Answer: t=2
Step-by-step explanation:
[tex]1=t+\sqrt{2t} -3\\1-1=t+\sqrt{2t}-3-1\\0= t+\sqrt{2t} -4\\Thus,\\t+\sqrt{2t} -4=0\\Let`s\ \sqrt{t} =x\geq 0\\\Rightarrow\ x^2+\sqrt{2} x-4=0\\x^2-\sqrt{2} x+2\sqrt{2}x-4=0\\ x(x-\sqrt{2})+2\sqrt{2} ( x-\sqrt{2})=0\\ (x-\sqrt{2})(x+2\sqrt{2})=0\\\\x-\sqrt{2} =0\\ x-\sqrt{2}+\sqrt{2}=0+\sqrt{2} \\ x=\sqrt{2}\\ \Rightarrow\ t=(\sqrt{2})^2\\ t=2\\\\x+2\sqrt{2} =0\\x+2\sqrt{2} -2\sqrt{2} =0-2\sqrt{2} \\x=-2\sqrt{2} \notin(x\geq 0)[/tex]
For a ride on a rental scooter , ahmad paid $3 fee to start the scooter plus 11 cents per minute of the ride. The total bill for Ahmad’s ride was $20.49. For how many minutes did ahmad ride the scooter
Ahmad spent 159 minutes for the scooter ride
How to calculate the amount of minutes needed for the ride ?Ahmad paid $3 fee to start the scooter ride
She also paid 11 cents per minutes of the ride
The total bill at the end of the ride is $20.49
The first step is to convert 11 cents to dollars
= 11/100
= 0.11
Therefore the number of minutes can be calculated as follows
20.49 = 0.11x + 3
collect the like terms
20.49 - 3 = 0.11x
17.49 = 0.11x
x= 17.49/0.11
x= 159
Hence Ahmad spent 159 minutes for the scooter ride
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Determine whether y varies directly with x . If so, find the constant of variation.
y=4 x-3
The required value of constant of variation, k does not exist for which x and y vary directly.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of constant of variation
When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion —-- 1
Given relation is y = 4x - 3
Comparing with equation 1, we get, that y does not vary directly with x
Hence, the required value of constant of variation does not exist.
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8 x 100 = 8 x 10^2 i don't know i need help please help!!!!!
Step-by-step explanation:
10^2=100x8 =800
800=8x100
10^2 =100.The reason is, you are basically doing 10x10=100x8=800.
Explain to a new student how to simplify the expression below. Show the updated expression after each step you take.
(-8)+(-3)+(-4)(7) ÷14+9(-2)
Answer:
-31
Step-by-step explanation:
You use pemdas which is
parathesis
exponents
multiply or divide, use in order
then add or subtract, use in order
(-8)+(-3)+(-4)(7)÷14+9(-2)
multiply first
-4*7=-28
(-8)+(-3)+(-28)÷14+9(-2)
Divide next
-28÷14=-2
(-8)+(-3)+(-2)+9(-2)
multiply again
9*(-2)=-18
(-8)+(-3)+(-2)+(-18)
now add
-8+(-3)=-11
(-11)+(-2)+(-18)
add again
-11+(-2)=-13
(-13)+(-18)
add for the last time
-13+(-18)=-31
Determine whether each expression is equivalent to 16^t-0.5
Answer:
its equivilant
Step-by-step explanation:
Equivalent expressions are:
[tex]2^{3t}.2^t[/tex] / 4 and [tex]8^{t}.2^t[/tex] / [tex]2^{0.5}.8^{0.5}[/tex].
Options B and C are the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Solve each expression.
[tex]16^{t-0.5}[/tex]
= [tex]2^{4t - 2}[/tex]
Now,
1)
[tex]2^{3t}.2^t[/tex] / 16
= [tex]2^{4t}[/tex] / [tex]2^4[/tex]
= [tex]2^{4t - 4}[/tex]
2)
[tex]2^{3t}.2^t[/tex] / 4
= [tex]2^{4t}[/tex] / [tex]2^2[/tex]
= [tex]2^{4t - 2}[/tex]
3)
[tex]8^{t}.2^t[/tex] / [tex]2^{0.5}.8^{0.5}[/tex]
= [tex]2^{3t + t}[/tex] / [tex]2^{0.5 + 1.5}[/tex]
= [tex]2^{4t}[/tex] / [tex]2^2[/tex]
= [tex]2^{4t - 2}[/tex]
Thus,
Equivalent expressions are:
[tex]2^{3t}.2^t[/tex] / 4 and [tex]8^{t}.2^t[/tex] / [tex]2^{0.5}.8^{0.5}[/tex].
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Write each number as a percent.
0.25
Answer: 25%
Step-by-step explanation:
0.25
25%
2^2x+1 _5(2x)+2=0
[tex]2 {x}^{2} + 1 - 5(2x) + 2 = 0[/tex]
Answer:
2x²-10x+3=0
Step-by-step explanation:
2x²+1 - 5(2x)+2=0
2x²+1 - 10x+2=0
Combine like terms.
2x²+1 - 10x+2=0
2x²-10x+3=0
Hope this helps!
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Have a great day!
help!! please its easy
The area of the quadrilateral ABCD is 26 square units
How to find the area of quadrilateral ABCD?The quadrilateral ABCD is a trapezoid, and it has the following parameters:
Parallel bases = BC and ADHeight = CEThe lengths of these sides can be calculated using
d = √[(x2 - x1)^2 +(y2 - y1)^2]
So, we have
BC = √[(0 - 4)^2 +(3 + 1)^2] = 4√2
AD = √[(-5 - 4)^2 +(4 + 5)^2] = 9√2
CE = √[(2 - 4)^2 +(-3 + 1)^2] = 2√2
The area of the quadrilateral ABCD is then calculated as
Area = 0.5 * (BC + AD) * CE
This gives
Area = 0.5 * (4√2 + 9√2) * 2√2
Evaluate
Area = 26
Hence, the area of the quadrilateral ABCD is 26 square units
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100 POINTS! ANSWER PLEASE! Order the following rational and irrational numbers from least to greatest. -2 3/5, square root of 20, 3.9, 10/3, 3 7/8
The given rational and irrational numbers can be ordered from least to greatest as follows; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.
What is the arrangement of the numbers in ascending order?It follows from the task content that the numbers given are rational and irrational numbers.
To order the numbers, they should be converted to decimal numbers as follows;
-2 3/5 = -2.6
√20 = 4.47
3.9 = 3.9
10/3 = 3.33
3 7/8 = 3.875
Hence, the order from least to greatest is; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.
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Explain your method for determining the efficient route of a network.
Determining the best path involves the evaluation of multiple paths to the same destination network and selecting the optimum or shortest path.
How is the best route to a network determined?
Finding the optimum route to take when sending packets is a router's main duty. The router looks through its routing table for a network address that corresponds to the packet's destination IP address in order to find the optimum route.7 types of routing protocols -
Routing information protocol (RIP)Interior gateway protocol (IGRP)Enhanced interior gateway routing protocol (EIGRP) Open shortest path first (OSPF) Exterior Gateway Protocol (EGP) Border gateway protocol (BGP) Immediate system-to-immediate system (IS-IS)Learn more about network
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What is the area, in square centimeters, of the isosceles trapezoid below? ¹8 cm 15.5 cm 5.7 cm
The area of the trapezoid is 169.6 cm² for the dimensions as 8 cm, 5.7 cm and 15.5 cm.
We are given that:
The dimensions of the trapezoid are:
Height = 8 cm
Shorter side = 5.7 cm
longer side = 15.5 cm
Area of the trapezoid will be:
A = (a + b) / 2 × h
Substituting the values in the formula, we get that:
A = (5.7 + 15.5) / 2 × 8 cm²
A = 21.2 × 8 cm²
A = 169.6 cm²
Therefore, we get that, the area of the trapezoid is 169.6 cm² for the dimensions as 8 cm, 5.7 cm and 15.5 cm.
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you rent an apartment that cost 1600 per month during the first year but the rest had to go by 12.5 per year what would be the rent of the apartment during the 10th year in
Answer: 2000
12.5÷100=0.125
1600×0.125×10=2000
how many times smaller is (4 x 10^4) than (1.25 x 10^2)
The number of times that (4 x 10⁴) is higher than (1.25 x 10²) is 3.2 × 10².
How to illustrate the information?It should be noted that the information is to find the number of times that (4 x 10⁴) is higher than (1.25 x 10²).
This will be calculated by dividing the values we have.
= (4 × 10⁴) / (1.25 × 10²)
= 3.2 × 10²
In conclusion, the number of times that (4 x 10⁴) is higher than (1.25 x 10²) is 3.2 × 10².
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om drove at a constant speed of 50 miles per hour for 2.5 hours.
Albert drove at a constant speed of 65 miles per hour for 2 hours.
Who drove farther? How many more total miles did he drive?
Use the equation d=r×t to solve.
Albert drove 5 miles farther than Tom if their speed were 50mi/h and 65 mi/hr.
What is the distance?Distance is the size or extent of the displacement between two places. Remember that the travel distance between two points is not the same as their distance from one another. The distance traveled is the total distance traveled to get from one place to another. Distance traveled is not a vector.
Tom's distance is calculated as
Put D= D₁, r = 50 miles per hour, and t = 2.5 hours in the distance formula
D₁ = (50 mi/h)·(2.5 h)
D₁ = 125 mi
Albert's distance is calculated as
Put D= D₂, r = 65 miles per hour, and t = 2 hours in the distance formula
D₂ = (65 mi/h)·(2 h)
D₂ = 130 mi
Comparing both the distances
Albert drove 130 -125 = 5 miles farther than Tom.
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Ella has 50 stickers of 10 pennies in each stack describe how to find how many pennies Ella has and all
the number of pennies that Ella has in all is 500 pennies.
Number of stickers = 50
Cost of each sticker = 10 pennies
Now, we need to find the total pennies Ella has.
We will use multiplication to find the same.
So, by using the operation of multiplication, we get that:
Number of pennies = 10 × 50 pennies.
Number of pennies = 500 pennies.
Therefore, we get that, the number of pennies that Ella has in all is 500 pennies.
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The relation between degrees Fahrenheit F and degrees Celsius C is described by the function F = (9/5)C+32 . In the following ordered pairs, the first element is degrees Celsius and the second element is its equivalent in degrees Fahrenheit. Find the unknown measure in each ordered pair.
d. (q, 19)
5:9 is degrees Celsius and the second element is its equivalent in degrees Fahrenheit.
What does a temperature in Fahrenheit mean?
Water freezes at 32 degrees Fahrenheit and boils at 212 degrees Fahrenheit on the Fahrenheit scale, which is used to measure temperature.It is denoted by the °F sign. The temperature had risen to 100 degrees Fahrenheit by mid-morning.F = (9/5)C+32
F = C x 9/5 + 32
C = (F - 32) x 5/9
The above equations could easily be derived by the following relationships:
Freezing Point = 0C or 32F and Boiling Point = 100C or 212F
Range from freezing point to boiling point = 100C or 180F,
i.e. C : F = 100:180 = 5:9
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1 more than 4 times x
Answer:
1+4×1
1+4
5
I think this is the correct answer if it isn't pls notify me
Evaluate: 100−20.2×4.5.
The value of given expression 100−20.2×4.5 is 9.1 .
Expression in maths is outlined because the assortment of numbers variables and functions by exploitation signs like addition, subtraction, multiplication, and division.BODMAS is Associate in Nursing descriptor for the sequence of operations to be performed whereas simplifying the mathematical expressions. Hence , BODMAS full form is Bracket, Order, Division, Multiplication, Addition, and Subtraction.We have given an expression 100−20.2×4.5 .
Using BODMAS we will first solve the multiplication term than the subtraction term .
We will do multiplication operation which is given by
20.2 × 4.5 = 90.9
Now , we will subtract 90.9 from 100 , we get
100 - 90.9 = 9.1
Hence , the value is 9.1
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1/3 +1/5
Greatest common multiple
Look at the information in the image below.
Francesca dropped an item from the top of
the Leaning Tower of Pisa. Its initial speed
was 0 m/s, its final speed was 33 m/s
and it took 3.4 s to fall to the ground.
Giving your answer to 1 decimal place,
work out s (the distance travelled), in
metres (m).
Si
Not to scale
s = 1/2 (u + v) t
where
s = distance travelled (m)
u = initial speed (m/s)
v = final speed (m/s)
t = time travelling (s)
The distance travelled by the item is 56.1 meters
As per the information provided that the initial speed was 0 m/s, final speed when the item touched the ground is 33 m/s and the total time it took to reach ground from the top of leaning tower of Pisa is 3.4 s
we need to find out the distance travelled by the item
let the distance travelled by the item be x
it can de found out using the formula given in the question itself
by substituting the values in the equation
s= 1/2 (u+v)t
x = 1/2(0+33)3.4
x= 1/2(112.2)
x= 56.1 m
hence, the distance travelled by the item is 56.1 meters
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A baseball glove originally cost 84.50.
Kenji bought it at 40 % off. How much was deducted from the original price?
F. 50.70
H. 33.80
G. 44.50
J. 32.62
33.80 was deducted from the original price costing 84.50.
84.50 × 40% = 33.80
That's it, the answer is H. 33.80
What is original price?The full cost of purchasing an asset is known as the original price. When calculating an asset's original cost, all of the costs associated with buying and using the asset are taken into account.
Included in these expenses are the purchase price as well as things like commissions, shipping, appraisals, warranties, installation, and testing. Equipment, real estate, and security instruments are all examples of asset types that can be valued using original cost.
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A rectangle has a perimeter of 84 cm and the length is 35 cm what is the width
Answer: width is 49
Step-by-step explanation: 84-35= 49
what is the least common dominator and the sum 5/8 - 5/12
Answer:
5/12
Step-by-step explanation:
Answer:
24 is the least common factor of 5/8 - 5/12.
What’s the answer help pls
Find x and AB if B is between A and C, AB=3x, BC=14, and AC=41.
The value of x is 9 and the measure of AB is 27.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We need to Find x and AB if B is between A and C,
Given that AB=3x, BC=14, and AC=41.
AB + BC = AC
3x+14=41
3x=27
X=9
Now substitute to find the AB;
AB=3(9)
AB =27
Therefore the value of x is 9 and the measure of AB is 27.
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The graph shows the velocity f(t) of a runner during a certain time interval:
Graph of line segment going through ordered pairs 0, 2 and 6, 8. Graph of another line segment going through ordered pairs 6, 8 and 8, 0. Label on the x axis is time in seconds, and label on the y axis is velocity in meters per second.
Which of the following describes the intercepts on the graph?
The initial velocity of the runner was 8 m/s, and the runner stopped after 2 seconds.
The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds.
The initial acceleration of the runner was 8 m/s2, and the runner stopped after 2 seconds.
The initial acceleration of the runner was 2 m/s2, and the runner stopped after 8 seconds.
The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds. Therefore, option (b) is correct.
The velocity of an object helps to calculate the speed of the object in a particular direction. A velocity-time graphs shows the speed and direction of an object that travels over a specific period of time. They are also known as speed-time graphs too.
The vertical axis represents the velocity of an object and horizontal axis represents the time taken to cover particular distance with the speed.
Here, the ordered pairs given in the question are (0,2), (6,8) going through one line segment and for other line segment it is (6,8) and (8,0) respectively. We have to conclude various statement that matches best for the ordered pairs given to us. Let's proceed to solve this.
For (0,2), this ordered pair conclude that: At t = 0 sec, the initial velocity of the runner was 2m/s respectively.
Similarly, for (6,8) this represents that at t = 6 sec the velocity of the runner reaches at maximum. i.e., 6m/s and acceleration is 1 m/s² also from this ordered pair for another line segment a state of deceleration begins which ultimately reduces the acceleration of an object.
For (8,0), this ordered pair represents that at t = 8 sec the velocity of the object which is the final velocity it become 0 m/s i.e., the runner stopped.
From all the ordered pair we have concluded that option (b) is correct which says that the initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds.
Hence, option (b) is correct.
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Some people think that the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, resembles a golf ball. The building is a sphere measuring 165 feet in diameter. A typical golf ball has a diameter of approximately 1.5 inches.
b. Find the volume of a golf ball to the nearest tenth.
A typical golf ball having a diameter of approximately 1.5 inches has a volume of 1.8 cubic inches.
Volume refers to the amount of space occupied by a three-dimensional object.
From the problem, the golf ball resembles the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida which is a sphere.
If a typical golf ball has a diameter of approximately 1.5 inches, and radius is half of the diameter, then the radius of the golf ball is approximately 0.75 inches.
The volume of the golf ball can be calculated using the formula for the volume of a sphere given by:
V = 4/3 π r^3
V = 4/3 π (0.75 inches)^3
V = 4/3 π (0.421875 cubic inches)
V = 1.767145868 cubic inches
Rounding off to the nearest tenth,
V = 1.8 cubic inches
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Find the area under the normal curve between the values z=-2.61 and z=0.4
Round your answer to 4 decimal places.
Answer:
0.6508
Step-by-step explanation:
The standard normal distribution has a mean μ= 1 and standard deviation σ = 0
The area under the normal curve for any z value say Z i.e. P(z ≤ Z) can be read off from the Standard Normal Tables or just use a statistical calculator
Using a calculator is best
I see the lower z score as - 2.61 and the upper z score as 0.4
P(-2.61 ≤ z ≤ 0.4) = P(0.4) - P(-2.61)
P(z ≤ 0.4) = 0.65542
P(z ≤ -2.6) = 0.0045271
P(z ≤ 0.4) - P(z ≤ -2.6) = 0.65542 - 0.0045271 = 0.6507588 = 0.6508 rounded to 4 decimal places
(Note: some calculators are able to directly compute the area between two z values)
Evaluate r + (-5) < -3.
r < -5
r < 2
r < -2
r < 5
Answer:
r<2
Step-by-step explanation:
r + (-5) < -3
r -5 < -3
r<-3+5
= r<2
Which most likely is a causal relationship?
An experimenter showed different causes for two patients’ lung cancer.
One experiment showed that all cancers can be cured by a new drug.
Experimenters show a link between adult-onset diabetes and obesity.
Experimenters show statistical data on diabetes drugs.
Experimenters show a link between adult-onset diabetes and obesity is most likely a causal relationship. Option C is correct.
What exactly is a causal connection?A causal relationship exists when one variable in a data set directly affects another variable.
As a result, one thing triggers another to happen. A causal link is also known as cause and effect.
According to studies and experiments, there is a clear causal link between adult-onset diabetes and obesity. A causal relationship demonstrates that one occurrence is the cause and the other is the outcome.
Researchers have found what is most likely a causal association between adult-onset diabetes and obesity.
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