The fraction 7/8 is a multiple of what unit fraction?

Answer:

(4, 5)

Step-by-step explanation:

All the medians intersect at the same point. RU and PS are medians so they intersect at the same point that medians QT and PS intersect.

Answer:

Using the identity rule:

[tex](a-b)^2 = a^2-2ab+b^2[/tex]

Given the equation:

[tex]x^2-12x+36 = 90[/tex]

Rewrite the above equation as:

[tex]x^2-2 \cdot x \cdot 6+6^2 = 90[/tex]

Apply the identity rule:

[tex](x-6)^2 = 90[/tex]

Take square root to both sides we have;

[tex]x-6 = \pm \sqrt{90}[/tex]

Add 6 to both sides we have;

[tex]x = 6\pm \sqrt{90}[/tex]

or

[tex]x = 6 \pm 3\sqrt{10}[/tex]

Therefore, the value of x are:

[tex]6+3\sqrt{10}[/tex] and [tex]6-3\sqrt{10}[/tex]

Answer:

The answer is actually 16/52.

Step-by-step explanation:

There are 13 hearts and 4 aces. However, one of the 4 aces is a heart, so there would only be 3 other aces.

13 hearts + 3 other aces = 16

There are 52 cards in a deck, so the probability would be 16/52.

The solution is : 1/4  is the probability that it has your favorite type of meat on it.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, we have,

given that,

At the sandwich shop, there are four different types of meat and three different types of cheese.

If you select a sandwich without looking,

then we need to find the probability.

Solution

There are four different types of meat and three different types of cheese

Probability = number of required outcome / number of possible outcome

Total amount of meat = number of possible meat = 4

If you only have one favorite type of meat the probability 1/4

Hence, the correct answer is Option B.

The solution is : 1/4  is the probability that it has your favorite type of meat on it.

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Answer: [tex]-7+(-10)+(-13)+(-16)+(-19)+(-22)=-87[/tex]

Step-by-step explanation:

Given finite sequence : -7, -10, -13, . . ., -22.

Difference between first and second term=[tex]-10-(-7)=-10+7=-3[/tex]

Difference between second and third term =[tex]-13-(-10)=-13+10=-3[/tex]

Hence, the common difference = -3

The next term after -13 =[tex]-13+(-3)=-13-3=-16[/tex]

The next term after -16 =[tex]-16+(-3)=-16-3=-19[/tex]

The next term after -19 =[tex]-19+(-3)=-19-3=-22[/tex].........which is the last term of the sequence.

Now, the sum of the given sequence =[tex]-7+(-10)+ (-13) + (-16) + (-19) + (-22) [/tex]

[tex]=-7-10-13-16-19-22= -87[/tex]

Answer:

1 - V = Smaller solid=512 cm³

    V = Larger solid=2197 cm³

2-  1.625² = 2.64

3 - SA of big solid is found 2535 cm²

Answer:

[tex]x = -4 \frac{+}{-} 2\sqrt{5\\}[/tex]

Step-by-step explanation:

Final answer:

Using the kinematic equation for vertical motion, the maximum height a tennis ball will reach when fired at an initial speed of 130 ft/s from a height of 2 feet is approximately 264.91 feet.

Explanation:

Calculating the Maximum Height of a Tennis Ball

The maximum height that a tennis ball will attain when fired vertically can be calculated using the kinematic equations that describe projectile motion. Given that the initial speed of the ball is 130 feet per second and it is launched from a height of 2 feet, we can use the equation for vertical motion:

v^2 = u^2 + 2gh

where v is the final velocity (0 ft/s at the highest point), u is the initial velocity (130 ft/s), g is the acceleration due to gravity (-32.2 ft/s^2, negative because it is directed downwards), and h is the height gained. Rearranging the formula to solve for h we get:

h = (v^2 - u^2) / (2g) = (0 - 130^2) / (2 * -32.2)

After calculating h, we add the initial launch height of 2 feet to find the maximum height above ground:

Maximum Height = h + 2 feet

By plugging in the values, we can find the maximum height to be:

Maximum Height = (0 - 16900) / (-64.4) + 2 ≈ 264.91 feet (rounded to the nearest hundredth).

Therefore, the maximum height attained by the tennis ball is approximately 264.91 feet.

Here, first we need to find the number of cameras that can be sold, so that total costs are equal to total revenues.

Let the number of cameras that can be sold be "x".

Total revenue = $ 14x

Total costs will be = $ 2100 + $9x

So, the equation that will be formed ⇒

14 x = 2100 + 9x

5x = 2100

x = 420

Thus, in order to make total costs equal to total revenues, 420 cameras are required to be sold.

If instead of 420, 470 cameras are sold, the daily profit will be calculated as under -

Total revenue = $ 14 × 470 cameras = $ 6,580

Total costs = $ 2100 + ( $ 9 × 470 cameras) = $ 6,330

Daily profit = Total revenue - Total costs = $ 6,580 - $ 6,330 = $ 250

To make the function differentiable, we need to make it continuous at x = 1 by ensuring that both sides of the function have the same value. The values of the constants b and c are b = 1 - c, where c is any real number.

The function given is:

f(x)={2xbx2+cxx ≤ 1  x > 1

To determine the values of the constants b and c such that the function is differentiable, we need to make sure that the function is continuous at x = 1 and both sides of the function have the same derivative at x = 1.

To do this, we need to find the limits of the function as x approaches 1 from both the left and the right sides.

From the given function, we can see that when x ≤ 1, the function is a polynomial and is differentiable for any value of b and c.

However, when x > 1, the function is not differentiable unless we choose the values of b and c such that the function becomes continuous at x = 1.

To make the function continuous, we need to make sure that both sides of the function have the same value at x = 1.

Substituting x = 1 into the given function, we have 2b(1)(1) + c(1) = b + c = 1 (since the function should be continuous at x = 1).

Therefore, the values of the constants b and c that make the function differentiable are b = 1 - c, where c is any real number.

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Choose the correct conic section to fit the equation. x^2/36-y^2=1 Circle Ellipse Parabola Hyperbola

Solution:

The general equation of circle is:-

(x-h)²+(y-k)=r²

The general equation of ellipse is:-

[tex] \frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{{b^{2}}}=1 [/tex]

The general equation of parabola is:-

y = a(x-h)²+k

The general equation of hyperbola is:-

[tex]\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{{b^{2}}}=1[/tex]

The equation of conic section is: x^2/36-y^2=1

[tex]\frac{(x-0)^{2}}{36}-\frac{(y-0)^{2}}{1}}=1[/tex]

[tex]\frac{(x-0)^{2}}{6^{2}}-\frac{(y-0)^{2}}{{1^{2}}}=1[/tex]

Hence, this is hyperbola.

Answer: Hyperbola Option (D)

Answer:

333 and 1000

Step-by-step explanation: