Answer:
x²-16
Step-by-step explanation:
x²-16 =0
Add 16 to both sides
x²-16 + 16 = 0 + 16
Simplify
x²= 16
For x²=(fa) the solutions are x = √(fa), -√(fa)
X=√16 ,X= -√16
√16=4
-√16 = -4
x=4, x= -4
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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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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Need a some help with explanation. Thank you
Answer:
C. (1, 3)
Step-by-step explanation:
The x-coordinate of a point is the measure of the horizontal distance a point is to the right of the y-axis. When the point is translated 4 units to the left, its x-coordinate is reduced by 4: x ⇒ x-4.
The y-coordinate of a point is the measure of the vertical distance a point is above the x-axis. When the point is translated 2 units up, its y-coordinate is increased by 2: y ⇒ y+2.
__
translated pointsThe translation 4 units left and 2 units up can be summarized by ...
(x, y) ⇒ (x -4, y +2)
Then the translated vertices are ...
Q(1, 3) ⇒ Q'(1 -4, 3 +2) = Q'(-3, 5)
R(5, 1) ⇒ R'(5 -4, 1 +2) = R'(1, 3) . . . . . . . matches choice C
S(3, 5) ⇒ S'(3 -4, 5 +2) = S'(-1, 7)
Of the points listed, the point (1, 3) matches a translated vertex.
what is the probability that a coin will land on heads
Answer:
50%
Step-by-step explanation:
When you toss a coin it will either land on tails or heads, so we have 2 possibilities who have the same chance of happening. Thus the probability that the coin lands on heads is 50% (same for tails).
Answer:
0.5
Step-by-step explanation:
Because probability is always between 0 and 1
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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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:
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.
help pls pls pls pls pls pls
Answer:
63
Step-by-step explanation:
(1/2) · b · h
(1/2) * 14 * 9 = 63
Answer: 63 in²
Step-by-step explanation:
The problem gives us the formula to use. We will simplify plug in the correct values and solve.
b = base
h = height
[tex]\displaystyle \frac{b*h}{2}[/tex]
[tex]\displaystyle \frac{14*9}{2}[/tex]
[tex]\displaystyle \frac{126}{2}[/tex]
63
63 square inches
You work 40 hours/week for 50 weeks and are given the option to be paid hourly or to go on salary. In which situation will you earn the most?
•
A. $30,000/year
B. $15.00/hour
C. $30,000/year with a 10% bonus
D. $15.00/hour and a $2,000 bonus at the end of the year
The answer is:
$30,000/year with a 10% bonus
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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. . . r
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:
What is the mode of the data represented in this line plot?
Enter your answer in the box.
Answer:
2
Step-by-step explanation:
Hey there!
In order to find the mode, you need to find the number thatis plotted the most
As you can see on the line plot, the number 2 has been plotted more than the other numbers
Meaning, that 2 is the mode
Answer:
2
Step-by-step explanation:
:)
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:
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]
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
if the sum of lengths of two adjacent sides of parallelogram is 5 units then what is the perimeter of the parallelogram
Answer: 10
Step-by-step explanation:
Opposite sides of a parallelogram are congruent, so the sum of the lengths of each pair of adjacent sides must be 5. Thus, the perimeter is 5(2)=10.
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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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 : 275. A baseball card sold for $241 in 1975 and was sold again in 1988 for $405. Assume that the growth in the value V of the collector's item was exponential.
The exponential growth rate of the baseball card given its price in 1975 and 1988 is 4.07%.
What is the exponential growth rate?The exponential growth rate is the rate of increase in the value of an asset with the passage of time.
Exponential equations have the form a[tex]b^{x}[/tex]
Growth rate = (future value / present value)^(1 / number of years)
(405 / 241)^(1/13) = 4.07%
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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:
the company sells laundry soap in boxes, 4 inches by 8
inches by 12 inches. The company wants to offer larger economy size boxes.
uit in ea
a. What changes in dimensions would give a box with double the volume?
Pls help...will give brainliest
Answer:
i think the answer is (-4,2)
Step-by-step explanation:
PLEASE HELP!!! ASAP, Will Mark Brainlest!!
Juan manages a restaurant which is currently hiring. On Tuesday he interviewed 3 waiters, 2 chefs, and 4 dishwashers. On Wednesday he interviewed 4 waiters, 4 chefs, and 4 dishwashers. Each day one woman applied for a job while the rest were men. What is the probability that the woman shared the same profession?
Probability helps us to know the chances of an event occurring. The probability that the woman shared the same profession is 0.334.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The probability of both being a waiter is,
P(Both Waiter) = (3/9)×(4/12) = 1/9
The probability of both being chefs,
P(Both Chef) = (2/9)×(4/12) = 2/27
The probability of both being a Dishwashers,
P(Both Dishwasher) = (4/9)×(4/12) = 4/27
Thus, the probability that the woman shared the same profession is,
Probability = P(Both Waiter) + P(Both Chef) + P(Both Dishwasher) = 0.33
Hence, the probability that the woman shared the same profession is 0.334.
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Find the key features of the equation and graph it. (Can you explain how to find them and not just the answers please)
Given a function in a table or in algebraic or graphical form, identify key features such as x- and y-intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. Use key features of an algebraic function to graph the function.
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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Write the quadratic equation in standard form:
Standard form ax²+bx+c=0
5x²+7+3x+3x=05x²+7+6x=05x²+6x+7=0Done
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%
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].
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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