Sally has 2 pets in her house. The weight of her dog is 50 pounds and the weight of her cat is 12 pounds. By how much is the weight of the dog more than the weight of the cat?

A. 38 lb.
B. 30 lb.
C. 28 lb.
D. 20 lb.

When x = 4, variable y is equal to 3 via proportional relationship.

directly proportional to each other, meaning that they vary in the same way. In other words, if one quantity increases or decreases by a certain factor, the other quantity also increases or decreases by the same factor.

We can start by observing that x and y are in a proportional relationship, which means that the ratio of y to x is constant. We can find this constant ratio by taking any pair of x and y values and dividing y by x. For example, let's use the first pair (x = 2/3 and y = 1/2):

y/x = (1/2) / (2/3) = (1/2) × (3/2) = 3/4

To find y when x = 4,

we need to multiply 4 by the constant ratio of 3/4:

y = (3/4) × 4 = 3

Therefore, when x = 4, y is equal to 3.

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Answer:

a of a is a

Step-by-step explanation:

a²% not sure of the answer

The solution is, by integrating ∫(3-2x)^10 dx using substitution, we get, -1/22.(3-2x)^11 +C.

In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.

here, we have,

∫(3-2x)^10 dx

now, let, 3-2x=u

so, -2. dx = du

i.e. by substitution we get,

∫u^10 du/-2

=1/-2 . ∫u^10 du

we know, ∫x^n= x^n+1/ (n+1) +c

so, we get,

⇒1/-2.1/11. u^11 +C

=-1/22.(3-2x)^11 +C

where, c=constant.

Hence, The solution is, by integrating ∫(3-2x)^10 dx using substitution, we get, -1/22.(3-2x)^11 +C.

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Answer:

1/32xp

Step-by-step explanation:

but not sure was there a picture to go with this

Answer: no one cares

Step-by-step explanation:

The Cookie Shop's profit at the end of January as a result of the 20% decrease was $12000.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let s represent the Cookie Shop's profit at the end of January. At the end of January, their profit had decreased by 20%:

Percentage decrease = 20% of 15000 = $3000

s = 15000 - 3000 = 12000

The Cookie Shop's profit at the end of January as a result of the 20% decrease was $12000.

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Answer:

11/15

Step-by-step explanation:

17/8 is to 17/20 as 11/6 is to x.

(17/8) / (17/20) = (11/6) / x

(17/8)x = 17/20 * 11/6

(17/8)x = 187/120

(8/17) * (17/8)x = 8/17 * 187/120

x = 11/15

Answer:

11/15

Step-by-step explanation:

just got it right !! :)

The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

The volume of the liquid in the bowl is given by the following integral:

\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)

where r = radius of the bowl and y = height of the liquid.

The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:

r = √{(4/(8-x)) - 1}² + 1²

The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:

h = (4/(8-x)) - 1

Substituting these equations into the volume integral:

\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)

Evaluate this integral using the following steps:

Expand the parentheses in the integrand.

Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.

Integrate each part separately.

The integral of the square root term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)

The integral of the linear term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)

Substituting these formulas into the integral:

V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h

Evaluating this integral:

V = π { 16/27 (8-h)³ - 16/18 (8-h)² }

The rate of change of the volume of the liquid is given by:

dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }

The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.

Substituting these values into the equation for dV/dt:

dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π

Solving this equation for the rate of change of the depth of the liquid:

dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹

Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

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Given the function;

First, we find the inverse of the function as;

Then, we get the domain of the inverse function, we have;

Thus, the graph of the function is;

Hence, the range of the function is;

CORRECT OPTION: B

Answer:

10(3x + 4y)

Step-by-step explanation:

the segment is 4 units long

hope this helps

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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The domain of \(y=4\log_5(x-3)\) is (d) all real numbers greater than 3.

The function is given as:

\(y=4\log_5(x-3)\)

Set the expression in bracket greater than 0

x -3 > 0

Add 3 to both sides

x > 3

Hence, the domain of \(y=4\log_5(x-3)\) is (d) all real numbers greater than 3.

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y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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Answer:

A reflection followed by a translation

Reflection: Reflect the shape at line x = 2

Translation: Translate the shape 5 units upward

Answer:

8×p≈c

Step-by-step explanation:

Because if each is 8 dollars you would multpy the number (Or Letter) by how many you want or have.

The cost of one candy bar is $2.35.

The meaning of unit price is a price quoted in terms of so much per agreed or standard unit of product or service.

Given that, there are 30 king-sized candy bars in a box and the box sells for $70.50, we need to find that how much does each candy bar in the box cost,

Since, the cost of all 30 candies is given collectively, i.e. $70.50,

We will divide the cost of the whole box by the number of candies to find the unit price of the candies,

Unit price = $70.50 / 30

= $2.35

Hence, the cost of one candy bar is $2.35.

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Answer:

9 =6x

Step-by-step explanation:

We know this is the answer because the -4x was cancelled out left to the equal sign, and 2x has now become 6x after adding 4x.

Answer:

9/6 or 1.5

Step-by-step explanation:

both are right

Answer:

Step-by-step explanation:

(y^2)/1600-(x^2)/81=1. y21600−x281=1 y 2 1600 - x 2

Answer: y21600x281=1 y 2 1600 - x 2

Step-by-step explanation: for sure chfjjgffjfj ;)

Answer:

y = 1/4

Step-by-step explanation:

hope this helps :)

The joint relative frequency of students who use a mobile device in an online class is approximately 32%.

The joint relative frequency of students who use a mobile device in an online class, we need to divide the frequency of the intersection of the "Mobile device" and "Online" categories by the total number of students (200 in this case) and express it as a percentage.

From the given two-way frequency table, we can see that the frequency for the intersection of "Mobile device" and "Online" is 64.

The joint relative frequency can be calculated as:

Joint Relative Frequency = (Frequency of intersection / Total number of students) × 100

Joint Relative Frequency = (64 / 200) × 100

Joint Relative Frequency ≈ 32%

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Answer:

3 in 730500

tens of thousands

3 in 73050

thousands

Answer:

10 times

Step-by-step explanation:

the value of the digit 3 in 730,500 is 10 times the value of the digit 3 in 73,050

730,500 (digit 3) = 30,000

73,050 (digit 3) = 3,000

30,000/3,000 = 10

Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

To convert the fraction 11/4 to a mixed numeral, we need to determine the whole number part and the fractional part.

Divide the numerator (11) by the denominator (4).

11 ÷ 4 = 2 remainder 3

The quotient 2 represents the whole number part, and the remainder 3 represents the fractional part.

Write the mixed numeral using the whole number part and the fractional part.

The mixed numeral for 11/4 is:

2 and 3/4

Therefore, Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

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The area of a triangle is:

12x² -18x - 12

The area of a triangle can be calculated using the formula:

A = 1/2 * b * h

where b is the base and h is the height of the triangle

We have:

b = -6x + 3

h =  4(x - 2) = 4x - 8

substituting into the formula:

A = 1/2 * (6x + 3) * (4x - 8)

A = 1/2 * (24x² -48x + 12x - 24)

A = 1/2 * (24x² -36x - 24)

A = 12x² -18x - 12

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The exact arc length of f(x)=√2x+1 is 4.5.

The arc length is the separation between two points along a curve segment. The arc length of a function f(x) is given by the formula,

\(L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx\)

Where f'(x) is derivative of function f(x). The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.

Finding the arc length of f(x)=√2x+1 0≤x≤4, using the formula,

First finding the derivative of function,

\(f'(x)=\frac{d(\sqrt{2x+1})}{dx} \\\\=\frac{2}{2\sqrt{2x+1}} \\\\=\frac{1}{\sqrt{2x+1}}\)

Now, putting the derivative of function f(x) in the formula of arc length L,

\(L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+(\frac{1}{\sqrt{2x+1}})^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+\frac{1}{2x+1}}}\\\\L=\int\limits^4_0 {\sqrt{\frac{2x+1+1}{2x+1}}}\\L=\int\limits^4_0 {\sqrt{\frac{1}{2x+1}}}\\\approx4.5\)

Therefore, the exact arc length of f(x)=√2x+1 is 4.5.

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Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.