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For angle 45 degree, hypotenuse side is 15 and base side is x.
Determine the measure of side x by using trigonometry.
[tex]\begin{gathered} \cos 45=\frac{x}{15} \\ 0.707=\frac{x}{15} \\ x=15\cdot0.707 \\ =10.605 \end{gathered}[/tex]Thus value of x is 10.605 m.
Answer: x = 10.605 m
Related Questions
A school choir needs to make t-shirts for its 75 members. A printing company charges $2 per shirt, plus a $50 fee for each color to be printed on the shirts. Write an equation that represents the relationship between the number of t- shirts ordered, the number of colors on the shirts and the total cost of the order. If you use a variable (letter) specify what it represents. In this situation, which quantities do you think can vary (change)? Which might be fixed (stay the same)?
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Let's begin by listing out the given information:
total number of members = 75
printing charge = $2 per shirt
colour print for each shirt = $50 fee for each color to be printed on the shirts
Let the number of t-shirts be represented as n
Let the number of colors on the shirts be represented as x
Let the total cost of the order be represented as C
Every member must have a t-shirt means
total number of members * printing charge + (colour print for each shirt * number of colors on the shirts) = total cost of the order
75 * 2 + 50 * x = C
150 + 50x = C
C = 50x + 150
The number of colors on the shirts (x) can vary change; if the number of colors used increases, the cost of the order increases & if the number decreases, the cost of the order decreases
The printing company charges is fixed as every member is to get a shirt
which is in an equation of the line through (0,0) and (-8,-5)?
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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)
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]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?
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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.
Solve for y.2y^2 - 10y + 44=(y-7)^2If there is more than one solution, separate them with commas.
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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
A person’s car uses 4 gal of gasoline to travel 156 mi. He has 3 gal of gasoline in the car, and he wants to know how much more gasoline he will need to drive 300 mi. If we assume that the car continues to use gasoline at the same rate, how many more gallons will he need ?
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The gallons that the person needs more is 4.7 Gallons.
How to calculate the value?Since the person’s car uses 4 gal of gasoline to travel 156 miles, the mile.per gallon will be:
= 156 / 4
= 39 miles per gallon.
Therefore, to travel for 300 miles, the gallons needed will be:
= 300 / 39
= 7.7 gallons
He has 3 gallons, the gallons left will be:
= 7.7 - 3
= 4.7 Gallons
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Write a compound inequality for the graph shown below.Use x for your variable.++-10-9-8-7 -6 -5 4-3-2-1002 3 4 5 6 7 8 9 10 xDand口口>DorOSONO?X
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The question said we should write a compound inequality of the given graph.
We are also asked to use x as the variable.
From the graph, we can see that both end values are shaded dots, which means x is inclusive of those two values.
Since:
x ≥ -5
and
x ≤ 6
Therefore, the compound inequality of the given graph is:
-5 ≤ x ≤ 6.
I'll upload pictures
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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
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.
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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.
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?
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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
*Be sure to simplify fractions and rationalize denominators if necessary.
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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 isotope Sr-85 is used in bone scans. It has a half-life of 64.9 days. If you start with a10-mg Sample, how much would be remaining after 50 days? Round to the nearest hundredth.
Answers
The formula for the half life is as follows:
[tex]N(t)=N_0\mleft(\frac{1}{2}\mright)^{\frac{t}{(t_{_{_{1)}}}}}[/tex]where N(t) is the final amount, N₀ is the initial amount, t is the time that passed, and t2 is the half-life.
The following are the given values in the problem:
[tex]\begin{gathered} N_0=10 \\ t=50 \\ t2=64.9_{} \end{gathered}[/tex]Substitute the values into the equation.
[tex]N(50)=10\mleft(\frac{1}{2}\mright)^{\frac{50}{64.9}}[/tex]Simplify the right side of the equation. Divide 50 by 64.9 and then raise 1/2 by the obtained quotient. And finally, multiply the obtained value by 10.
[tex]\begin{gathered} N(50)\approx10\mleft(\frac{1}{2}\mright)^{0.7704160247} \\ \approx10(0.5862483959) \\ \approx5.862483959 \end{gathered}[/tex]Therefore, after 50 days, it will become approximately 5.86 mg.
2. Find the measure of ZRST.(5x – 4):R(8x + 4)ºST
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From the picture we notice that the angles R and Q are the same. Furthermore the interior angle S of the triangle is:
[tex]180-(8x+4)[/tex]Then we have the equation:
[tex]2(5x-4)+180-(8x+4)=180[/tex]Solving for x we have:
[tex]\begin{gathered} 10x-8-8x-4=0 \\ 2x-12=0 \\ x=6 \end{gathered}[/tex]Now we plug the value of x in the expression for the angle RST, then:
[tex]8(6)+4=52[/tex]Therefore the angle RST is 52°.
Which expression is equivalent to 3 (m + 2) – 6 (2m + 4)? 15m + 30 15m + 3 - 9m - 18 -9m + 30
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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 of the following sets is a finite set of rational numbers
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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.
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.
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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
what is the answer to 2(4y-2)=10
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The given equation is expressed as
2(4y-2)=10
Got a tutor to help but they got the answer wrong and I need help again!
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STATEMENT:
SOLUTION:
ANSWER:
Enter the ordered pair for the vertices for (90, (QRST).уQ-RoSRQ=R'=(S'=T=(
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Let P(h,k) be the coordinates of a point in the figure. When the figure is rotated 90 degree about the origin in clockwise direction, the new coordinates become P'(k,-h).
Therefore,
Q(1,3)--->Q'(3,-1)
R(3,-3)--->R'(3,-3)
S(0,2)---->S'(2,0)
T(-2,1)---->T'(1,2)
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.
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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.
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
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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]Line I is parallel to line m. If the measure of >6 is 75^ what is the measure of <4?
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The measure of <4 = 75°
Explanation:Note that:
• <4 and <6 are alternative interior angles
,• Alternative interior angles are equal
Therefore, based on the points given above:
m<4 = m<6 = 75° (Alternative interior angles are equal)
The measure of <4 = 75°
Given a function f(x)=|7-4x| ,find the objects with an image 11
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Given the function f(x) defined as:
[tex]f(x)=|7-4x|[/tex]If the image is 11, the corresponding objects (x-values) are:
[tex]\begin{gathered} |7-4x|=11 \\ 7-4x=11\ldots(1) \\ 7-4x=-11\ldots(2) \end{gathered}[/tex]Solving (1) to find the first object:
[tex]\begin{gathered} 7-4x=11 \\ 7-11=4x \\ -4=4x \\ x=-1 \end{gathered}[/tex]Now, we solve (2) to find the second object:
[tex]\begin{gathered} 7-4x=-11 \\ 7+11=4x \\ 18=4x \\ x=4.5 \end{gathered}[/tex]Answer: -1 and 4.5
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?
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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.
estimate the answer the amount of money rick spends on gasoline in a year if the average amount he spends per month is $140.87.chose the correct estimate below a: $16,800b:$168 c:2,520d: $1,680
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Given data:
The given amount of money spend in a month is $140.87.
The expression for the given statement is,
[tex]1\text{ month =\$140.87}[/tex]Multiply the above expression by 12 on both sides.
[tex]\begin{gathered} 12(1\text{ month))=12(\$140.87)} \\ 1\text{ year=\$1690.44} \end{gathered}[/tex]Thus, the amount Rick spends in a year is $1690.44.
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.
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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
Kim bought new shoes and used a 12% off coupon. The original cost of the shoe is represented as s. The total amount Kim paid for the shoes is represented as s-0.12s= s, which means that _______ of 12% is the same as ___
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The difference s - 0.12s is equal to 0.88s. So, the first blank has to be 0.88.
The second blank is "decrease", and the last one is "multiplying by 0.88" because the difference is actually equivalent to 0.88s.
A standard deck of cards has 52 cards. Suppose you decide to play a game using only half of a standard deck. If you draw one card at a time from the half-deck, without replacement, how many different ways can you draw all of the cards? Remember that "without replacement" means that the cards are not returned to the deck after they are chosen. Write your answer in factorial notation.
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We are asked to determine in how many ways we can draw all of the cards in half a deck. Since in a deck there are 52 cards, in half a deck there are:
[tex]n=\frac{52}{2}=26[/tex]The number of ways in which the cards can be drawn is equivalent to the number of permutations. And this is equivalent to:
[tex]P=n![/tex]Where "p" is the number of permutations and n! is the factorial of the number of cards in half a deck. Substituting the values we get:
[tex]P=26![/tex]Solving the operations:
[tex]P=403291461126605635584000000[/tex]Thus we determine the number of ways the cards can be drawn.
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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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