Work out the area of the tapezium ABDE.​

Answer:

1)  x=16

2) x=15

3) x=10

Step-by-step explanation:

1)  Since the triangles are similar and the ratio of the sides is 1 : 2, 1/2=(3x-4)/(10x-72). Cross multiplying, we get 6x-8=10x-72.

10x-72=6x-8 |+72

10x=6x+64 |-6x

4x=64  |/4

x=16

2) Angles HGJ and KLJ are corresponding (they are equal angles).

So, 5x-2=9x-62.

5x-2=9x-62  |+62

5x+60=9x  |-5x

60=4x |/4

x=15

3) If KM is a perpendicular bisector, KJ=KL.

So, 4x+9=11x-61.

4x+9=11x-61 |-4x

9=7x-61   |+61

70=7x  |/7

x=10

Integers have a greater and more suitable range to be closed for subtraction than whole numbers.

According to the closure property of subtraction, the difference between two integers will always be an integer.

An integer is a number that ranges from minus infinity and infinity and is not a fraction.

Whereas all positive valued integers including 0 are whole numbers.

Now if we subtract a larger whole number from a smaller whole number, then the difference will obviously be negative. Hence, the result will be an integer and not a whole number.

example= 25 - 30

= -5

Here both 25 and 30 are whole numbers but -5 is not. But all three are considered integers.

Hence, subtraction is closed under integers and not whole numbers.

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The equation of a line that passes through [tex](-1,4)[/tex] and is parallel to the y-axis is [tex]x=-1[/tex]

The equation of the line passes through the point is [tex](-1,4)[/tex]

The line is parallel to the y-axis which means it cuts the x-axis at the point [tex](-1,0)[/tex]

The equation of the line parallel to the y-axis is [tex]x=-1[/tex]

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Amy's measurement of the salt's mass is not accurate because it is not close to the actual value. Amy's measurement of the salt's mass is precise because the individual measurements are similar.

In Mathematics, measurement can be defined as an act or process through which the size, weight, magnitude, quantity, volume (capacity), dimensions, or distance traveled by a physical object or body is taken, especially for the purpose of an experiment.

In Science, precision is a quality which is independent of accuracy because it only describes how close together are numerical values that are obtained in a series of measurements.

In conclusion, accuracy is a quality which measures how close a measurement is to the actual value.

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Complete Question:

Amy forgot to subtract the mass of the empty weighing dish from her measurements, and she reported the mass of the salt as 5.608 grams. Amy's measurement of the salt's mass (1) ______ accurate because (2) ______ . Amy's measurement of the salt's mass (3)_____ precise because (4) _______ .

1. is

is not

2. it is not close to the actual value

she used five different balances

the individual measurements are similar

3. is

is not

4. it is not close to the actual value

she used five different balances

the individual measurements are similar

On a test with a range of 110–410, these students received a mean score of 370 and a standard deviation of 50. What range would roughly 95% of the students' scores fall into, presuming a mound-shaped and symmetric distribution.

Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye color, and vehicle type.

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling. Categorical and numeric variables are the two basic types of variables that can be categorized.

The maximum height of the projectile will be 226 feet that is, as per question, the option c.

A quadratic equation , y = ax²+bx+c  (equation 1)

given, axis of symmetry is

x = [tex]\frac{b}{2a}[/tex]

As per the question:

The path of the projectile is modeled using the equation :

h(t) = -16t²+48t+190  (equation 2)

h(t) = height after t time.

comparing equation 1 and equation 2, we get

a = -16 and b = 48

further, t = [tex]\frac{48}{2(-16)}[/tex]

= [tex]\frac{48}{32}[/tex]

= 1.5sec

Substituting the found value in equation 2, we get

h(1.5) = -16(1.5)²+48(1.5)+190

h(1.5) = -36+72+190

h(1.5) = 226ft.

Thus, the maximum height of the projectile at 1.5 sec is, 226 feet.

Note that the full question is:

A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. The path of the projectile is modeled using the equation h(t) = –16t2 + 48t + 190.

What is the maximum height of the projectile?

A. 82 feet

B. 190 feet

C. 226 feet

D. 250 feet

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The value of x that makes the expressions equivalent is 8

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

4(x-5)= 32-20

Distribute the 4

4x-20=12

4x= 12+20 = 32

x= 32/4 = 8

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The relation that is able to model the decay is given as N = 690e^-0.04r. The quarterly rate of change is 0.21%.

We know that the term radioactivity has to do with the fact that the object is able to undergo the process of a spontaneous disintegration. The implication of this is that the element is going to be gradually be transformed into a different element and this is going to occur at a given rate which we have called the decay constant for the reaction.

We know that element X is a radioactive isotope such that its mass decreases by 4% every year then an experiment starts out with 690 grams of Element X.

It follows that;

Initial amount of X No = 690 g

Decay rate of X (r) = 0.04

Time taken for decay = t

Amount of X at time t = N

The model now becomes;

N = 690e^-0.04r

The  quarterly rate of change is obtained from;

A(t) = (1- 0.04)Ao

= 0.96 Ao

0.96Ao = Ao(1 - r)^30

0.94 = (1 - r)^30

30√0.94  = (1 - r)

r = -0.0021 or -0.21%

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There is no intersection and no solution to the system since the region above the line y=2x+2/3 and the region below the line y=2x+1/3 are the solutions to the inequalities y>2x+2/3 and y<2x+1/3, respectively.

In the given question, we have to find the solution of the system Y>2x+2/3 and y<2x+1/3 change.

We firstly draw the two lines y=2x+2/3, and y=2x+1/3.

They are parallel and the line y=2x+2/3 is located over the line y=2x+1/3.

There is no intersection and no solution to the system since the region above the line y=2x+2/3 and the region below the line y=2x+1/3 are the solutions to the inequalities y>2x+2/3 and y<2x+1/3, respectively.

The solution of y2x+2/3 is the region below the line y=2x+2/3, and the solution of y>2x +1/3 is the region above the line y=2x+1/3 when the inequality sign of both inequalities is reversed. This implies that the area between the two lines is where the system's solution lies.

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The right question is:

How will the solution of the system Y>2x+2/3 and y<2x+1/3 change? If the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?

Answer:$3.51

Step-by-step explanation:

$17.53 x 20% = 350.6

350.6/100 = 3.506

3.506 = $3.51

Answer:

This equation does not have the same solution as the original equation.

In conclusion, equations 1 and 2 have the same solution as the original equation (2.3p – 10.1 = 6.5p – 4 – 0.01p). Equations 3, 4, and 5 do not have the same solution.

Step-by-step explanation:

2.3p – 10.1 = 6.4p – 4

Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:

-6.4p + 2.3p = -4 + 10.1

Combining like terms, we have:

-4.1p = 6.1

Dividing both sides by -4.1, we get:

p = -1.49

This equation has the same solution as the original equation.

2.3p – 10.1 = 6.49p – 4

Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:

-6.49p + 2.3p = -4 + 10.1

Combining like terms, we have:

-4.19p = 6.1

Dividing both sides by -4.19, we get:

p = -1.46

This equation has the same solution as the original equation.

230p – 1010 = 650p – 400 – p

This equation does not have the same solution as the original equation.

23p – 101 = 65p – 40 – p

This equation does not have the same solution as the original equation.

2.3p – 14.1 = 6.4p – 4

Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:

-6.4p + 2.3p = -4 + 14.1

Combining like terms, we have:

-4.1p = 10.1

Dividing both sides by -4.1, we get:

p = -2.47

A raw score is the actual number of correct answers a person gets on a test, without any adjustment for factors such as difficulty or time. For example, if a student takes a test with 10 questions and answers 8 correctly, their raw score would be 8 out of 10.

A raw score is the actual number of correct answers a person gets on a test, without any adjustment for factors such as difficulty or time. This means that the raw score is not adjusted or changed in any way.

For example, if a student takes a test with 10 questions and answers 8 correctly, their raw score would be 8 out of 10. This means that the student answered 8 out of the 10 questions correctly, without any adjustment for difficulty or time.

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Answer:

MP = 12 cm

Step-by-step explanation:

4cm : 6cm

8cm : x

8 * [tex]\frac{6}{4}[/tex] = 12 cm

MP = 12 cm

Answer:

The answer is $87.5

Step-by-step explanation:

350 × 25 ÷ 100

8750/100 = 87.5

Thus, Mr. Wright deposit $87.5

The equation of the linear function is y = 8x - 5.

What is a linear function?

Slope formula:

m = (y₂ - y₁) /  (x₂ - x₁)

Taking first two points from the given table

m = (3 + 5) / 1 - 0

m = 8

slope m = 8

Use one slope and one point formula to find the linear equation

y - y₁ = m (x - x₁)

y + 5 = 8 (x - 0)

     y = 8x - 5

Hence, the equation of the linear function is y = 8x - 5.

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(a) There are 10 vertical rise per step.

(b) There are 58 steps needed to climb from road level to the 2nd floor.

What is angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

(a) First to find the vertical rise per step.

x = 13 x tan(37)

x = 9.80

x ≈ 10

Hence, there are 10 vertical rise per step.

(b) Now to find number of steps needed to climb from road level to the 2nd floor.

The total elevation = 24 + 24 = 48 feet

Vertical rise of each step = 10

To convert 48 feet into inches

⇒  48 x 12 = 576 inches

So, the number of steps = 576 / 10 = 57.6 ≈ 58

Hence, there are 58 steps needed to climb from road level to the 2nd floor.

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Answer:

$10.79

Step-by-step explanation:

1) Make an equation

40x + 48.67 = 480.17

where x is hourly pay

2) Solve

40x + 48.67 = 480.17

40x + 48.67 - 48.67 = 480.17 - 48.67

40x = 431.50

40x / 40 = 431.50 / 40

x = 10.79

Justification for the last two steps of the proof is

3. Reflexive Property of (Congruence) ≅

4. SSS (Side to Side to Side Congruence rule)

What is SSS congruence postulate ?

A type of triangle congruence rule called Side-Side-Side (SSS) asserts that two triangles are congruent if their three sides are equal to their respective three sides of another triangle. When the dimensions of the matching sides and angles of two or more triangles match, the triangles are said to be congruent.

3. Any geometric figure compared to itself is congruent to itself so this is why:

AC ≅ CA

∠B ≅  ∠B

4. Since we have a parallelogram, therefore we can say:

BC ≅ DA

BA ≅ DC

CA ≅ AC

Both triangles ABC and CDA satisfy the side to side to side congruence, since their 3 sides are congruent.

So, It's D.

P.S.

Notice that the angle measure information is not included in the data above that's why we cannot say it is SAS congruence.

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The equation y' = x + y + 1  is not seperable. Therefore the statement is false.

In mathematics, an ordinary differential equation (also known as an ODE) is an equation made up of one or more functions of a single independent variable and its derivatives. A function having one or more derivatives is a component of a differential equation.

Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.

If you can express a differential equation as y′=f(x)g(y), where f(x) is only a function of x and g(y) is only a function of y, then the problem is separable. Here, it is not the situation.

But we are not limited to solving separable differential equations. We frequently use integrating factors to solve linear first-order differential equations, such as this one. Using the product rule, multiply your differential equation by an integrating factor—in this example, e—and you get (eyy)′=eyy+eyy′=eyx,

which you may integrate to get your differential equation's solution. Finding integrating factors for generic linear first-order differential equations of the type y′+p(x)y=q may be done in a general way (x).

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The we should use ANOVA instead of several t-tests to evaluate the differences in the mean of three or more groups.

A t- test is a measurable test that is utilized to look at the method for two gatherings. It is many times utilized in speculation testing to decide if a cycle or treatment really meaningfully affects the number of inhabitants in interest, or whether two gatherings are not quite the same as each other.

The ANOVA test permits an examination of multiple gatherings simultaneously to decide if a relationship exists between them.

We ought to utilize ANOVA rather than a few t-tests to assess the distinctions in the mean of at least three gatherings on the grounds that without fail, we direct a t-test (between two gatherings) there is some opportunity that a Kind I blunder is being made while doing the test.

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Answer: No

Step-by-step explanation:

Graph: You can use the vertical line test to determine if it is a function. Draw a vertical line (going up and down) on the graph. If it only intersects one

point, then it is a function. If it crosses two points, it is not a function.

Chart: If the x repeats and the y does not repeat, it is not a function. y can repeat as much as it wants, as long as the x does not.

Lines: If one x connects to multiple y, it is not a function. If one y connects to multiple x, it is a function.

Coordinates: Same as the chart

Answer:

(-2^6) is 64, which is positive.

Step-by-step explanation:

To write -2^6 as repeated multiplication, we can write it as (-2)(-2)(-2)(-2)(-2)*(-2). To evaluate this expression, we can compute it as follows:

(-2)(-2)(-2)(-2)(-2)(-2)

= ((-2)(-2)(-2)(-2)(-2))(-2)

= ((((-2)(-2)(-2)(-2))(-2))(-2)

= (((((-2)(-2)(-2))(-2))(-2))(-2)

= (((((-2)(-2))(-2))(-2))(-2))(-2)

= (((((-2)(-2))(-2))(-2))(-2))(-2)

= (((-2)(-2)(-2))(-2))(-2)(-2)

= (((-2)(-2)(-2))(-2))(-2)(-2)

= ((-2)(-2))(-2)(-2)(-2)(-2)

= (-2)(-2)(-2)(-2)(-2)(-2)

= 64

Therefore, the result of (-2^6) is 64, which is positive.

The domain of the function d(t) describing the Haru's journey to his friend is

In the graph, the input values is the time in hours, t while the output value is distance covered, d in kilometers

The domain is controlled by the input values. considering the time used for the journey as shown in the graph. The journey started from point 0 to the end point 2.1

The maximum time is at 2.1 hours. For the minimum, this is when the journey started which is 0

The domain starts from 0, with 0 not inclusive to 2.1 with 2.1 included

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Answer:

Erin will pay a total of $21.196 in shipping and handling fees.

Step-by-step explanation:

To calculate the shipping and handling fees, we first need to find 20% of the price of the trampoline. Since 20% is the same as 0.20, we can multiply the price of the trampoline by 0.20 to find the shipping and handling fees. If the trampoline costs $105.98, then the shipping and handling fees would be $105.98 * 0.20 = $<<105.98*0.20=21.196>>21.196.

The difference between is 7-4 = 3

What are volume and area?

The area is the volume a flat, two-dimensional item occupies in a plane. The space occupied by a three-dimensional object is referred to as its volume. Area is measured in square units. Volume is measured in cubic units.

The volume formula is what.

The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."

Given that :

Cube 1 has volume = 343 cubic feet

Volume = [tex]a^{3}[/tex]

[tex]a^{3}[/tex] = 343

a = 7

Cube 2 has volume = 64 cubic feet

Volume = [tex]a^{3}[/tex]

[tex]a^{3}[/tex] = 64

a = 4

Hence the difference between is 7-4 = 3

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An apple cost $1.2 and the orange cost $1.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, she bought 5 apples and 4 oranges for $10. This will be 5a + 4o = 10

The friend bought 5 apples and 5 oranges for $11. This will be 5a + 5o = 11

Equate the equations

5a + 4o = 10

5a + 5o = 11

Subtract

o = 1

The value of orange is $1

The value of apple will be:

5a + 4o = 10

5a + 4(1) = 10

5a + 4 = 10

Collect like terms

5a = 10 - 4

5a = 6

Divide

a = 6/5

a = 1.2

Apple cost $1.2

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Answer:

29 years old

Step-by-step explanation:

Answer: 29

Step-by-step explanation: 29 but we want to round that up to 30 because 29 is odd but due to science and polls nobody likes the number 30 so we go back to 29 but it’s uneven so we go to 28 to make it even but we also don’t like that number so we go back to 29 and that how we get it.