The triangles are similar.

What is the value of x?

x2 – 3x – 28 = (x-7)(x+4)

Answer:

On the top:-28

On the bottom: -3

On the sides: -7 and 4

X2-3x-28=(x-7)(x+4)

Step-by-step explanation: I got it correct on Edge

Answer:

54 and 5

Step-by-step explanation:

56-2 is 54

7-5 is 2

have a good day my little friend learning his 1st addition

Answer:

64, 2

Step-by-step explanation:

Answer:

Edit: it's actually translation, sorry about that.

Step-by-step explanation:

Answer: I think it might be translation

Step-by-step explanation:

Translation: A slide of a slide of a shape on a coordinate plane. We can move a shape upward, downward, leftward, or rightward.

Answer:

y=1.4

x=-1.6

Step-by-step explanation:

Hi, to solve this system of equations we have to multiply the second equation by 2, and then subtract the first equation to the second one:

4x+y=-5  

-2x+2y=6

-4x+4y=12

+

4x+y=-5

__________

5y =7

y = 7/5 = 1.4

Replacing y=1.4 on any equation:

4x+1.4=-5

4x = -5-1.4

4x= -6.4

x=-6.4/4

x=-1.6

Feel free to ask for more if needed or if you did not understand something.

Answer:

B=28

Step-by-step explanation:

well, the midpoint of segment AB is the center of the circle, so

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 9 +1}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies \stackrel{center}{(2~~,~~5)}\)

now since we know AB is the diameter, so half that distance AB is its radius, so

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\)

\(AB=\sqrt{(~~6 - (-2)~~)^2 + (~~9 - 1~~)^2} \implies AB=\sqrt{(6 +2)^2 + (9 -1)^2} \\\\\\ AB=\sqrt{( 8 )^2 + ( 8 )^2} \implies AB=\sqrt{ 64 + 64 } \implies AB=\sqrt{ 128 } \\\\\\ AB=8\sqrt{2}\hspace{5em}\stackrel{\textit{half that is the radius}}{\cfrac{8\sqrt{2}}{2}\implies 4\sqrt{2}\implies \sqrt{32}} \\\\[-0.35em] ~\dotfill\)

\(\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{\sqrt{32}}{r}} \\\\\\ (x-2)^2~~ + ~~(y-5)^2~~ = ~~(\sqrt{32})^2\implies {\large \begin{array}{llll} (x-2)^2~ + ~(y-5)^2~ = ~32 \end{array}}\)

Answer:

52

Step-by-step explanation:

The correct answer is "Rejecting the null hypothesis that the population mean is 4 at the alpha level of 0.01."This is because we have evidence to support the research hypothesis that the population mean is not 4, and the result is statistically significant at the 0.01 level.

A 99% confidence interval for a population mean between 3 and 6 implies that there is a 99% chance that the population mean is between 3 and 6. The null hypothesis, H0, is that the population mean is 4. The alternative hypothesis, H1, is that the population mean is not equal to 4.Using the same data, if we test the null hypothesis that the population mean is 4 at the alpha level of 0.01, the result will be rejecting the null hypothesis that the population mean is 4 at the alpha level of 0.01.

This is because a 99% confidence interval means that the alpha level is 0.01. Thus, if we test the null hypothesis at the alpha level of 0.01 and get a result that is different from what we expect, then we reject the null hypothesis. Since the 99% confidence interval is between 3 and 6, we can say with 99% confidence that the population mean is not equal to 4, which means that we can reject the null hypothesis that the population mean is 4. Therefore, the correct answer is "Rejecting the null hypothesis that the population mean is 4 at the alpha level of 0.01."This is because we have evidence to support the research hypothesis that the population mean is not 4, and the result is statistically significant at the 0.01 level.

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the explanation of how heart disease progresses over time in part of her presentation would be best suited to a video.

Several different heart disorders are referred to as "heart disease." Coronary artery disease (CAD), which affects the blood flow to the heart, is the most typical kind of heart disease in the United States. A heart attack may result from reduced blood flow.

here,

Chest pain or discomfort, pain in the upper back or neck, heartburn, nausea, vomiting, extreme exhaustion, pain in the upper body, dizziness, and shortness of breath are all symptoms of a heart attack.

Heart palpitations are caused by an arrhythmia (palpitations). Heart failure symptoms include shortness of breath, exhaustion, or swelling of the legs, abdomen, or neck veins.

The three main risk factors for heart disease are excessive blood pressure, high cholesterol, and smoking. Nearly half of Americans (47%) have at least one of these three risks.

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Lemma 1 states that in a weighted, directed graph with a designated root, if we create a new set of edges E' by removing edges from the root to each vertex except itself.

Lemma 1 introduces the concept of an RDMST (Rooted Directed Minimum Spanning Tree) in a weighted, directed graph and highlights the relationship between the set of edges E' and the existence of cycles in the resulting graph T. It states that if T is not an RDMST, it must contain a cycle, indicating that removing certain edges from the root to other vertices can lead to cycles.

Lemma 2 focuses on the weight function w' and its impact on determining an RDMST. It states that the resulting graph T is an RDMST rooted at the designated root in the original graph if and only if it is an RDMST rooted at the designated root in the graph with the modified weight function w'. This lemma demonstrates that adjusting the weights of the edges based on the weights of the vertices preserves the property of being an RDMST.

Overall, these two lemmas provide insights into the properties and characteristics of RDMSTs in weighted, directed graphs and offer a foundation for understanding their existence and construction.

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The distance from the center of dilation, P, to.the image vertice S' is; 6 units.

It follows from the task content that the center of dilation of the triangle QRS is point P and the length of segment PS in the pre-image is; 8 units.

Hence, since the dilation factor as given in the task content is; three-fourths, it therefore follows that the distance of point P to S' in the image is; (3/4) × 8 = 6units.

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Answer:

27, 29, 31, 33

Step-by-step explanation:

Let x represent the smallest odd integer then...

x+2 represents the second

x+4 represents the third

x+6 represents the fourth

We can use this to set up an equation:

x+x+2+x+4+x+6=120

Combine like terms

4x+12=120

Subtract 12 from both sides

4x=108

Divide both sides by 2

x=27

The integers are 27, 29, 31, 33

Answer:

7 3/5

Step-by-step explanation:

2/5(1-4(-6)) + 1/2(2*1 + -6) = 2/5(24) + 1/2(-4)

                                         = 9 3/5 + (-2)

                                         = 7 3/5

Answer:

8

Step-by-step explanation:

2/5 [1- (4*-6)] + 1/2 (2*1 + -6)

= 2/5 (1 - - 24) + 1/2 (2 - 6)

= 2/5 + 48/5 + 1 - 3

50/5 -2

= 10 - 2

= 8

Answer:

Find the slope of the original line and use the point-slope formula y−y1=m(x−x1)to find the line parallel to y=4x.

y=4x+4

Step-by-step explanation:

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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Answer:

6.45 × 10³

Step-by-step explanation:

4.5 × 10² + 6 × 10³ = 0.45 × 10³ + 6 × 10³ = (0.45 + 6) × 10³ = 6.45 × 10³

Answer:

450 and 6000

Step-by-step explanation:

4.5 × 10²

4.5 × 100

450

6 × 10³

6 × 1000

6000

Yes, The preimage and the image have the same shape and size.

The reflection of an object across an axis is creating an image that has the same shape and size.

A triangle ABC is reflected over the x-axis to form A'B'C'

When reflected over an axis, the coordinate of the other axis is changed to its additive inverse.

(x,y)-------> (x,-y)

Let the coordinate of the triangle is  (1,1),(3,5),(3,1)

The image of the triangle when reflected over x-axis is

(1,1),(3,5),(3,1)       ------------->    (1,-1),(3,-5),(3,-1)

The shape of a right-angled triangle is the same in the image, the length of the side is same, it is just an image of the same shape and size.

The figure is attached with the answer.

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The expression when evaluated is 17

From the question, we have the following parameters that can be used in our computation:

a = 2, b = 3, c = 4 and d = 12

Also, we have

20 - 2b/a

Substitute the known values in the above equation, so, we have the following representation

20 - 2b/a = 20 - 2 * 3/2

Evaluate

20 - 2b/a = 17

Hence, the solution is 17

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Answer:

44

Step-by-step explanation:

All angles on a triangle add up to 180 degrees so 180-(65+71) will give you 44

The correct answer is b. 19.25%.The effective annual rate (EAR) is the annual interest rate that accounts for compounding effects.

To calculate the EAR, we use the formula: EAR = (1 + i/n)^n - 1, where i is the nominal interest rate and n is the number of compounding periods per year. In this case, the nominal interest rate is 18% and it is compounded semi-annually, which means there are two compounding periods per year. Substituting these values into the formula, we get: EAR = (1 + 0.18/2)^2 - 1 = 0.1925, or 19.25%.

Therefore, the correct answer is b. 19.25%. This represents the effective annual rate for an 18% nominal interest rate compounded semi-annually, taking into account the compounding effects over the course of a year.

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Answer:

Below

Step-by-step explanation:

4 [x-3] + 2    = y    is not discontinuous anywhere

However    4 / [x-3]  + 2   DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!

Equation: x + 2 = 4Solution: x = 2.

An equation is a mathematical expression that uses symbols, such as numbers and variables, to represent a relationship between two or more values or quantities. Equations are used to describe physical laws, solve problems and to make predictions. Equations are fundamental to all areas of mathematics and science, and their use is essential for understanding and exploring the natural world.

The equation x + 2 = 4 can be used to represent the hanger. It states that if you add two to any number, the result is four. In other words, if you have two hangers, when you add them together, you get four. Therefore, the equation can be solved by reasoning that the two hangers must have a combined value of two, so x = 2.

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The value of x = 4

The value of y = 3

7x + y = 33    ......eq(1)

3x + y = 17     .....eq(2)

Here subtract eq(2) from eq(1), we get

4x = 16

therefore x = 16/4

x = 4.

Now to get the 'y' value, substitute the 'x' value in eq(2)...

3(4) +y = 17

y = 5

Therefore,

x = 4

y = 3

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Answer:

m = -k/7

Step-by-step explanation:

(to) Solve for m;

7m + k = 0.         Given

      - k     -k        Subtract K from both sides

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

      7m = -k        K becomes negative since it was subtracted

        _      _

        7      7         Divide both sides by 7 to get m by itself

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

        m = -k/7      Answer

Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

By using the concept of Depreciation, it is obtained that

Warrem's body  metabolize half of the 84 mg of caffeine in 4.71 hours

What is Depreciation?

Depreciation is the reduction in the value of a product at a certain rate over a certain period of time.

Here the concept of Depreciation has been used

Let the time taken to metabolize half of the 84 mg of caffeine be t hours

Damien's body metabolizes caffeine at a rate of 13.7% per hour

By the problem,

\(84(1 - \frac{13.7}{100})^t = 42\\\\(1 - \frac{13.7}{100})^t = \frac{42}{84}\\\\(1 - \frac{13.7}{100})^t = \frac{1}{2}\\\\(\frac{100 -13.7}{100})^t = \frac{1}{2}\\\\(\frac{86.3}{100})^t = \frac{1}{2}\\\\(\frac{863}{1000})^t = \frac{1}{2}\\\\t(ln(\frac{863}{1000}) = -0.693\\\\-0.147t = -0.693\\\\t = \frac{0.693}{0.147}\\\\t = 4.71 \ hours\)

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Time is 9:42 a.m. when they meet will at the starting point again.

We have, Cheko and Sharko started running at the same time and starting point. The shape of ground or stadium is circular. Time taken by Cheko to complete the one round of stadium

= 7 minutes

Time taken by Sharko to complete the one round of stadium = 6 minutes.

At 9.00 a.m, both are start running together. We have to calculate time they will meet at the starting point again. So, they will starting together after LCM ( 7, 6) minutes. LCM stands for least common multiple of 7 and 6. The factors of 7 and 6 are the following, 7 = 1×7

=> 6 = 2× 3 × 1

So, LCM (6,7 ) = 2×3×7×1 = 42 minutes

Thus, the again starting time = 9:00 a.m. + 42 minutes = 9: 42 a.m.

Hence, the required time is 9: 42 a.m.

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By solving the word problem given, the interest that was earned is calculated as: $60.

Given the word problem above, to find how much interest earned, we solve as shown below:

New balance after earning interest = $420

Let the original balance be represented as x

Therefore, we would create the following equation to find the value of x:

7/6 of x = 420

7/6 × x = 420

7/6x = 420

Solve for x by multiplying both sides by 6/7

7/6x  × 6/7 = 420 × 6/7

x = (420 × 6)/7

x = 360

The original balance is $320

Interest = New balance - original balance

Interest = $420 - $320

Interest = $60

Thus, solving the word problem given, the interest that was earned is calculated as: $60.

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Answer:

I think its this:

thirty - seven and six hundred ninety - one hundred thousanths.

Step-by-step explanation:

Hope this is right!