‼️‼️‼️‼️HELP‼️‼️‼️

Ron is 3 years older than Sherry, who is 4
years less than twice as old as John. Which of
the following represents Ron's age, if J = John's age?

[tex]3x + y = - 4 \\ 3x + 0 = - 4 \\ 3x = - 4 \\ x = \frac{ - 4}{3} = - 1.333[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

◉ [tex] \bm{Last \: option \: (D.)}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Write the equation in slope-intercept form. Then solve y.

▪ [tex]\small\longrightarrow \sf{3x-3x + y = −3x -4}[/tex]

▪ [tex]\small\longrightarrow \sf{y= -3x-4}[/tex]

Identify the x-intercept,

[tex]\small \sf \longrightarrow{3x + 0 = - 4}[/tex]

[tex]\small\longrightarrow \sf{3x=-4}[/tex]

[tex]\small\longrightarrow \sf{x = - \dfrac{4}{3} }[/tex]

[tex]\small\longrightarrow \sf{x = -1.33}[/tex]

The graph has the next properties:

[tex]\small\longrightarrow \sf{Slope: \: 3}[/tex]

[tex]\small\longrightarrow \sf{x-intercept: \: (-1.33,0)}[/tex]

[tex]\small\longrightarrow \sf{y-intercept: \: (0,4) }[/tex]

A rule which describes the transformations that maps ΔJKL to ΔJ"K"L" is: D. translation of -2 units x, 0 units y composition 90 degree rotation about point 0.

A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on the diagram (see attachment), we can infer and logically deduce that a rule which describes the transformations that maps triangle JKL to triangle J"K"L" is a rotation of 90 degrees about the origin and then translated 2 units left.

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Answer:

5.75 - 5 3/4

Step-by-step explanation:

1 Cup = 0.0625 gallons

92 cups = 5.75 gallons

The distance from Balloon A to Balloon B, d ≈ 1,052 feet

What is distance ?

The given parameters are;

The angle at which Balloon A rises, x° = 50° above horizontal

The angle at which Balloon B rises, y° = 78° above horizontal

The (vertical) distance of Balloon A to the ground, h = 1,000 ft.

The required parameter;

The distance from Balloon A to Balloon B, d

We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule

Let,

The height of the balloon strings are equal

The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.

The distance of the Balloon A  from Charlie, l₁, is given as follows;

l₁ × sin(x°) = h₁

∴ l₁ = h₁/(sin(x°))

Which gives;

l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.

l₁ ≈ 1,305.41 ft.

For Balloon B, we get;

h₁ = h₂ = 1,000 ft.

∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.

l₂ ≈ 1,022.34 ft

The angle between the balloon strings, θ = 180° - (x° + y°)

∴ θ = 180° - (50° + 78°) = 52°

The angle between the balloon strings, θ = 52°

By cosine rule, we have;

d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))

∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet

Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet

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Answer:

14 children

Step-by-step explanation:

Half the children like pets and a quarter of the children do not, so another quarter does not have preference. Let x = total number of children, and we would have this equation.

0.25x = 7

x = 28

Since we are asked to give the number of children who like pets, 28/2 = 14 is the answer.

The power series representation for the function, so the interval of convergence is (-9,9).

The definition of convergence refers to 2 or more matters coming together, joining collectively, or evolving into one. An example of convergence is when a crowd of people all move collectively into a unified organization.

Convergence is when two or extra matters come collectively to shape a brand new whole, like the convergence of plum and apricot genes within the plucot. Convergence comes from the prefix con-, meaning collectively, and the verb verge, because of this to show closer to.

The simple concept of convergence permits multiple responsibilities to be accomplished on a single device, which efficiently conserves space and power. for example, as opposed to wearing separate devices – like a cell cellphone, digital camera, and virtual organizer – each era converges on a single tool or telephone.

We have given f(x)=1/(9+x)

f(x)=(1/9)*(1/(1-(-x/9))

f(x)=summation of (n=0 to infinity) [1/9*(-x/9)n]

=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]

f(x)=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]

Let an=(-1)n*(xn/9n+1)

using the Ratio Test

L=lim n-->infinity|an+1/anL=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]/[(-1)n*(xn/9n+1)]|

=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]*[9n+1/(-1)n*(xn)]|

=lim n-->infinity|(-1)*(x)/9)|

=|-x/9|<1

x/9<1 and x>9>-1

x<9  and x>-9

x is -9<x<9

for x=9 the series ,summation of (n=0 to infinity) [(-1)n*(9n/9n+1)] =summation of (n=0 to infinity) [(-1)n*(/9)]

=1/9*summation of (n=0 to infinity) [(-1)n]

By the geometric series this summation of (n=0 to infinity) [(-1)n] diverges

=1/9*diverges

the series diverges for x=9

for x=-9 the series ,summation of (n=0 to infinity) [(-1)n*(-9)n/9n+1)] =summation of (n=0 to infinity) [(-1)2n*(/9)]

=1/9*summation of (n=0 to infinity) [(-1)2n]

which is diverges

so the interval of convergence is (-9,9)

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Answer:

look above

Step-by-step explanation:

hope it helps

The graph of the four linear equations is the one we can see below, such that:

Here we have the set of linear equations:

We want to graph these 4 lines on the same coordinate axis.

The line:

y = -3

Is an horizontal line at y = -3

The line:

x = -3

Is a vertical line at x = -3.

And the other two are common linear equations that are graphed in the usual way, then the graph of all the linear equations is the one you can see below.

Where:

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The value of the functions f(x) and g(x) will be √(4x + 3) and √2. Then the correct option is B.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

If (f g)(x) = h(x) such that h(x) = √(8x + 6). Then we have

(f g)(x) = h(x)

f(x) · g(x) = h(x)

Then put the value of h(x), then we have

f(x) · g(x) = √(8x + 6)

f(x) · g(x) = √2(4x + 3)

f(x) · g(x) = √(4x + 3) × √2

Thus, the value of the functions f(x) and g(x) will be √(4x + 3) and √2.

Then the correct option is B.

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The total number of ways in which 4 questions can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336

We are given;

Total number of objective questions = 5 questions

Number of choices of first 2 questions = 3 choices

Number of choices of last 3 questions = 4 choices

Number of ways of answering the first 2 questions = 3 * 3 = 9 ways

Number of ways of answering the last 3 questions = 4 * 4 * 4 = 64 ways

Total number of ways of answering the five questions = 9 * 64 = 576 ways

Now, she has to answer only 4 which means it can be either 2 of the first and 2 of the last of 1 of the first and 3 of the last.

Thus, total number of ways of answering 4 questions if it is fist 2 and last 2 = 9 * 16 = 144

Total number of ways of answering 4 questions if 1 of the first and 3 of the last = 3 * 64 = 192

The total number of ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336

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Answer: 25 ?

Step-by-step explanation:

Answers:

16 cm²

24 cm²

40 cm²

Step-by-step explanation:

     The area of a rectangle can be found with A = L * W where A is the area, L is the length, and W is the width.

     [1] First shaded area

A = L * W

A = (4 cm) * (12 cm - 5 cm - 3 cm)

A = (4 cm) * (4 cm)

A = 16 cm²

     [2] Second shaded area

A = L * W

A = (2 cm) * (12 cm)

A = 24 cm²

     Lastly, we add them together.

16 cm² + 24 cm² = 40 cm²

[tex]5(1.5)=\boxed{7.5 \text{ yd}}[/tex]

The length of the curved border or arc is 7.5 yards.

the length of the arc = [tex]\theta \times r[/tex]

given that [tex]\theta[/tex] = 1.5 radian

radius = 5 yards

then the length of arc from the above formula

[tex]l = \theta \times r\\l = 1.5 \times 5 = 7.5[/tex] yards

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Minimum: 59

Lower Quartile: 67

Median: 76

Upper Quartile: 86

Maximum: 92

Interquartile Range: 19

Answer:

[tex]\huge\boxed{\sf x < 4}[/tex]

Step-by-step explanation:

-4x + 7 > x - 13

Subtract x to both sides

-4x - x + 7 > -13

-5x + 7 > -13

Subtract 7 to both sides

-5x > -13 - 7

-5x > -20

Divide -5 to both sides

x < -20/-5

[tex]\rule[225]{225}{2}[/tex]

Answer:

[tex]x < \bf 4[/tex]

Step-by-step explanation:

[tex]-4x + 7 > x -13[/tex]

We have to make [tex]x[/tex] the subject of the equation:

• Subtract [tex]x[/tex] from both sides:

[tex]-4x - x + 7 > -13[/tex]

⇒ [tex]-5x + 7 > -13[/tex]

• Now subtract 7 from both sides:

[tex]-5x > -13 - 7[/tex]

⇒ [tex]-5x > -20[/tex]

• Next divide both sides by -5, and remember that dividing an inequality by a negative number reverses the inequality symbol:

[tex]x < \frac{-20}{-5}[/tex]

⇒ [tex]x < \frac{20}{5}[/tex]

⇒ [tex]x < \bf 4[/tex]

Answer:

Maximum/Minimum Value:  (0,−2)   is a local minima (1/8,8)  is a local maxima

Explanation: Use the derivative to find the maximum and minimum

Answer:

Period = ¹/₄

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function:

f(x) = A cos(B(x + C)) + D

where:

Given function:

[tex]y=-5 \cos (8 \pi x)+3[/tex]

Comparing the given function with the standard form:

[tex]\implies \sf Period=\dfrac{2 \pi}{B}=\dfrac{2 \pi}{8 \pi}=\dfrac{1}{4}[/tex]

Therefore, the period of the given function is ¹/₄.

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A function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.

To find a function, C(x), to model the water used by the car wash on a shorter day:

Given information -

Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.

We are trying to find:

Therefore, a function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.

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The correct question is given below:

The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.

Write a function, C(x), to model the water used by the car wash on a shorter day

Considering the standard deviation, the data-set has no outliers.

For the given data-set, the mean is:

(35+31+29+34+6+31+32+30)/8 = 28.5.

Hence the standard deviation is:

[tex]S = \sqrt{\frac{(35-28.5)^2+(31-28.5)^2+(29-28.5)^2+(34-28.5)^2+(6-28.5)^2+(31-28.5)^2+(32-28.5)^2+(30-28.5)^2}{8}} = 8.7[/tex]

A measure is said to be an outlier if it is more than 3 standard deviations for the mean. Hence the thresholds are:

Since all values are between 2.4 and 54.6, the data-set has no outliers.

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Answer:

Step-by-step explanation:

Use pythagorean theorem (a^2+b^2=c^2). The diagonal represents c and the width represents b or a. 8^2+b^2=10^2->64+b^2=100->b^2=36->b=6. So your height would be 6.

Answer:

The value of

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b \: [/tex]

is

[tex] \frac { 19}{8} [/tex]

Step-by-step explanation:

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b[/tex]

where,

Thus, substitute these values to the given equation to find the values.

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b ... \: substitute \: \\ given \: values \\ (1) {}^{2} - ( - 3)(2) {}^{ - 3} - 1( - 3) {}^{1} - 2 \\ 1 + 3 \: ( \frac{1}{8} ) - 1( - 3) - 2 \\ 1 + \frac{3}{8} + 3 - 2 \\ \frac{11}{8} + 3 - 2 \\ \frac{35}{8} - 2 \\ \frac{19}{8} = 2 \frac{3}{8} [/tex]

Hope it helps

Answer:

a. 9m

Step-by-step explanation:

Pi = 3.14 = 22/7

formula :

Area of a Sector of a Circle = (central angle)/360 * πr² =

(central angle)/360 * πr² = Area of a Sector of a Circle

43/360 * Pi * r^2 = 30.39

r^2 = (30.39 * 360) / (Pi * 43)

r^2 = (30.39 * 360) / (22/7 * 43)

r = √ (30.39 * 360 * 7) / (22 * 43)

r = √76582.8/946

r = √80.9543340381

8.99746264444 which is roughly

9

The radius of the sector will be 9m. The correct option is A.

The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc segment by simulating it as a network of connected line segments.

The radius will be calculated as below:-

Area of a Sector of a Circle = (central angle)/360 * πr² =

(Ф)/360 * πr² = Area of a Sector of a Circle

43/360 * Pi * r²= 30.39

r² = (30.39 * 360) / (Pi x 43)

r²= (30.39 x 360) / (22/7 x 43)

r = √ (30.39 x 360 x 7) / (22 x 43)

r = √76582.8/946

r = √80.9543340381

r = 9

Therefore, the radius of the sector will be 9m. The correct option is A.

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Answer:

ANSWER:  mix 120 ml of 35% acid solution with 60 ml of 65% acid                      solution to obtain 180 ml 0f 45% acid solution

Step-by-step explanation:

If x = number of ml of 35% acid solution and 60 = number of ml of 65% acid solution, then x + 60 = number of ml of the mixture.

Acid content of first ingredient + acid content of second ingredient = acid content of the mixture

So, 0.35x + 0.65(60) = 0.45(x + 60)

    0.35x + 39 = 0.45x + 27

                12 = 0.10x

               120 = x

The area of ​​the figure Magda shaded with side lengths of 1 and √2 centimeter is equal to 1.21 cm².

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

In order to calculate the area of ​​the figure Magda shaded with side lengths of 1 and √2 centimeter, we would determine the area of ​​each triangle as follows:

For triangle 1, we have:

Area = 1/2 × b × h

Area = 1/2 × 1 × 1

Area = 0.5 cm².

For triangle 2, we have:

Area = 1/2 × b × h

Area = 1/2 × √2 × 1

Area = 0.71 cm².

Total area = Area of triangle 1 + Area of triangle 2

Total area = 0.5 + 0.7

Total area = 1.21 cm².

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Complete Question:

Magda used a 1 cm square grid to draw the shaded figure, using right triangles. 1 cm 3 cm √2 cm 1 cm 1 cm what is the area of ​​the figure Magda shaded?​

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Take note that there is a vertical asymptote at x = -4. This means that our function has the form:

▪ [tex]\longrightarrow \sf{F (x)=\dfrac{A}{x + 4} }[/tex]

[tex]\leadsto[/tex] By comparing it with the given options, the correct option is A.

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

◉ [tex] \bm{A. \: \: F(x)= \dfrac{1}{x + 4} }[/tex]

68 is the wrong number in the sequence 808, 408, 208,108, 68

A number system is defined as a system of writing to express numbers.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The given sequence is 808, 408, 208,108, 68

Eight hundred eight, Four hundred and eight, two hundred and eight, one hundred eight and sixty eight.

808, 408, 208,108, 68

Let us find the difference between the consecutive numbers

400, 200, 100, 40

As we observe the first three terms having the common ratio where as 40 and 100 has different ratio.

Hence, 68 is the wrong number in the sequence 808, 408, 208,108, 68

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Answer:

B.) x + 4y = 7

Step-by-step explanation:

(Step 1) ----------------------------------------------------------------------------------------------

To find the equation, we first need to find the slope using the point-slope form:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope, "x₁" and "y₁" represent the values from the first point, and "x₂" and "y₂" represent the values from the second point.

Point 1: (-1, 2)                     Point 2: (3, 1)

x₁ = -1                                   x₂ = 3

y₁ = 2                                   y₂ = 1

y₁ - y₂ = m(x₁ - x₂)                                  <----- Point-slope form

2 - 1 = m(-1 - 3)                                      <----- Insert values

1 = m(-4)                                                <----- Subtract

-1/4 = m                                               <----- Divide both sides by -4

(Step 2) ---------------------------------------------------------------------------------------------

The given equations are in the slope-intercept form. The general structure looks like this:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. To find the y-intercept, you can plug the newfound slope and values from one point into the equation.

x = -1

y = 2

m = -1/4

y = mx + b                                              <----- Slope-intercept form

2 = (-1/4)(-1) + b                                       <----- Insert values

2 = 1/4 + b                                              <----- Multiply -1/4 and -1

8/4 = 1/4 + b                                           <----- Make common denominators

7/4 = b                                                    <----- Subtract both sides by 1/4

(Step 3) ---------------------------------------------------------------------------------------------

The equation in slope-intercept form is thus: y = -1/4x + 7/4.

While this equation is accurate, it seems that it must be slightly manipulated. Therefore, we need to alter this equation to look like one of the answer choices. For instance, we can multiply the entire equation by 4 to remove the denominator.

y = -1/4x + 7/4                                         <----- Equation

4y = -x + 7                                               <----- Multiply all terms by 4    

x + 4y = 7                                               <----- Add "x" to both sides

The mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides

Inequalities are expressions that have unequal values, when compared

The inequality is given as

-4x > 120

When 4 is added to both sides, the inequality becomes

4 - 4x > 120 + 4

The above is not the solution to the inequality.

The solution is as follows:

We have:

-4x > 120

Divide both sides inequality by -4

x < -30

Hence, the mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides

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Answer:

748.23 in^2.

Step-by-step explanation:

Area = 1/2 * apothem * perimeter

        = 1/2 * 14.7 * 101.8

        =  748.23 in^2.

Answer:

748.23

Step-by-step explanation:

Using it's concept, the average rate of change of the function on the interval [6,13] is given by:

[tex]r = \frac{f(13) - f(6)}{7}[/tex]

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In this problem, we want to find the rate in the interval [6, 13], which is given as follows:

[tex]r = \frac{f(13) - f(6)}{13 - 6} = \frac{f(13) - f(6)}{7}[/tex]

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