The statement that describes the type of solutions of the specified equation is the third option C.;
C. The equation has two valid solutions and no extraneous solutions
What is a solution of an equation?A solution to an equation are values of the variables of the equation that make the equation true.
The possible equation obtained from a similar question on the website can be presented as follows;
4/(3·x + 1) = x/(2·x + 10)
The above equation expressions can be combined into a quadratic equation as follows;
4 × (2·x + 10) = x × (3·x + 1)
8·x + 40 = 3·x² + x
3·x² + x - 8·x - 40 = 0
3·x² - 7·x - 40 = 0
3·x² - 15·x + 8·x - 40 = 0
3·x·(x - 5) + 8·(x - 5) = 0
(3·x + 8)·(x - 5) = 0
x = -8/3 and x = 5
Therefore, the equation has two valid solutions and no extraneous solutions
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can everyone help idek how to do this?
The perimeter of the tri9angle MNO is P = 58 units.
How to find the perimeter of the triangle?The perimeter of the triangle is equal to the sum of the lengths of the sides, we know that:
OM = 23
NM = 18.4
To find the missing side we can use the similar triangle that we have next to it.
We can see that that OM is correspondent to LJ
Then if the scale factor between the triangles is K, we can write:
18.4 = 10*K
18.4/10 = K = 1.84
Now, NO is correspondent to KL, then:
NO = 1.84*9
NO = 16.6
Then the perimeter is:
P = 16.6 + 23 + 18.4
P = 58 units.
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Find a and b such that f(x) can be written as f(x) = (x +a) (5) 3 −b
The value of variables a and b are,
a = - 4,
b = - 2
WE have to given that;
Function is,
⇒ f (x) = x³ - 12x² + 48x - 62
Now, We can simplify for change the function in the form of
f (x) = (x + a)³ + b as;
⇒ f (x) = x³ - 12x² + 48x - 62
⇒ f (x) = x³ - 12x² + 48x - 62 - 2 + 2
⇒ f (x) = (x - 4)³ + 2
Hence, We get;
By comparing we get;
a = - 4,
b = - 2
Thus, The value of variables a and b are,
a = - 4,
b = - 2
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Need help with this question
The height d as shown in the right angled triangle is 4.95.
What is height?Height is the vertical distance between two points.
To calculate the height d as shown in the right angled triangle, we use the formula below
Formula:
d = hcos∅.............. Equation 1From the diagram in the question,
Given:
h = 7∅ = 45°Substitute these values into equation 1
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I need help please!!!
Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.
I prefer Wills method because it is easier and less complicated.
How to solve differences?Wills method:
(5x + 6x) - (2x - 1)
Subtract both 2x and -1
5x + 6x - 2x - - 1
5x + 4x + 1
In conclusion, Wills method is preferred when both methods are compared.
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Haley try to solve the equation log⇩4 2x=5. She got the wrong answer. What was her mistake? What should the correct answer be?
Help DUE! ASAP HELP ASAP
Answer:
Step-by-step explanation:
[tex]log_{4}2x = 5 \\2x = 4^5\\2x = 2^{10}\\x = \frac{2^{10}}{2}\\ x = 2^9\\x = 512[/tex]
Mistake is in step - 3 .
What is the answer???
Answer:
2ab(b + 4 - 3a)
Step-by-step explanation:
a^2b + 2ab^2 + 8ab - 7a^2b
= 2ab^2 + 8ab + a^2b - 7a^2b
= 2ab^2 + 8ab - 6a^2b
= 2(ab^2 + 4ab - 3a^2b)
= 2a(b^2 + 4b - 3ab)
= 2ab(b + 4 - 3a)
How could you estimate the extra cost per month of borrowing $50,000 for 30 years at 11% instead of 10%?
Borrowing $50,000 for 30 years at 11% instead of 10% would result in an extra cost of approximately $44.63 per month.
To estimate the extra cost per month of borrowing $50,000 for 30 years at 11% instead of 10%, you can follow these steps:
Calculate the monthly payment for each interest rate:
The formula to calculate the monthly payment for a fixed-rate loan is:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M is the monthly payment,
P is the principal amount (loan amount),
r is the monthly interest rate (annual interest rate divided by 12),
n is the total number of monthly payments (number of years multiplied by 12).
Let's calculate the monthly payment at 10% interest rate first:
P = $50,000
r = 10% / 100 / 12 = 0.0083333 (monthly interest rate)
n = 30 years * 12 = 360 (total number of monthly payments)
M1 = $50,000 * (0.0083333 * (1 + 0.0083333)^360) / ((1 + 0.0083333)^360 - 1)
Calculate the monthly payment at 11% interest rate using the same formula:
P = $50,000
r = 11% / 100 / 12 = 0.0091667 (monthly interest rate)
n = 30 years * 12 = 360 (total number of monthly payments)
M2 = $50,000 * (0.0091667 * (1 + 0.0091667)^360) / ((1 + 0.0091667)^360 - 1)
Calculate the difference in monthly payments:
Extra cost per month = M2 - M1
Now let's perform the calculations:
M1 ≈ $446.92 (monthly payment at 10% interest rate)
M2 ≈ $491.55 (monthly payment at 11% interest rate)
Extra cost per month = $491.55 - $446.92 ≈ $44.63
Therefore, borrowing $50,000 for 30 years at 11% instead of 10% would result in an extra cost of approximately $44.63 per month.
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An investment of $2000 is put in account that earns 4% interest, compounded quarterly. Find the amount of money, rounded to the nearest dollar, in the account after
8 years.
Use the formula A = P(1+r/n)^nt to help you find the answer.
Answer: $275
Step-by-step explanation:
Which expression is equal to 3√5/√11
A.√33/5
B.3√55/11
C.3√55/√11
D.O√55/11
Answer:
B
Step-by-step explanation:
3√5/√11 = 2.02
3√55/11 = 2.02
so,
3√5/√11 = 3√55/11
Please help and thank you so much
Answer:
SSS∆KLM ~ ∆UTSStep-by-step explanation:
You want to know the postulate used to declare the triangles similar, and the corresponding similarity statement.
Side ratiosThe side length ratios of the larger triangle are ...
45 : 63 : 90 = 5 : 7 : 10 . . . . . divide by 9
For the smaller triangle, they are ...
25 : 35 : 50 = 5 : 7 : 10 . . . . . divide by 5
The ratios of the three side lengths are the same, so the triangles are similar by the SSS postulate.
Similarity statementOne triangle is designated as ∆KLM. In terms of (reduced) ratio units, the sides in order are ...
KL = 10, LM = 7, MK = 5
The corresponding sides in the smaller triangle are ...
UT = 10, TS = 7, SU = 5
This means the similarity statement must be written as ...
∆KLM ~ ∆UTS . . . . . . matches the last choice
__
Additional comment
It is generally helpful to list the sides in some recognizable order (here, longest to shortest) so that the correspondence is clear.
<95141404393>
Find the value of 3a when a = -4.
(b)- 7
(d) -12
(a) 7
(c) 12
Answer:
(d) -12
Step-by-step explanation:
3a = _____
a = -4
3(-4) = ___
3(-4) = -12
The answer is (d) -12
A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The survey reported a confidence interval that between 22% and 32% of the residents supports the plan. What is the margin of error on the survey? Do not write ± ± on the margin of error.
Answer:
[tex]\Huge \bold{\boxed{\boxed{\text{5\%}}}}[/tex]
Step-by-step explanation:
To calculate the margin of error for the survey, we need to use the formula:
[tex]\large \text{Margin of error} = \large \text{$\frac{\text{Range of values}}{2}$}[/tex]
The range of values is the difference between the upper and lower bounds of the interval. In this case, the lower bound is 22% and the upper bound is 32%, so the range of values is:
[tex]\large \text{Range of values = 32\% - 22\% = 10\%}[/tex]
Substituting this value into the formula, we get:
[tex]\large \text{Margin of error = $\frac{10\%}{2}$ = 5\%}[/tex]
Therefore, the margin of error on the survey is 5%.
(−3+x)=kx+9
what does x=
Answer:
Step-by-step explanation:
he correct answer for the domain of function p(x) is:
Domain: [1, ∞)
This means that x can take any value greater than or equal to 1, including 1 itself. The square root function (√x) is defined for non-negative real numbers, so x must be greater than or equal to 0. In this case, since we have √x - 1 in the function, x must be greater than or equal to 1 to avoid a negative value under the square root. Additionally, there are no other restrictions on the domain, so any value of x greater than or equal to 1 is allowed.
Se está construyendo una escalera que inicia a 4.10 m para alcanzar una altura de 2.35 m calcular la longitud de la escalera y cual es su ángulo de elevación 0 .
The length of the ladder is 4.72 meters and its angle of elevation is 30.4 degrees.
Using the Pythagorean theorem:
Length of the ladder = √(height² + horizontal distance²)
= √(2.35² + 4.10²)
= √(5.5225 + 16.81)
= √22.3325
≈ 4.72 meters
To calculate the angle of elevation (θ), we can use the trigonometric function sine:
sin(θ) = height / length of the ladder
θ = arcsin(height / length of the ladder)
θ = arcsin(2.35 / 4.72)
θ ≈ 30.4 degrees
Therefore, the length of the ladder is 4.72 meters and its angle of elevation is 30.4 degrees.
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The Translation of given question is:
A ladder is being constructed that starts at 4.10 m and reaches a height of 2.35 m. Calculate the length of the ladder and its angle of elevation.
Help please!! Thank youuuuu!!!
I’ll give brainliest if you show work as well.
The value of x from given parallel lines is 2.
In the given figure, three lines are parallel and two lines are passing through.
When three or more parallel lines are cut by two transversals, the line segments formed are proportional.
That is, 2x/x = (x+4)/(4x-5)
2/1 = (x+4)/(4x-5)
2(4x-5)=1(x+4)
8x-10=x+4
8x-x=4+10
7x=14
x=2
Therefore, the value of x from given parallel lines is 2.
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In the equation, y = 2 sin
000
A
B
с
O
1
x, which statements are true? Select all that apply.
2
The period is 4π
The amplitude is 2
The period is
1
2
76
The amplitude is-
2
The period of the function is 4π, and the amplitude is 2.
Given data ,
Let the function be represented as f ( x ) = y
Now , the value of f ( x ) is
y = 2sin ( 1/2 )x
To find the period and amplitude of the function y = 2sin((1/2)x), we can use the standard form of a sine function: y = Asin(Bx).
In this case, the amplitude (A) is 2.
The amplitude represents the maximum displacement from the midpoint of the sinusoidal function.
To find the period, we can use the formula:
Period = (2π) / |B|.
B = 1/2.
Period = (2π) / |1/2|
P = (2π) / (1/2) = 2π * 2/1 = 4π
Hence , the period of the function is 4π, and the amplitude is 2.
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Matthew examines the relation shown in the below.
{(4,-11), (3,1), (0,1), (2,6), (3, -1)}
Is the relation a function? Why or why not?
No. There are x values which map to more than 1 y-value.
Yes. Every y-value maps to exactly 1 x-value.
No. There are y-values which map to more than 1 x-value.
Yes. Every x-value maps to exactly 1 y-value.
No, there are x values which map to more than 1 y-value.
Given that Matthew examines the relation as shown in the below.
{(4, -11), (3,1), (0,1), (2,6), (3, -1)}
We need to check whether the relation is a function or not,
So, we know that,
A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.
If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.
Here we can see that the y values are repeated, so it is not a function.
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What two whole numbers does sqrt 3 11 lie between
The third root of 11 lies between the whole numbers 2 and 3.
How to estimate a non-exact square root?The estimate of a non-exact root of x is done finding two numbers, as follows:
The greatest number less than x that is a perfect root, which we call a.The smallest number greater than x that is a perfect root, which we call b.The number for this problem is given as follows:
Cubic root of 11.
For the parameters, we have that:
The cube of 2 is of 2³ = 11.The cube of 3 is of 3³ = 27.Hence the third root of 11 lies between 2 and 3, as 2³ < 11 < 3³.
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1. Explain and illustrate the difference between and (4) 2. Explain and illustrate the difference between ratio and proportional reasoning. Do not copy definitions from any source but use your own understanding. (4) 3. Illustrate with a drawing or diagram what "fifth" means in each of the following instances: ordinal number unit fraction 4. Show with a diagram 3, using the following: 1.1 the area model 1.2 set mode 1.3 the length model (3) 2. A rectangular piece of paper has a perimeter of 54 cm. Its length is 1 of its width. Find its dimensions. (3) 3. If the given regular hexagon represents one whole: 3.1 Show three sixths. 3.2 Write the equivalence 6.1 above. Represent in the figure given to prove that a set of two halves 3 3 + 6 6 make a whole. 6.3.1 Draw a number line showing a whole made of six equal parts. Show the sum of two halves on the same number line. 6.3.2 Show how you would teach equivalence to grade 4 learners using the number line provided. Your focus should be on the Preparatory MTE1502/102/0/2023 strategy in 5.2 in your study guide. Follow the steps and show how you would unpack the process to solve the problem given. 3 10 of her birthday cake and ㅈ the cake was bought for the birthday? 7.2What fraction is missing to make the cake whole? 7.1 Mavis ate ate of it. What fraction of (4) (1) (1) (2) (3) (3) (2) (2) 3 3/6
The difference between 1/5 and 2/10 is that they are different representations of the same value.
The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.
"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.
The diagram can be used to illustrate fraction concepts.
How to solve1/5 is simple, but 2/10 can be reduced to 1/5 by dividing both numbers by 2. They are both 0.2 or 20%. 1/5 and 2/10 are different fractions with different purposes.
Use 1/5 for 5 parts and 1/5 (simplified from 2/10) for 10 parts. 1/5 and 2/10 = 0.2, ratio reasoning emphasizes ratios between quantities. A 2:3 boys-to-girls ratio compares the constant ratio between changing quantities.
Proportional reasoning maintains constant ratios between quantities, while ratio reasoning uses fractions or ratios to compare relationships. For instance, if distance doubles, so does speed.
Step 3/5: "Fifth" is the ordinal number for the object five places away in a sequence. See diagram. The fifth circle is 1/5 of a whole in unit fraction sequence. Imagine a rectangle divided into five equal parts, each shaded to show 1/5. Shaded part = 1/5 of whole.
To show 25/7 with area model, make 7x25 rectangle and split into 7 equal parts. 25/7 per part.
1.2 The set model:
To represent 25/7, divide 25 objects into 7 equal sets, resulting in 3 objects per set with 1 left over. This represents the fraction of 25/7.
1.3 The length model:
To show 25/7 on a length model, draw a line of 25 units and divide it into seven equal parts. Each part represents 1/7 or 25/7.
Step 5/5
Let's assume the width of the rectangular piece of paper as x cm. Then the length of the paper would be:
Now we know that the perimeter of the rectangle is given by the formula:
So, for this rectangle:
54 = 2(5x + x)
Simplifying and solving for x, we get:
54 = 2(6x)
27 = 6x
x = 4.5 cm
Therefore, the width of the paper is 4.5 cm and the length is 5 times the width which is 22.5 cm.
The difference between 1/5 and 2/10 is that they are different representations of the same value.
The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.
"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.
The diagram can be used to illustrate fraction concepts.
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Precalc question below.
The number of additional copies you could ship by ordering 128 instead of 127 copies is 0 copies.
We have,
To determine the number of additional copies you could ship if you ordered 128 copies instead of 127 copies, we need to compare the costs of ordering each quantity using the given function C(n).
For n = 127:
C(127) = $6.91 x 127 = $878.57
For n = 128:
C(128) = $5.16 x 128 = $660.48
By subtracting the cost of ordering 127 copies from the cost of ordering 128 copies, we can determine the cost difference:
Cost difference = C(128) - C(127)
= $660.48 - $878.57
= -$218.09
Since the cost difference is negative, it means that ordering 128 copies is cheaper than ordering 127 copies.
However, the question asks for the number of additional copies, so we need to consider the whole number of copies.
Rounding down to the nearest whole copy, the number of additional copies you could ship by ordering 128 instead of 127 copies is 0 copies.
Thus,
The number of additional copies you could ship by ordering 128 instead of 127 copies is 0 copies.
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What is the slope below
Answer: -5/4
Step-by-step explanation:
A certain airline requires that carry-on luggage is designed to fit within a rectangular prism with a length of 22 inches, a height of 14 inches, and a width of 9 inches. What is the maximum possible volume of a piece of carry-on luggage?
The maximum possible volume for a piece of carry-on luggage is given as follows:
2772 cubic inches.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The dimensions for this problem are given as follows:
22 inches, 14 inches and 9 inches.
Hence the volume is given as follows:
22 x 14 x 9 = 2772 cubic inches.
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Solve the system of equations using elimination. 6x + 6y = 36 5x + y = 10 (1, 5) (2, 0) (3, 3) (4, 2)
Answer:
begin equation begin cases x = 1y = 5 end cases end equation. Rearrange like terms to the same side of the equation
Step-by-step explanation:
begin equation begin cases x = 1y = 5 end cases end equation. Rearrange like terms to the same side of the equation
name miles hours
doug 28 2.3
primo 34 2.1
Camillo 57 1.4
Bryan 49 1.2
The table above shows the number of miles driven by four drivers and the number of hours each person drove. Which person drove the fastest?
Answer: Bryan drove the fastest.
Step-by-step explanation: To find out who drove the fastest, we need to calculate the speed of each person. Speed is given by the formula distance/time.
For Doug:
Speed = 28 miles / 2.3 hours = 12.17 miles/hour
For Primo:
Speed = 34 miles / 2.1 hours = 16.19 miles/hour
For Camillo:
Speed = 57 miles / 1.4 hours = 40.71 miles/hour
For Bryan:
Speed = 49 miles / 1.2 hours = 40.83 miles/hour
How many fewer people in the 18-25 year age group have
some form of technology career compared to all other
age groups combined?
Technology Career types for
different age groups (as a number)
41+ yrs
36-40 yrs
26-35 yrs
18.25
690
782
1.784
1673
24312
3.215
2.709
3.567
4.673
14326
15,822
Please select the correct answer from the options
shown.
a. 26,191
b. 28,345
c. 30,139
d. 33,469
Given statement solution:- The fewer people in the 18-25 year age group result is negative, it indicates that the 18-25 year age group has more people with some form of technology career than all other age groups combined. None of the options provided (a, b, c, d) are correct.
To find the number of fewer people in the 18-25 year age group with some form of technology career compared to all other age groups combined, we need to sum up the technology career numbers for all age groups except the 18-25 year age group and then subtract it from the number for the 18-25 year age group.
Sum of technology career numbers for age groups other than 18-25 years:
(41+ yrs) + (36-40 yrs) + (26-35 yrs) = 24312 + 3.215 + 2.709 = 24318.924
Number of fewer people in the 18-25 year age group compared to all other age groups combined:
1673 - 24318.924 = -22645.924
Since the fewer people in the 18-25 year age group result is negative, it indicates that the 18-25 year age group has more people with some form of technology career than all other age groups combined. Therefore, none of the options provided (a, b, c, d) are correct.
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A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap. Each lipstick has a radius of 0.6 inch and a height of 2.4 inches. How many total square inches of gift wrap will the makeup artist need to wrap 3 lipsticks? Leave the answer in terms of π.
9.04π square inches
10.8π square inches
11.3π square inches
14.4π square inches
The number of square inches or area of gift wrap that the makeup artist will need is 10.8π square inches.
Given that,
A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap.
Radius of each lipstick = 0.6 inch
Height of the lipstick = 2.4 inches
Now,
Area of the each lipstick = 2πrh + 2πr², where r is the radius and h is the height.
Area = 2π (0.6) (2.4) + 2π (0.6)²
= 2.88π + 0.72π
= 3.6π
Area of the wrap for 3 lipsticks = 3 × 3.6π = 10.8π square inches.
Hence the area is 10.8π square inches.
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Using trial and improvement, find the solution between 3 and 4 for the following equation: 2 x 3 − x 2 = 100 Give your answer rounded to 1 DP.
The solution is, After decreasing £16870 by 3% we get, £16363.90.
Here, we have,
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
First, find the percentage of £16870 by 3%
%value = 3% * 16870
= (3 / 100) * 16870
= 506.1
Now, just minus with actual value
New value = actual value - %value
We know, actual value = £16870 and %value = 506.1
so, New value = 16870 - 506.1
we get, New value = £16363.90
Therefore, After decreasing £16870 by 3% we get, £16363.90
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complete question:
Decrease £16870 by 3%
Give your answer rounded to 2 DP.
find the expected value of the winnings from a game that has the following payout I cannot proceed without your help :)
The expected value of the winnings from the game is $3.24.
To find the expected value of the winnings, we multiply each possible payout by its corresponding probability and sum them up.
Expected Value = (2 x 0.64) + (4 x 0.18) + (6 x 0.12) + (8 x 0.04) + (10 x 0.02)
Expected Value = 1.28 + 0.72 + 0.72 + 0.32 + 0.20
Expected Value = 3.24
Therefore, the expected value of the winnings from the game is $3.24.
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A bottle holds 750 milliliters of iced tea.
I fluid ounce 30 milliliters
Approximately how many fluid ounces of iced tea does the bottle hold, rounded to the nearest whole number?
The number of fluid ounces of iced tea does the bottle hold is 25.
Given that, a bottle holds 750 milliliters of iced tea.
1 fluid ounce has 30 milliliters.
Here, the number of fluid ounces = Total quantity of iced tea/Quantity of fluid in a fluid ounce
= 750/30
= 25
Therefore, the number of fluid ounces of iced tea does the bottle hold is 25.
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a) Write a direct variation equation that represents the situation of a group of snow geese migrating 375 miles in 7.5 hours.
C
b) Every year geese migrate 3,000 miles from their winter home in the southwest United States to their summer home in the Canadian Arctic. How many hours of
flying time does it take the geese to migrate? (Use your equation from part a)
Answer:f=60a(60)
hope this helps bye