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3 years ago

Given that line t is the perpendicular bisector of JK and GK=8.25 find GJ

Mathematics

1 answer:

Paraphin [41]3 years ago

5 0

1. As you can see in the figure attached, the <span> line "t" is the perpendicular bisector of JK, and divides the triangle in two equal right triangles. This means that both triangles are congruent. Therefore, both have equal dimensions. Keeping this on mind, you have the followiig:

2. Both triangles are congruents, then:

GK=GJ

3. So if the lenght GK is 8.25, the length GJ has the same length:

GJ=8.25

4. Therefore, the answer is:

GJ=8.25</span>

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The 50th term of an arithmetic sequence is 86 and the common difference is 2. Find the first three terms of the sequence.

Nesterboy [21]

$a_n=a_{n-1}+d=a_{n-2}+2d=\cdots=a_1+(n-1)d$

which means

$a_{50}=86=a_1+49\times2\implies a_1=-12$

which in turn means the next two terms are $a_2=-10$ and $a_3=-8$ .

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2 years ago

CD has endpoints C(-3, 4) and D(1, -2). Find the coordinates<br> of its midpoint.

Natalija [7]

Answer:

Midpoint (-1 , 1)

Step-by-step explanation:

Formula: (midpoint)

Let the point A(x , y) be the midpoint of CD.

$x=\frac{x_c+x_D}{2} =\frac{-3+1}{2} =\frac{-2}{2} =-1$

$y=\frac{x_C + y_D}{2} =\frac{4+(-2)}{2} =\frac{2}{2} =1$

Then

A(-1 , 1)

4 0

1 year ago

Read 2 more answers

The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. What ar

Degger [83]

Answer:

The minimum value of the bill that is greater than 95% of the bills is $37.87.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 28, \sigma = 6$

What are the minimum value of the bill that is greater than 95% of the bills?

This is the 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

$Z = \frac{X - \mu}{\sigma}$

$1.645 = \frac{X - 28}{6}$

$X - 28 = 6*1.645$

$X = 37.87$

The minimum value of the bill that is greater than 95% of the bills is $37.87.

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3 years ago

Plums cost $0.77 per pound Mangoes cost $1.32 per pound Write an expression that can be used to find the cost of buying p pounds

marissa [1.9K]

Answer:

The graphs below show the cost y of buying x pounds of fruit. One graph shows the cost of buying x pounds of peaches, and the other shows the cost of buying x pounds of plums.

Which kind of fruit costs more per pound? Explain.

Bananas cost less per pound than peaches or plums. Draw a line alongside the other graphs that might represent the cost y of buying x pounds of bananas.

IM Commentary

This task allows students to reason about the relative costs per pound of the two fruits without actually knowing what the costs are. Students who find this difficult may add a scale to the graph and reason about the meanings of the ordered pairs. Comparing the two approaches in a class discussion can be a profitable way to help students make sense of slope.

Solutions

Solution: Slope as Unit Rate

The graph that represents the cost of x pounds of peaches is steeper, so it must have a larger slope. The slope can be interpreted as the unit rate; in this case it tells you the cost of a single pound of fruit.

Since the slope for the peach graph is greater than the slope of the plum graph, the cost of a pound of peaches is greater than the cost of a pound of plums.

For b, students should realize that the cost per pound of bananas will be represented by a slope that is less than either of the other two, and draw a line through the origin labeled "Bananas" and lying below both of the other graphs.

Solution: Adding a scale to the graph

Students who prefer to work with specific numbers can approach this problem by sketching in a scale on the x-axis and y-axis. For example, if they decided that a pound of peaches might cost a dollar, then they might plot the point (1,1) on the line labeled "Peaches", then fill out the rest of the scale accordingly. They could then read off the cost of a pound of plums and see that it is less than for peaches.

For the second question, they could choose any price per pound b for bananas that is less than the one they read off for plums, and then draw a line from the origin through the point (b, 1), and label it "Bananas".

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2 years ago

What's the mean of 8, 17, 9, 3, 13

Gnom [1K]

Mean is a form of average, and in order to find this we add up all the numbers then divide by the amount of numbers we have.

So, we have 5 numbers here. (8, 17, 9, 3, and 13)

8 + 17 + 9 + 3 + 13 = 50

50/5 = 10

The mean of those five numbers is 10.

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3 years ago