Create your own unique real-world example and use matrices to solve it.

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Answer:

The amount that results from investing $5000 at 3% compounded continuously for 5 years is $5800

Step-by-step explanation:

We are given:

Principal Amount (P) = $5000

Years (t) = 5

Rate (r) = 3% or 0.03

We need to find New Amount (A)

The formula used is: \(A=P(1+\frac{r}{n})^{nt}\)

Since amount is compounded continuously so n=1

Putting values and finding A

\(A=P(1+\frac{r}{n})^{nt}\\A=5000(1+\frac{0.03}{1})^{1*5}\\A=5000(1+0.03)^5\\A=5000(1.03)^5\\A=5000(1.16)\\A=5800\)

So, New Amount (A) = $5800

The amount that results from investing $5000 at 3% compounded continuously for 5 years is $5800

Answer:

I think it's 21,600 I don't know

I don't know what grade you are in but I think this is the answer

The smallest positive debt that can be paid off using sticker trading is $7$ dollars.

To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.

Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.

The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.

In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.

Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer: True

Explanation: The domain of a quadratic function in standard format is always all real numbers, meaning you can substitute any real number for x. The range of a function is the set of all real values of y that you can get by plugging real numbers into x.

Linear function is almost always going to be all real numbers. The range of a non-horizontal linear function is all real numbers no matter how flat the slope might look.

The perimeter of the floor in the scale drawing is 36 inches.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

The scale of the drawing is 10 inches for 40 feet, which means that every inch in the drawing represents 4 feet in reality.

To find the perimeter of the floor in the scale drawing, we can add up the length of each side in the drawing, where every inch represents 4 feet.

The length of the floor is 40 feet, which is equal to 10 inches in the scale drawing (40/4=10). So, the length of the scale drawing is 10 inches.

The width of the floor is 32 feet, which is equal to 8 inches in the scale drawing (32/4=8). So, the width of the scale drawing is 8 inches.

Therefore, the perimeter of the floor in the scale drawing is:

P = 2(length + width)

= 2(10 + 8)

= 2(18)

= 36 inches

hence, the perimeter of the floor in the scale drawing is 36 inches.

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Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

The answer is (180,80)

To solve this problem, we have to plot the graph, using a tool. This question relates to an inequality and graphical method is a reliable approach to solve inequality problem.

The given question is an inequality situation where we are asked to use graph to solve.

The data given are

The inequality for this problem is given is as

\(12x + 8y > 2500\\x + y < 280\)

Kindly find the attached image as the graph and solution to this problem.

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Answer:

After the discount $527.12

You save $71.88

Step-by-step explanation:

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

Her speed is of 2 miles per hour.

Step-by-step explanation:

Velocity:

The velocity is given by the following formula:

\(v = \frac{d}{t}\)

In which v is the velocity, d is the distance and t is the time.

2/3 mile in 1/3 hour .

This means that \(d = \frac{2}{3}, t = \frac{1}{3}\)

Which unit rate describes antoinettes speed in miles per hour?

This is v. So

\(v = \frac{d}{t} = \frac{\frac{2}{3}}{\frac{1}{3}} = \frac{2}{3}*\frac{3}{1} = 2\)

Her speed is of 2 miles per hour.

Answer:

I believe it's 9/8 miles per hour

Step-by-step explanation:

v = d/t = (3/4 mile)/(2/3 hour) = (3/4)/(2/3) miles per hour = (3/4)(3/2) miles per hour = 9/8

The distance between the points B and C is 12m

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

for the coordinates B (-14,-5) and C(-14, 7), then x1 = -14 ,x-2= -14 , y1= -5 and y2= 7

therefore d =√((x2 – x1)² + (y2 – y1)²) = √((-14– -14)² + (-5 – 7)²)

d=√((0)² + 12²)

d=√144

d= 12m

therefore the distance between the points B and C is 12m.

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The surface area of a cylinder is 284m² and it's volume is 366.9m³

To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:

From the given question, the data are;

a. The surface area of the cylinder is;

SA = 2π(4)² + 2π(4)(7.3)

SA = 283.999≈284m²

b. The volume of the cylinder is

v = πr²h

v = π(4)²(7.3)

v = 366.9m³

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Answer: b

Step-by-step explanation:

By the alternate interior angles theorem, the angle of elevation and the angle of depression have the same measure.

The measure of angle A is 32 degrees or the measure of the angle of elevation is 32 degrees option (b) 32 degrees is correct.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

It is given that:

The right-angle triangle is shown in the picture.

The right-angle triangle is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

As the two lines are parallel to each other and a transversal is intersect the parallel lines so the angle would be same as 32 degrees

The angle A = 32 degrees

Thus, the measure of the angle A is 32 degrees or the measure of the angle of elevation is 32 degrees option (b) 32 degrees is correct.

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Step-by-step explanation:

Sol'n,

Here,

We can see that the Marked Price is Rs.80

a discount of x percent is added such that the new price i.e. SP with discount becomes about Rs.60

Now,

We know that,

Discount Percentage = (MP-SP with discount/SP with discount)×100%

= (80-60/60)×100%

=33.33%

Hence, by this we can conclude the discount percentage to be of about 33.33%..

The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.

To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.

The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.

To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:

Impact on income = Loss - Avoidable costs

Impact on income = $205,000 - ($1,295,000 + $119,000)

Impact on income = $205,000 - $1,414,000

Impact on income = -$1,209,000

The negative sign indicates a decrease in income.

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Answer:

\(t=\frac{78-75}{\frac{7}{\sqrt{20}}}=1.917\)  

The degrees of freedom are given by:

\( df= n-1 = 20-1=19\)

The p value would be given by:

\(p_v =2*P(t_{19}>1.917)=0.0704\)  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 75 and the best option would be:

a. No

Step-by-step explanation:

Information given

\(\bar X=78\) represent the sample mean

\(s=7\) represent the sample standard deviation

\(n=20\) sample size  

\(\mu_o =75\) represent the value that we want to test  

\(\alpha=0.05\) represent the significance level for the hypothesis test.  

t would represent the statistic

\(p_v\) represent the p value

Hypothesis to test

We want to check if the true mean is different from 75, the system of hypothesis would be:  

Null hypothesis:\(\mu =75\)  

Alternative hypothesis:\(\mu \neq 75\)  

The statistic is given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\) (1)  

Replacing we got:

\(t=\frac{78-75}{\frac{7}{\sqrt{20}}}=1.917\)  

The degrees of freedom are given by:

\( df= n-1 = 20-1=19\)

The p value would be given by:

\(p_v =2*P(t_{19}>1.917)=0.0704\)  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 75 and the best option would be:

a. No

Answer:

a:(5x+3)+(3x+7)=180°

linear angle

Answer:

6.10%

Step-by-step explanation:

For every round since we are choosing with equal probability, then the probability of choosing from either of the bags is 1/2

Here, this scenario is only possible when a particular bag has been chosen 10 times and the other bag has been chosen 6 times ( meaning a particular bag has been emptied and for a particular bag to be emptied, all of its content would have been picked)

Now on the 17th trial, an empty bag is chosen

Therefore the required probability will be;

16C0 * (1/2)^10 * (1/2)^6 * 1/2 = 0.0610 = 6.1%

The maximum displacement is 5 centimeters.

The time required for one oscillation is π seconds.

The frequency is 1 / π Hz.

Equation to model the motion of the object is x(t) = 5 × cos(2t)

The maximum displacement from equilibrium can be determined by observing that the object is pulled down 5 centimeters from its rest position.

In simple harmonic motion, the amplitude represents the maximum displacement from equilibrium.

The period of oscillation is given as π seconds.

The period (T) is the time required for one complete oscillation.

The frequency (f) is the reciprocal of the period and represents the number of oscillations per unit time.

Thus, the frequency is the inverse of the period: f = 1 / T.

To model the motion of the object, we can use the equation for simple harmonic motion:

x(t) = A×cos(ωt + φ)

A = 5 centimeters (maximum displacement),

T = π seconds (period),

f = 1 / π Hz (frequency).

To find ω, we can use the relation ω = 2π / T:

ω = 2π / π = 2 radians/second.

The equation to model the motion of the object is:

x(t) = 5 × cos(2t)

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The third option that is the distance is the absolute value of the difference describes the relationship between distance and difference.

We know that the distance between two points is the difference of those two values.

But as the distance between two points can never be negative,  we will write the absolute value of the difference as the distance between the two points.

Here we can see that,

a - b = -1  when distance = 1

a - b = 5  when distance = 5

a - b = 3  when distance = 3

Hence, the relationship between difference and distance is described by the third option.

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Your answers are right because the x's can not repeat

so 1.it is a function

2.it is a function

3.it is not a function bc "d" and "m" both repeat 2 times

4.it is not a function bc 2 repeats 2 times

Hope this helps

Have a great day/night

Feel free to ask any questions  

For each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.

This means that in a 6-pound bag of the blend, they would use \(3 \times 6 = 18\)pounds of Guatemalan coffee.

Let's assume that x pounds of Guatemalan coffee are used per pound of the blend.

Given information:

Cost of Guatemalan coffee = $11/lb

Cost of the other coffee = $5/lb

Desired cost of the blend = $8/lb

Total weight of the blend = 6 pounds

To find the ratio of Guatemalan coffee to the total blend, we can set up the equation:

\((x \times 11 + (6 - x) \times 5) / 6 = 8\)

In this equation, \((x \times 11)\) represents the cost of the Guatemalan coffee in the blend, and\(((6 - x) \times 5)\) represents the cost of the other coffee in the blend.

The numerator is the total cost of the blend, and we divide it by 6 (the total weight of the blend) to find the cost per pound.

Now, let's solve the equation for x:

(11x + 30 - 5x) / 6 = 8

6x + 30 = 48

6x = 48 - 30

6x = 18

x = 18/6

x = 3

Therefore, for each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.

This means that in a 6-pound bag of the blend, they would use \(3 \times 6 = 18\)pounds of Guatemalan coffee.

To summarize, to achieve a cost of $8 per pound for a 6-pound bag of blend, Cold Beans should use 3 pounds of Guatemalan coffee per pound of the blend.

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Answer:

example of two like terms:

example of two unlike terms:

Answer:

2x and 5x are like terms, 2x and 3y are not. 3 and 5 are like terms, 6y and 2 are not. etc.

Step-by-step explanation:

For something to be a like term, they either have to have the same variable (ex: x and y and any other variable that may be used) or both be whole numbers (1, 2, 3, etc.)  No mixing the two.

f(x) =-2x^2+3x

g(x)=7x-2

find (g/f)(-2)​

we know that

step 1

Find f(-2)

step 2

Find g(-2)

step 3

Divide both results

therefore

Answer:

10.315

Step-by-step explanation:

Answer:

Step-by-step explanation:

vertical

Answer:

80 gallons

Step-by-step explanation:

First to find this, we must divide 10 by 4, and yes I know this will give us a decimal, but it must be done. This division will give us 2.5, we must then multiply 2.5 by 32, as we are given 32 gallons for 4 loads of dishes, and if 2.5 times 4 loads is 10 loads, then we must multiply 32 by 2.5 as well, giving us the answer, 80 gallons

Answer:

80 gallons

Step-by-step explanation:

The answer is 80 gallons when using the distributive, and communitive property of multiplication and division.

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