Answers
Answer: Missing segment = 45
Step-by-step explanation:
Concept:
Here, we need to know the idea of a similar triangle, ratio, and cross-multiplication.
In similar triangles, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other.
A ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Cross-multiplication means multiplying the numerator of each fraction by the other's denominator or the other way round.
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
Let x be the length of missing segment
Step One: write the proportion ratio
56 / 56 + 24 = 105 / 105 + x
Step Two: Cross-multiplication
56 (105 + x) = 105 ( 56 + 24)
Step Three: Simplify parenthesis and expand it
56 ( 105 + x) = 105 (80)
5880 + 56x = 8400
Step Four: Subtract 5880 on both sides
5880 + 56x - 5880 = 8400 - 5880
56x = 2520
Step Five: Divide 56 on both sides
56x / 56 = 2520 / 56
x = 45
Hope this helps!! :)
Please let me know if you have any questions
Related Questions
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW. THIS IS NOT A TEST OR AN ASSESSMENT!!!. Please help me with these math questions. Chapter 10 part 2
3. How do solving for solving to a rational function differ from solving for solutions to a rational inequality? How they are similar?
4. How is the difference quotient of a function determined? And how is the difference quotient related to the secant line? Is there a pattern for the difference quotient of linear functions?
Answers
9514 1404 393
Answer:
3. sign changes in the denominator need to be taken into account
4. difference quotient: (f(x+h) -f(x))/h; It is the slope of the secant line. For linear functions, the slope is constant, as is the difference quotient.
Step-by-step explanation:
3. When solving the equation f(x) = 0, where f(x) is a rational function, only the numerator zeros need to be considered.
When solving the inequality f(x) ≤ 0, or f(x) < 0, both numerator and denominator zeros need to be considered. As with solving any inequality, multiplying or dividing by a negative number changes the sense of the comparison.
Example
f(x) = x/(x-2) changes sign at both x=0 and x=2. Then three regions need to be considered when solving f(x) < 0. Those are x < 0, 0 < x < 2, and 2 < x.
__
4. The difference quotient is defined as ...
dq = (f(x +h) -f(x))/h
The difference quotient is essentially the average slope between (x, f(x)) and (x+h, f(x+h)). That is, it is the slope of the secant line between those two points.
For linear functions, the slope is a constant. The difference quotient is a constant equal to the slope of the line.
Example
f(x) = ax +b . . . . . a linear function with a slope of 'a'
The difference quotient is ...
(f(x+h) -f(x))/h = ((a(x+h)+b) -(ax+b))/h = (ax+ah+b -ax -b)/h = ah/h = a
The difference quotient is the slope of the line.
Which ordered pair would form a proportional
relationship with the points in the graph?
O (44)
O (69)
O (9,6)
O (8,5)
Answers
6,9
8,9
Use the discriminant to describe the roots of each equation. Then select the best description.
7x² + 1 = 5x
Answers
Answer:
Imaginary roots
Step-by-step explanation:
The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].
Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:
[tex]7x^2-5x+1=0[/tex]
Now assign variables:
[tex]a\implies 7[/tex] [tex]b\implies -5[/tex] [tex]c\implies 1[/tex]The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].
What does this tell us about the roots?
Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.
The length of a rectangle is five times its width. If the perimeter of the rectangle is 108 in, find its area.
Answers
Answer:
Step-by-step explanation:multiple 5 times 108 and that gives you your answer..
HELP PLS I DONT KNOW THIS ONE
Answers
Answer:
1
-------------
(x+2)(x-4)
Step-by-step explanation:
x+4 x+3
------------- * --------------
x^2+5x+6 x^2 -16
Factor
x+4 x+3
------------- * --------------
(x+3)(x+2) (x+4)(x-4)
Cancel like terms
1 1
------------- * --------------
(1)(x+2) (1)(x-4)
1
------------- x cannot equal -3, -4, -2, 4
(x+2)(x-4)
Please show your steps
Answers
Answer:
M of aftershock = 4.90
Step-by-step explanation:
5.6 = log(x/1)
[tex]10^{5.6} = 398107.1 \\[/tex]
1/5 * 398,107.1 = 79,621.4
[tex]10^{m} =[/tex] 79,621.4
m = log (79,621.4) = 4.90
I want to know how to solve this equation
Answers
Answer:
one property of log is that if the log expressions have the same base (in this case, 2), then you can multiply the added logs.
The answer would then be D
Suppose a certain study reported that 27.7% of high school students smoke.
Random samples are selected from high school that has 632 students.
(i) If a random sample of 60 students is selected, what is the probability that
fewer than 19 of the students smoke?
(ii) If a random sample of 75 students is selected, what is the probability that
more than 17 of the students smoke?
Answers
The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.
Given:
Probability of student smoke,
P = 27.7%
= 0.277
Number of students (n) = 632
[tex]q = 1-p[/tex]
[tex]=1-0.277[/tex]
[tex]=0.723[/tex]
(i)
Here,
Number of students (n) = 60
then,
⇒ [tex]n_P=60\times 0.277[/tex]
[tex]=16.62[/tex]
⇒ [tex]n_q=60\times 0.723[/tex]
[tex]=43.38[/tex]
We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.
Now,
[tex]\mu = n_P= 16.62[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]= \sqrt{60\times 0.277\times 0.723}[/tex]
[tex]=3.9664[/tex]
Now,
⇒ [tex]P(X<19) = P(X<18.5)[/tex]
[tex]=P(Z_{18.5})[/tex]
The Z-score is:
= [tex]\frac{18.5-16.62}{3.4664}[/tex]
= [tex]0.5423[/tex]
hence,
The probability will be:
⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]
or,
⇒ [tex]P(Z<19) = 0.7062[/tex]
(ii)
Here,
Number of students (n) = 75
[tex]\mu = n_P = 75\times 0.277[/tex]
[tex]=20.775[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]=\sqrt{75\times 0.277\times 0.723}[/tex]
[tex]=3.8756[/tex]
Now,
⇒ [tex]P(X>17) = P(X> 17.5)[/tex]
[tex]=1-P(X \leq 17.5)[/tex]
[tex]=1-P(Z_{17.5})[/tex]
The Z-score is:
= [tex]\frac{17.5-20.775}{3.8756}[/tex]
= [tex]-0.9740[/tex]
then, [tex]P(Z_{17.5}) = 0.165[/tex]
hence,
The probability will be:
⇒ [tex]P(X>17) = 1-0.165[/tex]
[tex]=0.835[/tex]
Learn more about Probability here:
https://brainly.com/question/9825651
for the binomial distribution with n=4 and p=0.25
a)find the probability of three success
b)at the most three success
c)two or more failures
Answers
Answer:
a.) .0469
b.) .9961
c.) .9492
Rounded these check below for full answers
Step-by-step explanation:
a.)
[tex]{4\choose3}*.25^3*(1-.25)=.046875[/tex]
b.)
Porbability of at most 3 successes is equal to 1-p(4)
p(4)=
[tex]{4\choose4}*.25^4=.003690625[/tex]
1-.003690625=.99609375
c.)
two or more failures is equa lto
p(0)+p(1)+p(2)=
[tex]{4\choose0}*.25^0*(1-.25)^4+{4\choose1}*.25^1(1-.25)^3+{4\choose2}*.25^2*(1-.25)^2=.94921875[/tex]
The word "theory" is composed of the letters of the split alphabet. Three cards are taken out at random and stacked in a row one after another in order of appearance. How many possible compounds can be made up of the letters of this word?
Answers
Answer:
There would be [tex]120[/tex] of them.
Step-by-step explanation:
There are [tex]6[/tex] distinct letters in the word "[tex]\verb!theory![/tex]".
Hence, there would [tex]6[/tex] possible choices for the first letter that was selected.
Since the chosen card won't be placed back in the pool, there would be only [tex](6 - 1) = 5[/tex] possible choices for the second letter.
Likewise, there would be [tex](6 - 2) = 4[/tex] choices for the third letter.
[tex]6 \times 5 \times 4 = 120[/tex]. In other words, there are [tex]120[/tex] possible ways to draw three cards out of [tex]6[/tex] one after another.
Since the question states that the order of the cards matters, it won't be necessary to eliminate repetitions such as "[tex]\verb!the![/tex]" and "[tex]\verb!het![/tex]" from the number of combinations.
You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten.
Answers
Answer:
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
Step-by-step explanation:
There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.
At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just
[tex]\frac{4}{52}[/tex]
After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is
[tex]\frac{4}{51}[/tex]
Now to get the total probability we need to multiply the two probabilities together
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
Find the derivative on the value of x=-4
[tex]y=(6x-5)\sqrt{8x-3}[/tex]
Answers
[tex]\\ \sf\longmapsto y=(6x-5)\sqrt{8x-3}[/tex]
[tex]\\ \sf\longmapsto y=6(-4)-5\sqrt{8(-4)-3}[/tex]
[tex]\\ \sf\longmapsto y=-24-5\sqrt{-32-3}[/tex]
[tex]\\ \sf\longmapsto y=-29\sqrt{-35}[/tex]
[tex]\\ \sf\longmapsto y=-29\times 35i[/tex]
[tex]\\ \sf\longmapsto y=-1015i[/tex]
Find the missing side lengths leave your answer as a racials simplest form
Answers
Answer:
m=[tex]7\sqrt3[/tex]
n=7
Step-by-step explanation:
Hi there!
We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14
We need to find the lengths of m and n
Firstly, let's find the measure of the other acute angle
The acute angles in a right triangle are complementary, meaning they add up to 90 degrees
Let's make the measure of the unknown acute angle x
So x+60°=90°
Subtract 60 from both sides
x=30°
So the measure of the other acute angle is 30 degrees
This makes the right triangle a special kind of right triangle, a 30°-60°-90° triangle
In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is [tex]\frac{a}{2}[/tex], and the leg opposite from the 60 degree angle is [tex]\frac{a\sqrt3}{2}[/tex]
In this case, a=14, n=[tex]\frac{a}{2}[/tex], and m=[tex]\frac{a\sqrt3}{2}[/tex]
Now substitute the value of a into the formulas to find n and m to find the lengths of those sides
So that means that n=[tex]\frac{14}{2}[/tex], which is equal to 7
And m=[tex]\frac{14\sqrt3}{2}[/tex], which simplified, is equal to [tex]7\sqrt3[/tex]
Hope this helps!
You need to build a box from an 8 inchby 10 inch piece of cardboard. To do this, you cut out squares of length x from the four corners of the box in order to fold the sides up. Verify that the volume of the box is given by the equation:
V= 4x^3â36x^2+ 80x
Answers
Answer:
Step-by-step explanation:
From the attached image below, let assume we have a square of diameter x by x which is to be cut from each corner of the cardboard sheet.
Thus, from the diagram
the length = 8 - 2x the width = 10 - 2x and the height = x
So, the volume V = L*w*h
Volume (V) = (8 - 2x) (10 - 2x) x
V = (80 - 16x - 20x +4x²)x
V = 80x -36x² + 4x³
By rearrangement:
V = 4x³ - 36x² + 80x
Which points lie on the graph of f(x) = loggx?
Check all that apply.
Answers
Step-by-step explanation:
f(x)=log(x)
=d(log(x)/dx)
=>y=1/x
VG¯¯¯¯¯¯¯¯=12.2 in. PG¯¯¯¯¯¯¯¯=13.1 in. Find the radius of the circle.
Answers
Answer:iiii
Step-by-step explanation:iiiii
Answer:
17.9
Step-by-step explanation:
A scale drawn on the map shows that 1 inch represents 40 miles. If tuo cities
are 25 inches apart on the map, what is the distance between them in real
life?
Answers
Answer:
Im pretty sure its 1,000 miles (dont forget the unit)
Step-by-step explanation:
Determine if this problem is a inverse variation or direct variation problem! This means that:
equation would be:
1=40
25=x
cross multiply*
x=25*40
x=1,000 miles apart! (dont forget the unit)
If this doesnt work then try this equation!
1=40
25=x
Multiply 1*40 and 25 *x
40=25x......
40/25= 1.6
x=1.6! (Extra step)
Cheers!
Answer: 100 Miles
Step-by-step explanation: took the miles and got it correct.
(Also it's 2.5 inches apart, not 25.)
When is the Declaration of Independence?
Answers
Answer:
July 4th, 1776.
Step-by-step explanation:
By issuing the Declaration of Independence, adopted by the Continental Congress on July 4, 1776, the 13 American colonies severed their political connections to Great Britain. The Declaration summarized the colonists' motivations for seeking independence.
i need help with this question asapppppp
Answers
9514 1404 393
Answer:
$11,680.58
Step-by-step explanation:
Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.
__
The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.
The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...
0.205×21,465 = 4400.325 ≈ 4400.33
The the total tax due on $70,000 is ...
$7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000
_____
Additional comments
The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.
__
Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.
≤ 48535 -- income × 0.15
≤ 97069 -- income × 0.205 -2669.425
≤ 150,473 -- income × 0.26 -8008.22
≤ 214,368 -- income × 0.29 -12,522.41
> 214,368 -- income × 0.33 -21,097.13
In this case, the second row of this simpler table would give the tax on $70,000 as ...
tax = 70,000 × 0.205 -2669.425
tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above
Find the missing side length image below
Answers
Answer:
40
Step-by-step explanation:
Based on the Proportional Transversal Theorem, the three parallel lines hat intersects the two transversals, divides the transversal lines proportionally.
Therefore, we would have the following ratio:
28/35 = ?/50
Cross multiply
35*? = 50*28
35*? = 1,400
Divide both sides by 35
? = 1400/35
? = 40
A truck is said to get 18 miles per gallon on a highway, but this value can fluctuate, at most, by 4 miles per gallon. Which of the following absolute value inequalities matches this scenario? Question 23 options: |x + 18| ≤ 4 |x – 18| ≤ 4 |x – 4| > 18 |x + 18| > 4
Answers
Answer:
the correct answer is |x – 18| ≤ 4
just took the test
Step-by-step explanation:
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+320
The ball hits the ground after____ seconds
Answers
Answer:
28 seconds ..............
Determine the dimension of the vector space. M4,2
STEP 1: Determine the number of linearly independent vectors needed to span M4,2. The basis for M4,2 has linearly independent vectors.
STEP 2: Using the result from Step 1, determine the dimension of M4,2.
Answers
Answer:
STEP 1
M_{4,2} is set of 4x2 matrices hence each matrix has 4*2=8 entries. Each entry can be filled independently.
Hence its basis has 8 linearly independent vectors.
STEP 2
Dimension= cardinality of basis = 8.
HELP PLS ! ! !
What is |1 − 8i|?
A) √-65
B) 65
C) √65
D) √13
Answers
Answer:
C) SQRT(65)
Step-by-step explanation:
the magnitude of 1-8i is given by the following:
sqrt(a^2+b^2)
sqrt(1^2+8^2)
=sqrt(1+64)
=sqrt(65)
It is to be noted that the magnitude of |1 − 8i| is √(65) (Option C)
What is the computation of the above?To find the magnitude (or absolute value) of a complex number, we use the formula |a + bi| = √(a² + b²). In this case, the complex number is 1 - 8i.
Using the formula, we have -
|1 - 8i| = √(1² + (-8)²)
= √(1 + 64)
= √65
Hence, the magnitude of 1 - 8i is √65.
So the correct answer is C) √65.
Learn more about magnitude at:
https://brainly.com/question/30337362
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A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 70 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.2 m3/min how fast is the water level rising when the water is 20 cm deep?
Answers
Answer:
dv = surface area * dh
so
dv/dt = surface area * dh/dt
width at surface = 40 + (80-40)(30/40)
= 40 + 30 = 70 cm = 0.70 m
so
surface area = 9 * .7 = 6.3 m^2
so
.3 m^3/min = 6.3 m^2 * dh/dt
and
dh/dt = .047 meters/min or 4.7 cm/min
Step-by-step explanation:
A population is equally divided into three class of drivers. The number of accidents per individual driver is Poisson for all drivers. For a driver of Class I, the expected number of accidents is uniformly distributed over [0.2, 1.0]. For a driver of Class II, the expected number of accidents is uniformly distributed over [0.4, 2.0]. For a driver of Class III, the expected number of accidents is uniformly distributed over [0.6, 3.0]. For driver randomly selected from this population, determine the probability of zero accidents.
Answers
Answer:
Following are the solution to the given points:
Step-by-step explanation:
As a result, Poisson for each driver seems to be the number of accidents.
Let X be the random vector indicating accident frequency.
Let, [tex]\lambda=[/tex]Expected accident frequency
[tex]P(X=0) = e^{-\lambda}[/tex]
For class 1:
[tex]P(X=0) = \frac{1}{(1-0.2)} \int_{0.2}^{1} e^{-\lambda} d\lambda \\\\P(X=0) = \frac{1}{0.8} \times [-e^{-1}-(-e^{-0.2})] = 0.56356[/tex]
For class 2:
[tex]P(X=0) = \frac{1}{(2-0.4)} \int_{0.4}^{2} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{1.6} \times [-e^{-2}-(-e^{-0.4})] = 0.33437[/tex]
For class 3:
[tex]P(X=0) = \frac{1}{(3-0.6)} \int_{0.6}^{3} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{2.4} \times [-e^{-3}-(-e^{-0.6})] = 0.20793[/tex]
The population is equally divided into three classes of drivers.
Hence, the Probability
[tex]\to P(X=0) = \frac{1}{3} \times 0.56356+\frac{1}{3} \times 0.33437+\frac{1}{3} \times 0.20793=0.36862[/tex]
HELP. Use the grouping method to factor the polynomial below completely.
x^3 – 5x^2 + 3x - 15
A. (x^2 + 5)(x-3)
B. (x^2 - 3)(x+5)
C. (x^2 - 5)(x+3)
D. (x^2 + 3)(x - 5)
Answers
Answer:
D
Step-by-step explanation:
(x^2+3)(x-5)
That's the answer
Cristina is sending out thank you cards for birthday presents. She has pink (P), blue (B), and green (G) cards, and white (W) and yellow (Y) envelopes to send them in. She chooses a card and an envelope at random for each person. What is the sample space for possible combinations? Enter a list of text [more] Enter each outcome as a two-letter "word", with the first letter for the card and the second letter for the envelope. For example, PW would be a pink card in a white envelope. Separate each element by a comma.
Answers
Answer:
PW, BW, GW, PY, BY, GY
Step-by-step explanation:
We need to determine the sample space
pink(P), blue (B), and green (G) cards, (W) and yellow (Y) envelopes
Each color card can match with each color envelope
Start with the white envelopes and each color card
and then the yellow envelopes with each color card
PW BW GW
PY BY GY
Which is a direct proportion
y = -4
y = 2x + 1
y = 6
y = 2/3x
Answers
Answer:
y=2x+1
Step-by-step explanation:
y is directly proportional to x if it increases as x increases
equation that passes 1,3 and slope of 2 in point slope form
Answers
Answer:
y-3 = 2(x-1)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y-3 = 2(x-1)
Answer:
3=2x+1
Step-by-step explanation:
Use the equation y=mx+b
where y is the y component, x is the variable and b is the x intercept
