In the figure lines l, m, and n are parallel. A classmate says you can use the corollary to side-splitter theorem to find x. Explain your classmate's error. (image attached)thank you ! :)
Answers
The corollary to the side-splitter theorem is the following.
If we have two transversal lines to three parallel lines, like this:
The following proportion holds:
\(\frac{AB}{BC}=\frac{DE}{EF}\)Therefore, the corollary relates the sides of the figure and not the distance between the transversal. Therefore, the corollary can't be used to determine the value of "x".
Related Questions
Use a table of areas to obtain the shaded area under the standard normal curve.
Answers
The shaded area under the standard normal curve is 2.58%.
According to z-score table,
Area for < 2.23 = 0.9871
Area for >2.23 = 1 - 0.9871
= 0.0129
Area for < 2.23 = 0.0129
Total area = 0.0129 + 0.0129
= 0.0258
Area percent = 0.0258*100
= 2.58%
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What is the area of the region of points
satisfying the inequalities x ≤ 0, y ≤ 0, and
y ≥ |x + 4| − 5?
Answers
the area of the region of points satisfying the inequalities x ≤ 0, y ≤ 0, and y ≥ |x + 4| − 5 is 12.5 square units.
In a time of t seconds, a particle moves a distance of s meters from its starting point, where s = 6t^2 + 4.
(a) Find the average velocity between t = 1 and t = 1 + k if (i) h = 0.1 (ii) h = 0.01 (iii) h = 0.001 Enter the exact answers.
(i) When h = 0.1, the average velocity between t = 1 and t = 1 + h is m/sec.
(ii) When h = 0.01, the average velocity between t = 1 and t = 1 + h is m/sec.
(iii) When h = 0.001, the average velocity between t = 1 and t = 1 + h is m/sec.
(b) Use your answers to part (a) to estimate the instantaneous velocity of the particle at time t = 1. Round your estimate to the nearest integer. The instantaneous velocity appears to be m/sec.
Answers
Answer:
(a)
i) \(V=12.6m/s\)
ii) \(V=12.06m/s\)
iii) \(V=12.006m/s\)
(b)
\(V = 10m/s\)
Step-by-step explanation:
Given
\(s = 6t^2 + 4\)
Solving (a): Average velocity between t = 1 and t = 1 + h
When t = 1
\(t_1 = 1\)
\(s_1 = 6t^2 + 4 = 6 * 1^2 + 4 = 6 + 4 =10\)
i) h = 0.1
When t = 1 + h
\(t_2 = 1 + 0.1 = 1.1\)
\(s_2= 6t^2 + 4 = 6 * (1.1)^2 + 4 = 11.26\)
Average velocity is then calculated as:
\(V = \frac{s_2 - s_1}{t_2 - t_1}\)
\(V = \frac{11.26 - 10}{1.1- 1} = \frac{1.26}{0.1} = 12.6\)
\(V=12.6m/s\)
ii) h = 0.01
When t = 1 + h
\(t_2 = 1 + 0.01 = 1.01\)
\(s_2= 6t^2 + 4 = 6 * (1.01)^2 + 4 = 10.1206\)
Average velocity is then calculated as:
\(V = \frac{s_2 - s_1}{t_2 - t_1}\)
\(V = \frac{10.1206 - 10}{1.01- 1} = \frac{0.1206}{0.01} = 12.06\)
\(V=12.06m/s\)
ii) h = 0.001
When t = 1 + h
\(t_2 = 1 + 0.001 = 1.001\)
\(s_2= 6t^2 + 4 = 6 * (1.001)^2 + 4 = 10.012006\)
Average velocity is then calculated as:
\(V = \frac{s_2 - s_1}{t_2 - t_1}\)
\(V = \frac{10.012006 - 10}{1.001- 1} = \frac{0.012006 }{0.001} = 12.006\)
\(V=12.006m/s\)
Solving (b): Instantaneous velocity at t = 1
When t = 1
\(t = 1\)
\(s = 6t^2 + 4 = 6 * 1^2 + 4 = 6 + 4 =10\)
Velocity is:
\(V = \frac{s}{t}\)
\(V = \frac{10}{1}\)
\(V = 10m/s\)
Describe what a loan discount point is and what effect it has on a home loan.
Answers
Answer:
A loan discount point reduces the interest rate that is paid on a home loan. One point reduces the interest rate by 1/8 of a percent, which reduces the amount of the monthly payment.
Step-by-step explanation:
The meaning that loan discount points have is the fact that they are fees that are used to buy down rates.
The effect of a loan discount point on a home loanThe effect that the loan discount point has on home loan is the fact that it helps to lower loans by about 0.25 percent.
The points helps you on your home loan by giving you a lower interest rate which then means that you have to pay lower over time.
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Find the slope of the tangent line to the curve defined by 4x2+5xy+y4=370
at the point (−9,−1)
Answers
Answer:
The slope of the tangent line to the curve at the given point is -11/7.
Step-by-step explanation:
Differentiation is an algebraic process that finds the gradient (slope) of a curve. At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.
Given function:
\(4x^2+5xy+y^4=370\)
To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.
Begin by placing d/dx in front of each term of the equation:
\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)
Differentiate the terms in x only (and constant terms):
\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)
Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:
\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
Use the product rule to differentiate terms in both x and y.
\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)
\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:
\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)
\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)
To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)
Therefore, slope of the tangent line to the curve at the given point is -11/7.
Find the limit of the difference quotients for f(x) = x2+2x+1 if a= -1
Answers
The limit of the difference quotients for f(x) = x^2 + 2x + 1 as x approaches -1 is indeterminate.
To find the limit of the difference quotients for the function f(x) = x^2 + 2x + 1 as x approaches -1, we need to evaluate the following expression:
lim(x→-1) [f(x) - f(-1)] / (x - (-1))
First, let's substitute the values into the expression:
lim(x→-1) \([(x^2 + 2x + 1) - (-1^2 + 2(-1) + 1)] / (x + 1)\)
Simplifying further:
lim(x→-1) \([(x^2 + 2x + 1) - (1 - 2 + 1)] / (x + 1)\)
lim(x→-1)\([x^2 + 2x + 1 - 0] / (x + 1)\)
lim(x→-1) \((x^2 + 2x + 1) / (x + 1)\)
Now, we can directly substitute x = -1 into the expression:
\((-1^2 + 2(-1) + 1) / (-1 + 1)\)
(1 - 2 + 1) / (0)
0 / 0
We have obtained an indeterminate form of 0/0. This indicates that we need to further simplify the expression or use other techniques, such as L'Hôpital's rule, to evaluate the limit. However, without additional information or simplification, we cannot determine the precise value of the limit at x = -1.
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Which expressions are equivalent to 24-7? Choose all the correct answers. Show your work.
Answers
The equivalent expressions to \(24^{-7}\) are given as follows:
C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)
F. \((24^3 \times 24^4)^{-1}\)
What are are equivalent expressions?Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.
The exponent in the denominator can be moved to the numerator with the changed signal, hence:
\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)
Applying the power of power rule, we multiply the powers, hence:
\((24^7)^{-1} = 24^{-7}\)
When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:
\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)
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Un hombre posee 50 acciones con un valor de 30 cada una , la corporación declaró un dividendo del 6% pagadero en acciones ¿cuantas acciones poseía entonces?
Answers
el hombre tenía 50 acciones.
La pregunta es, ¿cuántas acciones poseía el hombre si declararon un dividendo del 6% pagadero en acciones y tenía 50 acciones con un valor de $30 cada una?Para calcular cuántas acciones tenía el hombre,
se puede utilizar la siguiente fórmula:Dividendos = Número de acciones * Precio por acción * Tasa de dividendosDe esta fórmula,
podemos despejar el número de acciones. Así, tenemos:Número de acciones = Dividendos / (Precio por acción * Tasa de dividendos)De los datos del problema, se sabe que el hombre tenía 50 acciones con un valor de $30 cada una.
Además, la corporación declaró un dividendo del 6% pagadero en acciones. Por lo tanto, la tasa de dividendos es del 6%.Para resolver el problema, primero debemos calcular el valor del dividendo que se pagará en acciones.
Para ello, se debe multiplicar el valor de las acciones del hombre por la tasa de dividendos.
Así, tenemos:Valor del dividendo = 50 acciones * $30 * 0.06 = $90El valor del dividendo es de $90. Ahora, podemos sustituir este valor en la fórmula para calcular el número de acciones que tenía el hombre.
Así, tenemos:Número de acciones = $90 / ($30 * 0.06) = 50 accionesPor lo tanto,
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4.
The Freshman Class treasury has 30
ten- and twenty-dollar bills that have
a total value of $430. How many of
each bill do they have?
Answers
There are 13 $20 bills and 17 $10 bills, respectively.
A linear equation is what?Constants and variables are used in conjunction to create linear equations. A linear equation with one variable is shown in the following standard form: Where a 0 and x is the variable, ax + b = 0.
Due to that,
There are 30 bills in all.
Total = $430
Let,
x = the number of $20 bills.
Amount in $10 banknotes = (30-x)
20x+10(30-x) = 430
20x+300-10x = 430
10x = 430-300
10x = 130
x = 13
$20 bills: x = 20; y = 13.
30 x = 30 13 = 17 = number of $10 banknotes
Therefore, there are 13 $20 bills and 17 $10 banknotes.
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Find the ordered triple $(p,q,r)$ that satisfies the following system:
\begin{align*}
p - 2q &= 3, \\
q - 2r &= -2, \\
p + r &= 9.
\end{align*}
Answers
The ordered triple (p, q, r) that satisfies the given system of linear equations is (7, 2, 2).
To solve the given system of equations:
Start with the first equation: p - 2q = 3.
Multiply this equation by 2 to eliminate the coefficient of q: 2p - 4q = 6.
Next, we'll combine this equation with the second equation: q - 2r = -2.
Add the two equations together: (2p - 4q) + (q - 2r) = 6 + (-2).
Simplifying, we get: 2p - 3q - 2r = 4.
Now, let's consider the third equation: p + r = 9.
Rearrange this equation: p = 9 - r.
We can substitute this value for p in the equation we obtained in step 3:
2(9 - r) - 3q - 2r = 4.
Simplify the equation: 18 - 2r - 3q - 2r = 4.
Combining like terms, we have: -4r - 3q = -14.
We now have a system of two equations with two variables:
-4r - 3q = -14, (Equation 1)
q - 2r = -2. (Equation 2)
To solve this system, we can use various methods such as substitution or elimination. Here, we'll use the substitution method.
From Equation 2, we can solve for q:
q = 2r - 2.Substituting this value for q in Equation 1, we have:
-4r - 3(2r - 2) = -14.
Simplify and solve for r:
-4r - 6r + 6 = -14,
-10r = -20,
r = 2.
Now, substitute the value of r back into Equation 2 to solve for q:
q - 2(2) = -2,
q - 4 = -2,
q = 2.
Finally, substitute the values of q and r into Equation 3 to solve for p:
p + 2 = 9,
p = 7.
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25. Three students contributed a total of $200 towards a building for the aged. Azar contributed 50% of it, Sunil 25% and the rest was contributed by a girl Becky. How much money did Becky contribute? rice he lost 25% of its weight
Answers
Becky contributed $50 towards the building for the aged.
Let's calculate the amounts contributed by each student:
Azar contributed 50% of the total amount:
Amount contributed by Azar = 50% of $200
= (50/100) × $200
= $100
Sunil contributed 25% of the total amount:
Amount contributed by Sunil = 25% of $200
= (25/100) × $200
= $50
Now, we can calculate the amount contributed by Becky:
Total contribution by Azar and Sunil = $100 + $50 = $150
The remaining amount contributed by Becky can be found by subtracting the total contribution by Azar and Sunil from the total amount:
Amount contributed by Becky = Total amount - Total contribution by Azar and Sunil
= $200 - $150
= $50
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Make clothes as a fish tank the that is 25 inches long 12 inches wide and 15 in deep what volume of the water can the tank hold
Answers
The tank having shape of a rectangular prism, the volume of tank will be
4,500 inches³.
What exactly is a prism?
A prism is a three-dimensional geometric object that has a pair of identical, parallel polygonal bases and flat, parallelogram-shaped sides connecting them. The most common type of prism is a rectangular prism, which has two rectangular bases and four rectangular sides.
Prisms are classified based on the shape of their bases. For example, if the bases of a prism are triangles, it is called a triangular prism, if the bases are pentagons, it is called a pentagonal prism, and so on.
Now,
To calculate the volume of water that the tank can hold, we need to use the formula for the volume of a rectangular prism:
Volume = Length x Width x Height
Plugging in the values given:
Volume = 25 inches x 12 inches x 15 inches
Volume = 4,500 cubic inches
Therefore,
the tank can hold 4,500 inches³ of water.
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{Question 9} Please help! Need this by tonight! Thanks so much! {Click on picture}
Answers
Step-by-step explanation:
3x + 2y = -18
Set y = 0
3x + 2 × 0 = -18
3x + 0 = -18
3x = -18
x = -6
.: the x-intercept = -6
You can choose to put it in coordinate form (-6, 0).
\(Answer: \boxed {(-6,0)}\)
Step-by-step explanation:
The x-intersection coordinate of the equation 3x+2y=-18 is (x,0)
Hence, y=0
3x+2(0)=-18
3x+0=-18
3x=-18
Divide both parts of the equation by 3:
x=-6
Thus, (-6,0)
HELP!!!
FIRST TO ANSWER GETS BRAINLEST!!!
Jack writes the following expression to compare the temperature on two winter days.
Choose >, < or = from the drop-down menu to make the statement true.
-2°C Choose...
-5°C
Answers
Answer:
-2 Celsius >-5 Celsius is the answer.
Answer:
-2 > -5
Step-by-step explanation:
think about which of the two numbers is nearest to 0
how do u graph the solution y=2x-1 iready
Answers
Answer:
Step-by-step explanation:
y=mx+b
m= slope and b= y intercept
you'll start with a point on the y axis on -1
and the slope will go up so towards the right corner up but 2/1 points
you and a friend have created a carnival game for your classmates. you plan to charge $1 for each time a student plays, and the payout for a win is $5. according to your calculations, the probability of a win is .05 what is your expected value for this game?
Answers
Answer:
The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.
Step-by-step explanation:
Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing
In this case:
Probability of Winning = 0.05
Payout for Win = $5
Cost of Playing = $1
Expected Value = (0.05 * $5) - $1
Expected Value = $0.25 - $1
Expected Value = -$0.75
Which of the following phrases in bold is an example of informal English?
After basketball practice Julie hit the books.
I really don't want to do my homework today.
Both Kelli and Rosa were late to the party.
Will ran down the street to catch the bus.
PLEASE HELP ME!!!!!!
Answers
Will ran down the street to catch the bus.
Hope this helps, thanks,
CoDBiarex
Answer:
After basketball practice Julie hit the books.
Step-by-step explanation:
Informal English often uses slang words that not everyone understands.
Q. A pharmacist mixes 3 grams of compound
with 5,000 milligrams of solution to create a
prescription. How many total grams is the
prescription?
A. 8 grams
B. 800 grams
C. 8,000 grams
Answers
Answer:
8 grams
Step-by-step explanation:
Answer:
b.
Step-by-step explanation:
dawg its b
fv=100000, pmt=4000, i/y=5%, n=10, what is pv?
Answers
The Present value is $6,139.132.
We have,
FV=100000, pmt = 4000, I =5%, n=10
So, The present value formula is
PV=FV / (1 + \(i)^n\)
So, PV = 100, 000 / (1+ 5/100\()^{10\\\)
PV = 100,000 / (1+ 0.05\()^{10\\\)
PV = 100, 000/ (1.05\()^{10\\\)
PV = 100,000 / 1.6288946
PV= $6,139.132
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A swimmer can swim 24 1/4 meter pool in 1/7 of a minute. How many meters can the swimmer swim per minute?
Answers
Answer:
24 1/4 * 7 = 169 3/4
Answer this Fraction based Question I will provide you 50point + make you as brainliest.
Answers
It is given that 2/5 of all patients admitted to ward 17.
Remining fraction is:
1 - 2/5 = 5/5 - 2/5 = 3/5So 3/5 of patients admitted to ward 18.
Since 1/6 of all patients moved to another ward, and the reminder assigned as before, the initial fraction becomes:
1 - 1/6 = 6/6 - 1/6 =5/6Now, 3/5 of the new fraction, 5/6 is admitted to ward 18.
That is:
3/5*5/6 = 3/6 = 1/2This is half of the patients.
The difference of the number of the patients admitted to ward 17 is the same fraction of the number of infected:
10*2/5 = 4So the difference of patients is 4.
select all the ways to prove triangles are similar and select one true statement regarding angles and sides. a a stands for congruent angles and s stands for proportional sides b sss~ c sas~ d aas~ e a stands for proportional angles and s stands for congruent sides f asa~ g aa~ h a stands for congruent angles and s stands for congruent sides
Answers
The ways to prove triangles are similar are SSS rule, SAS rule, ASA rule and AAS rule
The rules of congruence of triangle are
SSS rule : If three sides of the triangle is equal to the three sides of another triangle, both triangles are congruent
SAS rule : If two sides and one included angle of one triangle is equal to the two sides and one included angle of another triangle, then both triangles are congruent
ASA rule : If two angles and one includes side of one triangle is equal to the two angles and one included side of another triangle, then both triangles are congruent
AAS rule : If two angles and one non-included sides of one triangle is equal to the two angles and one non-included side of another triangle, then both triangles are congruent
Therefore, theses are the rules of congruence of the triangle
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Help please due tonight
Answers
Step by step; Use the pythagorean theorem. (a^2 + b^2 = c^2 )
To find G-J;
7^2 + 3^2 = c^2
49 + 9 = c^2
58 = c^2
square both sides to isolate C, and the square root of 58 doesn’t simplify so we leave it alone.
sqr58
To find G-H;
4^2 + 7^2 = c^2
16 + 49 = c^2
65 = c^2
This, same as last time, 65 doesn’t simplify. Leave it.
sqr65
To find J-H;
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
Finally, one that simplifies! Square root 25.
5
Simplify the product 5/n+1 times n+1/n+3
Answer is 5/n+3 = simple
Answers
Answer:
\(\frac{5}{n+1}\times \frac{n+1}{n+3}=\frac{5}{n+3}\)
Step-by-step explanation:
Given the expression
\(\frac{5}{n+1}\times \frac{n+1}{n+3}\)
Let us simplify
\(\frac{5}{n+1}\times \frac{n+1}{n+3}\)
\(\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}\)
\(=\frac{5\left(n+1\right)}{\left(n+1\right)\left(n+3\right)}\)
\(\mathrm{Cancel\:the\:common\:factor:}\:n+1\)
\(=\frac{5}{n+3}\)
Therefore,
\(\frac{5}{n+1}\times \frac{n+1}{n+3}=\frac{5}{n+3}\)
Answer:
C
Step-by-step explanation:
5n+1/n+3
The diagram shows 28 lattice points, each one unit from its nearest neighbors. Segment AB meets segment CD at E. Find the length of segment AE.
Answers
Answer:
\(\frac{5\sqrt{5} }{3}\)
Answer:
\(\frac{5\sqrt{5}}{3}\)
Step-by-step explanation:
Extend DC to F. Triangle FAE and DBE are similar with ratio 5:4. Thus, AE=(5AB)/9, AB=\(\sqrt{3^2+6^2} =\sqrt{45} =3\sqrt{5}\) and \(AE=\frac{5(3\sqrt{5})}{9}\) which can be simplified to \(\frac{5\sqrt{5}}{3}\).
Hope this helped! :)
What is the slope of the line that passes through the points (6, -10)and (3, -13)?Write your answer in simplest form.
Answers
Answer:
The slope is 1 and your equation is y = x - 16
Step-by-step explanation:
(6, -10) & (3, -13)
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(-13 - (-10)) / (3 - 6)
Simplify the parentheses.
= (-13 + 10) / (-3)
= (-3) / (-3)
Simplify the fraction.
=-3/-3
= 1
This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.
y = 1x + b
or
y = x + b
To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (3, -13). Plug in the x and y values into the x and y of the standard equation.
-13 = 1(3) + b
To find b, multiply the slope and the input of x(3)
-13 = 3 + b
Now, subtract 3 from both sides to isolate b.
-16 = b
Plug this into your standard equation.
y = x - 16
This is your equation. From this we can see that the slope is 1.
Check this by plugging in the other point you have not checked yet (6, -10).
y = x - 16
-10 = (6) - 16
-10 = 6 - 16
-10 = -10
Your equation is correct.
Hope this helps!
The following are the number of departmental stores in 10 cities: 35, 27, 24, 32, 42, 30, 34, 40, 29 and 38.If we want to select a sample of 15 stores using cities as clusters and selecting within clusters proportionalto size, how many stores from each city should be chosen? (Use a starting point of 4).
Answers
Answer:
24
Step-by-step explanation:
:) hope this help
There are two questions on this slide. Please answer both to the best of your ability6. What is the measure of angle AED? How do youknow?D50°B7. What is the measure of angle DEB? How do youknow?
Answers
angle CEA and angle AED are supple
∠CEA
NEED ANSWER ASAP!!
How much water should be added to 18 mL of 15% alcohol solution to reduce the concentration to 9%?
Answers
I will mark you brainiest!
If one of the sides of the regular polygon pictured has a side length of 3x + 2, what is the length of all the sides?
A) 18x + 2
B) 3x + 2
C) 18x + 12
D) 12x + 18
