How to solve multi step equations

The quadratic function for this problem is given as follows:

The roots of the quadratic function in the context of this problem are given as follows:

Hence the linear factors of the function are given as follows:

Hence the function is:

y = a(x + 1)(x + 8).

When x = 0, y = 4, hence the leading coefficient a is obtained as follows:

8a = 4

a = 0.5.

Hence the factored form of the function is of:

y = 0.5(x + 1)(x + 8).

The standard form of the function is given as follows:

y = 0.5(x² + 9x + 8)

y = 0.5x² + 4.5x + 4.

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Answer: Multiply the centimeters number by 10.

Step-by-step explanation: There are 10 millimeters in every centimeter.

Leaving the TV on for two weeks while on vacation would cost you approximately $4.46.

To calculate the cost, we need to determine the total energy consumed by the TV while you were on vacation and then convert it to dollars.

First, let's calculate the energy consumption in kilowatt-hours (kWh):

Power (in kilowatts) = Voltage (in volts) * Current (in amps) / 1000

Power = 120 V * 0.96 A / 1000 = 0.1152 kW

Now, we need to find the total energy consumed in kilowatt-hours (kWh) over the two-week period:

Energy (in kilowatt-hours) = Power (in kilowatts) * Time (in hours)

Energy = 0.1152 kW * 24 hours/day * 14 days = 38.4512 kWh

Next, let's calculate the cost of this energy consumption:

Cost = Energy (in kilowatt-hours) * Cost per kilowatt-hour

Cost = 38.4512 kWh * $0.116/kWh = $4.46 (rounded to two decimal places)

Therefore, leaving the TV on for two weeks while on vacation would cost you approximately $4.46.

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The length of MS is 10 cm and diameter of the circle is RS

Given that the midpoint of PQ is M

RM is 10 cm and PQ is 24 cm

We have to find the length of MS

As M is midpoint then RM=MS

MS = 10 cm

Now the diameter of the circle is RS because it passes through middle of the circle which is center O

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AC=5cm

CB=4cm

hypotenuse=5²+4²=25+16=41

hypotenuse=√41=6.40cm

Answer:

16

Step-by-step explanation:

divide 6 by 3/8 by multiplying 6/1 by 8/3

The total number of possible call letters is:

2 * 26 * 25 * 24 = 31,200

(a) If the first letter must be K or W and no letter may be repeated, then there are two choices for the first letter and 26 choices for the second, third, and fourth letters. This gives the total of:

2 * 26 * 25 * 24 = 31,200

different 4-letter radio station call letters.

(b) If repeats are allowed but the first letter must still be K or W, then there are again two choices for the first letter, but now there are 26 choices for each of the second, third, and fourth letters. This gives a total of:

2 * 26 * 26 * 26 = 35,152

different 4-letter radio station call letters.

(a) If the first letter must be K or W and no letter may be repeated, we need to choose 4 letters in total. Since the first letter must be K or W, we have 2 choices for the first letter. For the second letter, we can choose any of the remaining 26 letters of the alphabet. However, since we cannot repeat letters, we have 25 choices left for the third letter, and 24 choices left for the fourth letter.

Therefore, the total number of possible call letters is:

2 * 26 * 25 * 24 = 31,200

(b) If repeats are allowed but the first letter must still be K or W, we still need to choose 4 letters in total. Again, we have 2 choices for the first letter, but now we can choose any of the 26 letters for the second, third, and fourth letters since repeats are allowed.

Therefore, the total number of possible call letters is:

2 * 26 * 26 * 26 = 35,152

So, in summary, if repeats are not allowed, we have fewer choices for the second, third, and fourth letters, and the total number of possible call letters is smaller. If repeats are allowed, we have more choices for each letter, and the total number of possible call letters is larger.

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Answer:

degree x π/180 = radian

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

1) -290° × π/180 = -5.061rad

3) 970° × π/180 = 16.93rad

5) 510° × π/180 = 8.901rad

7) 210° × π/180 = 3.665rad

9) 240° × π/180 = 4.189rad

11) -945° × π/180 = -16.49rad

13) 315° × π/180 = 5.498rad

15) -520° × π/180 = -9.076rad

17) 300° × π/180 = 5.236rad

19) 555° × π/180 = 9.687rad

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

i hope this helps!

Answer:

let the remaining sides be X and Y

perimeter = X + Y + 13

24 = X + Y + 13

11 = X + Y ---(1).

Area = 1/2 * base * height

24 = 1/2 * X * Y

XY = 48.-----(2)

solving eq 1 and 2

X + Y = 11

XY = 48

Xy + y² = 11y

Xy = 48

y²= 11y - 48

y² -11y + 48 = 0

no real solution of this equation.

Answer:

Step-by-step explanation:

the triangle is NOT a 3–4–5 or multiple,

so it is not a right triangle or your data is wrong.

Answer:

I want to say that it is E

Step-by-step explanation:

Well in terms of probability there is a 50% chance the coin will land heads and a 50% chance the coin will land tails. Since probability isn't definite you can never really get a precise number of each side. the most you could do is predict/guess

The most likely outcome is: E. They are all equally likely.

Each individual toss of a fair coin has an equal probability of being a heads or tails, regardless of what the previous tosses were. Therefore, all of the outcomes listed are equally likely. The order in which the heads and tails occur does not affect the probability of the overall outcome.

So, even though (i) has an equal number of heads and tails in an alternating pattern and (iii) has all heads, they are both equally likely to occur. The same goes for (ii) and (iv), which have an equal number of heads and tails but in a random order.

Therefore, The most likely outcome is: E. They are all equally likely.

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Answer:

3\(\sqrt{3}\)

Step-by-step explanation:

in a 30-60-90 triangle, the side across from 60° is \(\sqrt{3}\) multiplied by the side across from 30°

the side across from 90° (the hypotenuse) is double the side across from 30°

9514 1404 393

Answer:

  3x +2y +24 = 0

Step-by-step explanation:

In general, the equation of a perpendicular line can be found by swapping the coefficients of x and y, then negating one of them. The value of the constant will be what is required to make the line pass through the given point.

The equation will be of the form ...

  3x +2y +c = 0

At the given point, (x, y) = (-6, -3), we have ...

  3(-6) +2(-3) +c = 0 . . . . substitute the given point coordinates

  -18 -6 +c = 0 . . .simplify

  c = 24 . . . . . . . . add 24

The general-form equation for the line is ...

  3x +2y +24 = 0 . . . . . shown in blue in the attachment

Given:

The expression is

\(4y^2+y-45\)

To find:

The value of the given expression when y=-5.

Solution:

We have,

\(4y^2+y-45\)

Putting y=-5, we get

\(4(-5)^2+(-5)-45\)

\(=4(25)-5-45\)

\(=100-50\)

\(=50\)

Therefore, the value of the given expression is 50 when y=-5.

Step-by-step explanation:

just think it through. it can only be the first option. the sides 7 and 4 are together 11, and they can only meet, when putting them flat on the 11 side. but yes, if you do that, they will meet, as 11 = 11.

the result would be an extreme triangle : appearing just as one, flat line (length 11), the angles being 180°, 0° and 0°.

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct option is A.

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

Sides 7 and 4 are together 11, and they can only meet when they are flat on the side with a length of 11 units. However, if you do this, they will meet touch overlap on each other since 11 units = 11 units.

This will result in an extreme triangle which will more of look more like a straight line and will have angles of measure as 180°, 0°, and 0°.

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stem-and-leaf plots for the sets of data are attached.

What is stem-and-leaf plot?

In a stem and leaf plot, the values of the data are divided into a stem and a leaf, creating a singular table. The initial digit or digits are written in stem format, and the final digit is written in leaf format.

Data can be arranged in a way that makes it simple to see the frequency of various sorts of values using a stem and leaf plot, also known as a stem and leaf diagram. It is a graph with numerical data displayed in a sequential manner. Each value of the data is divided into a stem and a leaf.

A stem and leaf plot is depicted as a customised table with each data value's initial or last digit divided into a stem and the leaf's final digit.

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Answer:

A

Step-by-step explanation:

g

\(g(x) = f(x - 2) + 4\)

A function assigns the value. The equation of the function g(x) will be f(x-2)+4.

A function assigns the value of each element of one set to the other specific element of another set.

Given f(x) is a function which is shifted two units to the right and 4 units upwards. Therefore, in the function f(x) we need to add -2 to the value of the x for the function to move right, while we need to add 4 to the overall function to move it four units upwards.

Hence, the equation of the function g(x) will be f(x-2)+4.

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Answer:

When solving, you will get a false statement, and therefore there is no solution.

Step-by-step explanation:

Let's try to solve the system of equations. In this case, I used the substitution method and substituted 4x + 5 for the y in y = 4x-2:

\(4x + 5 = 4x - 2\\5 = -2\)

In trying to combine the terms with the variable x, the 4x on both sides canceled themselves out, leaving me with 5 = -2. That is a false statement, as 5 does not equal -2. Therefore, since we cannot reach a solution, there is none.

two lines y = 4x+5 and y = 4x – 2 are parallel, then there is no  intersection point.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given wo lines are y = 4x+5 and y = 4x – 2

These two lines are parallel because there slope is 4 for both.

Let us solve these two equations algebraically to find out intersection point.

4x+5=4x-2

5=-2

Since 4x is cancelled on both sides and has no x variable means there is no intersection point.

Hence for two lines y = 4x+5 and y = 4x – 2 are parallel, then there is no  intersection point.

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75 is the biggest number with which 525 and 3000 can be divided, making it the greatest common factor.

Finding all common factors between two integers and choosing the biggest one yields the highest common factor (HCF). It is the most powerful divisor for any pair of integers that can divide the inputted numbers evenly or fully. The largest of all the common factors between two or more integers is known as the Highest Common Factor (HCF). A number that divides two or more integers precisely is referred to as a common factor. Factors are numerical combinations that we may multiply to produce another number. These are the "common factors" when we determine the factors of two or more integers and discover some of those factors are the same (or "common").

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A plane flying just above the equator around the world 3 1/2 times would cover a distance of 4.375 x 10⁴ miles.

If an airplane travels around the world just above the equator once, it covers a distance of 1.25 x 10⁴ miles. To find how many miles it would cover if it flew around the world 3 1/2 times, we need to multiply this distance by 3.5:

1.25 x 10⁴ miles x 3.5 = 4.375 x 10⁴ miles

To understand this calculation, we need to know that 3 1/2 times means 3.5 times. So, we multiply the distance covered in one round of the world by 3.5 to find the total distance covered in 3 1/2 times around the world.

We use standard form to express the answer in a more compact and convenient way, where 4.375 x 10⁴ represents the number 43,750 in scientific notation.

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Answer: 7/8

Step-by-step explanation:

The volume of the solid is 603.19 cubic feet

The formula for the volume of a hemisphere is (2/3)πr³.

Since the radius of the hemisphere is not given,

Assume it to be the same as the radius of the cone, which is 6 feet.

So, the volume of the hemisphere is,

⇒ (2/3)π(6³) = 144π cubic feet

The formula for the volume of a cone is (1/3)πr²h,

where r is the radius and h is the height.

Put in the values we have, we get,

⇒ (1/3)π(6²)(12) = 144π/3

                        = 48π cubic feet

Find the total volume of the composite solid by adding the volumes of the hemisphere and the cone,

⇒ Total volume = Volume of hemisphere + Volume of cone

⇒ Total volume = 144π + 48π

⇒ Total volume = 192π cubic feet

Finally, rounding to the nearest hundredth,

The volume of the composite solid is 603.19 cubic feet.

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We have to find out the probability of getting 6 and 3,

Since this only one roll it is not possible to get 2 numbers in one roll

So, I will presume you want the probability of getting 6 or 3,

Total number of outcomes= {1,2,3,4,5,6} = 6 outcomes

Number of favorable outcomes = {3,6} = 2 outcomes

Probability of rolling 6 or 3 = \(\frac{Number'of 'favorable' outcomes}{Total' number 'of' outcomes}\)

= 2/6

= 1/3 or 0.33333%

Therefore the probability of rolling 6 or 3 is one in three chances

Happy to help :)

If u have any doubts or questions , feel free to ask

Answer:

SEE BELOW

Step-by-step explanation:

INTERRIOR ANGLES

3.

∠A + ∠B + ∠C = 180

(180 - 103) + (3x - 14) + (3x + 9) = 180

6x = 180 - 77 + 14 - 9

x = 108 / 6

x = 18

m∠ACB = (3x - 14)

             = 3(18) - 14

             = 40

m∠ABC = (3x + 9)

              = 3(18) + 9

              = 63

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

INTERRIOR ANGLES

4.

∠A + ∠B + ∠C = 180

(180 - 97) + (2x + 2) + (14x - 1) = 180

16x = 180 - 83 - 2 + 1

x = 96 / 16

x = 6

m∠BCA = 2x + 2

             = 2(6) + 2

             = 14

m∠ABC = 14x - 1

             = 14(6) - 1

             = 83

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

EXTERIOR ANGLES

5.

∠B

180 - 15x + 20

15x = 180 + 20

   x = 200/15

   x = 13.33

∠C

180 - 9x + 10  

9x = 190

 x = 190/9

 x = 21.11

∠E

180 - 17x + 2

17x = 182

  x = 182/17

  x = 10.706

m∠BEF = 17x + 2

             = 17 (10.706) + 2

             = 184

m∠ABC = 15x + 20

             = 15(15.33) + 20

             = 220

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

EXTERIOR ANGLES

6.

first solve x by adding all the interior angles = 180

∠B + ∠E + ∠C = 180

2x + x + 93 = 180

3x = 180 - 93

x = 87/2

x = 43.5

m∠BEC = 360 - x

             = 360 - 43.5

             = 316.5

m∠ABC = 180 - 2x

             = 180 - 2(43.5)

             = 93

Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.

Here,

Given :

cost of blackberry = 88 euroes

cost of sugar = 650 euroes

Jam bottles costs =87.75

total cost for to make 15 jars is

=> 15 * (87.75+650+88)

=> 15 * 825.75

=>  12,386.25 euroes

Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

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As per the given functions A(x) and B(x), at the month 8th the price of his phone be less with website B than website A.

The term function in math is known as a relationship between inputs where each input is related to exactly one output.

Here we have given that Asher is able to sell his cell phone on two different websites, A and B.

And in the given table, the different rates are represented by the functions A(x) and B(x), where t is time in months.

While we looking into the given question, we have identified that there are two functions are listed as follows:

A(x) = 80(0.86)ˣ

B(x) = 80 - 8t

When we plot the function on the graph, then we get the graph like the following,

Through the graph, we have identified that on the point of (8, 23.93) and (8,16) has been the resulting point.

Therefore, the correct option is (d).

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The measure of angle 7 is 82°.

A transversal is defined as a line that passes through two lines in the same plane at two distinct points in the geometry

Given:

angle 6= 98°

As, angle 6 and 7 forms a linear pair then

angle 6 + angle 7 = 180

98 +  angle 7= 180

angle= 180-98

angle 7 = 82°

Hence, angle 7 is 82°.

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Answer:

They are the same line

Step-by-step explanation:

When you have equations of line and want to compare them, make sure the y is isolated (by itself)

the second equation -2y = 4x-8 is not isolated

To isolate, divide both sides by -2

\(\frac{-2y}{-2} =y\)

\(\frac{4x-8}{-2} = -2x+4\)

Now you have y=-2x+4, which is the same equation as the first!

(remember that if you divide a negative number by a negative number, you will get a positive one)

Answer:

The lines are the same if you divide both sides by -2 for the equation:-2y=4x-8 to get a slope formula. As you can see, after doing that, the equations are the same.

Step-by-step explanation:

y=-2x+4

-2y=4x-8

-2y/-2=(4x-8)/2

y=-2x+4

Step-by-step explanation:

"If the sum of 2 angles is 180°, then each is the supplementary angle of the other".