The value of x is 6.
What are complementary?Complementary angles are angles that sum up to 90°.
Analysis:
For angles A and B, to be complementary, the sine of angle A must be equal to the cosine of angle B.
sin A = cos B
5X+9 = 3x+21
5x - 3x = 21 - 9
2x = 12
x = 6
In conclusion, the value of x to make angles A and B complementary is 6.
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vFind the mean and median of the data set. 3, 5, 6, 2, 10, 9, 7, 5, 11, 6, 4, 2, 5, 4
Step-by-step explanation:
2, 2, 3, 4, 5, 5, 5, 6, 6, 7, 9, 10
_
2+2+3+4+5+5+5+6+6+7+9+10 = 64 ÷ 12 = 5.3
_
Mean: 5.3
Median: 5
1. Write the point where the linear equation 3x + 4y = 12 cuts the x-axis.
Answer:
(4,0)
Step-by-step explanation:
The point where the line cuts the x-axis is called the x-intercept.
x-intercept is when y = 0.
So given y = 0,
3x+4(0) = 12
3x = 12
x = 12/3
x = 4
therefore the point is (4,0)
determine the radius and center of the circle with the following equation
x^2+y^2-12x+24y-10=6
Answer:
Center: (6, -12)
Radius: 4
Step-by-step explanation:
Complete the squares
[tex]x^2+y^2-12x+24y-10=6\\\\x^2-12x-10+y^2+24y=6\\\\x^2-12x-10+46+y^2+24y+144=6+46+144\\\\(x^2-12x+36)+(y^2+24y+144)=196\\\\(x-6)^2+(y+12)^2=196[/tex]
Comparing with the standard form equation [tex](x-h)^2+(y-k)^2=r^2[/tex], since [tex]r^2=196[/tex], then the radius of the circle is [tex]r=14[/tex]. Also, the center of the circle would be [tex](h,k)\rightarrow(6,-12)[/tex].
What conclusions can be drawn about finding the quotient in scientific notation? Check all that apply. Start Fraction (9.6 times 10 Superscript negative 8 Baseline) Over (3.2 times 10 Superscript 4 Baseline) End Fraction A.The coefficient of the solution is 6.4, the difference of the original coefficients. B.The exponent of the solution is –12, the difference of the original exponents. C.The coefficient of the solution must be greater than or equal to one but less than 10. D.The quotient is 3.0 × 10-12 E.The solution is a very large number
The quotient of the expressions (9.6 x 10⁻⁸) and (3.2 x 10⁴) is 3.0 × 10⁻¹². Then the correct option is D.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
The expressions are given below.
(9.6 x 10⁻⁸) and (3.2 x 10⁴)
Then the quotient of the expressions will be
⇒ (9.6 x 10⁻⁸) / (3.2 x 10⁴)
⇒ (3 x 10⁻⁸) / (10⁴)
⇒ 3 x 10⁻⁸ x 10⁻⁴
⇒ 3 x 10⁻⁸⁻⁴
⇒ 3 x 10⁻¹²
Then the correct option is D.
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Point D is the midpoint of AB and point E is the midpoint of BC. Select all of the statements to the right that must be true.
Answer + Step-by-step explanation:
» ABC ≅ DBE
» DE // AC
(properties of the mid-segment of a triangle)
» Length of DE = 1/2 length of AC
(properties of the mid-segment of a triangle)
» ∠BDE = ∠DAC
(Corresponding angles)
Part B
What is the area of the target that earns at least 30 points on a throw?
Select the correct from the drop-down menu.
the area is ____ square inches.
a) 16
b) 49
c) 121
d) 144
The area of the target which earns 30 points on a throw.
Solution:[tex]\huge\boxed{Formula: a= \pi{r}^{2}}[/tex]
[tex]4+3[/tex]
[tex]=7[/tex]
Let's solve
We have to find the answer in terms of π so, we'll just have to multiply the radius by itself.
[tex]a={7}^{2}[/tex]
[tex]\large\boxed{a= 49 \pi\: {in}^{2}}[/tex]
Hence, the area of the target which earns 30 points on a throw is 49π square inches.
Answer= Option B
PLEASE HELP ME ASAP
Does the series converge or diverge? If it converges, what is the sum? Show your work
The series is a convergence series and the sum of the series is -8/3
The type of the seriesThe series is given as:
[tex]\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}[/tex]
The above series has the following properties:
First term; a = -4Common ratio, r = -1/2Start by calculating the absolute value of the common ratio
Absolute value = |-1/2|
This gives
Absolute value = 1/2
The above value is less than 1.
It means that the series converges.
The sum of the seriesThis is calculated using:
[tex]S_{\infty} = \frac{a}{1 -r}[/tex]
So, we have:
[tex]S_{\infty} = \frac{-4}{1 + \frac 12}[/tex]
Evaluate the sum
[tex]S_{\infty} = \frac{-4}{\frac 32}[/tex]
Evaluate the quotient
[tex]S_{\infty} = \frac{-8}{3}[/tex]
Hence, the sum of the series is -8/3
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In one day, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda. Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk. Marian consumes 510 calories by drinking 3 servings of milk and 1 soda. Using matrices to solve, how many calories are in 1 serving of milk?
Therefore, 110 calories are in 1 serving of milk.
Given, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda.
Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk.
Marian consumes 510 calories by drinking 3 servings of milk and 1 soda.
What are Linear Programming problems?Linear programming, commonly known as LP, is a straightforward technique for representing complex real-world interactions by means of a linear function.
Now,
Let the calories in one serving of milk be x
Let the calories in one serving of juice be y
Let the calories in one serving of soda be z
For Joe, the equation to show the amount of calories is
2x + y + z = 530 -----(1)
For Darius, the equation to show the amount of calories is
x + 2y = 370 ------(2)
For Marian, the equation to show the amount of calories is
3x + z = 510 ------(3)
Now, y=370/2-x/2 and z=510-3x substitute in the equation 2x + y + z = 530.
2x+185-0.5x+510-3x=530
⇒695-1.5x=530
⇒1.5x=165
⇒x=110 calories
Hence, 110 calories are in 1 serving of milk.
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I need help asap please? and this is for the math question? what is the missing angle?
Answer:
the missing angle or the exterior angle is 120
Step-by-step explanation:
180-60=120
Answer:
90 degrees.
Step-by-step explanation:
The square symbol at the unlabeled angle means 90 degrees. Also, a triangle's interior angles equal 180. We already have 30 and 60, so 30+60=90. Now, subtract this from 180. 180-90=90. The answer is 90 degrees.
Hope this helps!
Please help soon!!!!!!
Solving the exponential function, it is found that the times that will take to have the desired measures are given by:
a) 3.6 hours.
b) 38.51 hours.
c) 56.98 hours.
What is the exponential function for the amount of Carbon-10 after t hours?The function is given by:
[tex]A(t) = 140(0.5)^{\frac{t}{19.255}}[/tex]
Solving for t, we have that:
[tex](0.5)^{\frac{t}{19.255}} = \frac{A(t)}{140}[/tex]
[tex]\log{(0.5)^{\frac{t}{19.255}}} = \log{\frac{A(t)}{140}}[/tex]
[tex]\frac{t}{19.255} = \frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]
[tex]t = 19.255\frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]
In item A, we have that A(t) = 123, hence:
[tex]t = 19.255\frac{\log{\frac{123}{140}}}{\log{0.5}}[/tex]
t = 3.6 hours.
In item B, we have that A(t) = 35, hence:
[tex]t = 19.255\frac{\log{\frac{35}{140}}}{\log{0.5}}[/tex]
t = 38.51 hours.
In item C, we have that A(t) = 18, hence:
[tex]t = 19.255\frac{\log{\frac{18}{140}}}{\log{0.5}}[/tex]
t = 56.98 hours.
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In a track field competition, A discus has a radius of 11 centimeters. What is the circumference, I centimeters, of the discus?
Given the radius of the discus used in the track field competition, the circumference of the discus is 69.08cm.
What is the circumference of the discus?Note that; a circumference is the perimeter of a circle or ellipse.
It is expressed as C = 2πr
Where r is the radius and π is the constant pi ( π = 3.14 )
Given that;
Radius of the discus r = 11cmCircumference C = ?C = 2πr
C = 2 × 3.14 × 11cm
C = 69.08cm
Therefore, given the radius of the discus used in the track field competition, the circumference of the discus is 69.08cm.
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Bentley leans a 22-foot ladder against a wall so that it forms an angle of 74 degrees with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary
The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The Height on the wall till which the ladder reaches is 21.148 ft.
What is Sine (Sinθ)?The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
Sin(θ) = Perpendicular/Hypotenuse
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
The height of the wall can be found by using the trigonometry ratios, therefore, the height of the wall can be determined as,
Sin(74°) = (Height on the wall)/(Length of the wall)
Sin(74°) = (Height on the wall)/22 ft
(Height on the wall) = 21.148 ft
Hence, the Height on the wall till which the ladder reaches is 21.148 ft.
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Answer:
21.15
Step-by-step explanation:
A person standing close the the edge on the top of a 80 foot building throws a baseball vertically upward. the quadratic function h(t) = -8t^2 + 32t + 80 models the ball's height above the ground, h(t), in feet, t seconds after it was thrown.
How do I efficiently determine...
-- how many seconds it takes until the ball reaches max height
-- the maximum height
-- how many seconds it takes until the ball hits the ground
without graphing?
The number of seconds it takes until the ball reaches max height is 2 seconds and the maximum height is 112 feet, and the number of seconds it takes until the ball hits the ground will be 6.9 seconds.
What is a projectile motion?When a body is thrown in the air then the motion under the gravity is known as projectile motion.
A person standing close the the edge on the top of a 80 foot building throws a baseball vertically upward. the quadratic function
h(t) = -8t² + 32t + 80 models the ball's height above the ground, h(t), in feet, t seconds after it was thrown.
The number of second to reach at maximum height will be
We know that at maximum height, the rate will be zero. Then we have
h'(t) = 0
-16t + 32 = 0
t = 2 seconds
Then the maximum height will be
h(t) = -8(2)² + 32 x 2 + 80
h(t) = -32 + 64 +80
h(t) = -32 + 144
h(t) = 112 feet
Then the number of the seconds to reach at the ground will be
-8t² + 32t + 80 = -80
-8t² + 32t + 160 =0
t² - 4t - 20 = 0
Then t will be
[tex]\rm t = \dfrac{-(4) \pm \sqrt{(-4)^2 - 4 * 1 * -160}}{2*1}[/tex]
Then we have
t = 6.9 and -2.9
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−−→
A
B
=
(
x
y
)
What values should
x
and
y
take?
−−→
A
B
=
(
x
y
)
What values should
x
and
y
take?
Note: Each horizontal or vertical division represents one unit.
X=
Y=
Answer:
X=1 and Y=4
By counting eacht vetmrtical divided units
Laura worked 8 hours today. She spent
the time in meetings, on the phone,
and the rest of the time on the computer.
Make a circle graph to show how Laura
spent her work day.
55. a rubber ball is dropped from a height of 60 feet. if it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.
The required total distance the ball travels, approximately, is 180 feet.
Let's denote the height of the first fall as a (initial height of 60 feet), and the distance covered during each rebound as r (two-thirds the distance of the previous fall).
The first fall distance (a) is 60 feet.
The first rebound distance (r) is (2/3) * 60 feet.
The total distance covered during the first fall and rebound cycle is:
60 + (2/3) * 60 = 60 + 40 = 100 feet.
Now, for the subsequent cycles, the ball will continue to fall and rebound in the same pattern:
Second fall distance = r * a
= (2/3) * 60
= 40 feet.
Second rebound distance = r*(2/3) * 60
= (2/3) * 40
= 80/3 feet.
The total distance covered during the second fall and rebound cycle is:
40 + (80/3) ≈ 66.67 feet.
The pattern will continue for the subsequent cycles.
To represent this as an infinite geometric series, we can write:
Total distance = [tex]a + (a * r) + (a * r^2) + (a * r^3) + ...[/tex]
Where:
a = 60 feet (height of the first fall)
r = 2/3 (rebound factor)
Using the formula for the sum of an infinite geometric series:
Total distance = a / (1 - r)
Total distance = 60 / (1 - 2/3)
Total distance = 60 / (1/3)
Total distance = 60 * 3
Total distance = 180 feet.
Therefore, the total distance the ball travels, approximately, is 180 feet.
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What is the slope of the line with this equation y = 7x - 3 ? Explain.
Answer:
7
Step-by-step explanation:
y=mx+bm=pendiente
por lo tanto:
pendiente=7
Hii!
__________________________________________________________
Answer:
Slope = 7! ^^
Step-by-step explanation:
Note that the equation is given to us in slope intercept form.
The slope intercept formula is y=mx+c.
m denotes the slope
c denotes the y intercept.
/--------------\
The slope of the line that we are working with is 7.
Remember how I said that the slope of the line y=mx+c is m?
Similarly, the slope of the line y=7x-3 is 7! ^^
--
Hope that this helped! Best wishes.
--
Which equation can pair with x 2y = 5 to create an inconsistent system?
The equation that can be paired with x + 2y = 5 to create an inconsistent system is given by:
2x + 4y = 3.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
An inconsistent system is a system that has no solutions, and it happens when the coefficients of x and y are multiples, and the independent terms are not.
Hence:
x + 2y = 5.
2x + 4y = 3.
Is inconsistent, as the variables are each multiplied by 2, but the independent term is not.
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Answer:
A
Step-by-step explanation:
Edge.
What is the value of x.
Answer:
Step-by-step explanation:
x + x + 36 = 180
2x + 36 = 180
2x = 144
x = 72
Polygon ABCDE is reflected to produce polygon. A B C D E. what is the equation for the line of reflection
The graph of f(x) = 3.2x-3 is shown below. g(x) is a transformation of f(x).
How would you write the equation for the function g(x)?
Answer:
C. g(x) = 3·2^x +2
Step-by-step explanation:
The graph of g(x) appears to be a translation upward of the graph of f(x).
__
To find the equation of g(x), we can add 5 to f(x), since the translation appears to be 5 units. (The y-intercept of f(x) is 0; the y-intercept of g(x) is 5.)
g(x) = f(x) +5
g(x) = (3·2^x -3) +5
g(x) = 3·2^x +2
__
You can also determine the correct choice by looking at the value at x=0:
A. g(0) = 3 +6 = 9
B. g(0) = 1 +3 = 4
C. g(0) = 3 +2 = 5 . . . . matches g(0) on the given graph
D. g(0) = 3
Please help me!! High School algebra 2 math. Big Ideas Math
Answer:
x = 8
Step-by-step explanation:
Hello!
The missing angle in the triangle can be found by subtracting 90° and 45° from 180°. The missing angle is 45°.
This means that the triangle is isosceles, as there are two congruent base angles, 45° and 45°.
The side lengths opposite these two angles are congruent.
We can see that 8 is opposite 45°, and x is opposite 45°. Therefore, x must be equal to 8.
The value of x is 8.
Answer:
x = 8
Step-by-step explanation:
The interior angles of a triangle sum to 180°.
The given triangle is a right triangle, so the missing angle is 45°
⇒ 180° - 90° - 45° = 45°
As the triangle has 2 equal angles, this means it is an isosceles triangle (with its vertex at the right angle). An isosceles triangle has legs of equal measure, therefore [tex]x=8[/tex].
Proof
This can be proven by using the tan trigonometric ratio to calculate the value of x.
Tan trig ratio
[tex]\sf tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = 45°O = 8A = xSubstituting the given values into the equation and solving for x:
[tex]\implies \tan (45^{\circ})=\dfrac{8}{x}[/tex]
[tex]\implies x=\dfrac{8}{\tan (45^{\circ})}[/tex]
[tex]\implies x=\dfrac{8}{1}[/tex]
[tex]\implies x=8[/tex]
State fundamental theorems
Answer:
Step-by-step explanation:
What is the equation of a line with a slope of -3 and a y-intercept of 4?
A. y= 4x+3
B. y= 4x-3
C. y=-3x-4
D. y=-3x+4
Answer:
y = -3x+4
Step-by-step explanation:
The slope intercept form of a line is given by
y = mx+b where m is the slope and b is the y intercept
y = -3x+4
Step-by-step explanation:
We have,
Slope (m) = -3y-intercept (c) = 4We know that,
y = mx+c
y = -3x+4
Hence, option (D) is correct.
I will give brainliest! 40 points!
ling wants to determine the average distance she travels each day in her car. she records the odometer reading, which measures the distance the car has traveled, each morning for a week.
day 1 2 3 4 5 6 7
odometer (mi) 10,150 10,211 10,424 10,769 10,884 11,155 11,477
what is the mean distance ling travels each day? show your work.
Answer:
221.16
Step-by-step explanation:
Find the difference between each day. Add all the differences together, then divide that number by 6 (the number of differences) to find the mean.
Answer:
189.57 miles per day.
Step-by-step explanation:
I took the test
Clare makes a pattern of shapes each shape in the pattern is 1 unit longer and 1 unit taller than the shape before it which picture could show the first three shapes in Clare pattern?
Answer:
triagle
Step-by-step explanation:
it is tringle because because this pattern other is tall and other is short it gona be isocelese triagle
Janine sketched a quick graph. "Looks like the solution is (-30, -91)." Is she right? How do you know? Be
clear and complete.
Answer:
- -=+ we should just add it to make the
Through a regular hexagon whose base edge is 8cm and whose height ii 12cma hole in the shape of the right prism with ots end being rhombus with diagonals of 6cm and 8cm is drilled find the total surface area and volume of the remaining soild?
The total surface area of the remaining solid is 48(4+✓3) centimeters square.
How to calculate the surface area?Through a regular hexagonal prism whose base edge is 8 cm and the height is 12 cm, a hole in the shape of a right prism.
The formula for the total surface area will be:
= Total surface area=2(area of the base)+ parameter of base × height
where,
Height= 8cm
Parameter of base=12(2) = 24
Area of the base= 6×✓3/4×4² = 64✓3/4
The surface area of the remaining solid will be:
= 2(64✓3/4) + 24 × 8
= 2(64✓3/4 + 192
With the hole is a rhombus prism with the following parameters:
diagonal 1 = 6, diagonal 2 = 8, height = 12
The volume is:
V1 =0.5 × d1 × d2 × h
V1 = 0.5 × 6 × 8 × 12
V1 = 96
The dimensions of the hexagonal prism are:
Base edge (a) = 8
Height (h) = 12
The volume is
V2 = (3✓(3)/2)a²h
V2 = (3✓3)/2) × 8² × 12
V2 = 1152✓3
The remaining volume is
V = V2 -V1
V = 1152✓3 - 96
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Which of the following is the equation of the quadratic function below?
10
-10
10
O A. y = x² +9x-18
OB. y=x²-2x+1
C. y=x²-9x+18
OD. y=x²+2x-1
-10
Answer:
ehhhh probably C cuz it makes more sense
The graph shows the relationship between the number of months different students practiced boxing and the number of matches they won:
Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)
Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)
The y-intercept is 3.75, and the equation of the line of best fit is
y = 1.5x + 3.75, and after 13 months, 23 matches could be won.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
Part A:
As we can see in the graph, the line crosses the y-axis at a certain point between 3 and 4.5.
So the y-intercept lies between 3 and 4.5
We can take the middle of these two values to get the approximate value of the y-intercept.
b = (3+4.5)/2 = 3.75
We know the line of the best fit is:
y = mx + b
y = mx + 3.75
b is the y-intercept and m is the slope of a line
Plug the point (9, 18) in the equation to get the value of m:
18 = 9m + 3.75
m = 1.5
y = 1.5x + 3.75
Plug x = 13 months in the above equation:
y = 1.5(13) + 3.75
y = 23.25 ≈ 23 number of matches that could be won
Thus, the y-intercept is 3.75, and the equation of the line of best fit is
y = 1.5x + 3.75, and after 13 months, 23 matches could be won.
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