Answer:
Step-by-step explanation:
sin=y/r
cos=x/r
sin=21/29
cos=x/29
x^2+y^2=r^2
x^2+21^2=29^2
x^2+441=841
x=sqrt(841-441)
x=20
cos=20/29
Only |
sin + | All Positive
---------------------|-------------------
only | Only cos +
tan + |
Answer:
C
Step-by-step explanation:
Using the trigonometric identity
sin²x + cos²x = 1 ⇒ cosx = ± [tex]\sqrt{1-sin^2x}[/tex]
Given
sinx = [tex]\frac{21}{29}[/tex], then
cosx = [tex]\sqrt{1-(\frac{21}{29})^2 }[/tex] ( positive since 0 < x < 90 )
= [tex]\sqrt{1-\frac{441}{841} }[/tex]
= [tex]\sqrt{\frac{400}{841} }[/tex] = [tex]\frac{20}{29}[/tex]
8. A right cone has a volume of 8,579 m3 and a radius of 16 m. Find its altitude.
A. 32.0 m
B. 27.6 m
C. 2.7 m
D. 64.2 m
Answer:
Option A is correct.
Step-by-step explanation:
The formula used for finding the volume of right cone is:
Volume of Right cone = (1/3)π.r².h
We need to find altitude i.e h
Volume of cone=V = 8579 m^3
Radius=r = 16m
Altitude =h =?
Putting values,
8579 = (1/3) * 3.14 * (16)^2*h
8579 = 1/3 * 3.14 * 256 *h
8579 = 267.95 * h
=> h = 8579/267.95
h = 32.0 m
So, Altitude of right cone is 32.0 m
Option A is correct.
What is the order of rotational symmetry for the figure
Answer:
Order of symmetry = 1
Step-by-step explanation:
First of all we will define rotational symmetry.
Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.
The order of rotational symmetry is how many times it matches the original shape during the rotation.
The given shape, when rotated will only have the shape like original shape after one complete rotation so the order of symmetry is one ..
What is the solution to the equation 9-3x = 7?
Answer:
x = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given
9 - 3x = 7 ( subtract 9 from both sides )
- 3x = - 2 (divide both sides by - 3 )
x = [tex]\frac{-2}{-3}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\huge{\boxed{x=\frac{2}{3}}}[/tex]
Add [tex]3x[/tex] on both sides. [tex]9=7+3x[/tex]
Subtract 7 from both sides. [tex]2=3x[/tex]
Divide both sides by 3. [tex]\boxed{\frac{2}{3}}=x[/tex]
Jorie leaves work 30 minutes late. She decides to make up time by taking the toll road instead of side streets. She can travel four times faster by taking the toll road. Create an equation to represent her total travel time, including wait time, where x is the number of minutes the drive was expected to take.
A. y = \frac{1}{4}x -30
B. y = 4x - 30
C. y = \frac{1}{4}x + 30
D. y = 4x + 30
Answer:
OPTION C
Step-by-step explanation:
We know that the toll road is 4 times faster than the side streets.
If 'x' represents the number of minutes she usually spend taking the side streets. The [tex]\frac{1}{4} x[/tex] represents the time she takes taking the toll road.
Also we need to create an equation to represent her total travel time, including wait time. Therefore, the equation is:
[tex]y = \frac{1}{4}x + 30[/tex]
Therefore, the correct solution is the OPTION C.
Answer:
c
Step-by-step explanation:
took the test but give the other guy brainliest he deserves it
Keri and his friends are on their way to visit some family friends who lives 1050 miles away from them.based on the route they shoes they expect to complete their trip in three days. The distance and average speeds for the first two days driven are shown below:
First day : 5 hours at an average speed of 70 miles per hour
Second day: 7 hours at an average an average speed of 65 miles per hour
If the average speed on the third day is 70 miles per hour how many more hours will it take for them to reach their friends home
Answer:
3.5 hours
Step-by-step explanation:
5 x 70 = 350
7 x 65 = 455
350 + 455 = 805
1050 - 805 = 245
245/ 70 = 3.5
They will take an additional 3.5 hours on the third day to reach their destination.
Explanation of the distance covered in the first two days and how much more time it will take on the third day to reach their destination.
The distance covered in the first two days can be calculated using the formula:
Distance = Speed x Time
First day: 5 hours x 70 mph = 350 milesSecond day: 7 hours x 65 mph = 455 milesTherefore, after the first two days, they have covered a total distance of 350 + 455 = 805 miles. They have 1050 - 805 = 245 miles left to travel.
On the third day, at an average speed of 70 mph, they will cover the remaining 245 miles. Therefore, the time it will take for them to reach their friends' home on the third day is:
Time = Distance / Speed = 245 miles / 70 mph = 3.5 hours
They will take an additional 3.5 hours on the third day to reach their destination.
What is the value of p?
Answer:
D. 35 degrees.
Step-by-step explanation:
125 = p + 90 (by the external Angle of a Triangle theorem).
p = 125 - 90
p = 35 degrees (answer).
Answer:
35 degrees
Step-by-step explanation:
Ok so that angle that has the 125 degree is adjacent to an angle inside the triangle. These adjacent angles are actually supplementary because they are formed by a straight-edge. So the angle inside adjacent to the 125 degree angle is 180-125=55 degrees.
Same logic applies to angle adjacent to the 90 degree angle. The angle adjacent to the 90 degree angle is also supplementary to the 90 degree angle. So 180-90=90 degrees for the other inside angle next to the 90 degree angle.
So the figure formed here is a triangle. The angles in this triangle should add up to be 180 degrees. So we have the equation 90+55+p=180.
Let's solve this by first simplifying the 90+55 part!
145+p=180
Subtract 145 on both sides:
p=180-145
Simplify.
p= 35 degrees
if you lose 3 1/2 pounds the first week of your diet and 2 2/3 pounds the second week, how many pounds do you still need to lose to reach your goal of losing 10 pounds?
Answer:
3 5/6
Step-by-step explanation:
3 1/2 plus 2 2/3 equals 6 1/6. 10 minus 6 1/6 equals 3 5/6. So they still need to lose 3 5/6 pounds to reach their go of losing 10 pounds.
let's firstly convert the mixed fractions to improper fractions, and then subtract.
[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{goal}}{10}-\stackrel{\textit{first week}}{\cfrac{7}{2}}-\stackrel{\textit{second week}}{\cfrac{8}{3}}\implies \cfrac{10}{1}-\cfrac{7}{2}-\cfrac{8}{3}\implies \stackrel{\textit{using an LCD of 6}}{\cfrac{(6)10-(3)7-(2)8}{6}} \\\\\\ \cfrac{60-21-16}{6}\implies \cfrac{23}{6}\implies 3\frac{5}{6}[/tex]
On a quiz worth 5 points, eight students earned a 5, two students earned a 4, five students earned a 3, six students earned a 2, five students earned a 1, and zero students earned a zero. Find the class average on this quiz.
Express your answer rounded to the tenths place.
Answer:
Step-by-step explanation:
[tex]\frac{8(5)+2(4)+5(3)+6(2)+5(1)}{26}[/tex]
Now we simplify:
[tex]\frac{80}{26}[/tex]
[tex]\frac{40}{13}[/tex]
Now we divide:
[tex]3.1[/tex]
A high school coach needs to buy new athletic shorts for the 15 members of the basketball team. The coach must spend less than $200 and needs to determine how much he can spend per pair of shorts. Write and solve an inequality to determine the maximum price for each pair of shorts. What does the solution represent?
Answer:
15x < 200; x < 13.33; the maximum price for a pair of shorts
Step-by-step explanation:
1. Set up the inequality
Let x = price of a pair of shorts. Then
15x = price of shorts for the team
You have one condition:
15x < 200
2. Solve the inequality
[tex]\begin{array}{rcl}15x & < & 200\\\\x & < & \dfrac{200}{15}\\\\x & < & \mathbf{13.333}\\\end{array}[/tex]
3. Meaning of solution
The solution represents the maximum price the coach can pay for a pair of shorts.
If the coach pays $13.33 per pair, the total cost for the team will be $199.95, and the condition is satisfied.
Answer: The coach may spend up to $13.33 per pair of shorts.
Step-by-step explanation:
Hi, to answer this question we have to write an inequality with the information given:
Number of shorts: 15 (for 15 members) Budget: $200So, we have to multiply the number of shorts by the price of each one, we will represent the price with the variable "x".(15x)
That cost must be equal or less to 200.
Mathematically speaking
15 x ≤ 200
Solving for x
x ≤200/15
x ≤ 13.33
This solution represents that the coach may spend up to $13.33 per pair of shorts.
Feel free to ask for more if needed or if you did not understand something.
A number cube has 6 faces, numbered from 1 to 6. If the cube
is rolled six times, what is the probability that a face with a 6
comes up exactly once?
[tex]|\Omega|=6^6\\|A|=6\cdot 5^5\\\\P(A)=\dfrac{6\cdot5^5}{6^6}=\dfrac{5^5}{6^5}=\dfrac{3125}{7776}\approx40.2\%[/tex]
The probability that a face with a 6 comes up exactly once will be 0.40.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
A number cube has 6 faces, numbered from 1 to 6.
If the cube is rolled six times.
Then the probability that a face with a 6 comes up exactly once will be
The total number of the event will be
Total event = 6⁶
Total event = 46656
Favorable event = 6 x 5⁵
Favorable event = 18750
Then the probability will be
P = 18750 / 46656
P = 3125 / 7776
P = 0.40
More about the probability link is given below.
https://brainly.com/question/795909
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If a rectangle's length is y−2 and the width is 3y+2 write an expression for the perimeter and an expression for the area.
Answer:
Area = [tex]3y^2 - 4y - 4[/tex] units square.
Perimeter = 8y units.
Step-by-step explanation:
Area of a rectangle = length * width.
Perimeter of a rectangle = 2*(length + width).
It is given that length = y−2 units and width = 3y+2 units. To find the area and the area of the rectangle in terms of y, simply put the length and the width in the above area and perimeter equations.
Area = length * width = (y-2)*(3y+2).
Expanding the expression gives:
Area = 3y^2 + 2y - 6y - 4 = (3y^2 -4y - 4) units square.
Similarly,
Perimeter = 2*(length + width) = 2*(y-2 + 3y+2) = 2*4y = 8y units.
Therefore, the expression for the area and the perimeter of the given rectangle is ([tex]3y^2 - 4y - 4[/tex]) units square and (8y) units respectively!!!
Find the value of y for the following system of equations. -x - y = 7 x - y = 9
Answer:
y = -8
Step-by-step explanation:
It is given that,
-x - y = 7 ---(1)
x - y = 9 ---(2)
To find the solution
Add eq (1) and eq(2) we get
-x - y = 7 ---(1)
x - y = 9 ---(2)
0 - 2y = 16
y = 16/(-2) = -8
Substitute the value of y in eq(1)
-x - y = 7 ---(1)
-x - -8 = 7
-x + 8 = 7
x = 8 - 7 = 1
Therefore x = 1 and y = -8
Lucy Furr must supply 2 different bags of chips for a party. She finds 10 varieties at her local grocer. How many different selections can she make?
Answer:
she can make 50 different selections!
Step-by-step explanation:
To find the different selections that can be made, we use the formula:
nCr = n! / r! * (n - r)!. Where 'n' represents the number of items available and 'r' represents the nuber of items being chosen
In this case:
'n' equals 10 and 'r' equals 2. Therefore:
[tex]10C_{2} = \frac{10!}{2!(10-2)!} = \frac{10!}{2!8!} = \frac{90}{2} =50[/tex]
So she can make 50 different selections!
Answer: 45
Step-by-step explanation:
The combination of n things taking r at a time is given by :-
[tex]C(n;r)=\dfrac{n!}{(n-r)!}[/tex]
Given : Lucy Furr must supply 2 different bags of chips for a party.
She finds 10 varieties at her local grocer.
Then the number of different selections she can make is given by :-
[tex]C(10;2)=\dfrac{10!}{2!(10-2)!}\\\\=\dfrac{10\times9\times8!}{2\times8!}=\dfrac{90}{2}=45[/tex]
Hence, the number of different selections she can make= 45
Here is the histogram of a data distribution.
Which best describes the shape of this distribution?
Answer:
B. Unimodal-Skewed
Step-by-step explanation:
A distribution is called unimodal if it has only one hump in the histogram.
A symmetric distribution is equally divided on both sides of the highest hump.
The given histogram has only one hump at 4 and as it is not symmetrically distributed, it is skewed.
So the correct answer is:
B. Unimodal-Skewed ..
Answer:
B. Unimodal Skewed
Step-by-step explanation:
The Histogram given in figure has one peak and it is skewed to the right So, it is Right Skewed Unimodal Histogram.
Moreover, Unimodal means the distribution has one peak, Skewed means this peak is present in either the left or right side of the center of the distribution.
Option A is incorrect because the given histogram is not symmetric, it is skewed distribution.
Option C can't be taken because uniform means the size of bars is approximately same for the given distribution.
Options D & E is not correct because the given distribution is not Bimodal it has only one peak.
Derive the equation of the parabola with a focus at (−5, −5) and a directrix of y = 7.
f(x) = −one twenty fourth(x − 1)2 − 5
f(x) = one twenty fourth(x − 1)2 − 5
f(x) = −one twenty fourth(x + 5)2 + 1
f(x) = one twenty fourth(x + 5)2 + 1
Answer:
[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]
Explanation
The directrix y=7, is above the y-value of the focus. The parabola must will open downwards.
Such parabola has equation of the form,
[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]
where (h,k) is the vertex.
The vertex is the midway from the focus to the directrix
The x-value of the vertex is x=-5 because it is on a vertical line that goes through (-5,-5).
The y-value of the vertex is
[tex]y = \frac{ 7 + - 5}{2} [/tex]
[tex]y = \frac{ 2}{2} = 1[/tex]
The equation of the parabola now becomes
[tex]{(x + 5)}^{2} = - 4p(y - 1)[/tex]
p is the distance from the focus to the vertex which is p=|7-1|=6
Substitute the value of p to get:
[tex]{(x + 5)}^{2} = - 4 \times 6(y - 1)[/tex]
[tex]{(x + 5)}^{2} = - 24(y - 1)[/tex]
We solve for y to get:
[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]
Answer:
f(x) = −one twentyfourth (x + 5)2 + 1
Step-by-step explanation:
Petro was given this system of equations.
-14x-2y = 24
14x+8y = -12
Petro’s work is shown in the table. Where, if anywhere, did Petro first make a mistake?
-
A) step 1
B) step 2
C) step 3
D) no mistake
Answer:
Option C step 3
Step-by-step explanation:
we have
-14x-2y=24 ------> equation A
14x+8y=-12 -----> equation B
step 1
Solve the system by elimination
Adds equation A and equation B
-14x-2y=24
14x+8y=-12
---------------------
-2y+8y=24-12
6y=12
The step 1 is correct
step 2
Solve for y
Divide by 6 both sides
6y/6=12/6
y=2
The step 2 is correct
step 3
Find the value of x
substitute the value of y in the equation A
-14x-2(2)=24
-14x-4=24
14x=-4-24
14x=-28
x=-2
The step 3 is not correct
therefore
Petro first make a mistake in Step 3
Answer:
Step 3 in the correct answer. Thx. Just to verify with everyone it is step 3.
Step-by-step explanation:
On Edge 2020 got it correct.
Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]
A. 26.47 units²
B. 28.53 units²
C. 33.08 units²
D. 27.28 units²
Answer:
Option B [tex]28.53\ units^{2}[/tex]
Step-by-step explanation:
The area of quadrilateral ABCD is equal to the area of triangle ABD plus the area of triangle ADC
we know that
Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.
Let
a,b,c be the lengths of the sides of a triangle.
The area is given by:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
where
p is half the perimeter
[tex]p=\frac{a+b+c}{2}[/tex]
step 1
Find the area of triangle ABD
we have
[tex]a=AB=2.89\ units[/tex]
[tex]b=BD=8.59\ units[/tex]
[tex]c=DA=8.6\ units[/tex]
Find the half perimeter p
[tex]p=\frac{2.89+8.59+8.6}{2}=10.04\ units[/tex]
Find the area
[tex]A=\sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex]
[tex]A=\sqrt{10.04(7.15)(1.45)(1.44)}[/tex]
[tex]A=\sqrt{149.89}[/tex]
[tex]A=12.24\ units^{2}[/tex]
step 2
Find the area of triangle ADC
we have
[tex]a=AC=4.3\ units[/tex]
[tex]b=AD=8.6\ units[/tex]
[tex]c=DC=7.58\ units[/tex]
Find the half perimeter p
[tex]p=\frac{4.3+8.6+7.58}{2}=10.24\ units[/tex]
Find the area
[tex]A=\sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex]
[tex]A=\sqrt{10.24(5.94)(1.64)(2.66)}[/tex]
[tex]A=\sqrt{265.35}[/tex]
[tex]A=16.29\ units^{2}[/tex]
step 3
Find the total area
[tex]A=12.24+16.29=28.53\ units^{2}[/tex]
Answer:
B.) 28.53 units²
Step-by-step explanation:
I got it correct on founders edtell
which of the following is the quotient of the rational expressions shown below 2x/4x+3 divided x-1/2x
Answer:
4x^2/4x^2-x-3
Step-by-step explanation:
boomchakalaka
The quotient is 4x²/4x²-x-3.
What's known as a quotient?
In mathematics, a quotient is a quantity produced with the aid of the department of numbers.
How do you discover a quotient?The quotient is the solution acquired whilst we divide one range by using every other. for example, if we divide the quantity 4 by means of 2, we get the end result as 2, that's the quotient.
Learn more about quotient here: brainly.com/question/629998
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A boy is flying a kite. The length of the string is 61 meters and the
horizontal distance between the boy and the kite is 60 meters. Assuming
there is no slack in the string, find the height of the kite from the ground.
Answer:
11 meters
Step-by-step explanation:
Using the Pythagorean Theorem
a^2 + b^2 = c^2
a^2 + 60^2 = 61^2
a^2 + 3600 = 3721 (subtract 3600 from both sides)
a^2 = 121 (square root both sides so a^2 becomes a)
a = 11
Answer:
11 meters.Step-by-step explanation:
This problem models a right rectangle, where the hypothenuse is the length of the string, and the legs are the height and the horizontal distance. So, to find the answer, we just have to use the pythagorean theorem
[tex]a^{2}=b^{2}+c^{2}[/tex]
Where
[tex]a=61;b=60;c=x[/tex]
Replacing and solving for [tex]x[/tex], which is the height
[tex]a^{2}=b^{2}+c^{2}\\61^{2}=60^{2}+x^{2} \\x^{2}=61^{2}-60^{2}\\x=\sqrt{3721-3600}=\sqrt{121}=11[/tex]
Therefore, assuming there is no slack in the string, the height of the kite from the ground is 11 meters.
i need help please can someone help
Answer:
x = 8Step-by-step explanation:
[tex]\sqrt{\dfrac{896z^{15}}{225z^6}}=\dfrac{xz^4}{15}\sqrt{14z}\\\\\sqrt{\dfrac{896z^{15}}{225z^6}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\sqrt{\dfrac{(64)(14)z^{15-6}}{225}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\=\dfrac{\sqrt{64}\cdot\sqrt{14}\cdot\sqrt{z^9}}{\sqrt{225}}=\dfrac{8\cdot\sqrt{14}\cdot\sqrt{z^{8+1}}}{15}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{z^8z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]
[tex]=\dfrac{8\sqrt{14}\cdot\sqrt{z^8}\cdot\sqrt{z}}{15}=\dfrac{8\sqrt{14}\cdot\sqrt{z^{4\cdot2}}\cdot\sqrt{z}}{15}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{(z^4)^2}\cdot\sqrt{z}}{15}\qquad\text{use}\ (\sqrt{a})^2=a\\\\=\dfrac{8\sqrt{14}\cdot z^4\cdot\sqrt{z}}{15}=\dfrac{8z^4\sqrt{14}\cdot\sqrt{z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{8z^4\sqrt{14z}}{15}[/tex]
[tex]\dfrac{8z^4\sqrt{14z}}{15}=\dfrac{xz^4\sqrt{14z}}{15}\iff x=8[/tex]
12. A fruit basket contains oranges and grapefruits. One-third of the orange
and one-fourth of the grapefruits were spoiled. You threw away 4 oranges
and 7 grapefruits. How many pieces of fruit were in the basket?
Answer:
There were 12 + 28 = 40 pieces of fruit in the basket.
Step-by-step explanation:
Suppose there were x oranges and y grapefruit.
Then we have
1 /3 x = 4
x = 4*3 = 12.
1/4 y = 7
y = 7*4 = 28.
Check each set that includes the number shown 5/9 a. natural numbers b.whole numbers c.integers d. rational numbers e.irrational numbers f.real numbers
Answer:
5/9 from these categories can only be classified as rational and real.
Step-by-step explanation:
Natural numbers are counting numbers. People don't ever say the number 5/9 when counting people. So 5/9 is not natural.
Whole numbers are counting numbers plus also including 0. So we already said 5/9 is not natural and it is definitely not 0 so 5/9 is not whole.
Integers are whole numbers plus the opposite of the whole numbers. 5/9 is not whole and it is certainly not negative so we don't need to even consider if is the opposite of a whole number.
Rational numbers are numbers that can be expressed as a fraction where the top and bottom are integers. 5/9 is a rational number because 5 and 9 are whole numbers which are integers.
Irrational numbers are numbers that aren't rational. Our number 5/9 is rational so it isn't irrational.
Real numbers are any number that isn't imaginary. Doesn't include the imaginary unit. Our number doesn't include the imaginary unit so it is real.
Answer:
d. Rational Numbers
f. Real Numbers
Step-by-step explanation:
The number shown is 5/9
Let us see the options one by one
a. Natural numbers
Natural numbers consists of counting from 1 to infinity. The fractions are not included in the natural numbers hence it will not be the correct answer.
b. Whole numbers
Whole numbers is the set of natural numbers along with zero so it is also not the right answer.
c. Integers
Integers are combination of negative and positive whole numbers hence it is also not correct.
d. Rational numbers
Rational numbers are numbers which can be written in the form of p/q where p and belong to integers and q is not equal to zero. It is correct as the number is 5/9 where 5 is also an integer and 9 is also an integer. Also 9 ≠ 0 so 5/9 is a rational number.
e. As the number is rational, it cannot be irrational
f. Real numbers
As real numbers is the set of all rational and irrational numbers, 5/9 will also be a part of the set .. Hence it is also correct ..
Its for a test i need to take and this is a review question just need to know how to solve it
Find the value of y .
(Either leave your answer as a fraction, or round to the nearest hundredth.)
Answer:
y=5/3 or y=1.67
Step-by-step explanation:
In this problem we have that
(5x+8)=21x ----> given problem
21x-5x=8
16x=8
x=0.5
In the same way
Remember that the slope of a line is a constant
so
20y-2=17y+3
Solve for y
20y-17y=3+2
3y=5
y=5/3 or y=1.67
QUIZ
ALU
0 2 O) A 5 OU
Which shows the four-term polynomial and factored form of x2 + 6x-27?
O x2 + 3x – 9x - 27 = (x + 3)(x -9)
O x2 + 6x – 3x-27 = (x + 6)(x – 3)
O x2 + 9x -3x – 27 = (x + 9)(x – 3)
O x2 + 3x – 6x-27 = (x + 3)(x-6)
Answer:
C
Step-by-step explanation:
O x² + 9x -3x – 27 = (x + 9)(x – 3)
x² + 6x - 27 = (x + 9)(x - 3)
-12=f-7 help please
Answer:
f=-5
Step-by-step explanation:
1) Add 12 to both sides
2) You should get f=-5
Answer:
[tex]\huge \boxed{F=-5}\checkmark[/tex]
Step-by-step explanation:
First, switch sides.
[tex]\displaystyle F-7=-12[/tex]
Then, add by 7 from both sides of equation.
[tex]\displaystyle F-7+7=-12+7[/tex]
Simplify, to find the answer.
[tex]\displaystyle -12+7=-5[/tex]
[tex]\huge \boxed{F=-5}[/tex], which is our answer.
A cierta hora del dia los rayos solares forman un angulo de 60° con el suelo. ¿Que sombra dara el arbol de 7 m de altura? Auxilioooooo por favorecer help!!
Answer:
4.04 m
Step-by-step explanation:
El arbol y el suelo forman un angulo de 90°. Son los catetos de un triangulo rectangulo.
Los rayos solares forman un angulo de 60° con el suelo y forman la hipotenusa del triangulo.
Se tiene un triangulo rectangulo de angulos de 30°-60°-90°.
En este genero de triangulo, el cateto mayor mide [tex] \sqrt{3} [/tex] veces el cateto menor.
cateto menor = [tex] \dfrac{7}{\sqrt{3}} [/tex]
[tex] = \dfrac{7\sqrt{3}}{3} [/tex]
[tex] = 4.04 ~m [/tex]
The length of the shadow of the tree would be -
s = {7/√3}.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that at a certain time of day the sun's rays make an angle of 60° with the ground.
Assume that the length of the shadow is [x] meters. Using the trigonometric ratios, we can write -
tan (60) = (height of tree {h})/(length of shadow {s})
sin(60)/cos(60) = (height of tree)/(length of shadow)
(√3/2)/(1/2) = {7/s}
√3/2 x 2 = 7/s
√3 = 7/s
s = {7/√3}
Therefore, the length of the shadow of the tree would be -
s = {7/√3}.
To solve more questions on functions, expressions and polynomials, visit the link below -
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{The question in english is -
At a certain time of day the sun's rays make an angle of 60° with the ground. What shade will the 7 m tall tree cast?}
PLEASE, I NEED HELP NOW!!!!!!
Find the approximate area of a circle that has a radius of 14 feet. Round your answer to the nearest hundredth.
A = ___ ft2
Don't forget to round!
Answer:
1934.2
Step-by-step explanation:
3.14*14=43.98 squared=1934.2
Answer:
615.75
Step-by-step explanation:
Use A = πr², letting r = 14, so that:
A = π(14)²
≈ 615.75 ft²
Rounding to the nearest hundredth would make the answer 618
Graph the linear equations in three points: -x-2y=-10
Answer:
Step-by-step explanation:
Rewrite -x-2y= -10 as -2y= x - 10 and then as y = (-1/2)x + 5.
Then choose any 3 x values and find the corresponding y values using this formula. For example:
x y = (-1/2)x + 5 (x, y)
----- -------------------- ---------
0 5 (0, 5)
-4 (-1/2)(-4) + 5 = 7 (-4, 7)
6 (-1/2)(6) + 5 = 2 (6, 2)
Plot these three points and then draw a line through them.
Answer:
0,5 2,6 4,7
Step-by-step explanation:
You have to solve the equation by keeping y on its own. The equation is
y=-1/2x-5
Coordinates are:
0,5 2,6 4,7
Identify an equation in point-slope form for the line perpendicular to
y=-4x – 1 that passes through (-2,7).
Answer:
[tex]\large\boxed{y=\dfrac{1}{4}x+\dfrac{15}{2}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\==================================[/tex]
[tex]\text{We have}\ y=-4x-1\to m_1=-4\\\\\text{Therefore}\ m_2=-\dfrac{1}{-4}=\dfrac{1}{4}.\\\\\text{The equation of a line perpendicular to}\ y=-4x-1:\\\\y=\dfrac{1}{4}x+b\\\\\text{Put the coordinates of the point (-2, 7) to the equation:}\\\\7=\dfrac{1}{4}(-2)+b\\\\7=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\7\dfrac{1}{2}=b\to b=7\dfrac{1}{2}=\dfrac{7\cdot2+1}{2}=\dfrac{15}{2}\\\\\text{Finally:}\\\\y=\dfrac{1}{4}x+\dfrac{15}{2}[/tex]