Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Correct choice = B[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Take HJ = a, GH = b and GJ = c
a = b + 2 c = a + b - 17 a + b + c = 73put the value of a from equation 1 in equation 2
[tex]\qquad❖ \: \sf \:c = (b + 2) + b - 17[/tex]
[tex]\qquad❖ \: \sf \:c = 2b - 15[/tex]
now, put the value of a and c in equation 3
[tex]\qquad❖ \: \sf \:b + 2 + b + 2b - 15 = 73[/tex]
[tex]\qquad❖ \: \sf \:4b - 13 = 73[/tex]
[tex]\qquad❖ \: \sf \:4b = 86[/tex]
[tex]\qquad❖ \: \sf \:b = 21.5 \: \: in[/tex]
Now, we need to find HJ (a)
[tex]\qquad❖ \: \sf \:a = b + 2[/tex]
[tex]\qquad❖ \: \sf \:a = 21.5 + 2[/tex]
[tex]\qquad❖ \: \sf \:23.5 \: \: in[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Option B is correctAnswer:
23.5 in
Step-by-step explanation:
To find the length of HJ in triangle GHJ, create three equations using the given information, then solve simultaneously.
Equation 1
HJ is two inches longer than GH:
⇒ HJ = GH + 2
Equation 2
GJ is 17 inches shorter than the sum of HJ and GH:
⇒ GJ + 17 = HJ + GH
Equation 3
The perimeter of ΔGHJ is 73 inches:
⇒ HJ + GH + GJ = 73
Substitute Equation 1 into Equation 2 and isolate GJ:
⇒ GJ + 17 = GH + 2 + GH
⇒ GJ + 17 = 2GH + 2
⇒ GJ = 2GH - 15
Substitute Equation 1 into Equation 3 and isolate GJ:
⇒ GH + 2 + GH + GJ = 73
⇒ 2GH + GJ = 71
⇒ GJ = 71 - 2GH
Equate the two equations where GJ is the subject and solve for GH:
⇒ 2GH - 15 = 71 - 2GH
⇒ 4GH = 86
⇒ GH = 21.5
Substitute the found value of GH into Equation 1 and solve for HJ:
⇒ HJ = 21.5 + 2
⇒ HJ = 23.5
Related Questions
The mean of a normally distributed data set is 118, and the standard deviation is 16.
a) Use the standard normal table to find the probability that a randomly-selected data value is greater than 140.
b) Use the standard normal table to find the probability that a randomly-selected data value is less than 90.
Answers
Step-by-step explanation:
a)
z = (140 - 118)/16 = 22/16 = 11/8 = 1.375 ≈ 1.38
in the z-table this gives us the p-value : 0.91621
that is the probability of values 140 and below.
for above 140 we need to calculate the value of the other side of the bell-curve :
1 - 0.91621 = 0.08379
b)
z = (90 - 118)/16 = -28/16 = -7/4 = -1.75
in the z-table this gives us the p-value : 0.04006
that is the probability of values of 90 and below.
About 5% of the population has a particular genetic mutation. 300 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 300. Round your answer to two decimal places.
Answers
If the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.
Given sample size be 300 and about 5% of the population has a particular genetic mutation.
We are required to find the standard deviation for the number of people with the genetic mutation in groups of 300.
Sample size=300
The standard deviation for the number of people with the genetic mutation is calculated as:
Standard deviation=[tex]\sqrt{np(1-p)}[/tex]
Use the known values in the above formula.
Standard deviation=[tex]\sqrt{300*0.05(1-0.05)}[/tex]
=[tex]\sqrt{14.25}[/tex]
=3.77
Hence if the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.
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Heyy i just need some help with questions 21and 25 if anyone could help me and show the work that would be amazing thank you!!
Answers
Step-by-step explanation:
21) f(x)=1/x-6. g(x)=7/x+6
f(g(x))=f(7/x+6)=1÷7/x+6 - 6=x+6/7 - 6
g(f(x))=g(1/x-6)=7÷1/x-6 - 6 =7(x-6) - 6
simplify forward
25)f(x)=|x| g(x)=5x+1
f(g(x))=f(5x+1)=|5x+1|=5x+1=g(x)
g(f(x))=g(|x|)=5|x|+1=5x+1=g(x)
Harry took a loan from the bank.
DDD represents Harry's remaining debt (in dollars) after ttt months.
D=-200t+9000D=−200t+9000D, equals, minus, 200, t, plus, 9000
What was the size of Harry's loan?
Answers
The amount of Harry's loan is $9000.
A loan is when money is lent to another person with the understanding that it would be repaid, along with interest.
According to the question,
A bank loan is taken up by Harry.
After t months, D indicates Harry's outstanding debt (in dollars).
D=-200t+9000
In order to find the initial size of Harry's loan, the time(t)=0, that is, the time when no debts had been paid.
The negative sign in the expression of D denotes the payment of debt.
Substituting t=0, we get,
D=-200*0+9000
D=9000
Thus, the amount of loan taken by Harry is $ 9000.
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Which pair of angles are vertical angles? AngleWRU and AngleSRT AngleWRS and AngleVRT AngleVRU and AngleTRS AngleVRT and AngleSRT
Answers
Step-by-step explanation:
important of festival in nepali languages for class seven
Answer:
b
Step-by-step explanation:
X
-5
Probability 17
-3
-2 0
0 2
13 33 16 11
3
.10
Find the probability that x <-3
Answers
The value of the probability is 0.30
How to determine the probability?Using the table of values, we have:
P(x <= -3) = P(x = -5) + P(x = -3)
From the table of values, we have:
P(x = -5) = 0.17
P(x = -3) = 0.13
Substitute the known values in the above equation
P(x <= -3) = 0.17 + 0.13
Evaluate the sum
P(x <= -3) = 0.30
Hence, the value of the probability is 0.30
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an angle exceeds three times its complement by 10 find it. please explain properly i will mark as brilliant
Answers
Answer:
It's supplementary angle I think
Answer:
one angle is 20° and the other is 70°
Step-by-step explanation:
Complementary angles add up to 90°.
Here it is given that an angle exceeds 3 times its complement by 10. So, we are taking the complement as x. Since it exceeds its complement 3 times, we are multiplying the complement 3 times. so we get [tex]3x[/tex].
Now we also need to add 10, so we get the final equation [tex]3x+10[/tex], which is the second angle.
As of now, first angle = x and second angle = 3x+10.
Since they are complementary angles, both angles add up to 90°
⇒ 1st angle + 2nd angle = 90°
∴ [tex]x+3x+10 = 90[/tex] [since 3x and x are like expressions, we should add 3x + x = 4x]
⇒ [tex]4x = 90 - 10[/tex] [by transposing 10 from LHS to RHS]
⇒ [tex]4x = 80[/tex]
⇒ [tex]x = \frac{80}{4}[/tex] [by transposing 4 from LHS to RHS]
⇒ [tex]x = 20[/tex]
∴The complementary angle is 20° and the given angle is [(3 × 20) + 10)] = 70°
a number line shows the whole numbers from 0 to 10 describe where you would plot square root 30
Answers
Find the magnitude and direction of each resultant for the given vectors. Round each side to the nearest tenth and round each angle to the nearest degree.
w = < 5, 6 >, x = < -1, 14 >
Answers
The magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.
Magnitude of the resultant vector
Sum of vectors in x direction, ∑X = 5 - 1 = 4
Sum of the vectors in y direction, ∑Y = 6 + 14 = 20
Resultant vector = √(∑X² + ∑Y²)
Resultant vector = √(4² + 20²) = 20.4 units
Direction of the vectorθ = arc tan (ΣY/ΣX)
θ = arc tan (20/4)
θ = arc tan (5)
θ = 78.7⁰
θ ≈ 79⁰
Thus, the magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.
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Tara cuts a 300 inch long spool of yarn into two pieces of different sizes. The longer piece is three times as long as the shorter piece. How long is the shortest piece?
Answers
Answer:
75 inches
Step-by-step explanation:
Let x = the short side
Let y = the long side
x + y = 300
y = 3x
Plug 3x for y into the first equation:
x + 3x = 300
4x = 300 Divide both sides by 4
x = 75
Is 25x²-40xy+16y²a perfect square number? why?
Answers
Answer:
yes
Step-by-step explanation:
25x² - 40xy + 16y² can be factored as
(5x - 4y)² ← a perfect square
A new baby grew 3/4 of an inch in June and 7/16? 4- in July. How many total inches did the baby grow during these two months?
Answers
Answer:
The baby grew 1 3/16 inches
Step-by-step explanation:
A new baby grew:
3/4 of an inch in June,7/16 of an inch in July.Total inches during two months:
3/4 + 7/16 = Fractions with different denominators3*4/(4*4) + 7/16 = Multiply the first fraction by 4 12/16 + 7/16 = Add numerators19/16 = Numerator is greater than denominator(16 + 3)/16 = Convert to mixed fraction16/16 + 3/16 = 1 + 3/16 = 1 3/16 AnswerLine passes through the point (8,4) and a slope of 5/4. Write equation in slope-intercept
Answers
Answer:
Step-by-step explanation:
y - 4 = 5/4(x - 8)
y - 4 = 5/4x - 10
y = 5/4x - 6
2[tex]\pi[/tex] x 24 simplified
Answers
Answer: [tex]48\pi[/tex]
Step-by-step explanation:
[tex](2 \times 24)\pi=48\pi[/tex]
1. A foot contains 12 inches. 5 inches is what fraction of a foot?
Answers
Answer:
5/12
Step-by-step explanation:
a foot =12 inches
fraction of 5 inches=5/12
What is the solution to the system of equations?
y = 2/3 x + 3
X= -2
Answers
The solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)
Solving system of equationsFrom the question, we are to determine the solution to the given system of equations
The given system of equation is
y = 2/3 x + 3 ----------- (1)
x= -2 ----------- (2)
The value of x has been given in the second equation of the system of equations.
Now, we will determine the value of y
From the second equation, we have that
x = -2
Substitute the value of x into the first equation,
y = 2/3 x + 3
y = 2/3 (-2) + 3
y = -4/3 + 3
y = 5/3
Hence, the solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)
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what are the 5 different way to solve the quadratic equations
Answers
Step-by-step explanation:
A quadratic equation is a equation with a degree of 2. Below are the 5 ways to solve a quadratic equation.
Factoring - First, make sure that one side of the equation is 0. Turn the equation into a product of two binomials and set each one to 0. Solve both to get both solutions.Completing the Square - Add to both sides such that one side becomes a square of a binomial. Square root both sides and solve with algebra.Square Roots - If one side of the equation is a perfect square, square root both sides and solve normally.Graphing - Make one side of the equation 0 and graph. The x-intercepts are the solutions.Quadratic Formula - First, make the equation follow the form [tex]ax^2+bx+c=0[/tex]. Then, use the formula [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] to get the solutions.(questions in image)
A. Which plane contains line b?
B. Name 3 Collinear Points
C. Name the plane containing point W
D. Name two points not coplanar with points T and Q
E. At which line do the planes M and N intersect
Answers
Answer:
1. Plane N
2. Points P, Q, R
3. Plane CRW …
4. Points K and H
5. Line a
Which of the following linear equations corresponds to the table above?
OA. y=4x-3
OB. y=¹/4x-3
OC. y=¹/4x+3
OD.
y = 4x + 3
Answers
[tex]given \: that \: its \: linear \\ m = \frac{15 - 3}{3 - 0} = \frac{12}{3} = 4 [/tex]
[tex]b = y(0) = 3 \\ y = 4x + 3 \: [/tex]
Option DAnswer:
D) y = 4x + 3
Step-by-step explanation:
Equation of line in slope y-intercept form:[tex]\sf \boxed{\bf y = mx +b}[/tex]
Here, m is the slope and b is y intercept.
At y intercept, x = 0
From the table, y intercept = 3
Choose any two points from the table to find the slope.
(0 ,3) & (3,15)
[tex]\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{15-3}{3-0}\\\\=\dfrac{12}{3}\\\\=4[/tex]
m = 4 ; b = 3
Equation of line:
y = 4x + 3
please help!!!
Using long division, what is the quotient of this expression?
3x42x³-x-4
x²+2
OA. 3x²
3x - 4
OB. 3x² + 2x + x² + 2
O C.
3x² 2x
O D.
-
2x
3x² + 2x
- 6 +
-
- 5+
-
3x + 8
x² + 2
-
3x+6
x²+2
5x8
x² + 2
Rese
Answers
Check the picture below.
notice, the dividend and divisor must be in descending order, and when one of the variables is "missing", is really not missing, it simply has a coefficient of 0.
Here is the solution process:
3 x² - 2 x - 6
x² + 0x + 2 | 3 x⁴ - 2 x³ + 0 x² - x - 4
3 x⁴ + 0 x³ + 6 x²
- 2 x³ - 6 x² - x - 4
- 2 x³ + 0 x² - 4 x
- 6 x² + 3 x - 4
- 6 x² + 0 x - 12
3 x + 8
Long division:
Standard: [tex]\sf{3x^{2} -2x-6+\dfrac{3x+8}{x^{2} +2} \ \ \to \ \ \ Option \ "A" }[/tex]Quotient: 3x² - 2x - 6Rest: 8 + 3xTherefore, the correct option is "A".
The difference of the square of a number and 36 is equal to 5 times that number. Find the positive solution.
Answers
Answer:
x=-4, x=9
Step-by-step explanation:
We write this into words:
difference = subtraction
square = ^2
a number = x
is equal to = =
5 times that number = 5x
x^2-36 = 5x
write in standard form
x^2-5x-36
what adds to -5 and multiplies to -36?
-9 and 4!
(x-9)(x+4)
x-9 = 0
x= 9
x+4 = 0
x=-4
Answer:
9
Step-by-step explanation:
Let the number = x.
x² - 36 = 5x
x² - 5x - 36 = 0
(x - 9)(x + 4) =0
x = 9 or x = -4
Answer: 9
if tan theta = 1/√5 then verify the identity sin²theta + cos²theta = 1
Answers
The identity of sin²Ф + cos²Ф = 1 is verified below
How to evaluate Trigonometry Ratio ?Trigonometry ratio can be evaluated by following the laid down rules with the the use of table and calculator
Given that tan Ф = 1/√5
Where Tan Ф = Opposite / adjacent
We can calculate the hypotenuse by using Pythagoras theorem
Hyp² = 1² + (√5)²
Hyp² = 1 + 5
Hyp = √6
sin Ф = opp / hyp
sin Ф = 1/√6
sin²Ф = 1/6
cos Ф = adj / hyp
cosФ = √5 / √6
cos²Ф = 5/6
sin²Ф + cos²Ф = 1/6 + 5/6
sin²Ф + cos²Ф = 6/6
sin²Ф + cos²Ф = 1
Therefore, the identity of sin²Ф + cos²Ф = 1 is verified.
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If a certain train fare costs $5.00 for the first
10 miles of service, $0.25 per mile for the next
40 miles, and $0.10 per mile for each additional
mile, what would the train fare be to travel a
total distance of 100 miles?
Answers
Answer:
$20
Step-by-step explanation:
$5.00 = 10miles
$0.25(40) = 40 miles
Remaining miles: 100 - (10 + 40) = 50
0.10(50) = 50 miles
5.00 + 0.25(40) + 0.10(50)
5.00 + 10.00 + 5.00
$20.00 for 100 miles
It takes 3 liters of paint to cover an area of 24 square meters. What percentage increase in the quantity of paint would be required to cover an area of 50.4 square meters?
Answers
Answer:
110 [%].
Step-by-step explanation:
if the initial area is 24 m² and final area 50.4 m², then the required percentage can be calculated as:
[tex]\frac{50.4}{24}*100-100=110[/tex] ,
where 50.4/24*100 - the final percentage.
P.S. It means, the final value of the paint is 3*2.1=6.3 [liters].
What is
6/7 of 2/3.
Answers
Step-by-step explanation:
[tex] = \frac{6}{7} \times \frac{2}{3} \\ [/tex]
[tex] = \frac{12}{21} \\ [/tex]
Change into lowest term...
[tex] = \frac{4}{7} \\ [/tex]
...
Explanation: 6/7 = .8572, 2/3 = .6667
.8572 x .6667 = .5714 = 4/7
I hope that this helped! :)
MR MARK MARKS HIS CLASS ON A NORMAL CURVE. THOSE WITH z-SCORES ABOVE 1.8 WILL RECEIVE AN A, THOSE
BETWEEN 1.8 AND 1.1 WILL RECEIVE A B, THOSE BETWEEN 1.1 AND -1.2 WILL
RECEIVE A C, THOSE BETWEEN -1.2 AND -1.9 WILL RECEIVE A D, AND THOSE
UNDER -1.9 WILL RECEIVE AN F.
FIND THE PERCENT OF GRADES THAT WILL BE
A, B, C, D, AND F.
Answers
Using the normal distribution, it is found that the percentages are given as follows:
3.59% of the grades will be A.9.98% of the grades will be B.74.92% of the grades will be C.8.64% of the grades will be D.2.87% of the grades will be F.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The prorportion of students who receive an A is one subtracted by the p-value of Z = 1.8.
Looking at the z-table, Z = 1.8 has a p-value of 0.9641.
1 - 0.9641 = 0.0359.
3.59% of the grades will be A.
For B, it is the p-value of Z = 1.8 subtracted by the p-value of Z = 1.1, hence:
0.9641 - 0.8643 = 0.0998.
9.98% of the grades will be B.
For C, it is the p-value of Z = 1.1 subtracted by the p-value of Z = -1.2, hence:
0.8643 - 0.1151 = 0.7492.
74.92% of the grades will be C.
For D, it is the p-value of Z = -1.2 subtracted by the p-value of Z = -1.9, hence:
0.1151 - 0.0287 = 0.0864.
8.64% of the grades will be D.
For F, it is the p-value of Z = -1.9, hence 2.87% of the grades will be F.
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Use identities to find the values of the sine and cosine functions for the following angle measure.
θ, given that cos 20 =12/13 and θ terminates in quadrant I. Find sin θ and cos θ. Can you explain how do it and what is the answer?
Answers
Using the cosine double angle formula,
[tex]\cos 2\theta=2\cos^2 \theta-1=\frac{12}{13}\\\\2\cos^{2} \theta=\frac{25}{13}\\\\\cos^{2} \theta=\frac{25}{26}\\\\\boxed{\cos \theta=\frac{5}{\sqrt{26}}}[/tex]
(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)
Using the Pythagorean identity,
[tex]\sin^2 \theta+\cos^2 \theta=1\\\\\sin^2 \theta+\frac{25}{26}=1\\\\sin^2 \theta=\frac{1}{26}\\\\\boxed{\sin \theta=\frac{1}{\sqrt{26}}}[/tex]
(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)
which of the following best describes the graph below?
Answers
The correct answer is the option A because in one-to-one functions, each y value corresponds to only one x value.
Which arithmetic sequence has a common difference of -21? ( only one is correct )
a) {873, 894, 915, 936, …}
b) {32, 20, 8, -4, …}
c) {1,245; 1,224; 1,203; 1,182; …}
d) {1,563; 1,587; 1,611; 1,635; …}
Answers
Answer: c) {1,245; 1,224; 1,203; 1,182; …}
Step-by-step explanation:
Concept:
For this question, we just go by eliminating each answer until we get the correct one
Given information
Common difference = -21 (decreasing sequence)
Answer Choice: a) {873, 894, 915, 936, …}
894 - 873 = 21
915 - 895 = 21
936 - 915 = 21
Since the common difference is 21, not -21
[tex]\large\boxed{FALSE}[/tex]
Answer Choice: b) {32, 20, 8, -4, …}
20 - 32 = -12
8 - 20 = -12
-4 - 8 = -12
Since the common difference is -8, not -21
[tex]\large\boxed{FALSE}[/tex]
Answer Choice: c) {1,245; 1,224; 1,203; 1,182; …}
1224 - 1245 = -21
1203 - 1224 = -21
1182 - 1203 = -21
Since the common difference is -21
[tex]\Huge\boxed{TRUE}[/tex]
Answer Choice: d) {1,563; 1,587; 1,611; 1,635; …}
1587 - 1563 = 24
1611 - 1587 = 24
1635 - 1611 = 24
Since the common difference is 24, not -21
[tex]\large\boxed{FALSE}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Question 10 of 25
Which pair of functions are inverses of each other?
Answers
[tex]f(x) = \sqrt[3]{11x} \\ y = \sqrt[3]{11x} \\ x = \sqrt[3]{11y} \\ x {}^{3} = 11y \\ y = \frac{x {}^{3} }{11} [/tex]
Option A eliminated[tex]f(x) = \frac{x}{7} + 10 \\ y = \frac{x}{7} + 10 \\ x = \frac{y}{7} + 10 \\ x - 10 = \frac{y}{7} \\ y = \frac{x - 10}{7} [/tex]
Option B eliminated[tex]f(x) = \frac{7}{x} - 2 \\ y = \frac{7}{x} - 2 \\ x = \frac{7}{y} + 2 \\ x - 2 = \frac{7}{y} \\ y = \frac{7}{x - 2} [/tex]
Option C eliminatedBy elimination it's DConfirmation:[tex]f(x) = 9x - 6 \\ y = 9x - 6 \\ x = 9y - 6 \\ x + 6 = 9y \\ y = \frac{x + 6}{9} = g(x)[/tex]
