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Answer:

3

Step-by-step explanation:

There are 4.5 diamonds, which represent 9 hours in total.

This corresponds to 9/3 = 3 circles.

Answer:

3 circles

Step-by-step explanation:

For the pig, it's 4.5 squares. Each square is two hours, and 4.5*2 is 9. Each circle is 3 hours, and 9 divided by 3 is 3. Therefore, the answer is 3 circles.

Let other one be x

ATQ

\(\\ \sf\longmapsto x+\dfrac{-8}{17}=-8\)

\(\\ \sf\longmapsto\dfrac{17x-8}{17}=-8\)

\(\\ \sf\longmapsto 17x-8=17(-8)=-136\)

\(\\ \sf\longmapsto 17x=-136+8\)

\(\\ \sf\longmapsto 17x=-128\)

\(\\ \sf\longmapsto x=\dfrac{-128}{17}\)

Answer:

\(let \: the \: unknown \: = x \: and \: y \\ x + y = - 8 \\ y = \frac{ - 8}{17} \\ x - \frac{8}{17} = - 8 \\ x = - 8 + \frac{8}{17} \\ x = \frac{17 \times - 8 + 8}{17} \\ x = \frac{ - 136 + 8}{17} \\ x = \frac{ - 128}{17} \\ thank \: you\)

Answer:

since those are angles on a straight line.

we work out as follows

∠DBA and ∠DBC are making linear pair.

Linear pair of angles are formed when two lines intersect each other at a single point.

\(\rm \large\longrightarrow \: \: x \: + \: 126 \degree \: = \: 180 \degree\)

\(\rm \large\longrightarrow \: \: x \: = \: 180 \degree \: - \: 126 \degree \)

\(\rm \large\longrightarrow \: \: x \: = \: 54 \degree\)

Answer:

Your answer is

equation y=-4x+4

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At the end of the fifth day, a bricklayer has laid 324 bricks on the job.

Multiplication is a mathematical arithmetic operation.

It is also a process of adding the same types of expression to some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given, a bricklayer lays 4 bricks on the first day on the job.

On each day thereafter, he lays three times the number of bricks he laid on the previous day.

And he continued his pattern.

Let x be the number of bricks he laid in the previous day.

Then according to the question,

The number of bricks in total is = 3x

For the second day, x =4

Number of the bricks he laid on the second day = 12

Now the x =12 for the third day.

Number of the bricks he laid on the third day = 36

Now x = 36 for the fourth day.

Number of the bricks he laid on the fourth day = 108

Now the x = 108 for the fifth day.

Number of the bricks he laid on the fifth day = 324

Therefore, 324 bricks he has laid at the end of the fifth day.

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Answer:

  3 km/h

Step-by-step explanation:

You want to know the speed of the river current if floating 36 km downstream takes 9 h longer than the trip upstream in a boat with a speed relative to the current of 15 km/h.

The relation between time, speed, and distance is ...

  time = distance / speed

If c represents the speed of the current, then 15-c is the speed upstream. The relation between the travel times is ...

  36/(15 -c) = 36/c -9

Multiplying by c(15-c), we have ...

  36c = 36(15 -c) -9(c)(15-c) . . . . . . . multiply by c(15-c)

  36c = 540 -36c -135c +9c² . . . . . eliminate parentheses

  9c² -207c +540 = 0 . . . . . . . collect terms

  c² -23c +60 = 0 . . . . . . . . divide by 9

  (c -20)(c -3) = 0 . . . . values that make the factors zero are c=20, c=3

The speed of the current is 3 km/h.

__

Additional comment

The speed of the current cannot be greater than 15 km/h, or the boat could not go upstream. The speed of the current cannot be greater than 4 km/h, or the trip downstream would take less than 9 hours.

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Answer:

  D

Step-by-step explanation:

As is often the case with multiple choice questions, a simple check of the reasonableness of the answers will identify the correct one.

Here, the key is that the center of mass will be at the non-zero mass if one of them is zero. Assuming m2 = 0, the center of mass will have coordinates (x1, y1).

Checking the offered expressions when m2=0, we have ...

  A. (m1x1/(2m1), m1y1/(2m1)) = (x1/2, y1/2) ≠ (x1, y1)

  B. (m1(x1 +x2)/(2m1), 0) = ((x1+x2)/2, 0) ≠ (x1, y1)

  C. (m1x2/m1, m1y2/m1) = (x2, y2) ≠ (x1, y1)

  D. (m1x1/m1, m1y1/m1) = (x1, y1) . . . . . the answer we're looking for

Answer:

144cm2

Step-by-step explanation:

Answer:

C. Rhombus.

Step-by-step explanation:

A rhombus is quadrilateral who each pair of opposite side are parallel and congruent and whose each diagonal is perpendicular to the other diagonal, which bisectors it.

In the cases of rectangle, parallelogram and trapezoid, diagonals are not perpendicular to each other. In the case of the trapezoid, only one pair of sides are parallel.

In consequence, right answer is C.

The sum of the exterior angle of the pentagon is 360 degrees.

The polygon above is a pentagon. A pentagon is a polygon with 5 sides.

If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle. The sum of the exterior angles of a polygon is 360°.

Therefore, the sum of the measure of the exterior angles of the pentagon as shown is 360 degrees.

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a. The domain of a(r) is \(A(r)= 2\pi r^{2} + 16\pi r\).

b. The radius r as a function of a is \(r = -4 +\sqrt{\frac{A}{2\pi } +16\) .

The three-dimensional solid shape of a cylinder is made up of two circular bases joined by a curving surface that is created by folding a rectangle. A cylinder's top and bottom faces are parallel to one another. There are 3 faces, 2 edges, and 0 vertices in all.

In this question, we must apply our understanding of cylinders to determine the function that most accurately captures its value:

\(r = -4 +\sqrt{\frac{A}{2\pi } +16\)

The area domain of A can be represented as:

\(A(r)= 2\pi r^{2} + 16\pi r\)

Let's divide the equation by 2π and write A(r) as just A to get:

\(r^{2} + 8r = \frac{A}{2\pi }\)

So, after we sum on both sides we get,

\(r^{2} +8X +16 =\frac{A}{2\pi } + 16\)

\((r+4)^{2} = \frac{A}{2\pi } +16\)

By taking the square root of the previous equation and then figuring out r, we get:

\(r = -4 +\sqrt{\frac{A}{2\pi } +16\)

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1 / 3 of peanut butter cookies as the number of boxes of lemon cookies sold

Given: Lila sold 1/3 as many boxes of lemon cookies as peanut butter cookies

What is algebra?

Algebra is a domain in mathematics that is used to describe a problem statement in a short and more precise way, simply by pointing the key points. If consist a sequence or combination of characters containing letters, numbers, symbols and more. It is very helpful in assuming conditions where a single or multiple object or element is under the influence of single or multiple objects or elements. We can easily describe it with the help of algebra. Sometimes the assumed expression itself becomes a solution for a given problem when the unknown variable values are known.

We can also make predictions with our expressions for a future event.

Hence algebra plays an important in our life knowingly or unknowingly and even our names, words etc. all can be thought of as the unknown variables with a name and we are the instances which are acting as values for particular names in unique ways.

Every problem's solution is unique to the problem but it can be extended to make relations with other problems with a similar approach or thoughts.

Now let's solve the given question:

Let the number of boxes of lemon cookies sold be x and the number of boxes of peanut butter cookies sold be y.

According to the question,

boxes of lemon cookies = 1/3 boxes of peanut butter cookies

Hence Lila sold 1 / 3 of peanut butter cookies as the number of boxes of lemon cookies.

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Answer:

Direction of the boat is 43.05° and the speed is 21.66 knot

Step-by-step explanation:

yacht speed = 20 knots

yacht bearing = 185° = 85°  below the negative horizontal x-axis

wind speed = 15 knots

wind bearing = 290° = 20° above the negative horizontal x-axis

we find the x and y components of the boat velocities

for yacht,

x component = -20 cos 85° = -1.74 knots

y component = -20 sin 85° = -19.92 knots

for the wind,

x component = -15 cos 20° = -14.09 knots

y component = 15 sin 20° = 5.13 knots

total x component  Vx = -1.74 + (-14.09) = -15.83 knots

total y component Vy =  -19.92 + 5.13 = -14.79 knots

Resultant speed of the boat = \(\sqrt{Vx^{2} + Vy^{2} }\)

==> \(\sqrt{15.83^{2} + 14.79^{2} }\) = 21.66 knot

direction of boat = \(tan^{-1} \frac{Vy}{Vx}\)

==> \(tan^{-1} \frac{14.79}{15.83}\) = 43.05°

The slope of the tangent line to the polar curve \(r = 3 + 4cos(θ)\) at the point specified by \(θ = π/3 is -√3/3.\)

To find the slope of the tangent line to the polar curve at the given point, we need to convert the polar equation into Cartesian coordinates and then take the derivative with respect to x or y.

We can use the following equations to convert from polar coordinates to Cartesian coordinates:

\(x = r cos(θ)\\y = r sin(θ)\)

So for the given polar equation, we have:

\(r = 3 + 4cos(θ)\\\x = (3 + 4cos(θ))cos(θ)\\y = (3 + 4cos(θ))sin(θ)\)

Now we can find the slope of the tangent line at the point specified by θ = π/3 by taking the derivative of y with respect to x:

\(dy/dx = (dy/dθ)/(dx/dθ)\\= [(3 + 4cos(θ))cos(θ) - (3 + 4cos(θ))sin(θ) d(cos(θ))/dθ] / [(3 + 4cos(θ))sin(θ) + (3 + 4cos(θ))cos(θ) d(cos(θ))/dθ]\)

Substituting θ = π/3, we get:

\(dy/dx = [(3 + 4cos(π/3))cos(π/3) - (3 + 4cos(π/3))sin(π/3) d(cos(π/3))/dθ] / [(3 + 4cos(π/3))sin(π/3) + (3 + 4cos(π/3))cos(π/3) d(cos(π/3))/dθ]\)

Simplifying this expression, we get:

\(dy/dx = -√3/3\)

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The true statement about the function are;

⇒ The function is positive for all real values of x, where x < –1.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The graph of the function;

f(x) = –(x + 3)(x – 1)

Now,

Graph of the function is shown in attached image.

Which is a parabola, It goes through (- 3, 0), has a vertex at (- 1, 4), and goes through (1, 0).

Clearly, When x < -1

Take x = 0 < -1

The value of function;

f(x) = –(x + 3)(x – 1)

    = - (0 + 3) (0 -1)

    = -3 x -1

    = 3

The function is positive.

Thus, The true statement about the function are;

⇒ The function is positive for all real values of x, where x < –1.

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Answer:

5

Step-by-step explanation:

1.24 × 4 = 5

or it can be 1.24 ÷2 =0.265

Answer:

The answer is 48a-6b-14

Step-by-step explantion:

simplify by combining liketerms:

-6- 2b•3 -6a+ 10a• 3-16÷ 2- 4 • -6a

-6-6b-6a+30a -8+24a

48a-6b-14

Good luck!

Answer:

78 adult tickets were sold that day

Step-by-step explanation:

The absolute maximum and minimum values of the function f(x, y) = x^2 + y^2 - 2y on the set R = {(x, y): x^2 + y^2 ≤ 9} can be found by analyzing the critical points and the boundary of the region R.

To find the critical points, we take the partial derivatives of f(x, y) with respect to x and y, and set them equal to zero. Solving these equations, we find that the critical point occurs at (0, 1).

Next, we evaluate the function f(x, y) at the boundary of the region R, which is the circle with radius 3 centered at the origin. This means that we need to find the maximum and minimum values of f(x, y) when x^2 + y^2 = 9. By substituting y = 9 - x^2 into the function, we obtain f(x) = x^2 + (9 - x^2) - 2(9 - x^2) = 18 - 3x^2.

Now, we can find the maximum and minimum values of f(x) by considering the critical points, which occur at x = -√2 and x = √2. Evaluating f(x) at these points, we get f(-√2) = 18 - 3(-√2)^2 = 18 - 6 = 12 and f(√2) = 18 - 3(√2)^2 = 18 - 6 = 12.

Therefore, the absolute maximum value of f(x, y) is 12, which occurs at (0, 1), and the absolute minimum value is also 12, which occurs at the points (-√2, 2) and (√2, 2).

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Answer:

60°

Step-by-step explanation:

as they are a linear pair

120°+x=180

x=180-120

x=60°

The given differential equation y x²y² = x² is a nonlinear and not separable differential equation, which corresponds to option (D).

A linear differential equation can be written in the form dy/dx + P(x)y = Q(x), where P(x) and Q(x) are functions of x. In this equation, the term x²y² makes it nonlinear.

A separable differential equation can be written in the form g(y)dy = f(x)dx, where g(y) and f(x) are functions of y and x, respectively. However, in the given equation, we cannot separate the variables y and x to obtain such a form.

To solve this particular differential equation, one approach is to rewrite it in a more manageable form. Let's rearrange the terms:

x² = y/(x²y²)

Now, we can multiply both sides by (x²y²) to eliminate the denominator:

x²(x²y²) = y

This equation is still nonlinear but can be used to find a particular solution for y given a specific initial condition.

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Answer:

5. B x=4

6. C x=18

7. B x=78

8.

9. 6 cups

10. B 7 in

Step-by-step explanation:

5. X /12= 48/144

You can simplify the fraction 48/144 by diving both numerator and denominator by 12.

(48/12)/(144/12)=4/12

So, x/12=48/144 is same as

x/12=4/12

So, x=4

6)

15/5=x/6

Cross multiply

5x=15*6

5x=90

x=90/5

x=18

7) 26/ x = 17/51

17x=26*51=1,326

x=1326/17

x=78

8)

x/14=9/3

Cross multiply

3x=14*9=126

x=126/3=42

9)

1 1/2 cups is 3/2 cups

5/(3/2)=20/x

Cross multiply

5x=20*(3/2)=10*3=30

x=30/5=6 cups

10)

52/28=13/x

x=(28*13)/52=7 inches

Answer:

∠ W = 30°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos W = \(\frac{adjacent}{hypotenuse}\) = \(\frac{WY}{WX}\) = \(\frac{2\sqrt{21} }{4\sqrt{7} }\) = \(\frac{1}{2}\) \(\sqrt{\frac{21}{7} }\) = \(\frac{\sqrt{3} }{2}\) , then

∠ W = \(cos^{-1}\) ( \(\frac{\sqrt{3} }{2}\) ) = 30°

Answer:

300

Step-by-step explanation:

Answer: 300

Step-by-step explanation: 0.75×400=300

hope this helped :)

Answer: 254

Step-by-step explanation:

89 + 38 x 2

89 + 38 = 127

127 x 2 = 254

The number or amount of ounces of the 75% tangy mustard sauce must the chef have used is: 20 ounces .

First step

Since 5 ounce sauce containing 50% tangy

Hence:

5 oz×.50 tangy

=2.50 oz-tangy

Second step

(5+x)×0.7=3.5+0.7x

Third step

2.50+0.75x=3.5+0.7x

Collect like term

0.75x-0.7x=3.5-2.50

0.05x=1

Divide both side by 0.05

x=1/0.05

x=20 ounces

Therefore the number of ounces of the 75% tangy mustard sauce must the chef have used is: 20 ounces .

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Rounding to the nearest tenth, the orange's volume is approximately 464.7 cubic centimeters.

Here, we have,

To find the volume of the orange, we can use the formula for the volume of a sphere:

V= 4/3 πr³

where r is the radius of the sphere.

Given that Sarah measures the radius of the orange as 4.8 cm, we can now calculate the volume:

V= 4/3 π (4.8)³

V= 4/3 π (110.592)

V≈ 4/3 ×110.592×3.14159

V≈464.65 cubic centimeters

Rounding to the nearest tenth, the orange's volume is approximately 464.7 cubic centimeters.

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