What is the value of K?
Answer:
0
Step-by-step explanation:
ik my math
The value of k in the solution [tex]x=\frac{5\pm i\sqrt{k}}{8}[/tex] of the quadratic equation 4x² - 5x = -6, is 71.
Given a quadratic equation:
4x² - 5x = -6
It is required to find the solution of the quadratic equation first.
It is known that the solution of the quadratic equation of the form ax²+bx+c can be written as [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].
Here, the equation can be written as:
4x² - 5x + 6 = 0
Here, a = 4, b = -5 and c = 6.
Substitute.
[tex]x=\frac{-(-5)\pm \sqrt{(-5)^2-4(4)(6)}}{2(4)}[/tex]
[tex]x=\frac{5\pm \sqrt{25-96}}{8}[/tex]
[tex]x=\frac{5\pm \sqrt{-71}}{8}[/tex]
Now, [tex]\sqrt{-71} =\sqrt{-1} \sqrt{71}[/tex].
But, [tex]\sqrt{-1} =i[/tex]
So, the solution is:
[tex]x=\frac{5\pm i\sqrt{71}}{8}[/tex]
Hence, the value of k is 71.
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A school is arranging a field trip to the zoo. The school spends 778.88 dollars on passes for 28 students and 4 teachers. The school also spends 241.64 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
The total money spent on a pass and lunch for each student is $850.14.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.
here,
As mentioned in the question, Passes for 28 pupils and 4 teachers cost the school $778.88 and the school also spends $241.64 on lunch for kids only.
Total number of person = 28 + 4
= 32
Cost per pass = 778.88 / 32
= $24.34
Total passes of students = 25 × 24.34 = 608.5
Total spend on lunch of student = 241.64
Total spend on lunch = 241.64 + 608.5 = $850.14
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-5 = t + 6 1/3 solve for t
Answer: t=-34/3 or -11 1/3
Step-by-step explanation:
isolate t
t+19/3=-5
subtract both sides with 19/3
t=-34/3 or -11 1/3
Answer:
-34/3
Step-by-step explanation:
-5=t+6 1/3
6 1/3= 19/3
-5=t+19/3
-t. -t
-5-t=19/3
+5. +5
-t=34/3
/-1. /-1
t= - 34/3
what is 2⅘ equivalent to?
Answer:
2.8
Step-by-step explanation:
Answer:
2.8
Step-by-step explanation:
4/5ths is just .8 in fraction form. Add it on to your 2 and you've got your answer.
NEED ASAP PLEASE!
A company is interested to know the variation in yearly sales amount for all 5 salespeople in the company.
The dataset shown below is the sales amount sold by the 5 salespeople in the company (expressed in thousands of dollars):
40,60,65,70,80
Find the variance for this dataset.
The variance in the sample data is 220
We are given the following data of 5 salespeople (expressed in thousands of dollars); 40, 60, 65, 70, 80
How is standard deviation calculated?Suppose that the considered data set is
Then, its standard deviation is the positive square root of the variance of this data set. Variance of data set is the sum of squared differences of the data values from its mean to the total count of data values.
Thus, we get:
[tex]\sigma = \sqrt{\dfrac{1}{n} \sum_{i=1}^{n} (x_i-\overline{x})^2[/tex]
In the formula above, x represents the mean of the data points, x is the value of an individual data point, and N is the total number of data points.
x = (40+60+65+70+80)/5
x=63
So, the mean of the sample data is 63
Variance =
[tex]\sigma^2 = \dfrac{\sum_{\forall x_i} (x_i - \overline{x})^2}{n}[/tex]
Therefore, the variance is 220
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7m + 29 = 2m + 9 ( please show work toooooo )
Answer:
m = -4
Step-by-step explanation:
7m + 29 = 2m + 9
-2m -2m
--------------------------
5m + 29 = 9
-29 -29
-----------------------
5m = -20
÷5 ÷5
--------------------
m = -4
I hope this helps!
help please and thank you
Answer:
1) 9x
2) 3b
3) 3m
4) 5a
5) 7x
6) 3a + 5b
7) 9x - 4
8) 2b + m
9) 13a + b + 6c
10) 9b + 1
11) 7p
12) 2a + b -10
Step-by-step explanation:
Criteria: I can explain what happens to lines and angles in a dilation.
Triangle DEF is a scaled copy of Triangle ABC}, answer the following question equations that could be used to solve for x.
7 ÷ x = 1.5 is the equation used to solve for x.
Given,
Triangle DEF is a scaled copy of triangle ABC.
We have to find the equation to solve for x.
Scaled Copy;-
A scaled copy is a representation of a figure in which each length from the original representation has been multiplied by the same amount. Triangle ABC, for instance, is a scaled version of triangle DEF. Triangle DEF's side lengths were calculated by multiplying each side length from triangle ABC by 1.5.
Here,
Length of side AB = 6
Length of side DE = 4
Let y be the value used for scaling.
Then,
6 = 4y
y = 6/4 = 1.5
So,
Length of side BC ÷ x = 1.5
7 ÷ x = 1.5
7 = 1.5x
x = 7/1.5
x = 4.67
That is,
The equation used for getting the value of x is 7 ÷ x = 1.5
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Find x in this equation
Answer:
5
Step-by-step explanation:
[tex]\triangle HBK \cong \triangle NBK[/tex] by SAS. Using CPCTC, [tex]3x=x+10 \implies 2x=10 \implies x=5[/tex].
Convert 97°C to degrees Fahrenheit.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=(F-32)
9
F ==C+32
5
97 °C
= F
Answer: 97 degrees Celsius is 206.6 degrees Fahrenheit.
Substitute 6 for x and evaluate the expression below.
|x + 10 - X
Answer: 16-x
Step-by-step explanation:
Collect like terms.
-x + (6 + 10)
Simplify.
16 - x
From my calculations using the Cymath calculator, 16 - x would be the answer, Hope I could help.
Which of the following equations has a maximum at (9,7)?
A.
y = -x2 − 14x − 58
B.
y = -x2 − 18x − 88
C.
y = -x2 + 14x − 40
D.
y = -x2 + 18x − 74
The equation which will have the maximum value at (9,7) is [tex]y = -x^{2} + 18x-74[/tex]
What is an equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 4x + 6 = 15 consists of the two equations 4x + 6 and 15, which are separated by the 'equal' sign.
How do you find the maximum value of an equation ?The graph's transition from increasing to decreasing must be identified in order to determine the maximum. We look at the second derivative and see when the value changes from positive to negative to determine the rate at which the graph goes from increasing to decreasing.
According to the given information
[tex]y = -x^{2} + 18x-74[/tex]
The equation which will have the maximum value at (9,7) is [tex]y = -x^{2} + 18x-74[/tex]
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PLEASEE HURRY
Frank is wanting to create a scale model of the Eiffel Tower. The real Eiffel Tower is 984 feet tall and 328 feet wide at its base. If Frank's model is 12 inches tall, how wide (in inches) must his scale model be?
Answer:
4 Inches.
Step-by-step explanation:
To find the width of Frank's scale model, we need to first determine the scale of the model. This can be done by dividing the height of the real Eiffel Tower by the height of Frank's model. Since the real Eiffel Tower is 984 feet tall and Frank's model is 12 inches tall, the scale of the model is 984 / 12 = 82 feet per inch.
Next, we can use this scale to determine the width of the model. Since the real Eiffel Tower is 328 feet wide at its base, and the scale of the model is 82 feet per inch, the width of the model must be 328 / 82 = 4 inches.
Therefore, the width of Frank's scale model of the Eiffel Tower must be 4 inches.
quadratic equation in standard form:
17=5-6 z-z²
Answer:
i think z would be 17
Step-by-step explanation:
If 2 sides of a triangle are 10 and 20, what is the possible range of the 3rd side?
Answer:10<x<30
Step-by-step explanation:
According to the triangle side theorem all you need to do is this.
Difference of the two sides<x<Sum of the two sides.
That will give you the range your looking for. For the difference always remove the smaller number from the bigger number so you can always have positive integers.
Answer: 10<x<30
Step-by-step explanation: The third side of the triangle has to be greater than the difference of the other two sides and smaller than the sum of the other two sides.
A surveyor determines that the angle of elevation to the top of a building from a point on the ground is 31.3. He then moves back 57.9 feet and determines that the angle of elevation is 23.5°. What is the height of
the building?
Round your answer to four decimal places
Answer:23 203 feet
Step-by-step explanation:
Write an equation of a line with the given slope and y-intercept.
m = 1, b = 4
Answer: " y = x + 4 ".
Step-by-step explanation:
We shall write the equation of a line written in slope-intercept format;
that is, " y = mx + b " ;
in which y is isolated as a single variable on the 'left-hand' side of the question, and with no "coefficient"—
{except for the implied coefficient of 1 }; and:
m refers to the slope of the line—and is the coeffcient of x ;
and b refers to the y-intercept—or more specifically, the value of the y-coordinate when "x = 0" [i.e. the value of the y-coordinate where the line crosses the x-axis].
So: We can plug the given values: m = 1 ; and b = 4 ; into the equation:
" y = mx + b " ; as follows:
→ y = 1x + 4 ; Note: By convention, we often omit the 1 as the coefficient of x —since the 'stand-alone' variable, x ; has an implied coefficent of x ; and we can write the equation:
→ y = x + 4 ; which is our answer.|
______
Hope this is helpful to you! Best wishes!
______
Consider the proportions m/n=1/2 and n/k =2/5. What is the ratio m/k?EXPLAIN YOUR REASONING WITH ALL STEPS
Answer:
To find the ratio m/k, we need to combine the proportions m/n and n/k. One way to do this is to multiply the fractions to get the product m/k. This can be done by multiplying the numerators to get m, then multiplying the denominators to get k.
For example, if we let m=1, n=2, and k=5, then we have the following:
m/n = 1/2
n/k = 2/5
If we multiply the numerators and denominators to get the product m/k, we get:
(1 * 2) / (2 * 5) = 2/10 = 1/5
Therefore, the ratio m/k is 1/5.
Another way to find the ratio m/k is to use the fact that proportions are equivalent to equations. We can set up an equation using the given proportions, then solve for m/k.
For example, using the same values as before, we have:
m/n = 1/2
n/k = 2/5
We can set up an equation by setting the two proportions equal to each other:
m/n = (1/2) = n/k = (2/5)
Then we can cross-multiply to solve for m/k:
m/n * n/k = (1/2) * (2/5)
(m * 2) / (n * 5) = 1/5
m/k = (2/5) = 1/5
Therefore, in this case, the ratio m/k is also 1/5.
In general, to find the ratio m/k given the proportions m/n and n/k, we can either multiply the fractions or set up and solve an equation using the given proportions.
If you good w functions come help me out
Answer: Number one is a function
Number two is not a function
Number three is a function
Step-by-step explanation:
An easy way to determine functions in situations like these is to look and see if there are multiple outputs for the same X. If there are it is not a function. There can be multiple X values that go to the same Y value however.
Farmer Smith has 160 feet of fencing that she is using to make a rectangular enclosure for her chickens. She will use the side of an existing chicken coop as one side of the enclosure and use the fencing for the other three sides.
Which function gives the area A, in square feet, as a function of the length of one of the sides perpendicular to the existing coop
Answer:
C
Step-by-step explanation:
2 times 50 find the product or quotient
Answer:
product is the answer good luck on your test
find the equation of the straight line passing through the point (3, 5) which is perpendicular to the line y=3x+2
what is y
The equation of the line is y = -x/3 + 6.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction
We have the line y = 3x + 2
The slopes of perpendicular lines are negative reciprocals of each other.
The slope of the given line is m=3 the slope of the perpendicular line is -1/3.
Then the equation of the line;
y = -x/3 + b
And b is the y-intercept of the perpendicular lines passes through the point
(3,5).
Substituting the (3, 5) to the required line;
5 = -3/3 + b
b = 6
Now the line is y=-x/3 + 6
Therefore, the equation of the line is y = -x/3 + 6.
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Solve for x.
3.4>x+2/3
Answer:
x < 2 11/15
Step-by-step explanation:
Hope this helps!
hi everyone, I'm studying for a math test. I just have one specific question: are all equations in the format y=mx+b linear equations? Or do I still need to graph it and check if it is a straight line first??
Yes, all equations in the format y=mx+b are linear equations. In this format, "m" represents the slope of the line and "b" represents the y-intercept, which is the point where the line intersects the y-axis. This means that all equations in this format will produce a straight line when graphed.
However, it is always good practice to graph the equation to confirm that it is a straight line. This will also allow you to see the slope and y-intercept of the line, and check if they match the values of "m" and "b" in the equation.
Michael had 20 minutes to do a three-problem quiz. He spent 11 9/10
minutes on questions A and 4 3/4 minutes on question B. How much time did he have left for question C?
Gavin has 6 9/20 minutes to solve the 3rd problem.
Find the solution ?An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters. A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.Add the time for the first two problems:
9 3/4 + 3 4/5
To add fractions rewrite them so they have a common denominator:
3/4 = 15/20
4/5 = 16/20
Now you have:
9 15/20 + 3 16/20 = 12 31/20 = 13 11/20 minutes.
Now subtract that from the time allowed:
20 - 13 11/20 = 6 9/20 minutes.
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five apple pies were shared equals by 12 people. How much pie did each pie
Answer:2.4
Step-by-step explanation:20 - 8.99 = 2.4
Given the following table of values of the polynomial f(x), what is the minimum number of zeros of f(x) that are guaranteed to exist by the Intermediate Value Theorem?
The number of zeros of f(x) that are guaranteed to exist by the Intermediate Value Theorem is given as follows:
0.
What is the Intermediate Value Theorem?The intermediate value theorem defines that if a continuous function passes in two points, it will pass through all the points between these two values.
The zeros of a function are all the values of x for which the function assumes a value of zero.
Hence, if for a value of x = a the function is positive, and then for a value of x = b > a the function is negative, or vice versa, a zero is guaranteed to exist in the interval between a and b.
In this problem, the function does not assume any negative values, hence a zero is not guaranteed to exist in the function, and the number is of zero.
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Is 70/100 equal to 7/10?
Answer:
Yes
Step-by-step explanation:
A simple way to know is by simplifying them.
70/100 divided by 10 is 7/10
First divide 70 by 10: you get 7
Then divide 100 by ten: you get 10
Subtract the expressions.
Pls help asap
(8.21n − 5.3) − (7 + 11.8n)
−3.59n − 12.3
−35.90n − 4.8
13.51n − 4.8
20.01n + (−12.3)
Answer:
I will gladly help (see explanation)
Step-by-step explanation:
1. 8.21n−5.3−(7+11.8n)
Distribute the Negative Sign:
=8.21n−5.3+−1(7+11.8n)
=8.21n+−5.3+(−1)(7)+−1(11.8n)
=8.21n+−5.3+−7+−11.8n
Combine Like Terms:
=8.21n+−5.3+−7+−11.8n
=(8.21n+−11.8n)+(−5.3+−7)
=−3.59n+−12.3
(Hope his helped, Good Luck! )
Answer:
-3.59 - 12.3
Step-by-step explanation:
Algebraic ExpressionsAlgebraic Expressions are similar to numerical expressions but instead of just numbers, alphabet variables are being used as well.
Note: BODMAS rule applies to Algebraic Expressions as well.
Eg. 7x + 4 + 5y + 4x = 11x + 5y + 4
SolutionGiven from the question:
(8.21n - 5.3) - (7 + 11.8n)
= 8.21n - 5.3 - 7 - 11.8n
= 8.21n - 11.8n - 5.3 - 7
= -3.59n - 12.3
Therefore, the answer is -3.59 - 12.3.
HELP ASAP PLS AND USE THE ANSWERS GIVEN!
Simplify the expression.
negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
−13.16
−9.89
0.49
20.11
The value of the given Fraction expression is -6.93.
What is Fraction?
A fraction is a mathematical expression that represents the division of a whole number or quantity into parts. It is written as two separate numbers, a numerator and a denominator, separated by a slash. The numerator represents the number of parts being considered, and the denominator represents the total number of parts. Additionally, fractions can also represent parts of a whole number. For example, the fraction 1/2 represents one part of a whole number that has been divided into two equal parts. Fractions can also be combined to create a sum of parts.
So, we have
-15 - 3.7 + 9.15/5 * 3^2 - 4.7
Evaluate the quotient and the exponent
So, we have
-15 - 3.7 + 1.83 * 9 - 4.7
Evaluate the product
-15 - 3.7 + 16.47 - 4.7
Evaluate the sum and the difference
-6.93
Hence, the value of the given fraction expression is -6.93 (none of the options is correct)
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