Answer:
Step-by-step explanation:
∠5 = ∠1 {Alternate exterior angles are congruent}
8x - 19 = 7x - 3
Add 19 to both sides
8x = 7x - 3 + 19
8x = 7x + 16
Subtract 7x from both sides
8x - 7x = 16
x = 16
∠5 = 8x - 19
= 8*16 - 19
= 128 - 19
∠5 = 109
∠5 + ∠4 = 180 {linear pair]
109 + ∠4 = 180
∠4 = 180 - 109
∠4 = 71°
8(x-5)=8x+40
Kara said the answer was x=0 and Matt said there are no solutions. Who is correct?
Matt is correct. The expression has no solution.
What are algebraic expressions?Algebraic expressions are known as expressions of numbers using letters or alphabets without their actual values.
They are composed of integer constants, variables, and the algebraic operations such as addition, subtraction, division and others
From the expression given, we have that;
8(x-5)=8x+40
First, let's expand the bracket
8x - 40 = 8x + 40
collect like terms
8x - 8x = 40 + 40
0 = 80
We can see that the expression does not have a solution as 'x' the variable was 0.
Thus, Matt is correct. The expression has no solution.
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Which expressions are equivalent to 3p+15
Answer:
Left most and the one u selected
Step-by-step explanation:
7p-4p+15 = 3p+15
3(p+5) = 3p + 3 * 5 = 3p + 15
2p-p+15 = p+15
3(p+15) = 3p+45
if correct, pls mark 5 star, thanks, and brainliest!
1 and 2.
7p - 4p + 15
3p + 15
3 (p + 5)
(3 • p) + (3 • 5)
3p + 15
I hope this helps let me know if you need any more help :)
50 points
Is this statement always, sometimes, or never true?
If m∠C and m∠D sum to 90°, then sin(C)=cos(D).
Always
Sometimes
Never
Answer: it is always true
Step-by-step explanation:
A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the height h of water in the tank in feet after t seconds is described by dh dt А. 2gh AW where A and A, are the cross-sectional areas of the water and the hole in square feet, respectively. (a) Solve for h(t) if the initial height of the water is H. Give its interval I of definition in terms of the symbols Awr An, and H. Use g = 32 ft/s2. (4„VH – 44,4) h(t) = osts 4A 4VĀ By hand, sketch the graph of h(t). h h H H/2 t h h H/2H H t (b) Suppose the tank is 11 ft high and has radius 2 ft and the circular hole has radius in. If the tank is initially full, how long will it take to empty? (Round your answer to two decimal places.) sec
The height of water in the tank in feet after t seconds can be expressed as h(t) = H - (Aw/Ah) 2gh t2, where Aw and Ah are the cross-sectional areas of the water and the hole in square feet respectively,
and g is the gravitational acceleration (32 ft/s2). The interval of definition for h(t) is 0 ≤ t ≤ H/2gh.
The graph of h(t) is a parabola with its vertex at (H/2gh, H) and is symmetric about the line t = H/2gh. It starts at (0, H) and gradually decreases to (H/2gh, 0).
Given the tank is 11 ft high, has radius 2 ft and the circular hole has radius in, and it is initially full, the time it will take to empty can be calculated as: t = √(2H/gAh) = √(22/(32 x π(0.52))) = 3.87 seconds. Therefore, it will take approximately 3.87 seconds to empty.
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The box plots show Lauren's chemistry scores and her biology scores. Chemistry 2 box plots. The number line goes from 50 to 100. For chemistry, the whiskers range from 55 to 90, and the box ranges from 60 to 85. A line divides the box at 80. For biology, the whiskers range from 50 to 90, and the box ranges from 60 to 80. A line divides the box at 70. Biology Lauren used the steps below to determine the differences in the medians and the interquartile ranges. Step 1 Find the median for chemistry: 80 Find the median for biology: 70 Step 2 Find the difference in the medians: 80 minus 70 = 10 Step 3 Find the interquartile range for chemistry: 85 minus 80 = 5 Find the interquartile range for biology: 80 minus 70 = 10 Step 4 Find the difference in the interquartile ranges: 10 minus 5 = 5 Lauren determined that the difference in the medians is greater than the difference in the interquartile ranges. Which explains Lauren's error?
Answer:
The error is in Step 3:
She should have calculated the interquartile range as,
Chemistry = 85 - 60 = 25
Biology = 80 - 60 = 20
Step-by-step explanation:
*In a box plot, the median is the point on the number line where a line divides the rectangular box.
Thus, from the information given in the question about the box plots, the median for Chemistry = 80 (this is where a line divides the box)
Median for Biology = 70
The difference in the median = 80 - 70 = 10.
*Lauren didn't make any mistake in Step 1 and 2, as he equally got the same values.
==>The interquartile range in a box plot is simply the difference in the ranges (Q3 - Q1).
From the given information, the interquartile range for Chemistry = 85 - 60 = 25 (this is the difference in the ranges of the box)
Interquartile range for Biology = 80 - 60 = 20
The difference in interquartile range = 25 - 20 = 5
*Lauren made an error in Step 3 when calculating the interquartile range for both Chemistry and Biology, even though he arrive at the same value of the difference in the interquartile range we got as calculated above.
Answer:
to simplyify it the answer is D
Step-by-step explanation:
What is the perimeter of the following rectangle?
Answer:
C
Step-by-step explanation:
\(x^2 +8+x^2+8+x^2+6x-3+x^2+6x-3\)
\(x^2+x^2+x^2+x^2=4x^2\)
\(6x+6x=12x\)
\(8+8-3-3=10\)
Ans: \(4x^2+12x+10\)
suppose that a softball team is composed of 13 employees of a furniture store of whom 2 work part-time. what proportion of the team work part-time? either give the exact fraction or decimal, or round to three decimal places.
The proportion of the team that work part time is 2/13 or 0.154
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the equation will be
Let the total number of workers in the furniture store be = 13 employees
Let the number of workers who are part time = 2 workers
So , proportion of the team that work part time = number of workers who are part time / total number of workers in the furniture store
On simplifying , we get
The proportion of the team that work part time = 2 / 13
The proportion of the team that work part time = 0.154
Hence , the proportion is 2/13 or 0.154
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Lauren uses a calculator to find Three-fourths divided by StartFraction 3 plus 9 over 36 EndFraction and gets a result of Nine-fourths. Which statement best describes her work?
Answer:
11/20
Step-by-step explanation:
If an angle does not have a measure of 88°, then the angle is not an acute angle.
Snow Crest is 11,479.21 feet higher than Mt. Wilson. Write and solve an equation to find the elevation of Mt. Wilson. Let x represent the elevation of Mt. Wilson.
The equation representing the elevation of Mt. Wilson is x = 11,479.21 - Snow Crest
What are algebraic expressionsAlgebraic expressions are defined mathematical expressions that are made up of terms, variables, coefficients, factors and constants.
These algebraic expressions are also made up of arithmetic operations such as;
AdditionMultiplicationDivisionBracketParenthesesSubtractionFrom the information given, we have that;
Snow Crest is 11,479.21 feet higher than Mt. Wilson.
Let x represent the elevation of Mt. Wilson.
Let y represent Snow Crest
We have the expression as;
y = 11,479.21 + x
Make 'x' the subject, we have;
x = 11,479.21 - y
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What is the value of x in 3x+5+3
Answer:
Step-by-step explanation:
So since the question is no completed. The only way you can answer this is by simplifying it which is not the same as the value of x. It would be 3x+8
I need help I'm so confused
Answer:
Yeah me too buddy :(
Step-by-step explanation:
Which graph represents the linear equation y = −5x − 3?
a graph of a line that passes through the points negative 4 comma 0 and 0 comma negative 3
a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3
a graph of a line that passes through the points negative 1 comma 0 and 0 comma negative 5
a graph of a line that passes through the points negative 1 comma 4 and 0 comma negative 2
Answer: a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.
Step-by-step explanation: the y-intercept is where the line meets the y line which in this case is -3. I used slope formula to find the m of the equation ( slope ) take a look at the attached image to see how I solved it.
Answer:
a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.
Step-by-step explanation:
I neeeed help plssssssssssssssssssssssss
Answer:
I AINT SOLVING ALL THAT
Evaluate each expression
|30-5|-|-7|
Answer:
18
Step-by-step explanation:
|30 - 5| - |-7| = 18
т.N лежи на отсечката AB, така, че AN:NB=7:4, AN=22,4dm. Дължината на отсечката AB
I know the measure of angle m is 100 degrees. I did this multiple times and J and L are not 80 degrees so what are the measures of angles L and J?
Answer:
\(m\angle L = 100^{\circ}\).
\(m\angle J = 80^{\circ}\).
\(m\angle M = 100^{\circ}\).
Step-by-step explanation:
Since segment \(JM\) is parallel to segment \(KL\), quadrilateral \(JKLM\) is a trapezoid.
Segment \(JK\) and segment \(LM\) (the two legs of this trapezoid) are equal in length. Hence, trapezoid \(JKLM\) would be an isoscele trapezoid. By symmetry, \(m\angle L = m \angle K = 100^{\circ}\).
Line \(JK\) traverses line \(JM\) and line \(KL\). \(\angle J\) and \(\angle K\) are a pair of consecutive interior angles as they are both between \(JM\!\) and \(KL\!\) and are on the same side of the traversal, \(JK\!\).
Since line \(JM\) is parallel to line \(KL\), any pair of consecutive interior angles between these two lines would add up to \(180^{\circ}\) (supplementary angles.) Thus, \(\angle J\) and \(\angle K\) are supplementary angles; \(m\angle J + m\angle K = 180^{\circ}\).
Since \(m\angle K = 100^{\circ}\), \(m\angle J = 180^{\circ} - m\angle K = 180^{\circ} - 100^{\circ} = 80^{\circ}\).
Complete the equation of the line through (- 10, 3) and (-8, -8). Use exact numbers.
Answer: To find the equation of a line passing through two points, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one of the points, and m is the slope of the line.
To find the slope, we can use the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
So, let's plug in the values we have:
m = (-8 - 3)/(-8 - (-10)) = (-8 - 3)/2 = -11/2
Now we can use either point to find the equation. Let's use (-10, 3):
y - 3 = (-11/2)(x - (-10))
y - 3 = (-11/2)x - 55/2
y = (-11/2)x - 49/2
So the equation of the line through (-10, 3) and (-8, -8) is:
y = (-11/2)x - 49/2.
evaluate the expression when x=2 and y= -3. -x+2y
Answer:
-8
Step-by-step explanation:
It would be -2+2(-3)
Which means -2 plus 2 times -3
According to PEMDAS you have to do parenthesis first so 2 times -3 is -6 +-2=-8
So the answer is -8
Answer:
it would be -2 + 2(-3)
Step-by-step explanation:
the numbers given would replace the variables, so x would become -2 since its -x, and y would be (-3) in parenthesis since its to be multiplied (i believe if im remembering correctly) therefore it would become:
-2 + 2(-3)
keeping all the signs and proper places
hope this helped and is what you were looking for!!
+9) (b) У=3x-1 what are the n-values called in mathematics
Answer:
The n-values in this equation are called the coefficients.
Write an equation of the line that had a slope of -2 and passes through (4,-2)
Need help ASAP!!
Answer:
The equation is y = -2x + 6.
Step-by-step explanation:
Given that the slope-form equation is y = mx + b and the gradient is -2. So you have to find the value of b by substituting the coordinates into the equation :
\(y = mx + b\)
\(let \: m = - 2,x = 4,y = - 2\)
\( - 2 = - 2(4) + b\)
\( - 2 = - 8 + b\)
\(b = 6\)
\(y = - 2x + 6\)
when 64 is increased in the ratio 9 : 8, it becomes?
Recall that the ratio 9:8 can be written as follows:
\(\frac{9}{8},\)therefore, when 64 is increased in the ratio 9:8 we get:
\(64\times\frac{9}{8}=72.\)Answer: 72.
Answer:
72
Step-by-step explanation:
Since X : 64 = 9 : 8
Then we know X/64 = 9/8
Multiplying both sides by 64 cancels on the left64 × (X/64) = (9/8) × 64
X = (9/8) × 64Then solving for X X = 64 × (9/8)X = 72
Therefore 72 : 64 = 9 : 8
the formula for the sum of the degree measures of the interior angles of a polygon is S=180(n-2) Solve for ,n, the number of sides of the polygon, in terms of S
NEED STEP BY STEP EXPLANATION
Answer:
n = (S + 360)/180Step-by-step explanation:
Given formula:
S = 180(n - 2)Solving for n:
S = 180(n - 2) ⇒ open parenthesisS = 180n - 360 ⇒ isolate n180n = S + 360 ⇒ divide both sides by 180n = (S + 360)/180\(S = 180(n - 2) \\ S = 180n - 360 \\ 180n =( S + 360) \\ n = \frac{(S+ 360)}{180} \)
where, n =number of sides of polygon
S =sum of the degree measures of the interior angles of the polygon
After the first four games of a professional football season, three players scored a total of 80 touchdowns.
Duke Johnson scored 14 of the touchdowns.
Josh McCown scored 40% of the touchdowns.
Andre Roberts scored the remaining touchdowns.
How many touchdowns did Andre Roberts score?
A.20 touchdowns
B.28 touchdowns
C.32 touchdowns
D.52 touchdowns
find the missing side
Answer:
The sides thats missing duh, cmon
Step-by-step explanation:
y+x=1 2x+y=5 x+y=5 solve
Answer:
x=5-y
Step-by-step explanation:
Find the critical value Zα/2 that corresponds to the given confidence level. 88% Zal2 = (Round to two decimal places as needed.)
Answer:
1.44
Step-by-step explanation:
To find the critical value Zα/2 for a 88% confidence level, we need to first find α/2.
α/2 = (1-0.88)/2 = 0.06/2 = 0.03
Using a Z-table or calculator, we can find the Z-score that corresponds to a cumulative probability of 0.03 from the left tail, which is -1.44.
Therefore, the critical value Zα/2 for a 88% confidence level is 1.44 (positive or negative depending on the direction of the test).
-12 = 3(4c + 5)
step by step answer please!!
Answer:
I have been proved in attachment
Citrix Apps Apps CANVAS > Home EPB Intranet 7. -/2 points RogaCalcET4 13.5.017.Tutorial. Find r(t) and v(t) given a(t) and the initial velocity and position. a(t) = tk, v(0) = 4i, r(0) = 2; v(t) = r(t) = Additional Materials Tutorial +-12 points RogaCalcETA 19 rann
The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.
Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.
a = dv/dt
We have the following informations are available,
Initial velocity, v(0) = 4i
Initial position, r(0) = 2j
Acceleration at any time "t",
a(t) = tk
we have to determine the value of v(t) and r(t).
As we know, a(t) = dv(t)/dt = tk
integrating the above equation ,
v(t) = ∫tk dt = ( t²/2 )k + c
at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i
=> c = 4i
So, v(t) = ( t²/2 )k + 4i
Also, velocity is calculated by derivative of postion (r) with respect to time.
=> v(t) = dr(t) /dt
=> r(t) = ∫ v(t) dt
=> r(t) = ∫ ( t²/2 )k dt
integrating value of the right hand side,
r(t) = ( t³/2×3 )k +d
= (t³/6)k + d
At t = 0, r(0) = (0/6)k + d
=> r(0) = d = 2j
so, r(t) = (t³/6)k + 2j
Hence, the required position and velocity are
(t³/6)k + 2j and ( t²/2 )k + 4i.
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Suppose the risk-free return is 3%. The beta of a managed portfolio is 1.75, the alpha is 0%, and the average return is 16%. Based on Jensen's measure of portfolio performance, you would calculate the return on the market portfolio as:
12.3%
10.4%
15.1%
16.7%
The return on the market portfolio is approximately 10.4%.
Suppose the risk-free return is 3%. The beta of a managed portfolio is 1.75. To calculate the return on the market portfolio using Jensen's measure, we can use the Capital Asset Pricing Model (CAPM) formula:
Expected Return = Risk-Free Return + Beta * (Market Return - Risk-Free Return)
Given that the alpha is 0% and the average return is 16%, we can rewrite the formula:
16% = 3% + 1.75 * (Market Return - 3%)
Now, we solve for the Market Return:
13% = 1.75 * (Market Return - 3%)
13/1.75 = Market Return - 3
7.43 ≈ Market Return - 3
Market Return ≈ 10.43%
So, the return on the market portfolio is approximately 10.4%.
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