10. The perimeter of the rectangle to the right is 28 ft. What is the value of x?
Answers
ANSWER
x = 9
EXPLANATION
We have the rectangle with width 3 ft and length (2 + x) ft.
The perimeter of the triangle is 28 ft.
The perimeter of a rectangle is given as:
P = 2(L + W)
where L = length
W = width
Therefore, we have that:
28 = 2[(2 + x) + 3]
28 = 2(2 + x + 3) = 2(x + 5)
28 = 2x + 10
=> 2x = 28 - 10 = 18
Divide through by 2:
2x/2 = 18/2
x = 9
That is the value of x.
Related Questions
A grain silo is shown below:168 ft6 ftWhat is the volume of grain that could completely fill this silo, rounded to the nearest whole number? Use22/7 for pi
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Solution
Step 1
[tex]\begin{gathered} \text{The volume of the silo = volume of a cylinder + volume of the } \\ \text{ hemisphere} \\ The\text{ volume of the silo = }\pi r^2h\text{ + }\frac{2}{3}\pi r^3 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} \text{h = 168} \\ \text{r = 6} \end{gathered}[/tex]Step 3
[tex]\begin{gathered} Volume\text{ = }\frac{22}{7}\times6^2\times\text{ 168 + }\frac{2}{3}\times\frac{22}{7}\times\text{ 6}^5 \\ Volume\text{ = }19008\text{ + 452.5714286} \\ Volume\text{ =19460.571 } \end{gathered}[/tex]Final answer
19461
USMZABC = 40'and BỎ is the anglebisector of ZABC3y+6B.3x-134-2xD5y-18MZABD =[ ? 1°Enter
Answers
We want to calculate the value of
[tex]3x-1[/tex]However, x is unknown. For BD is "angle bisector"
[tex]3x-1=34-2x[/tex]Let us solve that equation for x:
[tex]3x+2x=34+1[/tex](-2x was sent to the left-hand side, and -1 was sent to the right-hand side)
[tex]5x=35[/tex][tex]x=7[/tex]Then,
[tex]3x-1=3(7)-1=21-1=20[/tex]Thus,
[tex]m\measuredangle ABD=20[/tex]14. A poll was taken of 13,875 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results are shown below.Education LevelMaleFemaleTotalHigh School or Less299934306429Bachelor's Degree315131736324Master's Degree4975061003Ph.D.5465119Total6701717413,875A person is selected at random. Compute the following probabilities.(a) What is the probability that the selected person is a male? (b) What is the probability that the selected person does not have a Ph.D.? (c) What is the probability that the selected person has a Master's degree? (d) What is the probability that the selected person is female and has a Master's degree?
Answers
Part a
What is the probability that the selected person is a male?
P=6,701/13,875
P=0.4830
Part b
What is the probability that the selected person does not have a Ph.D.?
P=1-119/13,875
P=0.9914
Part c
What is the probability that the selected person has a Master's degree?
P=1,003/13,875
P=0.0723
Part d
What is the probability that the selected person is female and has a Master's degree?
P=506/13,875
P=0.0365
Hi, can you help me to solve this problem, please!!!
Answers
The given parabola is:
[tex]y=-3x^2+3x-6[/tex]It is written in the form:
[tex]y=ax^2+bx+c[/tex]The axis of symmetry is given by the following formula:
[tex]x=-\frac{b}{2a}[/tex]Where a=-3 and b=3. Replace these values and solve for x:
[tex]\begin{gathered} x=-\frac{3}{2(-3)}=-\frac{3}{-6}=\frac{3}{6} \\ \text{Divide numerator and denominator by 3 to simplify} \\ x=\frac{3/3}{6/3}=\frac{1}{2} \end{gathered}[/tex]Therefore, the axis of symmetry is x=1/2
Neglecting air resistance, the distance (d) that an object fallsvaries directly as the square of the time (t) it has been falling.If an object falls 64 feet in 2 seconds, determine the distanceit will fall in 6 seconds.
Answers
where a is a constant, we can find a with the first statement:
"an object falls 64 feet in 2 seconds"
so:
[tex]\begin{gathered} 64=a(2)^2 \\ a=\frac{64}{2^2} \\ a=16 \end{gathered}[/tex]the complete equation is
[tex]d(t)=16t^2[/tex]now "determine the distance for 6seconds"
so, replace t=6 and find d
[tex]\begin{gathered} d(t)=16(6)^2 \\ d(t)=576ft \end{gathered}[/tex]the distance is 576ft
Question #1: The International Special Olympics were held in New York City. The USA team won 25 medals; Gold
[8], Silver [10], and Bronze [7]. Using the table below, construct a frequency distribution table that includes both
the relative frequency and the frequency percentage.
Class Level rf f%
Gold
Silver
Bronze
Answers
The frequency distribution table includes both the relative frequency and the frequency percentage given below.
Class Level Relative frequency frequency %
Gold 8/25 × 100 = 0.032 32%
Silver 10/25 × 100 = 0.04 40%
Bronze 7/25 × 100 = 0.028 28%
What is Relative frequency?The Relative frequency is an estimate or estimator of a probability in terms of statistics.
In straightforward situations, where the outcome of a trial just establishes whether the predetermined event has taken place, modeling using a binomial distribution may be suitable, and the empirical estimate is then the maximum likelihood estimate.
If specific conditions for the prior distribution of the probability are met, it is the Bayesian estimate for the same case. If a trial produces additional data, the relative frequency can be enhanced by adding new hypotheses in the form of a statistical model; if this model is fitted, it can be used to determine an estimate of the likelihood of the desired event.
To learn more about Relative frequency from the given link
https://brainly.com/question/16832475
#SPJ4
Compare two sequence 2 4 6 8 102 4 8 16 32
Answers
The given sequences are
[tex]\begin{gathered} 2,4,6,8,10\rightarrow(1) \\ 2,4,8,16,32\rightarrow(2) \end{gathered}[/tex]In the sequence (1):
[tex]\begin{gathered} 4-2=2 \\ 6-4=2 \\ 8-6=2 \\ 10-8=2 \end{gathered}[/tex]There is a common difference of 2
Then it is an arithmetic sequence
In the sequence (2):
[tex]\begin{gathered} \frac{4}{2}=2 \\ \frac{8}{4}=2 \\ \frac{16}{8}=2 \\ \frac{32}{16}=2 \end{gathered}[/tex]There is a common ratio of 2
Then it is a geometric sequence
The first sequence is increasing by 2
The second sequence is multiplying by 2
which is in an equation of the line through (0,0) and (-8,-5)?
Answers
To finde the equation of the line troughh the points (0;0) and (-8;-5) first you must find the slope of the line. You have to use the next formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Replacing the points in the previous formula
[tex]m=\frac{-5-0}{-8-0}=\frac{5}{8}[/tex]As the line passes trough the origin of coordinates (point (0;0)) the equation is:
[tex]y=\frac{5}{8}x[/tex]So the answer is y= 5/8 x (option B)
I'll upload pictures
Answers
Find similar triangles
Triangle PQS is similar to triangle PSR
Reason for this similarity is
RS/ PS = PS / QS
In consecuence
PS^2 = RS • QS
PART 3
RS = 4, RQ= 16. Find RP
Then
RP ^2 = RQ • RS
RP = √ (4•16) = 8
Write a system of equation to this real world situation .Number 1
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Let be "q" the number of quarters Kiara has and "d" the number of dimes she has.
According to the information given in the exercise, the total number of dimes are quarters Kiara has is 100. Based on this, you can set up the following equation, which will be Equation 1:
[tex]q+d=100[/tex]The total value Kiara has is $19, then knowing that 1 quarter is $0.25 and 1 dime is $0.10, you can set up the Equation 2:
[tex]0.25q+0.10d=19[/tex]Then, the System of equation for this situation is:
[tex]\begin{cases}q+d=100 \\ 0.25q+0.10d=19\end{cases}[/tex]The answer is:
- Equation 1:
[tex]q+d=100[/tex]- Equation 2:
[tex]0.25q+0.10d=19[/tex]c 1150Solve for the length of the arc, to the nearest tenth.2.08.016.150.3
Answers
ANSWER
8.0
EXPLANATION
If the central angle θ is in degrees and the radius is r, the length of the arc 's' is:
[tex]s=\frac{\theta}{360}\times2\pi r[/tex]In this problem θ = 115º, r = 4:
A company is designing a steamer for their upcomingThe design of the stream has an area of 12 in^2. If they wantto manufacture a larger version of the sign with an area of147 in^2, what scale factor would they need to use?
Answers
Given that the design of the stream has an area of 12 in^2.
We have to find the scale factor if the area of the larger version is 147 in^2.
It is known that the area of a scaled object will be equal to the scale factor squared.
Let the scale factor be x. So,
[tex]\begin{gathered} 12x^2=147 \\ x^2=\frac{147}{12} \\ x^2=12.25 \\ x=\sqrt[]{12.25} \\ x=3.5 \end{gathered}[/tex]So, the scale factor is 3.5.
Kenneth read a total of 320 pages over 32 hours. After a total of 42 hours of reading this week, how many pages will Kenneth have read in all? Assume the relationship is directly proportional.
Answers
From the question, we can deduce the following:
320 pages ==> 32 hours
Let's find how many pages Kenneth will read in 42 hours.
We have:
32 hours = 320 pages
42 hours = x pages
Apply the proportionality equation and solve for x.
[tex]\frac{320}{32}=\frac{x}{42}[/tex]Cross multiply:
[tex]\begin{gathered} 32x=320\times42 \\ \\ 32x=13440 \end{gathered}[/tex]Divide both sides by 32:
[tex]\begin{gathered} \frac{32x}{x}=\frac{13440}{32} \\ \\ x=420 \end{gathered}[/tex]Therefore, Kenneth will read 420 pages after a total of 42 hours.
ANSWER:
420 pages.
The graph below has the same shape as the graph of G(x) = x?, but it isshifted down five units and to the left four units. Complete its equation. Enterexponents using the caret (1); for example, enter x2 as x^2. Do not include"F(x) =" in your answer
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Use the Trapezoidal Rule to approximate ∫2−1ex2dx using n=4. Round your answer to the nearest hundredth.
Answers
What are the dimensions of a parallelogram in terms of the demensioms of the circle?
Answers
If we divide a circle into a number of equal segments then stack them in a row head-to-tail, the new shape is a parallelogram with bumpy sides, with the same area as the circle.
We can conclude the following:
1. The base of a parallelogram is approximately equal to half the circumference of the circle
2. The height of the parallelogram is approximately equal to the radius of the circle
3. The area of the parallelogram is equal to the area of the circle.
Mrs. Burke's biology class has 128 students, classified by academic year and major, as illustrated in the table. Mrs. Burke randomly chooses one student to collectyesterday's work.Mrs. Burke's Biology ClassAcademic Year Biology MajorsFreshmenSophomoresJuniorsSeniors19171617Non-Biology Majors17141018Step 2 of 2: What is the probability that she selects a senior, given that she chooses a biology major? Enter a fraction or round your answer to 4 decimal places, ifnecessary.
Answers
Total: 128 students
1. The probability that she selects a senior, given that she chooses a biology major is given by:
[tex]P=\frac{seniors}{biolog\text{y majors}}=\frac{17}{19+17+16+17}=\frac{17}{69}=0.2464[/tex]Answer: 0.2464
Solve for y.2y^2 - 10y + 44=(y-7)^2If there is more than one solution, separate them with commas.
Answers
Answer:
y=-5,y=1
Step-by-step explanation:
To solve this, we need to solve a quadratic equation, using the bhaskara formula.
Initially, let's place the equation in the standard format. So
[tex]2y^2-10y+44=(y-7)^2[/tex][tex]2y^2-10y+44=y^2-14y+49[/tex][tex]2y^2-y^2-10y+14y+44-49=0[/tex][tex]y^2+4y-5=0[/tex]Now we apply the bhaskara formula:
[tex]y=\frac{-(4)\pm\sqrt{4^2-4\ast1\ast-5}}{2\ast1}[/tex]Then
[tex]y=\frac{-4\pm6}{2}[/tex]So two solutions:
[tex]y^{^{\prime}}=\frac{-4+6}{2}=1,y^{^{\prime}^{\prime}}=\frac{-4-6}{2}=-5[/tex]The solution are y=-5,y=1
Which of the following sets is a finite set of rational numbers
Answers
The correct option is the third one.
In set notation, '...' indicates that the set is infinite. With this we can discard option 1 and 4.
If we look option 2, they're all irrational numbers.
Thus, the correct option is the third one.
HELP ASAP!
Put (-3y + 6 < x) in slope-intercept form.
Answers
Step-by-step explanation:
so slope intercept form is y=mx+b or in this case y<mx+b
so you just need to solve for y
start by subtracting 6 from both sides getting -3y< x + 6 than you just divided by a -3 when you divide by a negative number you have to change the inequality so you would get y> -(x+6)/3 that would be your answer hopefully that helps. have a great day
*Be sure to simplify fractions and rationalize denominators if necessary.
Answers
As given by the question
There are given that the vector:
[tex]\vec{v}=\vec{2i}+\vec{3j}[/tex]Now,
From the formula to find the unit vector in same direction is:
[tex]\vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert}[/tex]Then,
[tex]\begin{gathered} \vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\vec{2i}+\vec{3j}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\sqrt[]{2^2+3^2}\rvert} \end{gathered}[/tex]Then,
[tex]\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{2^2+3^2}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{4+9}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \end{gathered}[/tex]Then,
Rationalize the denominator:
So,
[tex]\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}}\times\frac{\sqrt[]{13}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{\sqrt[]{13}(2i}+\vec{3j})}{13} \\ \vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j \end{gathered}[/tex]Hence, the unit vector is shown below:
[tex]\vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j[/tex]The Honeywell HQ17 air cleaner takes twice as long as the EV25 to clean the samevolume of air. Together the two machines can clean the air in a 25-ft by 24-ft banquetroom in 10 minutes. How long would it take each machine working alone to clean the airin the room?
Answers
Given:
The Honeywell HQ17 air cleaner takes twice as long as the EV25 to clean the same
volume of air.
Let, x be the time taken by Honeywell EV25 air cleaner.
And 2x be the time taken by Honeywell HQ17 air cleaner.
Together the two machines can clean the air in 10 min.
[tex]\begin{gathered} x+2x=10 \\ 3x=10 \\ x=\frac{10}{3}=3.33\text{ min} \end{gathered}[/tex]So, time takes by Honeywell HQ17 air cleaner is,
[tex]2x=2(\frac{10}{3})=6.67\text{ min}[/tex]Answer:
The time taken by Honeywell EV25 air cleaner is 3.33 min.
The time taken by Honeywell HQ17 air cleaner is 6.67 min.
Assume the random variable x is normally distributed with mean μ = 83 and standard deviation o=4. Find the indicated probability.P(70
Answers
SOLUTION
Given the question in the image on the question tab;
[tex]P(70Now, we are going to find;[tex]P(-3.25[tex]Using\text{ statistical table for normal distribution; the probability is:}[/tex][tex]0.0662301762265\times100=6.623\%[/tex]
Final answer:
[tex]\begin{equation*} 6.623\% \end{equation*}[/tex]A small jet can fly 889 miles in 3.5 hours with a tailwind but only 651 miles in 3.5 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.
Answers
Given:
[tex]\begin{gathered} D_{is\tan ace\text{ travelled during tail wind}}=889miles \\ T_{\text{ime taken during tail wind}}=3.5hours \\ D_{is\tan ce\text{ travelled during headwind}}=651miles \\ T_{\text{ime taken during headwind}}=3.5hours \end{gathered}[/tex]To Determine: The speed of the jet in still air and the speed of the wind
Represent the speed of the jet in still air and the speed of the wind with unknowns
[tex]\begin{gathered} T_{he\text{ sp}eed\text{ of the jet in still air}}=x \\ T_{he\text{ sp}ed\text{ of the wind}}=y \end{gathered}[/tex]Note that the speed, distance, and time is related by the formula below
[tex]S_{\text{peed}}=\frac{D_{is\tan ce}}{T_{\text{ime}}}[/tex]Calculate the speed during the tailwind and the headwind
[tex]S_{\text{peed during tail wind}}=\frac{889}{3.5}=254milesperhour[/tex][tex]S_{\text{peed during headwind}}=\frac{651}{3.5}=186milesperhour[/tex]Note that during the tailwild, the speed of the wind and the speed of the jet in still air are in the same direction. Also during the headwind, the speed of the wind and the speed of the jet in still air are in opposite direction. Therefore average speed during the tailwind and the headwind would be
[tex]\begin{gathered} equation1\colon x+y=254 \\ equation2\colon x-y=186 \end{gathered}[/tex]Combine the two equations: Add equation 1 and equation 2 to eliminate y as shown below
[tex]\begin{gathered} x+x-y+y=254+186 \\ 2x=440 \\ x=\frac{440}{2} \\ x=220\text{ miles per hour} \end{gathered}[/tex]Substitute x = 220 in equation 1
[tex]\begin{gathered} x+y=254 \\ 220+y=254 \\ y=254-220 \\ y=34\text{ miles per hour} \end{gathered}[/tex]Hence:
The speed of the jet in still air is 220 miles per hour
The speed of the wind is 34 miles per hour
Find the area of the triangle. Round to the nearest tenth. a=28.5 b=33.4 c=22.3
Answers
solution
for this case we can use the Herons formula given by:
[tex]A=\sqrt[]{s(s-a)(s-b)(s-c)}[/tex]Where s is the semiperimeter given by:
[tex]s=\frac{a+b+c}{2}=\frac{33.4+28.5+22.3}{2}=42.1[/tex]And we can find the area on this way:
[tex]A=\sqrt[]{42.1(42.1-33.4)(42.1-28.5)(42.1-22.3)}=314.05[/tex]And rounded to the nearest tenth would be:
314.1
Which expression is equivalent to 3 (m + 2) – 6 (2m + 4)? 15m + 30 15m + 3 - 9m - 18 -9m + 30
Answers
To expand and then simplify the expression:
[tex]3(m+2)-6(2m+4)[/tex]We can follow the next steps:
1. Apply the distributive property:
[tex]3m+3\cdot2-12m-6\cdot4=3m+6-12m-24[/tex]Then, we need to algebraically sum the like terms:
[tex]3m-12m+6-24=-9m-18[/tex]Then, the equivalent expression for that given in the question is -9m - 18. It could be also -9(m+2) (using -9 as a common factor).
which property is illustrated by the statement 8 + 2 equals 2 + 8? A. Associative B. commutative C. Distributive D. Identity
Answers
8+2=2+8 is result of the commutative property. Then, the answer is option B
Answer the question below based on the two quadratic functions.Function 2хyFunction 1f(x) = x2 + 4x - 3-7-8-2.-1012.-7-41Which function has the graph with the smaller minimum value and what is the minimum value?Function 1 has the smaller minimum value of -2.Function 2 has the smaller minimum value of -1.Function 1 has the smaller minimum value of -7.O Function 2 has the smaller minimum value of -8.
Answers
1. Plotting the function or creating a table with values.
This is what you did, and you got that for x=-2 the functions reaches the minimum, to y= -7
Now, since you already know the minmum value for the first function, you can see that the first answer is false while the third one is true. But, is that value (-7) smaller than the minimum for function 2?
Looking at the table, we can see that function 2 reaches the minimum for x = -1, and it is equal to y = -8.
Since -8 < -7, function 2 minimum is smaller than function 1 minimum.
Then, answer #4 is the correct one.
f(x +h)-f(x)For the function defined as follows, find (a) f(x + h), (b) f(x + h) – f(x), and (c)f(x)= 4/x
Answers
Given the function:
[tex]f(x)=\frac{4}{x}[/tex]We will find the following:
a) f(x+h)
So, we will substitute with x = x+h
[tex]f(x+h)=\frac{4}{x+h}[/tex]b) f(x+h) - f(x)
[tex]\begin{gathered} f(x+h)-f(x)=\frac{4}{x+h}-\frac{4}{x} \\ \\ f(x+h)-f(x)=\frac{4x-4(x+h)}{x(x+h)} \\ \\ f(x+h)-f(x)=\frac{4x-4x-4h}{x(x+h)} \\ \\ f(x+h)-f(x)=\frac{-4h}{x(x+h)} \end{gathered}[/tex]c) [f(x+h) - f(x)]/h
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4h}{x(x+h)\cdot h} \\ \\ \frac{f(x+h)-f(x)}{h}=\frac{-4}{x(x+h)} \end{gathered}[/tex]I need help finding an answer to a math question. I just need to know how to solve it. The question is:A gallon of water weighs 8.34 pounds. The Patel family has a round, 12-foot diameter, above-ground pool. How much weight is added to the pool when it is filled with 3,110 gallons of water?
Answers
We know a gallon of water weighs 8.34 pounds.
If 3,110 gallos of water are used to fill the Patel family's pool, then the water weighs:
8.34 * 3,110 = 25,937.4 pounds.
Answer: 25,937.4 pounds of water are added to the pool