A summary about graphs

Answer:

Addition:

7+8=15

8+7=15
Subtration:

15-8=7

15-7=8

Step-by-step explanation:

You just have to include all numbers and make an equation that involves all three digits

Answer:

28

Step-by-step explanation:

Smallest common multiple of 2, 4 and 7 -> 28

In the parallelogram ABCD the triangles that are similar to ΔAEX is -

Option 1: ΔCFX, Option 2: ΔADC, and Option 5: ΔCBA

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

The parallelogram ABCD is given.

AC is the diagonal of the parallelogram and EF is a line segment parallel to AB and CD in the parallelogram.

In ΔAEX and ΔADC -

m ∠AEX ≅ m ∠ADC, since they are corresponding angles.

m ∠A ≅ m ∠A, since they are reflexive angles.

So, ΔAEX ~ m ∠ADC, by AA similarity.

Similarly, in ΔAEX and ΔCFX -

m ∠EAX ≅ m ∠XCF, since they are alternate interior angles.

m ∠AXE ≅ m ∠CXF, since they are vertical angles.

So, ΔAEX ~ m ∠CFX, by AA similarity.

Now, in ΔAEX and ΔCBA -

Since, EF is parallel to AB then AEFB is also a parallelogram because ABCD is a parallelogram.

Then m ∠E ≅ m ∠B, since they are opposite angles of parallelogram AEFB.

m ∠EAX ≅ m ∠ACB, since they are alternate interior angles.

So, ΔAEX ~ m ∠CBA, by AA similarity.

Therefore, the similar triangles are ΔADC, ΔCFX, ΔCBA.

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Answer:

(e) It means that your grade is 2 standard deviations above the mean for this exam.

Step-by-step explanation:

Z-score describes the number of standard deviations away from the mean. In this case, a z-score of +2.0 would be 2 standard deviations above the mean.

The given length measurements are converted and given below.

Unit conversion is a process with multiple steps that involve multiplication or division by a numerical factor or, particularly a conversion factor.

Given is to convert the given measurements as -

a) 192 km

b) 15500 dam

c) 85000 m

d) 3360 hm

e) 860000 dm

We can write the measurements as -

a) 192 km            

192 Km = 192000 meters

b) 15500 dam

15500 dam = 15500 x 10 = 155000 meters

c) 85000 m

85000 m = (85000/1000) Km = 85 Kilometers

d) 3360 hm

3360 hm = 3360 x 100 = 336000 meters

e) 860000 dm

860000 dm = 860000 x 0.1 = 860000 x 1/10 = 86000 meter

Therefore, the given length measurements are converted and given above.

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40 pounds (lb) is equivalent to 18.14 kilograms (kg). To convert pounds to kilograms, you need to use the conversion factor of 0.45359237 kg per pound.

This means that you can multiply the number of pounds by this conversion factor to get the equivalent weight in kilograms.

The conversion from pounds to kilograms is important when it comes to international trade and travel, where weight measurements are typically done in the metric system. Knowing how to convert between different units of measurement is also useful in scientific and engineering fields, where calculations may require using units from different systems.

It's important to note that weight and mass are not the same thing. Weight is a measure of the force exerted on an object by gravity, while mass is a measure of the amount of matter in an object. The conversion from pounds to kilograms assumes that the force of gravity is constant, but this may not always be the case in different parts of the world.

In summary, 40 pounds is equal to 18.14 kilograms, and knowing how to convert between different units of measurement is an important skill in various fields of study and in everyday life.

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Rounding up to the nearest whole number, the quarterback throws 3 passes in the fourth quarter to complete all of them.

Let's first find out how many passes the quarterback completed in the first three quarters:

18 passes completed out of 33 attempts in the first three quarters

= 18/33 = 0.545 (rounded to three decimal places)

We can then find the total number of passes attempted in the first three quarters by using the fact that the completion rate is the number of completions divided by the number of attempts:

0.545 = 18/x, where x is the total number of attempts in the first three quarters

Solving for x, we get:

x = 18/0.545 = 33

So the quarterback attempted 33 passes in the first three quarters.

Next, we can find the total number of passes attempted in the game by using the completion rate for the entire game:

0.625 = (18 + passes completed in the fourth quarter) / (33 + passes attempted in the fourth quarter)

Multiplying both sides by the denominator:

0.625 × (33 + passes attempted in the fourth quarter) = 18 + passes completed in the fourth quarter

20.625 + 0.625 × passes attempted in the fourth quarter = 18 + passes completed in the fourth quarter

Subtracting 18 and 0.625 × passes attempted in the fourth quarter from both sides, we get:

2.625 = passes completed in the fourth quarter - 0.625 × passes attempted in the fourth quarter

Adding 0.625 × passes attempted in the fourth quarter to both sides, we get:

passes completed in the fourth quarter = 2.625 + 0.625 × passes attempted in the fourth quarter

We don't know the exact number of passes attempted in the fourth quarter, but we can see that for every 1 pass attempted, the quarterback completes 0.625 - 0.545 = 0.08 more passes than in the first three quarters. So to complete all of his passes in the fourth quarter, he needs to attempt:

0.08 × x = 0.08 × 33 = 2.64

Question - A quarterback completes 18 of 33 passes during first three quarters of a football game. He completes every pass in the fourth quarter and 62.5% of his passes for the entire game. How many passes does the quarterback throw in fourth quarter?

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In metric system length measured by using kilometres, milimter and miles etc. Thus, the conversion of 2.25 inches to mili meters is equals to the 57.15 mm.

Inches (also called in. ) is a unit of measurement used in US customer measurement systems. It is also part of the imperial measurement system. A millimeter (abbreviation mm) is a unit of measurement in the metric system. Like the inch, it is used to measure the length of an object, especially small ones. "Millimetre" is the US spelling, while in the UK it is spelled "millimetre". To convert from one measurement unit to another, multiply by the conversion factor. Formula to convert inches to millimeters, [X] mm = 25.4 × [Y] in ---(1)

We need to convert 2.25 inches to millimeters. So using the formula, millimeter = 25.4 × 2.25 inches

= 57.15

Hence, required value is 57.15 mm.

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Answer:  p = 4

Step-by-step explanation:

Because 3 * 4 + 3 = 15 which is then multiplied by 4 equaling 60

Answer:

p=4

Step-by-step explanation:

4(3p +3) = 60

12p + 12 = 60

        -12   -12  

___________

12p = 48

p = 4

Range of the function is the set {-6.5, -5, -2}.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Domain of the function is the input values of the function and Range of the function is the output values.

Given function is,

F(x) = 3/4 x - 5

Domain of the function is -2, 0 and 4.

F(-2) = (3/4 × -2) - 5 = -13/2 = -6.5

F(0) = (3/4 × 0) - 5 = 0 - 5 = -5

F(4) = (3/4 × 4) - 5 = 3 - 5 = -2

Range = {-6.5, -5, -2}

Hence the required range of the given function is {-6.5, -5, -2}.

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The expression that is equivalent to 734 + 356 - 134 using addition instead of subtraction is:

734 + 356 + (-134)

Answer:

706+350 = 956

Answer:

a=3

Step-by-step explanation:

the sum of anterior angle of a triangle is =180

57+81+14a=180

138+14a=180

42=14a

42/14=14a/14

3=a

therefore a=3.

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Answer:

x > -11 and x < 11

Step-by-step explanation:

Find the absolute value of a number gives you its distance from zero, which  is just the numerical parts of it. From this we can reason that the numbers between -11 and 11 have an absolute value less than 11, as they are the numbers that are less than 11 away from zero. This can be represented as -11  < x < 11, and can be separated into x > -11 and x < 11 (the "and" is because x has to fulfill both conditions of being greater than -11 and less than 11).

F(1) is equal to 0 for the given function F(x).

In order to evaluate a function at a specific value, you simply substitute that value for the input variable in the function and simplify the resulting expression.

If you are given a specific function F(x) and are asked to evaluate it at a specific value, say F(1), then you would substitute x=1 in the function F(x) and simplify the expression.

For example, if [tex]F(x) = x^2 + 2x - 3[/tex], then to evaluate F(1), we substitute x=1 in the expression:

[tex]F(1) = (1)^2 + 2(1) - 3[/tex]

Simplifying the expression, we get:

F(1) = 1 + 2 - 3 = 0

Hence, F(1) is equal to 0 for the given function F(x).

A function is a mathematical rule that takes an input value, processes it, and produces an output value. The input value is called the independent variable, and the output value is called the dependent variable, because its value depends on the input.

A function can be represented in various ways, such as an algebraic expression, a graph, a table, or a verbal description. For example, the function f(x) = 2x + 1 is an algebraic expression that represents a linear function, where the independent variable is x and the dependent variable is f(x).

Functions are used to describe and model relationships between variables in various fields of mathematics, science, engineering, economics, and other disciplines. They are important tools for analyzing and solving problems, and they can be used to make predictions, optimize processes, and design systems.

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The number of games they win is 22 games for 54 game season.

What is proportion?
In mathematics, a proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities or values, usually expressed as a fraction. For example, the ratio of boys to girls in a class might be expressed as 3/5, meaning that for every 3 boys in the class there are 5 girls.

Explanation:
Assuming that Manchester United's winning and losing rates remain the same throughout the season, we can use a proportion to estimate how many games they would win in a 54 game season:

wins / total games = winning rate

Using the data given in the problem, we can find the winning rate as:

14 / 35 = 0.4

So, Manchester United's winning rate is 0.4, or 40%.

To estimate how many games they would win in a 54 game season, we can set up a proportion:

wins / total games = winning rate

x / 54 = 0.4

Solving for x, we get:

x = 54 * 0.4 = 21.6

Rounding to the nearest whole number, we get an estimate of 22 games that Manchester United would win in a 54 game season, assuming their winning and losing rates remain the same as the first 35 games.

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The other two exterior angles are the ones in option 4.

105° and 115°

Remember two things:

You can use any of these two to find the answer, I will use the first one.

If one of the exterior angles is 140°, then the only option that adds up to 360° is the  lastoption

140° + 115° + 105° = 360°

So that is the correct option.

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On the number line, mark the endpoint at 10 with a closed circle.  

Next, draw a ray to the right of 10.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would collect like-terms and rearrange the expression as follows;

1,558 + 60x ≥ 2,158

60x ≥ 2,158 - 1,558

60x ≥ 600

x ≥ 10

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Complete Question:

Solve the inequality from part A for x. 1,558 + 60x ≥ 2,158.

Then use the drawing tools to graph the solution set on the number line.

On the number line, ________________.  

Next, draw a ray to the ____ of 10.

The Coordinates after dilation of 1.5 about the origin is

F'(1.5, -1.5)

G'(0, 3)

H'(1.5, 3)

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

Given:

We have the Coordinates F(1, -1), G(0, 2), H(1, 2).

As, the Dilation Rule for point (x, y) about origin with scale factor h

h(x, y)------>(hx, hy)

Applying the Dilation Rule we get

F(1, -1)-----> 1.5 F'(1, -1)-----> F'(1.5, -1.5)

G(0, 2)-----> 1.5 G'(0, 2)-----> G'(0, 3)

H(1, 2) -----> 1.5 H'(1, 2)-----> H'(1.5, 3)

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Answer:

Step-by-step explanation:

4(x + 4) + 2x = 52

4x + 16 + 2x = 52

6x = 52 - 16

6x = 36

x = 36 : 6

x = 6

Answer:

[tex] \sf \: x = 6[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 4(x + 4) + 2x = 52

Then the value of x will be,

→ 4(x + 4) + 2x = 52

→ 4x + 16 + 2x = 52

→ 6x + 16 = 52

→ 6x = 52 - 16

→ 6x = 36

→ x = 36 ÷ 6

→ [ x = 6 ]

Hence, the value of x is 6.

43% of the total trip had they travelled when Tallulah fell asleep

percentage, a relative value indicating hundredth parts of any quantity.

Given that Tallulah's family took a road trip to the Grand Canyon.

Tallulah slept for the last 129 miles of the trip.

the total length of the trip was 300 miles

We have to find the percentage of the total trip had they travelled when Tallulah fell asleep

x/100×300=129

3x=129

Divide both sides by 3

x=43%

Hence, 43% of the total trip had they travelled when Tallulah fell asleep

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Answer:

Answer: The length of the path would be 35 yds.

Step-by-step explanation:

We can use the formula for the area of a right triangle to find the length of the other leg. Once we know the lengths of both legs, we can use the Pythagorean theorem to find the length of the hypotenuse.

Let's call the length of the shortest side (the leg) "a", and let's call the length of the other side (the other leg) "b". We know that a = 21 yd and the area of the triangle is 294 yd^2. So we can use the formula for the area of a right triangle to solve for b:

area = (1/2) * a * b

294 = (1/2) * 21 * b

b = (2 * 294) / 21

b = 28

Now we know that a = 21 yd and b = 28 yd. We can use the Pythagorean theorem to find the length of the hypotenuse (c):

c^2 = a^2 + b^2

c^2 = 21^2 + 28^2

c^2 = 441 + 784

c^2 = 1225

c = sqrt(1225)

c = 35

Therefore, the length of the path along the longest side of the playground would be 35 yds.

Answer:

35 yards.

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. Let's call the other leg of the triangle "x" and the length of the hypotenuse (the path the council would like to add) "c". Then we have:

Area of triangle = (1/2) * base * height

294 = (1/2) * 21 * x

x = 28

Now we can use the Pythagorean theorem to find "c":

c^2 = 21^2 + 28^2

c^2 = 441 + 784

c^2 = 1225

c = sqrt(1225)

c = 35

So the length of the path the council would like to add is 35 yards.

The value of y co-ordinate of point Q is found to be -20 or 10 by using the distance formula.

What does the coordinate geometry distance formula mean?

In coordinate geometry, the distance formula is used to compute the distance between two specified points.

The distance formula is D=

It is used to determine the distance between two locations (x1,y1)(x1,y1)) and (x2,y2)(x2,y2).

Given: Points P and Q are separated by 17 units. The coordinates of point P are (5, 5) and point Q are (-3,y).

Using the distance formula,

PQ = [tex]\sqrt{(x2-x1)^{2} +(y2 - y1)^{2} }[/tex]

17²  = 64 - y² +25 +10y

289-64-25 = - y² + 10y

y² + 10y - 200 = 0

On solving the quadratic equation we get,

y = -20, 10

Therefore, the value of y co-ordinate of point Q is found to be -20 or 10 by using the distance formula.

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Answer:36

Step-by-step explanation:360 * 0.1 = 36 or 360/10 = 36

The Laplace Transform Method can be used to solve all of these equations except for equation (e).

a.) Yes, the Laplace Transform Method can be used to solve this third-order linear differential equation with constant coefficients and a nonhomogeneous term.

b.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with constant coefficients.

c.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.

d.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with variable coefficients.

e.) No, the Laplace Transform Method cannot be used to solve this first-order nonlinear differential equation.

f.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.

g.) Yes, the Laplace Transform Method can be used to solve this first-order nonlinear differential equation.

h.) Yes, the Laplace Transform Method can be used to solve this first-order linear differential equation with constant coefficients and a nonhomogeneous term.

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The sale price of the shoes is $45.

Your friend bought a new pair of shoes that had a regular price of $75. The regular price is the original or full price of the item before any discounts or promotions are applied.

Your friend said that he got a 40% discount on the shoes. A discount is a reduction in price from the regular price, often as a promotion or incentive to encourage customers to purchase the item. In this case, the discount is 40% of the regular price.

To calculate the sale price of the shoes, we need to subtract the discount amount from the regular price. The discount amount is 40% of $75, which is:

Discount amount = 40% x $75

Discount amount = $30

Now, we can find the sale price by subtracting the discount amount from the regular price:

Sale price = Regular price - Discount amount

Sale price = $75 - $30

Sale price = $45

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The value of pp when qq equals 2 is: 294

If pp is inversely proportional to the square of qq, it means that pp*qq²=k, where k is the constant of proportionality.

Given that pp is 24 when qq is 7, we can find the value of k:

24*7² = k

k = 1176

Now, we can use this value of k to find pp when qq is equal to 2:

pp*2² = 1176

pp*4 = 1176

pp = 1176/4

pp = 294

Therefore, when qq is equal to 2, pp is equal to 294.

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Answer: 9

Step-by-step explanation:

First plug in 3 for x.

Then you get 3^2

Now you solve and you get 9. Its the same as saying 3 * 3 = 9.

Answer:

410 is the outlier.

What is an outlier?

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal.

In simpler words, it is the number that is significantly bigger or smaller than the rest of the numbers, and 410 is it.

Step-by-step explanation:

Hope it helps! =D

Answer: Use the formula C (percent change/ percent difference) = x (the final value)-Y (the initial value) / Y, or C= x-y/y

Step-by-step explanation: This is the official formula. I found that it's easier to use the bigger value in the top x-y first, so you don't have to calculate the absolute value, but other than that the formula is correct.

The value of x in the two congruent triangles is 3.9 and length CB is 53.9.

The value of x can be determined by applying the principle of congruent theorem.

The congruent theorem states that, if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other.

( 11x + 11 ) / 77 = 21 / 30

11x + 11 = 53.9

11x = 53.9 - 11

11x = 42.9

x = 42.9 / 11

x = 3.9 units

The length of CB = ( 11 x 3.9 ) + 11 = 53.9

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