Let the function f be defined as p (x) = -5 (-3x + 4) and function g be
defined as m (x)= 5x - 2 (5x - 6). What value of x satisfies the
equations m (x)= p (x)?

Answer:

164 minutes

Step-by-step explanation:

$8 + $0.06m = $17.84

To isolate the m, first bring the eight to the other side

0.06m = 9.84

then divide both sides by 0.06

m = 164

Answer:

(-11/24)

Step-by-step explanation:

  3         5

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

  8         6

 3(3)    5(4)

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

 8(3)     6(4)

  9        20       - 11

------- - ------- = -------

  24      24        24

I hope this helps!

The actual roots ordered from least to greatest is -45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45

Rational roots are roots of a quadratic equation which can be expressed as a ratio or are elements of rational numbers.

Since we have that the possible rational roots are  ±1, ±3, ±5, ±9, ±15, and ±45.

We list the actual roots as follows

+1, -1, +3, -3, +5, -5, +9, -9, +15, - 15, +45 and -45

Since we require the actual roots from least to greatest knowing that the largest negative number is the least and tha largest positive number is the greatest, rearranging, we have

-45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45

So, the actual roots are -45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45

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The given expression is proved by the necessary changes.

cosec 2A + cosec 4A = cot A - cot 4A​

Cosec 2 A + Cot 4 A = Cosec 4 A - Cot 2 A

Taking LHS  :

⇒Cosec 2 A + Cot 4 A

⇒Cosec 2 A + ( Cot 2 A )2

⇒Cosec 2 A + ( Cosec 2 A - 1 )2    (  we know:1+ Cot 2 θ =  Cosec 2 θ )

⇒Cosec 2 A +  Cosec 4 A  + 1  - 2 Cosec 2 A

⇒ Cosec 4 A  + 1  - Cosec 2 A

⇒ Cosec 4 A  + 1  - ( 1 + Cot 2 A)

⇒ Cosec 4 A  + 1  -  1 - Cot 2 A

⇒ Cosec 4 A  - Cot 2 A

or cosec2A+cosec4A=cotA-cot4A

Hence Proved.

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The expression x³ + 3x² - 10x + 24 cannot be factorized

From the question, the polynomial is given as

x3+3x2−10x+24

Rewrite the polynomial properly

So, we have the following representation

x³ + 3x² - 10x + 24

Next, we represent the above expression on a graph

From the attached graph, we can see that the polynomial expression only cross the x-axis at x = -5.569

This implies that the expression cannot be factored

So, we cannot further rewrite the given expression

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The Ratio of money made by Jackie and Liana by selling lemonade is 2/3

What does a math ratio mean?

Definitions: If b is not equal to 0, then an ordered pair of numbers a and b, denoted as a/b, is a ratio. A proportion is an equation that equalizes two ratios. You could, for instance, write the ratio as follows: 1: 3 in the case of 1 boy and 3 girls.

How is a ratio calculated?

By typically dividing two figures, ratios contrast them. If you were comparing one data point (A) to another data point, your formula would be A/B. (B). You are multiplying information A by information B, as indicated by this. For instance, if A is 5 and B is 10, your ratio will be 5/10.

Given that

Jackie earn = $24

Liana earn = $36

Ratio of their earning = 24/36 = 2/3

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The other ways of rewriting the expression are (xˣ)⁽²⁾ or xˣ²

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

x^(x^2)

Rewrite the expression properly

So, we have the following representation:

x⁽ˣ⁾⁽²⁾

The only ways the above expression can be rewriting the expression is by changing the positions of the brackets or removing the brackets entirely

Other than that, there are no other ways of rewriting the expression

So, we have

(xˣ)⁽²⁾ or xˣ²

Hence, the expressions are (xˣ)⁽²⁾ or xˣ²

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The interest is $57 on a $1900 investment at 3% for 1 year

Given,

In the question:

Principal = $1900

Rate of interest = 3%

Time = 1

Now, According to the question:

Principal = $1900

Rate of interest = 3%

Time = 1

Substitute:

Principal = $1900

Rate of interest = 3%

Time = 1  into formula Interest = P x R x T

I = 1900 x 0.03 x 1

Calculate the product or quotient:

I = 57

Hence, The interest is $57 on a $1900 investment at 3% for 1 year.

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The probability that a woman has a malignant tumor in her breast is 7.5%. ie 75

Let  + = mammogram result is positive

B = tumor is benign

M = tumor is malignant.

Note that Bc = M.

given that P(M) = .01,

so P(B) = 1 − P(M) = 0.99.

We are also given the conditional probabilities

P(+ | M) = .80 and

P(− | B) = .90, where the event − is the complement of +

P(+ | B) = .10

Bayes’ formula:-

P(M | +) = P(+ | M) P(M) / (P(+ | M)P(M) + P(+ | B)P(B))

= 0.80 × 0.01 / (0.80 × 0.01 + 0.10 × 0.99)

=0.075

So the chance would be 7.5%. ie 75

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The relation that is a function in the option is graph C.  

A function relates an input to an output.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

In a simpler term, a function relates each element of a set with exactly one element of another set (possibly the same set).

In a function, the x value is exactly related to a single y value,  exactly, means that a function is single valued. It will not give back 2 or more results for the same input.

Therefore, the only graph that follows the rule of a function is graph C.

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They will require 4 (4/11) days to complete the remaining work together.

Time is the duration during which any activity or work happens or continues.  Work is a task or set of activities to achieve a certain result

It takes Ann alone 10 days to translate a document.

Ann's work in one day = 1/10

In 2 days = 2 / 10

Work left = 8 / 10

Ben alone now takes 12 days to translate a document.

Ben's work in one day = 1/12

We will now use addition.

Combined work of both Ann and Ben in 1 day = 1 / 10 + 1 / 12 = 11 / 60

Time taken to complete the rest of the work = 8 / 10 ÷ 11 / 60

= 48 / 11 = 4.4 days.

As a result, they need 4 (4/11) days to finish the remaining work together.

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The ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint 4:9.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint.

So, the ratio of gallons of blue paint to gallons of yellow paint is

= 5 to 9  or 5:9

Now, ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint

= 1- 5/9

=4/9

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We see BC is in the middle of the lines AB and BD, therefore mABC + mCBD = mABD.

We're given mABD = 75, mABC = 40.

Therefore, mCBD = mABD - mABC = 75 - 40 = 35.

Answer:

∠CBD = 35°

Step-by-step explanation:

We are told in the question that m∠ABD = 75° and m∠ABC = 40°. We are then asked what the value of m∠CBD is.

As we can see from the diagram, ∠ABD is made up of the angles ABC and CBD. Therefore:

∠ABD = ∠ABC + ∠CBD

⇒ 75° = 40° + ∠CBD

⇒ 75° - 40° = 40° + ∠CBD - 40°       [

⇒ 35° = ∠CBD

∴ ∠CBD = 35°

Answer:

y = 12

Step-by-step explanation:

We'll use the form of an equation of a straight line of y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

We are told the slope, m, is -2.

That leads to:  y = -2x + b

y = -2x + b

B, the y-intercept, can be found by using the given point (3,28) in the equation (it falls on the line, so must be a valid solution to the equation.  Use the given x and y in the equation and solve for b:

            y = -2x + b

           28  = -2*(3) + b

           28  = -6 + b

b = 34

The equation is y = -2x + 34

Use this to find y when x = 11:

  y = -2(11) + 34

  y = -22 + 34

  y = 12

y is 12 when x is 11

     See the attached graph.

do you mean 712 or 7.12?

If for 712 it is 1808.48

if for 7.12 it is 18.0848

The value of Angle DAF, x is 21°

Given,

Line BC parallel to line DE

The value of Angle ABC = 54°

The value of Angle BAC = 105°

We have to find the value of angle DAF

Here,

Angle DAF = x

Now,

Angle ABC = Angle DAB (Alternate interior angles)

So,

Angle DAB = 54°

Then,

Angle DAF, x = 180 - (105 + 54) (Linear pair of angles)

Linear Pair of Angles;

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.

That is,

Angle DAF, x = 180 - 159

Angle DAF, x = 21°

Therefore,

The value of Angle DAF, x is 21°

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An open circle at 5 and a bold line starting at 5 and pointing to the right (>) is the correct representations of the inequality

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given: the inequality –3(2x – 5) < 5(2 – x)

First, we have to solve for x in the inequality

–3(2x – 5) < 5(2 – x)

Clear the parenthesis:

-6x + 15 < 10 - 5x

Collect like terms:

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1:

x > 5              ( Note:  Divide both sides by -1 will change the < to > )

This is what will determine our answer

Since our answer is x > 5.  An open circle will be at 5 and a bold line starts at 5 and is pointing to the right (>)

Therefore, the correct representations of the inequality is  an open circle is at 5 and a bold line starts at 5 and is pointing to the right r

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Answer: .................................................

how many ways can the seating be arranged?

answer = 128 ways

correct or what???

The two-column table to prove ∠ABC ≅ ∠DBE using the angle addition postulate is presented as follows;

Statements  [tex]{}[/tex]                                                  Reasons

1. ∠ABD is a right angle   [tex]{}[/tex]            1. Given

∠CBE is a right angle

2. ∠ABD are complementary  [tex]{}[/tex]    2. Definition of complementary angles

3. ∠CBE are complementary  [tex]{}[/tex]     3. Definition of complementary angles

4. ∠ABC ≅ ∠DBE   [tex]{}[/tex]                       4. Congruent complements theorem

The angle addition postulate states that the when two angles are placed side by side such that they share a common ray, the measure of the angle formed by the two angles is the sum of the measure of the individual angles.

∠ABD = ∠ABC + ∠CBD (angle addition postulate)

∠ABD = 90° (definition of right angle)

∠ABC + ∠CBD = 90° (substitution property of equality)

∠ABC and ∠CBD are complementary (definition of complementary)

Similarly

∠CBE = ∠CBD + ∠DBE (angle addition postulate)

∠CBE = 90° (definition of right angle)

∠CBD + ∠DBE = 90° (substitution property of equality)

∠CBD and ∠DBE are complementary (definition of complementary)

∠ABC is a complementary angle to ∠CBD and ∠DBE is a complementary angle to ∠CBD

Therefore;

∠ABC is congruent to ∠DBE (congruent complements theorem)

The congruent complement theorem states if an angle ∠A is a complement to an angle ∠C and if an angle ∠B is also a complement of angle ∠C then ∠A is congruent to ∠B.

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The coordinates of G' after the rotation = (6, 5)

In this question we have been given a point G, located at (-5, 6) is rotated 270° counterclockwise.

We need to find the coordinates of G' after the rotation.

a point (-5, 6) is located in the second quadrant.

First 90° counterclockwise rotation gives (-6, -5)  because x & y are interchanged and in Quadrant III both coordinates will be negative.

Second 90° counterclockwise rotation yields (5,-6) because x & y are interchanged and in Quadrant IV the y coordinate will be negative.

Last 90° counterclockwise rotation yields (6, 5) because x & y are interchanged and in Quadrant I both coordinates will be positive.

Therefore, the coordinates of G' after the rotation = (6, 5)

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Part a: Monthly percent rate = y/x

Part b:  APR = y/x × 12.

For the given question;

Average daily balance sheet of Suzanne's is  x dollars.

Finance charges = y

Part a: monthly percentage rate

Finance charge = Monthly percent rate × Average daily balance

Monthly percent rate = Finance charge/Average daily balance

Monthly percent rate = y/x

Part b: APR

Thus,

For 12 months.

APR = y/x × 12

Thus, the value of APR for the period of 12 months is APR = y/x × 12 .

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The cost of a pizza with an 11 inch radius is  $26.86

In this question, the cost of a pizza varies directly as the square of its radius.

Let C be the cost of pizza and r be the radius of Pizza.

We have been given the direct proportionality between the cost of pizza and the radius of Pizza.

C ∝ r²

If a pizza with a 6 inch radius costs $8.00

8 = k * 6^2

where k is the proportionality constant.

8 = k * 36

k = 0.222

We need to find the cost of pizza with an 11 inch radius.

so, we get an equation,

C = k * 11^2

substitute above value of k

C = 0.222 * 11^2

C = 0.222 * 121

C = $26.86

Therefore, the cost of a pizza with an 11 inch radius is  $26.86

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Answer:   17/2578  (Decimal: 0.006594)

Step-by-step explanation:

That's the answer :)

The scale factor in the simplest form of a fraction of the triangles will be 43/78.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

The triangle on the right is a scaled duplicate of the triangle on the left.

The ratio of the side of a big triangle to the side of a small triangle. Then we have

Scale factor = 43 / 78

The scale factor in the simplest form of a fraction of the triangles will be 43/78.

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The equation that models the total amount of money y you pay if you buy x yards of fabric is y = 9.50x - 6

Given,

You have a coupon for a $6 discount at a fabric shop. You purchase fabric for $9.50 per yard.

We have to find an equation that models the total amount of money y you pay if you buy x yards of fabric.

Here,

The equation for the situation be like;

y = 9.50x - 6

Where,

y is the total amount paid

x is the number of yards of fabric you bought

That is,

The equation that models the total amount of money y you pay if you buy x yards of fabric is y = 9.50x - 6

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Answer:

128

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]14^2+x^2=18^2 \\ \\ 196+x^2=324 \\ \\ x^2=128 \\ \\ x=\sqrt{128}[/tex]

The answer is 3/25π m/h.

acc to our question-

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

hence,The answer is 3/25π m/h.

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