The triangles can be proven congruent using the ASA congruence postulate.
∠ABK is congruent to ∠CBK.BK is congruent to BK (common side )∠AKB is congruent to ∠CKB.Thus, we can say that triangles ABK and CBK are congruent.
Triangles are congruent, according to the Angle Side Angle Postulate (ASA), if any two angles and their included side are equivalent in the triangle. The side between two angles is considered an included side.
Additionally, you can confirm that your two triangles are congruent by employing the Side Angle Side Postulate (SAS). In this case, we choose a side and its equivalent side on two triangles rather than two angles.
Triangles are said to be congruent according to the SAS Postulate if any pair of corresponding sides and their included angle are also congruent.
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Write y-2=-1(x+7) in standard form
Y=mx+b is standard form.
y-2= -x-7
+2 +2
y= -x-5
Steve buys last year's best-selling novel, in hardcover, for $26.35. This is with a 15% discount from the original price. What was the original price of the novel?
Step 1 of 2 : Use the variable x to set up an equation to solve the given problem. Set up the equation, but do not take steps to solve it.
Answer:
$30.30
Step-by-step explanation:
$26.35*15%=$3.95
Then you add $26.35 and $3.95 to get $30.30
1. Write two expressions that are equivalent to the expression listed below. You can use the equation editor to input your answers.
(x^{1/3)²
Two index that are equivalent to the index (x^{1/3)² are:- 1) X⁽²/³⁾, 2) (∛X)²
What are index ?
An index can be assigned to a number or variable. A value raised to the power of a variable's (or a constant's) value is its index. The exponents or powers are other names for the indices. It displays how many times a particular number must be multiplied. It takes the following form:
a(m) = a × a × a ×……× a (m times)
The base in this case is a, and the index is m.
The index instructs a certain integer (or base) to be multiplied by itself a specified number of times, where the number of times is determined by the index raised to the base. It is a condensed way of expressing large sums of information and calculations.
[tex]X^b . X^A. X^n = X^b^a^n[/tex]
Example: 2^3 = 2 × 2 × 2 = 8
[tex][X^\frac{1}{3} ]^2[/tex][tex]= X^\frac{2}{3}[/tex]
We can also write the same index as;
[tex]A^\frac{1}{n}=\sqrt[n]{A}[/tex]
[tex]X^\frac{2}{3}=[\sqrt[3]{x}]^2[/tex]
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Next O Quiz 6.2
10
Select the correct answer.
According to the Dietary Guidelines for American 2015, you should limit your fat intake to what percentage of your total calories?
OA. Less than 10%
OB. 25-35%
C.
OD.
45-55%
65-75%
Reset
Next
According to the Dietary Guidelines for American 2015, you should limit your fat intake to 25% - 35% of your total calories. The correct option is B.
What is dietary guidelines?Food-based dietary guidelines also known as dietary guidelines are intended to serve as a foundation for public food and nutrition policies, health and agricultural policies, and nutrition education programs aimed at promoting healthy eating habits and lifestyles.
Calories are the units of energy released by your body when it digests and absorbs food. The higher the calorie content of a food, the more energy it can provide to your body. When you consume more calories than you require, your body stores the excess calories as fat. Even fat-free foods can be high in calories. In this case, the fay should not be more than 35%.
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A scientist uses a submarine to study ocean life. She begins at sea level, which is an elevation of 0 feet. She travels down 21.1 feet. She then ascends 19.1 feet. Next, she travels down a second time, 80.7 feet. How many feet must she now ascend to get back to sea level?
Based on the elevation of the scientist after descending and traveling directly up, the number of feet she needs to ascend to get to sea level will be; 82.7 feet.
How to find the elevation?To find the number of feet that the scientist needs to travel up to get back to sea level, you need to find her current elevation.
The current elevation of the scientist is:
= 0 - 21.1 + 19.1 + 80.7
= 82.7 feet
In other words, the scientist is 82.7 feet below sea level.
To get back to sea level therefore, the scientist will need to travel 82.7 feet directly up.
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Determine the slope of the line that passes through the following points. m=5/7, or m=7/5, or m=1/3, or m=3
Between (5,10) and (15,70), a line runs. As a result, the slope of the line through the supplied locations is 3.
What is slope?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line.
A line's slope is determine by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-
P1 = (x1, y1) and P2 = (x2, y2)
Hence, Between (5,10) and (15,70), a line runs. As a result, the slope of the line through the supplied locations is 3.
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CHALLENGE:
3. There are less than 30 students in Mr. Klein's math class. On a
test, % of the class received a "B", %4 received a "C", % received a "D",
and % failed. How many more students received a "B" than received
an "A"?
Answer: ???
Step-by-step explanation:
You have to put in the numbers for the percentages.
Window Rock Recruitment Agency just placed Alejandro Rivera in a job as an assistant
pharmacist. The job pays $71,500 annually. The agency fee is equal to 40% of the first
5 weeks' pay. Demonstrate and explain how you would be able to determine what he will
earn during the first 4 weeks if he pays the agency fee weekly?
Answer: To determine Alejandro's earnings for the first 4 weeks, we first need to calculate his weekly pay. To do this, we divide his annual salary by the number of weeks in a year:
Annual salary / 52 weeks/year = weekly pay
$71,500 / 52 weeks/year = $1,375/week
Next, we need to determine the agency fee that Alejandro will pay each week. The agency fee is equal to 40% of the first 5 weeks' pay, so we multiply Alejandro's weekly pay by 40% to get the agency fee:
Weekly pay * 40% = agency fee
$1,375/week * 40% = $550/week
Finally, to determine Alejandro's earnings for the first 4 weeks, we multiply his weekly earnings by the number of weeks:
Weekly pay * number of weeks = earnings
$1,375/week * 4 weeks = $5,500
So, Alejandro will earn $5,500 during the first 4 weeks of his new job, after paying the agency fee each week.
Bonds Payable has a balance of $810,000, and Premium on Bonds Payable has a balance of $8,910. If the issuing corporation redeems the bonds at 102, what is the amount of gain or loss on redemption?
a. $8,910 gain
b. $8,910 loss
c. $7,290 loss
d. $7,290 gain
To determine the gain or loss on the redemption of the bonds, you need to compare the redemption price to the carrying value of the bonds. The carrying value of the bonds is the amount that the bonds are recorded as being worth on the issuing corporation's balance sheet. This is calculated by adding the Bonds Payable balance and the Premium on Bonds Payable balance.
In this case, the carrying value of the bonds is $810,000 + $8,910 = $818,910. If the bonds are redeemed at a price of $102, the gain or loss on the redemption can be calculated as follows:
Gain or loss on redemption = Redemption price - Carrying value of bonds
= $102 - $818,910
= -$817,810
Since the gain or loss on the redemption is a negative number, this indicates that the redemption price was lower than the carrying value of the bonds, resulting in a loss. The correct answer is therefore: c. $7,290 loss.
A line has a slope of 14/19 and passes through the point 0,15 what is its equation in slope intercept form
Answer: y = 14/19x+15
Step-by-step explanation: using the equation y = mx+b, m is your slope and b is the y-intercept. plug your slope (14/19) and y-intercept (15) into the equation and you’ve got your answer in slope-intercept form
Determine whether the quadratic function shown below has a minimum or
maximum, then determine the minimum or maximum value of the function.
f(x) = -2(x - 5)(x-7)
The vertex (3, -16) is the maximum point on our quadratic equation.
Maximum and minimum values of the function:When we compare the given Quadratic function with the general form
ax² +bx +c,
If the value of a is positive then the Quadratic function will have a minimum value, and the graph of the function opens up.
If the value of a is negative then the Quadratic function will have a maximum value, and the graph of the function opens downwards.
Here we have
f(x) = -2(x - 5)(x-7)
f(x) = -2 [x²-7x - 5x + 35 ]
f(x) = -2 [x²-12x + 35 ]
f(x) = -2x² + 12x - 35
Compare f(x) with ax²+ bx + c
=> a = -2, b = 12, and c = - 35
Here,
a = -2 is a negative value then the function f(x) will have maximum value
And the graph of the function opens down.
The formula for the x coordinate of the vertex = -b/2a
The coordinate of x = -(12)/2(-2) = 3
Now substitute x = 3 in f(x) to find y-coordinate
=> f(3) = - 2(3)² +12(3) - 35
=> f(3) = -2(9) + 36 - 35
=> f(3) = - 16
Therefore, y-coordinate = -16
Therefore,
The vertex (3, -16) is the maximum point of the quadratic equation.
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WORD PROBLEM:
You have 200 meters of fencing to enclose two adjacent rectangular pens for livestock. The total area of the enclosed region is 1400 square meters. What are the dimensions of each pen?
The dimensions of each of the rectangular pens are given as follows:
8.41m and 41.58 m.
How to obtain the dimensions of the pen?The pen have rectangular format, as shown by the image given at the end of the answer, hence the dimensions are obtained from the area and the perimeter of the pen.
For each pen, the dimensions are given as follows:
Length: x.Width: y.For the entire pen, the dimensions are given as follows:
Length: 2x.Width: y.You have 200 meters of fencing to enclose two adjacent rectangular pens for livestock, hence the perimeter is given as follows:
2(2x + y) = 200
2x + y = 100.
The total area of the enclosed region is 1400 square meters, hence:
2xy = 1400.
From the first equation, we have that:
y = 100 - 2x.
Replacing in the second, the length x is obtained as follows:
2x(100 - 2x) = 1400
-4x² + 200x - 1400 = 0
4x² - 200x + 1400 = 0.
The solutions are of:
8.41m and 41.58 m.
Which gives the dimensions of the pen.
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. When the length of a side of a square is increased by 5, the perimeter of the new
square is 60.
Which equation can be used to find the length of the side of the original square?
A. 4(x + 5) = 60
B.
4(x-5) = 60
C.
4x + 5 = 60
D.
4x5 = 60
The equation that can be used to find the length of the side of the original square is 4(x+5) = 60. Option A. is the answer
How to determine which equation can be used to find the length of the side of the original square?Given that:
When the length of a side of a square is increased by 5, the perimeter of the new square is 60.
Let x represent the length of the side of the original square
when x is increased by 5, you have (x+5)
Perimeter (P) = 4 × length of the side
Thus, 4(x+5) = 60
Therefore, the equation to find the length of the side is 4(x+5) = 60
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If quadrilateral A' B' C' D' = D8 (ABCD), which of the following statements are true? Select all that apply.
So the correct statement is A and D
Quadrilateral A'B'C'D' and ABCD will be similar only if s>= 1 The corresponding side lengths are Related by AB = s.A'What is a Quadrilateral?
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners.
The Latin words quadra, which means four, and latus, which means sides, are combined to form the English term quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides.
These are the several kinds of quadrliaterals:
Trapezium ParallelogramSquares Rectangle Rhombus KiteQuadrilateral A'B'C'D' = D8(ABCD) as we know two quadrilateral will be congruent in case of unit length scaling factor and corresponding side length corresponds like AB,BC,CD,DA
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Select the correct answer. What is the range of y = sin 0 ? Ο Α. B. C. D. [-1.1] [0,⁰0) all real numbers 277
The range of the sine function is:
R: {x ∈ R| -1 ≤ x ≤1}
It can also be written as [-1, 1], so that is the correct option.
What is the range of the sine function?For a function y = f(x) we define the range as the set of the outputs, this is, the set of the possible values of y.
In this case, our function is y = sin(θ)
Remember that the maximum value of the sine is sin(π/2) = 1
And the minimum is sin(3π/2) = -1
So the maximum value of y is 1 and the minimum is -1, thus, the range is the set of all real numbers between these two, then we can write the range as:
R: {x ∈ R| -1 ≤ x ≤1}
It can also be written as [-1, 1]
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Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50. The inequality below represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers.
Ling can therefore purchase 0 to 12 bags, but no more is the right decision.
How to calculated the inequality?Ling has been instructed to spend no more than $40.00 on party décor. She has already spent $10.00 on streamers but also plans to purchase bags of balloons. The price of a bag of balloons is $2.50.
Given her spending cap and how much she has already spent on streamers, the inequality 10 + 2.5x ≤ 40 indicates x, the number of bags she can purchase.
Subtracting 10 from both sides of our inequality, let's find x by reversing the inequality.
10 - 10 + 2.5 x ≤ 40 - 10
2.5 x ≤ 30.
We will now divide our inequality by 2.5 on both sides.
2.5 x / 2.5 ≤ 30 / 2.5
x ≤ 12.
Ling can therefore purchase 0 to 12 bags, but no more is the right decision.
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Answer:
Step-by-step explanation:
Ling can therefore purchase 0 to 12 bags, but no more is the right decision.
leght multipy by breath
Answer:
equal to area of rectangle
Step-by-step explanation:
Please mark me brainlest
Which point shows the approximate location of [tex]\sqrt{7}[/tex] plotted on the number line
The position of the √7 on the number line is slightly right of the 2.6.
What is a number line?
A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
Here,
In general conclusion,
√4< √7 < √9
2 < √7 < 3
So, the value of the √6 lies between 2 and 3.
√6 = 2.6457
Hence, the position of the √7 on the number line is slightly right of the 2.6.
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g(x)=x^4-3x^3-8x^2-6x-20, find zeros
Answer:x=-2,5, -[tex]i\sqrt{2}[/tex], +[tex]i\sqrt{2}[/tex]
Step-by-step explanation:
Now let's look at the data from all the Buffalo. If we calculate the 60% confidence interval for every buffalo's count (i.e. data sample), how many Cls do we expect to contain the true mean? Store your answer in theoretical_hits. Then we need to check our theoretical answer with our actual data. Calculate the 60% confidence interval for each buffalo's count. Then commpute how many of those Cls contain the true mean. Assume that the true mean is 25,000. Store this value in sample_hits . Does this value match the theoretical value? It may be helpful to visualize the Confidence Intervals, along with the true mean. Create a plot for the Confidence intervals for the first 40 rows of the dataframe. Also plot true_mean=25000 as a horizontal dotted line. This plot will not be graded, but may help you get a better understanding of different confidence intervals for the same underlying population. We recommend looking into the ggplot package to help with this task.
15000 Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).
Given that,
We have to calculate let's now examine the Buffalo's collective data. How many Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).
We know that,
Theoretical hits= confidence interval × total no. of buffaloes
= 0.6×(buffaloes)
Sample hits = count among total no. of buffaloes, from which how many of inside 25000, that will be sample hits.
So,
=0.6×25000
=15000
Therefore, 15000 Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).
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Preeti discovers that her roommate Shari recently experimented with methamphetamine. Preeti, worried about her roommate, informs Shari that there are risks associated with methamphetamine use, such as the induction of symptoms associated with ____.
psychosis
Preeti informs Shari that there are risks associated with methamphetamine use, such as the induction of symptoms associated with Psychosis
Psychosis is a combination of symptoms resulting in an impaired relationship with reality. It can be a symptom of serious mental health disorders. People who are experiencing psychosis may have either hallucinations or delusions.
If someone is experiencing an episode of psychosis, the main symptoms include:
hallucinationsdelusionsdisorganized behaviorAccording to the question,
Preeti discovers that her roommate Shari recently experimented with methamphetamine. Preeti, worried about her roommate, informs Shari that there are risks associated with methamphetamine use, such as the induction of symptoms associated with Psychosis
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Three less than the product of 7and a number is 4 .
Answer:
Step-by-step explanation:
Let
n--------> the number
we know that
1) the sentence" Three less than the product of seven and a number" represent the expression------>
2) the sentence" is four more than the number"
represent the expression ------->
3) the complete sentence" Three less than the product of seven and a number is four more than the number" represent the expression
represent the expression ------->
therefore
the answer is
(7n-3) =(n+4)
3/5x = 12 x 5
_x = _
Answer:
X=100
Step-by-step explanation:
I assume you want to find the value of x.
3/5x=60
5/3*60=x
x=20*5=100
prove that for every integer exists a multiple of that number that is composed of only ones and zeros in the decimal system
Let n be a positive integer. Consider the n+1 integers 1,11, 111,1111,... (where the last integer in this list is the integer with n+1 - 1s in its decimal expansion).
Note that there are n possible remainders when an integer is divided by n. Because there are n+1 integers in this list, by the pigeonhole principle there must be two with the same remainder when divided by n. The larger of these integers the smaller one is a multiple of n, which has a decimal expansion consisting entirely of 0s and 1s.
For example, take n=7
we have, 1,11, 111,1111,...,11111111
The remainder possible when any number is divided by 7 is 0,1,2,3,4,5,6
These are the remainders when the numbers in the first list are divided by 7 gives 1,4,6,5,2,0,1,4.
Now you can see that we have 7 pigeonholes {0,1,2,3,4,5,6} and 8 pigeons {1,11, 111,1111,...,11111111} so there needs to be at least one pigeonhole where 2 pigeons will reside.
In this case, we have 11%7=4 and 11111111%7=4
Their difference, i.e. 11111111-11=11111100 is divisible by 7.
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The snack bar sold 75% of its inventory of bags of chips. If the snack bar still has 37 bags of chips, how many
bags did they sell?
The bags of chips sold are 111.
What is percentage?The percentage is the term use to tell the hundredth part of something.
Given that, The snack bar sold 75% of its inventory of bags of chips, and the snack bar still has 37 bags of chips,
Let the original number of bags of the chips be x,
Since, 75% is already sold, so left number of bags are = 100%-75% = 25%
Therefore,
25% of x = 37
x = 37x4
x = 148
The number of bags sold = 75% of 148
= 75x148/100
= 111
Hence, they sold 111 bags of chips.
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Probability and Statistics Question
we want to find the number of hours (or rather days) until only 4.25% of the drives fail.
that means for an exponential distribution we have
P(X < x) = 1 - e^(-Lx)
L = 1/mean = 1/12500
and we need to find x, so that P(X <x) = 0.0425 (that is 4.25% converted into a probability).
so, we get
0.0425 = 1 - e^(-x/12500)
0.0425 - 1 = -e^(-x/12500)
-0.9575 = -e^(-x/12500)
0.9575 = e^(‐x/12500)
ln(0.9575) = -x/12500
-x = ln(0.9575)×12500
x = -ln(0.9575)×12500 = - -0.043429558...×12500 =
= 0.043429558...×12500 = 542.8694741... hours
after 542.8694741... hours = 22.61956142... days
it is expected that 4.25% of the hard drives fail.
you left out to what decimal this should be rounded. and if you need hours or days. in case of doubt use hours (as the only other time information is given in hours).
please round yourself as you need.
Tim's mathematics teacher asked him to explain the expression -8. 7. Which answer should Tim give?
A The expression represents 7 groups of 8 positives.
B The expression represents 8 groups of 7 positives.
(C) The expression represents 7 groups of 8 negatives.
(D) The expression represents 8 groups of 7 negatives.
Answer:
C
Step-by-step explanation:
Because it says -8 x 7, the * is negative and the 7 is positive.
Help me thank y so much
The relation is:
(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)
Is a function, because each element in the domain is mapped to a single element in the range.
Do the ordered pairs represent a function?A relation maps elements from one set, called the domain, into another set, called the range.
For example, the element x mapped into element y is written as (x, y).
Particularly, a relation is a function if each element from the domain is mapped into only one element of the range.
So, if we had two points like (2, 4) and (2, 5), then the relation is not a function (because the element 2 is mapped into two different elements of the range).
Here the relation is:
(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)
So the input x = 1 appears twice, but both times is mapped to the same element, so this relation is a function.
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A rectangle piece of metal has an area of 32 square centimeters. Its perimeter is 24 centimeters. What are the dimensions of the piece
The dimensions of the piece are l = 8 and b =4.
What are dimensions?
The minimal set of coordinates required to specify any point within a mathematical space is the dimension of that space. Because only one coordinate is required to specify a point on a line, it has a dimension of one.
Here,
Let the length of a rectangular piece of metal = l cm
And the breadth of a rectangular piece of metal = b cm
Perimeter of a rectangular piece of metal = 2(l+b) = 24 cm
Or, l+b = 24/2
Or, l+b = 12 -------- (1)
Area of a rectangular piece of metal = l×b = 32 cm²
Or, l×b = 32 ------- (2)
We know that,
(l - b)² = (l+b)² - 4×l×b
(l - b)² = (12)² - 4×32
(l - b)² = 144 - 128
(l - b)² = 16
(l - b)² = 4
l - b = 4 --------- (3)
Adding equations (1) and (3), we get
l+b+l-b = 12 + 4
2l = 16
l = 8
Now, we put the value of l in equation(1) and we get
8 + b = 12
b =4
Hence, the dimensions of the piece are l = 8 and b =4.
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[tex]\frac{1}{3}+\frac{1}{105}-\frac{1}{21}[/tex]