Linear equations test

The answers are a) OL = 46.2, CT = 92.4, ST = 41 and LT = 46.2

b) parallelogram ABCD is a rectangle.

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

a) Given that, the flag of Scotland is a rectangle with white stripes as the diagonals. In rectangle SCOT, SO = 92.4, and CO = 41.

We need to find the measure of CT, OL, ST and LT,

We know that, the diagonals of a rectangle bisects each other and are congruent, and its opposite sides are equal,

Therefore,

OL = SO/2 = 92.4/2 = 46.2

CT = SO = 92.4

ST = CO = 41

LT = OL = 46.2

b) Given are vertices of parallelogram, A(-6, -2), B(-3, 3), C(2, 0), D(-1, -5), we need to verify if this is a rectangle or not,

Since, the diagonals of a rectangle are congruent, so, we will find AC and BD and see if they equal or not if equal then it is a rectangle.

Distance between two points is =

D = [tex]\sqrt{(x_{2}-x_1)^2+(y_2-y_1)^2 }[/tex]

AC = √(2+6)²+(2)² = √68

BD = √(-1+3)²+(-5-3)² = √68

∵ AC = BD, therefore, parallelogram ABCD is a rectangle.

Hence, the answers are a) OL = 46.2, CT = 92.4, ST = 41 and LT = 46.2

b) parallelogram ABCD is a rectangle.

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Answer:5/8

Step-by-step explanation:

Lowest common denominator is 24

15/24 > 8/24

5/8>1/3

Answer:

we can't find it by herons formula. but here is your answer.....

Step-by-step explanation:

[tex]\\\sqrt{22}\\\\we can do by long division method \\ the actual value of \sqrt{22} = 4.69041575982343.\\well \sqrt{22} itself is in the simplest form[/tex]

Answer:

q1= n/4

is the formulato fine lower quartile

The equation that represents the situation is m= 1/8s-10

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

When

s= 0, m= -10

When

s= 80, m= 0

[tex]\frac{0-(0-10)}{80-0} = \frac{10}{80} = \frac{1}{8}[/tex]

m-0 = 1/8(s-80)

m= 1/8s-10. The equation

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Answer:

133

Step-by-step explanation:

All 3 angles of a triangle must equal 180, so let's make these equal to that

[tex](x + 13) + (10x + 13) + (2x - 2) = 180[/tex]

Now let's combine the X's and the regular numbers together.

[tex]13x + 24 = 180[/tex]

Next, subtract 24 to get all the numbers on the right side.

[tex]13x = 156[/tex]

And lastly, we divide by 13 to get X alone

[tex]x = 12[/tex]

Since Q is (10x + 13), we plug that 12 in

[tex]10(12) + 13 = 133[/tex]

The answer is that it depends on the specific countable sets being considered and how they are being combined.

The union of countably infinite sets can be countable, as in the case of the union of all positive integers and all negative integers, which is also countable.

However, the union of countably infinite sets can also be uncountable. For example, consider the union of all the intervals [n, n+1) for n = 1, 2, 3, .... Each of these intervals is countable (since it contains all the real numbers between two integers, which is a countable set), but the union of these intervals is the uncountable set of all real numbers greater than or equal to 1. Therefore, the union of these countably infinite sets is uncountable.

So the answer is that it depends on the specific countable sets being considered and how they are being combined.

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Answer:

[tex]\dfrac{1}{12}[/tex]

See the explanation for more details

Step-by-step explanation:

Not sure if you want this as a word problem or not. So here goes anyway

3 friends decided to share 1/4 of a pizza equally. How much of the original pizza portion did each get

In equation form:
[tex]\dfrac{1}{4} \div 3[/tex]

When dividing, flip the divisor so it is the reciprocal of the original divisor

Then multiply both the dividend and the flipped value

[tex]\textrm{Reciprocal of 3 = }[/tex] [tex]\dfrac{1}{3}[/tex]

[tex]\dfrac{1}{4} \div 3 = \dfrac{1}{4} \times \dfrac{1}{3}[/tex]

[tex]= \dfrac{1 \times 1}{4 \times 3} \\\\= \dfrac{1}{12}[/tex]

This is the quotient

First we need to select the subject to create the great paper outline template. Then follow the steps to create a paper.

Step 1: Choose the topic for the paper.

Step 2: Make a list of all the concepts you wish to discuss or incorporate.

Step 3: Separate similar concepts into smaller groupings.

Step 4: Put your concepts in order of importance: What ought the reader to discover first? What matters the most? Which conclusion will best suit your paper?

Step 5: Make good headers and subheadings for your documents.

Step 6: Format the outline in decimal, full-sentence, or alphanumeric form.

Step 7: State and review the paper by oneself first.

Follow all the steps to create the great paper outline template.

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Answer:

After 3 hours.

Step-by-step explanation:

60 + 30x = y

40x = y

Beach Shack:

60, 90, 120, 150, 180, 210

Surf Shop:

40, 80, 120, 160, 200

Answer:

Step-by-step explanation:

The area of a rectangle is given by the product of its length and width. Therefore, the area of the rectangle is:

A(x) = L(x) ⋅ W(x) = 2x(8x^2 - 4x + 1)

Simplifying the expression, we get:

A(x) = 16x^3 - 8x^2 + 2x

Therefore, the answer is (D) (L ⋅ W)(x) = 16x3 − 8x2 + 2x.

The mean distance that the ball was thrown is approximately 38.92/12 = 3.24 feet.

To find the mean distance that the heavy ball was thrown, we need to calculate the sum of all the distances and then divide by the total number of throws:

(20+25+25+31+33+34+41+41+45+50+56+67)/12 = 467/12 ≈ 38.92

So, the mean distance that the ball was thrown is approximately 38.92/12 = 3.24 feet.

This means that on average, the ball was thrown a distance of 3.24 feet. However, it's important to note that the mean can be influenced by outliers, which in this case is the one throw of 6.7 feet.

So, while the mean is a useful measure of central tendency, it's important to also consider other measures such as the median and mode to get a complete picture of the data.

The mean is the sum of all the values in a dataset divided by the total number of values. It provides an estimate of the central location of the data and can be a useful summary statistic for describing a dataset. However, the mean can be influenced by outliers, which are values that are significantly different from the rest of the data.

In this case, the one throw of 6.7 feet is an outlier because it is much further than any other throw, and it will increase the mean value.

For this reason, it's important to consider other measures of central tendency such as the median and mode. The median is the middle value in a dataset, and it's not affected by outliers. The mode is the value that appears most frequently in a dataset and can provide useful information about the typical or most common value in the data.

By considering all three measures (mean, median, and mode), we can get a more complete picture of the data and make better inferences or conclusions about it.

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Let's call the number of months that it takes Pablo to save $700 as "m". The amount of money Pablo has saved after "m" months can be represented by the equation:

y = 200 + 125m

where y is the total amount of money saved after "m" months.

To find the number of months it will take Pablo to save $700, we can set y equal to $700 and solve for m:

700 = 200 + 125m

500 = 125m

m = 500 / 125 = 4

So it will take Pablo 4 months to save $700.

The equation in slope-intercept form is:

y = 125m + 200

where m is the number of months and y is the total amount of money saved. The slope of the line is 125, which represents the amount added to the savings each month, and the y-intercept is 200, which represents the initial amount of money Pablo received for graduation.

Answer:

162cm²

Step-by-step explanation:

Formula of square with diagonals=1/2*d²

=1/2*(18)²

=1/2*324cm²

we get,

=162cm²

The number of birds they can take care on that day is zero.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 2.5b + 5r = 80.

Where, b represents the number of birds and r represents the number of reptiles.

On a given day. If the business cares for 16 reptiles, Therefore,

2.5b + 5(16) = 80.

2.5b + 80 = 80.

2.5b = 0.

So, They can not take care of any birds during the day.

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Answer: easy, the answer is x^6 (look at the image for the solution and make sure to give me brainliest)

Step-by-step explanation:

Answer:

(108 - (48 x 2)) / 3 = p

Step-by-step explanation:

;)

The proportion used to find the value of a is a/18 = 16/a

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Given are three similar triangles, (refer to attached figure to separately see the similar triangles)

We know that, similar triangle have corresponding sides in equal ratio,

Therefore,

a/18 = 16/a

Hence, the proportion used to find the value of a is a/18 = 16/a

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Answer:

W > 28

W has to be greater than 28

Through the aid of future value If no withdrawals or new deposits are made, the account's value following the tenth deposit should be $15,093.47.

The implied value of an asset as of a particular date in the future based on a growth rate assumption is known as the Future Value (FV). This area of mathematics examines how random events happen. The value might be between 0 and 1. The mathematical idea of probability aids in predicting the possibility of specific events. In general, probability relates to how probable something is to happen. The interest rate assumption, or the rate of return on the initial amount of capital invested, or the present value, determines the projected future value (PV).

Calculation of the value:

The initial deposit is $1.200

The rate of interest is 5%

Now the future value be like

 [tex](1200\times\frac{(1+0.05)^9-1}{0.05} )\times(1+0.05)+1,200\\\\\(1200\times(\frac{1.5513-1}{0.05} )\times(1+0.05)+1,200\\\\(1200\times11.0265)\times(1.05)+1,200\\\\13893.4711+1,200\\$15,093.47[/tex]

Through the aid of future value If no withdrawals or new deposits are made, the account's value following the tenth deposit should be $15,093.47.

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The area of the isosceles trapezoid is 72 square units.

A quadrilateral having at least one set of parallel sides and equal length non-parallel sides is called an isosceles trapezium. To put it another way, it is a trapezium whose two non-parallel sides are congruent. The trapezoid's parallel sides are referred to as the bases, and the segments that link the bases are referred to as the legs. The angle between the bases of an isosceles trapezoid determines its height.

Given:

[tex]\[d = 12 \quad \text{(length of one diagonal)}\][/tex]

Let;

[tex]\[h = \text{height of the trapezoid}\][/tex]

[tex]\[a = \text{smaller base of the trapezoid}\][/tex]

[tex]\[b = \text{larger base of the trapezoid}\][/tex]

Using the given information that the height and median are equal, we have:

[tex]Median(m)=\frac{1}{2} {(a+b)}\\\\Height(h)=\frac{1}{2} {(a+b)}\\\\2h=a+b ........(1)[/tex]

[tex]\[\text{Area} = \frac{1}{2} \cdot (a + b) \cdot h\][/tex]

[tex]\[\text{Area} = m \cdot h\] = h^2 ............(2)[/tex] (∵ [tex]Median(m)=\frac{1}{2} {(a+b)}[/tex] and m=h)

Now,

[tex]\[ d = \sqrt{h^2 + \frac{(a+b)^2}{4}} \][/tex] for isosceles trapezoid,

[tex]\[ 12^2 = h^2 + \frac{(a+b)^2}{4}}[/tex]

[tex]\[ 12^2 = h^2 + \frac{(2h)^2}{4}}[/tex]   (∵from eq (1))

[tex]\[ 12^2 = h^2 + {(h)^2}}\\ \\144= 2h^2\\\\h^2=72 ..........(2)[/tex]

Lastly, we may change the values of "a," "b," and "h" in the following formula to find the area as;

[tex]\[\text{Area} = \frac{1}{2} \cdot (a + b) \cdot h\][/tex]

[tex]\[\text{Area} = \frac{1}{2} \cdot (2h) \cdot h\][/tex]

[tex]\[\text{Area} = h \cdot h\] = h^2 = 72 sq units[/tex]

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Answer: Can you help me with the questions that I asked today.

Step-by-step explanation: Please.

Answer:

(To shawnrg

ask me the questions. I'm not promising I'll be able to help

Step-by-step explanation:

By the help of inequality properties The maximum number of interviews is 644.

Let x = number of undergraduate students hired, y = number of graduate students hired, z = number of faculty members hired, n = number of interviews

The objective function is:

Maximize n = 30x + 32y + 33z

The constraints are:

x + y + z ≤ 20

100x + 150y + 200z ≤ 3200

x, y, z integers and ≥ 0 The solution is x = 0, y = 16, z = 4, n = 644

0 undergraduate students, 16 graduate students, and 4 faculty members should be hired to maximize the number of interviews. The maximum number of interviews is 644.

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Answer:

Reese will first need to use point slope Formula to plug in- 4   for x1,  8 for y1, and 3 for the m

Reese's final answer will be y = 3x + 20, which is written in slope intercept Form.

Step-by-step explanation:

The answers in terms of the choices and order in which the blanks appear are

H. Point Slope

E. -4

I. 8

B. 3

C. y=3x+20

G. Slope Intercept

The point slope form for a line
y - y1 = m(x - x1)

Pugging in x1 = -4, y1= 8 and m = 3 gives
y -8 = 3(x - (-4))

y - 8 = 3x + 12  Move -8 to right side
y = 3x +12 + 8
y = 3x + 20

The intersection point of the exponential and linear equation is at (3.748, 14.993).

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

The equations are given below.

[tex]\rm y = 2 \left ( \dfrac{1}{5} \right )^{x - 5}[/tex]

The graph of the exponential equation is drawn.

y = 4x

The graph of the linear equation is also drawn.

From the graph, the intersection point of the exponential and linear equation is at (3.748, 14.993).

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The measure of the central angle subtended by minor arc ab, to the nearest degree is 67.

A minor arc is a part of a circle that is created by two points on the circumference of the circle.

To find the measure of the central angle subtended by the minor arc ab, we need to use the formula for the circumference of a circle, which is C = 2πr. The length of the minor arc ab is 12 feet, which is a part of the circumference of the circle. So, we can write an equation:

12 = C * (arc ab / C)

where C is the circumference of the circle and arc ab is the length of minor arc ab. We know that the radius of the circle is 10 feet, so we can find the circumference of the circle using the formula for circumference:

C = 2πr = 2π * 10 = 20π

Substituting the value of C in the equation above, we get:

12 = 20π * (arc ab / 20π)

Dividing both sides of the equation by 20π, we get:

12 / 20π = (arc ab / 20π)

We can now find the central angle subtended by the minor arc ab by using the formula:

Central angle = 2 * arctan(arc ab / 2r)

Substituting the values, we get:

Central angle = 2 * arctan(12 / (2 * 10)) = 2 * arctan(0.6)

Using a calculator, we can find that the value of arctan(0.6) is about 33.7 degrees. Hence, the central angle subtended by minor arc ab is:

Central angle = 2 * 33.7 = 67.4 degrees

Rounding off to the nearest degree, we get that the central angle subtended by minor arc ab is 67 degrees.

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Answer:

1.59

Step-by-step explanation:

Rounding to the hundredths has the same meaning as rounding to the second decimal place. Since the third decimal place is 7, we have to round up the decimal. Therefore the rounded value would be 1.59

I hope this makes sense to you. I am generally good with following up with additional questions. Feel free to leave a comment if you have any questions or you can also message me as well!

Answer:

since p is irrational it is not expressible as a ratio of two integers and has an infinite and nonrecurring expansion when expressed as a decimal

Step-by-step explanation:

so a

Answer:

(1-5n)(25m^2+5n+1

Step-by-step explanation: