Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answers
Answer:
A) -2 - i√3 , -2 + i√3
Step-by-step explanation:
Solve using quadratic formula
x² + 4x + 7 = 0
The Almighty Formula
= -b ± √b² - 4ac/2a
Where ax + bx² + c = 0
From the above question
a = 1, b = 4, c= 7
Hence,
-4 ± √4² - 4 × 1 × 7/2 × 1
-4 ± √16 - 28/2
=( -4 ± √-12)/2
Since
b² - 4ac < 0
We have two complex roots
Simplifying
( -4 ± √-12)/2
= -4/2 ± √-12/2
= -2 ± 2√3i/2
= -2 ± √3i
Therefore,
-2 - √3i , -2 + √3i
or
-2 - i√3 , -2 + i√3
Option A , is the correct answer
Related Questions
u get brainliest if you anser first and is right if i get this wrong i fail pls help me
for 50 points
Answers
Using the five digits 7, 7, 8, 8, and 8 once each, how many positive five-digit integers can be formed?
Answers
Answer:
There are 5 choices for the first digit, 5 choices for the second digit, 4 choices for the third digit, 3 choices for the fourth digit, and 2 choices for the fifth digit.
A triangle has an angle that measures 115°. The other two angles are in a ratio of 6:7. What are the measures of those two angles?
Answers
Answer:
30° ; 35°
Step-by-step explanation:
Recall:
Sum of angles in a triangle = 180°
One of the 3 angles = 115
The sum of the other 2 Angles will be :
(180 - 115) = 65°
The other two angles are in the ratio 6:7
Hence,
Each of the two angles can be calculated thus :
Angle 2 :
Sum of ratio = 6 + 7 = 13
(6 / 13) * 65 = 30°
Second angle :
(7 / 13) * 65 = 35°
A marketing research company desires to know the mean consumption of meat per week among males over age 50. They believe that the meat consumption has a
mean of 3.5 pounds, and want to construct a 95 % confidence interval with a maximum error of 0.08 pounds. Assuming a standard deviation of 0.6 pounds, what is
the minimum number of males over age 50 they must include in their sample? Round your answer up to the next integer.
Answers
Answer:
we get a required sample size of 122.
Step-by-step explanation:
We can use the following formula to calculate the required sample size:
n = (Z * sigma / e)^2
where:
n is the required sample size
Z is the z-score corresponding to the desired confidence level (e.g. for a 95% confidence level, Z = 1.96)
sigma is the standard deviation of the population
e is the maximum error allowed
Plugging in the given values, we get:
n = (1.96 * 0.6 / 0.08)^2 = 121.6
Rounding up to the next integer, we get a required sample size of 122.
What does a 30 60 90 triangle look like?
Answers
The 30-60-90 triangle is shaped like half of an equilateral triangle.
A special right triangle with angles 30°, 60°, and 90° is called a 30-60-90 triangle. Since 30° is the smallest angle in the triangle, the side opposite to the 30° angle is always the smallest.
The side opposite to the 60° angle is the longer leg, and finally, the side opposite to the 90° angle is the largest side of the right triangle, also known as the hypotenuse.
30°-60°-90° Triangle Rule:
In a 30-60-90 triangle, we can find the measure of any of the three sides by knowing the measure of at least one side in the triangle. This is known as the 30-60-90 triangle rule.
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What are the factors of 2x^2 7x 3?
Answers
The factors of 2[tex]x^{2}[/tex] + 7x + 3 are ( x + 3) and (2x + 1)
Now, According to the question:
The given function is :
f(x) = [tex]2x^2+7x+3[/tex]
To find the factors of [tex]2x^2+7x+3[/tex] we need to split the middle term, that is, 7x.
7x = 6x + x
Therefore, 2[tex]x^{2}[/tex] + 7x+ 3 can be written as 2[tex]x^{2}[/tex] + 6x + x + 3 .
On taking '2x' common from first two terms and +1 from next two terms we get
2x (x + 3) +1 (x + 3)
(x + 3) (2x + 1)
Thus, the factors of 2x2 + 7x + 3 are (x+3) and (2x+1)
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The complete question is this:
What are the factors of 2x^2+7x +3?
3. How many groups 1/2 of days are in 1 week?
groups
Answers
Given there are 7 days in a week, we can divide 7 by 1/2 to find that:
7 / 1/2 = 14
Hence, 14 groups of 1/2 days are in 1 week.
Please help! Thanks :DD
Answers
Answer:
A. 58 square cm
Step-by-step explanation:
From the composite figure,
A1 = [tex]\frac{1}{2}[/tex] x base x height
= [tex]\frac{1}{2}[/tex] x 2 x 3
= 3 [tex]cm^{2}[/tex]
A2 = length x width
= 8 x 2
= 16 [tex]cm^{2}[/tex]
A3 = [tex]\frac{1}{2}[/tex] (a + b) h + [tex]\frac{1}{2}[/tex] x base x height
= [tex]\frac{1}{2}[/tex] (10 + 12) 3 + [tex]\frac{1}{2}[/tex] x 2 x 3
= [tex]\frac{1}{2}[/tex] (22) 3 + 3
= 11 x 3 + 3
A3 = 33 + 3
= 36 [tex]cm^{2}[/tex]
Total area = A1 + A2 + A3
= 3 + 16 + 36
= 58 [tex]cm^{2}[/tex]
HELP
Ps; i am only writing like this becase i need people to see this
Answers
Thanks dude!
Step-by-step explanation:
Can i have brainly?
What’s the area of a square is all sides are 6 feet long?
Answers
Answer:
36 sq ft
Step-by-step explanation:
The area of a square is equal to the length of one side squared. Therefore, if all sides of a square are 6 feet long, the area of the square is 6 feet * 6 feet = 36 square feet.
Answer:
36
Step-by-step explanation:
you multiply just two of the sides hxw and you get your answer
resuelve la siguiente operacion +1 + (-1)=
Answers
Answer:
0
Step-by-step explanation:
+ 1 + (-1)
1 + (-1)
1 - 1
look at the screenshot, please. (no links)
Answers
Answer: 14
Step-by-step explanation: 18 x 14 = 252
Answer:
14
Step-by-step explanation:
recall that area of figure, A= length x. breadth
and A=252
and b=18
therefore, 252= 18b
l= 252/18
l= 14
therefore p= 14
How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16 cm, the iron being 2 cm thick throughout? If 1 cubic cm of iron weighs 15 g. find the weight of the open box in kg
Answers
The weight of the open box in kg is 28,800 cm3 x 15 g/cm3 = 432,000 g = 432 kg.
Hope this helps!
(b) If the radius of wheel is 7cm, how far it travels in three rotation
Answers
The wheel will travel 131.8cm in 3 rotations.
The radius of the wheel, r = 7cm
Number of rotations, n= 3
distance covered in 1 rotation= circumference of circle=2πr
distance covered in 3 rotation= 2πr x 3
where π=3.14(fixed)
=2 x 3.14 x 7 x 3
Distance=131.88cm
Therefore, the distance covered in 3 rotations is 131.88cm
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Answer:
132cm
Step-by-step explanation:
use formula 22/7 *diameter which is 7*2 getting the answer as 44.For three rotations multiply the answer by three
Sherane rolls a standard, six-sided number cube.
What is the probability of rolling a multiple of 3?
Answers
Step-by-step explanation:
3 and 6 are multiples of 3
6 sides of a dice
2/6= 33%
Bought a board game for $30. The board game is now worth $55. Calculate the percent change in the game's value.
Answers
PLEASE I NEED HELP ASAPPPP!!!!!
The scatter plot shows the number of pumpkins that have been picked on the farm during the month of October: A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Pumpkins and the x axis is labeled Days in October
Part A: Using computer software, a correlation coefficient of r = 0. 51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm. (5 points)
Answers
A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.
What is a Scatter Plot?A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.
Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.
Part A:
The correlation coefficient of r = 0.51 is valid based on the provided scatter plot.
Part B:
The amount of fertilizer applied in connection to the kilograms of pumpkins harvested on the farm can be a scenario where a causal relationship exists.
Hence, A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.
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What is the value of p so that the line passing through (6, 2) and (10, p) has a slope
of -2?
Answers
Answer:
P = -6
Step-by-step explanation:
y2-y1 / x2-x1 = slope formula
p-2/10-6 =
p-2 over 4
P would be -6 since -6-2 = -8, and -8/4 = -2
What are 3 horizontal lines?
Answers
The 3 horizontal line refers the equivalent relation.
The term horizontal line in math defined as a straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system.
Here have to find the meaning of 3 horizontal line.
As per the definition of horizontal line, the three horizontal line also known as triple line defines the equivalent relation of the term.
Here the equivalent that is not the same as 'equals'
Where the double bar is more common and generally implies equality on the other hand the triple bar or equal sign with three lines means congruent or, more generally, an arbitrary equivalence relation.
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A solution of 60 quarts of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar
Answers
On solving the provided question we can say that by equation 180 water must be added to make a solution that is 5% sugar
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here, the equation is -
1200=300+5x
900 = 5x
x=180
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Write the word sentence as an equation. Then solve the equation.
9 is the difference of a number n and 7.
An equation that represents this word sentence is
The solution is n =
Answers
Answer:
see below
Step-by-step explanation:
9 is the difference of a number n and 7.
Let's break this down.
"is" represents the equal sign.
"the difference" represents subtraction.
9 = n - 7
Now let's solve the equation.
9 = n - 7
Add 7 to both sides.
16 = n
Hope this helps!
EASY POINTS!! EASY POINTS!!
A factory ships sunglasses in boxes that each have the same number of sunglasses. The table shows the data for 4 shipments.
Which rate represents the relationship in the table?
A. 100 sunglasses per 4 boxes
B. 5 sunglasses per 125 boxes
C. 4 sunglasses per 100 boxes
D. 225 sunglasses per 8 boxes
NO LINKS OR FILES!!!
Answers
Answer:
A
Step-by-step explanation:
2 boxes has 50 glasses
times by 2 and its equal to A
Answer: A or B
Step-by-step explanation:
Over the closed interval [3,8] for which function can the extreme value theorem be applied?
Answers
Answer:
A
Step-by-step explanation:
The extreme value theorem can be applied on an interval if the function is continuous in the entire interval. Testing the continuity for each function, we get that the correct option is the third option.
Continuity:
A function f is continuous at an interval if all points in the interval are in the domain of the function, and, for each point of [tex]x^{\ast}[/tex], the limit exists and:
[tex]\lim_{x \rightarrow x^{\ast}} = f(x^{\ast})[/tex]
First function:
At [tex]x = 4[/tex], the denominator is 0, and so, the extreme value theorem cannot be applied.
Second function:
At [tex]x = 5[/tex], the denominator is 0, and so, the extreme value theorem cannot be applied.
Third function:
The only point there can be a discontinuity is at [tex]x = 4[/tex], where the definition of the function changes. First we have to find the lateral limits, and if they are equal, the limits exist:
To the left(-), it is less than 4, so we take the definition for x < 4.
To the right(+), it is more than 4, so we take the definition for x >= 4.
[tex]\lim_{x \rightarrow 4^{-}} h(x) = \lim_{x \rightarrow 4} \frac{9x}{10-x} = \frac{9*4}{10-4} = \frac{36}{6} = 6[/tex]
[tex]\lim_{x \rightarrow 4^{+}} h(x) = \lim_{x \rightarrow 4} x + 2 = 4 + 2 = 6[/tex]
The lateral limits are equal, so the limit exists, and it's value is 6.
The definition at [tex]x = 4[/tex] is [tex]h(x) = x + 2[/tex], so [tex]h(4) = 4 + 2 = 6[/tex].
Since [tex]\lim_{x \rightarrow 4} = h(4)[/tex], the function is continuous over the entire interval, and this is the correct answer.
Fourth function:
There can be a discontinuity at [tex]x = 5[/tex], so we test the limits:
[tex]\lim_{x \rightarrow 5^{-}} h(x) = \lim_{x \rightarrow 5} -x = -5[/tex]
[tex]\lim_{x \rightarrow 5^{+}} h(x) = \lim_{x \rightarrow 5} x^2 - 20 = 5^2 - 20 = 25 - 20 = 5[/tex]
Different limits, so the limit does not exist and the function is not continuous at [tex]x = 5[/tex], and the extreme value theorem cannot be applied.
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i need help with this question?
Answers
Answer:
4.5π[tex]cm^2[/tex] will be your answer!
Step-by-step explanation:
Oki... So the area of a circle is radius x radius x π
So.....
Lemme find what the radius's are
4.5 ÷ 2 = 2.25
2.25 - 1.5 = 0.75
2.25 x 2.25 x π = 5.0625π
0.75 x 0.75 x π = 0.5625π
And subtract.
5.0625π - 0.5625π = 4.5π
In the figure below ∠B=63∘. What is the measure of arc DB in degrees? (4 points) 27 126 54 63
Answers
Answer:
54
Step-by-step explanation:
63 x 2 = 126
180 - 126 = 54
In Ellen's math class, there were 2 boys to every 3 girls. Which of the following could be the ratio of girls to boys in the class? As a fraction
Answers
Answer:
A . 17/21
B . 14/21
C . 7/14
D. 11/17
Step-by-step explanation:
Answer:
Answer is B: 14 to 21
Step-by-step explanation:
The ratio "2 to 3" was multiplied by 7 to get this ratio. All the other following are incorrect.
The length of an object in feet is equal to 3 times it's length in yards. The length of the boat is 36 feet. Write and solve a multiplication equation to find the length of the boat in yards
Answers
In linear equation ,The length of waterslide is 12 yards.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Given that,
The length of an object object in feet is equal to 3 times it’s length in yards
The length of wall water side slide is 36 feet
Let "y" be the length of object in yards
From given,
Length in feet = 3 times length in yards
36 = 3 * y
3y = 36
y = 36/3
y = 12
Thus length of waterslide is 12 yards.
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the ratio of dogs to cats is 1 dog to 2 cats. which of the following is a way to write this ratio? please help me!!
Answers
a colon means "to" in probability math so 1:2 doubles as 1 to 2. this also applies for the third answer as it is 1 to 2. 1/2 is also another way to write 1 to 2 since it is showing the number of dogs on the top and cats on the bottom.
good luck in your class! have a good day :)
a) Write down the mathematical name of this shape.
what is the shape called
Answers
Answer:
What shape? i don't see no shape
Answer:
What shape? Can you add in a picture or something? That would be very helpful in trying to figure out what shape we're dealing with.
12 POINTS!!!
Write the equation of the exponential function (y=ab^x) through the point (2,36) and (5,972).
Answers
Answer:
Step-by-step explanation: