The expression below represents the perimeter, in feet, of Manual’s garden.

15 + 2x + 7 + 15 + 2x + 7

Use exactly two terms to write an equivalent expression to represent the perimeter, in feet, of Manual’s garden.

The area, measured in square feet, of Manual’s garden is found by calculating 15(2x + 7). Manual incorrectly says the area can also be found using the expression 30x + 7.

Describe the error in Manual’s expression. Also, find the difference, in square feet, between the actual area of Manual’s garden and the area found using his expression as a part of your explanation.

Manual’s friend Sasha designs a square garden. Each side measures 3x + 5 in length.

The perimeter of Sasha’s garden is how much larger than the perimeter of Manual’s garden?

The positive integer for which g(x) first exceeds f(x) is 178 according to the number line.

The function f of (x) is used to denote a linear algebra that can be represented on the graph.

Given that:

We are to determine a positive integer for which g(x) first exceeds f(x). Using the following option;

Therefore, we can conclude that the positive integer for which g(x) first exceeds f(x) is 178 according to the number line.

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Answer:

6

Step-by-step explanation:

first, we start with 2 dozen = 2 * 12 = 24 cookies

next, cole eats 2/3 of the cookies

2/3 of the cookies = 2/3 * 24 = 16

we are then left with

original # - # of cookies cole ate = 24 - 16 = 8

next, jim eats 1/4 of the cookies left

cookies left = 8

1/4 of cookies left = 1/4 * 8 = 2

cookies left - cookies jim eats = cookies still in jar = 8 - 2 = 6

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

1. Convert both mixed numbers into improper fractions:

[tex]\frac{15}{4} x = \frac{5}{4}[/tex]

2. Multiply both sides by 4:

4 · [tex]\frac{15}{4} x=\frac{5}{4}[/tex] · 4

15x = 5

3. Isolate x:

x = 1/3

hope this helps!

The horizontal and vertical axes of a graph can have any names you like. If the independent variable represents something in particular, the horizontal axis is usually named so as to indicate that.

A coordinate system is a system in geometry that uses one or more integers, or coordinates, to determine the position of points or other geometric components in a unique way.

The horizontal and vertical axes of a graph can have any names you like. If the independent variable represents something in particular, the horizontal axis is usually named so as to indicate that. In a graph of distance versus time, for example, the independent variable is likely to be time, and the horizontal axis is likely to be named something that suggests that--"t," for example, or perhaps "days".

It is fairly convenient to use "x" to name a general independent variable. The corresponding dependent variable in a two-variable relation is conventionally called "y". The horizontal axis in x-y graphs is usually labelled "x" and is called the "x-axis."

This convention is sufficiently well-used that we often call the horizontal number line of the graph the "x-axis" even if it is labelled something else.

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This solution shows that 6 is included in the solution due to the equal sign and not true for the inequality  4x − 5 < 19 since 6 is excluded

Inequalities are equation not separated by an equal sign

Given the inequality expression

4x − 5 ≤ 19

4x ≤ 19 + 5

4x ≤  24

x≤ 6

This solution shows that 6 is included in the solution due to the equal sign and not true for the inequality  4x − 5 < 19 since 6 is excluded

Given the equation

4x + 3 = 23

4x = 23 - 3

4x =20

x = 5

Hence 5 is the solution from the given set

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Answer:

Rational

Step-by-step explanation:

All fractions are rational numbers but it is not necessary that all rational numbers are fractions.

Have a nice day! :)

Step-by-step explanation:

i got confused whether it is 7/2 or /2-1

Answer:

Step-by-step explanation:

The mode is the number of most repeated data in the set.

Given set 2, 1, 4, 7, 1 has mode 1 (repeated twice).

If we add 1 to the set the mode will remain 1 as it will repeat three times, so the mode won't change.

There is no change in mode, so the mode decrease is zero.

Answer:

The mode would not decrease

Step-by-step explanation:

Given set of numbers:  2, 1, 4, 7, 1

The mode is most frequently occurring data value.

Therefore, 1 is the mode of the given data set as there are two of this data value.

If we add 1 to the data set, the set becomes:  2, 1, 4, 7, 1, 1

Therefore, 1 is still the mode since there are now three of this data value.

In conclusion, the mode would stay the same.

The area inside one leaf of the rose: r=6sin(6θ) is 3π/2 after evaluating the integral over the limit 0 to  π/6

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have:

r=6sin(6θ)

First we have to find the limits:

r = 0

6sin(6θ) = 0

θ = nπ/6

n = 0 to n = 1

θ = 0 to  θ = π/6

[tex]\rm Area = \int\limits^{\dfrac{\pi}{6}}_0 {6sin6\theta} \, d\theta[/tex]

After calculating the above definite integral, we will get:

Area = 3π/2

Thus, the area inside one leaf of the rose: r=6sin(6θ) is 3π/2 after evaluating the integral over the limit 0 to  π/6

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Answer:

2x + 10 = x

Step-by-step explanation:

Let him mows x

Robert mows

The movement of the particle on the circle is its displacement.

The value of dy/dt at this time is -9/2.

Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.

A particle moves on the circle x^2 + y^2=25 in the XY-plane for time t≥0. At the time when the particle is at the point (3,4), dxdt=6.

The equation of the circle is given as:

[tex]\rm x^2 + y^2=25[/tex]

Differentiate with respect to time

[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0[/tex]

Substitute all the values in the equation

[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0\\\\2(3) \times 6+2(4)\times \dfrac{dy}{dt}=0\\\\ 6 \times 6+8 \times \dfrac{dy}{dt}=0\\\\ 36+8\times \dfrac{dy}{dt}=0\\\\ 8\times \dfrac{dy}{dt}=-36\\\\ \dfrac{dy}{dt}= \dfrac{-36}{8}\\\\ \dfrac{dy}{dt}= \dfrac{-9}{2}[/tex]

Hence, the value of dy/dt at this time is -9/2.

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Since the pivot pillar is 1 m above the ground, maximum angle can the seesaw beam move is 26.39°

The maximum angle can be gotten using trigonometric ratios answer the question,

Trigonometric ratios are the ratios of the sides of a triangle.

Angles are a measure of rotation or bearing.

Given that the seesaw plank is 4.5 m long and the pivot pillar is 1 m above the ground, when the seesaw is at maximum angle, it forms a right angled triangle with the ground.

It also forms a smaller similar triangle with the same maximum angle Ф which is gotten from the trigonometric ratio

sinФ = h/L where

So, Ф = sin⁻¹(h/L)

= sin⁻¹(1 m/2.25 m)

= sin⁻¹(1/2.25)

= sin⁻¹(0.4444)

= 26.39°

So, maximum angle can the seesaw beam move is 26.39°

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A first step in solving the equation 1/4 x + 1/2 = 3/4x will be answer A multipllied by 4 on both sides.

What is an equation?

The equation is actually a relationship between the numbers and the variables.The given equation is  1/4 x + 1/2 = 3/4x

Now the solution of the equation will be:-

1/4 x + 1/2 = 3/4x

By multiplying with 4 the equation will become:-

x+2=3x

3x-x=2

2x=2

x=1

Hence the solution of the given equation will be x=1

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Answer:A

Step-by-step explanation:

Multiplying each by 1/4.We have;4x1/4 + 4x1/2 = 4x3/44/4 + 4/2 = 12/41 + 2 = 33=3This is the most effective way.

Answer:

[tex]P(X=3)\approx27\%[/tex]

Step-by-step explanation:

Use the binomial distribution

[tex]\displaystyle P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}\\\\P(X=3)=\binom{4}{3}(0.52)^3(1-0.52)^{4-3}\\\\P(X=3)=\frac{4!}{3!(4-3)!}(0.52)^3(0.48)^1\\ \\P(X=3)=0.26996736\\\\P(X=3)\approx0.27\\\\P(X=3)\approx27\%[/tex]

Therefore, the probability that exactly 3 students out of 4 randomly chosen students have brown hair is about 27%

Answer:

$332.64

Step-by-step explanation:

Since we are applying a discount to a price tag, we will be decreasing the amount of that price tag.

In this case, we will be taking 20% off of $415.80. This means that our new price tag will be 80% of what it originally was. To find the answer, we must first change 80% into a decimal.

80% ->  [tex]\frac{80}{100}[/tex] -> 0.980

Next, we multiple $415.80 by 0.80 as shown below:

[tex]415.80(0.80)[/tex]

Our answer will be:

$332.64

Answer:

[tex]\textsf{Area of a triangle}=\dfrac{1}{2} ab \sin C[/tex]

(where [tex]a[/tex] and [tex]b[/tex] are the sides, and [tex]C[/tex] is the included angle)

[tex]\textsf{Area of a sector}= \dfrac{\theta}{360} \pi r^2[/tex]

(where [tex]\theta[/tex] is the angle in degrees and [tex]r[/tex] is the radius)

Therefore, using the above formulas:

[tex]\begin{aligned}\textsf{Area of segment } \rm (A) & = \textsf{area of sector}- \textsf{area of triangle}\\& = \dfrac{\theta}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin \theta\\\end{aligned}[/tex]

Given:

Substitute the given values into the formula and solve for r:

[tex]\begin{aligned}\implies 20 & = \dfrac{90}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin 90\\\\20 & = \dfrac{1}{4} \pi r^2 - \dfrac{1}{2}r^2 (1)\\\\20 & = \left(\dfrac{1}{4} \pi -\dfrac{1}{2}\right)r^2\\\\20 & = \left(\dfrac{\pi -2}{4}\right)r^2\\\\r^2 & = 20\left(\dfrac{4}{\pi -2}\right)\\\\r^2 & =\dfrac{80}{\pi-2}\\\\r & =\sqrt{\dfrac{80}{\pi-2}}\\\\r & = 8.37\: \sf (2\:dp)\end{aligned}[/tex]

Answer:

25 to 3 power ÷ 3 = 69

Answer:

Step-by-step explanation

the figure is composed of a square with an isosceles right triangle inside, we find the area of ​​the square and we take away the area of ​​the triangle.

Triangle area = lxl, right-angled triangle area side by side divided by two.

8 * 8 = 64cm²

6 * 6 : 2 = 18 cm²

Area of the shaded region

64 - 18 = 46 cm²

You are given a vector in the XY plane that has a magnitude of 87. 0 units and a y component of -66. 0 units. The direction of the vector V is;

We know that the formula for 2 vectors like this in the x and y directions is; A = xi^ + yj^

Where A is the magnitude of the resultant

x is the value of the x-component

y is the value of the y-component

We are given;

Magnitude of vector = 84 units

Y-component of the vector = -67 units

Thus,

[tex]A = \sqrt(x^2 + y^2)\\\\87 = \sqrt(x^2+ (-66)^2)\\\\87^2= x^2+ 4356\\\\7569 = x^2+ 4356\\\\x= \sqrt(7569 - 4356)\\\\x = 56.68 units[/tex]

From A above, let us take the positive value of the x-component and as such our original vector will be;

A = 56.68i^ - 66j^

The direction of the vector V is;

[tex]\theta = tan^{-1} \dfrac{y}{x} \\\\\theta = tan^{-1} \dfrac{-66}{56.68} \\\theta =-27.15°[/tex]

Since it points entirely to the negative x-axis, then the angle is;

180 - (-27.15) = 207.15°

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The region outside the circle r = 3 and inside the circle r = - 6cos θ is given below.

[tex]\rm Area = \dfrac{12\pi - 9\sqrt3 }{2}[/tex]

When the two curves intersect then they bound the region is known as the area bounded by the curve.

The region outside the circle r = 3 and inside the circle r = - 6cos θ

Then the value of the θ will be

[tex]\begin{aligned} -6\cos \theta &= 3\\\\\cos \theta &= -\dfrac{1}{2}\\\\\theta &= -\dfrac{2\pi}{3}, \dfrac{2\pi}{3} \end{aligned}[/tex]

Then the area will be given as

[tex]\rm Area = \dfrac{1}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [-6 \cos \theta)^2 - 3^2 ] d \theta \\\\\\Area = \dfrac{1}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [18 (2\cos ^2 \theta ) - 9]d \theta \\\\\\Area = \dfrac{9}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [2(1 + \cos 2\theta ) - 1] d \theta \\\\\\Area = \dfrac{9}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [2 \cos 2\theta ) + 1] d \theta \\\\[/tex]

[tex]\rm Area = \dfrac{9}{2} [ \sin 2\theta + \theta ] _{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} \\\\\\ Area = \dfrac{9}{2} [ \sin 2( \frac{2\pi}{3}) +\frac{2\pi}{3} - \sin 2 (\frac{2\pi}{3}) - \frac{2\pi}{3}] \\\\\\[/tex]

On simplifying, we have

[tex]\rm Area = \dfrac{12\pi - 9\sqrt3 }{2}[/tex]

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Answer:

= 0,16m

Step-by-step explanation:

we are given the ratio there the 2 is for the image 9 is for the car so we say 9 divide by 11 multiply by 0,2

The Solution of -x +y = 84, x + 3y = 12, x - 7y + z = 15 be [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

The correct option is (C)

The inverse of matrix is another matrix, which on multiplying with the given matrix gives the multiplicative identity.

Given equation are:

-x +y = 8

4x + 3y = 12

x - 7y + z = 15

So,

[tex]\left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right] \;*\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

then,

[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \; \left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right]^{-1} \; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

Now, Calculating the inverse of Matrix we have,

[tex]\left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right]^{-1} \;[/tex] =      [tex]\left[\begin{array}{ccc}-3/7&1/7&0\\4/7&1/7&0\\31/7&6/7&1\end{array}\right][/tex]

so, [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \;\left[\begin{array}{ccc}-3/7&1/7&0\\4/7&1/7&0\\31/7&6/7&1\end{array}\right]\; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-12/7\\44/7\\425/7\end{array}\right][/tex]

 [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

Hence ,[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

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The completed code to generate and save a number in the program which allow a user to guess a number from (1,10) is input.

Program or programming is the combination of codes. These codes are used to generate the program such that a machine can understand the inputs given to it.

The program is written to allow a user to guess a number. This number should be between the number 0 to 10.

Here, the input is needed to a machine or computer, for which it's process the number and show if the guessed number is correct or not.

Hence, the completed code to generate and save a number in the program which allow a user to guess a number from (1,10) is input.

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If d is the common difference between consecutive terms, then

[tex]a_4 = a_3 + d = a_2 + 2d[/tex]

We have [tex]a_2 = 64[/tex] and [tex]a_4 = 100[/tex], so

[tex]a_4 - a_2 = 100 - 64 = 36 = 2d \implies d = 18[/tex]

Then the 1st term in the sequence is

[tex]a_2 = a_1 + d \implies 64 = a_1 + 18 \implies a_1 = 46[/tex]

and the n-th term would be

[tex]a_n = a_1 + (n-1) d \implies a_n = 46 + 18 (n-1) \implies \boxed{a_n = 18n + 28}[/tex]

The number of tops on the 6th day based on the exponential model is 64, and the number of tops on the 6th day based on the linear model is 17.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where a is a constant and a>1

First day class collected = 2 tops

Third day class collected = 8 tops

The exponential function can be modelled:

[tex]\rm D(N) = 2^N[/tex]

D(1) = 2  (first day)

D(3) = 8  (third day)

D(6) = 64 (sixth day)

The linear function can be modeled:

D(N) = 3N -1

D(1) = 2  (first day)

D(3) = 8 (third day)

D(6) = 17 (sixth day)

Thus, the number of tops on 6th day based on exponential model is 64, and the number of tops on the 6th day based on the linear model is 17.

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Answer:

m = 3

Step-by-step explanation:

see image.

6/8 = 3/4

Use the picture in the problem or use algebra to find m. See image.

Answer:

X intercepts are (-4,0) and (2,0)

Step-by-step explanation:

use the desmos graphing calculator for a simple answer

Answer:

24

Step-by-step explanation:

6/2 = x/8

x=24

24 oil changes

Answer:

750 mL

Step-by-step explanation:

Unit Conversion Rate

Solving

Answer:

750

Step-by-step explanation:

.75 x 1000 = 750

multiply volume value by 1000

hope this helps!