Which of the following side lengths can form a triangle?

A) 2in, 3in, and 7in

B) 21cm, 23cm, and 44cm

C) 12mm, 36mm, and 53mm

D) 14ft, 17ft, and 30ft

Answer:

z = 12

Step-by-step explanation:

12 divided by .5 = 6.

Step-by-step explanation:

The prime factorization of 12 is

 12 = 2²×3

To find denominators suitable for your purpose, you need to group the factors

 {1, 2, 2, 3}

into two groups with different products that share at least one of the numbers that is not 1.

For example, your grouping could be (2, [2), 3], where a 2 is shared. That is, your denominators could be 2*2=4 and 2*3=6.

Another possible grouping is (1, [2), 2, 3], giving rise to denominators of 2 and 12.

Yet another is (1, [3), 2, 2], for denominators of 3 and 12.

Using the first grouping, a pair of mixed numbers matching your requirement might be

 1 3/4, 5 1/6

Answer:

79

Step-by-step explanation:

A square that has side length [tex]l=2 ft[/tex] has area [tex]2^2=4ft^2[/tex].

A circle that has a diameter 20 feet has area [tex]A=\frac{\pi d^2}{4}[/tex]

We substitute the diameter into the formula to obtain;

[tex]A=\frac{\pi \times 20^2}{4}=100\pi ft^2[/tex]

The number of squares that has area 4 feet square that can fit into a circle with area [tex]100\pi ft^2[/tex] is

[tex]=\frac{100\pi}{4}=25\pi=78.5398[/tex]

When we round to the nearest whole number; we have 79 squares.

Approximately 79 squares of size 2 ft by 2 ft can fit into a circle with a diameter of 20 feet.

To accurately determine how many 2ft by 2ft squares can fit into a circle with a diameter of 20 feet, let's perform a step-by-step calculation:

1. Calculate the area of the circle:

 [tex]\[ \text{Area of the circle} = \pi r^2 \][/tex]

  Given the diameter is 20 feet, the radius r is 10 feet:

[tex]\[ \text{Area of the circle} = \pi \times 10^2 = 100\pi \approx 314.16 \text{ square feet} \][/tex]

2. Calculate the area of one 2ft by 2ft square:

[tex]\[ \text{Area of one square} = 2 \times 2 = 4 \text{ square feet} \][/tex]

3. Calculate the theoretical maximum number of squares that can fit into the circle by dividing the area of the circle by the area of one square:

[tex]\[ \text{Theoretical number of squares} = \frac{\text{Area of the circle}}{\text{Area of one square}} = \frac{314.16}{4} \approx 78.54 \][/tex]

4. Round to the nearest whole number:

[tex]\[ \text{Rounded number of squares} = 79 \][/tex]

Answer:

-3(t - 7) = 24

t - 7 = -8

t = -1

Final answer:

The correct solution to the equation -3(t-7) = 24 is t = -1, which contradicts the reference indicating solutions for a different quadratic equation.

Explanation:

The equation presented, -3(t-7) = 24, does not yield the solutions t = 3.96 and t = -1.03 as the provided reference indicates. Instead, those solutions seem to be related to a different quadratic equation. To solve the given linear equation for t, you need to perform the following steps:

Therefore, the solution to the equation -3(t-7) = 24 is t = -1.

To find the probability that between 15% and 25% of a random sample of 275 traffic accidents involving an injury involve driver distraction, calculate the z-scores for both percentages and use the standard normal distribution.

To find the probability that between 15% and 25% of a random sample of 275 traffic accidents involving an injury involve driver distraction, we need to calculate the z-scores for both percentages and use the standard normal distribution.

Answer:

81

Step-by-step explanation:

To evaluate substitute x = - 2 into the expression

4( - 2)² - 20(- 2) + 25

= (4 × 4) + 40 + 25 = 16 + 40 + 25 = 81

Answer:

A. 2n-5

Step-by-step explanation:

Answer:

small and gaseous.

It would be A small and rocky and the planets names are Mercury, Venus, Earth, and Mars

Answer: The answer is A.

Step-by-step explanation: The only valid conclusion that is listed in the options is choice A. The correct one is that the length of a person’s foot is a cause of their shoe size, which implies that there is also a correlation between the length of a person’s foot and their shoe size.

Final answer:

The large box weighs 13.5 kilograms and the small box weighs 6 kilograms.

Explanation:

To solve this problem, we can assign variables to represent the weight of each type of box. Let's say the weight of a large box is L and the weight of a small box is S.

From the given information, we can set up a system of equations:

2L + 5S = 57 (Equation 1)

8L + 3S = 126 (Equation 2)

We can solve this system of equations using the method of substitution or elimination. Let's use elimination:

Multiply Equation 1 by 8 and Equation 2 by 2 to eliminate the S variable:

16L + 40S = 456 (Equation 3)

16L + 6S = 252 (Equation 4)

Subtract Equation 4 from Equation 3:

34S = 204

Solve for S: S = 6

Substitute the value of S into Equation 1:

2L + 5(6) = 57

2L + 30 = 57

2L = 27

Solve for L: L = 13.5

Therefore, the large box weighs 13.5 kilograms and the small box weighs 6 kilograms.

Similar is when a figure has the same shape, but different size.

Answer: 3, 1, 2

To find the unit rate divide the total miles by the total hours:

225 / 4 = 56.25 miles per hour

Answer:

It's B.

Step-by-step explanation:

A trunk has six faces . The total  surface area will be the sum of the areas of these faces.

The surface area of a rectangular prism (like a trunk) is the total area of the surface of the object and can be found using the formula A = 2lw + 2lh + 2wh, where 'l' represents length, 'w' represents width and 'h' represents height.

The surface area of a trunk, or any three-dimensional object, refers to the total area that the surface of the object occupies. In the case of a trunk, if we consider it as a rectangular prism (a box shape), that surface area can be found by adding the areas of all six faces of the prism. The formula to calculate the surface area (A) of a rectangular prism is A = 2lw + 2lh + 2wh where l denotes length, w width, and h height. Let's say, for example, that your trunk has a length of 3 units, a width of 4 units, and a height of 2 units. The surface area would then be 2*(3*4) + 2*(3*2) + 2*(4*2) = 24 + 12 + 16 = 52 square units.

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I think it is the first.I would choose that.

Answer:

9/6 and 3/2

Step-by-step explanation:

Let's remember the definition of "constant of proportionality":

The constant of proportionality is the constant value of the ratio k of two proportional quantities x and y; usually written y = kx.

In our case, x is the cups of milk and y is the cups of pancake mix. We need to find out k.

9 = k*6

9/6 = k

If we simplified the fraction, we have 3/2 (is equivalent to 9/6).

The correct answers are 3/2 and 9/6.

Answer:

A: x > 3/4

Step-by-step explanation:

First you simplify the equation.

Simplify 1/3x

Then Simplify the left side.

1/2-x/3<x/3

Move x/3 to the left side of the equation by subtracting it from both sides.

1/2-x/3-x/3<0

Now simplify the left side.

1/2-2x/3<0

Find the LCD of the terms of the equation. In this case it's 6.

Multiply each term by 6 and simply.

3-2x<2x

Move all terms that contain a x to the left side of the inequality.

3-4x<0

Subtract 3 from both sides.

-4x<-3

Now divide each term by -4 and simplify.

This gives us our answer of x > 3/4.

Hope this helps. :)

Answer:

Option A

fraction numerator square root of 2 over denominator 2 end fraction

Step-by-step explanation:

The answer can be obtained using a calculator.

It corresponds to a notable identity

sin (45) =  [tex]\sqrt{2}[/tex] / 2

sin (45) = 0.7071

[tex]\sqrt{2}[/tex] / 2  = 0.7071

Please see attached picture

Answer: y = −2

Step-by-step explanation:

* Hopefully this helps:) Mark me the brainliest:)

Answer:

D

Step-by-step explanation:

(0.5, 0) and (0, -2)

Answer:

See explanation

Step-by-step explanation:

1. Draw the dotted line y=-x. This line must be dotted, because the inequality y<-x is with sign < (without notion "or equal to"). Then shade the region that contains all values of y that are less than -x (bottom part that is shaded in red on the attached diagram).

2. Draw the solid line y=x-2. This line must be solid, because the inequality y≤x-2 is with sign ≤ (with notion "or equal to"). Then shade the region that contains all values of y that are less or equal to x-2  (bottom part that is shaded in blue on the attached diagram).

3. Their common part (region that is shaded in both red and blue colors) represents both inequalities.

It's this one, just did the test.

Answer:

B

Step-by-step explanation:

The volume (V) of a rectangular prism is

V = lbh

where l is the length, b the width and h the height

We are looking for 3 values that multiply together to give 10

Considering each of the options

A

100 × [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = 25 ≠ 10

B

10 × [tex]\frac{1}{2}[/tex] × 2 = 10

C

5 × 2[tex]\frac{1}{2}[/tex] × 2[tex]\frac{1}{2}[/tex] = 31.25 ≠ 10

D

10 × 10 × [tex]\frac{1}{2}[/tex] = 50 ≠ 10

B is the only possible dimensions for the prism

Answer:

The volume of the rectangular prism is [tex]V=442.341\ cm^{3}[/tex]

The surface area of the rectangular prism is [tex]SA=384.62\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=LWH[/tex]

substitute the values

[tex]V=(12.7)(8.1)(4.3)=442.341\ cm^{3}[/tex]

The surface area of the rectangular prism is equal to the area of its six faces

so

[tex]SA=2(8.1)(4.3)+2(12.7)(8.1)+2(12.7)(4.3)=384.62\ cm^{2}[/tex]

Answer:

y=2x+(-7)

Step-by-step explanation:

y=2x+c

solve for c

-1=2(3)+c

-1=6+c

-6-1=c

c=-7

y=2x+(-7)

Answer:

[tex]\large\boxed{y+1=2(x-3)}[/tex]

Step-by-step explanation:

The point-slope form of the equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

We have the slope m = 2 and the point (3, -1). Substitute:

[tex]y-(-1)=2(x-3)\\\\y+1=2(x-3)[/tex]

[tex] \cos(A) + \cos( B ) + \cos(C) \\ = 2 \cos( \frac{A + B}{2} ) \cos( \frac{ A- B}{2} ) + 1 - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2\cos( \frac{\pi - C}{2} ) \cos( \frac{A - B}{2} ) - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2 \sin \frac{C}{2} \cos( \frac{A - B}{2} ) - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \sin \frac{C}{2}] \\ = 1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \cos( \frac{A + B}{2} )] \\ = 1 + 2 \sin\frac{C}{2} \times 2 \sin( \frac{ \frac{A + B}{2} +\frac{A - B}{2} }{2} ) \sin( \frac{ \frac{A + B}{2} - \frac{A - B}{2} }{2} ) \\ = 1 + 4 \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}[/tex]

Answer:

The equation in point slope form is y= 2/3x+13/3

Step-by-step explanation:

In order to find the equation you need to find the slope, to find the slope you need to graph the two points and use the rise over run method, after using this you can conclude that the slope (m) is 2/3.

To find the y intercept you should plug in one of the points into the point slope formula which is y=mx+b.

Using the first point I get the equation 5=2/3(1)+b, next you isolate the b to get the equation, -b=2/3-5

Then write all the numerators above the common denominator getting 2-15/3

With this you get -b=-13/3 and then you can divide both sides by -1 to get a positive b.

Plug all of these into y=mx+b getting y=2/3x+13/3

The product of 4xy and (y^2 + 2x) is calculated by distributing 4xy to the terms in the parenthesis, resulting in the answer 4xy^3 + 8x^2y.

The question is asking to calculate the product of 4xy and (y^2 + 2x). To solve it, you can distribute 4xy to the terms inside the parenthesis. This gives you:

Therefore, the product of 4xy and (y^2 + 2x) is 4xy^3 + 8x^2y.

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Answer: to find f(-4)

Answer:

 2.1125 feet

Step-by-step explanation:

the vertex will be the maximum value of this parabola.  

the general form for a quadratic equation is:  ax² + bx + c, for this equation,

a = -0.2, b = 1.3, and c = 0

find the vertex by first using the formula x = -b/(2a)

x = -1.3/(2*-0.2)

  x = -1.3/-0.4

    x = 3.25

Now plug in that x value to find the actual maximum height

y = -0.2(3.25)² + 1.3(3.25)

    y = -0.2(10.5625) + 4.225

          y = -2.1125 + 4.225

                  y = 2.1125 feet

The maximum height the mouse can jump is approximately 2.1125 feet.

To find the maximum height the mouse can jump, you need to determine the vertex of the parabolic path because the vertex represents the highest point on the path. The equation of the path is given as:

y = -0.2x^2 + 1.3x

To find the vertex, you can use the formula:

x_vertex = -b / (2a)

Where "a" is the coefficient of the x^2 term, and "b" is the coefficient of the x term in the equation.

In your equation, a = -0.2 and b = 1.3. Plug these values into the formula:

x_vertex = -1.3 / (2 * (-0.2))

x_vertex = -1.3 / (-0.4)

x_vertex = 3.25

Now that you have the x-coordinate of the vertex, you can find the corresponding y-coordinate by plugging it back into the equation:

y = -0.2x^2 + 1.3x

y_vertex = -0.2(3.25)^2 + 1.3(3.25)

Calculate:

y_vertex = -0.2(10.5625) + 4.225

y_vertex = -2.1125 + 4.225

y_vertex = 2.1125

for such more question on height

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Answer:

Step-by-step explanation:

Look at the picture.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points (0, 4) and (-2, -2). Substitute:

[tex]m=\dfrac{-2-4}{-2-0}=\dfrac{-6}{-2}=3[/tex]

Answer:

-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

A. 250 x .32 = 80

B. 250 x .44 = 110 So, the answer is berries.

Final answer:

Out of 250 surveyed individuals, 80 people prefer peaches. Berries are the preferred choice of more than 100 people.

Explanation:

A total of 250 people were surveyed about their favorite fruit. To find out how many people prefer peaches, we calculate 32% of 250 people. This calculation is done by multiplying the total number of people by the percentage of those who prefer peaches:

250 people x 32% = 250 x 0.32 = 80 people

Therefore, 80 people prefer peaches.

To determine which type of fruit more than 100 people prefer, we apply the same calculation method. Here are the calculations:

Berries: 250 x 44% = 110 people

Peaches: 250 x 32% = 80 people

Cherries: 250 x 24% = 60 people

More than 100 people prefer berries.

Answer:

104.65 km/hour

Step-by-step explanation:

We need to convert miles to kilometers.  The miles cancel so

65 miles         1.61 kilometers      104.65km

--------------- * -------------------   = -----------------

hour                1 mile                      hour

The speed limit is 104.65 km/hour