The age of a father is 2 less than 7 times the age of his son. In 3 years, the sum of their ages will be 52. If the son’s present age is s years, which equation models this situation? A. B. C. D.

By algebraic handling and factoring, we conclude that the equivalent equation for the expression - 7 · x - 60 = x² + 10 · x is (x + 5) · (x + 12) = 0.

In this question we have a quadratic function which must be factored by algebraic handling:

- 7 · x - 60 = x² + 10 · x

x² + 10 · x + 7 · x + 60 = 0      Compatibility with addition/Modulative property

x² + 17 · x + 60 = 0      Definition of addition

(x + 5) · (x + 12) = 0      x² + (- a - b) · x + a · b = 0/Result

By algebraic handling and factoring, we conclude that the equivalent equation for the expression - 7 · x - 60 = x² + 10 · x is (x + 5) · (x + 12) = 0.

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Answer:

[tex]6n \geq -24[/tex]

Step-by-step explanation:

First let's provide a variable for "a number" and call it [tex]n[/tex].

So "six times a number" could be written as [tex]6*n[/tex].

"Is at least" in mathematical terms means "greater than or equal to" or

≥

Putting this altogether gives the expression:

[tex]6n\geq -24[/tex]

Answer:

3

Step-by-step explanation:

18-15=3

Answer:

first option, 3

Step-by-step explanation:

The interquartile range is the difference between Q3 and Q1.

Q1 is the lower bound of the box = 15

Q3 is the upper bound of the box = 18

 Q3 - Q1

= 18 - 15

= 3

The answer is:
   " m∠BAC = 45° ;  m∠ABC, = 64° ; and:  m∠ACB = 70° ."
__________

Step-by-step explanation:

To find the measure of ∠BCA {"m∠BCA"} :

<BCA is supplementary to " 110 " ; that is, both, or all, of all the measurements that form a "line or line segment";  or any portions thereof,

that can be written in:  "slope-intercept format"

  that is, on Cartesian plane:  " y = mx + b " ;

  in which:  "y" is isolated on the "left-hand side" of the equation; as a single, isolated variable;

  and in which:  "m" is the "slope" (if applicable); and the coefficient to the "x"  value'

  and in which "b" is the "y-intercept"; or more precisely"
    the value of the "y-coordinate"—in: "(x, y)" format —at which:
    " x = 0" ; that is, in the format:  " (0, b)."
_________________
So, to find
m∠BCA :  Subtract our given value, "110" ; from "180" ; as follows:
_________________

  " (180 − 110) = 70" ;
__________________
Now:   Note a triangle, by definition, has 3 (three) sides and 3 (three) angles—and all three (3) angles of a triangle add up to 180°.

So:  We just solved for  m∠ACB ; which is:  70° .

Now shall solve for the value of "x" ; & then find the value of all 3 (three) sides of this triangle

Since all angles within a triangle add up to 180: Let's add them up:
  " 70  +  3x + 20 + 3x = 180 " ;

 Combine the "like terms" on the "left-hand side" of the equation:
  " +3x + 3x = 6x " ;  "+ 70 + 20 = 90 ";
And rewrite the equation:
  "  6x + 90 = 180 " ;

Now, subtract "90" from Each Side of the equation:
  "  6x + 90 − 90 = 180 − 90 " ;
to get:   " 6x = 90 " ;

Now, divide Each side of the equation by "6" ;

  to isolate "x" on one side of the equation ;
    and to solve for "x" :
   " 6x / 6 = 90 / 6 ;

to get:  " x = 15 " ;
________________
Now, we are asked to find:
1)  " m∠BAC = 3x " ;  Plug in "15" for "x" ; and solve:
                     "3x = 3(15) = 45 " ;
2)  " m∠ABC = "(3x + 20)" ; Plug in "15" for "x"; and solve:
                     "3(15) + 20 = 45 + 20 = 65 " ;
3)  " m∠ACB  = 70 " ; (as per our calculated value);

To check our work—do these 3 (three) numbers add up to 180?

   "45 + 65 + 70 =? 180 ? " ;

   " 110 + 70 = " 180 "? Yes!
__________
So: The answer is as follows:
   " m∠BAC = 45° ;  m∠ABC, = 64° ; and:  m∠ACB = 70° ."
__________
Hope this is helpful to you!  Best wishes!

the answer is XG and that is the answer to your question ❓ ok she will he hi she

Explanation:

Normally x = 1 maps to y = f(x) = 1 for the parent function f(x) = x^2

However, the red curve shows x = 1 leads to y = 16 instead. This is a jump of "times 16"

We must multiply the f(x) outputs by 16 to get the g(x) outputs.

g(x) = 16*f(x)

g(x) = 16x^2

Deductive Reasoning is the practice of arriving at a mathematical conclusion by simply analyzing the facts using the knowledge of the related concepts.

Looing at ΔOAB and ΔOEF

It is clear that

OB = OF (O is the midpoint)

∠OBA = ∠OFE = 90°

Therefore

∠AOB = ∠EOF (Vertically Opposite Angles)

⇒ ΔOAB ≅ ΔOEF and

∠ A ≅ ∠E.

QED

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Answer:

2M + 3  hrs

Step-by-step explanation:

Lisa spent doing her mathematics homework = M  hrs

the amount of time spent watching television was 3 hours more than twice the time she spent doing her mathematics homework.

lisa spent on watching television = 2M + 3  hrs

Total time spent on these two activities = M + 2M + 3

= 3M + 3 hrs

3 M  +  3 = 30

=> 3M  = 27

M = 9

The area of a regular polygon is one-half the product of its apothem and its perimeter. Often the formula is written like this: Area=1/2(ap), where a denotes the length of an apothem, and p denotes the perimeter.

Step-by-step explanation:

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Answer:

See below

Step-by-step explanation:

mx + b = y           subtract 'b' from both sides of the equation

mx = y - b            now, divide both sides by 'x'

m  = (y-b)/x

The cuboid can hold 27.2 cubic inches of popcorn

A right rectangular prism is also called the cuboid. it is a solid three dimensional shape with 6 faces, 12 edges and 8 vertices.

Analysis:

Volume of cuboid = length x width x height

                              = 5 x 3 x 29/4 = 108.75 cubic inches

When it is quarter full, volume = 1/4 x 108.75 = 27.2 cubic inches

In conclusion, the volume of the cuboid is 27.2 cubic inches.

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Answer:

60%

Step-by-step explanation:

So, this question is saying the bowls can be between a diameter of 6.95 and 7.05

Box 1, 3 and 5 are in this margin.

Box 2 and 4 are not.

3/5 boxes can be included.

3/5 is 6/10

6/10 is 60%

[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]

[tex] \sf x - \frac{4}{x} + C[/tex]

Step-by-step explanation:

[tex] \sf \longmapsto \int \frac{ {x}^{2} + 4 }{ {x}^{2} }dx \\ \\ \\ \sf \longmapsto \int \frac{ {x}^{2} }{ {x}^{2} } dx + \int \frac{4}{ {x}^{2} } dx \\ \\ \\ \sf \longmapsto \int 1dx + 4 \int \frac{1}{ {x}^{2} } dx \\ \\ \\ \sf \longmapsto x + 4( \frac{{x}^{ -2 + 1}}{ -2 + 1} ) + C \\ \\ \\ \boxed{ \longmapsto x - \frac{4}{x} + C} [/tex]

The vertical asymptotes are x = 2 and horizontal asymptotes are y = 3 and the parent graph is shifted two to the right and three to the top.

It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.

We have a graph of a hyperbola:

[tex]\rm y=\dfrac{\left3x+14\right}{x-2}[/tex]

The above equation represents the hyperbola.

We can write the above equation as:

[tex]\rm y=3+\dfrac{\left20\right}{x-2}[/tex]

The vertical asymptotes: x = 2

The horizontal asymptotes: y = 3

Thus, the vertical asymptotes are x = 2 and horizontal asymptotes are y = 3 and the parent graph is shifted two to the right and three to the top.

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To solve this, we need to use our trigonometric equations:

 ⇒ look at the diagram attached

Let's examine what the problem wants:

Let's examine what the problem gives us:

Let's solve:

  [tex]tan(27)=\frac{x}{15} \\x=15*tan(27)\\x=7.64[/tex]

Answer: 7.6 (rounded to the nearest tenth)

Hope that helps!

Answer:

Step-by-step explanation:

Proof

AB||CD                          Given

<1 = <2                           Given

<2 = <3                          Alternate interior angles of Parallel lines

<1 =  <3                          Substitution for <2 from Given.

AC = AB                        the sides opposite equal angles are equal

Answer:

CE = 4.6 ft

Step-by-step explanation:

(a)

given 2 secants drawn from an external point to the circle , then

the product of the external part of one secant and the entire secant is equal to the product of the other secant's external part and that entire secant, that is

BE × BC = AB × DB

(b)

substituting given values into the equation

BE × 10 = 3 × 18

10 BE = 54 ( divide both sides by 10 )

BE = 5.4 ft

then

CE = CB - BE = 10 - 5.4 = 4.6 ft

Answer:

x = 1

Step-by-step explanation:

-33 + 8x = -9x - 18 + 2

8x+ 9x = -18 + 2 + 33

17x = -16 + 33

17x = 17

x = 1

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The fraction of the red haired students are boys will be 2 / 5.

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The dual bar chart shows the hair colour of boys and girls in a year group.

The total number of the boys and girl will be

Total = 6 + 9

Total = 15

Then the fraction of the red haired students are boys will be

⇒ 6 / 15

⇒ 2 / 5

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[tex]~~~~~~~c = \dfrac{a^2 +3b}{4}\\\\\implies 4c = a^2 +3b\\\\\implies 3b = 4c-a^2\\\\\implies b = \dfrac{4c-a^2}{3}[/tex]

Answer:

b = [tex]\frac{(4c-a^2)}{3}[/tex]

Step-by-step explanation:

[tex]c=\frac{a^{2}+3b }{4}[/tex]

First, let us multiply both sides by 4.

4c = a² + 3b

Now let us take a² to the left side.

4c - a² = 3b

Now to make b as the subject let us divide both sides by 3.

[tex]\frac{(4c-a^2)}{3} =\frac{3b}{3}[/tex]

Therefore,

b = [tex]\frac{(4c-a^2)}{3}[/tex]      

Answer:

2 feet

Step-by-step explanation:

1 foot = 12 inches

2 feet=24 inches

Answer:

2 feet

Step-by-step explanation:

12 x 2 is 24.

In the scenario above,  James can we create a function to combine the two by   f ( x ) = 8 x + 118.

In the question above, to be able to create a function, we have to show that;

s ( x ) = 102  

a ( x ) = 8 ( x + 2 )

So, a function that combines the two will be:

f ( x ) = s ( x ) + a ( x ) = 102 + 8 ( x + 2 ) =

= 102 + 8 x + 16

Therefore    f ( x ) = 8 x + 118

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The worth of the cd at the end of 7 years will be $384,101.79.

When an investment earns an interest that is compounded continuously, it means that it earns interest continuously.

The formula for calculating future value when there is continuous compounding is : A x e^r x N

Where:

2375 x (e^3.14) x 7 = $384,101.79

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Step-by-step explanation:

I think 2.20e23 because it said bodies not body

Answer:

Given units of measures of volume:

Units of measure:

1. Water in a rectangular pool → m³

2. an ice cube before it melts → cm³

3. a dice → mm³

4. a blackboard eraser → cm³

5. oil in a rectangular box → dm³

To convert liters to cubic meters, divide by 1000:

⇒ 6700 L³ = 67000 L = 6700 ÷ 1000 = 6.7 m³

To convert liters to cubic centimeters, multiply by 1000:

⇒ 28 L³ = 28 L = 28 × 1000 = 28,000 cm³

Answer:

slope = - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

given f(4) = 6 and f(- 2) = 8 , then 2 points on the line are

(4, 6 ) and (- 2, 8 )

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (- 2, 8 )

m = [tex]\frac{8-6}{-2-4}[/tex] = [tex]\frac{2}{-6}[/tex] = - [tex]\frac{1}{3}[/tex]

Answer:

K=4.44444444444

Step-by-step explanation:

k/6=15/18.

Cross multiply.

k*18=18k.

6*15=80.

18k=80.

18k/18=80/18.

k=4.44444444444

Answer:

The correct answer is 742,000

Step-by-step explanation:

Answer:

742,000

Step-by-step explanation:

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