7. Find the value of each variable
(5x- 7)
(8x-55)

The two triangles are similar.

Similar triangles are triangles that have the same shape, but their sizes may vary.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The side lengths of two similar triangles are proportional. That is, if ΔABC is similar to ΔDEF , then the following equation holds:

AB / DE  = AC / DF = BC / EF

Hence,

6 / 3 = 10 / 5 = 8 / 4 = 2 / 1

This common ratio is called the scale factor .

The symbol ∼ is used to indicate similarity.

Therefore, the triangles are similar.

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a) 10 additional days are required for both to cost the same.

b) The cost is 70$.

At Johan's Rental:

Rent= (50+2x)$

At Martinez Rent:

Rent= (30+4x)$

For both the cost same

By using Elimination method,

50+2x = 30+4x

50-30 = 4x-2x

20 = 2x

x = 10

10 additional days are required for both to cost the same.

Cost = 50+2x

= 50+2*10

=50+20

=70.

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Chester made 9 sales and Vickie made 16 sales this week

Base salary of Vickie = $70

Vickie's commission per sale = $24

Base salary of Chester = $142

Chester's commission per sale = $9

Both people earned the same amount this week. Let x represent the number of sales made by Vickie, then sales made by Chester is x+7

Formulating the equation we get:

Base salary of Vickie + Vickie's commission per sale*Number of sales = Base salary of Chester + Chester's commission per sale*Number of sales

= 70 + 24x = 142 + 9(x+7)

70+24x = 142+9x+63

70+24x = 205+9x

15x = 135

x = 9

Chester sales = 9

Vickies sales = 9+7 = 16

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Answer:

42%

Tell me if you need expalining!

Step-by-step explanation:

Answer:

13440ml a week

Step-by-step explanation:

8x240=1920

1920x7=13440

13440is the amount of mls a week

Answer:

13440ml

Step-by-step explanation:

8 x 240 = 1920ml  (per day)

(8 x 240) x 7 = 13440ml   (7 days = 1 week)

Answer:

210 days

Step-by-step explanation:

7 x 30 = 210 days

Answer:

210

Step-by-step explanation:

A Friday occurs every 7 days.

A new moon occurs (approximately) every 30 days.

We need the smallest number that is a multiple of both 7 and 30.

We need the least common multiple (LCM) of 7 and 30.

This is the same as finding the least common denominator for two fractions that have denominators 7 and 30.

First, we find the prime factorizations of the two numbers.

7 = 7

30 = 2 × 3 × 5

The LCM is the product of common and not common factors with the larger exponent.

LCM = 2 × 3 × 5 × 7 = 210

Answer: 210

P.S. This is the correct answer for this problem, but the problem is stated incorrectly since a new moon occurs approximately every 29.5 days, so in reality, the true answer is not 210 days.

Answer:

[tex] \dfrac{7^{36}}{9^{24}} [/tex]

Step-by-step explanation:

(9^6 x7^-9)^-4=

[tex] = (9^6 \times 7^{-9})^{-4} [/tex]

[tex] = 9^{-24} \times 7^{36} [/tex]

[tex] = \dfrac{7^{36}}{9^{24}} [/tex]

The most appropriate choice for Distance will be given by:

The ball takes [tex]3s[/tex] to reach a height of [tex]45[/tex] [tex]m[/tex].

What is Distance?

The length of the path an object takes without taking into account the direction of motion of the object is known as distance.

If [tex]s[/tex] is the speed of the object and [tex]t[/tex] is the time, then

Distance = [tex]s \times t[/tex]

Here,

[tex]H(t) = 30t - 5t^2[/tex], [tex]t[/tex] is the time in seconds

For finding the time taken by the ball to reach a height of [tex]45[/tex][tex]m[/tex], we need to substitute [tex]H(t) = 45[/tex]

Now putting [tex]H(t) = 45[/tex]

[tex]45 = 30t - 5t^2\\5t^2 - 30t+45 = 0\\ 5(t^2 -6t + 9)=0\\t^2 -6t+9=0\\t^2-3t-3t+9=0\\t(t-3)-3(t-3)=0\\(t-3)(t-3)=0\\t-3 = 0\\t = 3s[/tex]

So the ball takes [tex]3s[/tex] to reach a height of [tex]45[/tex] [tex]m[/tex].

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Answer:

2 dimes and 5 pennies

Step-by-step explanation:

2 dimes (d) is 10 and 5 pennies (p) is 5

75+p+d=100

75+p=80

80+d=100

Answer: 3 quarters, 2 dimes, 1 nickel.

Step-by-step explanation: 3 quarters are worth 75 cents, 2 dimes are worth 20 cents, and 1 nickel is worth 5 cents! Hope this helps

The statement can be described as an Invalid Conclusion.

An invalid conclusion arises from a series of statements where the premises are true but the conclusion is not true. The premises in the statements above are all true.

For instance, it is true that if you go fishing you will need a rod. It is also true that if you go fishing you will need bait. But there is no laid down rule that if you bring your fishing rod, you will also need to bring a bait. So, this is an invalid conclusion.

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Answer:

w = 20

Step-by-step explanation:

a) Flip the equation.

-3/4 w = -15

b) Multiply both sides by 4/(-3).

(4/-3) * (-3/4 w) = (4/-3) * (-15)

w = 20

The number of strawberry they picked is about 4050.

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

89 kg = 89000 g conversion

89000=22=4045.45 ≈4045

{unit conversion}

≈4050

The number of strawberry {nearest lo} is about 4050

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Answer:

185

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

250

244

18

10

are one of the answers

give this 5 stars if correct

Answer:

g(-3) = 16

Step-by-step explanation:

To find g(-3), we need to plus -3 into the given function. So, g(-3) = |2(-3) - 10|. Now we solve using PEMDAS. Two times -3 is -6, then we have g(-3) = |-6-10| which is essentially g(-3) = |-16|. Lastly, we take the absolute value of |-16| which is just 16, therefore g(-3) = 16.

Given

Find

showing that angles H and F are supplementary.

Explanation

Let angle F , which is subtended by minor arc GHE.

so , angle F = half of angle GHE by subtended angle theorem.

similarly , angle H is the angle subtended by major arc GFE.

so , angle H = half of the angle subtended by major arc.

since , total angle around J is 360 degree.

as we know , the sum of angle subtended by minor arc and major arc is 360 degree.

so , angle F + angle H = 1/2(360) = 180 degree.

Final Answer'

Hence , H and F are supplementary angles.

The height of the plane PA is given as; 1591 ft

There are different trigonometric ratios such as;

cos θ = adjacent/hypotenuse

sin θ = opposite/hypotenuse

tan θ = opposite/adjacent

Now, looking at the given image showing plane and bridge indicated by lines, we can use one of the trigonometric ratios to get the height of the plane PA as;

PA/3000 = tan B

now angle B = 28 degrees from alternate angles postulate. Thus;

PA/3000 = tan 28

PA = 3000 * tan 28

PA = 3000 * 0.5317

PA = 1591 ft

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[tex]tan 28^o = \frac{PA}{3000}[/tex]

tan 28° · 3000= PA

(use a scientific calculator)

1595.128= PA

height = 1595

The inequality that represents, the number of shirts he needs to remove to meet the flight requirements is 0.75p + 50ibs  ≤ 49

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Let the weight of Rodney suitcase be p

First the contents inside must weigh less than 50lbs.

x < 50

The suitcase weighs 4 pounds and the contents he wants to pack weigh 49 pounds.

0.75p < 49

Therefore, 0.75p + 50ibs  ≤ 49

The inequality that represents, the number of shirts he needs to remove to meet the flight requirements is 0.75p + 50ibs  ≤ 49

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The remainder of f(x) is 385.

What are the 5 steps of long division?

The five steps of long division are given by:

Step 1: Divide

Step 2: Multiply

Step 3: Subtract

Step 4: Bring down

Step 5: Repeat

Given,

f(x) = x3 + 5x2 –32x – 7 is divided by x – 4

To find the Remainder

Now, The solution is:

             [tex]x^{2} -9x+98[/tex]

[tex]x-4\sqrt{x^3+5x^2-32x-7}\\[/tex]

         [tex]x^{3} - 4x^2[/tex]

        -     +

      -----------------------------

                [tex]9x^{2} -32x[/tex]

                [tex]9x^{2} +36x[/tex]

              -        -

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

                       98x -7

                       98x - 392

                       -       +

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

             Remainder  385

Hence, The remainder of f(x) is 385.

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Answer:

x = 8

Step-by-step explanation:

The angles shown are vertical angles

Vertical angles are congruent (equal to each other)

This means that 8x + 36 = 5x + 60

Using this equation we can solve for x

8x + 36 = 5x + 60  

==> subtract 36 from both sides

8x = 5x + 24

==> subtract 5x from both sides

3x = 24

==> divide both sides by 3

x = 8

Answer:

8x + 36 = 5x + 60

8x = 5x + 24

3x = 24

x = 8

The possible change in volume that results from the error in measuring the radius is 32. 06 millimeters

It is important to note that the formula for volume of a sphere is expressed by;

Volume = 4/3 πr³

Given that;

Based on the information given, we have the measure of the radius to be 5 mm, with a possible measurement error of 0.1 mm

The original value of radius  = 5mm

Radius after the measurement error = 5 + 0. 1 = 5. 01mm

Let's substitute the values into the formula

Volume = 4/ 3 (3.14)(5)³

We then expand the bracket

Volume = 4/ 3 (392.5)

Volume = 523. 3 cubic millimeters

For radius of the measurement error = 5.01mm

Volume =  4/ 3 (3.14)(5.1)³

Then, expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 cubic millimeters

Change in volume = 555. 4 - 523. 3 = 32. 06 cubic millimeters

Hence, the change in volume is given as 32. 06 cubic millimeters

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The sequence {3, 6, 12, 6, 3, ...} is not a function

The sequence is given as

{3, 6, 12, 6, 3, ...}

In the above sequence, we can see that the sequence has repeated numbers

The repeated numbers are 3 and 6

These numbers are repeated twice

For a sequence of numbers to represent a function, the numbers in the sequence must be distinct

Hence, the sequence is not a function

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10 pounds of less expensive tea should be used in the mixture.

Inferior tea price = $2.00

Superior tea price = $5.00

Blended tea price = $4.25

Solution:

Price of 40 pounds of a custom blended tea = $4.25 * 40 = $170

Let x be the inferior tea quantity and

(40 - x) be the superior tea quantity.

2x + 5(40 - x) = 4.25 * 40

2x + 200 -5x = 170

-3x = -30

x = 10

Therefore, 10 pounds of less expensive tea should be used in the mixture.

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It is said that the ratio of point B to point AC is 2: 3.

This implies;

BC/AB = 3/2

BC = 3(b - a)/2

Thus;

AB + BC Equals AC

AC equals b-a plus 3(b-a)/2.

b-a - 3b/2 - 3a/2 = AC

AC = 5b/2 - 5a/2

AC = ⁵/₂(b - a) (b - a)

Using the same vector addition law, we can state that;

OC = AC – AO

OC = ⁵/₂(b - a) - (-a) (-a)

Given that giving OA is the inverse of -a, I used -a for AO.

Thus;

OC = 5b/2 - 5a/2 + a

OC = (⁵/₂)b - (³/₂)a

OC = ¹/₂(5b - 3a) (5b - 3a)

What is vector addition law?

Objects with both direction and magnitude are referred to be vectors. When two vectors have the same magnitude and direction, they are deemed to be one and the same. A line and an arrow are used to symbolize these geometrical objects. This arrow points in the direction of the vector, and the line's length indicates the vector's magnitude. These arrows, therefore, have a starting point and an ending point. Physical quantities like velocity, displacement, and acceleration are represented by vectors.

Notation A vector is frequently written in bold letters, such as an or b.

As seen on the right side, a vector may alternatively be expressed as the letters for its head and tail with an arrow above it.

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Answer:

  (d)  h(x) = 1/4x

Step-by-step explanation:

You want to know the inverse of the function f(x) = 4x.

The inverse of y = f(x) will be the solution to x = f(y).

  x = f(y)

  x = 4y . . . . . . substitute the argument in the function definition

  x/4 = y . . . . . divide by 4 to solve for y

The inverse function is ...

  h(x) = (1/4)x

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= 3 {x}^{2} + 9x - 30[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The values of x where a parabola cuts the x - axis (y = 0) are the roots of the quadratic equation.

I.e -5 and 2 for the given problem.

and the equation can be represented as :

[tex]\qquad\displaystyle \tt \rightarrow \: y = a(x - x1)(x- x2)[/tex]

where, x1 and x2 are the roots of the quadratic equation, a is a constant value (depicting strech in curve)

Now, plug in the values :

[tex]\qquad\displaystyle \tt \rightarrow \: y= a(x- 2)(x - ( - 5))[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = a(x- 2)(x+ 5)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = a( {x}^{2} + 5x - 2x - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= a( {x}^{2} + 3x - 10)[/tex]

Now, we need to find the value of a, for that let's use the coordinates of a point lying on the curve (1 , -18)

[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a( {1}^{2} + 3(1) - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a(1 + 3 - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a( - 6)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: a = ( - 18) \div ( - 6)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: a = 3[/tex]

Now, we got all required values. let's plug the value of a in equation, and we will get the required equation of parabola.

[tex]\qquad\displaystyle \tt \rightarrow \: y= 3( {x}^{2} + 3x - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= 3 {x}^{2} + 9x - 30[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

[tex]\textsf{Factored form}: \quad f(x)=3(x-2)(x+5)[/tex]

[tex]\textsf{Standard form}: \quad f(x)=3x^2+9x-30[/tex]

Step-by-step explanation:

Factored form of a quadratic function

[tex]f(x)=a(x-p)(x-q)[/tex]

where:

Given x-intercepts:

Substitute the given x-intercepts into the formula:

[tex]\implies f(x)=a(x-2)(x+5)[/tex]

To find a, substitute the given point (1, -18) into the equation and solve for a:

[tex]\implies -18=a(1-2)(1+5)[/tex]

[tex]\implies -18=a(-1)(6)[/tex]

[tex]\implies -6a=-18[/tex]

[tex]\implies a=3[/tex]

Therefore, the equation of the function in factored form is:

[tex]\boxed{ f(x)=3(x-2)(x+5)}[/tex]

Expand the brackets:

[tex]\implies f(x)=3(x^2+3x-10)[/tex]

[tex]\implies f(x)=3x^2+9x-30[/tex]

Therefore, the equation of the function in standard form is:

[tex]\boxed{f(x)=3x^2+9x-30}[/tex]

we get x=y =0 which gives 0 perimeter or x=y this implies rectangle must be a square

1. Method of Langrage Multipliers:

To find the extremum values of f(x,y) subject to constraint g(x,y) = k

find all values of x,y and λ, such that :

Δλ(f,x) = λΔg(x,y)

And  g(x,y) = k

2. let the two side of the rectangle be x and y

therefore

f(x,y) = xy And g(x,y)= 2(x+y)=p

fₓ=λgₓ => y=2λ ----------------- 1

fy = λgy => x = 2λ----------------2

using equation and 1 and 2

λ=0, but this is not possible because tis implies x = y = 0, which gives  0 perimeter

or

x=y

Hence the rectangle must be a square

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Answer:

so the width is 16/35 miles

Step-by-step explanation:

Length - 7/8 miles

Area - 8/20 miles

we know from the equation that area = Length x width

we need to rearrange so the width = Area ÷Length

width = 8/20 ÷ 7/8

= 8/20 × 8/7

= 16/35

The probability that a randomly chosen battery pack lasts longer than 260 hours is 0.69.

What is a normal distribution?

The normal distribution is a probability distribution that is symmetric about the mean and demonstrates that data that are closer to the mean are more likely to occur than data that are farther from the mean.

Since the life span of the battery pack is known to be Normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = life spans of battery packs.

µ = mean life span

σ = standard deviation

From the information given,

µ = 250 hours

σ = 20 hours

The probability that a battery pack lasts longer than 260 hours. It is expressed as

P(x > 260) = 1 - P(x ≤ 260)

For x = 260

z = (260 - 250)/20 = 0.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.69

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The probability that a randomly chosen battery pack lasts longer than 260 hours is 0.69.

What is a normal distribution?

The normal distribution is a probability distribution that is symmetric about the mean and demonstrates that data that are closer to the mean are more likely to occur than data that are farther from the mean.

Since the life span of the battery pack is known to be Normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = life spans of battery packs.

µ = mean life span

σ = standard deviation

From the information given,

µ = 250 hours

σ = 20 hours

The probability that a battery pack lasts longer than 260 hours. It is expressed as

P(x > 260) = 1 - P(x ≤ 260)

For x = 260

z = (260 - 250)/20 = 0.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.69

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2)

When we say that w = 4, it means that we can rewrite the expression and instead of "w", we will put "4", so

Now we have a numerical expression to solve, we can easily solve it!

Therefore, the final answer is

5)

Here we will do the same thing, the "hard" part is solving the numeric expression, it will be a little bit harder than the 2).

Again, repeat the same process, rewrite the expression, and instead of "m" you put "5"

Again, another expression to simplify, remember that we always solve what is inside ( ) first, and we have a multiplication inside ( ) so we must solve it first

Now we solve the multiplication inside ( ) we can do the subctration

The last step is just to solve another multiplication

Now we simplified everything we can have the final answer:

6)

Here we have a division, but it's similar with 5) and 2), we have

No secrets, repeat the process, but here, "a" will turn into "15", then

We can do the multiplication at the numerator of the fraction

Now we can simplify the fraction, 30 divided by 3 is 10, then

Now just do the sum and it's done!

Hence the final answer is

ANSWERS:

1) 43

2) 13

3) 67

4) 12

5) 39

6) 23