The diagonal of a square is 8 cm.
What is the length of the side of this square?
Give your answer as an exact surd in its simplest form

Answer:

She has 9 nickels, and 8 dimes.

Step-by-step explanation:

We know that she has a total of $1.25. We know that a nickel is $0.05, and that a dime is $0.10.

9x$0.05=$0.45

8x$0.10=$0.80

Answer:

9 nickels

8 dimes

Step-by-step explanation:

.05(n + 1) + .10n = 1.25

.05n + .05 + .10n = 1.25

.15n = 1.20

n = 1.2 / .15

n = 8

but there are 9 nickels because there is "one more nickel than dimes"

(-10/252) x (1/0.9165) = 0.0175 rad/sec is the equation for theta/dt.

Angle theta in the displayed figure can be expressed as

Theta sin = 10/sin

The angle will change at the following rate:

(-10/x2)(dx/dt) = cos theta(theta/dt)

Now, when x equals 25 feet, we require d theta/dt.

The fishing line is reeled in at a rate of

dx/dt = -1 ft/sec.

Now, if x equals 25, then Cosine equals

[ (x2-100)]

Cosine equals [ (252-100)]/25 = 0.9165So,

(-10/x2)(dx/DT)(1/cos theta) = theta/DT

The formula for theta/it is (-10/252)x(1/0.9165) = 0.0175 rad/sec.

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it's 7 it's 7 it's 7 it's 7 it's 7 it's 7it's 7 it's 7 it's 7it's 7 it's 7 it's 7

Answer:

C

Step-by-step explanation:

3x^2-30x=72

3(x^2-10x)=72

x^2-10x=24

Then do the subtitules

Answer:C

Give me brainlliest

Answer:   C   x = -2

Step-by-step explanation:

\(3x^{2} - 30x - 72 = 0\)

[Add 72 on both sides]

\(3x^{2} - 30x = 72\)

[Factorise Left Hand Side of equation to get 3 on one side of a bracket]

\(3(x^{2} -10x) = 72\)

[Divide each side by 3 to just get the brackets and the x's on one side]

\(x^{2} -10x = 24\)

[Minus 24 on both side as the equation must = 0]

\(x^{2} -10x-24=0\)

[Solve the square on the left hand side]

\((x-12)(x+2)=0\)

[Solve for x on left hand side - two possible answers]

\(x-12=0 \\ x=12\)

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

[The answer '12' is not in the option for the question so '-2' is the answer]

Answer:

The value of x is 7 if the equation can be reduced to (x + 9)³ = 4096 after applying the properties of the integer exponent option (C) 7 is correct.

What is an integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The equation is:

After solving:

(x + 9)³ = 4096

x + 9 = ∛4096

x + 9 = 16

x = 7

Thus, the value of x is 7 if the equation can be reduced to (x + 9)³ = 4096 after applying the properties of the integer exponent option (C) 7 is correct.

The option that is correct about a probability distribution is D. All or the above.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

In this case, the sum of all possible outcomes must equal 1, the outcomes must be mutually exclusive and the probability of each outcome must be between 0 and 1 inclusive

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Answer:

P=26 cm A=40 cm^2

Step-by-step explanation:

Perimeter:

5+5+8+8=26

Area:

8x5=40

Answer:

Circumference of the Circle is 2π(radius)= 2πr

Answer:

I would say it is 2 pie r

Step-by-step explanation:

The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.

Given that,

For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290

We have to find the data of IQR.

We know that,

IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.

IQR Formula is Q₃ - Q₁

So,

Q₃ = 290

Q₁ = 200

Then ,

IQR = Q₃ - Q₁

IQR = 290 - 200

IQR = 90

Therefore, The value of IQR is 90.

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If he water in Earth’s oceans has a volume of about 3.2x10⁸ cubic miles, it would take 3.52x10²⁰ gallon jugs to hold all the water in Earth's oceans.

To calculate how many gallon jugs it would take to hold all the ocean water on Earth, we need to multiply the volume of the water by the conversion factor from cubic miles to gallons.

Given that the water in Earth's oceans has a volume of about 3.2x10⁸ cubic miles and there are about 1.1x10¹² gallons in 1 cubic mile, we can calculate the total number of gallons using the following equation:

Total gallons = (Volume in cubic miles) x (Gallons per cubic mile)

Substituting the given values, we get:

Total gallons = (3.2x10⁸) x (1.1x10¹²) = 3.52x10²⁰

This number is very large and is written in scientific notation to make it more manageable. Scientific notation is a compact way of writing very large or very small numbers using a power of ten. In this case, the number is expressed as a coefficient (3.52) multiplied by 10 raised to the power of 20 (10²⁰).

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Answer:

s = 9

Step-by-step explanation:

We can find the slope given two points

m = (y2-y1)/(x2-x1)

 9 = (s-0)/(9-8)

 9 = (s)/1

S = 9

The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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Answer:

When I do not get a perfect score on my test, I feel __dissapointed________.

Step-by-step explanation:

Answer:

Step-by-step explanation:

scared to go home

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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The function F(x, y) has a local maximum at (-2, -3), saddle points at (2, -3) and (-2, 1), and a local minimum at (2, 1).

To find the critical points and classify them as local maxima, local minima, or saddle points, we need to find the partial derivatives of the function F(x, y) and evaluate them at each critical point.

Given the function F(x, y) = x³ - 12x + y³ + 3y² - 9y, let's find the partial derivatives:

∂F/∂x = 3x² - 12

∂F/∂y = 3y² + 6y - 9

To find the critical points, we set both partial derivatives equal to zero and solve the resulting system of equations:

3x² - 12 = 0 --> x² = 4 --> x = ±2

3y² + 6y - 9 = 0 --> y² + 2y - 3 = 0 --> (y + 3)(y - 1) = 0 --> y = -3 or y = 1

Therefore, the critical points are (-2, -3), (2, -3), and (-2, 1).

To classify these critical points, we use the second partial derivatives test. The second partial derivatives are:

∂²F/∂x² = 6x

∂²F/∂y² = 6y + 6

Now, let's evaluate the second partial derivatives at each critical point:

At (-2, -3):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since both second partial derivatives are negative, the point (-2, -3) corresponds to a local maximum.

At (2, -3):

∂²F/∂x² = 6(2) = 12 (positive)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since the second partial derivative with respect to x is positive and the second partial derivative with respect to y is negative, the point (2, -3) corresponds to a saddle point.

At (-2, 1):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(1) + 6 = 12 (positive)

Since the second partial derivative with respect to x is negative and the second partial derivative with respect to y is positive, the point (-2, 1) corresponds to a saddle point.

Therefore, the critical points are classified as follows:

Local maximum: (-2, -3)

Saddle points: (2, -3) and (-2, 1)

Local minimum: (2, 1)

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Answer: 1<x<3

Step-by-step explanation:

There are 3  rules in one that are needed for this problem

1st:  you can never get a 0 at the bottom of a denominator so x \(\neq\) 1

\(\sqrt{x-1}=0\\ x-1=0\\x=1\) would make a value of 0 on the bottom of a denominator which is not allowed.

2nd:  you can never get a - under the square root so x cannot be less than 1

3rd.  you can never get a log that is equal to 0 or less than 0 so x

3-x=0

-x=-3

x=3

so x cannot =3 or be greater than 3

the values that x CAN be are  1<x<3

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the required data are not given.

I will use the following data as an illustration of how to calculate median and range.

We have:

\(x: 11, 13, 14, 15, 18, 20\)

Calculate range

Identify the highest and the least

\(Highest = 20\)

\(Least = 11\)

So, the range is:

\(Range = Highest -Least\)

\(Range =20-11\)

\(Range =9\)

Calculate the median

The number of data we are using is 6 (i.e. even).

So, the position of the median item is:

\(Median =\frac{1}{2}(n+1)\)

\(Median =\frac{1}{2}(6+1)\)

\(Median =\frac{1}{2}*7\)

\(Median =3.5th\)

A decimal result implies that the median is the mean of the integer values before and after the result.

In this case, the median is the mean of the item at 3rd and 4th positions.

So:

\(Median = \frac{14+15}{2}\)

\(Median = \frac{29}{2}\)

\(Median = 14.5\)

The position of the mass in the undamped spring-mass system can be represented by the equation u(t) = (A cos(ωt) + B sin(ωt)) / k. Therefore, position of the mass at any time t in feet is given by u(t) = 4.5 cos(4t).

In this case, the external force acting on the system is 108 cos(4t) lb. To determine the position of the mass, we need to solve the differential equation that represents the motion of the system.

Using Newton's second law, F = ma, and considering that the mass m = 24 lb, the equation becomes:

24 * d^2u/dt^2 = 108 cos(4t)

Simplifying, we have:

d^2u/dt^2 = 4.5 cos(4t)

This is a second-order linear homogeneous differential equation with a constant coefficient. The solution to this equation will be a linear combination of the homogeneous and particular solutions.

The homogeneous solution, representing the free oscillation of the system, is u_h(t) = C1 cos(2t) + C2 sin(2t).

The particular solution, representing the forced motion caused by the external force, can be assumed in the form u_p(t) = A cos(4t) + B sin(4t).

By substituting u_p(t) into the differential equation, we can determine the values of A and B.

Solving the differential equation for the particular solution, we find:

A = 18 and B = 0

The complete solution for the position of the mass in feet is:

u(t) = (18 cos(4t)) / 4

Simplifying further, we get:

u(t) = 4.5 cos(4t)

Therefore, the position of the mass at any time t in feet is given by u(t) = 4.5 cos(4t).

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The closest answer choice to this result is C: 5%, which is not very close. Therefore, the correct answer is not given as a choice The total area of Kelly's home is: 2,100 square feet.

2,100 square feet

To find the percentage of Kelly's home that is taken up by her office, we need to calculate the area of her office and divide it by the total area of her home.

The area of Kelly's office is:

812 feet x 1214 feet = 986,768 square feet

The total area of Kelly's home is:

2,100 square feet

To find the percentage of Kelly's home taken up by her office, we divide the area of her office by the total area of her home and then multiply by 100 to convert the answer to a percentage.

(986,768 square feet / 2,100 square feet) x 100 = 469.41%

This means that Kelly's office takes up almost 470% of her home, which doesn't make sense because it's impossible for an office to take up more area than the entire home.

The error occurred because we calculated the area of Kelly's office in square feet, but we need to calculate it in square feet relative to her entire home.

To do this, we need to divide the area of her office by the area of her home and then multiply by 100 to convert the answer to a percentage.

(986,768 square feet / 2,100 square feet) x 100 = 47%

Therefore, approximately 47% of Kelly's home is taken up by her office.

The closest answer choice to this result is C: 5%, which is not very close. Therefore, the correct answer is not given as a choice

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Answer:

The answer is -1/9

Step-by-step explanation:

The slope of a perpendicular line is the opposite reciprocal.

To find the slope you take the given slope (9) and flip the reciprocal which results it turning into 1/9.

Then make it the opposite value. Like switching a negative to a positive or a positive to a negative. For this case, you make 1/9 into a -1/9

Assume the three students will receive a minimum of 250 points overall. Ahmed received x + 5 points and Ayo received x - 3 points, respectively, if Mohammed received x points.

The marks Mohammed received are represented by the variable x, and we use this number to determine the marks Ahmed and Ayo received.

The formula for the three boys' combined marks is: x + (x + 5) + (x - 3) = 250.

Expanding and figuring out x

3x + 2 = 250

3x = 248

x = 82

Therefore, Mohammed received at least 82 points, Ahmed received 87 points, and Ayo received 79 points. If the final score is precisely 250, they might have obtained these minimal marks.

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Answer:

points are free?

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

clockwise is rotating it to the right. And then 180 rotation would cause the image to be flipped upside down

Answer:

y = (4/5)x + 16

Point-slope form:

y - 12 = (4/5)(x + 5)

Step-by-step explanation:

slope = m; (-5, 12)

m = (4/5)    (x₁, y₁)

y - y₁ = m(x - x₁)

y - 12 = (4/5)(x - (-5))

y - 12 = (4/5)(x + 5)

y - 12 = (4/5)x + 4

  +12                +12

--------------------------

y = (4/5)x + 16

I hope this helps!

On solving the provided question, we can say that by equation

30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

x = amount (ton) of vegetables sold on day one; y = amount (ton) of vegetables sold on day two. Z = the amount of vegetables sold on the third day (in tons).

\(x=y-3\\z=(5/9)*(x+y)\\x+y+z=98\\x+y+[(5/9)*(x+y)]=98\\ 9x+9y+5x+5y=882\\14x+14y=882\\x=y-3\\14x+14y=882\)

solution

\(x=30\\y=33\\x+y+z=98---- > z=98-(x+y)---- > z=98-63--- > 35\)

30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.

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Answer:

y=2/3x+-1

Step-by-step explanation:

Answer:

The minimum number of fish each must have caught is 90 fishes

Step-by-step explanation:

The number of fishes Tisha's net can hold = 15

The number of fishes Dana's net can hold = 18

Let the total number of fishes both Tisha and Dana caught = X

15 × A = 18 × B = X

Therefore, X is the lowest common multiple (LCM) of 15 and 18 given as follows;

15 = 3 × 5

18 = 3 × 6

Therefore, the LCM of 18 and 5 = 3 × 5 × 6 = 90

Which gives, the minimum number of fish each must have caught = 90 fishes.

Answer:

A negative number

Step-by-step explanation:

Answer:

19.445

Step-by-step explanation:

Answer:

2bs + b^2, this is the equation to find the surface area. B is base length and s is slant height.

Step-by-step explanation:

From the data points given the linear equation in slope-intercept form is y = -1/2x + 4.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first two data points are - (-3,5.5) and (-1,4.5)

The slope-intercept form of the equation is -

y = mx + b

m represents the slope of the linear equation.

To find the value of m use the formula -

(y2 - y1)/(x2 - x1)

Substitute the values into the equation -

(4.5 - 5.5)/[(-1) - (-3)]

Use the arithmetic operation of subtraction -

(-1)/(-1 + 3)

-1 / 2

So, the slope m is m = -1/2

Now, the equation becomes y = -1/2x + b

To find the value of b substitute the  values of x and y in the equation -

5.5 = -1/2(-3) + b

5.5 = 3/2 + b

5.5 = 1.5 + b

b = 5.5 - 1.5

b = 4

So, now the equation becomes - y = -1/2x + 4

The graph for the equation is plotted.

Therefore, the equation is y = -1/2x + 4.

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