Answer: 1/3 ± √29/3i
Step-by-step explanation:
To solve these equations, move everything to one side:
3x^2-2x+10 = 0
This cannot be factored, so use the quadratic formula:
x = -(-2) ± √( (-2)^2 - 4(3)(10)) / 2
x = (2 ± √4 - 120) / 6
x = 2 ± (√116 • i) / 6
x = 2 ± (2√29•i) / 6
x = 1/3 ± (√29/3)i
What is this expression in simplified form?
2/135*6 - 3√15*6
A. 9x³√10
OB. 8³/30
C. 119³√15
D. 3x³√15
4
Answer: The expression in simplified form is D. 3x³√15
To simplify the expression, we can first simplify the fractions.
2/1356 can be simplified to 12/225.
Then, we can use the distributive property to simplify the expression further.
12/225 - 3√156 = 12/225 - 18√15
The last step is to combine the terms,
12/225 - 18√15 = (-6/75) - (6√15) = -6/5 * (1/5 - √15) = -6 * (- √15/5) = 3 * √15 * 6
Therefore, the simplified form of the expression is D. 3x³√15
Step-by-step explanation:
Cmonnn I will give Brainly just be quick plssss
Answer:
D) 7----------------------------------
Solve the equation:
-3 - (- 8) - (- 2) = x-3 + 8 + 2 = x-3 + 10 = x10 - 3 = x7 = xx = 7Answer:
[tex] \sf \: d) \: x = 7[/tex]
Step-by-step explanation:
Given equation,
→ -3 - (-8) - (-2) = x
Now the value of x will be,
→ -3 - (-8) - (-2) = x
→ x = -3 - (-8) - (-2)
→ x = -3 + 8 + 2
→ x = 5 + 2
→ [ x = 7 ]
Hence, the value of x is 7.
What is the solution to the system of equations x-y=-1 and x-3y=-13?
why did you choose this answer?
Answer:
(5,6)
Step-by-step explanation:
x -y = -1
x - 3y = -13 ⇒ multiply through by -1 ⇒ -x + 3y = 13 Add this to the first equation
-x + 3y = 13
x - y = -1
2y = 12 Divide both sides by 2
y = 6
To find y substitute 6 for y in the equation x - y = -1
x - 6 = -1 Add 6 to both sides
x = 5
(5,6)
What is the product of the complex numbers below?
(3-2)(1+7i) please help
Answer:
6125555566/6661234567
A sailor is on the top deck of a ship that is anchored near shore, 200 feet from a lighthouse. The sailor can see the top of the lighthouse by looking up at a 21° angle of elevation and can see the bottom of the lighthouse by looking down at a 14° angle of depression.
How tall is the lighthouse?
Enter your answer in the box. Round to the nearest tenth of a foot.
The height of the lighthouse is 76.4 feet.
What is the angle of elevation?
The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.
We can use the concept of trigonometry to solve this problem. We know that the angles of elevation and depression are formed by the line of sight of the sailor and the height of the lighthouse.
We can use the tangent function to relate these angles to the height of the lighthouse.
Tangent of angle of elevation = opposite side / adjacent side
Tangent of angle of depression = opposite side / adjacent side
Let h be the height of the lighthouse.
tan(21) = h / 200
tan(14) = h / (200 + h)
now we can use these equations to find h,
h = (200 * tan(21)) = (200 * (opposite side/adjacent side)) = (200 * (h/200))
h = 200 * tan (21)
and
h = (200* h)/(200+h) * tan(14)
we can now use these equations to find the value of h.
h = 200 * tan(21) = 200 * 0.38197 = 76.394
Therefore, the height of the lighthouse is 76.4 feet (approx).
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The same number goes into each box to make the two ratios below equivalent.
4 0
36
Which number goes into both boxes?
6
09
12
18
27
Answer:
12
Step-by-step explanation:
4 / 12 = 12 / 36 so answer : 12
That was just by looking.....here is mathematical way :
4/ x = x/36 cross multiply
144 = x^2
x = 12
can someone look at this please? it’s due in like five minutes
The inequality equations for the rides High-Bounce, Climb-A-Thon, and Twirl-O-Coaster are 55<h<7, h<60, and h>=58 respectively.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides.
Let the unknown height be h.
For the ride High-Bounce, the height requirement is between 55 and 72 inches tall.
This can be written in the inequality form as 55<h<72.
For the ride Climb-A-Thon, the height requirement is under 60 inches tall.
This can be written in the inequality form as h<60.
For the ride Twirl-O-Coaster, the height requirement is 58 inches minimum.
This can be written in the inequality form as h>=58.
The representations of these inequalities on number lines is given below.
Therefore, the inequalities are - 55<h<7, h<60, h>=58.
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Previous 5
2023 F
5
Graphing Polynomial Functions: Mastery Test
Select the correct answer.
Identify the end behavior and the zeros of function h.
h(z) = -³ 92² + 4x + 96
Based on these key features, which statement is true about the graph representing function h?
The graph is positive on the intervals (-8, -4) and (3, 0o).
The graph is negative on the intervals (-oo, -8) and (-4, 3).
O C. The graph is positive on the intervals (-00, -8) and (-4, 3).
OD. The graph is negative on the intervals (-3, 4) and (8,00).
OA.
OB.
Reset
Next
According to the end behavior of the function h(z) = 5x³-9x²+4x+96, the graph is positive on the intervals (-∞, -8) and (-4, 3).
What is a polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
The given polynomial function is -
h(z) = 5x³-9x²+4x+96
The end behavior of a function f(x) describes the behavior of the function as x approaches +∞, and as x approaches -∞.
Domain of function h(z) = -∞<x<∞
The end behavior of the function h(z) is -
lim x→∞, (5x³-9x²+4x+96) = ∞
as x→∞, h(z)→∞
lim x→-∞, (5x³-9x²+4x+96) = -∞
as x→-∞, h(z)→-∞
Therefore, the graph is positive on the intervals (-∞, -8) and (-4, 3).
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Equal letters represent equal digits, and different letters represent different digits, Find the 5-digit number ABCDE
Observing the given question, This is the problem of cryptarithmetic , Using the rules based on cryptarithmetics, The answer is 10890.
What do you mean by cryptarithmetic problem?Mathematical conundrums called cryptarithmetic problems use letters from the alphabet in place of the digits. Use the trial-and-error procedure while keeping in mind the aforementioned considerations to solve cryptarithmetic problems by replacing values for the letters. Depending on whether we have a carry from A+A or not, A can now either be 2 or 3. However, since E=2, A must be 3, and there is a carry as a result.
Why is cryptarithm important?Cryptarithm, a type of mathematical game where the object is to solve an arithmetic puzzle in which the numerical digits have been replaced with letters. Cryptarithm, a type of mathematical game where the object is to solve an arithmetic puzzle in which the numerical digits have been replaced with letters.
Applying cryptarithmetic rules,
First alphabets can't be zero and same digit can't be used for different alphabets.
we get, CBDE + ABAE = AEDCE as 9480+1410 = 10890
AEDCE = 10890.
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25. What must be the value of y below so that the line passing through the points (4,4) and (-3, y) has a slope of -2 ?
A. 18
B. 10
C. 2
D. -6
Answer:
A. 18
Step-by-step explanation:
............... .....k
Which is the graph of y = 3^√x+1-2?
The graph of the function y = ∛(x +1 ) - 2 is represented by the graph represented by option 1.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
The graph of the function y = ∛(x +1 ) - 2 is attached with the answer below,
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Pls, answer the question below.
Answer:
-6 , 19 , 29
Step-by-step explanation:
range = output which is required
domain = input which are given -2,3,5
simply plot the value domain one by one in given equation
Solve for mzA:
D
M/A=
C
101
B
The value of ∠A is 101°.
What is parallelogram?A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.
Given a quadrilateral,
whose opposite sides are parallel, the figure is parallelogram,
property of a parallelogram says
ABCD is a parallelogram, where AB || CD and AD || BC.
Also, AB = CD and AD = BC
so ∠A = ∠C & ∠B = ∠D
given ∠C = 101°
so ∠A = ∠C = 101°
Hence the value of ∠A is 101°.
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Loren and Julie have different part time jobs after school. They are both paid at a constant rate of dollars per he
The table below show Loren and Julie's total income (amount earned) for working a given amount of time.
Loren
Hours 2 4 6 8 10 12 14 16 18
Dollars 18 36 54 72 90 108 ? ? 162
Julie
Hours 3 6 9 12 15 18 21 24 27
Dollars 36 ? 108 144 180 216 ? 288 324
How much money would Julie eam for working 16 hours?
Since Julie earns a constant rate of $12 per hour, for working 16 hours based on mathematical operations, she will earn $192.
What are mathematical operations?The basic mathematical operations involve addition, subtraction, division, and multiplication.
These operations combine parts of the mathematical operations with their assigned operands and the equation symbol (=) to solve mathematical problems.
In this situation, we employ division and multiplication operations to solve the requirement.
Loren and Julie's Total Income Table
LorenHours 2 4 6 8 10 12 14 16 18
Dollars 18 36 54 72 90 108 ? ? 162
Loren's Constant Rate of Pay (Hourly Rate) = $9 ($162/18)
JulieHours 3 6 9 12 15 18 21 24 27
Dollars 36 ? 108 144 180 216 ? 288 324
Julie's Constant Rate of Pay (Hourly Rate) = $12 ($324/27)
Total hours worked = 16
Total earnings = $192 ($12 x 16)
Thus, when Julie works 16 hours, she earns $192.
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3. Which of the following expressions is best represented by the model below? 1000 1000 A. 3x1 10 B. 3x-2 0009 X -1 C. 3x6 D. 3x 8
Answer:
A I THINK
Step-by-step explanation:
It takes 4 oz. of cherry syrup, 4 oz. of grenadine, and 1
quart of white soda to make a batch of Shirley Temples.
To make them for a party, how much white soda would
you need to buy if you had a quart of cherry syrup and a
quart of grenadine?
Answer:
8 quarts of white soda
Create pattern with the rule n x 2
Step-by-step explanation:
n×2=?
The n means 1 then. 1×2 series
1 × 2 = 2
It costs $2.25 to rent bowling shoes. Each game costs $2.50. You have $12.25 in your pocket.
Write and solve an equation to find how many x games you can bowl.
Answer:
You can bowl up to 4 games.
Step-by-step explanation:
2.25 + 2.50x ≤ 12.25
Let x = the number of games you bowl
2.25 + 2.50x ≤ 12.25 Subtract 2.25 from both sides
2.25 - 2.25 + 2.50x ≤ 12.25 - 2.25
2.50x ≤ 10 Divide both sides by 2.50
[tex]\frac{2.50x}{2.50}[/tex] ≤ [tex]\frac{10}{2.50}[/tex]
x ≤ 4
How to solve these problems?
The problems for production staff are solved as below.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
1. Knit
Number produced by 1 worker in a day = 50 pairs
Annual production goal = 780,000 pairs
Daily production goal = 780,000 / 260 = 3000 pairs
Production staff needed = 3000 / 50 = 60 workers
2. Tube
Number produced by 1 worker in a day = 40 pairs
Annual production goal = 946,400 pairs
Daily production goal = 946,400 / 260 = 3640 pairs
Production staff needed = 3640 / 40 = 91 workers
3. Athletic
Number produced by 1 worker in a day = 60 pairs
Annual production goal = 1,138,800 pairs
Daily production goal = 1,138,800 / 260 = 4380 pairs
Production staff needed = 4380 / 60 = 73 workers
4. Booties
Number produced by 1 worker in a day = 24 pairs
Annual production goal = 343,200 pairs
Daily production goal = 343,200 / 260 = 1320 pairs
Production staff needed = 1320 / 24 = 55 workers
5. Children's
Number produced by 1 worker in a day = 84 pairs
Annual production goal = 518,000 pairs
Daily production goal = 518000 / 260 = 1992.3 pairs
Production staff needed = 1992.3 / 84 = 23.7 workers
Hence the production staff needed has been solved.
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The bearing of P from Q is 040°.
The bearing of R from Q is 124°.
QR = QP.
Work out the bearing of R from P.
The bearing of R from P is 172°.
What are bearing(angles)?The horizontal angle between an object's direction and either north or another object is known as a bearing or azimuth in navigation. You can specify the angle value in a number of different angular units, including degrees, mils, and grad.
The angle between the magnetic north and the absolute bearing
The angle between the craft's forward motion and the relative bearing.
Given The bearing of P from Q is 040°.
The bearing of R from Q is 124°.
QR = QP.
Bearing angles are 180 degrees different than forward-bearing angles. This difficulty can be resolved by combining these relations with the standard angle sum relation for triangles.
Angle PQR will be the difference in the bearings from Q to P and Q to R:
∠PQR = 124° -40° = 84°
Triangle PQR is isosceles, so the base angle at P will be ...
∠QPR = (180° - 84°)/2 = 48°
The bearing from P to R will be 48° less than the bearing from P to Q. The bearing from P to Q is 180° more than the bearing from Q to P.
PR bearing = PQ bearing - ∠QPR
= PQ bearing - 48°
= (40° +180°) - 48° = 172°
Hence, The bearing of R from P is 172°.
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if 1,100 completely satisfied 740 somewhat satisfied 160 not satisfied what percent of the people surveyed were completely satisfied with the car?
The answer would be 55% because if you add 1,100 740 and 160 you get 2000 which means that 2000 people were surveyed then you'll do 1,100 by 200 and get 55 and that's your percent.
The percentage of the people surveyed who were completely satisfied with the car was 55 %.
How to find the percentage ?To find the percentage of people surveyed who were completely satisfied with the car, you first need to find the number of people who were survyed. This can be found by adding up all the number of people who participated in the survey :
= 1, 100 + 740 + 160
= 2, 000 people
The percentage of the people surveyed who were completely satisfied with the car is therefore:
= People completely satisfied / Number of people who participated x 100 %
= 1, 100 / 2, 000 x 100 %
= 55 %
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You have 99 cats and 77 dogs and 10998 horses what is the ratio of dogs to cats?
The ratio of dogs to cats is 7 to 9
How to determine the ratio of dogs to cats?From the question, we have the following parameters that can be used in our computation:
You have 99 cats and 77 dogs and 10998 horses
The ratio is represented as
Ratio = Dogs : Cats
Substitute the known values in the above equation, so, we have the following representation
Dogs : Cats = 77 : 99
Divide by 11
Dogs : Cats = 7 : 9
Hence, the ratio is 7 to 9
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A new manufacturing process requires 45 minutes to produce a piece of furniture. If the old process took 1 hour and 20 minutes what is the percent of change in production time and is it a percent increase or a percent decrease? Round your answer to the nearest hundredth.
There is a percent decrease of about 43.75%
What is Percentage?Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of whole is always taken as 100. They are used like fractions and decimals i.e ways to describe parts of a whole. While using percentages, the whole is considered to be made up of a hundred equal parts. The symbol % is used to show that a number is a percentage
New Process = 45 mins
Old Process = 1 hour and 20 minutes (80mins)
Increase/Decrease = Old Process - New Process
Increase/Decrease = 80 - 45
Increase/Decrease = 35
Therefore there is reduction in the manufacturing process;
% decrease = (35/80) x 100
% decrease = 43.75%
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what is the slope of line that passes through points (-2,7) and (-3,3)
Considering the expression of a line, the slope of line that passes through points (-2,7) and (-3,3) is 4.
What is a linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are the variables.m is the slope.b is the ordinate to the origin and represents the y-intercept of the line.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m can be calculated as:
m= (y₂ - y₁)÷ (x₂ - x₁)
Slope in this caseIn this case, being (x₁, y₁)= (-2, 7) and (x₂, y₂)= (-3, 3), the slope can be calculated as:
m= (3 -7)÷ (-3 -(-2))
m= (3 -7)÷ (-3 +2)
m= (-4)÷ (-1)
m= 4
Finally, the slope is 4.
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Jayden has $7.69. His coach will give him $3.21 every mile he runs If he run 18 miles how much will he have
ASAP!!! HURRY!!
Answer:
Jayden will earn $3.21 x 18 = $<<3.21*18=57.78>>57.78 from running 18 miles.
So he will have $7.69 + $57.78 = $<<7.69+57.78=65.47>>65.47 in total.
Step-by-step explanation:
help please I need it
Answer:
x =5 units
Mark me as a brainiest
In regression analysis, the error term e is a random variable with a mean or expected value of
1
x
0
u
You are given the following information about y and x.
Explanatory Variable Response Variable
3 5
1 3
4 4
3 6
5 8
a) The least squares estimate of the slope or b₁ equals
b) The least squares estimate of the intercept or b₀ equal
c) The point estimate of y when x=2 is
a) The least squares estimate of the slope (b₁) can be calculated using the formula:
b₁ = (n∑(xy) - (∑x)(∑y)) / (n∑(x^2) - (∑x)^2)
Where n is the number of observations, x and y are the explanatory and response variables, respectively.
b₁ = (5*(35+13+44+36+58) - (3+1+4+3+5)(5+3+4+6+8)) / (5*(3^2+1^2+4^2+3^2+5^2) - (3+1+4+3+5)^2) = 0.8
b) The least squares estimate of the intercept (b₀) can be calculated using the formula:
b₀ = (∑y - b₁*(∑x))/n
b₀ = (5+3+4+6+8-0.8*(3+1+4+3+5))/5 = 3.4
c) The point estimate of y when x=2 can be calculated using the equation of the line:
y = b₀ + b₁x
y = 3.4 + 0.82 = 4.8
So the point estimate of y when x=2 is 4.8
What are random variable?In probability and statistics, a random variable is a variable whose possible values are numerical outcomes of a random event. It is a function that maps outcomes of a random experiment to a real number. It can be discrete, meaning it can take on only a countable number of values, or it can be continuous, meaning it can take on any value within a given range. The probability distribution of a random variable describes the likelihood of different outcomes occurring. It can be used to calculate expected values, variances, and other measures of statistical dispersion.
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Need help asap! Im confused, i dont get the question.
Answer:
6
Step-by-step explanation:
See the screenshot below.
how to solve the correlation coefficient are between the age of a car X and the car is mileage why is 0.639 what percent of the variation in mileage cannot be explained by differences in the cars ages
The percent of the variation in mileage that cannot be explained by differences in the cars ages is 36.1%.
What is correlation coefficient?A statistical indicator of the strength of a linear relationship between two variables is the correlation coefficient. A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively correlated, the value either rises or falls together.
The correlation r between the age of a car x , and the cars mileage, y is 0.639. This means that 63.9 % of the variation in mileage can be explained by the differences in the cars ages, 100 – 63.9 = 36.1% of the variation cannot be explained.
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which point represents 2 1/3 -5/6 and -3 1/2 on the number line
Answer:
Provided at image
Step-by-step explanation:
Green dot = -3.5
Red dot = -5/6
Orange dot = 2.3
Since there are 5 lines between every 1 number, you can divide 100/6 to see the distance between the lines (16.6666) and plug in the points.
