(y = \frac{-5x}{2} - 3\), which the inequality excludes.

Analytically, if we can find one of the two inequalities where it is not a solution, it is not a solution of the system.

A: (0, 0)

\(y \geq x+2\\0 \geq 0 + 2\\0 \geq 2\\false\)

A is not a solution

B: (-2, 2)

\(y \geq x+2\\2 \geq -2 + 2\\2\geq 0\\true\)

\(y > \frac{-5x}{2} -3\\2 > \frac{-5(-2)}{2} - 3\\2 > 5 - 3\\2 > 2\\false\)

B is not a solution

C: (0, 2)

\(y \geq x+2\\2 \geq 0 + 2\\2 \geq 2\\true\\\\y>\frac{-5x}{2}-3\\2 > -3\\true\)

C is a solution

D:

\(y \geq x + 2\\6 \geq -1 + 2\\6 \geq 1\\true\\\\y > \frac{-5x}{2} - 3\\6 > \frac{-5(-1)}{2} - 3\\6 > \frac{5}{2} - \frac{6}{2}\\6 > \frac{-1}{2}\\true\)

D is a solution

Answer:

(x + 5) and (x -1)

Step-by-step explanation:

Given

The attached graph

Required

The \(factors\) of the graph

The x \(values\) are where the \(curve\) \(touches\) the x-axis

The first is at:

\(x = -5\)

Add 5 to both sides

\(x +5= -5+5\)

\(x +5= 0\)

This implies that the first factor is: (x + 5)

The second is at:

\(x =1\)

Subtract 1 from both sides

\(x - 1 = 1 - 1\)

\(x - 1 = 0\)

This implies that the other factor is: (x - 1)

A. The null hypothesis H₀ and the alternative hypothesis H₁ are:

H₀: μ = 35 minutes       H₁: μ > 35 minutes

B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.

C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.

A Type II error occurs when the null hypothesis is false, but the test does not reject it.

In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.

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Answer:

its half of 8 so 8/2=4

Step-by-step explanation:

Answer:

4cm

Step-by-step explanation:

The diameter is double the radius of a circle.

Here, the diameter is 8cm so the radius will be half of it (8/2)=4.

Hope this helps you :)

Answer:

x = -9

Step-by-step explanation:

ANGLES IN A TRIANGLE ADD UP TO 180°

50° + 80° = 130°

180° - 130° = 50

x+59 = 50

x = -9

The angle 7 is the alternative interior angle to angle 2.

Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.

They are the angles that are on opposite sides of the transversal and inside the two parallel lines.

Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.

We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.

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Answer:

0.127

Step-by-step explanation:

The probability values for the questions posed are :

A.)

Number of students Taking a public speaking class majoring in business administration.

P(PS or BA) = 55/100 = 11/20

Therefore, the probability of PS or BA is 11/20

B.)

For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.

Hence, as inferred from P(A|B) ; probability of A given B.

C.)

P(PS|BA) = n(PSnBA) / n(BA)

n(PS) = 10+20 = 30

n(PSnBA) = 10

P(PS|BA) = 10/30 = 1/3

Therefore , the probability of PS|BA is 1/3.

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Answer:

Step-by-step explanation:

Use points on the graph:

Find the slope:

The y-intercept is known b = 7, so the equation is:

Slope

Equation

Answer:

Let s = smaller number

l = larger number

s + l = 31

2s = l + 11

2(31 - l) = l + 11

62 - 2l = l + 11

3l = 51, so l = 17 and s = 14.

The larger number is 17, and the smaller number is 14.

The  quotient of 302 ÷ (9.1 x \(10^4)\) in scientific notation is approximately 3.31868131868 x \(10^1\)

Dividing 302 by 9.1 gives:

302 ÷ 9.1 ≈ 33.1868131868

Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:

33.1868131868 ≈ 3.31868131868 x\(10^1\)

Therefore, the quotient of 302 ÷ (9.1 x \(10^4\)) in scientific notation is approximately 3.31868131868 x\(10^1\)

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In this case, we can identify two similar triangles like this:

Since VX is a bisector of ZC it cuts ZC into two equal-length segments, then ZY and YC have the same length and we can formulate the following expression:

ZY = YC

ZY = 18

Since we are dealing with similar triangles, we can formulate the following expressions for VYZ and ZYX:

By replacing 18 for ZY and 27 for XY, we get:

By multiplying both sides by 18, we can solve for 18, to get:

By adding the length of VY to the length of XY, we get:

VY + XY = 12 + 27 = 39

Adding VY to XY we should get VX, which is the diameter of the circle. Then VX = 39

Answer:

Listed below

Step-by-step explanation:

Looking at this problem, we can see that for each new dot, 3 lines are added. So, if we wanted to solve for the number of lines and dots for each box, we can use this equation if n = dots:

Inserting 4 into the equation as n:

So, if there are 4 dots, there will be 13 lines.

Solving for the 5 box:

So, if there are 5 dots, there will be 16 lines.

Solving for the 6 box:

So, if there are 6 dots, there will be 19 lines.

To solve for the number of lines with n dots, we use the equation listed above. (4 + [(n - 1) × 3] =?)  

To solve for the number of lines if there are 50 dots, we can use the same equation with 50 as n:

So, if there are 50 dots, there will be 151 lines.

To solve for the number of dots if there are 85 lines, we can simply count on from 19 with 6 dots.

Therefore, there are 85 lines in the pattern with 34 dots.

The zeros and the multiplicities are

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

f(x) = (x + 6)³(x - 11)²(x - 6)(x + 5)³

The power of each factor are the multiplicities

So, we have

Zero(s) of multiplicity one:

x - 6 = 0

Zero(s) of multiplicity two:

x - 11 = 0

Zero(s) of multiplicity three:

x + 6 = 0 and x + 5 = 0

When evaluated, we have

Zero(s) of multiplicity one:

x = 6

Zero(s) of multiplicity two:

x = 11

Zero(s) of multiplicity three:

x = -6 and x = -5

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Answer:

y = x + 3

Step-by-step explanation:

given line in slope/intercept form:

y = x -1/2

slope of the perpendicular line = 1

equation of the line

y - 2 = x + 1

y = x + 3

Answer:

y=-x+1

Step-by-step explanation:

since the line is perpendicular to 2y=2x-1, this means that its slope with be the opposite reciprocal of the line 2y=2x-1 's slope.

first, we should find the slope of the line 2y=2x-1:

2y=2x-1

y=x-1/2

therefore, the slope of 2y=2x-1 is 1.

the opposite reciprocal of 1 is -1.

so far, we have this:

y=-x+b

to find b (the y-intercept) we can plug the point (-1,2) into the equation we have so far and solve for b.

y=-x+b

2=-(-1)+b

2=1+b

b=1

so, the equation of the line that passes through (-1,2) and is perpendicular to 2y=2x-1 is:

y=-x+b

In a Right Triangle, the easiest way to solve the measure of the one side when two sides are given is by Pythagorean Theorem.

Where,

a = Opposite Side

b = Adjacent Side

c = Hypotenuse

Let's rotate the figure to better understand the problem,

Let's now find the value of x,

Thus, x = 10

Answer:

Gradient normal x gradient tangent = -1 is a mathematical expression that relates the normal and tangent vectors of a curve in three-dimensional space. The gradient of a scalar function is a vector that points in the direction of the greatest rate of increase of the function. The normal vector is perpendicular to the surface defined by the function, and the tangent vector is a vector that lies on the surface and points in the direction of the curve.

In mathematics, the cross product of two vectors is a vector that is orthogonal to both vectors, and the magnitude of the cross product is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between them. In this case, the normal and tangent vectors of a curve form an orthogonal basis, meaning that they are perpendicular to each other. The expression gradient normal x gradient tangent = -1 says that the magnitude of the cross product of the normal and tangent vectors is equal to -1. This means that the normal and tangent vectors form a right-handed coordinate system, where the cross product is negative because the normal vector points in the opposite direction to the positive z-axis.

The manager can find the volume of the container using the formula lwh. The employee correctly determines that the container can be filled with 3 layers of 21. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the volume of one bento box. The volume found by using the formula is equal to the volume of the total number​of bento boxes in the container.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = LWH

Where:

Part a.

Therefore, the manager can use the following formula;

Volume of container = LWH

Volume of container = 7/2 × 3/2 × 3/2

Volume of container = 63/8 cm³.

Part b.

For the number of bento boxes that can fill the container, we have:

Number of bento boxes = Volume of container/Volume of bento boxes

Number of bento boxes = 63/8/(1/2)³

Number of bento boxes = 63/8/1/8

Number of bento boxes = 63/8 × 8

Number of bento boxes = 63 bento boxes = 3 layers × 21.

Part d.

Volume of container = Volume of bento boxes

63/8 cm³ = 63 × 1/8 cm³

63/8 cm³ = 63/8 cm³ (equal).

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Answer:

7%

Step-by-step explanation: i took the test and got it right

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Answer:

44

Step-by-step explanation:

if 22 miles = 1/2

then, 22 times 2 = 44 miles

ANSWER= 44 miles

FE = 15 units as per the Pythagoras theorem.

∠D = 65°

A right-angled triangle is another situation in which the right angle is applied.

A triangle is referred to as a right-angled triangle if one of its three angles is 90 degrees.

A right-angled triangle's three interior angles all add up to 180 degrees, thus if one angle is always 90 degrees, the other two must also always add up to 90 degrees.

Now in the triangle given,

DF = 8, DE = 17

Using Pythagoras theorem, we can get FE.

FE² = DE² - DF²

FE ² = 289 - 64

FE² = 225

FE = 15

Now using the principles of angles in a right angle triangle:

∠D + ∠F + ∠E = 180°

∠D = 180 - 90 - 25

∠D = 65°

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Answer:

Step-by-step explanation:

She bought the tv for 80% of the original price. Therefore the original price is higher than $999. Now you can cancel options C and D because they are smaller than $999.

so the original price of the tv is 120% of $999 is $ 1198.80

Therefore the correct option is option B

Answer:

The answer is down below

Step-by-step explanation:

v-u=◇velocity

\( = 9 - 5\)

◇velocity =4ms‐¹

acceleration =◇velocity/time

\(a = \frac{4}{5} \)

\(a = 0.8m {s}^{ - 2} \)

Change in velocity:

\( \sf \:final \: velocity - initial \: velocity = change \: in \: velocity\)

\( \therefore \tt \delta \: v = 9 - 5 \\ \tt = 4m {s}^{ - 1} \)

To find acceleration:

\( \rm \: a = \frac{ \triangle \: v}{\triangle \: t} \)

\( \rm \: a = \frac{ 4}{5 - 0} = \frac{4}{5} = 0.8m {s}^{ - 1} \)

Answer:

True

Step-by-step explanation:

4*(-5)=-20

-20=-20

Answer:

4 * -5 = -20; true

Step-by-step explanation:

4 * -5 = -20

This is true because 4 * -5 is -20.