3x+4y-5z=8
1x+0y+2z=-3
4x-3y+0z=6
|`3 4 (-5)`||`x`| |`8`|
| 1 0 2 | |y |=|-3 |
|.4 (-3) 0 .||.z.| |.6.|
Express the following rate as a unit rate.
answering 36 questions in 3 minutes
18 questions per minute
12 questions per minute
15 questions per minute
36 questions per minute
The answer is 12 questions per minute as you divide 36 by 3
Answer=12 questions per minute
Answer:
12
Step-by-step explanation:
WHAT ARE THE ELEMENTS NEEDED TO PROVE SIMILARITY BETWEEN TWO FIGURES? EXPLAIN.
Answer:
AAA (Angle Angle Angle) Proving that the angles are the same (Or of the same ratio if diluted), if this is true, the two figures are similar.
SSS (Side Side Side) Proving all the sides are the same size (Or again of the same ratio) also proves similarity.
SAS (Side Angle Side) If two sides and the angle in between are the same, then the triangles are similar.
Step-by-step explanation:
EX)
Triangle A has sides 10, 5, and 12
Triangle B has sides 20, 10, and 24
The relationship is the same between both triangles, just that the sides are multiplied by 2. This is SSS
If Triangle A has two sides 5 and 10 with an angle of 25 degrees, then Triangle B must have that same angle alongside those two sides, or at least a consistent ratio if diluted. Proof SAS
If Triangle A and B have the same angles, they are similar.
Which is the most appropriate to describe a quantity decreasing at a steady rate
Which is the most appropriate to describe a quantity decreasing at a steady rate?
With a linear equation.
The monthly payment for a home loan is given by a function f(p,r,n)f(p,r,n) where pp is the principal (the initial size of the loan), rr the interest rate, and nn the length of the loan in months. interest rates are expressed as a decimal: a % interest rate is denoted by r=0.06r=0.06. if p=400000,r=0.06p=400000,r=0.06, and n=192n=192(a 16-year loan), then the monthly payment is f(400000,0.06,192)=1195f(400000,0.06,192)=1195. furthermore, with these values we have
a) The monthly payment increases by approximately $6.60 for a $1000 increase in the principal. b) The monthly payment increases by approximately $39.25 for an increase in the interest rate from 0.075 to 0.08. c) The monthly payment increases by approximately $32.81 for a decrease in the loan term from 26 years to 24 years.
To solve these problems, we'll use the partial derivatives of the monthly payment function with respect to the principal P, interest rate r, and the length of the loan in months N.
Given values:
- Principal P = 450,000
- Interest rate r = 0.075
- Loan term N = 312 (26 years)
- Monthly payment [tex]\( f(450000, 0.075, 312) = 1962 \)[/tex]
Partial derivatives:
- [tex]\(\frac{\partial f}{\partial P} = 0.0066 \)[/tex]
- [tex]\(\frac{\partial f}{\partial r} = 7849 \)[/tex]
- [tex]\(\frac{\partial f}{\partial N} = -1.3672 \)[/tex]
a) The change in monthly payment per 1000 increase in loan principal
The partial derivative [tex]\(\frac{\partial f}{\partial P}\)[/tex] tells us the rate of change of the monthly payment with respect to the principal. To find the change in the monthly payment for a $1000 increase in the principal:
[tex]\[\Delta f \approx \frac{\partial f}{\partial P} \cdot \Delta P\][/tex]
Here, [tex]\(\Delta P = 1000\):[/tex]
[tex]\[\Delta f \approx 0.0066 \cdot 1000 = 6.6\][/tex]
So, the monthly payment increases by approximately $6.60 for a $1000 increase in the principal.
b) The change in monthly payment if the interest rate changes from [tex]\( r = 0.075 \) to \( r = 0.08 \)[/tex]
The partial derivative [tex]\(\frac{\partial f}{\partial r}\)[/tex] tells us the rate of change of the monthly payment with respect to the interest rate. To find the change in the monthly payment for a change in the interest rate from 0.075 to 0.08, we calculate the difference in the rates:
[tex]\[\Delta r = 0.08 - 0.075 = 0.005\][/tex]
Then, using the partial derivative:
[tex]\[\Delta f \approx \frac{\partial f}{\partial r} \cdot \Delta r\][/tex]
[tex]\[\Delta f \approx 7849 \cdot 0.005 = 39.245\][/tex]
So, the monthly payment increases by approximately $39.25 for an increase in the interest rate from 0.075 to 0.08.
c) The change in monthly payment if the length of the loan changes from 26 to 24 years
The partial derivative [tex]\(\frac{\partial f}{\partial N}\)[/tex] tells us the rate of change of the monthly payment with respect to the length of the loan in months. To find the change in the monthly payment for a change in the loan term from 26 years (312 months) to 24 years (288 months), we calculate the difference in months:
[tex]\[\Delta N = 288 - 312 = -24\][/tex]
Then, using the partial derivative:
[tex]\[\Delta f \approx \frac{\partial f}{\partial N} \cdot \Delta N\][/tex]
[tex]\[\Delta f \approx -1.3672 \cdot (-24) = 32.8128\][/tex]
So, the monthly payment increases by approximately $32.81 for a decrease in the loan term from 26 years to 24 years.
The complete question is
The monthly payment for a home loan is given by a function f(P, r, N) where P is the principal (the initial size of the loan), r the interest rate, and N is the length of the loan in months. Interest rates are expressed as a decimal: A% interest rate is denoted by r = 0.075. If P = 450000, r = 0.075 and N = 312 (a 26-year loan), then the monthly payment is f(450000, 0.075, 312) = 1962. Furthermore, with these values we have
[tex]\frac{\partial f}{\partial P}=0.0066, \quad \frac{\partial f}{\partial r}=7849, \quad \frac{\partial f}{\partial N}=-1.3672[/tex]
Estimate
a) The change in monthly payment per 1000 increase in loan principal.
b) The change in monthly payment if the interest rate changes from r = 0.075 to r = 0.08
c) The change in monthly payment if the length of the loan changes from 26 to 24 years.
1.
Use technology or a z-score table to answer the question.
The expression P(z<1.45) represents the area under the standard normal curve below the given value of z.
What is P(z<1.45)?
0.0735
0.0749
0.9251
0.9265
2.Use technology or a z-score table to answer the question.
The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 60. Jake scored 520 on the test.
What percent of students scored below Jake?
Round your answer to the nearest whole number.
33%
57%
63%
72%
3.Use technology or a z-score table to answer the question.
Lengths of newborn girls are normally distributed with a mean of 49.2 cm and a standard deviation of 1.8 cm. Consider a group of 2000 newborn girls.
Approximately how many girls will be 51 cm or shorter?
1683
1856
1928
1964
4.The number 0.9967 represents the area under the standard normal curve below a particular z-score.
What is the z-score?
Enter your answer, as a decimal to the nearest hundredth, in the box.
5.Use technology or a z-distribution table to find the indicated area.
Suppose ages of cars driven by company employees are normally distributed with a mean of 8 years and a standard deviation of 3.2 years.
Approximately 75% of cars driven by company employees are older than what age?
2.1
4.8
5.9
10.2
Answer:
1.) 0.9265
2.) 63%
3.) 1683
4.) 5.9
I hope this helped and give me brainiest please
Answer:
Step-by-step explanation:
1) From standard distribution table we find that
P(Z<1.45) = 0.5+0.4265
=0.9265 Option d
2) Given that X, The scores on a standardized test is N(500,60)
percent of students who scored below Jake
[tex]=100*P(X<520)\\=100*P(Z<\frac{20}{60} )\\=100(0.5+0.1293)\\=62.93%\\=63%[/tex]
3) X, lengths of new born girls is N(49.2, 1.8)
n = 2000
P(X<51) = P(Z<1) =0.84
No of girls =2000(0.84) =1683
4) P(Z<2.72) is the answer
5)X, ages of cars driven is N(8,3.2)
75% correspond to z=0.675
X = 8+0.675(3.2) =10.16=10.2
The points A, B, C, and D are taken in order on the circumference of a circle. Chords AC and BD intersect at point E. mABarc = 76° and mCDarc = 80°. Draw chord AD. Find m∠AEB.
Answer:
∠AEB = 78°see attached for a drawingStep-by-step explanation:
The angle where the chords cross is the average of the two intercepted arcs:
∠AEB = (∠AOB +∠COD)/2 = (76° +80°)/2 = 78°
___
Chord AD connects points A and D.
A grocery store has 12 cartons of yogurt for sale, of which 3 are raspberry what is the probability that a randomly selected carton of yogurt will be raspberry?
a) 1/2,
b) 1/4,
c) 1/3
d) 4/5
Answer:
Your answer would be 1/4
Step-by-step explanation:
The probability that a randomly selected carton of yoghurt will be raspberry is 1/4. The correct option is b.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that a grocery store has 12 cartons of yoghurt for sale, of which 3 are raspberry.
The probability that a randomly selected carton of yogurt will be,
Probability = Number of favourable outcomes / Number of sample
Probability = 3 / 12
Probability = 1 / 4
Therefore, the probability that a randomly selected carton of yoghurt will be raspberry is 1/4. The correct option is b.
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Match the following items by evaluating the expression for x = -6.
x^-2
x^-1
x^0
x^1
x^2
Choices:
1/36
-6
36
1
-1/6
x^-2 matches 1/36
x^-1 matches -1/6
x^0 matches 1
x^1 matches -6
x^2 matches 36
Explanation:When evaluating expressions with exponents for a specific value, we simply substitute that value for x and follow the order of operations (PEMDAS). Here's the breakdown for each expression:
x^-2: (-6)^-2 = 1/(-6)^2 = 1/36
x^-1: (-6)^-1 = 1/(-6) = -1/6
x^0: (-6)^0 = 1 (any non-zero number raised to the power 0 equals 1)
x^1: (-6)^1 = -6 (any non-zero number raised to the power 1 equals itself)
x^2: (-6)^2 = (-6) * (-6) = 36
Therefore, the matches are as listed above.
a thermometer read -17° f at 1:00 am. by 2:30 am the temperature has dropped 9.1 degree f. what was the temperature at 2:30 am?
Answer:
The temperature was -26.1° f at 2:30 am.
Step-by-step explanation:
* In this type of problems, we must think about
- What is the meaning of wards;
above and below or
raised and dropped or
increased and decreased
- For above , raised , increase
we will add the value of them to the initial value
- For below , dropped , decreased
we will subtract the value of them from the initial value
* In our problem:
- The reading of thermometer is -17° f at 1:00 am.
- The temperature has dropped 9.1° f when the time was 2:30 am.
* Lets use the explanation above
- We will subtract 9.1 from -17
∴ -17 - 9.1 = -26.1° f
* The temperature was -26.1° f at 2:30 am.
Final answer:
To find the temperature at 2:30 am, you subtract the temperature drop of 9.1°F from the initial temperature of -17°F, resulting in a new temperature of -26.1°F.
Explanation:
If a thermometer read -17°F at 1:00 am and by 2:30 am the temperature has dropped by 9.1 degrees Fahrenheit, we calculate the new temperature by simply subtracting the temperature drop from the initial temperature. Subtracting a negative change from the current temperature results in an even lower temperature because you are going further down the scale.
Here's the calculation:
Initial temperature at 1:00 am: -17°F
Temperature drop by 2:30 am: 9.1°F
New temperature at 2:30 am: -17°F - 9.1°F = -26.1°F
Our goal is to make add-on sales during 85% of sales. If you make 35 sales, how many add-on sales do.You need to make to meet the goal?
Answer:
30 add-on sales to make the goal
Step-by-step explanation:
multiply 35*85% (or 0.85)
35*0.85 = 29.75
Since you can't make 0.75 of a goal, round up to the next highest number = 30
The scale on a map is 1: 25 000. How many kilometers on the ground is represented by 9 cm on the map?X
1 cm : 25000 cm
Convert 25000cm to km = 1cm : 0.25 km9cm = 9 x 0.25 km9cm = 2.25 kmOn a map with a scale of 1:25,000, 9 cm represents 225,000 km on the ground.
Explanation:To find how many kilometers on the ground is represented by 9 cm on the map, we can use the scale given. The scale is 1:25,000, which means that 1 cm on the map represents 25,000 cm on the ground. Since we want to find the number of kilometers, we need to convert the units. 1 km is equal to 100,000 cm. So we can set up the proportion: 1 cm (on the map) / 25,000 cm (on the ground) = 9 cm (on the map) / x km (on the ground). Cross multiplying, we get 1 * x km = 25,000 * 9 cm. Solving for x, we find that x = 225,000 km.
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At a school 141 students play at least one sport. This is 30% of students at that school. How many students are at the school
Answer:
There are 470 students at the school.
Step-by-step explanation:
141 / x = 3 / 10 since 3/10 is equal to 30% you're looking for a denominator that corresponds equally to 141 and when simplified, 141 / x equals 3 / 10.
Use algebra to solve: 141 * 10 = 3x → 1410 = 3x → 470 = x.
Final answer:
There are 470 students at the school.
Explanation:
In the given question, we are dealing with a basic percentage problem. We are told that 141 students, which is 30% of all students at the school, are playing at least one sport. To find the total number of students in the school, we need to solve for the whole when a part and its percentage are known.
Let x represent the total number of students at the school. According to the question:
30% of x = 141 students
We can set up the equation:
0.30 * x = 141
To find x, we'll divide both sides of the equation by 0.30:
x = 141 / 0.30
Performing the division gives us:
x = 470
Therefore, there are 470 students at the school.
Find the circumference of a cercle with the radious of 5.5 in. Use 3.14 for n round the nerest tenth
Answer:
34.54 in
Step-by-step explanation:
c = 2π r
c = 2 (3.14)(5.5)
c = 34.54 in
What is the are of a triangle (picture provided)
Answer:
Area Δ = 102.3 units² ⇒ The answer is (d)
Step-by-step explanation:
* Use the formula of the area:
∵ Area of the triangle = 1/2 (a)(b) sin(C)
∵ We have the length of the 3 sides
∴ Use cos Rule to find the angle C
∵ cos(C) = (a² + b² - c²)/2ab
∵ a = 25 , b = 13 , c = 17
∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650
∴ m∠C = 39°
∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²
∴ The answer is (d)
Answer:
Area Δ = 102.3 units² ⇒ The answer is (d)
Step-by-step explanation:
Use the formula of the area:
∵ Area of the triangle = 1/2 (a)(b) sin(C)
∵ We have the length of the 3 sides
∴ Use cos Rule to find the angle C
∵ cos(C) = (a² + b² - c²)/2ab
∵ a = 25 , b = 13 , c = 17
∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650
∴ m∠C = 39°
∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²
∴ The answer is (d)
A car travels 2 5/8 miles in 3 1/2 minutes at a constant speed. Which equation represents the distance, d, that the car travels in m minutes?
Answer:
[tex]d=0.75m[/tex]
Step-by-step explanation:
Let
d------> the distance in miles
m----> the time in minutes
we know that
The speed is equal to divide the distance by the time
so
[tex]speed=d/m[/tex]
we have
[tex]d=2\frac{5}{8}\ miles=\frac{2*8+5}{8}=\frac{21}{8}\ miles[/tex]
[tex]m=3\frac{1}{2}\ minutes=\frac{3*2+1}{2}=\frac{7}{2}\ minutes[/tex]
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
so
In this problem the speed is the constant of proportionality
[tex]d=km[/tex]
Find the value of k
[tex]k=\frac{(21/8)}{(7/2)} =0.75\frac{miles}{minute}[/tex]
[tex]d=0.75m[/tex] ----> linear equation that represent the distance, d, that the car travels in m minutes
Plz help me
When graphed, which function has a horizontal asymptote at 4?
A.f(x)=2x-4
B.f(x)=2(3^x)+4
C.f(x)=-3x+4
D.f(x)=3(2^x)-4
Answer:
It is B.
Step-by-step explanation:
f(x) = 2(3^x) + 4
As x approaches negative infinity 2(3^x) approaches zero and f(x) approaches 4.
Answer:
B.[tex]f(x)=2(3^x)+4[/tex]
Step-by-step explanation:
We have to find that which graph has horizontal asymptote at 4
We know that to find the horizontal asymptote , we simply evaluate the limit of the function as it approaches to infinity or it approaches to negative infinity.
A.[tex]f(x)=2x-4[/tex]
[tex]\lim_{x\rightarrow \infty}(2x-4)=\infty[/tex]
[tex]\lim_{x\rightarrow -\infty}(2x-4)=-\infty[/tex]
Limit of function does not exits, so function have not horizontal asymptote.
B.[tex]f(x)=2(3^x)+4[/tex]
[tex]\lim_{x\rightarrow \infty}(2(3^x)+4)=\infty[/tex]
[tex]3^{\infty}=\infty [/tex]
[tex]\lim_{x\rightarrow -\infty}(2(3^x)+4)=4[/tex]
Because [tex]3^{-\infty}=0[/tex]
Hence, function have horizontal asymptote at 4.
C.[tex]f(x)=-3x+4[/tex]
[tex]\lim_{x\rightarrow \infty}(-3x+4)=\infty[/tex]
[tex]\lim_{x\rightarrow -\infty}(-3x+4)=-\infty[/tex]
Hence, function have not horizontal asymptote.
D.[tex]f(x)=3(2^x)-4[/tex]
[tex]\lim_{x\rightarrow \infty}(3(2^x)-4)=\infty[/tex]
Because [tex]2^{\infty}=\infty[/tex]
[tex]\lim_{x\rightarrow -\infty}(3(2^x)-4)=-4[/tex]
[tex]2^{-\infty}=0[/tex]
Hence, function have horizontal asymptote at -4.
Therefore, option B is true.
What is SIN A?
Question 4 options:
3/4
4/3
3/5
4/5
Final answer:
The value of sin A cannot be determined without knowing the value of angle A.
Explanation:
The question is asking for the value of sin A. In mathematics, sin A represents the sine of angle A. The sine function is a mathematical function that relates the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right triangle.
The correct answer to the question is 3/5. To find this value, you need to know the value of angle A. Without that information, we cannot determine the exact value of sin A.
Final answer:
The correct value of SIN A from the given options cannot be determined without additional context. SIN A refers to the ratio of the side opposite to angle 'A' to the hypotenuse in a right triangle or the y-coordinate on the unit circle at angle 'A'. Possible values are within the range of -1 to 1.
Explanation:
The question 'What is SIN A?' is seeking the trigonometric value of the sine function at a particular angle denoted by 'A'. When presented with options like 3/4, 4/3, 3/5, and 4/5, we need additional information regarding angle 'A' or the context of a right triangle or unit circle to determine the correct value. Without this information, we cannot definitively answer which option is correct.
Generally, in a right triangle, SIN A would represent the ratio of the length of the side opposite to angle 'A' to the length of the hypotenuse. Therefore, it is a value between -1 and 1. The options 3/4 and 3/5 could potentially be correct since they are within this range, but 4/3 cannot be because it exceeds this range. In a unit circle context, sin A would represent the y-coordinate of a point on the circle's circumference at an angle 'A' from the x-axis.
Find the length of '' c '' using the pythagorean theorem. A triangle has a height of 5, and length of 12
Answer: 13
Step-by-step explanation:
[tex]5^{2} + 12^{2} = c^{2} \\25 +144= c^{2} \\\sqrt169= \sqrt c^{2} \\13=c[/tex]
Find the length of the arc shown in brown. Leave your answer in terms of pi.
Answer:
The length of the arc is [tex]8\pi\ ft[/tex]
Step-by-step explanation:
we know that
The measure of the arc shown in brown is equal to
[tex]180\°-60\°=120\°[/tex] -----> by central angle
Remember that
The length of the arc of the complete circle (360 degrees) is equal to the circumference
[tex]C=\pi D[/tex]
we have
[tex]D=24\ ft[/tex]
substitute
[tex]C=\pi (24)=24 \pi\ ft[/tex]
so
by proportion
Find the length of the arc for a measure of [tex]120\°[/tex]
[tex]\frac{24\pi }{360} \frac{ft}{degrees} =\frac{x }{120} \frac{ft}{degrees}\\ \\x=120*(24\pi )/360\\ \\ x= 8\pi\ ft[/tex]
the library is 5miles from the post office how many is the yards is the library from the post office
1 mile =1760 yd so 5 miles to the library=8800 yd yards hope this helps
Angle 3 and angle 4 are supplementary angles. Angle 3 is 88°. What is the measure of angle 4?
1. You do 180-88 because supplementary angles add up to 180°.
2. 180-88=92°. Angle 4 is 92°
Answer:
92 degrees
Step-by-step explanation:
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Select the correct answer from each drop-down menu. ∆ABC has A(-3, 6), B(2, 1), and C(9, 5) as its vertices. The length of side AB is units. The length of side BC is units. The length of side AC is units. ∠ABC ≈ °.
Answer:
√50
√65
√145
105 °
Step-by-step explanation:
Given the coordinates
A(-3, 6)
B(2, 1)
C(9, 5)
To find the length of AB ,AC and BC, we will use distance formula
√((x2-x1)² + (y2-y1)²)AB:
√(2+3)² + (1-6)²
√5²+5²
√50
BC:
√(9-2)² + (5-1)²
√7² + 4²
√49+16
√65
AC:
√(9+3)² + (5-6)²
√12²+1²
√145
To find ∠ABC
cos(B) = c² + a² − b² / 2ca
= 65 + 50 - 145 / 2(√65)(√50)
cosB = -0.26311
B = cos^-1(-0.26311)
= 105 °
Answer:
√50
√65
√145
105 °
Step-by-step explanation:
V^2-8v=0 solving quadratic equation
Answer:
v = 0, or v = 8
Step-by-step explanation:
The quadratic can be factored, then the zero product rule applied.
v^2 -8v = 0
v(v -8) = 0
A product will be zero when any of the factors is zero. So, the solutions are values of v that make the factors be zero.
v = 0
v -8 = 0 . . . ⇒ . . . v = 8
Anita earns 60 points every time she shops at a grocery store.She needs a total of 2,580 points to receive a free prize.So far she has earned 480 points.How many more times will Anita have to shop at the grocery store in order to earn the additional points she needs for a prize?
Answer: 43 more times
2580÷60=43.
Step-by-step explanation: 43×60 =2580
This proves that 43 times is correct.
Answer:
c 43
Step-by-step explanation:
A non toxic furniture polish can be made by combining vinegar and oil. The amount of oil should be five times the amount of vinegar. How much of each ingredient is needed in order to make 27 oz of furniture polish?
There should be 4.5 oz of vinegar and 22.5 oz of oil
-5x+y=0
x+y=27
-6x=-27
Which statement about function F and Function G is true?
Answer:
C. Both functions have a y-intercept of -2
Step-by-step explanation:
A. Function F in decreasing then increasing, therefore it's incorrect
B. Function F is symmetrical about the y-axis, but Function G is not
C. Both functions intercept the y-axis at (0,-2) so it's correct
D. Only function G shows a linear relationship.
To look at a picture of what Function G looks like. Press y= on your Ti-84 calculator (top left) put the function in, and then press graph (top right)
This is 100% correct. I took algebra 1 last year.
Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli department at least 260260260 person-hours per week. Tom has one part-time employee who works 202020 hours per week. Each full-time employee works 404040 hours per week. Write an inequality to determine nnn, the number of full-time employees Tom must schedule, so that his employees will work at least 260260260 person-hours per week.
Answer:
6
Step-by-step explanation:
260=20+40n
subtract 20
240=40n
divide by 40
n=6
Find the value of X. Round to the nearest 10th. diagram not to scale. (Image attached)
Will give BRAINLIEST to the first to answer correctly and please show your work :)
Answer: [tex]x=10.2[/tex]
Step-by-step explanation:
The triangle shown in the image attached is a right triangle.
Therefore, you can calculate the value of x as you can see below:
[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]
In this case, you have that:
adjacent=x
hypotenuse=11
[tex]\alpha=22\°[/tex]
Therefore, when you substitute values and solve for x, you obtain the following result:
[tex]cos(22\°)=\frac{x}{11}\\\\x=11*cos(22\°)\\x=10.2[/tex]
Answer:
The value of x = 10.2
Step-by-step explanation:
From the figure we can see a right angled triangle. One side and one angle are given.We have to find one side of triangle.
Points to remember
Cos θ = Adjacent side/Hypotenuse
To find the value of x
Here θ = 22°, Hypotenuse = 11, Adjacent side =?
Cos 22 = Adjacent side/Hypotenuse = x/11
x = 11 * Cos 22 = 11 * 0.9271 = 10.2 units
rewrite the following equation in exponential form. log^5 25=2
logb(x) = y is equivalent to b^y =x
y = 2
b = 5
x = 25
Substitute the values to get 5^2 = 25
You are standing 50 meters from a hot air balloon that is preparing to take off. The angle of the elevation to the top of the balloon is 28. Find the height of the balloon
Answer:
27 meters
Step-by-step explanation:
Think of it like a right triangle. One leg is 50m long (the distance you are from the balloon) and the goal is to find the other leg of the triangle. From the place you're standing, the angle is 28°. In relation to that angle, you're given the adjacent side (50m) and need to find the opposite side. Recall SOH-CAH-TOA. You have to use tangent to get the length. Tan = opposite/adjacent. The tan of 28 = x / 50. Use algebra to solve: tan28 (50) = x; aproximately 26.6m = x. So, the height of the hot air balloon is roughly 26.6m or 27m depending on how you round.