Answer:
So we must determine the distance between our two given points and that can be found using the distance formula [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
Plugging the values into the equation and solve
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(-9-5)^2+(-2-6)^2}[/tex]
[tex]d=\sqrt{(-14)^2+(-8)^2}[/tex]
[tex]d=\sqrt{196+64}[/tex]
[tex]d=\sqrt{260}[/tex]
[tex]d=16.125\ units[/tex]
Therefore, our final answer is that the distance is 16.125 units
Hope this helps! Let me know if you have any questions
what’s the area and perimeter for this problem?
Answer:
Area=153.75 divdided by 2 = 76.88
permitere= 8 + 10.25+18.8=37.05
Step-by-step explanation:
Pls help...will give brainliest
Answer:
i think the answer is (-4,2)
Step-by-step explanation:
enter your answer to the nearest tenth x 9 12
Answer:
x = 36.9°
Given:
opposite side: 9
adjacent side: 12
angle: x
Using tane rule:
[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]
Solve:
[tex]\sf tan(x) = \dfrac{9}{12}[/tex]
[tex]\sf x = tan^{-1}(\dfrac{9}{12})[/tex]
[tex]\sf x = 36.87[/tex]
[tex]\sf x = 36.9[/tex]
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
since the given triangle is an right angled triangle we can use Trigonometric ratios here :
[tex]\qquad \sf \dashrightarrow \: \tan(x) = \dfrac{9}{12} [/tex]
[tex]\qquad \sf \dashrightarrow \: \tan(x) = \dfrac{3}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: x= tan { }^{ - 1} \bigg( \dfrac{3}{4} \bigg)[/tex]
[tex]\qquad \sf \dashrightarrow \:x \approx37 \degree[/tex]
Mt. etna is now 11,013 feet tall after growing 100 feet. what was the percent change in its height, rounded to the nearest tenth?
Answer:
0.9%
Step-by-step explanation:
The percentage change is found by multiplying the fractional change by 100%. The fractional change is the change amount divided by the original amount.
__
change in height = 100/11013 × 100% ≈ 0.0090802 × 100% ≈ 0.9%
How much force does the atmosphere exert on one side of a vertical wall 4. 00-m high and 10. 0-m long?
A force of 4.05×10⁶ N was exerted on one side of the wall.
What is the force?Force is an external agent capable of changing the state of rest or motion of a particular body. It has a magnitude and a direction.
The following data were obtained from the question:
Breadth (B) = 4 m
Length (L) = 10 m
Standard pressure (P) = 101325 Nm¯²
Next, we shall determine the area of the wall. This can be obtained as follow:
Area (A) = length (L) × breadth (B)
A = 10 × 4
A = 40 m²
Finally, we shall determine the force exerted on one side of the wall as follow:
Standard pressure (P) = 101325 Nm¯²
Area (A) = 40 m²
Pressure (P) = Force (F) /Area (A)
101325 = F/40
F = 101325 × 40
F = 4.05×10⁶ N.
Therefore, a force of 4.05×10⁶ N was exerted on one side of the wall.
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PLEASE HELP ME OUT ASAP :(
Answer:
Step-by-step explanation:
Cylinder A:r = 3 cm
Volume = 27π cm³
[tex]\sf \boxed{\text{Volume of cylinder=$\pi r^2h$}}[/tex]
[tex]\sf \pi*3*3*h = 27 \pi\\[/tex]
[tex]h = \dfrac{27 \pi}{\pi * 3 * 3}\\\\ \boxed{\bf h = 3 \ cm}[/tex]
Cylinder B:[tex]\sf \r_A : r_B = 3 : 9[/tex][tex]\sf r_A : r_B = 3 : 9[/tex]
= 1 : 3
[tex]\sf h_A : h_B = 1 : 3\\[/tex]
[tex]\sf \dfrac{3}{h_B}=\dfrac{1}{3}\\\\ cross \ multiply,\\\\ 3*3 = 1*h_B\\\\ h_B = 9 \ cm[/tex]
Volume of cylinder B = π * 9 * 9 * 9
= 729π cm³
[tex]\sf V_A : V_B = 27 \pi :729 \pi[/tex]
= 1 : 27
Volume of cylinder A to volume of cylinder B = 1 : 27Drag vegetables to represent each total weight shown.
[tex]3 b(broccolis=\frac{1}{8} )=\frac{3}{8}[/tex]
[tex]4c(carrots=\frac{1}{6})=\frac{4}{6}[/tex]
Lastly:
[tex]2t(tomatoes=\frac{1}{4})=\frac{2}{4}[/tex]
Select the correct answer. what is the range of ? a. (-[infinity], 1] b. [1, [infinity]) c. [6, [infinity]) d. (-[infinity], [infinity])
The range of the graph is the set of output values, and the range is (d) (-infinity,infinity)
How to determine the range?From the graph in the complete question, we can see that the output values (i.e. the y values) extend indefinitely on both sides of the graph
This means that the range of the graph is the set of all real numbers.
This in other words means that (-infinity,infinity)
Hence, the range of the graph is (d) (-infinity,infinity)
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Using Rolle's theorem prove that the function has at most one root on the given interval [tex]f(x)=x^3-12x+11, [-2,2][/tex]
f(x) = _ at x = _ x = _
Answer:
Show that if [tex]f(a) = f(b) = 0[/tex] for some [tex]a,\, b \in [-2,\, 2][/tex] where [tex]a \ne b[/tex], then by Rolle's Theorem [tex]f^{\prime}(x) = 0[/tex] for some [tex]x \in (-2,\, 2)[/tex]. However, no such [tex]x[/tex] exists since [tex]f^{\prime}(x) < 0[/tex] for all [tex]x \in (-2,\, 2)\![/tex].
Note that Rolle's Theorem alone does not give the exact value of the root. Neither does this theorem guarantee that a root exists in this interval.
Step-by-step explanation:
The function [tex]f(x) = x^{3} - 12\, x + 11[/tex] is continuous and differentiable over [tex][-2,\, 2][/tex]. By Rolle's Theorem. if [tex]f(a) = f(b)[/tex] for some [tex]a,\, b \in [2,\, -2][/tex] where [tex]a \ne b[/tex], then there would exist [tex]x \in (a,\, b)[/tex] such that [tex]f^{\prime}(x) = 0[/tex].
Assume by contradiction [tex]f(x)[/tex] does have more than one roots over [tex][-2,\, 2][/tex]. Let [tex]a[/tex] and [tex]b[/tex] be (two of the) roots, such that [tex]a \ne b[/tex]. Notice that [tex]f(a) = 0 = f(b)[/tex] just as Rolle's Theorem requires. Thus- by Rolle's Theorem- there would exist [tex]x \in (a,\, b)[/tex] such that [tex]f^{\prime}(x) = 0[/tex].
However, no such [tex]x \in (a,\, b)[/tex] could exist. Notice that [tex]f^{\prime}(x) = 3\, x^{2} - 12[/tex], which is a parabola opening upwards. The only zeros of [tex]f^{\prime}(x)[/tex] are [tex]x = (-2)[/tex] and [tex]x = 2[/tex].
However, neither [tex]x = (-2)[/tex] nor [tex]x = 2[/tex] are included in the open interval [tex](-2,\, 2)[/tex]. Additionally, [tex]a,\, b \in [-2,\, 2][/tex], meaning that [tex](a,\, b)[/tex] is a subset of the open interval [tex](-2,\, 2)[/tex]. Thus, neither zero would be in the subset [tex](a,\, b)[/tex]. In other words, there is no [tex]x \in (a,\, b)[/tex] such that [tex]f^{\prime}(x) = 0[/tex]. Contradiction.
Hence, [tex]f(x) = x^{3} - 12\, x + 11[/tex] has at most one root over the interval [tex][-2,\, 2][/tex].
Jason can make 15 birdhouses in 3 weeks. At that rate, how many birdhouses can he make in 5 weeks?
Answer:
25 houses in 5 weeks
Step-by-step explanation:
15 house / 3 week * 5 week = 25 houses
Raj left home at 1 pm to travel 675km to visit his sister. he averaged 110km/h for the first part of the trip during which he had a 1 hour rest, and 90km/h for the second part of the trip during which he had a 30 minute rest. he reached his destination at 9pm. the number of minutes taken for the first part of the trip, to the nearest minute______
q9 pg 164 foundations of mathematics and pre-calculus 10
The time used for the first part of the trip in minutes is 270 minutes.
How to find the time used for the trip?Total distance travelled = 675 km
He travelled from 1pm to 9pm.
He rested for 1 hour 30 minutes. The total time used for the trip is 6 hours 30 minutes.
let
the time used for the first part of the trip = x
Therefore,
speed = distance / time
distance = 110x
the time used for the first part of the trip = 6.5 - x
distance = 90(6.5 - x)
distance = 585 - 90x
Hence,
110x + 585 - 90x = 675
20x + 585 = 675
20x = 675 - 585
20x = 90
x = 90 / 20
x = 4.5 hours = 270 minutes
Therefore, the time used for the first part of the trip is 270 minutes.
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The cone to the right has a height of 11 in. and a volume of
103.62 in. Find the radius of the base.
Answer:
2.99924 in
Step-by-step explanation:
Volume of a cone
V = pi x r^2 x h/3
So to solve this problem you plug in the number we already have which is the volume and the height
103.62 = pi x r^2 x 11/3
28.26 = pi x r^2
28.26/pi = r^2
[tex]\sqrt{\frac{28.26}{\pi } }[/tex] = r ≈ 2.99924
Write the quadratic equation in standard form:
Standard form ax²+bx+c=0
5x²+7+3x+3x=05x²+7+6x=05x²+6x+7=0Done
A circular pool is surrounded by a circular walkway. The radius of the pool is y − 4 and the radius of the full circle formed by the walkway is y + 4. Write a polynomial that represents the area of just the walkway itself, not including the space covered by the pool.
(The area of a circle is given by A = πr 2, where r represents the radius of the circle.)
The area of the walkway itself is π[(y + 4)²- (y - 4)²] the radius of the pool is y − 4 and the radius of the full circle formed by the walkway is y + 4
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Area of circle = π * radius²
The area of the walkway itself = π(y + 4)² - π(y - 4)² = π[(y + 4)²- (y - 4)²)
The area of the walkway itself is π[(y + 4)²- (y - 4)²] the radius of the pool is y − 4 and the radius of the full circle formed by the walkway is y + 4
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What are the solutions to the system of the equations below
Step-by-step explanation:
option D is correct answer
Answer:
C
Step-by-step explanation:
[tex]\text{Plug} ~(x,y) = ( 2,0)~ \text{in both equations.}\\\\3*0 = 2-2\implies 0=0\\\\0 = -2(2) +4 \implies 0=0\\\\\text{Hence x =2 and y =0.}[/tex]
Which of the following could be a mirror line on a coordinate plane?
A
(1, 1)
B
(0, 10)
C
the origin
D
the x-axis
Answer: D
Step-by-step explanation:
This is the only option that is a line.
Mr. Washington drills a water well. Ground conditions cause an increase of 5% to the cost per meter, c. In addition, the cost of equipment is $1,400. He calculates the cost of his well using the expression 1, 400 + 1.05c . What other expression could he have used?
Mrs. Taylor would like to construct a confidence interval for the number of highlighters that are borrowed and not returned in her classroom. At the end of a semester, she loaned 115 highlighters and found that 68% were not returned. What is the confidence interval at a 90%confidence level?
A.
(60.9%,75.1%)
B.
(58%,78%)
C.
(67.3%,68.7%)
D.
(65.4%,71.6%)
The confidence interval at a 90% confidence level is (60.9%,75.1%) if in the end of a semester, she loaned 115 highlighters and found that 68% were not returned option (A) is correct.
What is the margin of error(MOE)?It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.
The formula for finding the MOE:
[tex]\rm MOE = Z\times{\sqrt \dfrac{p(1-p)}{n}\\[/tex]
Where Z is the z-score at the confidence interval
p is the population proportion
n is the number of samples.
We have p = 68% = 0.68
n = 115
Z score for 90% confidence interval = 1.64
[tex]\rm MOE = 1.64\times{\sqrt \dfrac{0.68(1-0.68)}{115}\\[/tex]
MOE = 0.071
So the confidence interval will be:
= (0.68-0.071, 0.68+0.071)
= (0.609, 0.751) or
= (60.9%, 75.1%)
Thus, the confidence interval at a 90% confidence level is (60.9%,75.1%) if in the end of a semester, she loaned 115 highlighters and found that 68% were not returned option (A) is correct.
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A spherical cabinet knob has a radius of 1.5 inches. Find the volume of thevcabinet knob.
Answer:
V=14.12 in³
Step-by-step explanation:
This is a tough one. To find the volume, you'll need the followimg equation:
[tex]\frac{4}{3} \pi {r}^{3}[/tex]
The 3 next to the R is an exponent. An exponent involves multiplying the radius by itself. So it would look like this: 1.5×1.5×1.5
Next, you must multiply the result by 3.14. So it would be 3.375×3.14. And finally, you must multiply that result by 4 and divide by 3. So 10.59×4 to get 42.36 then divide that by 3. 42.36 divided by 3 is 14.2. (Answer can vary from time to time and you may need to round up)
The coordinates of a triangle are (1,-1), (3,0), and (1,-4). find the coordinates of
the translated triangle if it is enlarged by a scale factor of 2.
If it is enlarged by a scale factor of 2. Then the coordinates of the translated triangle will be (2, -2), (6, 0), and (2, -8).
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
The coordinates of a triangle are (1,-1), (3,0), and (1,-4).
If it is enlarged by a scale factor of 2.
Then the coordinates of the translated triangle
(1,-1) → (2, -2)
(3,0) → (6, 0)
(1,-4) → (2, -8)
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There are 7 times as many females as males on the maths course at university.
What fraction of the course are female?
Give your answer in its simplest form
Answer:
1/8 of males as females are 7 times of males are x then females are 7x so the fraction of males x will be 1/8
Step-by-step explanation:
HELP WITH THIS PLEASEEE HURRY
Answer:
0.01%
Step-by-step explanation:
There's no need to worry about a problem like this, it's easy. All you have to do is find the area of the smaller rectangle, being 50, then find the area of the other one, 5000, and divide the smaller by the larger and transfer it to a percentage. 50/5000 = 0.01 = 0.01%
The numbers in this sequence increase by 40 each time
30,70,110,150
the sequnce is continued with the same rule
which number in the sequnce will be closest to 300
Answer:
The number closest to 300 would end up being 310!
Step-by-step explanation:
If it took 1.5 qt to f paint to paint the wall on the left how many quarts will be needed to paint the wall on the right?
2.5 quarts will be needed to paint the wall on the right.
What is area of rectangle?The product of length and breadth.
Area of rectangle= length * breadth
Area of first wall = l * b
= 12*7
= 108 st. ft.
Area of 2nd wall
= l*b
=18*10
=180 sq. ft.
If 1.5 qt required to paint the 108 sq. ft. area
For 1 sq ft, paint would be need= 1.5/108
For 180 sq ft paint needed = 1.5*180/108
= 2.5 qt
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Part c what are the dimensions of the rectangular prisms you identified in parts a and b? list dimensions for all your decompositions (sets of shapes).
previous:
part a
think about splitting this shape into rectangular prisms. what is the least number of rectangular prisms in which you can split the shape? answer: 3
part b
in how many different ways can you split the shape to get the same number of rectangular prisms you identified in part a?
answer: 2
The dimensions of the rectangular prisms are the side lengths of the rectangular prism
How to determine the dimensions?A rectangular prism has the following dimensions
Length, width and height
This means that the dimensions of the rectangular prisms are the length, width and height of the prism
To determine the dimension, we simply take the value of the above terms i.e. length, width and height
How to split the rectangular prism?To split the rectangular prism, we simply consider the faces of the rectangular prism.
A rectangular prism has 6 faces
Hence, there are 6 shapes when the rectangular prism is split
Note that the question is incomplete, so I gave a general explanation
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4) An architect is designing a tapered office
tower where the ground floor (floor 0) is
the largest and the floor space is reduced
by 5% per floor. If the ground floor has
an area of 1,140.0 m², what is the area of
the 9th floor?
The area of the 9th floor is 718.48 m² if the ground floor(floor 0) is the largest and the floor space is reduced by 5% per floor.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent :
[tex]\rm y = a^x[/tex]
where a is a constant and a>1
We know we can find the exponential decrease by the below formula:
[tex]\rm y = a(1-r)^n[/tex]
We have a = 1140 m²
r = 5% = 0.05
n = 9
[tex]\rm y = 1140(1-0.05)^9[/tex]
y = 718.48 m²
Thus, the area of the 9th floor is 718.48 m² if the ground floor(floor 0) is the largest and the floor space is reduced by 5% per floor.
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write a standard equation of the circle with the center of (-10,7) and a radius of 4
Answer:
The answer is (x + 10)² + (y – 7)² = (4)².
Step-by-step explanation:
Given;The centre of the circle = (-10, 7)Radius of the circle = 4To Find;Standard equation of the circle.Formula;(x – a)² + (y – b)² = r²It is the general equation with centre (a, b) and radius r.Here, a = (-10), b = 7 and r = 4.
So,
(x – a)² + (y – b)² = r²
[x – (-10)]² + (y – 7)² = (4)²
(x + 10)² + (y – 7)² = (4)²
Thus, The standard equation of the circle with the centre of (-10, 7) and a radius of 4 is
(x + 10)² + (y – 7)² = (4)².
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f
4df
4
f
4f4.f
f.
4f.
4f.
4.f4
.4ff4.
Answer:
what?
Step-by-step explanation:
Answer:
please reformat the question to be readable !
Step-by-step explanation:
PLEASE HELP!!! ASAP, Will Mark Brainlest!!
A radio stállon reports news and weather, every 20 minutes for 4 minutes, If the radio is turned on at a random time, what is the probabillty that the news and weather report Is NOT on? F 0.2 H 0.6 G 0.4 J 0.8
The probability that the news and weather report Is NOT on will be 0.8. Then the correct option is J.
What is probability?Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.
A radio station reports news and weather, every 20 minutes for 4 minutes.
If the radio is turned on at a random time.
Then the probability that the news and weather report Is NOT on will be
P = 1 - 4/20
P = 1 - 0.20
P = 0.8
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