4. E is between D and F. If DE = 3x + 2, EF = 18, and DF = 5x, find the value of x.

Answer: [tex]y=-((x-2)/\sqrt{2} )^{2} +4[/tex]

Step-by-step explanation:

This equation has it's parabola starting at (2,4)

So, we know that our equation will include (x-2) and +4

Next, we see the parabola is upside down, so we need a -

Next, we see the equation is wider than normal, so we need to divide x by something.

at x = -2, a normal graph would go through (0,0) , but this one goes through  (0,2)

at x = -2, [tex]2^{2} =4[/tex]

but we see at x = -2, [tex]x^{2} =2[/tex]

[tex]x=\sqrt{2}[/tex]

If the cafeteria ordered 400 paper plates. They used 226 at breakfast. They bought 100 more. Then, they used some plates for lunch. Now there are 78 plates. The number of  plates that was used at lunch is 196.

Given :

Paper plates ordered = 400 plates

Plates used for breakfast = 226

Additional plate bought = 100

Plate used for lunch = ?

Hence,

Let calculate the plate left after breakfast

Number of plates = Paper plates ordered - Plates used for breakfast

Number of plates = 400 plates - 226 plates

Number of plates = 174 plates

Now let determine the plates that were used for lunch

Pates used for lunch :

Pates used for lunch = (174 + 100) -78

Pates used for lunch = 274 -78

Pates used for lunch = 196 plates

Therefore we can conclude that the number of  plates that was used at lunch is 196 plates .

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Answer:

The smallest of the three integers is 17. (17, 19, 21)

The volume of the solution  A that we require in the fusion reaction is 3.9x10^-7 L

The term fusion has to do with a kind of nuclear reaction in which there is the combination of two light nuclei to have a heavier nucleus. This is the kind of process by which energy is produced in the sun.

Given that;

If we conduct fusion of hydrogen in 1 liter of solution A, the energy that i obtained is 7.6x10^10 J. Then the energy that any one of the homes could use is  3x10^4 J.

Let x be the volume of the solution A that we need. It the follows that;

x * 7.6x10^10 J = 3x10^4 J

x =  3.9x10^-7 L

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Missing parts;

if you could generate energy by fusing the hydrogen in solution a, how much of the solution would you need to generate the electrical energy used daily in a certain home? energy released by fusion of hydrogen in 1 liter of solution A = 7.6*10^10 Electrical energy used daily in a certain family home = 3*10^4

a) 10.7

b) ΔABE~ΔACD | Angle Angle Similarity

1) Analyzing that triangle, and considering they are similar we can write out the following to find x

a) If they are similar their corresponding sides are proportional, therefore we can write a pair of ratios.

The smallest hypotenuse over the largest hypotenuse as well as there is a proportionality between those two corresponding legs 8 and 18.

b) In the last statement of that proof table, we can tell that the last line is well written as:

ΔABE~ΔACD | Angle Angle Similarity

The Angle Angle Similarity states that:

Note that in that table there are two instances in which there is a reference to two congruent angles.

A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width. The square number will be [tex]\frac{625}{28561}[/tex].

A square is a common polygon with four equal sides and angles that are each 90 degrees in length.

A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width.

Many objects can be found in your surroundings that have a square shape. The chessboard, craft sheets, bread slice, picture frame, pizza box, wall clock, etc. are typical instances of this shape.

Specifications of a Square

[tex](\frac{25}{169})^{2} = \frac{625}{28561}[/tex]

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Answer:

(√25/69)^2

Step-by-step expla$nation:

You might see this as cheating but technically it is the correct answer :)

Hope this helps ^^

btw is this RSM?

Answer:Explanation:

Option 1: Vertically compressed by a factor of 4, reflected across the x-axis, and shifted right 6 units and down 2 units.

iven the parent function:

If y is vertically compressed by a factor of 4, we have:

Next, a reflection across the x-axis will give:

If the result is shifted

Finally, a shift downwards by units gives:

Thus, the graph of g(x) is the graph of y vertically compressed by a factor of 4, reflected across the x-axis, and shifted right 6 units and down 2 units.

he firsyt option is correct.

we have

-2x+8y=-14 ------> equation A

-4x+y=-13 ------> equation B

solve the system

using the elimination method

step 1

multiply by -2 equation A

-2[-2x+8y=-14] -----> 4x-16y=28 -------> equation C

step 2

Adds equation B and equation C

-4x+y=-13

4x-16y=28

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

-15y=15

solve for y

y=-1

Find the value of x

substitute the value of y in any equation

-4x+y=-13 ------> equation B

-4x+(-1)=-13

-4x=-13+1

-4x=-12

x=3

therefore the solution is

Answer:

X = 1/5

Step-by-step explanation:

16 - 10X = 14

10X = 2

X = 0.2

Answer

x=0.2

-16+10x=-14

10x=-14+16

10x=2

10x÷10=2÷10

x=0.2

Angle JKL has a measure of 24 degrees while angle LKM has a measure of 12 degrees

The possible question is added at the end of the solution and as an attachment

From the attached figure, we have the following angles

From the attached figure, we can see that:

Angle 1 is twice the measure of angle 2

This is so because, the angle 1 is the vertex angle of an isosceles triangle

While the angle 2 is half of it

So, we have

Angle 1 = 2 * Angle 2

Substitute the known values in the above equation

So, we have

2 * 3x = 5x + 4

Evaluate the product

So, we have

6x = 5x + 4

Evaluate the like terms

x = 4

Substitute x = 4 in the equations JKL=5x+4 and LKM=3x

So, we have

JKL= 5 x 4 + 4

LKM = 3 x 4

Evaluate the equations

So, we have

JKL= 24

LKM = 12

Hence, the measures of the angles are JKL= 24 and LKM = 12, respectively

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Answer: 3*3*3*3*3*3

Step-by-step explanation:

The value of 9³ = 3ˣ and x = 6

9³ = 3 x 3 x 3 x 3 x 3 x 3

9³ = 3⁶

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be A

The number A = 9³

The value of A = 729

Now , the number 9³ can be expressed as the power of 3

So , the equation will be

9³ = ( 3² )³

    = 3³ˣ²

    = 3⁶

    = 729

Therefore , the value of 9³ = 3⁶

Hence , The value of 9³ = 3ˣ and x = 6

9³ = 3 x 3 x 3 x 3 x 3 x 3

9³ = 3⁶

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commutative property

That's what you call the property 7x8 = 8x7

commutative property!

Answer:

y = ± 13

Step-by-step explanation:

If y² = 169 then y = √169

√169 is either +13 or -13

This is usually written using the plus/minus sign

√169 = ± 13

1) In this problem, we need to isolate the variables on the left side.

Notice that in two steps we can solve the problem.

2) Thus the answer is

Answer: X1= 7 - sqrt{17} over 4

              X2= 7 + sqrt{17} over 4

Answer:

327 x 564

1648+2092+1685

190068

Step-by-step explanation:

im pretty sure that this is right. and the bold letter are the missing ones

It is known that:

Therefore, 40 quarts in gallons is:

So to fill 40 quart bottles, atleast 10 gallons of oil will be needed.

Hence the tank of 12 gallons should be used since it has more than 10 gallons of oil.

The two gallon one does not have enough oil.

Option B that means the second option is correct.

"The 2 gallon tank is not enough ,but the 12 gallon tank is enough".

the area of the pie that Carol will bake will be equal to 249.51 inches².

We are given the circumference of the pie as = 56 inches.

As pie is in the shape of a circle, we will use the formula for circumference to find the radius of the circle.

2 π r = 56 inches

2 × 22 / 7 × r = 56

r = 56 × 7 / ( 22 × 2)

r = 8.91 inches.

Area of circle is given by:

π r²

Substituting the values in the formula, we get that

A = 22 / 7 (8.91)²

A = 249.51 inches²

Therefore, we get that, the area of the pie that Carol will bake will be equal to 249.51 inches².

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The answer is 0.00650508866

ANSWER:

The probability is 0.018

STEP-BY-STEP EXPLANATION:

That 5% are defective means that 5 out of 100 tires are defective.

If 5 tires are selected, the probability that they are exactly defective is calculated as follows

Now, resolving

replacing:

The result of the addition of complex numbers 3+i and 2 - 3i will be 5-2i as the rule says "to add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts.".

Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation i² = -1.

The complex plane in mathematics is the plane made up of complex numbers, with real and imaginary numbers making up the x-axis (also known as the real axis) and the y-axis (also known as the imaginary axis) of the Cartesian coordinate system.

Here,

To add the complex numbers,

To add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts.

(3+i)+(2-3i)=5-2i

According to the rule, "to add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts," the sum of the complex numbers 3+i and 2 - 3i will be 5-2i.

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Point C represents √11 on number line

A number line is a visual depiction of numbers on a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction. A number line is exactly what it sounds like—a horizontal, straight line with numbers spaced evenly apart throughout its length. Since it's not a ruler, the distance between each number is irrelevant; instead, the numbers on the line specify how it should be used.

Given Data

Number:

√11

√11 = 3.31

Point C represents √11 on number line.

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The evaluated value of x from the line geometry given is 36.

An angle is the point where two lines meet. From the given diagram, the sum of the angles on the line is 180 degrees.

Take the sum to have

x + 3x + x = 180

Simplify

4x + x = 180

5x = 180

Divide both sides by 5

5x/5 = 180/5

x = 36

Hence the value of x from the diagram is 36

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The angle x in the parallel line is 123 degrees.

In the diagram, l₁ and l₂ are parallel.

l₃ and l₄ are perpendicular to each other.

Since l₁ and l₂ are parallel lines, the line l₃ is a transversal that cut across the parallel lines.

Angle relationship are formed such as corresponding angles, alternate angles, vertically opposite angle etc.

Therefore,

57 + x  = 180°

x = 180 - 57

Therefore,

x = 123 degrees.

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Answer:

A

Step-by-step explanation:

The multiplicative inverse property states that any number multiplied by its multiplicative inverse (also called reciprocal) results in 1.

The x and y intercepts of the given graph of the function are 3/2 and -1 respectively.

Intercepts of the line

The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the x-axis, then it is called the x-intercept. If a point crosses the y-axis, then it is called the y-intercept.

Given equation of the line:

y = (2/3)x - 1

To find the y -intercept, putting x = 0, we get,

y = (2/3)*0 - 1

y = 0 - 1

y = -1

Hence, the y - intercept is -1.

To find the x -intercept, putting y = 0, we get,

0 = (2/3)x - 1

1 = (2/3)x

x = 3/2

Hence, the x - intercept is 3/2.

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Answer:

74.44

Step-by-step explanation:

[tex]P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44[/tex]