Select the correct expressions in the table.
Which expressions are equivalent to the given expression?
Answers
Answer:
hope this helps :))
Step-by-step explanation:
i put it in a calculator and to get the a + bi standard form answer, then did the same with the other ones to see which one matched the former answer. also, can i pretty pretty please get brainliest? :))
The expressions that are equivalent to the given expression
(-√9 + √-4) - (2√576 + √-64) are
-3 + 2i - 2(24) - 8i, and-51 - 6i.What are Complex Numbers?The sum of a real and an imaginary number is a complex number. A complex number is denoted by the letter z and has the form a + ib. Both a and b are real numbers in this case. The value 'a' is known as the real component and is indicated by Re(z), whereas 'b' is known as the imaginary part and is denoted by Im (z). ib is also known as an imaginary number.
What is 'i' in a complex number?The letter 'i', often known as the iota, is used to denote the imaginary component of a complex integer. Additionally, the iota(i) may be used to find the square root of negative values. We know that i² = -1, therefore we utilize that to calculate the value of √-4 = √i²4 = ±2i. The essential characteristic of a complex number is the value of i² = -1.
How do we solve the given question?We are asked to choose the expressions from the table equivalent to the given expression: (-√9 + √-4) - (2√576 + √-64).
To check for the equivalent expression, we simplify the given expression and check at each step if we get an expression from the given table.
(-√9 + √-4) - (2√576 + √-64)
= (-√3² + √(2i)²) - (2√24² + √(8i)²)
= (-3 + 2i) - (2(24) + 8i) ... (∵ √a² = a)
= -3 + 2i - 2(24) - 8i (Equivalent to one expression)
= -3 + 2i - 48 - 8i
= -51 - 6i (Equivalent to one expression)
∴ The expressions that are equivalent to the given expression
(-√9 + √-4) - (2√576 + √-64) are
-3 + 2i - 2(24) - 8i, and-51 - 6i.Learn more about complex numbers at
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Related Questions
What is
\( {4}^{ - 3}\)
as a fraction?
Answers
Step-by-step explanation:
\( {4}^{ - 3} \)
\( = ( \frac{1}{4} )^{3} \)
I have double check this
Use an algebraic approach to solve the problem.
Abby has 37 coins, consisting only of dimes and quarters, worth $5.65. How many dimes and how many quarters does she have?
Answers
Answer:
13 quarters and 24 dimes
Step-by-step explanation:
13*.25=3.25
24*.1=2.4
3.25+2.4=5.65
find the coefficient of x7 when the following expression is expanded by the binomial theorem. x7 in (3x +4)10 the term
Answers
The coefficient of x7 in the expansion of (3x + 4)10 is 53,248,000.
To find the coefficient of x^7 in the expansion of (3x + 4)^10 using the binomial theorem, we need to identify the term that has x^7.
The binomial theorem states that (a + b)^n = Σ (nCk) * a^(n-k) * b^k, where k goes from 0 to n and nCk denotes the binomial coefficient, which is the combination of choosing k items from n.
In our case, a = 3x, b = 4, and n = 10. We need to find the term with x^7, so the power of a (3x) should be 3 (since 3x raised to the power of 3 is x^7). This means the term will have the form:
10C3 * (3x)^3 * 4^(10-3)
Now we calculate the coefficients:
10C3 = 10! / (3! * (10 - 3)!) = 120
(3x)^3 = 27x^{7}
4^7 = 16384
Now, we multiply the coefficients together:
120 * 27 * 16384 = 53,248,000
Therefore, the coefficient of x^7 in the expansion of (3x + 4)^10 is 53,248,000.
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Q1) How do I simplify (10)^8 divided by (10)^3 ?Q2) How do I simplify, Leaving the answer in index form: 4^14 divided by 4^10 ?
Answers
To simplify \((10)^8\) divided by \((10)^3\), you can use the rule of exponents that states when dividing two powers with the same base, you subtract their exponents.
In this case, (10)^8 divided by (10)^3 can be simplified as follows:
(10)^8 divided by \((10)^3 = 10^{8-3} = 10^5\)
Therefore, (10)^8 divided by (10)^3 simplifies to \(10^5\).
For the second question, to simplify \(4^{14}\) divided by \(4^{10}\) and express the answer in index form, you can again apply the rule of exponents. When dividing two powers with the same base, you subtract their exponents.
4^{14} divided by 4^{10} simplifies as follows:
4^{14} divided by 4^{10} = \(4^{14-10}\) = \(4^4\)
Therefore, 4^{14} divided by 4^{10} simplifies to 4^4.
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i dont know what is 2+2*3/8
Answers
its 2 and 3/4
cause 3/8*2 simplifys to 3/4
Answer:
2+2*3/8=2+.75=2.75
Step-by-step explanation:
You always want to multiplay before you add. You multiply the 2 by the 3/8 and add the two.
One sixth of a number is equal to triple that number less 136.
Let the unknown number be x. Write this word problem using the variable x.
Answers
In the diagram shown at the right, ABCD is a parallelogram and BF = 16. Find the area of ABCD. Explain your reasoning. (Hint: Draw auxiliary lines through point A and through point D that are parallel to EH.)
Answers
The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.
We know,
A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.
we have,
∠DEC ≅ ∠BFC Reason = All Right Angles with Equal dimensions are congruent.
∠C ≅ ∠C Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.
Δ DEC ≅ Δ BFC Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
≅ Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.
ABCD is a Rhombus Reason = Its sides are all congruent.
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complete question:
Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus
the obtained value must be compared against which of the following? a. test value b. critical value c. expected value
d. observed value
Answers
The obtained value must be compared against the critical value. Hence, the correct option is b.
In hypothesis testing, the critical value is a threshold or cutoff point that is determined based on the chosen significance level (alpha level) and the distribution of the test statistic. It helps in determining whether to reject or fail to reject the null hypothesis.
After calculating the test statistic (such as z-score or t-statistic) from the observed data, it is compared to the critical value associated with the chosen significance level.
If the test statistic exceeds the critical value, it falls into the critical region, leading to the rejection of the null hypothesis.
If the test statistic is less than or equal to the critical value, it falls into the non-critical region, resulting in a failure to reject the null hypothesis.
Therefore, the obtained value must be compared against the critical value to make a decision in hypothesis testing. Hence, the correct answer is option b.
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Rational zeros of polynomial function
Help!
Answers
Zeros of the given polynomial are -2, 2, -3/2, 3/2
What are zeroes of a polynomial?Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.
Given a polynomial 1/4(4\(x^{4}\) - 25\(x^{2}\) + 36)
1/4(4\(x^{4}\) - 25\(x^{2}\) + 36) = 0
(4\(x^{4}\) - 25\(x^{2}\) + 36) = 0
4\(x^{4}\) - 16\(x^{2}\) - 9\(x^{2}\) + 36= 0
4\(x^{4}\)(\(x^{2}\) - 4) - 9(\(x^{2}\) - 4) = 0
(4\(x^{4}\)-9)(\(x^{2}\) - 4) = 0
(x+2)(x-2)(2x+3)(2x-3) = 0
x = -2, 2, -3/2, 3/2
Hence, Zeros of the given polynomial are -2, 2, -3/2, 3/2
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PLEASE HELP ME DUE IN 7 MINUTES
Answers
Step-by-step explanation:
x=24
y=19
that is the answer. I am very sure
Answer:
3x =5y-23
X=44.33
Y=31. 199
Please help me with this.
Answers
Answer:
y = (-1/2)x + 4
Step-by-step explanation:
Slope (m): (-1/2)
down one, right two
y-intercept (b): 4
y = mx + b
The slope-intercept equation if the line is \(y=-\frac{1}{2}x+4\)
To find the slope, you must put the 2 points into the slope equation.
\(\frac{3-4}{2-0}=\frac{-1}{2}\)
And to find the y-intercept, you must find where the line crosses the y-axis.
(0,4)
State the slope and y=-intercept for the graph of the equation y= -2x + 7
Answers
Answer:
slope = -2
y-intercept = 7
Step-by-step explanation:
Slope formula: y=mx+b
In every equation that follows this formula, m is slope and b is y-intercept.
Answer:
-2 - slope
7 - y-intercept
Step-by-step explanation:
The equation is in slope-intercept form.
y = mx + b
m - slope
b - y -intercept
'-2' is in m's spot. It is the slope.
'7' is in b's spot. It is the y-intercept.
Hope this helps!
Please help me with this question please help
Answers
What level of measure is the variable representing zip codes?
Interval
Ordinal
Ratio
Nominal
Answers
The ratio of dye to pounds of clothing is constant. A worker develops the chart below to show the amount of dye needed
for different amounts of clothing.
Clothes Dyeing
Weight of clothing Cups of dye
(pounds)
21
3
42
9
84
12
105
15
For which weight of clothing is the ratio of weight to dye different from the other ratios?
21 pounds
42 pounds
84 pounds
105 pounds
Answers
Answer: The answer is 42
Step-by-step explanation:
I did the test too :)
The weight of clothing for which the ratio of weight to dye is different from the other ratios is 42 pounds.
To determine which weight of clothing has a ratio of weight to dye different from the other ratios, we need to compare the ratios for each weight.
Let's calculate the ratios for each weight of clothing by dividing the weight of clothing (in pounds) by the cups of dye:
For 21 pounds of clothing: 21 pounds / 3 cups = 7 pounds per cup
For 42 pounds of clothing: 42 pounds / 9 cups = 4.67 pounds per cup
For 84 pounds of clothing: 84 pounds / 12 cups = 7 pounds per cup
For 105 pounds of clothing: 105 pounds / 15 cups = 7 pounds per cup
From the calculations, we can see that for weights of 21 pounds, 84 pounds, and 105 pounds of clothing, the ratios of weight to dye are the same, which is 7 pounds per cup. However, the ratio for 42 pounds of clothing is different, which is 4.67 pounds per cup.
Therefore, the weight of clothing for which the ratio of weight to dye is different from the other ratios is 42 pounds.
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Compare the numbers
Answers
Answer:The answer is ≥ greater than or equal to
can you mark me Brainliest please
Complete the equation describing how x
and y are related
Answers
Answer:
y = x + -5
Step-by-step explanation:
Solution
To complete the equation, let's take two different points and plug their x- and y-coordinates into the equation. Then, we can solve for the question mark and see if we get the same number. I'll take (1, -4) and (2, -3):
(1, -4):
-4 = 1 + b-4 - 1 = 1 + b - 1b = -5(2, -3):
-3 = 2 + b-3 - 2 = 2 + b - 2b = -5Thus, the equation is y = x + (-5).
Can someone do it quickly since it’s a timed test
Paper 2
The scatter diagram shows the scores of 10 students
in their paper 1 and paper 2 Maths GCSE exams.
1001
A line of best fit has been drawn.
90
a) What type of correlation is shown
by the graph?
80
A
70
60
paper 2
50
40
b) A pupil who scored 50 in his paper 1
exam got ill and missed paper 2.
Use the line of best fit to predict what
his paper 2 mark could have been
30
20
10
10 20 30 40 50 60 70 80 90 100
paper 1
Answers
The correlation shown in the graph is a positive correlation and pupil might have scored 60 in paper 2.
How to plot a graph?A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
After that, we need to substitute the values of x's and y's into the coordinate geometry.
Given the graph,
a)
The overall value of paper 2 is increasing with respect to paper 1 from 40 to 90.
So it will be a positive correlation graph.
b)
If a pupil scored 50 in paper 1 then according to the best-fit line it might score 60 because the line is intersecting at 60 in paper 2 with respect to paper 1.
Hence "The correlation shown in the graph is a positive correlation and pupil might have scored 60 in paper 2".
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Answer:
a)positive
b)61
Step-by-step explanation:
Trust me the answer is correct!
(a) select one of the pairs of systems and write down its number. (b) for the pair selected, identify each system and state one function of that system. (c) explain how the two systems work together to help maintain homeostasis in an individual.
Answers
a. Pair 2 is selected.
b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.
c. The two systems work together by sharing the region of the mouth and upper throat.
First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.
How does the respiratory system and the digestive system work together?The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.
The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.
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What is the answer?
l-8l+4(-5+9)/2.
A-24
B-12
C-16
D-0
Answers
Answer:
C. 16
Step-by-step explanation:
1. Calculate the absolute value
|-8|+4(-5+9)/2
2. Reduce the fraction with 2
8+4(4/2)
3. Multiply
8+4(2)
4. Calculate
8+8 = 16
Taylor is struggling with literal equations. She has tried to solve the equation below for several times but still can't get the correct answer. Her steps that she used to solve for m are shown below. In which step is she making an error?
Answers
The step 3y = 80v + x is incorrect, as 3y = 80v - x is the correct step by subtraction property of equality.
In this question, we have been given Taylor is solving a literal equation (x + 3y) / 2 = 40v
We have been given her steps that she used to solve for y.
We need to find an error in the steps.
First we solve given literal equation for y.
(x + 3y) / 2 = 40v
x + 3y = 40v × 2 .................(Multiply both the sides by 2)
x + 3y = 80v
x + 3y - x = 80v - x ...................(Subtract x from both the sides)
3y = 80v - x
y = (80v - x)/3 ............(Divide each side by 3)
If we observe Taylor's steps, we can see that there's an error in the step 3y = 80v + x.
Therefore, the step 3y = 80v + x is incorrect, as 3y = 80v - x is the correct step by subtraction property of equality.
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3. Solve your equation to find the distance Jane’s trainer bikes. Show your work.
4. How much farther does Jane travel than her trainer?
(my previous answers so this will make sense)
1. The total distance jane bikes and runs is 28 miles.
2. Janes trainer bikes a distance of 20 miles.
Answers
Jane travels 8 miles much farther than her trainer. The solution is obtained using arithmetic operations.
What are arithmetic operations?
By combining operands with one arithmetic operator, an arithmetic operation is given. The built-in functions add, subtract, divide, and multiply additionally allow for the specification of arithmetic operations.
3. Using pythagoras theorem, we get the equation as D² = 12² + 16².
⇒D² = 144 + 256
⇒D² = 400
⇒D = √400
⇒D = 20
4. Jane has traveled 28 miles in total whereas her trainer has traveled 20 miles.
So, the difference is 28-20= 8 miles
Hence, Jane travels 8 miles much farther than her trainer.
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One angle of an isosceles triangle is known to be 68°. What would be one of the other angles?
a 44°
b 55°
c 66°
d 112°
Answers
Answer:
44
Step-by-step explanation:
Isosceles triangles have two angles that are equal. If the two equal angles are 68
We have 68, 68, and an unknown angle x
They add to 180
68+68+x = 180
136+x=180
x =180-136
x =44
Mateo compró un artefacto gastando los 3/7 de su dinero, quedándole 360 soles, ¿Cuál era el dinero que tenía Mateo al inicio?
Answers
Answer:
840 soles
Step-by-step explanation:
Sea la cantidad de dinero que Mateo tenía al principio = x
Mateo compró un artefacto gastando 3/7 de su dinero, dejándole 360 soles,
Por eso,
3/7 × x = 360 soles
3x / 7 = 360 soles
Multiplicar cruzada
3x = 7 × 360 soles
x = 7 × 360 soles / 3
x = 840 soles
Por tanto, el dinero que tenía Mateo al principio es de 840 soles
help me plz !!!!!!!!! >,
Answers
Answer: 21/28
Step-by-step explanation: you know 75/100 is 0.75, which means whatever is on top of 28 has to be less than 28 so the answer is less than 1. I just plugged in numbers until I got the right answer.
For the list {12, 15, 13, 20, 23, 27, 25, 36, 40}, how many elements will be compared to find 25 using linear search
Answers
7 elements will be compared to find 25 using linear search
What is linear search?A linear search, also known as a sequential search, is a technique used in computer science to locate an element inside a list.Up until a match is discovered or the entire list has been searched, each element of the list is successively checked.In worst-case linear time, a linear search performs at most n comparisons, where n is the length of the list.A linear search has an average case of n+1/2 comparisons if each element is equally likely to be searched, but the average case can be impacted if the search probability for each element differ.Since other search algorithms and schemes, such the binary search algorithm and hash tables, provide substantially faster searching for all but short lists, linear search is rarely practical.To learn more about linear search with the given link
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Solve for y.
6x + y = 10
Answers
\(6x + y = 10 \\ y = 10 - 6x \\ y = 10 - 6x,x∈ℝ\)
Solved✔︎Answer:
y = 10 - 6x
Step-by-step explanation:
6x + y = 10
=> y = 10 - 6x
Find an equation in slope-intercept form of the line that has slope –7 and passes through point A(8,-4)
a.) y = 52x + 7
b.) y = 7x + 52
c.) y = -7x - 52
d.) y = -7x + 52
Answers
Answer:
y = -7x + 52
Step-by-step explanation:
y = -7x - b
-4 = -7(8) + b
-4 = -56 + b
52
A cell phone company uses the equation C=$0.15t+$35.00 to determine the total cost, C, for a month of service based on the number of text messages, t. Identify the slope.
Answers
Slope is $0.15 of the equation of cost C=$0.15t+$35.00.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Given that A cell phone company uses the equation C=$0.15t+$35.00
C is the total cost for a month of service.
t is the number of text messages.
We have to find the slope of the equation.
slope is 0.15 and 35.00 is the y intercept of the equation given.
Hence, slope is $0.15 of the equation of cost C=$0.15t+$35.00.
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graph each linear inequality (3.)x-y>5 m= , b=(5.) y ≥ -5/3 x + 1. m=. b= -2x+y<5 m=. b=(7.) 4x-2y -8. m=. b=2x-y<4 5. m=. b=
Answers
For a equation of the form:
\(\begin{gathered} y=mx+b \\ or \\ ymx+b \\ or \\ y\le mx+b \\ or \\ y\ge mx+b \end{gathered}\)m = slope
b = y-intercept
for:
\(\begin{gathered} x-y>5 \\ \text{solve for y:} \\ y-------(5)
\(\begin{gathered} y\ge-\frac{5}{3}x+1 \\ m=-\frac{5}{3} \\ b=1 \\ ----- \\ y<2x+5 \\ m=2 \\ b=5 \end{gathered}\)(7)
\(\begin{gathered} y<2x+4 \\ so\colon \\ m=2 \\ b=4 \\ ------- \\ y<2x+5 \\ so\colon \\ m=2 \\ b=5 \end{gathered}\)
