The third vertex of the isosceles triangle is (a/2, b).
Let one vertex of the triangle lies on the base of the x-axis as 'a' which is written as (a,0)
Similarly, the other vertex of the triangle lies on the base of the y-axis as 'b' which is written as (0,b)
Let other vertex be at origin (0, 0)
An isosceles triangle is a triangle that has at least two sides of equal length.
Hence, the vertex of the triangle is (a/2, b).
To learn more about vertex click here:
https://brainly.com/question/29030495
#SPJ4
Solve for y
6x-3y=36
y = 2x - 12
Step-by-step explanation:Move all terms that don't contain y to the right side and solve.6x - 3y = 36In order to solve this linear equation, we need to group all the variable terms on one side, and all the constant terms on the other side of the equation. In our example, the term 6x will be moved to the right side. Notice that a term changes sign when it 'moves' from one side of the equation to the other.We need to get rid of expression parentheses. If there is a negative sign in front of it, each term within the expression changes sign. Otherwise, the expression remains unchanged. In our example, there are no negative expressions.Therefore, y = 2x - 12I want to know how I can solve this question.
For the right triangle shown in the picture, recall the trigonometric identity of the cosine function:
[tex]\cos (B)=\frac{a}{c}[/tex]Isolate a from the equation:
[tex]a=c\cdot\cos (B)[/tex]Substitute for c=6.3 and B=43.8°:
[tex]a=6.3\cos (43.8)[/tex]Use a calculator to evaluate the expression:
[tex]\begin{gathered} a=4.547089437\ldots \\ \approx4.6 \end{gathered}[/tex]Need help making sure I have everything correct if wrong please advise Thank you
To question 16, we see that for every change of plus 2 drinks, they pay an additional value of $2.50. It means that each drink does cost half of this value.
This way, the equation that will give the value of the total cost will be:
[tex]Y=1.25\times X[/tex]Where X stands for the number of drinks, and 1.25 is the value of a single drink.
From the solution presented above, we are able to conclude that the rate of change represents the value of a unitary drink, in the present situation.
13) Which of the following algebraic representations would result in a reduction dilation?A. (x,y) → x,y)C. (x,y) →x,0.75y)AnswerB. (x,y) → (-2x.-2y)D. (x,y) →x,y)acxiy) (tx, tyTriangles JKN and MKL are shown below.KMN14) Which of the following congruency statements is true about the two triangles?Angwer BA. L and ZN ZM B. ZNZL and ZK-ZK2N and CL areCongruentC. ZNZL and ZMD. UN and ZMZL Eck and Zk aze congruen15) Are triangles JKN and MKL similar?Yes16) If you answered YES for question 15, explain how you know they are similar. If you answered NO forquestion 15, explain how you know they are not similar.
16) We know that the triangles are similar because the three angles are equal in both triangles:
The angles in K are opposite by the vertex, so they are equal.
We also know that angles L and N are equal too.
By the rule of the sum of the angles in a triangle, we know that the third angle has to be equal.
Also, the side opposite to the angle N and L in each triangle have the same measure, so we can conclude that the triangles are similar.
Find the probability of at least 6 failuresin 7 trials of a binomial experiment inwhich the probability of success in anyone trial is 9%.p=[?1%Round to the nearest tenth of a percent.
Find the missing side or angle. Round to the nearest tenth. a=4 b=5 c=7
Using the law of cosines, the missing angles are:
A = 34.1°, B = 44.4°, C = 101.5°
What is the Law of Cosines?The law of cosines is used to solve a triangle when given the lengths of the three sides of a triangle, and it is expressed by the formula:
c² = a² + b² - 2ab × Cos C.
Given the following:
a = 4 b = 5 c = 7Find C by substituting the values into the law of cosines formula:
7² = 4² + 5² - 2 × 4 × 5 × Cos C
49 = 16 + 25 - 40 × Cos C
49 = 41 - 40Cos C
49 - 41 = -40Cos C
8/-40 = Cos C
-0.2 = Cos C
C = Cos^(-1)(-0.2)
C = 101.5°
Find B using the Law of Sines:
sin B/b = sin C/c
Substitute
sin B/5 = sin 101.5/7
(sin B)(7) = (sin 101.5)(5)
sin B = (sin 101.5)(5)/7
sin B = 0.69995
B = Sin^(-1)(0.69995)
B = 44.4°
Find the measure of angle A using the triangle sum theorem:
A = 180 - 101.5 - 44.4
A = 34.1°
Learn more about the law of cosines on:
https://brainly.com/question/4372174
#SPJ1
Hi can you help explain this question. I have trouble writing statement and reasons for this question please. I get lost.
For the given figure, we will prove the triangles BGH and BDH are congruent.
So, the proof will be as follows:
Statement Reason
1) m∠F = m∠FEG = m∠FGE Given
2) ΔFGE is an equilateral triangle from (1), the definition of an equilateral Δ
3) FG = GE from (2), the definition of equilateral Δ
4) FG = ED Given
5) m∠ GEH = m∠DEH Given
6) EH = EH Reflexive property
7) ΔGEH ≅ Δ DEH SAS postulate
8) GH = DH from (7) CPCTC
9) m∠GHE = m∠DHE from (7) CPCTC
10) m∠GHB = m∠DHB Definition of supplementary angles
11) HB = HB Reflexive property
12) ΔBGH ≅ ΔBDH SAS postualte
13) ΔAGB is an isosceles Δ Given
14)AG = AB Definition of isosceles Δ
15) ΔBCD is an isosceles Δ Given
16) CB = CD Definition of isosceles Δ
17) CB = AG Given
18) m∠CDB = m∠CBD Definition of isosceles Δ
19) m∠ABG = m∠AGB Definition of isosceles Δ
20) m∠CDB = m∠AGB Given
21) m∠ABG = m∠CBD Transitive property
22) Δ AGB ≅ ΔCBD AAS postualte
(3x869)+(19x528)+428(3)(1049)=a
a=
The value of a in the equation (3x869)+(19x528)+428(3)(1049)=a is 1359555
How to evaluate the expression?From the question, the equation to evaluate is given as
(3x869)+(19x528)+428(3)(1049)=a
Rewrite the above equation to make it legible
So, we have the following equation
(3 x 869) + (19 x 528) + 428(3)(1049) = a
Evaluate the products in the expression
So, we have the following equation
2607 + (19 x 528) + 428(3)(1049) = a
Evaluate the other products in the expression
So, we have
2607 + 10032 + 428(3)(1049) = a
Remove the brackets in the equation
So, we have the following equation
2607 + 10032 + 1346916 = a
Evaluate the sum
1359555 = a
Rewrite as
a = 1359555
Hence, the solution to the equation is 1359555
Read more about equations at
https://brainly.com/question/21405634
#SPJ1
Are the following Parallel, Perpendicular, or neither: y = 2x - 5 and -x + 2y = -5
two lines are parallel if their slope is equal
equation of line is
y=mx+c
where m=slope
for y=2x-5
m=2
for -x+2y=-5
2y=-5+x
y=-5/2+x/2
m=1/2
lines are nor parallel becuase m (slope) is not equal
now we will test for perpendicularity
perpendicular lines have slopes that are reciprocal of each other
first line , m=2
second line, m=1/2
2 and 1/2 are reciprocals
therefore, the lines are perpendicular
A researcher numbers each household in the city and uses a random number generator to select individual households for the sample. By chance, none of the households chosen were households of single millennials. This is an example of Answer
. }.
A company's receipts gives a website where customers can fill out a survey to receive a coupon. This is an example of Answer
.
Your friend forgot she was supposed to conduct a poll of your high schools' students. She asks everyone in your homeroom if they think the school should have a new mascot. She presents the results to the student council. This is an example of Answer
undercoverage bias
1. The type of bias that the researcher would be making here based on the fact that the households were not that of single millennials is the sampling bias.
2. The voluntary response bias is the type of bias that is being done where the receipts of the website would be the bias that would occur from the company's website.
3. The under coverage bias is what would happen in this scenario given that the friend would not have to ask all of the persons that would be used for the study.
What is a research bias?This is the term that is used to refer to the systematic error that would occur in research due to the researchers methods.
1. The answer is the sampling error due to the fact that the random generator was what was used. This would end up giving a sample that would not show the true representation of all of the population.
2. The voluntary response bias is what would be made here because those filling the form are doing it voluntarily.
3. The undercoverage bias is made here because the opinion of the entire school population is not well represented here.
Read more on research bias here:
https://brainly.com/question/4095022
#SPJ1
Find the max and min values
100 +14.75 %
Step-by-step explanation:
100+14.75%
100+14=114
=114.75%
When solving the system of equations below, which expression could be substituted for x in the second equation? x=4−y
3x+2y=15
The expression that we can replace in the second equation is 4 - y, doing that, we will get the solutions:
x = -8 and y = 12
How to solve the solve the system by substitution?
Here we have the system of equations:
x=4−y
3x+2y=15
Notice that x is already isolated on the first equation, so we can substitute that in the second equation. Then we will get:
3x+2y=15
3*(4 - y) + 2y = 0
So the expression that could be substituted for x in the second equation is 4 - y.
And now we get:
12 - 3y + 2y = 0
12 = y
And the value of x is:
x = 4 - y = 4 - 12 = -8
Learn more about systems of equations.
https://brainly.com/question/13729904
#SPJ1
Jeremiah keeps a record of how many pages he reads each day. He read 40% fewer pages today than yesterday. If he read 90 pages today, how many pages did he read yesterday?
Answer: 126
Step-by-step explanation:: 90 ÷ 10 = 9 (10%) 9 × 4 = 36 (40%) 90 + 36 = 126
What is x in this equation 6(x+7)=-12
Answer:
x = -9
6x + 42 = -12
6x = -54
x = -9
Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.
Which choice represents the sample space, S, for this event?
S = {PQR}
S = {PQR, PRQ, QPR, QRP, RPQ, RQP}
S = {PQ, PR, QR}
S = {PQ, QP, PR, RP, QR, RQ}
The resulting sample space of the given situation is S = {PQ, QP, PR, RP, QR, RQ}
Sample space:
Sample space refers the collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.
Given,
Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.
Here we need to find the sample space for the event.
Let us consider,
P represents Patty
Q represents Quinlan
R represents Rashad
And through the question we have know that, the teacher drawn two card at a time,
So we have consider that the teacher is going to draw out of the hat one first, without replacement, and then draw another one.
The first chosen one will be the president, and that could be P, Q or R, Now, the chosen second one is the Vice president, and already one has already being drawn, that could only be two fellows.
Therefore, the total of likely outcomes is PQ,QP, PR, RP, QR, RQ, one paired up with either of the two remaining in the hat.
So, the resulting sample space is
S = {PQ, QP, PR, RP, QR, RQ}
To know more about Sample space here.
https://brainly.com/question/28043513
#SPJ1
There are 60 members in the school glee club. The glee club needs to raise at least $5,000 for a trip toa national competition. The school agreed to contribute $1,000 toward the trip. Which of theinequalities below shows the amount of money that each glee club member needs to raise to help payfor the trip.a) 60x + 1,000 > 5,000b) 60x + 5,000 > 1,000c) 1,000x + 60 < 5,000
Let x be the amount raised by each club member. Since there are 60 members, the amount raised by them would be
[tex]60x[/tex]Now, we know the school contributed $1,000. Now, the amount raised is:
[tex]60x+1000[/tex]Since this amount has to be at least $5,000, we have that the inequality that shows the amount of money that each glee club member needs to raise to help pay for the trip is:
[tex]60x+1000>5000[/tex]Answer: Option A
If x=5,solve for y.(Recall you can ue either original equation).y=x-6-2x+3y=-13
Using first equation
y=x-6
substitute x = 5 into the equation
y = 5-6
y = -1
Or
Using second equation
-2x+3y=-13
substitute x = 5 into the equation
-2(5) + 3y = -13
-10 + 3y = -13
3y = -13 + 10
3y = -3
y = -3/3
y = -1
Shane is a building engineer and is determining the length of an access ramp needed to reach a step 1.5 feet off the ground. He knows the length of the ramp, r, in feet, can be expressed with the equation below.First, Shane finds that sin(4.5°) ≈ 0.08. Using his calculator, he then calculates the length of the ramp as shown below.What could Shane do to make his calculation more accurate? A. Use sin(4.5°) in his calculator instead of 0.08. B. Remeasure the angle with a different tool. C. Use the Pythagorean theorem to find the length of the ramp. D. Use a different trigonometric function to find the length of the ramp.
Statement Problem: Shane is a building engineer and is determining the length of an access ramp needed to reach a step 1.5 feet off the ground. He knows the length of the ramp, r, in feet, can be expressed with the equation below.
First, Shane finds that sin(4.5°) ≈ 0.08. Using his calculator, he then calculates the length of the ramp as shown below.
What could Shane do to make his calculation more accurate?
Solution:
The length of the ramp, r, in feet is expressed using the sine ratio;
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \sin 4.5^o=\frac{1.5}{r} \\ r=(\frac{1.5}{\sin 4.5})ft \\ \end{gathered}[/tex]Hence, Shane's calculation would be more accurate if he uses sin (4.5 degrees) in his calculator instead of 0.08
CORRECT OPTION: A
Manuel was examining the product of 48 x 0.73. He realized that he could create other multiplication problems that have the same product. Select whether each expression has the same product as 48 x 0.73. 6.NS.3 No Yes 0 0 43 x 0.78 0 0 4.8 * 7.3 o 0,48 x 73 o 7.8 * 4.3 0 0 480 x 0.073 roto of 283 miles per hour. Nora walks at a rate of
We will solve as follows:
*First: We find out the value of the product:
[tex]48\cdot0.73=35.04[/tex]Now, we find out from the other expressions:
*First:
[tex]43\cdot0.78=33.54[/tex][No]
*Second:
[tex]4.8\cdot7.3=35.04[/tex][Yes]
*Third:
[tex]0.48\cdot73=35.04[/tex][Yes]
*Fourth:
[tex]7.8\cdot4.3=33.54[/tex][No]
*Fifth:
[tex]480\cdot0.073=35.04[/tex][Yes]
If Rie’s legs are 99cm long, and Rie is 165cm tall. What percentage of Rie’s body is legs?
The percentage of Rie's body that is Rie's legs is: 60%.
What is Percentage?A percentage can be defined as an amount in each hundred or, simply put, a proportion of a quantity in relation of a whole.
How to Find the Percentage of a Quantity in a Whole?To find the percentage of a quantity in a whole, divide the quantity by the whole quantity, then multiply the quotient by 100.
The "whole" in this problem is Rie's height, which is: 165 cm
The "quantity" in the context of this question is the length of Rie's leg, which is: 99 cm.
Therefore, to find the percentage of Rie's legs in Rie's body, we have the following:
99/165 × 100
= 0.6 × 100
= 60%.
Therefore, Rie's leg is 60% of Rie's body.
Learn more about percentage on:
https://brainly.com/question/24877689
#SPJ1
the altitude (i.e., height) of a triangle is increasing at a rate of 3.5 cm/minute while the area of the triangle is increasing at a rate of 4.5 square cm/minute. at what rate is the base of the triangle changing when the altitude is 7.5 centimeters and the area is 87 square centimeters?
The rate at which the base of the triangle is changing is equal to,
dB = -6.3 cm/minutes.
From the data given in the question.
The rate of increase in the area of the triangle, dA = 4.5 cm/minute
The rate of increase in the altitude of the triangle, dH = 3.5 cm/minute
The Area of the triangle, A = 87 square centimeters
The altitude of the triangle, H = 7.5 centimeters
The equation for the area of a triangle is equal to
A = 0.5×B×H
Plug in A and H to solve for B at that point:
87 = 0.5×B×7.5
B = 23.2
Differentiate the equation for the area of a triangle to find the rate of change of the area of a triangle (dA):
dA = 0.5× dB× H + 0.5×B × dH.
Plug in known variables to solve for the rate of change of the base dB
dA = 0.5 × dB × H + 0.5 × B × dH
4.5 = 0.5 × dB × 7.5 + 0.5 × 23.2 × 3.5
The rate at which the base of the triangle is changing is equal to,
dB = -6.3 cm/minutes.
Learn more about Triangles at
https://brainly.com/question/27683633?referrer=searchResults
#SPJ4
two people dined at the la fiesta grill where the food cost was $36.54 to that a tax of 4.12 was added what ha the percentage of this tax round your answer to the nearest tenth
The percentage of the tax is 11.26%
Percentage:
Percentage is defined as the number or ratio that can be expressed as a fraction of 100. If you want to calculate percent of a number, divide the number by the whole and multiply by 100.
Given,
Two people dined at the la fiesta grill where the food cost was $36.54 to that a tax of 4.12 was added .
Here we need to find the tax in percentage.
Let us consider x be the percentage of tax has been added to the food.
The the given details, we have identified the following details,
Amount of the food = $36.54
Tax amount = $4.12
So, it can be written as,
x% of $36.54 = $4.12
Here we need the percentage value so we have to move the other to the right side, then we get,
x% = $4.12/36.54
x% = 0.1126
To convert it into percentage, then we have to multiply it by 100, then we get,
x = 11.26
Therefore, the tax percentage is 11.26%.
To know more about Percentage here.
https://brainly.com/question/28269290
#SPJ1
←
Mattie Evans drove 140 miles in the same amount of time that it took a turbopropeller plane to travel 540 miles. The speed of the plane was 200 mph faster than the speed of the car
Find the speed of the plane.
The speed of the plane was
(Simplify your answer.)
mph.
Since the speed of the turbopropeller plane was 200 mph faster than the speed of the car, the speed of the turbopropeller plane is equal to 70 mph.
How to determine the speed of this plane?In order to solve this word problem, we would assign variables to the distance and speed of both Mattie's car and the turbopropeller plane, and then translate the word problem into algebraic equation as follows:
Let d₁ represent the distance covered by Mattie.Let v₁ represent the speed of Mattie's car.Let d₂ represent the distance covered by the turbopropeller plane.Let v₂ represent the speed of the turbopropeller plane.Translating the word problem into an algebraic equation, we have;
v₂ = v₁ + 200
Since Mattie and the turbopropeller plane travled at the same time, we have:
Time = distance/speed
Time = d₁/v₁ = d₂/v₂
Time = 140/v₁ = 540/v₁ + 200
Cross-multiplying, we have:
140(v₁ + 200) = 540v₁
140v₁ + 28,000 = 540v₁
Next, we would rearrange the equation by collecting like terms as follows:
540v₁ - 140v₁ = 28,000
400v₁ = 28,000
Speed of plane, v₁ = 28,000/400
Speed of plane, v₁ = 70 mph.
Read more on speed and distance here: https://brainly.com/question/25920823
#SPJ1
Let n =2 and z=4. Evaluate the following (8/n)n -✓z
x + m = p - n + yx Solve for x
Answer:
[tex]x=\frac{-m-n+p}{-y+1}[/tex]
Step-by-step explanation:
The __________ shows the number of data items with values less than or equal to the upper class limit of each class.
Answer: Cumulative frequency distribution
Step-by-step explanation: Not entirely sure but I believe you are looking for this definition based on the question. Hope this helps :)
a door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. suppose the true proportion is 0.07. if 492 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.03? round your answer to four decimal places.
The probability that the sample proportion will differ from the population proportion by less than 0.03 exists 0.9909.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Let the true proportion exists 0.07
number of samples exists 492 then we get
√(0.07)(1−0.07)/492 ≈ 0.01150291586
Since the true value of the population proportion exists 0.07, the value of p^ must fall between 0.04 and 0.10 in order for the error of estimation to be less than 0.03.
Therefore, the probability that the sample proportion will differ from the population proportion by less than 0.03 exists 0.9909.
To learn more about probability refer to:
brainly.com/question/13604758
#SPJ4
Which equation could represent the relationship shown in the scatterplot?
Scatter plot with x axis labeled variable x and y axis labeled variable y. Points go from lower left to upper right.
Drevae WashingtonExpected ValueMar 08, 1:24:47 PM?Scarlett volunteers on the weekend at the Central Library. As a school project, shedecides to record how many people visit the library, and where they go. On Saturday,429 people went to The Youth Wing, 382 people went to Social Issues, and 424 wentto Fiction and Literature.On Sunday, the library had 1100 total visitors. Based on what Scarlett had recordedon Saturday, about how many people should be expected to go to The Youth Wing?Round your answer to the nearest whole number.Answer:Submit Answerattempt 1 out of 2RIDeltaMath - Googl.W April Spirit WeekResume from vae..
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Get the total number of visitors on saturday
[tex]382+429+424=1235[/tex]STEP 2: Get the proportion/probability of the people who went to the Youth Wing on Saturday
[tex]\begin{gathered} \Rightarrow\frac{\text{number of Youth Wing}}{\text{Total number of visitors}} \\ \Rightarrow\frac{429}{1235}=0.347368421 \end{gathered}[/tex]STEP 3: Get the expected number of people to visit the Youth Wing on Sunday
[tex]\begin{gathered} \text{Expected value}=\text{proportion}\times total\text{ number of visitors on Sunday} \\ \text{Expected Value=}0.347368421\times1100=382.1052632 \\ \text{Expected Value of people from Youth Wing }\approx382 \end{gathered}[/tex]Hence, the expected number of people to visit the Youth Wing on Sunday is approximately 382 people
Find an equation of the line parallel to the graph of y = -5x-3 that passes throughthe point of (3,2). Write your equation in slope-intercept form.
Parallel lines has the same slope. In our case, the slope is -5. Then, the searched line has the form:
[tex]y=-5x+b[/tex]where b is the y-intercept.
We can find b by substituting the given point (3,2) into the las equation. Then, we have
[tex]2=-5(3)+b[/tex]which gives
[tex]\begin{gathered} 2=-15+b \\ 2+15=b \\ 17=b \end{gathered}[/tex]Therefore, the parallel lines is given by
[tex]y=-5x+17[/tex]