(04.02 LC)
Triangle ABC is similar to triangle PQR, as shown below:
Two similar triangles ABC and PQR are shown. Triangle ABC has sides AB = c, BC = a, and AC = b. Triangle PQR has sides PQ = r,
Which ratio is equal to b:q? (1 point)
b:a
c:r
r:a
q:c
∆ABC~∆PQR
AB~PQ , c~r
c:r
Answer:
The correct option is 2.
Step-by-step explanation:
It is given that triangles ABC and PQR are similar triangles.
The sides of the triangle ABC are AB = c, BC = a, and AC = b. Triangle PQR has sides PQ = r, QR=p and PR=q.
If two triangles are similar, then their corresponding sides proportional.
Since ABC and PQR are similar triangles, therefore
[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}[/tex]
[tex]\frac{c}{r}=\frac{a}{p}=\frac{b}{q}[/tex]
It can be written as
[tex]\frac{c}{r}=\frac{b}{q}[/tex]
[tex]\frac{a}{p}=\frac{b}{q}[/tex]
Therefore b:q is equal to c:r or a:p. Option 2 is correct.
What is the 40th term of the arithmetic sequence?
21,18,15,12,9....
A: -99
B: -96
C: 6
D: 138
The 40th term of the arithmetic sequence 21,18,15,12,9.. is -96
using Arithmetic progression formula,
a = first term = 21
common difference = d = 18 - 21 = - 3
Therefore,
aₙ = a + (n - 1)d
a₄₀ = 21 + (40 - 1)-3
a₄₀ = 21 +(39)(-3)
a₄₀ = 21 - 117
a₄₀ = -96
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A four-character secret code can begin with any two of the five vowels and end with any two numerals, from 0 to 9. How many different four-character secret codes are possible?
Your math teacher manages a campground during summer vacation. He loves math so much that he has mapped the campground on a coordinate grid. The campsites have the following coordinate: Brighton Bluff at B(2,2), ponaganset peak at P(4,10) and harmony hill at h(12,2) he wants to build showers that are equidistant from all three campsites. Find the coordinates of the point where the shower should be placed.
Answer:
(5,5)
Step-by-step explanation:
Step 1) Find the perpendicular bisector of BP Step 2) Find the perpendicular bisector of BH Step 3) The intersection point of the perpendicular bisector is where the showers would be built. This is the circumcenter of the circumscribed circle. After doing all of this, you should get that answer.. (5,5)
8 less than a number n is less than 11
Final answer:
To find the number n in the inequality '8 less than a number n is less than 11', we can set up and solve the inequality n - 8 < 11. The answer is that the number n is less than 19.
Explanation:
The question states that 8 less than a number n is less than 11. To solve this, we can set up the inequality:
n - 8 < 11
To isolate n, we can add 8 to both sides:
n < 11 + 8
n < 19
So, the answer is that the number n is less than 19.
A student earns $10 per hour for tutoring and $7 per hour as a teacher's aide. To have enough free time for studies, he can work no more than 20 hours per week. The tutoring center requires that each tutor spends at least three hours per week tutoring, but no more than eight hours per week. How many hours should he work to maximize his earnings?
hours of tutoring hours as a teacher's aide What is the maximum profit? $
He should work 20 hours every week to optimize his profits. The maximum profit will be $164.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
He should tutor as many hours as possible because he is paid more for it. He may only work for a maximum of 20 hours every day. He must tutor for at least 3 hours but no more than 8 hours to optimum profit, he must tutor for 8 hours leaving 12 hours as a teacher's helper.
To optimize his profits, he should work 20 hours every week.
⇒ 8(10) + 12(7)
⇒ 80 + 84
⇒ 164
Therefore, he should work 20 hours every week to optimize his profit and the maximum profit will be $164.
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To borrow money, you pawn your guitar. Based on the value of the guitar, the pawnbroker loans you $960. One month later, you get the guitar back by paying the pawnbroker $1,472. What annual interest rate did you pay? Round to the nearest tenth of a percent. ...?
The annual interest rate paid for the pawned guitar is calculated to be 640%, which is obtained by dividing the interest paid by the original loan amount to find the monthly rate and then multiplying by 12.
Explanation:To calculate the annual interest rate paid for pawning the guitar, we need to first determine the total interest paid, then the monthly interest rate, and finally convert that to an annual rate. The interest paid is the difference between the amount received from pawning the guitar and the amount paid to redeem it, which is $1,472 - $960 = $512.
As the loan was for one month, we can determine the monthly interest rate by dividing the interest paid by the principal amount. This gives us $512 / $960 = 0.5333 or 53.33%. To find the annual interest rate, we multiply the monthly rate by 12 (the number of months in a year). Thus, the annual interest rate is 53.33% * 12 = 640%.
It's important to note that this is an extremely high rate of interest, which is not uncommon for pawnshop loans or other short-term high-risk loans.
how to do rational numbers
When you pay a bill in full, you are
What is the smallest positive value for x where y=sin2x reaches its maximum? How do you figure this out? ...?
To find the smallest positive value for x where y = sin^2x reaches its maximum, we can set sin^2x = 1 and solve for x. The smallest positive value of x where y = sin^2x reaches its maximum is pi/2.
Explanation:To find the smallest positive value for x where y = sin^2x reaches its maximum, we need to consider the properties of the sine function. The sine function oscillates between -1 and +1, with the maximum value of sin^2x being 1. Since the maximum value of sin^2x is 1, we can set sin^2x = 1 and solve for x.
Applying the property of sin^2x = 1, we have:
sin^2x = 1
Taking the square root of both sides, sinx = ±1
Since we are looking for the smallest positive value of x, we take sinx = 1
This means that x = π/2 + 2πn, where n is an integer.
Therefore, the smallest positive value for x where y = sin^2x reaches its maximum is π/2.
Five people are sitting around a circle. Some always tell the truth, whilst others always lie. Each person claims to be sitting between two liars. How many of them are telling the truth?
A 0 B 1 C 2 D 3 E 4
The answer is: B. 1 - Only one of the five people is telling the truth.
In this scenario, we are given that five people are sitting around a circle. Some always tell the truth, while others always lie. Each person claims to be sitting between two liars.
Let's analyze the possibilities:
If all five people were telling the truth, each person's claim of sitting between two liars would be true. However, this would mean that all five people are telling the truth, which contradicts the given information.
If none of the five people were telling the truth, each person's claim of sitting between two liars would be false. However, this also contradicts the given information.
Given these two possibilities, we can conclude that there must be a combination of truth-tellers and liars among the five people.
Considering the options given:
A. 0: This suggests that none of the people are telling the truth. However, this contradicts the given information that some people always tell the truth.
B. 1: This suggests that only one person is telling the truth. In this case, this person's claim of sitting between two liars would be true, while the claims of the other four people would be false. This option aligns with the given information and is a valid possibility.
C. 2, D. 3, E. 4: These options suggest that multiple people are telling the truth. However, if more than one person tells the truth, their claims of sitting between two liars cannot all be true.
Based on the analysis, the answer is:
B. 1 - Only one of the five people is telling the truth.
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Suppose you are making yourself a sandwich. How many different sandwiches can you make if you have four choices in bread, two choices in meat, and five choices in cheese?
A piece of wood that is 3/4 meter long is being cut into smaller pieces that are each 1/10 meter long.which equation could be solved to find the number of pieces,n,that can be made?
Nine wolves, eight female and one male, are to be released into the wild three at a time.
If the male wolf is to be in the first released group and order does not matter, in how many ways can the first group of three wolves be formed?
The correct answer is 28 ways.
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Answer:
Hence, we can form a group of three wolves in:
28 ways.
Step-by-step explanation:
We are given:
Nine wolves, eight female and one male.
We have to release three at a time also the male wolf is to be in the first released group and order does not matter
Then we have to choose 2 female wolves out of 8
as the order does not matter so we have to use combination
Hence, it is given as:
[tex]8_C_2=\dfrac{8!}{2!\times (8-2)!}\\\\8_C_2=\dfrac{8!}{2!\times 6!}\\\\8_C_2=28[/tex]
Hence, we can form a group of three wolves in:
28 ways.
In the diagram, which angle is part of a linear pair and part of a vertical pair?
The options of the question are
A.)BFC B.)CFG C.)GFD D.)EFA
we know that
A linear pair forms a straight angle which contains [tex] 180 [/tex]º, so you have [tex] 2 [/tex] angles whose measures add to [tex] 180 [/tex] degrees, which means they are supplementary.
Vertical Angles are two angles whose sides form two pairs of opposite rays (straight lines).Vertical angles are congruent
in this problem
Part a) Linear Pair
1) m∠EFA+m∠EFD=[tex] 180 [/tex]°
angles ∠EFA and ∠EFD are a linear pair
2) m∠BFD+m∠EFD=[tex] 180 [/tex]°
angles ∠BFD and ∠EFD are a linear pair
3) m∠BFD+m∠BFA=[tex] 180 [/tex]°
angles ∠BFD and ∠BFA are a linear pair
4) m∠BFA+m∠AFD=[tex] 180 [/tex]°
angles ∠BFA and ∠AFD are a linear pair
Part b) Vertical angles
1) m∠EFA=m∠BFD
angles ∠EFA and ∠BFD are a vertical angles
2) m∠AFB=m∠EFD
angles ∠AFB and ∠EFD are a vertical angles
therefore
the answer is the option
D.) EFA
Factor out the greatest common factor: 16a3 - 8a5
The area of egypt is 386,700 square miles. the area of wyoming is about 97,818 square milesegypt is about how many times as large as wyoming?explain how you solved the problem
Marquis has a gross pay of $816. By how much will his gross pay be reduced if Marquis has the following items withheld?
federal tax of $92
Social Security tax that is 6.2% of his gross pay
Medicare tax that is 1.45% of his gross pay
state tax that is 22% of his federal tax
Answer:
His gross pay would be reduced $174.66.
Step-by-step explanation:
Gross pay of Marquis = $816
His withholding are :
Federal tax = $92.00
Social security tax = 6.2% of $816
= 0.062 × 816
= $50.592
Medicare tax = 1.45% × 816
= 0.0145 × 816
= $11.832
State tax = 22% × 92
= 0.22 × 92
= $20.24
Total withholding = 92 + 50.59 + 11.83 + 20.24
= $174.66
His net pay = $816 - $174.66 = $641.34
His gross pay would be reduced $174.66
Which Equation represents this problem?
Pauline can spend $36 on bus fare each week. She needs to ride the bus 5 days a week. How much can she spend each day on bus fare?
A.
36 + b = 5
B.
5 x b = 36
C.
5 ÷ b = 36
D.
36 – b = 5
Kala made 20000 in taxable income last year. Suppose the income tax rate is 0.15 for the first 8500 plus 0.19 for the amount over 8500 . How much must Kala pay in income tax for last year?
What is the slope of the line whose equation is -3x y=12?
reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. The microphone itself is placed on the focus of the parabola. If the parabola is 60 inches wide and 30 inches deep, how far from the vertex should the microphone be placed?
Identify the type of conic section that has the equation 9x^2+ 16y^2 = 144 and identify its domain and range.
Answer:
B ) ellipse.Domain: { -4 ≤ x ≤ 4 }Range: { -3 ≤ y ≤ 3 }
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The equation [tex]\(9x^2 + 16y^2 = 144\)[/tex] represents an ellipse. Its domain is \([-4, 4]\) and its range is \([-3, 3]\).
The equation [tex]\(9x^2 + 16y^2 = 144\)[/tex] represents an ellipse. To identify its domain and range, we need to understand its shape and orientation.
Step 1: Standard Form of an Ellipse
The standard form of an ellipse with its center at the origin is [tex]\( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)[/tex], where \( a \) and \( b \) are the semi-major and semi-minor axes lengths, respectively.
Step 2: Compare Equations
Comparing the given equation [tex]\( 9x^2 + 16y^2 = 144 \)[/tex] with the standard form, we see that [tex]\( a^2 = \frac{144}{9} = 16 \)[/tex] and [tex]\( b^2 = \frac{144}{16} = 9 \).[/tex]
Step 3: Determine Axis Lengths
This means the semi-major axis length \( a \) is [tex]\( \sqrt{16} = 4 \)[/tex]and the semi-minor axis length \( b \) is [tex]\( \sqrt{9} = 3 \).[/tex]Step 4: Shape of the Ellipse
Since \( a > b \), the ellipse is stretched more horizontally than vertically, meaning it's wider than it is tall.
Step 5: Domain and Range
The domain of the ellipse is determined by the values of \( x \) and the range by the values of \( y \). For this ellipse, the \( x \)-values vary from \( -4 \) to \( 4 \) (domain), and the \( y \)-values vary from \( -3 \) to \( 3 \) (range).
Therefore, the domain is \([-4, 4]\) and the range is \([-3, 3]\).
The quotient of a number and –1.5 is 21
If ABCDE is a regular pentagon and diagonals EB and AC intersect at O, then what is the degree measure of angleEOC?
If ABCDE is a regular pentagon and diagonals EB and AC intersect at O, then the degree measure of angle EOC is 108°.
In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:
Sum of interior angles = 180 × (n - 2)
Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.
Sum of interior angles = 180 × (5 - 2)
Sum of interior angles = 180 × 3
Sum of interior angles = 540°.
Therefore, the measure of each interior angle is given by;
Interior angle of a pentagon = 540°/5
Interior angle of a pentagon = 108°
From triangle EAO, we have:
2m∠EOA = 180° - (54 + 54)°
m∠EOA = 72°/2
m∠EOA = 34°
Now, we can determine the measure of angle EOC;
m∠EOC = 180° - (34 + 34)°
m∠EOC = 108°
A recipe calls for of a 1/3 cup of milk for 12 cookies. how many cups of milk are needed to make 108 cookies?
Given the matrices A and B below, find A + B and 3A
The value of A+B is [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex] and the value of 3A is [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex] .
How to add two matrices?To add two matrices, we have to add the element present in the same position in the respective matrices.
(A+B)ij= Aij + Bij
where i is the no. of row and j is the no. of column.
How to multiply a scalar by the matrix?In order to multiply a scalar by the matrix, we have to multiply that scalar with every element of the matrix.
nA= nAij
Here given matrix is
A= [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]
and the other matrix is
B= [tex]\left(\begin{array}{ccc}1&0\\10&-1/2\\3&1\end{array}\right)[/tex]
The sum of the matrix is A+B= [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]+ [tex]\left(\begin{array}{ccc}1&0\\10&-1/2\\3&1\end{array}\right)[/tex]
⇒ A+B =[tex]\left(\begin{array}{ccc}2+1&-3+0\\0+10&5+(-1/2)\\7+3&-2+1\end{array}\right)[/tex]
⇒ A+B= [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex]
the value of 3A= 3 [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]= [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex]
Therefore the value of A+B is [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex] and the value of 3A is [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex] .
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what is the slope of
18x-15y=20?
I don't know what to do ?
Which lines are parallel if m4 = m5? Justify your answer.
The lines r and s are parallel
What are angles in parallel lines?
Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equalCorresponding angles are equalCo-interior angles add up to 180°Given data ,
From the figure m4 = m5
And , m4 and m5 are alternate angles
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size
So , m1 = m5 are corresponding angles
Or angle 1 = angle 5
Corresponding angles are the pairs of angles formed on the same side of the transversal that are either both obtuse or both acute and are equal in size.
Similarly , m2 = m6 or angle 2 = angle 6
Hence , the lines r and s are parallel by the properties of angles in parallel lines.
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