What is the value of x?

Answer:

66.390

Step-by-step explanation: 66.389 the 9 is thousandths, it rounds up to 66.390

Answer:

Step-by-step explanation: potential energy Ep = mgh

And g = 9.81 m/s². Ep = 0.0008 kg·9.81 m/s²· 22 m , unit is J

2 cups you need to fill the jug to 4.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

It depends on the size and markings of the jug.

If we assume that the jug is divided into equal intervals and each interval represents an equal volume,

then we can say that filling the jug to the second interval means that the jug is 1/2 full.

To fill the jug to the fourth interval, we need to fill the remaining 2 intervals, which means we need to add another 2 cups of liquid.

So, the answer is 2 cups.

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We want to find two numbers that meet the given restrictions, by solving a system of equations we will find that the two numbers are 15 and 64.

First, we define the two numbers as A and B.

From the given information we can write two equations:

A + B = 79

And the other one "79 when 5 is subtracted from thrice one of the numbers the result is 5 / 8 times the other number" can be written as:

3*A - 5 = (5/8)*B

So we need to solve a system of equations:

A + B = 79

3*A - 5 = (5/8)*B

We need to isolate one of the variables in one of the equations, I will isolate A on the first one:

A = 79 - B

Now we can replace that in the other equation:

3*(79 - B) - 5 = (5/8)*B

232 - 3*B = (5/8)*B

232 = 3*B + (5/8)*B = (29/8)*B

232*(8/29) = B = 64

Now that we know the value of B, we can use:

A = 79 - B = 79 - 64 = 15

So the two numbers are 64 and 15.

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The value of x in the figure is 50 degrees

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

The triangle

Using the above as a guide, we have the following:

The sum of angles is 180 degrees

So, we have

x + 40 + 90 = 180

Evaluate the like terms

x = 50

Hene, the solution is 50 degrees

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The angle sum property of a triangle indicates that the measure of the angle x° in the right triangle is 50°

A right triangle is a triangle that have two perpendicular sides.

The figure in the question, based on the rectangular angle mark in the right corner of the triangle, is a right triangle.

The measure of the right angle in the triangle = 90° (definition of a right angle)

The indicated acute interior angle of the right triangle = 40°
The angle addition property of a triangle indicates that the sum of the interior angles of a triangle is 180°

Therefore, according to the angle addition property, we get;

x° + 40° + 90° = 180°

Subtracting 40° + 90° from both sides, we get;

x° + 40° + 90° - (40° + 90°) = 180° - (40° + 90°)

x° = 180° - (40° + 90°) = 50°

x° = 50°

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Answer:

Step-by-step explanation:

Here you go mate

Step 1

-3x<3  Equation/Question

Step 2

-3x<3  Simplify

-3x<3

Step 3

-3x<3  Divide by -3

Answer

x>-1

Answer:

\(-18p^{5} -30p^{4} +6p^{3}\)

Step-by-step explanation:

\((-6p^{3} )(3p^2+5p-1)\)

\((-6p^3)(3p^2)+(-6p^3)(5p)+(-6p^3)(-1)\)

\(-18p^{5} -30p^{4} +6p^{3}\)

hope this helps.....

Answer:

Step-by-step explanation:

y=mx+b

m= slope and b= y intercept

you'll start with a point on the y axis on -1

and the slope will go up so towards the right corner up but 2/1 points

The graph of the transformed quadratic function is on the image at the end.

Here we can see the graph of the parent quadratic function:

f(x) = x^2

And we want to find the graph of the transformed function:

y = f(x + 1) + 2

This is a translation of 1 unit to the left and 2 units up of the graph that we can see on the image.

Replacing f(x)by x^2 we will get:

y = (x + 1)^2 + 2

The graph of this transformed function is:

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Kindly check below

1) For this problem, let's start out with the Ellipse

So, the key features of an Ellipse are:

a,a = (2) Semi-major axis ( the sum of the semi-major axis yields the longer axis of an ellipse), a=6

b,b =(2) Semi-minor axis (the sum of the semi-minor axis yields the shorter axis of an ellipse), b=4

F1, F2 (Foci)=(2√5,0), (-2√5,0)

A1,A2 =(6,0), (-6,0) Vertices (the endpoints of the semi-major axis)

B1, B2 =(4,0), (-4,0) Co-vertices (the endpoints of the semi-minor axis)

Domain: [-6,6] The set of entries of a function, usually represented by x

Range: [-4,4] The set of outputs of a function, usually represented by y

The general formula for an ellipse

2) Now, let's move on to the next conic section. The Hyperbola

In this sketch, we've got the following features:

A_1, A_2: The vertices of a hyperbola are at (5,-1) and (-3,1)

F_1, F_2: Foci of a hyperbola

In red: The asymptotes, (in this case slant ones. They set the boundaries where the hyperbola does not trespass.

Note that these asymptotes have a slope, so we need to express them as linear equations

P: Generic point on the curve.

Domain: Set of entries of a hyperbola. We can tell that this hyperbola has the following Domain:

A hyperbola can be given with a general formula as well:

Answer:

x = number of pies

$13.00  + (X -1)($10.00 per pie) = cost

Step-by-step explanation:

Number of pies = x

Total cost of = dollars = d

d = x + 10x

Hope that helps!

Answer:

2.98

Step-by-step explanation:

Answer:

I hope this helps!

Answer: The answer is in the picture.

Step-by-step explanation: But what is the sum?

The height of a student with an arm span of 143 cm is most accurately predicted to be 143 cm.

The lacking graph is included.

The student heights and arm spans in a classroom are depicted in the graph below.

For most people, their arm span is about equal to their height. Mathematicians say the arm span to height ratio is one to one: your arm span goes once into your height.

The x-axis represents the height in cm

The y-axis represents the arm span in cm

We must determine the height of a pupil whose arms are 143 cm long. The value of the specified arm span is not shown on the graph.

To get the best prediction of the height, we will select the line that best fits the data (the sold line in the graph shown).

Points (150, 150) and (160, 160) are on the line. The x-coordinates and y-coordinate are equivalent.

y = x is the line's equation.

A student's arm span is 143 cm,

Which is represented by the letter y. Replace the value of y in the equation for the line that best fits the data:

y = 143 = x,

Where x is a student's height.

The student stands 143 cm tall.

Therefore,

The height of a student with an arm span of 143 cm is most accurately predicted to be 143 cm.

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Answer:

Solving gives us the result, x = 2, y = -1

Step-by-step explanation:

The system of equations is,

y = 2x-5

y=-2x+3

equating the two equations, we get,

(since y = y)

\(2x-5 = -2x + 3\\4x -5 = 3\\4x = 3+5\\4x=8\\x=8/4\\x=2\)

and then since y = 2x-5

\(y=2(2)-5\\y=-1\)

so, x =2, y = -1

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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Answer:

\(b1=1b2=1h=7b1=1b2=6h=2b1=6b2=9h=2\)

Using the pattern, the next 4 numbers in the sequence would be

3.2; 4.0; 4.8; 5.6

The given sequence seems to follow a pattern where each term is obtained by adding 0.8 to the previous term.

hence this is an AP sequence, with a common difference of 0.8, adding 0.8 to each term gives the next consecutive term

2.4 + 0.8 = 3.2

3.2 + 0.8 = 4.0

4.0 + 0.8 = 4.8

4.8 + 0.8 = 5.6

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sinθ = t/o

cosθ = m/o

tanθ = t/m

cscθ = o/t

secθ = o/m

cotθ = m/t

The correct option is  \(r^{-42}\) is not equivalent to \((r^{-7} )^{6}\) .

Variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation can all be found in an algebraic statement. In many branches of mathematics, science, engineering, and finance, issues are represented and solved using algebraic expressions.

The expression \((r^{-7} )^{6}\) can be simplified using the rule of exponentiation which states that raising a power to another power involves multiplying the exponents. Applying this rule, we get:

\((r^{-7} )^{6}\)   = \(r^{-42}\)

Therefore, the expression  \((r^{-7} )^{6}\)  is equivalent to  \(r^{-42}\), which is the first option given.

Option 1:  \(r^{-42}\) is not equivalent to \((r^{-7} )^{6}\) .

Option 2: 1/ \(r^{-42}\) is also not equivalent to \((r^{-7} )^{6}\) .

Option 4: \(r^{-1}\) is also not equivalent to  \((r^{-7} )^{6}\) .

Therefore, the correct option is (a)  \(r^{-42}\).

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Answer:

A

Step-by-step explanation:

Solution

We have the following inequality:

4y + 2(2y-4) < 2(2y+4)

We can distribute the terms and we got:

4y + 4y -8 < 4y +8

8y -8 < 4y +8

We cna subtract 4y in both sides and we got:

4y -8 < 8

Adding 8 in both sides we got:

4y < 16

And dividing both sides by 4 we got:

y < 16/4

y < 4

And in the interval form would be:

a. Monthly payment for the bank's car loan is $407.67

b. Monthly payment for the savings and loan association's car loan is $315.99

c. Total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

The cost of borrowing money, usually expressed as a percentage of the amount borrowed, is what a lender charges a borrower to use their money. This cost is known as an interest rate.

(a) To find the monthly payment for the bank's car loan, we can use the formula for the present value of an annuity:

\(PV = PMT * \frac{1 - (1 + \frac{r}{n})^{(-n*t)}}{\frac{r}{n} }\)

putting the given values,

⇒ \(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*5)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $407.67

Therefore, the monthly payment for the bank's car loan is $407.67

(b) To find the monthly payment for the savings and loan association's car loan, we can use the same above formula:

where PV is still $21,000, PMT is the monthly payment, r is still 0.065, n is still 12, but t is now 7 years x 12 months/year = 84 payments.

putting the given values,

\(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*7)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $315.99

Therefore, the monthly payment for the savings and loan association's car loan is $315.99.

(c) Bank's car loan: $407.67 x 60 = $24,460.20

Savings and loan association's car loan: $315.99 x 84 = $26,495.16

Therefore, the bank's car loan would have the lowest total amount to pay off, by: $26,495.16 - $24,460.20 = $2,034.96

Therefore, the total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

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24 more footballs were donated than helmets in the given ratio problem.

Ratio refers to the quotient of two values. The expression a:b or a/b can be used to represent the ratio of a to b. A is the antecedent and b is the consequent in both scenarios. Every time we make comparisons, ratios appear.

For simplicity, they are typically expressed in the simplest terms. In a school with 1,000 students and 50 teachers, there are 20 students for every teacher.

The golden ratio of classical architecture is an example of an aspect ratio, which is the ratio of a rectangle's width to height. A proportion is an equation that results from setting two ratios equal to one another.

Lets 3x be the no. of helmet and 7x be football distributed.

total pieces = 3x + 7x

3x + 7x = 60

10x = 60

x = 60/10

x = 6

3x = 3(6) = 18

7x = 7(6) = 42

Difference = 42 - 18

                  = 24

Thus, 24 more footballs were donated than helmets in the given ratio problem.

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The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

F(-x) = 0

Step-by-step explanation:

What is F(-x)?

F(-x) = F(-1)

F(x) = x³ + 1                              F(-1)

F(-1) = -1³ + 1

F(-1) = -1 + 1

F(-1) = 0

So, F(-x) = 0

Answer:

f(-1) = 0

Step-by-step explanation:

Evaluating a function for f(-x) is the same as evaluating it for f(-1).

So we plug in -1 instead.

f(-1) = x³ + 1  

      = (-1)³ + 1 (here we cube -1)

      = -1 + 1     (here we subtract)

      = 0           (and, this is the answer)

\(\therefore\) The answer is f(-1) = 0

Answer:

x - intercept: ( - 2, 0 )

y - intercept: ( 0, -3 )

Step-by-step explanation:

Answer:

The right answers are 1,4 and 6

Answer:

x-3 =0

6=2x

x^2 = 9

Step-by-step explanation:

substitute the values, and you will get the answer!

have a great day!!

According to the information, we can infer that the area of this polygon is 34 units².

To find the area of the figure we must graph it and divide it into different segments. Then we find the area of all the segments and add them to get the total area.

Rectangle 1

6 * 3 = 18

Rectangle 2

2*4=8

Triangle 1

2 * 4 / 2 = 4

Triangle 2

2 * 4 / 2 = 4

Total Area

18 + 8 + 4 + 4 = 34

Based on the above, we can infer that the total area of the polygon is 34 ² units.

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The length of line having mid point B ⇒  7x - 2.

Given that,

B is the mid point of AC

And also given that

length of segment AB = 2x+5

And length of segment BC = 5x - 7

A straight path established by linking a group of points in a plane is known as a line. It is a one-dimensional form with only a length and no width or height. A line can extend indefinitely in both ends in opposite directions. To indicate a line, we can use upper case characters.

Now since B is the mid point of AC,

So, The line AC is sum of the line segment AB and line segment BC.

Therefore,

AC = AB+BC

     = (2x+5)+(5x - 7)

     = 7x - 2

Hence,

The length of AC is 7x - 2

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