Look at the figures. How can you prove these triangles are congruent?



∆ABC ≅ ∆DEF by the SAS Postulate.

∆ABC ≅ ∆DEF by the SSS Postulate.

It is not possible to determine if the triangles are congruent.

The answer provides the total number of combinations of ice cream cones based on flavors, cone types, and toppings.

The number of different combinations of ice cream cones that can be created considering different flavors of ice cream, types of cones, and toppings:

The width of a rectangle with an area of 96 square feet and a width to length ratio of 2:3 is 8 feet.

In this mathematics problem, we are given the area of a rectangle (96 square feet) and the ratio between its width and length (2:3). The equation representing the area of a rectangle is Length x Width. Given that the area of the rectangle is 96 sq ft, and the ratio of width to length is 2:3. Let's assign the width to be 2x and the length to be 3x. Then, you would multiply these two together and set it equal to the area: (2x) * (3x) = 96 square feet. Simplifying this gives 6x2 = 96. Dividing both sides by 6 gives you x2 = 16. Taking the square root of both sides gives x = 4. Therefore, the width of the rectangle, which is 2x, is 2 * 4 = 8 feet.

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Answer:

Here, l is the length of the rectangle and w is the width of the rectangle

To Compare the values, you must calculate each given situation.

Area of a rectangle is equal to  length times width.

i.e, [tex]A = l \times w[/tex]

(A)

if l = 8 units and w= 6 units,

then;

[tex]A = l \times w[/tex] = [tex]8 \times 6 = 48 unit^2[/tex]

(B)

if l =7 units  and w = 7 units

[tex]A = l \times w[/tex] = [tex]7 \times 7 = 49 unit^2[/tex]  

Therefore, the Part B would yield a larger area.

If l -7 units and w = 7 units , the area of larger floor is 49 square units.

To find the dimensions of a rectangle with a given area and perimeter, set up and solve a system of equations.

Let's assume that the length of the rectangle is x cm and the width is y cm.

Given that the area of the rectangle is 180 cm², we have the equation x*y = 180.

Also, the perimeter of the rectangle is 58 cm, which gives us the equation 2x + 2y = 58.

By solving these two equations simultaneously, we can find the dimensions of the rectangle.

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The question is asking to find the parametric equations of the line with the equation 2x+3y=5, which are x=t and y=(5-2t)/3 where t is a parameter.

To obtain parametric equations for the line 2x + 3y = 5, first, solve for y, yielding y = (5 - 2x)/3. Introduce a parameter, often denoted as t, representing the 'time' a point travels on the line. When x = t, substitute it into the y equation, resulting in y = (5 - 2t)/3. Hence, the parametric equations for the line are x = t and y = (5 - 2t)/3. These equations express x and y in terms of the parameter t, allowing the representation of various points on the line as t varies, providing a concise and dynamic description of the line's behavior in a parametric form.

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The approximate probability is  0.40 .

Random selection refers to how the sample is drawn from the population as a whole, while random assignment refers to how the participants are then assigned to either the experimental or control groups.

Probability measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.

Probability of an event P(E) = (Number of favorable outcomes) ÷ (Total outcomes ).

According to the question

The table below shows the number of U.S. residents with health insurance in 2015, in thousands, categorized by age group and annual income.

Now,

if a U.S. resident with health insurance who was 35-64 in 2015 is selected at random,

The probability that this resident had an income between $50,000 and $74,999

As

By using formula of probability

Probability of an event P(E) = (Number of favorable outcomes) ÷ (Total outcomes ).

where

Total outcomes = Total resident had an income between $50,000 and $74,999  = 56,908

Number of favorable outcomes = U.S. resident with health insurance who was 35-64 in 2015 and income between $50,000 and $74,999  

= 7,185 + 14,978

= 22,163

Now,

Putting value in formula

Probability of an event P(E) = (Number of favorable outcomes) ÷ (Total outcomes ).

Probability of an event P(E) = [tex]\frac{22163}{56908}[/tex]

                                                = 0.389

                                                = 0.40 (approx.)

Hence, the approximate probability is  0.40 .

To know more about Random selection and probability here:

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To find JL, we simply add the lengths of JK and KL together which gives us 22 units.

If K is the midpoint of JL, it means that JK is equal in length to KL.

Thus, we can set up the equation 5x + 1 (for JK) equal to 7x - 3 (for KL) since these expressions represent the lengths of JK and KL respectively.

Solving the equation 5x + 1 = 7x - 3 for x, we find that x = 2. Substituting x back into the expression for either JK or KL yields the length of one segment, which in this case is 11 units for both JK and KL.

Answer: There is one outlier, indicating very few books were checked out on that day.

Step-by-step explanation:

The given data of he number of books checked out from a library during the first two weeks of the month:

36, 39, 40, 42, 45, 2, 38, 41, 37, 38, 35, 37, 35, 38

Here , all the data value are near to each other except one i.e. 2.

Since 2 is very small value as compare to the other data values.

It means 2 is the outlier for the data.

It means only 2 books were checked out on that day, which is much lesser number of books than the other day.

Hence, the statements is true based on the data set :

There is one outlier, indicating very few books were checked out on that day.

The bird can travel approximately 5.7 miles in 2.1 hours.

To find the number of miles the bird can travel in 2.1 hours, we need to convert the speed from feet per second to miles per hour. There are 5280 feet in a mile and 3600 seconds in an hour, so the bird's speed is 4.0 * 3600 / 5280 = 2.727 miles per hour. Multiplying this speed by 2.1 hours gives us a total distance of 2.727 * 2.1 = 5.7207 miles, rounded to the nearest tenth, which is 5.7 miles. Therefore, the answer is option C) 5.7 mi.

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To solve the equation with absolute value expressions, isolate the absolute value terms and solve two separate equations. The solutions are x = -1 and x = 1.

To solve the equation 1/2 - x/3 = 5/6 with the absolute value expressions, we need to isolate the absolute value terms and solve two separate equations. First, rewrite the equation as |-x/3| = 5/6 - 1/2. Since the absolute value of a number is always positive, we can remove the absolute value symbols by considering the positive and negative cases separately.

For the positive case, we have -x/3 = 5/6 - 1/2. Simplifying, we get -x/3 = 1/3. Multiplying both sides by -3, we find x = -1. For the negative case, we have -(-x/3) = 5/6 - 1/2. Simplifying, we get x/3 = 5/6 - 1/2. Combining like terms, we have x/3 = 1/3. Multiplying both sides by 3, we find x = 1. Therefore, the solution set to the equation is {-1, 1}.

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Answer: B

Step-by-step explanation:

Answer:

B. {3,9,12}

Step-by-step explanation:

test approved

soup can is in the shape of cylinder

given, base area = 9 pi

base area = area of circle = pi * r^2 = 9 * pi

r = 3

total surface area of cylinder = 2 *pi*r(h+r)

= 2*3(10+3) pi=  78 pi

area for the label needed to wrap around the can with

no overlaps 78 pi inches^2

To solve the quadratic equation 2x^2-2x-12=0, the quadratic formula is used yielding two solutions, x = 3 and x = -2.

To find the solutions for the quadratic equation 2x^2-2x-12=0, we can use the quadratic formula. The general form of a quadratic equation is ax^2 + bx + c = 0. For the given equation, the coefficients are a = 2, b = -2, and c = -12. Applying the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a), we substitute in our coefficients to get:

x = (2 ± √((-2)^2 - 4(2)(-12))) / (2(2))

x = (2 ± √(4 + 96)) / 4

x = (2 ± √(100)) / 4

x = (2 ± 10) / 4

Thus, the two solutions for x are:

Therefore, the two solutions of the quadratic equation 2x^2-2x-12=0 are x = 3 and x = -2.

To solve the equation 2x^2 - 2x - 12 = 0, we can use the quadratic formula. The solutions are x = 3 and x = -2.

To solve the equation 2x^2 - 2x - 12 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

For our equation, a = 2, b = -2, and c = -12. Plugging in these values, we get:

$$x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(2)(-12)}}{2(2)}$$

Calculating the values inside the square root:

$$x = \frac{2 \pm \sqrt{4 + 96}}{4}$$

$$x = \frac{2 \pm \sqrt{100}}{4}$$

$$x = \frac{2 \pm 10}{4}$$

So the two solutions to the equation are:

$$x = \frac{2 + 10}{4}$$

$$x = \frac{12}{4}$$

$$x = 3$$

and

$$x = \frac{2 - 10}{4}$$

$$x = \frac{-8}{4}$$

$$x = -2$$

Final answer:

The students need 9 more blankets to reach their goal of donating 50 blankets. This is a part-whole problem because we are looking for the unknown number of blankets needed to complete the whole goal.

Explanation:

The student club set a goal of donating 50 blankets to a local shelter, with Ms. Carter’s class and Mr. Moriarti’s class contributing towards this goal. To determine how many more blankets are needed, we need to use addition and subtraction. We add the number of blankets collected by both classes then subtract that total from the goal. Ms. Carter’s class gathered 18 blankets and Mr. Moriarti’s class gathered 23 blankets. The sum of their contributions is 18 blankets + 23 blankets = 41 blankets. The goal is 50 blankets, so we subtract the number collected from the goal: 50 blankets – 41 blankets = 9 blankets. So, the answer is that the students need 9 more blankets to reach their goal of 50.

This is a part-whole problem because the unknown number of blankets that are still needed is part of the whole goal of 50 blankets. The problem does not compare the amounts collected by each class, nor does it compare the number still needed with the number collected; instead, it regards the collected blankets as part of the complete set, which is why we can dismiss the other options.

Answer:

the perimeter is [tex]8\sqrt{2} +2\sqrt{10}[/tex]

Step-by-step explanation:

It is given that PQRS is a parallelogram

with sides SR=[tex]4\sqrt{2}[/tex]  and QR = [tex]\sqrt{10}[/tex]

We know that the opposite sides in a parallelogram are equal

so we have

PQ= SR= [tex]4\sqrt{2}[/tex]

PS= QR= [tex]\sqrt{10}[/tex]

Now to find the perimeter of parallelogram we add all the sides

perimeter = [tex]PQ+SR+PS+QR[/tex]

                =[tex]4\sqrt{2} +4\sqrt{2} +\sqrt{10} +\sqrt{10}[/tex] ( plug the values)

                =[tex]8\sqrt{2} +2\sqrt{10}[/tex]

hence the perimeter is [tex]8\sqrt{2} +2\sqrt{10}[/tex]