Answer:
[tex]\frac{2\sqrt{2} }{3}[/tex]
Step-by-step explanation:
The sine of an angle is defined as the ratio between the opposite side and the hypotenuse of a given right-angled triangle;
sin x = ( opposite / hypotenuse)
The opposite side to the angle x is thus 1 unit while the hypotenuse is 3 units. We need to determine the adjacent side to the angle x. We use the Pythagoras theorem since we are dealing with right-angled triangle;
The adjacent side would be;
[tex]\sqrt{9-1}=\sqrt{8}=2\sqrt{2}[/tex]
The cosine of an angle is given as;
cos x = (adjacent side / hypotenuse)
Therefore, the cos x would be;
[tex]\frac{2\sqrt{2} }{3}[/tex]
Answer:
[tex]cos(x) =\±2\frac{\sqrt{2}}{3}[/tex]
Step-by-step explanation:
We know that [tex]sen(x) =\frac{1}{3}[/tex]
Remember the following trigonometric identities
[tex]cos ^ 2(x) = 1-sin ^ 2(x)[/tex]
Use this identity to find the value of cosx.
If [tex]sen(x) =\frac{1}{3}[/tex] then:
[tex]cos ^ 2(x) = 1-(\frac{1}{3})^2[/tex]
[tex]cos ^ 2(x) =\frac{8}{9}[/tex]
[tex]cos(x) =\±\sqrt{\frac{8}{9}}[/tex]
[tex]cos(x) =\±2\frac{\sqrt{2}}{3}[/tex]
Please help IDK how to do this!
A painter leans a 12 ft ladder against a building. The base of the ladder is 5 ft from the building. To the nearest foot, how high on the building does the ladder reach?
For this problem you must do Pythagorean theorem:
[tex]a^{2} + b^{2} =c^{2}[/tex]
In this example 10ft is c and 7ft is a (or it could be b, and you'll be solving for a instead of b. It's the same thing, since a and b are both legs)
Plug what you know into the equation:
[tex]7^{2} +b^{2} = 10^{2}[/tex]
49 +b^{2} = 100
Bring 49 to the right side by subtracting it:
b^{2} = 51
Now you still must isolate b. The opposite of squaring is taking the square root so take the square root of both sides to cancel it from the left side:
[tex]b =\sqrt{51}[/tex]
b = 7.1414
b ≈ 7 ft
Hope this helped!
HELP ME PLEASE! I really need help on this question
Answer:
given
Step-by-step explanation:
The vertically opposite angles, ∠4 and ∠2 are equals.
What is vertically opposite angles?Vertical angles are angles opposite each other where two lines cross.
What is linear pair?A linear pair can be defined as two adjacent angles that add up to 180° or two angles which when combined together form a line or a straight angle.
According to the given question.
On line m, we have
∠4 + ∠1 = 180 degrees ...(i) (by linear pair)
On line n, we have
∠1 + ∠2 = 180 degrees ...(ii) (by linear pair)
from equation (i) and (ii)
∠4 + ∠1 = ∠1 + ∠2
⇒ ∠4 = ∠2
Hence, we proved that the vertically opposite angles ∠4 and ∠2 are equals.
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Complete the solution table from left to right for the quadratic function. (I did not select an answer, that was a mistake) Thank you!
Answer: OPTION D
Step-by-step explanation:
To complete the table, you need to substitute the values of "x" given in the table into the quadratic equation [tex]y=x^{2}-x-6[/tex] to obtain the corresponding value of "y".
Then:
When [tex]x=-5[/tex] :
[tex]y=(-5)^{2}-(-5)-6[/tex]
[tex]y=24[/tex]
When [tex]x=-3[/tex] :
[tex]y=(-3)^{2}-(-3)-6[/tex]
[tex]y=6[/tex]
When [tex]x=-1[/tex] :
[tex]y=(-1)^{2}-(-1)-6[/tex]
[tex]y=-4[/tex]
When [tex]x=2[/tex] :
[tex]y=(2)^{2}-(2)-6[/tex]
[tex]y=-4[/tex]
Point O is the center of the circle. What is the value of x?
Answer:
66°
Step-by-step explanation:
Since segments MN and MP are tangent to the circle, then
[tex]\angle MPO=\angle MNO=90^{\circ}[/tex]
The sum of the measures of all interior angles of the quadrilateral is equal to 360°, so
[tex]\angle NOP+\angle MPO+\angle MNO+\angle NMP=360^{\circ}\\ \\114^{\circ}+90^{\circ}+90^{\circ}+x^{\circ}=360^{\circ}\\ \\x^{\circ}=360^{\circ}-114^{\circ}-90^{\circ}-90^{\circ}\\ \\x^{\circ}=66^{\circ}[/tex]
Answer:
The value of x = 66°
Step-by-step explanation:
From the figure we can see that,
PM and MN are the tangent from the point M to the circle with center O
m<PON = 114°
To find the value of x
From the figure we can write,
m<PON + m<PMN = 180°
114 + x = 180
x = 180 - 114 = 66°
Therefore the value of x = 66°
what is the distance between (4,2) and (8,5)
Answer:
The distance between points P1 = (4,2) and P2=(8,5) is 5.
Step-by-step explanation:
Let P1 = (4,2) and P2=(8,5)
The distance between two points can be found using formula:
[tex]d(P,Q), \sqrt{(x_{2}-x_{1})^2+ (y_{2}-y_{1})^2}[/tex]
where x₁ = 4 , x₂=8, y₁= 2 and y₂ = 5
Putting values in the formula
[tex]=\sqrt{(8-4)^2+(5-2)^2} \\=\sqrt{(4)^2+(3)^2} \\=\sqrt{16+9} \\=\sqrt{25} \\=5[/tex]
So, the distance between points P1 = (4,2) and P2=(8,5) is 5.
Final answer:
The distance between the points (4,2) and (8,5) can be found using the Pythagorean Theorem. After calculating the squares of the differences in the x and y coordinates and adding them, the square root of the sum gives a distance of 5 units.
Explanation:
The distance between two points in a two-dimensional plane can be calculated using the Pythagorean Theorem. The coordinates of the points provided are (4, 2) and (8, 5). To find the distance, we calculate the difference in the x-coordinates and the difference in the y-coordinates, and then square both values before adding them together. This gives us the distance squared.
The formula is as follows:
d² = (x2 - x1)² + (y2 - y1)²
In this scenario:
d² = (8 - 4)² + (5 - 2)²
d² = (4)² + (3)²
d² = 16 + 9
d² = 25
Finally, we take the square root of the distance squared to get the distance:
d = √25
d = 5
The distance between the points (4,2) and (8,5) is 5 units.
find the magnitude and direction angle for the vector v = 5 cos 144°j
Answer:
5, 144°
Step-by-step explanation:
A vector with magnitude v and angle θ can be split into x and y components as:
vx = v cos θ
vy = v sin θ
Here, we're given the components and asked to find the magnitude and direction. By matching, we can see the magnitude is 5 and the angle is 144°.
So the answer is 5, 144°.
a building casts a shadow that is 348 meters long at the same time a person who is 2 meters tall casts a shadow that is 6 meters long how tall is the building
Answer:
The building is [tex]116\ m[/tex] high
Step-by-step explanation:
we know that
Using proportion
Let
x-----> the height of the building
[tex]\frac{2}{6}=\frac{x}{348}\\ \\x=2*348/6\\ \\x=116\ m[/tex]
Write two and thirty-one hundredths as a decimal number.
A) 0.231
B) 2.031
C) 2.31
D) 231.00
Answer:
c
Step-by-step explanation:
21. In your day-to-day routines, you likely use measurement to cook or do home renovations, such as adding new tile flooring. How do you imagine that you will use measurement in your healthcare career?
Answer:
Depending of the exact career but measurements are plentiful in the healthcare business.
First, you'll most likely deal with weight and height... since that's part of most health care consultations.
Then, if you deal with medication, you'll use grams, milligrams, milliliters, liters all the time. depending if the medication is in solid or liquid form.
Even as a nutritionist, you'll deal with grams and such for portion sizes.
There are countless of ways you'll use maths and measurements in the healthcare sector.
Answer:
Measurement can be used in healthcare career also. Like - the doctors and nurses are well trained to give medicines accurately as per measurement of milligrams or nano-gram. High doses can prove fatal with some medicines, so the correct measurement is very necessary.
Similarly, measurement is used in syrups. Like a child can be given upto 5 mg of syrup twice daily.
Kalon has $175 and needs to save at least $700 for a new computer. If he can save $35 per week, what is the minimum number of weeks Kalon will need to save to reach his goal?
700-175=525. 525/35=15
What is the missimg term in this aeithmetic sequence 9,14,19,_29,34,
ANSWER
The missing term is 24
EXPLANATION
The given arithmetic sequence is 9,14,19,_29,34
We can observe that:
[tex]14 = 9 + 5[/tex]
[tex]19 = 14 + 5[/tex]
Let the missing term be x, then
[tex]x = 19 + 5[/tex]
[tex]x = 24[/tex]
Therefore the missing term is 24.
What is the maximum number of relative extremes contained in the graph of this function f(x)=3x^4-x^2+4x-2
Answer:
Final answer is 3.
Step-by-step explanation:
Given function is [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].
Now we need to find about what is the maximum number of relative extremes contained in the graph of the given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].
Degree of the given function = 4.
Because degree is the highest power of variable.
Then relative number of extremas = degree - 1 = 4 - 1 = 3
Hence final answer is 3.
why is Pi never ending?
If the decimal expansion of pi would end, then it would have to be a rational number, ie pi could be written as a fraction pi = p/q with integers p and q. There are many proofs that this is not the case, but they are all a bit complicated
Pi is an irrational and transcendental number, meaning it never terminates or repeats. Its non-ending and non-repeating nature is reflected in its definition as the ratio of a circle's circumference to its diameter. Pi's transcendence ensures it cannot be expressed by any algebraic equation with rational coefficients.
Understanding the Nature of Pi ( 3.141592653589793237...)
Pi ( 3.14159...) is known to be a non-terminating, non-repeating decimal, which classifies it as an irrational number. This means that no matter how many digits you calculate, Pi will never repeat in a pattern nor end. The number has been calculated to trillions of digits without any repeating pattern emerging.
The non-ending nature of Pi arises from its definition as the ratio of a circle's circumference to its diameter. This ratio is the same for all circles, but it can never be expressed exactly by a fraction or a finite decimal.
Moreover, Ferdinand von Lindemann's proof that Pi is a transcendental number further solidifies that it cannot be the solution of any algebraic equation with rational coefficients, making Pi an essentially complex and infinite entity in mathematics.
A sum of $4200 was invested, part at 8% and the remainder at 11%. If $426.00 was earned in interest after one year, how much was invested at 11%?
Answer:
$3000 was invested at 11%.
Step-by-step explanation:
The total interest was $426. This was comprised of interest earned at 8% (represented by e) and (separately) interest earned at 11% (represented by v).
Then e + v = $4200 total investment, and
i = $426 = e(0.08)(1 year) + v(0.11)(1 year)
We eliminate the variable e as follows: since e + v = $4200, e = $4200 - v. Thus,
i = $426 = e(0.08)(1 year) + v(0.11)(1 year) becomes:
i = $426 = ($4200 - v)(0.08)(1 year) + v(0.11)(1 year)
This is one equation in one unknown, the amount of $ invested at 11%.
Performing the indicated multiplications:
426 = 4200(0.08) - 0.08v + 0.11v. Simplifying this further, we get:
426 = 336 + 0.03v.
Then 90 = 0.03v, and v = 90 / 0.03 = $3000.
$3000 was invested at 11%.
Describe each Locus
The set of all points in a plane that are 5 cm from a circle with radius 2 cm.
-
The set of all points in space that are a distance 6 in. from AB¯¯¯
Explanation:
1. The set of points 5 cm from the nearest point on a circle of radius 2 cm will be a circle with a radius 5 cm larger: a circle with a radius of 7 cm.
__
2. The set of points 6 in from the nearest point on a line will be a cylindrical shell 12 inches in diameter centered on the line.
If AB is a line segment, then the shell will have hollow hemispherical ends of radius 6 inches about the end points.
what is the y- value of the vertex of 4c^2+8x-8
Answer:
a =4 b=8 c=-8
y-value of vertex =
ah^2 + bh + c
where h = -b/2a
h= -8/8 =-1
y-value of vertex =
4(-1)^2 + 8*-1 -8
4 -8 -8
y value of vertex = -12
Step-by-step explanation:
Find 100,000 more than 3,489,234.
Answer:
The answer is 3,589,234
Step-by-step explanation:
Because it basically means addition meaning you just have to add it 3,489,234 + 100,000 gives you the answer
2. A painting is sold for $1,400, and its value
increases by 9% each year after it is sold. What
is the value of the painting after 8 years?
Answer:
$11,480
Step-by-step explanation:
1,400 x 0.9 = 1,260
1,260 x 8 = 10,080
1,400 + 10,080 = 11,480
consider the following precise wise-defined function
Answer:
11
Step-by-step explanation:
The x-value -4 is less than 3, so use the first formula for f: x^2 - 5.
Then f(-4) = (-4)^2 - 5 = 11
A ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour. which type of functions best model this situation?
Answer:
Linear Function
[tex]y=4x+18[/tex]
Step-by-step explanation:
Let
x----> the time in hours
y----> the total inches of snow on the ground
we know that
The function that best model this situation is the linear function
so
[tex]y=mx+b[/tex]
In this problem
[tex]m=4\frac{in}{h}[/tex]
[tex]b=18\ in[/tex] ----> the y-intercept
substitute
[tex]y=4x+18[/tex]
Answer:
Linear decreasing function best model this situation and the required function is
f(x)=4x+18
Step-by-step explanation:
It is given that a ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour.
If a function has constant rate of change, then the it is a linear function.
It the given case the rate of change is constant so linear function best model this situation.
The slope intercept form of linear function is
[tex]f(x)=mx+b[/tex] ... (1)
where, m is slope and b is y-intercept or initial value.
Ski resort has 18 inches of snow on the ground it means initial value is 18.
The snow is falling at a rate of 4 inches per hour. So, m=4.
Substitute m=4 and b=18 in equation (1).
[tex]f(x)=4x+18[/tex]
Therefore the required function is f(x)=4x+18.
What are all the possible values of x?
X3=216
[tex]\bf x^3=216\implies x=\sqrt[3]{216}\implies x=6[/tex]
Divide 216 by 3 to get your x-value
Simplify using the distributive property.
8(y + 12)
8y + 12
20y
20 + y
8y + 96
Answer:
8y+12
Step-by-step explanation:
What percent of 72 is 27?
if we take 72 as the 100%, what is 27 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 72&100\\ 27&x \end{array}\implies \cfrac{72}{27}=\cfrac{100}{x}\implies \cfrac{8}{3}=\cfrac{100}{x}\implies 8x=300 \\\\\\ x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5[/tex]
To calculate the percentage, divide the part (27) by the whole (72) and multiply by 100, resulting in 37.5%.
Percentage is a way of expressing a portion or fraction of a whole as a value out of 100. It is commonly used to compare relative quantities, represents proportions, or express the relationship between a part and a whole.
The term "percent" comes from the Latin phrase "per centum," which means "per hundred." It signifies that percentages are calculated on a scale of 100.
In practical terms, a percentage represents a fraction of a whole, where the whole is equal to 100%. It allows us to easily compare different quantities and understand their relative sizes or proportions.
To calculate a percentage, you typically divide the part (the specific quantity you want to express as a percentage) by the whole (the total or reference quantity) and then multiply by 100 to obtain the value as a percentage.
To calculate the percentage, you can divide the given number (27) by the total number (72) and then multiply the result by 100. So, to find out what percent 27 is of 72:
(27 ÷ 72) × 100 ≈ 37.5%
Therefore, 27 is approximately 37.5% of 72.
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Central Park in New York City is rectangular in shape, 4km in length and 0.8 km wide. How far would a run in central be?
Answer:
basically you have to calculate the perimeter-
Step-by-step explanation:
4+4+0.8+0.8=8+1.6=9.6
First you need to find the parameter
P= (L x 2)+(W x 2)
P=(4km x 2)+(0.8km x 2)
P=8km+1.6km
P=9.6km
A mason is building a rectangular foundation wall that is to be 75 feet by 40 feet.what is the total distance around the wall?
Answer: 230ft
Step-by-step explanation:
The perimeter is just all 4 sides added together, so,
75+75+40+40=230
The total distance around the wall is 230ft.
Please answer ASAP!
Picture provided.
Answer:
400cm2
Step-by-step explanation:
20 • 20 = 400
The answer is 400 cm squared.
Hope this helps!
If it does then I would appreciate it if you could make me brainliest.
What is the value of p?
Answer:
90
Step-by-step explanation:
Find the missing number.
a. 3 : 24 = ___ : 72
b. ___ : 18 = 5 : 9
c. 6: ___ = 36 : 36
A 9
B 10
C 6
Hope this helps;$
Answer:
a. 3:24 = 9:72.
b. 10:18 = 5:9.
c. 6:6 = 36:36.
Step-by-step explanation:
a. 72 / 24 = 3 so we multiply 3 by 3 to give 9.
b. 18/9 = 2 so we multiply 5 by 2 = 10.
c. The answer is 6.
If the mean of four numbers 2, 4, x and 6 is 5, then x is ?
Answer:
x = 8
Step-by-step explanation:
Step 1: Create an equation
(2+4+x+6) ÷ 4 = 5
Step 2: Solve the equation
(12+x) ÷ 4 = 5
(12+x) = 20
x = 8
The value of the unknown number x is 8.
The given numbers include:
2, 4, x, 6mean = 5The sum of the given numbers is calculated as follows;
2 + 4 + x + 6 = 12 + x
The mean of the given 4 numbers is calculated as follows;
[tex]\frac{12 + x}{4} = 5\\\\12 + x = 20\\\\x = 20 -12\\\\x = 8[/tex]
Thus, the value of the unknown number x is 8.
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A polynomial function can be written as (x + 2)(x + 3)(x − 5). What are the x-intercepts of the graph of this function? (1 point) (2, 0), (3, 0), (−5, 0) (−2, 0), (−3, 0), (5, 0) (2, 0), (3, 0), (5, 0) (−2, 0), (−3, 0), (−5, 0)
Answer:
(-2, 0), (-3, 0), and (5, 0)
Step-by-step explanation:
The x-intercept is found when y = 0.
So, we have to find x when (x + 2)(x + 3)(x - 5) = 0
We can do that by pulling apart all parts, because if one part = 0, the whole thing will have to be too (multiplication property of identity).
1. When x + 2 = 0, x = -2
2. When x + 3 = 0, x = -3
3. When x - 5 = 0, x = 5
That gives us (-2, 0), (-3, 0), and (5, 0)
Answer:
(-2, 0), (-3, 0) and (5, 0)Step-by-step explanation:
x-intercepts are for
(x + 2)(x + 3)(x - 5) = 0
The product is equal to 0 if one of the factors is equal to 0.
Therefore
x + 2 = 0 or x + 3 = 0 or x - 5 = 9
x + 2 = 0 subtract 2 from both sides
x = -2
x + 3 = 0 subtract 3 from both sides
x = -3
x - 5 = 0 add 5 to both sides
x = 5