Answer:
1 7/8
Step-by-step explanation:
Exact Form 15/8
Decimal Form 1.875
Mixed Number 1 7/8
Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.
AB = RS
AB = 2RS
ABC ~ RST
ABC = RST
m<BAC = m<SRT
m<BAC = 2m<SRT
The reflection transformation in the question is a rigid transformation,
therefore, the image and the preimage are congruent.
The statements that are true are;
AB = RS∠ABC ~ ∠RSTΔABC = ΔRSTm∠BAC = m∠SRTReasons:
The given parameter are;
Triangle ΔABC is reflected across the line 2·X, to map onto triangle ΔRST
Required:
To select the true statements
Solution:
A reflection is a rigid transformation, therefore, the distance between corresponding points on the image and the preimage are equal.
Therefore;
AB = RS
BC = ST
AC = RT
Given that the image formed by a reflection is congruent to the preimage, we have;
ΔABC ≅ ΔRST
∠ABC ≅ ∠RST
m∠ABC = m∠RST by the definition of congruency
∠BCA ≅ ∠STR
m∠BCA = m∠STR by the definition of congruency
∠BAC ≅ ∠SRT
m∠BAC = m∠SRT by the definition of congruency
Therefore, the true statements are;
AB = RS; Image formed by rigid transformation∠ABC ~ ∠RST; Definition of similarityΔABC = ΔRST; By definition of congruencym∠BAC = m∠SRT; by the definition of congruencyLearn more here:
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If you want to divide 4 by 2/5 you can multiply 4 by 5, then divide it by 2 or multiply it by 1/2.
Step-by-step explanation:
to divide by a fraction is the same as to multiply by the upside-down fraction.
in your example
4 / 2/5 = 4 × 5/2 = 20/2 = 10
by the way, also a whole number is a fraction.
4 = 4/1
so, fully formal, the whole operation above looks like
(4/1) / (2/5) = (4/1) × (5/2) = (4×5) / (1×2) = 20/2 = 10/1 = 10
Please help!
Suppose that the cross section of a piece of pipe looks like the diagram shown. Find the total outer diameter.
Answer:
-8
Step-by-step explanation:
What is the value of x in this equation? Enter your answer in the box.
(2.4 × 103) × (3 × 10x) = 7.2 × 109
Answer:
17.92
Step-by-step explanation:
The prices (in dollars) for a particular model of digital camera with 6.0
megapixels and an optical 3X zoom lens are shown here for 10 randomly selected online
retailers. Find 95% confidence interval of the true mean price for this particular
model.
225 240 215 206 211 210 193 250
225 202
Using the data given, the 95% confidence interval of the true mean is (205.20 ; 230.20)
Given the data :
225 240 215 206 211 210 193 250 225 202The confidence interval is defined as :
Since, sample size ls less than 30 we use a t-distribution table :
[tex] C.I = \bar{x} ± t_{α/2, n-1} \frac{s}{\sqrt{n}}[/tex]
Zcritical = [tex]t_{0.05/2, 9} = 2.26 [/tex] n = sample size = 10Using a calculator :
Mean, [tex]\bar{x} = 217.7 [/tex] Standard deviation, σ = 17.49Lower boundary = [tex] 217.7 - 2.26(\frac{17.49}{\sqrt{10}}) = 205.20[/tex]
Lower boundary = [tex] 217.7 + 2.26(\frac{17.49}{\sqrt{10}}) = 230.20[/tex]
Therefore, the confidence interval is (205.20 ; 230.20)
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The confidence interval is simply a range that contains the true mean of the population
The 95% confidence interval is [tex]\mathbf{(205,19, 230.20)}[/tex]
The given parameter is:
[tex]\mathbf{n = 10}[/tex]
Start by calculating the degree of freedom
[tex]\mathbf{df = n - 1}[/tex]
[tex]\mathbf{df = 10 - 1}[/tex]
[tex]\mathbf{df = 9}[/tex]
Next, calculate the mean
[tex]\mathbf{\bar x = \frac{\sum x}{n}}[/tex]
[tex]\mathbf{\bar x = \frac{225 + 240 + 215 + 206 + 211 + 210 + 193 +250 + 225 + 202}{10}}[/tex]
[tex]\mathbf{\bar x = \frac{2177}{10}}[/tex]
[tex]\mathbf{\bar x = 217.7}[/tex]
Calculate the standard deviation
[tex]\mathbf{\sigma = \sqrt{\frac{\sum (x - \bar x)^2}{n-1}}}[/tex]
[tex]\mathbf{\sigma = \sqrt{\frac{(225 -217.7)^2+ (240 -217.7)^2+..........+ (202 -217.7)^2}{10-1}}}[/tex]
[tex]\mathbf{\sigma = \sqrt{\frac{2752.1}{9}}}[/tex]
[tex]\mathbf{\sigma = 17.49}[/tex]
Calculate the standard error
[tex]\mathbf{SE = \frac{\sigma}{\sqrt n}}[/tex]
[tex]\mathbf{SE = \frac{17.49}{\sqrt {10}}}[/tex]
[tex]\mathbf{SE = 5.53}[/tex]
At 95%, df = 9. the t-value is:
[tex]\mathbf{t= 2.262}[/tex]
So, the confidence interval is:
[tex]\mathbf{CI = \bar x \pm t \times SE}[/tex]
So, we have:
[tex]\mathbf{CI = 217.7 \pm 2.262 \times 5.53}[/tex]
Split
[tex]\mathbf{CI = (217.7 - 2.262 \times 5.53, 217.7+ 2.262 \times 5.53)}[/tex]
[tex]\mathbf{CI = (205,19, 230.20)}[/tex]
Hence, the 95% confidence interval is [tex]\mathbf{(205,19, 230.20)}[/tex]
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Brita has a monthly budget of x dollars. Every month, $1,425 is spent on her mortgage. One-third of her remaining budget is spent on recreational activities. Which equation below can be used to determine the amount, in dollars, spent on recreational activities?
y=x−1,4253
y=1,425−x3
y=1,425+x3
y=x+1,4253
Answer:
y=1,425-×3
Step-by-step explanation:
the x has to be divided by the 1/3
Robin earned $4,320 in 9 weeks and worked 40 hours in each week. How much did he earn per hour?
you do 4320÷ 9= 108 and that's your answer right there
2x( 3x + 5 ) - 3 ( 2x^{2} - 2x + 3)
Answer:
16x - 9
Step-by-step explanation:
2x(3x + 5) - 3 (2x² - 2x + 3) ← distribute parenthesis
= 6x² + 10x - 6x² + 6x - 9 ← collect like terms
= 16x - 9
Answer:
16X-9
Step-by-step explanation:
(2x)(3x)+(2x)(5)+(-3)(2x²)+(-3)(-2x)+(-3)(3)
6x²+10x+6x²+6x +-9
combine like terms
6x² +10x +-6x² +6x+-9
(6x² +6x² )+(10x+6x)+(-9)
16x+-9
16x-9
Drag a statement or reason to each box to complete this proof.
Given: the measure of angle A C D equals 60 degrees. Prove: triangle A B C is an obtuse triangle. Art: A triangle A B C. Side B C of the triangle is extended as a ray through point D.
--
check images below!
Answer: 2. Linear pair postulate
4. 60 + mACB=180
5. mACB=120
6. definition of obtuse angle
The value of straight angle ∠BCD = 180° thus the angle ∠ACB = 180°- 60° = 120° therefore, the given triangle ABC is the obtuse triangle.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
As per the given triangle ABC with extended line CD.
Since CD is colinear with BC, therefore, BCD will be a single straight-line segment.
The ∠BCD is straight angle so it will be 180°.
∠BCD = ∠ACB + ∠ACD
∠ACB + 60 = 180
∠ACB = 180 - 60 = 120°.
An obtuse triangle is a triangle whose one or more interior angle is greater than 90°.
Since∠ACB > 90° therefore triangle ABC is an obtuse angle.
Hence "The value of straight angle ∠BCD = 180° thus the angle ∠ACB = 180°- 60° = 120° therefore, the given triangle ABC is the obtuse triangle".
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For brainily please help
Answer:
No
Step-by-step explanation:
7 + 3 = 10, and in order for this to make a triangle two sides must be greater than one side
Answer:
No
Step-by-step explanation:
two sides, say a and b, with a greater than or equal to b, ,put limits on the length of the third side, c: a-b < c < a+b.
a-b < c < a+b.
7-3 < 10 < 7+3
4 < 10 < 10
False,
If a van traveled 180 miles in 3 hours, how far could the van travel in 7 hours?
Answer:
42 miles
Step-by-step explanation:
180/3=6 6x7=42
Answer:
420 miles in 7 hours
Step-by-step explanation:
You divide 180 by 3 to get how much the van is traveling per hour. When you get the answer 60 multiply it by 7 then you have 420 miles in 7 hours.
What is the value of x if OB is
an angle bisector of
Answer:
x = 8
Step-by-step explanation:
Hi there!
We're given that OB is the angle bisector of angle AOC.
An angle bisector splits an angle into 2 equal halves. Therefore, angles AOB and BOC are equal.
We're given that angle AOB is 8x degrees and angle BOC is 16x-64 degrees.
Set up an equation:
[tex]8x=16x-64[/tex]
Combine like terms:
[tex]-8x=-64\\x=8[/tex]
Therefore, x = 8.
I hope this helps!
Id really appreciate if you could help me thx!
Answer:
-3/7
Step-by-step explanation:
1. The formula to find the slope of a line given two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]\frac{(2)-(5)}{(9)-(2)}[/tex] [tex]\frac{-3}{7}[/tex] [tex]-\frac{3}{7}[/tex]Therefore, the answer is -3/7.
please help me with math
Answer:
Hope this helps
Step-by-step explanation:
Write an equation of the line that passes through (2,7) and (0, - 5).
A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum height of 10 mm halfway across a horizontal distance of 80 mm.
Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)
Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)
The spider's movement is an illustration of a parabola.
The equation of the parabola is: [tex]\mathbf{y = -\frac{1}{320}(x - 80)^2 + 20}[/tex]The focus of the parabola is [tex]\mathbf{Focus = (80 ,-60)}[/tex]The directrix is: [tex]\mathbf{y = 100}[/tex].The axis of symmetry is: [tex]\mathbf{x = 80}[/tex](a) The equation
The spider passes through the origin.
So, we have:
[tex]\mathbf{(x,y) = (0,0)}[/tex]
The spider jumps to a maximum height of 20mm, midway 160mm.
So, the vertex is:
[tex]\mathbf{(h,k) = (80,20)}[/tex]
The equation of a parabola is:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
So, we have:
[tex]\mathbf{0 = a(0 - 80)^2 + 20}[/tex]
[tex]\mathbf{0 = 6400a + 20}[/tex]
Subtract 20 from both sides
[tex]\mathbf{6400a =- 20}[/tex]
Solve for a
[tex]\mathbf{a =- \frac{1}{320}}[/tex]
Substitute [tex]\mathbf{a =- \frac{1}{320}}[/tex] and [tex]\mathbf{(h,k) = (80,20)}[/tex] in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]
[tex]\mathbf{y = -\frac{1}{320}(x - 80)^2 + 20}[/tex]
(b) The focus, directrix and the axis of symmetry
The focus of a parabola is:
[tex]\mathbf{Focus = (h,k+p)}[/tex]
Where:
[tex]\mathbf{p = \frac{1}{4a}}[/tex]
So, we have:
[tex]\mathbf{p = \frac{1}{4\times -1/320}}[/tex]
[tex]\mathbf{p = -\frac{320}{4}}[/tex]
[tex]\mathbf{p = -80}[/tex]
So, we have:
[tex]\mathbf{Focus = (80 , 20-80)}[/tex]
[tex]\mathbf{Focus = (80 ,-60)}[/tex]
The axis of symmetry is:
[tex]\mathbf{x = h}[/tex]
So, we have:
[tex]\mathbf{x = 80}[/tex]
The directrix is:
[tex]\mathbf{y = k - p}\\[/tex]
So, we have:
[tex]\mathbf{y = 20+80}[/tex]
[tex]\mathbf{y = 100}[/tex]
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help me
The fire department is setting off fireworks. They notice that the casings of the fireworks hit the ground 78 seconds after the firework was launched. The firework exploded at a maximum height of 760.5 meters.
Identify how you see the x- and y-intercepts and vertex in the table, graph, and equation. (Hint: You may want to rewrite the equation in equivalent forms.)
The firework is an illustration of the equation of a parabola.
The x-intercepts are 0 and 78, the y-intercept is 0, and the vertex is (39,760.5)
The casings hit the ground after 78 seconds.
This means that, a point on the graph is:
[tex]\mathbf{(x,y) = (78,0)}[/tex]
The firework exploded at a maximum of 760.5.
This means that, the vertex is:
[tex]\mathbf{(h,k) = (39,760.5)}[/tex]
The equation of a parabola is:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
So, we have:
[tex]\mathbf{0 = a(78 - 39)^2 + 760.5}[/tex]
[tex]\mathbf{0 = a(39)^2 + 760.5}[/tex]
Subtract 760.5 from both sides
[tex]\mathbf{a(39)^2 =- 760.5}[/tex]
[tex]\mathbf{1521a =- 760.5}[/tex]
Solve for a
[tex]\mathbf{a =- \frac{760.5}{1521}}[/tex]
[tex]\mathbf{a =- 0.5}[/tex]
Substitute [tex]\mathbf{a =- 0.5}[/tex] and [tex]\mathbf{(h,k) = (39,760.5)}[/tex] in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]
[tex]\mathbf{y = -0.5(x - 39)^2 + 760.5}[/tex]
See attachment for the graph of [tex]\mathbf{y = -0.5(x - 39)^2 + 760.5}[/tex].
From the graph:
The x and y intercepts are the points where the graph crosses the x and y axes. The vertex is the maximum point on the graphFrom the equation:
Set x to 0, to calculate the value of y for the y-interceptSet y to 0, to calculate the value of x for the x-intercept.The vertex is represented as: (h,k)Hence, the x-intercepts are 0 and 78, the y-intercept is 0, and the vertex is (39,760.5)
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2. Transversals and parallel lines are unique in that if you know one angle measure, you know them all. Use the picture below to tell the value for EACH angle if <1 = 102. *
3 points
Answer:
1:102
2:78
3:102
4:78
5:102
6:78
7:102
8:78
Question 10
Luella has a bag with three Hershey Kisses, two Reese's Cups, five York Peppermint
Patties, and a Jolly Rancher. What is the probability that Luella will pull out a Reese's
Cup, eat it, and then pull out another Reese's Cup? Write your answer as a simplified
fraction
Using the probability concept, it is found that there is a [tex]\frac{1}{55}[/tex] probability that Luella will pull out a Reese's Cup, eat it, and then pull out another Reese's Cup.
A probability is the number of desired outcomes divided by the number of total outcomes.
Initially, there are 11 sweets, 2 of which are Reese's Cups, thus, there is a [tex]\frac{2}{11}[/tex] probability of pulling a Reese's Cup.Then, there will be 10 sweets, of which 1 will be a Reese's Cup, thus, [tex]\frac{1}{10}[/tex] probability of pulling another Reese's Cup.The probability of both events is the multiplication of the probabilities of each event, thus:
[tex]p = \frac{2}{11} \times \frac{1}{10} = \frac{2}{110} = \frac{1}{55}[/tex]
[tex]\frac{1}{55}[/tex] probability that Luella will pull out a Reese's Cup, eat it, and then pull out another Reese's Cup.
A similar problem is given at https://brainly.com/question/15536019
Determine
f(a + h) - f(a)
for f(x) = 1 - x2 and simplify.
Answer:
h^2+2ah
Step-by-step explanation:
When f(x) = 1-x^2
f(a) = 1 - a^2
f(a+h) = 1 - (a+h)^2
= 1 - a^2 + 2ah + h^2
Subtracting the two:
f(a+h) - f(a)
= (1 - a^2 + 2ah + h^2) - (1-a^2)
= 1 - 1 - a^2 + a^2 + 2ah + h^2
= 2ah + h^2
= h^2 + 2ah
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
Ben and Mack stopped at a restaurant to eat. Ben purchased 2 hot dogs and 2 drinks for $4.75. Mack purchased 3 hot dogs and 1 drink for
$7.75. Which system of equations can be used to determine the price of each hot dog, x, and each drink, y?
A. 2x + 2y = 4.75
3x + y = 7.75
OB. 2x + 2y = 7.75
3x + y = 4.75
OC. X + 2y = 7.75
2x + 3y = 4.75
D. x + 2y = 4.75
2x + 3y = 7.75
Answer:
A is the answer
Step-by-step explanation:
Let x equal hotdogs and y equal drinks
2 hotdogs plus 2 drinks = 4.75
3 hotdogs plus 1 drink = 7.75
Multiple Choice Find the mean: 12, 8, 7, 10, 8, 8, 10
Answer:
The mean is 9
Step-by-step explanation:
To find the mean, all you do is add up all the numbers and then divide by how many numbers there are. In this case, adding all then numbers up gives you 63, and there are a total of 7 numbers. 63 divided by 7 =9
CAN SOMEONE PLEASE HELP ME WITH THIS
Answer:
f= −x+3
7x
Step-by-step explanation:
fx = −1 3
x 7 x+ 7
-------------------------
x x
f= -x+3
7x
f= -x+3
7x
Answer:
A.
Step-by-step explanation:
f(x) = (3-x)/7
First we find x in terms of f(x:-.
7f(x) = 3 - x
x + 7f(x) = 3
x = 3 - 7f(x)
Now we replace x by f-1(x) and f(x) by x:
f-1(x) = 3 - 7x.
15x+7y=5 find the y-intercept
Answer:
slope: -15/7
intercept: ( 0, 5/7)
Step-by-step explanation:
14 A formula for determining the finite sum, S, of an arithmetic sequence of numbers is
S=n/2(a+b)
where n is the number of terms, a is the first term, and b is the last term.
Express b in terms of a, S, and n.
Answer:
b = 2S/n - a.
Step-by-step explanation:
S=n/2(a + b)
a + b = S / n/2
a + b = 2S/n
b = 2S/n - a.
If the formula for determining the sum of the given arithmetic sequence is S = n/2(a + b), then 'b' can be expressed as b = [(2S/n) - a].
What is an arithmetic sequence ?An arithmetic sequence is a sequence where the difference between any to consecutive terms are always equal.
Here, a and b are the first and the last terms respectively and n is the number of terms.
Therefore, the sum of the arithmetic sequence is:
S = n/2(a + b)
⇒ 2S/n = (a + b)
⇒ b = (2S/n) - a
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Tanya who's worked out a budget that allows her to pay her mortgage and save for her three young children's college funds
Answer: fixed rate mortgage
Step-by-step explanation:
Its correct
Fixed rate mortgage will be for Tanya who's worked out a budget that allows her to pay her mortgage and save for her three young children's college funds.
What is Fixed rate mortgage?A fixed rate mortgage is one in which the interest rate remains constant for the duration of the loan.
This means that the monthly payment amount remains constant, making budgeting and planning easier for borrowers.
Tanya should look for a mortgage with a low interest rate and a manageable monthly payment that fits into her budget.
A shorter loan term means a higher monthly payment but less overall interest paid over the life of the loan.
Tanya has worked out a budget that allows her to pay her mortgage while also saving for her three young children's college funds.
Thus, the answer is Fixed rate mortgage.
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Your question seems incomplete, the probable complete question is:
Tanya who's worked out a budget that allows her to pay her mortgage and save for her three young children's college funds Which Mortgage is Right?
What is 21,678 rounded to the nearest ten
Answer:
21,678 rounded to the nearest ten is 21,680
help asap plz with my math hw, i will give you thanks and 5stars
Answer:
it would be 15 or 14 that only came up when I did it
Step-by-step explanation:
The sides of a quadrilateral are the same length, q. The length of the fourth side is 7 inches. The perimeter of the quadrilateral is 40 inches. Write an equation that represents the situation
Answer:
3x = 33 in
Step-by-step explanation:
Joseph compared the graphs of two functions. The first function wasf(x)=−2x+6. The second function fits the values in the table: x 2 5 8 11 y 2 -4 -10 -16 What is the distance between the y-intercepts of the two functions?
Answer: No difference
Step-by-step explanation:
The function f(x)=-2x+6 will produce the very same points in the table.
x y y calculated
2 2 2
5 -4 -4
8 -10 -10
11 -16 -16
The points are all on the line y=-2x+6. They describe the same line, which will have the same intercept.