Answer:
50
Step-by-step explanation:
Complex numbers:i^2 = -1
First simplify the radicals. Then use FOIL method
[tex]\sf (3 + \sqrt{-16})(6-\sqrt{-64}) = (3 +\sqrt{i^2*4^2})(6-\sqrt{i^2*8^2})[/tex]
= ( 3 + 4i)(6 -8i)
= 3*6 - 3*8i + 4i*6 - 4i*8i
= 18 - 24i + 24i - 32i^2
= 18 - 24i + 24i - 32*(-1)
= 18 - 24i +24i + 32
= 18 + 32 - 24i + 24i
Combine like terms,
= 50
When Riley left her house in the morning, her cell phone battery was partially
charged. The charge remaining in Riley's battery, as a percentage, can be modeled by
the equation B = 40 - 5t, where t is the number of hours since Riley left her
house. What is the x-intercept of the equation and what is its interpretation in the
context of the problem?
Riley's phone had a 50% charge when she left her home in the morning. Equation B = 40 - 5t. The x-intercept of the equation is (8,0). After 8 hours, Riley battery has no charge left in it ( since Riley left her house).
Given that,
Riley's phone had a 50% charge when she left her home in the morning. Equation B = 40 - 5t, where t is the number of hours since Riley left her residence, can be used to predict the percentage of charge still in Riley's battery.
We have to find what is the equation's x-intercept and how is it interpreted in the problem's context.
The equation B=40-5t can be used to model Lauren's battery charge remaining as a percentage when t is the number of hours since she left her home.
Put B = 0 to determine the x-intercept. (In this case, the independent variable is "t," as x signified the independent variable).
0=40-5t
5t=40
t=40/5
t=8
Therefore, the x-intercept of the equation is (8,0).
After 8 hours, Riley battery has no charge left in it ( since Riley left her house).
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#2 The number of bacteria in a refrigerated food is given by N(T)=20T2-20T+120 for -2T14 Tand where T is the temperature of the food in Celsius.
(a)Explain the meaning of -2T14 in this context
(b)Determine the temperature the number of bacteria will be minimal?
(c)Find number of bacteria in a above
(d) Sketch a graph
From the given quadratic function, it is found that:
a) The interval -2 ≤ T ≤ 14 gives the range of the temperature of the food in Celsius.
b) The number of bacteria will be minimal for a temperature of 0.5 ºC.
c) The minimum number of bacteria is of 115.
d) The graph that models the situation is sketched at the end of the answer.
What does the quadratic function models in this problem?The quadratic function is given as follows:
N(T) = 20T² - 20T + 120, -2 ≤ T ≤ 14.
In which:
T is the temperature in Celsius of the food.N(T) is the number of bacteria in the food.The function has a domain of -2 ≤ T ≤ 14, meaning that these are the possible temperatures of the food.
For a concave up quadratic function, the minimum value happens when the input is of:
Tm = -b/2a.
For this problem, the coefficients of the quadratic function are as follows:
b = -20, a = 20.
Hence the temperature in which the number of bacteria will be minimal is of:
Tm = 20/40 = 0.5 ºC.
The number of bacteria with this temperature is given by the numeric value of the function when T = 0.5, that is, each instance of T in the function is replaced by 0.5, hence:
N(0.5) = 20(0.5)² - 20(0.5) + 120 = 115 bacteria.
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In Exercises 7-10, determine whether the table represents a linear or nonlinear function. Explain. (See Exam
8.
7.
X
X
y
4
y 16.8
1
5
2
12.6
10
8 12
7.4
3
15
16
1.2
4
20
10.
x 5
y
-9
X
y
-1
35
7
-3
9
-1
11
3
0
1
2
20 5 -10 pls help me
Answer:
every number has a correlating value
Step-by-step explanation:
$10,000 for 5 years at 4% interest
Simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.
As given in the question,
Simple Interest:
The simple interest is an amount that is paid for loan or borrowed money over a certain period at a fixed percentage of borrowed money.
Principal amount:
Principal amount is the money that is taken as loan or borrowed.
Formula of Simple Interest:
Simple interest = Principal amount × Rate × Time
Since,
Principal amount = $10,000
Rate = 4% per year
Time = 5 years
Then,
Simple interest = 10,000 × 4 × 5
Simple interest = $ 12000
Total value after 5 years = $ 12000
Principal amount = $ 10000
Interest Earned = (Total value) - (Principal amount)
Interest Earned = $ 12000 - $ 10000
Interest Earned = $ 2000
Therefore, simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.
The complete question is:
Fabian is taking out a loan in the amount of $10,000. His choices for the loan are a 5-year loan at 4% rate of interest .What is the amount of simple interest and interest earned Fabian would have to pay?
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The value for x that makes the equation 4×-2+3×-7=51 true
The value of x that makes the equation true is 60/7.
The given equation is:-
4x - 2 + 3x - 7 = 51
The given equation is a linear equation in one variable.
Linear equation in one variable
A linear equation in one variable is of the form of ax + b = 0, where a and b are any two integers and x is an unknown variable having only one solution. Example : 5x + 3 = 10.
We have to find the value of x that makes the equation true.
Simplifying the given equation, we get
(4x + 3x) - (2 + 7) = 51
7x - 9 = 51
7x = 51 + 9
7x = 60
x = 60/7
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What is the truth value for the following conditional statement?
p: false
q: true
~p~q
OTF F
OTF-T
OFF-T
OFT F
This is the right response: T F- F.
What is the explanation:
If the answer to the following question is p, then 2 + 2 = 4.
which is accurate, meaning that this statement has a truth value of True.
The following assertion q illustrates q: 7 + 1 Equals 7.
This is untrue, making the statement's truth value Untrue
As far as we are aware, "pq (p implication q)" means that the truth value of the implication is False only when the truth value of statement p is True.
The truth table reveals that the truth value of pq will be False
So T F → F
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What is the best estimate of 31 3/4 X 4 1/7 = ? Help Me?!!
The best estimate of fraction is 131.445.
What is fractions?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is [tex]\frac{1}{2}[/tex]
Given Data
31[tex]\frac{3}{4}[/tex] × 4[tex]\frac{1}{7}[/tex]
Solving mixed fractions
[tex]\frac{127}{4}[/tex] × [tex]\frac{29}{7}[/tex]
31.75 × 4.14
Multiplying
131.445
The best estimate of fraction is 131.445.
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9. Describe and correct the error in performing the operation.
X 4x²(3x - 2x² + 7) = 12x³ - 8x + 28x²
Answer:
12[tex]x^{3}[/tex]-8[tex]x^{4}[/tex]+ 28[tex]x^{2}[/tex]
Step-by-step explanation:
the second term should not be -8x, it should be -8[tex]x^{4}[/tex]
The product of powers principle tells us that when we are multiplying powers with the same bases, we add the exponents. 4[tex]x^{2}[/tex](2[tex]x^{2}[/tex]) is 8 but then we add the exponents 2 + 2 = 4
Find the volume of this solid.
Answer:
128m²
Step-by-step explanation:
separate the two solids.The cube and the cuboid
find the volume of the cube i.e.5³=115m²
find the volume of the cuboid i.e 1×1×3=3m²
add the two volumes
Answer:
128m²
Explanation:
Add all volumes, 5+5+4+6+3, then times that by the volume below.
When adding and subtracting with significant digits, it's important to consider decimal places in the numbers being added.
TRUE or FALSE?
Answer:
false
Step-by-step explanation:
The graph shows the velocity f(t) of a runner during a certain time interval:
Graph of line segment going through ordered pairs 0, 4 and 4, 8. Graph of another line segment going through ordered pairs 4, 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 4 m/s, and the runner stopped after 8 seconds.
The initial velocity of the runner was 8 m/s, and the runner stopped after 4 seconds.
The initial acceleration of the runner was 4 m/s2, and the runner stopped after 8 seconds.
The initial acceleration of the runner was 8 m/s2, and the runner stopped after 4 second
The description of the intercepts of the Graph segments passing through the points (0, 4), (4, 8), (4, 8) and (8, 0) is given by the option;
The initial velocity of the runner was 4 m/s and the runner stopped after 8 secondsWhat is a velocity time graph?A velocity time graph is a graph that shows how the velocity of an object changes with time
The given information on the graph are;
The coordinates of the points on the Graph of the first line segment = (0, 4) and (4, 8)
On Graph of the second line segment, the coordinates of the points = (4, 8), (8, 0)
The label of the axis of the graph are;
X–axis label = Time in seconds (s)
Y–axis label = Velocity in m/s
Required; The option that gives the description of the intercepts of the graph
Solution; The x and y–intercept are given as follows;
At the x–intercept the y–value is 0, which gives the x–intercept of the graph as the point (8, 0)
Given that the y–value which is the value of the velocity, is 0, it means that the runner stops at the point (8, 0), or after 8 seconds
At the y–intercept, the x–value is 0. The y–intercept is therefore the point (0, 4)
The 0 in the y–intercept means that the time is 0 seconds, which is the starting or initial time, while the 4 means that the velocity is 4 m/s.
Therefore, the y–intercept (0, 4) can be described as the initial velocity of the runner is 4 m/s
The description of the intercepts on the graph are therefore;
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Answer:
The initial velocity of the runner was 4 m/s, and the runner stopped after 4 seconds and then again after 8 seconds. Option A is the correct answer
Step-by-step explanation:
The intercepts on the graph can be described as follows:- The y-intercept is the point at which the line intersects the y-axis, and it represents the initial velocity of the runner. In this case, the y-intercept is at (0, 4), which means that the initial velocity of the runner was 4 m/s.- The x-intercept is the point at which the line intersects the x-axis, and it represents the time at which the runner stopped. In this case, there are two x-intercepts: one at (4, 8) and another at (8, 0).
This means that the runner stopped twice, once after 4 seconds and again after 8 seconds.
Therefore, the correct description of the intercepts on the graph is: The initial velocity of the runner was 4 m/s, and the runner stopped after 4 seconds and then again after 8 seconds. Option A is the correct answer.
Which diagram shows parallel lines cut by a transversal?
need help on this question
The coordinates of the vertex B' is (2,3)
Given,
The vertices of triangle ABC are
A = (-4,4)
B = (-2,3)
C = (-5,2)
and, reflected across the y-axis to produce the image of triangle A'B'C'
To find the coordinate of the vertex B'
Now, According to the question
For reflection across y-axis, the rule is:
(x, y) → (-x, y)
So, the image of B is:
(-2, 3) → (-(-2), 3)
(-2,3) → (2, 3)
Hence, The coordinates of the vertex B' is (2,3)
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On the axes below, make an appropriate scale and graph exactly one cycle of the trigonometric function y=16sin 1/2 x
For the given trigonometric function y =16sin1/2 x the graph shows the amplitude of 16 , graph of exactly one cycle is with period 4π , with no vertical and phase shift.
As given in the question,
Given trigonometric function :
y = 16sin 1/2 x
Attached graph of the given trigonometric function with
Amplitude = 16
Period = 4π
Vertical shift = None
Phase shift = none
Table for the required trigonometric function values which represent appropriate scale and graph exactly one cycle of the trigonometric function
x : 0 π 2π 3π 4π
y : 0 16 0 -16 0
Therefore, graph of trigonometric function y =16sin1/2 x shows the amplitude of 16 , graph of exactly one cycle is with period 4π , with no vertical and phase shift.
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On 1st January 2017, Samantha and Dyfan invested money into different
savings accounts.
They did not make any further payments into their accounts or withdraw any
money from their accounts.
Dyfan invested £3000 in a savings account that paid interest at a rate of
1.02% every 3 months.
Interest is paid on the last day of each 3-month period.
Calculate the date when Dyfan will first have over £3600 in his account.
Input note: give your answer in the form DD/MM/YY
(4 marks)
(8
The number of years when Dylan would have over £3,600 in his account is 18 June, 2021.
When would Dylan have over £3,600?The time that If the account earns interest every 3 months, it means that the value increases quarterly or 4 times a year. The account would increase at an exponential rate. This means that both the amount invested and the interest that has already been earned would increase in value 4 times a year.
The formula that can be used to determine the time is:
Time = In(FV / PV) / r
Where:
FV = future value
PV = present value
r = interest rate
t = In (£3,600 / £3,000) / 0.0102
t = In 1.2 / 0.0102 = 17.87 / 4 = 4.468 years
4 years = 2017 + 4 = 2021
0.468 x 12 = 5.616 months
January + 5 months = June
0.616 x 31 = 19 days
18 June, 2021
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Why can it help to line up the decimal
points before comparing and ordering
numbers with decimals?
Answer: Why it makes sense: When we compare or order decimals we need to compare place values just like we do with whole numbers. When the edges are “jagged” it makes it harder to compare each decimal place. Adding a zero in an empty place value makes it easier to compare the numbers.
Step-by-step explanation:
Answer:
you need to line them up to tell what place value each are in. if u don't the you won't known exactly what the product is equivalent to.
If the measure of 43 is 70 degrees, what is the measure of <6?
A. 20; ∠s 3 and 6 are complementary angles
B. 70; ∠ s 3 and 6 are alternate interior angles
C. 110; ∠ s 3 and 6 are supplementary angles
D. 180; ∠ s 3 and 6 are same-side interior angles
Answer:
b
Step-by-step explanation:
angle 3 and angle 6 are alternate interior angles which makes the congruent
Is the function linear? (actual answers please, i know someone could easily say yes or no)
Answer:
Obviously yes...
Step-by-step explanation:
Because there is not a single curve, hence the fn is linear.
Had it been if there are some curves, it may result in having more than one zeroes...
Cuz there's no curve it has only one zero, which made the fn linear..
Thanks.
pls pls help whoever gets it right gets marked brainliest
Answer:
Step-by-step explanation:
B
Please answer the question in the photo
Answer: 8
Step-by-step explanation:
180 degrees in a triangle, so 180 - 92 - 48 = 40
So, the missing angle is 40, which is equal to 5t, so
40 = 5t
t = 8
Find the distance from the point A(−2, 3) to the line y = 12x+1. Round your answer to the nearest tenth.
can some one help i will give 100 points and brainliest can you show your work step by step?
Rewrite in simplest terms: −4(8f+g)+9g−5(−2g+6f)
Select all the equations where x = -2 is a solution.
(Select all that apply.)
a. 3x - 5 = 1
b. 19 = 2(x-6)+3
c. 5 + 3x = -1
d. 2(x+5)=x+8
e. 4x = 4 + 2x
the leters c and d are correct for this equation
What is the equation for the line that passes through the coordinates (-4,-12)and(16,3)
The equation of the line that passes through these coordinates is 3x-4y= 36
How to calculate slope?
If you have the coordinates of two points on a line, you can use the slope formula to determine that line's slope. m=(y2-y1)/(x2-x1), or the ratio of the change in the y values to the change in the x values, is the slope formula.
To find the equation of the line we first have to find the slope which is represented by m.
The slope or m is given by : y₂ - y₁ / x₂ - x₁
thus, m= 3-(-12)/ 16-(-4)
m= 3+12/ 16+4 = 15/20
m= 3/4
The equation of a slope is y-y₁=m (x-x₁)
y- (-12) = 3/4 (x- (-4))
y+12 = 3/4 (x+4)
On solving it further we get:
4y+48= 3x+12
3x-4y= 36
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suppose abc is a right triangle with sides a, b, and c and right angle at c. use the pythagorean theorem to find the unknown side length. then find the values of the six trigonometric functions for angle b. rationalize the denominators when applicable.
The unknown length is 28. the values of the six trigonometric functions for angle b that is tan B = 7/24
From the question,
we are given
a = 96 and c = 100, to get the unknown side 'b',
we will substitute the given values into the formula above;
c² = a²+b²
100² = 96² +b²
b² = 100² - 96²
b² = 10,000 - 9216b²
= 784b = √784b = 28
Hence, the unknown length is 28.
To get tanB, we will use the SOH, CAH, TOA trigonometry identity.
According to TOA,
tan B = opposite/adjacenttan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)
Given, b = 28 and a = 96tan B = 28/96tan B = 4*7/4*24
tan B = 7/24
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The question is incomplete. Here is the complete question.
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.
One of your friends is working on their math homework. They decide to translate the phrase "subtract 3 from 5" like this:
3-5
Which statements below give a reason why your friend's expression is incorrect?
Select ALL that apply.
A.The expression is written with the wrong operation.
B.in subtraction, order matters and the expression in the incorrect order.
C.the expression should be written as an addition expression with the 5 being added to the 3
D. The expression was written in the order from the phrase which is incorrect
Answer:
B
Step-by-step explanation:
When you are taking 3 away from 5 it would be 5-3, when you are taking 5 away from 3 it would be 3-5, but in this case it is not so the answer would be B as the order is incorrect.
1 - 3x = 3x + 1
what does x equal?
Answer:
the value of x is -6
Step-by-step explanation:
1-3x= 3x+1
-3x -3x =1-1
-6x=0
-x=6
x= -6
Estimate the quotient of 41 ÷ 7.94.
4
5
6
7
PLS HELP QUICK!!!
help me solve 3<2p-3≤ 12 and graph the solution
The solution to the given inequalities is 3 < p and p ≤ 7.5. That is 3 < p ≤ 7.5.
The graph of the solution is shown below.
Solving Linear InequalitiesFrom the question, we are to solve the given inequalities
The given inequalities are
3 < 2p - 3 ≤ 12
We will solve the inequalities separately
That is
3 < 2p - 3 and 2p - 3 ≤ 12
Solve 3 < 2p - 3
3 < 2p - 3
3 + 3 < 2p
6 < 2p
6/2 < p
3 < p
Solve 2p - 3 ≤ 12
2p ≤ 12 + 3
2p ≤ 15
p ≤ 15/2
p ≤ 7.5
Hence,
Joining the two solutions together, the solution is 3 < p ≤ 7.5.
The graph is shown below.
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