The age of a father is to less than seven times the age of his son in three years the sum oftheir ages will be 52 if the sons presents age is S years which equation models this situation

Answer:

Initial amount: 20

Growth factor: The amount doubles for every integer increase of x

Step-by-step explanation:

I think the equation should be g(x) = 20(2^x) for it to be exponential.

The general form of an exponential equation is g(x) = a(b^x), where a is the initial amount when x = 0, and b is the base, or growth factor.

We can see the amount double by evaluating a few value..

g(0) = 20(2^0) = 20(1) = 20   (initial amount)

g(1) = 20(2^1)  =  20(2) = 40

g(2) = 20(2^2) = 20(4) = 80

g(3) = 20(2^3) = 20(8) = 160

This pattern will continue on

Substitute y = x + 2 into y = 3x - 2

x + 2 = 3x - 2

Solve for x in x + 2 = 3x - 2

x = 2

Substitute x = 2 into y = x + 2

y = 4

Therefore,

x = 2

y = 4

Answer:

CBX and FBC

Step-by-step explanation:

because they both are supplememntary

Adjacent angles share a common vertex and side, and do not overlap. Without a diagram, specific adjacent angles cannot be identified. Angle BAB' being equal to the angle of incidence is relevant to the geometry but does not determine adjacency.

Adjacent angles are two angles that have a common vertex and a common side, but do not overlap. By definition, they are next to each other on a plane and their shared side is called the ray. In the given question, we should look for two angles that meet this criteria.

The answer is not directly provided since it seems to be referencing a diagram that we do not have. However, in general, to determine adjacent angles in a diagram, you would look for angles that share a vertex and a common side. For example, if angle GMB and angle FBC shared a side and a vertex, they would be considered adjacent angles.

Given the information that the segment AB' is shared by triangles in two different mediums, and that angle BAB' is equal to the angle of incidence, this does not directly relate to the angles being adjacent but gives insight into the geometry of the situation.

Answer:

all real values of x

Step-by-step explanation:

The domain is the values that x can take

The domain is all real values of x

Answer:all real numbers

Step-by-step explanation:

Answer:

Step-by-step explanation:

Take 20( cosine of 75 degrees)

the answer is 5 ft

Answer:

5.18 feet

Step-by-step explanation:  

We have been given that a ladder that is 20 feet long is leaning against the side of a building if the angle formed between the ladder and the ground is 75 degrees.

We can see from the attachment that side with 20 feet is hypotenuse and side x is adjacent side to the angle 75 degrees.

[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]

Substitute the given values:

[tex]\text{cos}(75^{\circ})=\frac{x}{20}[/tex]

[tex]\frac{x}{20}=\text{cos}(75^{\circ})[/tex]

[tex]\frac{x}{20}*20=20*\text{cos}(75^{\circ})[/tex]

[tex]x=20*0.258819045103[/tex]

[tex]x=5.1763809[/tex]

[tex]x\approx 5.18[/tex]

Therefore, the bottom of the ladder is 5.18 feet away from the base of the building​.

Answer: -13

Step-by-step explanation:

5y -5y cancel out and the -12-1=-13 and that’s how you get -13.

The sum or difference of the given expression (5y-12)+(-5y-1) simplifies to -13.

The original problem presented is to evaluate the expression (5y-12)+(-5y-1). The operation between the two parenthesis is a sum (as indicated by the '+').

To solve, execute the operation in each parenthesis then execute the operation between. The operation inside the first parenthesis is a subtraction, yielding 5y-12. Similarly, the operation inside the second parenthesis is also a subtraction, yielding -5y-1. However, it is a good practice to treat subtraction of whole numbers as adding a negative. Finally, the operation between the two results is a sum (5y-12+(-5y-1)).

The desired result is achieved by applying the appropriate algebraic rules. So, we can rewrite this as: (5y-12) + (-5y -1) = 5y -12 -5y -1 = 0y -13 = -13.

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Answer:

= 8.9 units

Step-by-step explanation:

When a chord intersects with a tangent outside a circle then we use the relationship;

X ² = AO × BO, Where A and are the points of intersection of the chord an the circle, while O is the point of intersection between the chord and the tangent.

Therefore;

x² = 4 × 20 or 8 × 10

x² = 80

x = √80

= 8.944

 ≈ 8.9

Answer: 8.9

Step-by-step explanation:

x² = 4 × 20 or 8 × 10

x² = 80

x = √80

= 8.944

≈ 8.9

It will be 505.85.

Because 33.5 × 15.1 is 505.85.

33.5x15.1=505.85

505.85 miles is the answer.

Answer:

Mike = m pencils

Jen  = m + 3 pencils

Total = Mike + Jen

   = m+m+3

= 2m+3

Step-by-step explanation:

step 2: Chris added the exponents when he should have multiplied them

Answer:

Step 2

Step-by-step explanation:

Find the circumference of  the circle:

C = 2PIr = 2PI6 = 12PI

Arc XPY is 3/4 of the circle.

XPY = 3/4 x 12PI = 9PI

Any smooth curve connecting two points is called an arc. The length of arc XPY is 9π cm.

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

Length of an Arc = 2π×R×(θ°/360°)

where

θ is the angle, that which arc creates at the centre of the circle in degree.

A circle has 360°, while the angle made by arc XY is 90°. Therefore, the measure of the angle made by the arc XPY at the centre of the circle is 270°. Also, the radius of the circle is 6 cm, therefore, the length of XPY is,

Length of XPY = 2π×6cm×(270°/360°) = 9π cm

Hence, the length of arc XPY is 28.2743 cm.

Learn more about the Length of an Arc:

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Answer:

x = -3, x= 0, and x = 1.5

Step-by-step explanation:

The zeros of a function f(x) refers to the x-values for which f(x) = 0.

We simply graph the function and determine the points where the graph crosses the x-axis. Thus, we shall be solving the problem graphically;

From the attachment below, the graph of f(x) crosses the x-axis at;

x = -3, x= 0, and x = 1.5

The answer is:

[tex]sin(F)=\frac{OppositeSide}{Hypotenuse}=\frac{55}{73}=0.75[/tex]

[tex]cos(F)=\frac{AdjacentSide}{Hypotenuse}=\frac{48}{73}=0.66\\\\tan(F)=\frac{OppositeSide}{AdjacentSide}=\frac{55}{48}=1.15[/tex]

Since we are working with a right triangle, we can use the Pythagorean Theorem to know the missing side size (Opposite Side).

Pythagorean Theorem formula:

[tex]c^{2}=a^{2} +b^{2}[/tex]

Where:

[tex]c=hypotenuse=73\\a=AdjacentSide=48\\b=OppositeSide[/tex]

So, the opposite side will be:

[tex]OppositeSide=\sqrt{c^{2}-a^{2}}=\sqrt{73^{2}-48^{2}}=\sqrt{5329-2304} \\OppositeSide=\sqrt{3025}=55[/tex]

Then:

[tex]sin(F)=\frac{OppositeSide}{Hypotenuse}=\frac{55}{73}=0.75[/tex]

[tex]cos(F)=\frac{AdjacentSide}{Hypotenuse}=\frac{48}{73}=0.66\\\\tan(F)=\frac{OppositeSide}{AdjacentSide}=\frac{55}{48}=1.15[/tex]

Have a nice day!

Answer:

Sin F  = 0.7534

Cos F = 0.6575

Tan F= 1.145

Step-by-step explanation:

From the given figure we can see that,

triangle DEF is right angled triangle

Base = DF = 48

Hypotenuse = EF = 73

Height = ED

To find ED

We have ,

Hypotenuse² = Base² + Height²

EF² = DF² + ED²

ED² = EF² - DF² = 73² - 482

ED² = 3025

ED = √3025 = 55

To find Sin (F)

Sin ∅ =Opposite side /Hypotenuse

Sin F = ED/EF = 55/73 = 0.7534

To find Sin (F)

Cos ∅ =Adjacent side /Hypotenuse

Cos F =DF/EF = 48/73 = 0.6575

To find Sin (F)

Tan ∅ =Opposite side /Adjacent side

Tan F = ED/DF = 55/48 = 1.145

Answer:

20

Step-by-step explanation:

But you should know this already...

Answer:

System of Linear Equations

Step-by-step explanation:

Answer:

System of linear equations

Step-by-step explanation:

Answer:

The length is 22 and the width is 18.

Step-by-step explanation:

You can solve for the length by using the perimeter formula.

P = 2l + 2w.

You know P = 80. You also know the length is l and the width is w = l - 4.

80 = 2l + 2(l - 4)

80 = 2l + 2l - 8

80 = 4l - 8

88 = 4l

22 = l

This means the width which is 4 meters less is 22 - 4 = 18.

Answer:

see below

Step-by-step explanation:

Percent means out of 100

20% = 20/100 which can be simplified

20/100   Divide by 10 on top and bottom

=2/10   Divide by 2 on top and bottom

= 1/5

80% = 80/100 which can be simplified

80/100  Divide by 10 on top and bottom

= 8/10  Divide by 2 on top and bottom

=4/5

15% = 15/100   Which can be simplified

15/100  Divide by 5 on top and bottom

= 3/20

Randy caught quails at a slower rate

Answer:

Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution.

Parallel lines will have no solution in a system of equations because they never intersect, maintaining a constant distance apart and having the same slope.

In a system of equations, two parallel lines will have no solution. This is because parallel lines never intersect; they have the same slope but different y-intercepts and maintain a constant distance from each other.

According to the theorem if two straight lines do not meet a third line on the same plane, then they do not meet each other, which confirms that they are parallel.

Hence, option (a) 'Parallel Lines' is the correct answer to which type of lines will have no solution in a system of equations. In contrast, option (b) 'Intersecting Lines' represents lines that cross at a single point and have one solution where they intersect, which corresponds to that unique solution of the system.

Answer:

2yz^2-3z^2-5y+7

Step-by-step explanation:

you find the polynomial difference between the two (remember to distribute the negative sign when opening up the parenthesis of the second polynomial. combine like terms and your left with your answer.

Answer:

3yz^2-3z^2-5y+7

Step-by-step explanation:

got it right on test ! Hello!

The question involves predicting the temperature of water after six intervals using an exponential decay function. Without the exact values to form the function, we can infer that the temperature will likely be around option (b) 101°F after six intervals based on the pattern of decrease shown in the provided intervals.

The student's question is about using an exponential function to model the temperature decrease of water as it cools at room temperature.

To solve this problem, one would generally apply the formula for an exponential decay function, which is of the form w(t) = [tex]a * e^{(kt)[/tex], where w(t) is the temperature at time t, a is the initial temperature, e is the base of the natural logarithm, and k is the decay constant. Given the temperatures at specific intervals, one could use these to estimate the constants a and k.

However, without the necessary values to develop an equation, we instead look for the pattern in the temperature's decrease to predict the sixth interval's approximate temperature.

Examining the table provided:

We can see that the temperature is decreasing less with each interval. While it is not explicitly stated, it's reasonable to assume that an exponential decay function would fit this scenario. Without the exact function, we can make an educated guess based on the trend that after six intervals, the temperature will be less than 121°F and likely close to option (b) 101°F.

Answer:

YL=130 (PWP)

m<YPL=65 (Inscribed < th)

Step-by-step explanation:

Answer:

[tex]m\angle YPL=65^{\circ}[/tex]

Step-by-step explanation:

We have been given an image of a circle and we are asked to find the measure of angle YPL.

Since the degree measure of circumference of a circle is 360 degrees, so we can set an equation to find the measure of arc LY as:  

[tex]m\widehat{LY}+m\widehat{PL}+m\widehat{PY}=360^{\circ}[/tex]

Upon substituting our given values in above equation we will get,

[tex]m\widehat{LY}+80^{\circ}+150^{\circ}=360^{\circ}[/tex]

[tex]m\widehat{LY}+230^{\circ}-230^{\circ}=360^{\circ}-230^{\circ}[/tex]

[tex]m\widehat{LY}=130^{\circ}[/tex]

We can see that angle YPL is inscribed angle of arc LY, so the measure of angle YPL will be half the measure of arc LY.

[tex]m\angle YPL=\frac{1}{2}m\widehat{LY}[/tex]

[tex]m\angle YPL=\frac{1}{2}\times130^{\circ}[/tex]

[tex]m\angle YPL=65^{\circ}[/tex]

Therefore, the measure of angle YPL is 65 degrees.

The answer is C

Explanation; there are 2 triangles and 3 rectangles

The statement that describes the net of the prism is:

       C. Two triangular bases and three rectangular lateral faces

Net of a solid--

A net is a two dimensional figure which can be folded to get a three dimensional figure.

or we may say it is a pattern which is made when we scatter out different faces of the solid or three dimensional figure.

Answer:

The correct options are 1, 2, 3 and 4.

Step-by-step explanation:

The given function is

[tex]f(x)=2^x[/tex]

The above function is defined for all the values of x.

⇒ Therefore the domain is all real numbers x because the exponent of 2 can be any real number.

⇒ The x is exponent of 2, therefore the x-values increases by 1 unit, the y-value multiplies by 2.

Put x=0, to find the y-intercept.

[tex]f(x)=2^=1[/tex]

⇒The y-intercept is (0, 1).

The value of f(x) is always greater than 0 because powers of 2 are never negative.

[tex]f(x)>0[/tex]

⇒The graph never goes below the x-axis because powers of 2 are never negative.

⇒Therefore the range of the function is all positive real numbers.

Therefore the correct options are 1, 2, 3 and 4.

The True statements about the graph of the function [tex]y =2^x[/tex] are option a), b), c) and d). Refer the below solution for better understanding.

Given :

[tex]y = 2^x[/tex]

Solution :

Domain is all real numbers x because the exponent of 2 can be any real number.

x is exponent of 2, therefore the x-values increases by 1 unit, the y-value multiplies by 2.

At [tex]x=0[/tex],

[tex]y=2^0=1[/tex]

y intercept -- (0 , 1).

y is always greater than zero because power of 2 never be negative.

Graph never goes below the x-axis because powers of 2 are never be negative.

The range of the function is all positive real numbers.

Therefore all the options are correct.

For more information, refer the link given below

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To make 8 from 53/6, you need to subtract 5/6. This solution involves converting 8 to the same denominational fraction as 53/6 (which is 48/6) and then subtracting this from 53/6.

The question asks how much you need to subtract from 53/6 to make 8. To find out, we start by expressing the desired final number and the given fraction:

This demonstrates a basic understanding of fraction subtraction and the concept of working backwards to solve a problem, both of which are key skills in mathematics.

Answer:

Google says 9?

Step-by-step explanation:

Answer:

B. 6,700 m

Step-by-step explanation:

Mr. Gephart is traveling from his house to the history museum = 6.7 km

1 km = 1,000 m

so

6.7 x 1,000 = 6,700 m

Answer is B. 6,700 m

Answer:

Step-by-step explanation:

B. 6,700m

Answer:

Refer to step-by-step.

Step-by-step explanation:

To find the LCD of the different fractions, we first need to follow the steps of finding the LCD of algebraic fractions.

1st step: Factor

You need to factor out the expressions if they do not have a difference of two squares.

2nd step: Find the LCD of the coefficients.

You need to find the LCD of the coefficients before moving onto the variables.

3rd step: The variable part of the LCD will be every single variable you see, with the highest exponent.

So let's begin, since all the given denominators are already factored out, we can proceed straight to step 2.

[tex]\dfrac{5}{9m^{2}n}and\dfrac{5}{16mn^{3}}[/tex]

Now since we're dealing with the denominators, let's focus on them alone.

The LCD of 9 and 16 is 144

The LCD of variables m² and m is m²

The LCD of variables n and n³ is n²

So the LCD of the algebraic fractions [tex]\dfrac{5}{9m^{2}n}and\dfrac{5}{16mn^{3}}[/tex] is:

144m²n³

Now to the next one.

[tex]\dfrac{5+m}{8m^{4} n^{2} }and\dfrac{5+n}{18m^{2} n^{4} }[/tex]

The LCD of 8 and 18 is 72

The LCD of variables [tex]m^{4}[/tex] and m² is [tex]m^{4}[/tex]

The LCD of variable n² and [tex]n^{4}[/tex] is [tex]n^{4}[/tex]

So the LCD of the algebraic fractions [tex]\dfrac{5+m}{8m^{4} n^{2} }and\dfrac{5+n}{18m^{2} n^{4} }[/tex]is:

[tex]72m^{4} n^{4}[/tex]

Next one we have:

[tex]\dfrac{m+n}{12mn}and\dfrac{n+m}{18m^{3}n }[/tex]

The LCD of 12 and 18 is 36

The LCD of m and m³ is m³

The LCD of n and n is n

So the LCD of the algebraic fractions [tex]\dfrac{m+n}{12mn}and\dfrac{n+m}{18m^{3}n }[/tex] is:

36m³n

Last but not the least.

[tex]\dfrac{m-n}{24mn^{4}}and\dfrac{m-n}{16m^{4}n }[/tex]

The LCD of 24 and 16 is 48

The LCD of m and [tex]m^{4}[/tex] is [tex]m^{4}[/tex]

The LCD of [tex]n^{4}[/tex] and n is [tex]n^{4}[/tex]

So the LCD of the algebraic fractions [tex]\dfrac{m-n}{24mn^{4}}and\dfrac{m-n}{16m^{4}n }[/tex] is:

[tex]48m^{4} n^{4}[/tex]

Answer:

The answer is 50

Step-by-step explanation:

You add up all the numbers and divide the numbers by how many numbers there are.

The answer would be 50!

ANSWER

[tex](f\circ g)(x) = - 8 {x}^{2} + 4[/tex]

EXPLANATION

Given f(x)=-8x+4

and

g(x)=x²

We want to find find an expression for;

[tex]

(f\circ g)(x) = f(g(x))[/tex]

[tex]

(f\circ g)(x) = f( {x}^{2} )[/tex]

We substitute x² into f(x)=-8x+4

This will give us:

[tex]

(f\circ g)(x) = - 8 {x}^{2} + 4[/tex]