Answers
Answer:
27 ) x = 15°,
28 ) x = 18°
Step-by-step explanation:
27 ) We are given angle measures of 85 degrees, consecutively 6x + 5, each forming a linear pair;
85 + ( 6x + 5 ) = 180 ⇒ by definition of linear pair we have two measures of angles that add to 180°,
85 + ( 6x + 5 ) = 180 ⇒ take out ( ),
85 + 6x + 5 = 180 ⇒ combine like terms,
90 + 6x = 180 ⇒ subtract 90 from either side of equation,
6x = 90 ⇒ divide 6 on either side of equation,
Solution; x = 15°
28 ) We are given angle measures of 110 degrees, consecutively 3x + 16, each forming a linear pair;
110 + ( 3x + 16 ) = 180 ⇒ by definition of linear pair we have two measures of angles that add to 180°,
110 + ( 3x + 16 ) = 180 ⇒ take out ( ),
110 + 3x + 16 = 180 ⇒ combine like terms,
126 + 3x = 180 ⇒ subtract 126 from either side of equation,
3x = 54 ⇒ divide 6 on either side of equation,
Solution; x = 18°
Related Questions
Which is not a root of z3 + 8 = 0?
a. 2
b. -2
c. 1+1
d. 1-1-13
Please select the best answer from the choices provided
A
B
C
D
Answers
=================================================
Short explanation:
Plug z = 2 into the equation and you'll find that
z^3 + 8 = 2^3 + 8 = 8+8 = 16
but the result should be 0 since the original equation has 0 on the right side. Therefore, z = 2 is not a solution.
------------------------------------
Longer explanation:
Solve the equation for z to find the three roots.
z^3 + 8 = 0
(z+2)(z^2 - 2z + 4) = 0 ... sum of cubes factoring rule
z+2 = 0 or z^2 - 2z + 4 = 0
z = -2 or z^2 - 2z + 4 = 0
We see that z = -2 is one root. To find the other two roots, use the quadratic formula to solve z^2 - 2z + 4 = 0 for z
[tex]z = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\z = \frac{-(-2)\pm\sqrt{(-2)^2-4(1)(4)}}{2(1)}\\\\z = \frac{2\pm\sqrt{-12}}{2}\\\\z = \frac{2\pm\sqrt{-1*4*3}}{2}\\\\z = \frac{2\pm\sqrt{-1}*\sqrt{4}*\sqrt{3}}{2}\\\\z = \frac{2\pm i*2*\sqrt{3}}{2}\\\\z = \frac{2\pm 2i*\sqrt{3}}{2}\\\\z = \frac{2(1\pm i*\sqrt{3})}{2}\\\\z = 1\pm i\sqrt{3}\\\\z = 1+ i\sqrt{3} \ \text{ or } \ z = 1- i\sqrt{3}\\\\[/tex]
Therefore, the three roots of z^3+8=0 are [tex]z = -2, \ z = 1+i\sqrt{3}, \ z=1-i\sqrt{3}[/tex]
The value z = 2 is not part of the list of solutions.
We can verify each solution by plugging it back into the original equation. For instance, with z = -2, we get
z^3 + 8 = 0
(-2)^3+8 = 0
-8+8 = 0
0 = 0 ... solution is confirmed.
I'll let you check the other solutions.
An aircraft carrier left Port 35 traveling north five hours before a container ship. The container ship traveled in the opposite direction going 8 km/h faster than the aircraft carrier for seven hours after which time the ships were 303 km apart. What was the aircraft carrier's speed?
Answers
Answer:
21.75 km/h
Step-by-step explanation:
Let's call the aircraft carrier speed 'x', so the speed of the container ship is 'x+8'
The distance travelled can be found with the product of the speed and the time travelled: d = v * t
The aircraft carrier travelled five hours, so the distance travelled is:
d1 = x * 5 = 5x
Then, the container ship travelled seven hours, so the distance travelled is:
d2 = (x+8)*7 = 7x + 42
As they travelled in opposite directions, the distance between then is the sum of these distances, and it is equal 303 km, so we have that:
d1 + d2 = 303
5x + 7x + 42 = 303
12x = 261
x = 21.75 km/h
Answer:
The aircraft carrier's speed was 13 km/h
Step-by-step explanation:
The parameters given in the question are;
Time of departure of the aircraft carrier = 5 hours before the container ship
Speed of the container ship = 8 km/h faster than the aircraft carrier
Distance between the two ships after 7 hours = 303 km
Let the speed of the aircraft carrier be Z
∴ The speed of the container ship = Z + 8
Since the aircraft carrier left port 35 travelling North 5 hours earlier we have;
Total time of travel of the aircraft carrier at the time of measurement of the distance between the two ships = 5 + 7 = 12 hours
Therefore, since both ships are moving in opposite direction on the same line path, we have;
303 = 12×Z + 7 × (Z + 8) = 12·Z + 7·Z + 56
19·Z = 303 - 56 = 247
∴ Z = 247/19 = 13 km/h
Hence, the aircraft carrier's speed was 13 km/h.
Determine which consecutive integers do not have a real zero of f(x) = x^3+5x^2 -x -6 between them.
(-6,-5)
(-2,-1)
(-5,-4)
(1,2)
Answers
Answer:
(-6, -5).
Step-by-step explanation:
If there is a zero between the integers there will be a change of sign of f(x).
x^3 + 5x^2 - x - 6
f(1) = 1 + 5 - 1 - 6 = -1
f(-1) = -1 + 5 + 1 - 6 = -1
f(2) = 8 + 20 - 2 -6 = 20
There' a change of sign between f(1) and f(2) so there is a zero between (1, 2).
f(-2) = -8 + 20 + 2 - 6= 6
So there is also a zero between -1 and -2. (-2, -1)
F(-4) = 14, f(-5) = -1 = change of sign so there is also a zero in (-5,-4)
f(-6) = -36 - no change in sign between -5 and -6.
Question is in the image, it's due in tomorrow
Answers
Answer:
Since a and b are constant the answer is 6.5
Step-by-step explanation:
g(x) = 2x + 5
g(x) = y
y = 2x + 5
y - 5 = 2x
[tex]\frac{y-5}{2}[/tex] = x
[tex]g^{-1}[/tex](x) = [tex]\frac{x-5}{2}[/tex]
8 = h(1) and h(3) = 26
26 = a(3) + b
a = b
6.5 = 6.5
26 = 6.5(3) + 6.5
26 = 19.5 + 6.5
26 = 26
Square PQSR is inscribed in circle T. RS = 8_/2.
a. Find the length of the diameter of Circle T.
b. Find the Perimeter of PQSR.
c. Find the Circumference of Circle T.
Answers
Answer: Look at explanation, and hope it helps. Please mark as brainliest! Take care during these hard time.
Step-by-step explanation:
a.
A diagonal of a square inscribed in a circle is the diameter.
So, to find the diameter we know if we separate the square into two different 45-45-90 degree triangles where a and b is 8[tex]\sqrt{2}[/tex]. Use the 45-45-90 degree theorem shown in picture to find that the diagonal 8[tex]\sqrt{2}[/tex] times [tex]\sqrt{2}[/tex] equals 16.
So, the diagonal is 16, thus the diameter is 16.
b.
Multiply 8[tex]\sqrt{2}[/tex] times 4 to get 32[tex]\sqrt{2}[/tex] as the perimeter as there are 4 sides which are equal to RS
c.
The circumference of a circle is the diameter times [tex]\pi[/tex]. The diameter we know from a, which is 16. So, it is 16[tex]\pi[/tex]
anyone got da answer xd?
Answers
Answer:
i say C
Step-by-step explanation:
pi is 3.14 so you have to find either 3.13 or 3.15
For the function f(x)=10(x+5)−9, find the value of f(3)
Answers
Answer:
f(3) = 71
Step-by-step explanation:
f(x) = 10(x + 5) − 9
f(3) = 10(3 + 5) - 9
f(3) = 10(8) - 9
f(3) = 80 - 9
f(3) = 71
a ball is thrown into the air. After t seconds, the ball's height is given by h(t)+=12-3(t-2) squared where h is measured in feet. What is the maximum height of the ball?
Answers
Answer:A
+9
Step-by-step explan ation:
2020
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What is the value of log5 625?
Help me plz
Answers
Answer: The answer is 4.
log5 (625) can be interpreted as, "5to what power is equal to 625?
"Since 54=625,log5(625)=4
The value of the logarithm of 625 to base 5, log₅(625), obtained from the definition of logarithms is 4
What is a logarithm?The logarithm function logₐ(x) is the inverse of the exponential function, bˣ, which indicates that where, y = logₐ(x), then [tex]a^y[/tex] = x. Therefore, the logarithm function gives the power to which the base a must be raised to produce x.
With regards to log₅(625), the power to which the base, 5, should raised to produce 625 is required.
Whereby 5⁴ = 625, it can be concluded that log₅(625) = 4
Therefore, the value of log₅(625) is 4
Learn more on the logarithm of a number here: https://brainly.com/question/28845183
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Helppppppppppppppppppp
Answers
Answer:
volume of empty space is 1307.245in
Step-by-step explanation:
I'm pretty sure this is right because I found the volume of the cube which came out to be 2744 and the volume of the sphere which came out to 1436.755 and subtracted them.
23. The chair lift at a ski resort rises at an angle of 21° and attains a vertical
height of 1575 feet. How far does the chair lift travel up the side of a
mountain?
Answers
Answer:
The chair travels approximately 4,394.924 feet.
Step-by-step explanation:
We need to use trigonometric functions to solve this problem. You are given the opposite side of an angle and asked to find the hypotenuse. This means you must use sine, because sine is the ratio between opposite and hypotenuse.
Set up the equation as so:
sin(21) = 1575/x
(x being the hypotenuse). Solve for x by multiplying both sides by x and then dividing both sides by sin(21). Solve 1575/(sin(21)), and you get 4,394.924273, or 4,394.92
Chicago has a temperature of -10 degrees Fahrenheit. It is colder in Minneapolis than in Chicago. Select all the values that could represent the temperature of Minneapolis.
A. 112F
B. -18F
C. 1-8F
D. -12F
E. -20
Answers
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Simplify when it is possible.
10x2-y + x2 =
Answers
Answer:
11x2-y=
Step-by-step explanation:
well it's easy simplifying 10+1=11
Justin rolled a number cube 48 times. The cube landed on the number six 2
4 times. Is the experimental probability greater than or less than the
theoretical probability? Explain.
Answers
Answer:
greater than
Step-by-step explanation:
half the times the cube was rolled it landed on six the theoretical probability is only eight, 48 > 8
Lyana is painting her bedroom. Her room is 12’ x 18’. The ceilings are 8 feet high. She will need to put two coats of paint on. How many cans of paint will she need if the square footage of one can is 400 square feet?
Answers
Answer:
2 cans to cover the room but she will have a lot of paint left over
Step-by-step explanation:
12*18=216
the area of her room is 216 square ft.
216*2=432
she will need 2 cans
Answer:
Lyana will need 4 cans of paint to paint her whole room or only 3 if she doesn't paint the floor.
Step-by-step explanation:
Firstly we need to know how much paint she will need to use.
The area of her room is given by 2(ac+bc), where a is the length, b is the width and c is the height.
Applying that we get that the area of her room is 2*12*18+2*18*8=720.
This applies if we assume that she also paints the floor. If she doesn't we need to subtract the area of the floor which is 12*18=216. So 720-216=504
She will paint her room twice she the amount of paint she needs is twice the area:
720*2=1440
or if she does not paint the floor
504*2=1008
Now we answer how many cans is that by dividing by 400 and rounding up.
1440/400=3.6 she needs, therefore, 4 cans
1008/400=2.52 she needs 3 cans
What is the value of y?.
Answers
Answer:
54 degrees
Step-by-step explanation:
180- 72 = 108
108 divided by 2 = 54
Answer:
54°
Step-by-step explanation:
There is 180° is a triangle. We have 72° given already
180 - 72 = 108
Since there are two y's we divide by two
108 ÷ 2 = 54°
I hope this helps! ^_^
MATH HELP PLEASE!!!
cecile packages snack mix at a health food store.
She uses 13 of her supply of sunflower seeds to make a salted snack mix and 29 of her supply to make an unsalted snack mix. If Cecile uses 10 pounds of sunflower seeds, how many pounds of seeds are in her supply?
Answers
Answer: BRAINLIEST PLEASE
her supply has 18 pounds
Explanation:
Assume that the number of pounds in her supply is x.
We are given that:
She uses 1/3 x in salted mix and 2/9 x in unsalted mix.
This means that:
Total amount used = 1/3 x + 2/9 x = 5/9 x of her supply
Now, we are also given that:
She used 10 pounds of her supply.
This means that:
5/9 x = 10
5x = 9*10 = 90
x = 18 pounds
Hope this helps :)
The number of pounds of seeds in her supply is 18
Given:
let
her total supply = x
Supply of salted snack = 1/3x
Supply of unsalted snack = 2/9x
Total pounds of sunflower seed = 10
Total supply of sunflower seeds = salted snack + unsalted snack
10 = 1/3x + 2/9x
10 = (3x + 2x) / 9
10 = 5/9x
divide both sides by 5/9
x = 10 ÷ 5/9
x = 10 × 9/5
= (10 × 9) / 5
= 90/5
= 18
x = 18
Therefore, number of pounds of seeds in her supply is 18
Read more:
https://brainly.com/question/2261275
What is the value of x?
°x=32
°x=36
°x=37
°x=40
Answers
Answer: x= 40
Step-by-step explanation:
x + 4x -20=180
5x -20=180
+20 +20
5x= 200
x= 40
Answer:
A) x=32
Step-by-step explanation:
To work out the value of x you would first need to minus 20° from 180°, this gives you 160°. This is because the total angle in a straight line is 180° and that by subtracting 20 from 180 you are isolating the value of the x's.
The next step is to add up the number of x's in that angle. You can do this by adding the values of 4 and 1, this gives you 5.
The final step is to divide the angle 160 by the total number of x's of 5, this gives you 32°. This si because we had previously isolated the value of the 5x and so by dividing it by 5 so we would work out the value of x.
1) Minus 20 from 180.
[tex]180-20=160[/tex]
2) Add 4 and 1.
[tex]4+1=5[/tex]
3) Divide 160 by 5.
[tex]160/5=32[/tex]
please help me with this
Answers
Answer: 1,253
Step-by-step explanation:
Just multiply length, width, and height of both boxes and add them together. So 7x5x5= 175 and 11x14x7=1,078. 1,078+175=1,253
Howard is rock climbing. He descended 300 meters in 5 hours. Which is NOT equivalent to Howard’s average change in location per hour? A. 300/-5 meters per hour B. -300/5 meters per hour C. -(300/5) meters per hour D. -(-300/5 meters per hour
Answers
Answer:
D i think
Step-by-step explanation:
Answer
D. -(-300/5 meters per hour
Step-by-step explanation:
I took the quiz, and I got it right on time4learning 2022 I hope I helped and more importantly I hope you pass byee!!!
What percentage of customers choose vanilla ice cream?
A. 32.5%
B. 45%
C. 36%
D. 58%
Answers
Answer:
45%
Step-by-step explanation:
100%=36+26+18= 80 36/80 as a fraction is 45%
decide whether the following situation is looking for the part, the percent, or the whole: 81 of 271 pages in a book
Answers
Answer:
the whole
Step-by-step explanation:
i may be wrong
sorry
Answer:
Definitely percent
Step-by-step explanation:
Suppose the equation of a line is 2x - 4y = - 8. Which coordinate pair represents the y-intercept?
es )
A)
(0, 2)
B)
(20)
(0,0)
D
(0, -2)
No
Answers
Answer:
A
Step-by-step explanation:
Evaluate the expression of 2 + |6 - 2|
Answers
Answer:
The answer is 6
Step-by-step explanation:
2+4
Find the volume of each composite figure. Round to the
nearest tenth. (Hint) Find the Volume of both figures, then additional step is required to find your answer.
Answers
Answer:
1209.06 cubic feet
Step-by-step explanation:
use the formula for the volume of a cylinder and the volume of a rectangular prism, and then plug the values into that
The volume of the composite figure consisting of a cylinder and a rectangular prisms to the nearest tenth is 1209.1ft³.
What is a cylinder and a rectangular prism?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.1415 )
A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is width, l is length and h is the height
From the diagram, the figure consist of a cylinder and a rectangular prism.
For the cylinder;
Radius r = 4ftHeight h = 4ftVolume of the cylinder V_c = ?For the rectangular prism;
Width w = 14ftLength l = 12ftHeight h = 6ftVolume of the rectangular prism V_r = ?Volume of the cylinder.
V_c = π × r² × h
V_c = 3.1415 × (4ft)² × 4ft
V_c = 3.1415 × 16ft² × 4ft
V_c = 201.1ft³
Volume of the rectangular prism.
V_r = w × h × l
V_r = 14ft × 6ft × 12ft
V_r = 1008ft³
Now, the volume of the composite figure will be;
V = V_c + V_r
V = 201.1ft³ + 1008ft³
V = 1209.1ft³
Therefore, the volume of the composite figure consisting of a cylinder and a rectangular prisms to the nearest tenth is 1209.1ft³.
Learn more on volume of cylinder here: brainly.com/question/16788902
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Solve the inequality 3 x - 3 < 9
Answers
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x<4
The solution to the given inequality 3x - 3 < 9 is;
x < 4
We are given the inequality;
3x - 3 < 9
Using addition property of equality, add 3 to both sides to get;
3x - 3 + 3 < 9 + 3
3x < 12
Using division property of equality, divide both sides by 3 to get;
3x/3 < 12/3
x < 4
Read more at; https://brainly.com/question/21644280
Andy and Donald are both running toward the soccer ball during a game.
Andy's path is represented by the parametric equations x(t)=24+2/3t,y(t)=8+16t, where t is on the interval [0,50] and t is measured in tenths of seconds.
Donald's path is represented by the parametric equations x(t)=12+t,y(t)=5+1/4t, where t is on the interval [0,50] and t is measured in tenths of seconds.
Do the boys collide? If so, when do they collide?
Andy and Donald do not collide.
Andy and Donald collide at 4.8 seconds.
Andy and Donald collide at 2.4 seconds.
Andy and Donald collide at 3.6 seconds.
Answers
Answer:
Correct option: second one -> Andy and Donald do not collide.
Step-by-step explanation:
To find if the boys collide, we need to find if there is a common value of t where the their x position are equal and their y position are equal. To do this, we make x(t) of Andy equal to x(t) of Donald, , then if there is a value for t, we do the same for y(t) and check if the values of t are equal:
24 + 23t = 12 + t
22t = -12
t = -0.5455 seconds
As the time is negative, it will not occur, so the boys will never collide.
Correct option: second one
800, 400, 200, ___, 50, 25
Answers
Answer:
100
Step-by-step explanation: It is 100 because they are dividing by 2 each time, so it is 100.
Answer:
100
Step-by-step explanation:
hurry will give brainliest!!
Answers
Answer:
B and D
Step-by-step explanation:
A 13 ft ladder is resting on a wall. The angle the ladder makes with the floor is 45 degrees. How high off the ground is the top of the ladder?
Use the function y=13cos(theta) to find the answer
Answers
Answer: 9.19 ft
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.
Sin α = opposite side / hypotenuse
Where α is the angle of elevation of the ladder to the ground, the hypotenuse is the longest side of the triangle (in this case is the length of the ladder), and the opposite side (x) is distance between the top of the ladder and the ground.
Replacing with the values given:
Sin 45 = x/ 13
Solving for x
sin45 (13) =x
x= 9.19 ft
Feel free to ask for more if needed or if you did not understand something.