what is the measure of angle x

Answer:

3√2

Step-by-step explanation:

If you draw the diagonal, you have a 45°45°90° triangle.

The two legs are 3, so the hypotenuse is 3√2

Answer:  D

Step-by-step explanation:

To have a proportional relationship, the value of y divide by x has to have the same constant value and if you were to graph it, it has to go through the origin.

A is not proportional because it is not going through the origin.

B is also not proportional because it is also not going through the origin.

Now to find out if C is proportional divide the y value by x so see if they all have a constant change.

8/2 =4

16/4 = 4

24/8 = 3

32/ 12 = 2.6  

This is also not proportional .

D. 3/2 = 1.5

   6/4 = 1.5

 12/ 8 = 1.5  

 18/12 = 1.5  

This represents a proportional relationship  because they all have a constant change

The proportional relationship between x and y will be given by option D.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Let's check all the options:

Option A because the line has intercept.

Option B because the line is zero.

Option C:

The slope is given as,

Slope = (16 - 8) / (4 - 2) = 4

Slope = (24 - 16) / (8 - 4) = 2

Slope = (32 - 24) / (12 - 8) = 2

Option D:

The slope is given as,

Slope = (6 - 3) / (4 - 2) = 3/2

Slope = (12 - 6) / (8 - 4) = 3/2

Slope = (18 - 12) / (12 - 8) = 3/2

The proportional relationship between x and y will be given by option D.

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Answer:

2 bicycles

Step-by-step explanation:

as there were 5 bicycles and tricycles

now,

total no.of wheels = 16

2x + 3(6 - x) = 16

2x + 18 - 3x= 16

2 - x = 0

2 = x

therefore, there are 2 bicycles.

Answer:81

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

angles in a triangle add up to 180 so both of the other angles added equal to 110. 180-110=70

The inequalities which satisfy the number line shown is x>2 and x>=2.

We are given that;

The number line showing inequality

Now,

x>2 satisfies the equation by the given number line

x>=2 satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

Therefore, by the number line the answer will be x>2 and x>=2 .

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

---------------------------------

Given is the special right triangle.

It is a 45° isosceles right triangle. It has a property that the hypotenuse is √2 times the leg.

We have a hypotenuse of 28 units, so the leg is:

Answer:

14√2

Step-by-step explanation:

Here we need to find out the value of "x" in the given right angled triangle, here we can make use of trigonometric ratios to find out the value of x .

In a right angled triangle, sine is defined as the ratio of perpendicular and hypotenuse . With respect to angle 45° , x is the perpendicular and 28 is hypotenuse (side opposite to 90° ) .

So we have;

sin45° = x/28

1/√2 = x/28

x = 28*1/√2

x = 14 * (√2)² / √2

x = 14√2

Hence the value of x is 14√2 .

Answer:

Step-by-step explanation:

15% of 20 is 3

Therefore, the rate of change, in cm per minute, of the height when the height is 6 cm is approximately -6 cm/min.

Given,The width of the box = 10 cm Length of the box = 17 cmThe volume of the box = 527 cubic cm/minWe need to find the rate of change, in cm per minute, of the height when the height is 6 cm.We know that the volume of the box is given as:V = l × w × h where, l, w and h are length, width, and height of the box respectively.It is given that the width and length are being held constant.

Therefore, we can write the volume of the box as

:V = constant × h Differentiating both sides with respect to time t, we get:dV/dt = constant × dh/dtNow, it is given that the volume of the box is decreasing at a rate of 527 cubic cm per minute.

Therefore, dV/dt = -527.Substituting the given values in the above equation, we get:

527 = constant × dh/dt

We need to find dh/dt when h = 6 cm.To find constant, we can use the given values of length, width and height.Substituting these values in the formula for the volume of the box, we get:

V = l × w × hV = 17 × 10 × hV = 170h

We know that the volume of the box is given as:V = constant × hSubstituting the value of V and h, we get:

527 = constant × 6 cm

constant = 87.83 cm/minSubstituting the values of constant and h in the equation, we get

-527 = 87.83 × dh/dtdh/dt = -6.0029 ≈ -6 cm/min

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Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

The slope of the tangent line is:

a = (df(x1)/dx)

The slope of the normal one is:

a' = -1/(df(x1)/dx)

For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.

So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:

df(x1)/dx

And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:

a*(df(x1)/dx) = -1

a = -1/(df(x1)/dx)

Where df/dx reffers to the derivative of f(x).

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The value of y when (x = 12) is 84 and this can be determined by forming the linear equation with the help of the given data.

Given :

The following steps can be used to determine the value of y when x = 12:

Step 1 - Given that y varies directly as x, that means:

\(\rm y \; \alpha \; x\)

Step 2 - The above expression becomes:

y = kx   ----- (1)

Step 3 - Given that y = 35 when x = 5, that implies:

35 = 5k

k = 7

Step 4 - Put the value of k in equation (1).

y = 7x

Step 5 - Now, the value of y when x = 12 is:

y = 7(12)

y = 84

So, the value of y when (x = 12) is 84.

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Answer:20%

Step-by-step explanation:

Answer: 20%

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

An easy way to find the answer is when you see of that basically means to times(X) so that means 2/3 X 90 = 60

The value of the expression x² + 10x, when x = 2 is 24.

In the expression x² + 10x, x represents a variable, which is a placeholder for a value that can change. We are given that x = 2, which means we substitute 2 for x in the expression:

x² + 10x = 2² + 10(2)

Here, 2² means 2 raised to the power of 2, which is 2 multiplied by itself: 2² = 2 x 2 = 4.

10(2) means 10 multiplied by 2, which is 20.

So we can substitute these values in the expression:

x² + 10x = 2² + 10(2)

= 4 + 20

= 24

Therefore, when x is equal to 2, the value of the expression x² + 10x is 24.

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The complete question:

Evaluate the expression x² + 10x, when x = 2.

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

d=-6.5

Step-by-step explanation:

2d+13=0

2d=-13

d= -13/2

d=-6.5

Answer:

D

Step-by-step explanation:

-4(-2)^2 -3(-2) +2

-4(4) +6+2

-16+8

-8

Answer:

D

Step-by-step explanation:

(-2)^2 = 4

(-4)4 = -16

-3(-2) = 6

-16+6 = -10

-10+2 = -8

Answer:

x = 45

Step-by-step explanation:

Note that:

The sum of the interior angles of a quadrilateral is 360°.

Angle: ADC+BAD+ABC+BCD = 360°

Thus, Substitute  ∠ABC = 3x, ∠BAD = (2x-5) , ∠ ADC = (x+15), ∠ BCD = 80 turn into ADC+BAD+ABC+BCD = 360° :

Also known as :

(x+15) +(2x-5) + 3x+80=360

Solving for x

Add the numbers

x + 90+2x+3x=360

Combine like terms

6x + 90=360

subtract 90 from both sides

6x = 270

x = 45

Hence the value of x = 45

Kavinsky

Answer:

C. 45

Step-by-step explanation:

1) Sum of the interior angles of any shape:

(n - 2) x 180, where n is the number of vertices of a shape. In this case, we have 4 vertices.

= (4 - 2) x 180

= 2 x 180

= 360°

2) Add all the given values equating to 360.

2x - 5 + 3x + 80 + x + 15 = 360

6x + 90 = 360

6x = 360 - 90

6x = 270

x = 270/6

x = 45

The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Here is the table of the number of baseball cards for 0 to 4 packages and their corresponding ordered pairs:

Number of Packages, x | Number of Cards, y | Ordered Pair (x, y)

0 | 0 | (0, 0)

1 | 10 | (1, 10)

2 | 20 | (2, 20)

3 | 30 | (3, 30)

4 |40 | (4, 40)

To plot these points in the coordinate plane, we can use the horizontal axis for the number of packages (x) and the vertical axis for the number of cards (y), with each unit representing 1 package or 10 cards. Here is the plot:

|

50 |

45 |

40 ● (4, 40)

35 |

30 ● (3, 30)

25 |

20 ●(2, 20)

15 |

10 ● (1, 10)

5 |

0 ● (0, 0)

--------------

0 1 2 3 4

As we can see from the plot and the table, the relationship between the coordinates of the ordered pairs is linear, with the number of cards increasing by 10 for each additional package.

Specifically, the relationship can be described by the equation y = 10x, where y is the number of cards and x is the number of packages. This means that the slope of the line connecting any two points is always 10, and the y-intercept is 0.

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Answer:

-x^4, and (2√x)/x

Step-by-step explanation:

4. \(- \sqrt{ x^{8} } = - \sqrt{x^{4} *x^{4} } = -x^{4}\)

x^8 = x*x*x*x*x*x*x*x = (x*x*x*x)(x*x*x*x) = (x^4)(x^4)

5.

\(\sqrt{\frac{4}{x} } = \frac{\sqrt{4} }{\sqrt{x} } = \frac{2}{\sqrt{x} } \\\\\\\frac{2}{\sqrt{x} } * \frac{\sqrt{x} }{\sqrt{x} } = \frac{2\sqrt{x} }{x}\)

Answer:

Kindly check explanation

Step-by-step explanation:

33% is approximately 1/3 of a whole ; that is 1/3 of 100%

Hence, 59 / 3 = approximately 19

Approximately 20

Another way is to take 59 as 60, nearest 10, then divide by 3 to obtain ; (60 /3) = 20

To obtain 25% of 98.50

25% = 1/4th

Take value as 98 and divide by 4

Take value as 100 and divide by 4

2% of 150 people

2% = 1/50

Quick division of 150 into 50 places to obtain the approximate value.

To obtain the exact solution for the questions above :

Multiply 33% by 59

0.33 * 59 = 19.47

Multiply 25% by $98.50

0.25 * $98.50

$24.625

Multiply 2% by 150

0.02 * 150

= 3 people

Gone Fishing Four friends go fishing one day and bring home a total of 11 fish. If each person caught at least 1 fish, then C) One person caught fewer that 3 fish.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

It is given that Gone Fishing Four friends go fishing one day and bring home a total of 11 fish. If each person caught at least 1 fish, then we need to find the following must be true.

Therefore, the statement that is true C) One person caught fewer that 3 fish.

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The first blank is BAL and FGH

The second blank is AL

The third blank is CE and KI

The fourth and final blank is GH

According to the statement

we have given a diagram in which there are some angles and from these angles we have to find that the

Which opposite angles are congruent

The opposite side of AB

With GF angle which angle are congruent

Two angles are which are opposite to each other.

So, from a diagram it is clear that The angles which are congruent with each other is BAL and FGH. Because there positions are perfectly opposite and same  to each other.

And The opposite side of AB is AL because it is present at opposite position to each other.

And with GF angle GH are congruent angles.

So, The first blank is BAL and FGH

The second blank is AL

The third blank is CE and KI

The fourth and final blank is GH

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DISCLAIMER: This question is incomplete.Please see the complete question below.
QUESTION:
Select the correct answer from each drop-down menu.

For the figure shown, point D is a midpoint of , and point J is a midpoint in figure.

Since reflecting the points C, B, A, L, and K across line maps these points onto E, F, G, H, and I, respectively, the opposite angles

are congruent. Since reflecting the points L, K, J, I, and H across line maps these points onto B, C, D, E, and F, respectively, the opposite sides are congruent.

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