What is the slope of the line that passes through (−2, −4) and (3, 7) ?
A.9/ 7 B. 11/ 5 C. 3 D. I don't know.

Answer:

10

Step-by-step explanation:

There are 100 squares in this square, so each tiny square is 10 because you take the square root of 100.

Hope this helps! :)

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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Answer:

D.) 29

Step-by-step explanation:

Add 15 and 14

Answer:

1/ 6

7/ 12

Step-by-step explanation:

Answer:

7a) 1/7

7b) 7/12

Step-by-step explanation:

For 7a) you know that the denominator of 5/6 is equal to 6 so that means you should make 1 have a denominator of 6. To do that, you have to multiply the denominator and the numerator by 6 to get 6/6-5/6=?. With this, you could easily solve the two fractions because they have equal denominators. You subtract the numerator and keep the denominator. 6-5=1 so the answer is 1/6.

For 7b) I would first convert 1 3/12 into an improper fraction. To do that, you have to multiply the whole number by the denominator then add the numerator. It will look like this 12x1+3/12 which is equal to 15/12. This makes the question easier to solve. You then want to convert 2/3 to have a denominator of 12. To do that, you have to multiply 4 on the numerator and denominator. This will turn the fraction into 8/12. After you do that, you can easily subtract the fractions again. you do 15-8/12 which is equal to 7/12.

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Therefore , the solution of the given problem of equation comes out to be drops to the earth after 4 seconds because t=0 represents the initial height.

In mathematical formulas, the identical symbol expression (attempted to impose is used to denote the equality of two assertions. Many academic numbers are shown to be equal using mathematical equations, also known as assertions. For instance, the equal sign divides the answer y + 6 = 12 into two portions, which also contains the digits 12 and b + 6. One can determine how many lines each sign element correlates to.

Here,

The vertex of the parabolic graph is where the projectile reaches its highest point. Using the formula t=-b/2a, where a=-5 and b=20 from the provided equation, the vertex can be located.

Consequently,

=> t = -20/-10 = 2 seconds.

When t=2 is substituted into the equation,

=>

h=-5(2)2+20(2)=20 metres is obtained. The projectile can therefore be as high as 20 metres.

When h=0, the ball lands on the earth. In the provided equation, substituting h=0 results in

=> -5t²+20t=0, which can be factored as t(-5t+20)=0.

Consequently, t = 0 or t = 4 seconds.

The ball, however, drops to the earth after 4 seconds because t=0 represents the initial height.

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The expression 2^2 x 4 x (2^2)^4 / 2^2 x 2^5 can be written as a power of 2 as 2^3.

The expression 2^2 x 4 x (2^2)^4 / 2^2 x 2^5 can be written as a power of 2 by using the rules of exponents.

First, the numerator can be simplified by using the rule of exponents that states that when two terms with the same base are multiplied, the exponents can be added together.

2^2 x 4 x (2^2)^4 = 2^2 x 4 x 2^8

Then the denominator can be simplified by using the same rule.

2^2 x 2^5 = 2^7

The expression can be written as a power of 2 by dividing the exponent of the numerator by the exponent of the denominator.

2^2 x 4 x 2^8 / 2^7 = 2^3

Therefore, the expression 2^2 x 4 x (2^2)^4 / 2^2 x 2^5 can be written as a power of 2 as 2^3.

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Answer:

2/3 ≈ 0.666667

5/11 ≈ 0.454545

5/6 ≈ 0.833333

6/7 ≈ 0.857143

Step-by-step explanation:

Easiest and fastest way to do this is to use a calculator to find your decimals and then approximate.

Answer:

2/3 = 2 divided by 3 so 2 divided by 3 = 0.666667. We round up because it is a repeating decimal which goes on forever

5/11= 5 divided by 11 = 0.454545

5/6 = 5 divided by 6 =0.833333

6/7 = 6 divided by 7 = 0.857143

rounded up because it is an infinite decimal

Hope this helps

Step-by-step explanation:

a. The chi-square statistic is not significant at the α level of .01.

b. The chi-square statistic is significant at the α level of .05.

a. With a chi-square statistic of 3.86 and a critical value of 6.63 at α level of .01, we can compare the two values.

Since 3.86 < 6.63, this means that the chi-square statistic is not significant at the α level of .01.

In other words, the result is not statistically significant and we fail to reject the null hypothesis.

b. With a chi-square statistic of 67.81 and a critical value of 3.84 at α level of .05, we can again compare the two values.

Since 67.81 > 3.84, this means that the chi-square statistic is significant at the α level of .05.

In other words, the result is statistically significant and we reject the null hypothesis.

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Answer: The lowest possible product would be -6724 given the numbers 82 and -82.

We can find this by setting the first number as x + 164. The other number would have to be simply x since it has to have a 164 difference.

Next we'll multiply the numbers together.

x(x+164)

x^2 + 164x

Now we want to minimize this as much as possible, so we'll find the vertex of this quadratic graph. You can do this by finding the x value as -b/2a, where b is the number attached to x and a is the number attached to x^2

-b/2a = -164/2(1) = -164/2 = -82

So we know one of the values is -82. We can plug that into the equation to find the second.

x + 164

-82 + 164

82

Step-by-step explanation: Hope this helps.

Answer: 53 c

Step-by-step explanation:

If 8 oranges cost 60c

7 oranges will cost (7 x 0.60) / 8 = 0.53

Answer:

101.5

Step-by-step explanation:

Answer: 3 7/

Step-by-step explanation: Change 3 2/3 and 1 4/5 from mixed fraction to improper fraction, giving 11/2 (3×3=9, then 9+2=11) and 9/5 (1×5=5, then 5+4=9)1.

With 11/2 and 9/5, the LCM(Lowest Common Multiple) is 10. So 10÷2=5, then 5×11=55. Likewise, 10÷5=2, then 2×9=18.

55-18=37. Therefore the answer is 37/10. Change that back to mixed fraction and it gives you 3 7/10

Answer:

Option (A)

Step-by-step explanation:

Let the Sine of the given angle θ is,

Sinθ = \(\frac{x}{y}\)

Then θ = \(\text{Sin}^{-1}(\frac{x}{y} )\)

From the given values in the question,

Sinθ = \(\frac{7}{29}\)

θ = \(\text{Sin}^{-1}(\frac{7}{29} )\)

θ = 13.97°

Therefore, measure of the angle 'θ' will be 13.97°.

Option (A) will be the answer.

The function is given as g(n) = -n + 5 then the value of g(1) is 4. the correct option is B.

Function is a type of relation, or rule, that maps one input to specific single output. . Simplification usually involves making the expression simple and easy to use later.

The procedure in mathematics to utilize and analyze the function or expression to make the function or expression uncomplicated or more coherent is called simplifying and the process is called simplification.

From the given function, g(n) = -n + 5

By plugging in the value of 'x' in the bracket, we have;

g(n) = -n + 5

g(1) = -1 + 5

g(1) = 4

Therefore, the value of function is 4.

Hence, the correct option is B.

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Answer: c

Step-by-step explanation:

The diameter of Mikayla's cereal bowl, is 5.7 in

The distance from one point on a circle through the center to another point on the circle. It is also the longest distance across the circle.

Given that, the rim of Mikayla’s cereal bowl has a circumference of 18 inches. we need to determine the diameter of the cereal bowl,

Since, the rim is circular, therefore,

Circumference of circle = π × diameter

Therefore,

π × diameter = 18

Diameter = 18 / 3.14

Diameter = 5.7

Hence, the diameter of Mikayla's cereal bowl, is 5.7 in

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Answer: 9

Step-by-step explanation:

The value of x/y is 35/37. The correct answer is option B).

Let's start by the first right triangle and the inscribed square. We know that the square has side length x and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one vertex of the square coincides with the right-angle vertex of the triangle, we have that the side length x of the square is also the length of the altitude from the right angle to the hypotenuse of the triangle. Therefore, we can write:

x = \((3*4)/5 = 12/5\)

Now the second right triangle and the inscribed square:

We know that the square has side length y and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one side of the square lies on the hypotenuse of the triangle, we have that the sum of the areas of the two smaller squares is equal to the area of the larger square. Therefore, we can write:

\(x^{2} + y^{2} = 5^{2} = 25\)

Substituting\($x = {12}/{5}\) gives

\((12/5)^{2} + y^{2} = 25\)

Simplifying this equation gives

\(y^{2} = 25 - (144/25) = (25^{2} - 144)/25 = 481/25\)

Taking the square root of both sides gives

y = \(\sqrt{481}/5\)

Finally, we compute x/y:

x/y = \(12*\sqrt{481}/ \sqrt{481}*5\)

x/y = 35/37

The correct option is B)

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--The given question is incomplete, the complete question is

"A square with side length x is inscribed in a right triangle with sides of length 3, 4, and 5 so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length y is inscribed in another right triangle with sides of length 3, 4, and 5 so that one side of the square lies on the hypotenuse of the triangle. What is x/y?

(A) 12/13

(B) 35/37

(C) 1

(D) 37/35

(E) 13/12"

Answer:

C. -7.4

Step-by-step explanation:

-(5(-2) + 2) + (3(3) + 2(-4.2))

(-10+2) + (9 + -8.4)

-8 + 0.6

-7.4

The homogeneous and particular solutions to obtain the general solution to the differential equation.

The solution to the differential equation d²y/dt² + y = cos(t) with initial conditions y(0) = 0 and y'(0) = 0 can be found using the method of Variation of Parameters. The solution is:

y(t) = (1/2)*cos(t) - (1/2)tsin(t) + (1/2)*∫[0,t] sin(τ)*cos(τ)dτ

where the integral represents the convolution of the functions cos(t) and sin(t) with the Green's function of the differential equation, which is sin(t). The first two terms are the homogeneous solution of the differential equation, while the third term is the particular solution obtained using the method of Variation of Parameters.

To obtain this solution, we first find the homogeneous solution by assuming y(t) = Acos(t) + Bsin(t) and substituting it into the differential equation. We then solve for the constants A and B using the initial conditions. Next, we use the method of Variation of Parameters to find the particular solution, which involves finding two functions u(t) and v(t) and using them to construct the particular solution. Finally, we add the homogeneous and particular solutions to obtain the general solution to the differential equation.

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Answer:

x * 3/8(s) = 5/4

5/4 ÷ 3/8(s) = x

Step-by-step explanation:

Answer:

Step-by-step explanation:

How many 3/8 are in 5/4? We can set this number as x. Therre are x number of 3/8 that make up 5/4:

Therefore the PART A is: x* 3/8 = 5/4

On the other hand, 5/4 / 3/8 = x (this is just the reverse of what I mentioned earlier)

I hope this helps! :)

The general solution for the non-homogeneous equation is the sum of the homogeneous solution and the particular solution::

y(x) = c1 * cos(√-17i * x) + c2 * sin(√-17i * x) + (3/64) * e^8x

where c1 and c2 are arbitrary constants.

The method of undetermined coefficients is used to find a particular solution for a non-homogeneous linear ordinary differential equation of the form:

dy/dx + p(x)y = g(x)

where p(x) and g(x) are known functions. To use this method, we first find the general solution of the corresponding homogeneous equation:

dy/dx + p(x)y = 0

The general solution of this homogeneous equation can be written as:

y = c1 * y1(x) + c2 * y2(x)

where c1 and c2 are arbitrary constants and y1(x) and y2(x) are the linearly independent solutions of the homogeneous equation.

Next, we guess a particular solution yp of the non-homogeneous equation of the form:

yp = A * f(x)

where A is an unknown constant and f(x) is a function of x that matches the form of the forcing function g(x).

For the given equation: y'' + 17y = 3e^8x

The corresponding homogeneous equation is: y'' + 17y = 0

The characteristic equation is: r^2 + 17 = 0

The roots are: r = ±√-17i

So the general solution of the homogeneous equation is:

y = c1 * cos(√-17i * x) + c2 * sin(√-17i * x)

where c1 and c2 are arbitrary constants.

For the non-homogeneous equation, we guess a particular solution of the form:

yp = A * e^8x

where A is an unknown constant. Substituting this into the non-homogeneous equation, we have:

yp'' + 17yp = A * 8^2 * e^8x = A * 64e^8x

Comparing the right-hand sides of the two equations, we see that yp'' + 17yp = A * 64e^8x = 3e^8x, so A = 3/64.

Therefore, a particular solution for the non-homogeneous equation is:

y = yp = (3/64) * e^8x

The general solution for the non-homogeneous equation is the sum of the homogeneous solution and the particular solution:

y = c1 * cos(√-17i * x) + c2 * sin(√-17i * x) + (3/64) * e^8x

where c1 and c2 are arbitrary constants.

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The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.

To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.

The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.

To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.

To calculate the minimum sterilization time, we can use the following formula:

Minimum Sterilization Time = D-value × log10(N0/Nf)

Where:

D-value is the decimal reduction time (0.65 minutes).

N0 is the initial number of organisms (10^6).

Nf is the final number of organisms (10^6 × 10^-3).

Let's calculate it step by step:

Nf = N0 × 10^-3

= 10^6 × 10^-3

= 10^3

Minimum Sterilization Time = D-value × log10(N0/Nf)

= 0.65 minutes × log10(10^6/10^3)

= 0.65 minutes × log10(10^3)

= 0.65 minutes × 3

= 1.95 minutes

Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes

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Answer:

500.61

Step-by-step explanation:

5 multiplied by 100 = 500

1/10 = 0.1, So 6 multiplied by 0.1 = 0.6

1/100 = 0.01, So 1 multiplied by 1 = 0.01

500 + 0.6 + 0.01 = 500.61

\((5 \times 100) + (6 \times \frac{1}{10} ) + (7 \times \frac{1}{100} )\)

\(5 \times 100 = 500\)

\( \frac{6}{1} \times \frac{1}{10} = \frac{6}{10} = 0.60\)

\( \frac{7}{1} \times \frac{1}{100} = \frac{7}{100} = 0.07\)

\(500 + 0.60 + 0.07 = 500.67\)

Answer:

I believe its 10 but forgive me if I'm wrong

Answer:

-.2, 2.4

Step-by-step explanation:

answer on edge