The solution by using the quadratic formula is,
x = 4 + 2√6 i / 4 and x = 4 - 2√6 i / 4
What is Quadratic formula?
To solve a quadratic equation ax²+ bx + c = 0 , we use the quadratic formula,
x = - b ± √b² - 4ac / 2a
The given expression is;
- 2x² + 4x = 5
Now, The given equation is solve by using Quadratic formula as;
- 2x² + 4x = 5
Move terms to the left side
- 2x² + 4x - 5 = 0
- ( 2x² - 4x + 5 ) = 0
2x² - 4x + 5 = 0
Compare with quadratic equation ax²+ bx + c = 0 we get;
a = 2, b = -4, c = 5
Since, Quadratic formula is,
x = - b ± √b² - 4ac / 2a
Hence, Substituting all the values of a, b and c in quadratic formula we get;
x = - (-4) ± √(-4)² - 4*2*5 / 2*2
x = 4 ± √16 - 40 / 4
x = 4 ± √-24 / 4
x = 4 ± 2√-6 / 4 ( Since, i = √-1 )
x = 4 + 2√6 i / 4 and x = 4 - 2√6 i / 4
So, The solution by using the quadratic formula is,
x = 4 + 2√6 i / 4 and x = 4 - 2√6 i / 4
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Aleka and Helene both opened savings accounts that earn 2.5% interest a year. Aleka puts $2,500 into her account. Helene put $1,500 into her account and also saves $200 cash a year.
x = number of years
Aleka: f(x) = 2500(1.025)x
Helene: g(x) = 1500(1.025)x + 200x
Which function represents the difference, h(x) = f(x) – g(x), between the value of Aleka’s and Helene’s total savings after x years?
h(x) = –1000(1.025)x + 200x
h(x) = 1000(1.025)x + 200x
h(x) = 1000(1.025)x – 200x
h(x) = 4000(1.025)x + 200x
The function that represents the difference, h(x) = f(x) – g(x), between the value of Aleka’s and Helene’s total savings after x years is C. h(x) = 1000(1.025)x – 200x.
How to illustrate the function?It should be noted that Aleka and Helene both opened savings accounts that earn 2.5% interest a year. Aleka puts $2,500 into her account.
The function for Aleka will be:
= 2500 (1.025)^x
The function for Helene will be:
= 1500(1./25)^x + 200x
Therefore, the difference of the function will be 1000(1.025)x – 200x.
In conclusion, the correct option is C.
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alex invested $50,000 into two accounts. one account paid 2% interest and the other paid 7% interest. he earned 6.2% interest on the total investment. how much did he put into each account
The amount he put into the first account at 2% interest will be $8,000 and into the second account at 7% interest will be $42,000.
Given that,
Amount invested by Alex = $50,000,
Total interest earned = 6.2%,
Now,
Let,
Amount invested at 2% = x,
So,
Amount invested at 7% = (50,000 - x),
So,
According to the question,
7%(50000 - x) + 2%(x) = 6.2% * 50,000
we get,
0.07(50000 - x) + 0.02(x) = 0.062 * 50,000
3500 - 0.07x + 0.02x = 3100
3500 - 0.05x = 3100
We get,
0.05x = 3500 - 3100
0.05x = 400
x = 8000,
So,
Amount invested at 2% = $8000,
So,
Amount invested at 7% = (50,000 - 8000) = $42,000,
Hence we can say that the amount he put into the first account at 2% interest will be $8,000 and into the second account at 7% interest will be $42,000.
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I need help with this
Simplification - The process of making something less complicated and therefore easier to do or understand, or the thing that results from this process .
What is the simplification rule?
The general rule to simplify expressions is PEMDAS - stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Replace Question mark .
1.) 1/2 = 1× x / 2 ×10
1/2 = x / 20
x = 20 / 2
x = 10.
2.) 3/4 = 3 x 5 / 4× x
3/4 = 15 / 4x
12x = 60
x = 60 / 12
x = 5
3.) 7/8 = 7× 3 / x × 3
7/8 = 21 / 3x
21x = 21 × 8
x = 8
4.) 2/3 = x×4 / 3 × 4
2/3 = 4x / 12
12x = 24
x =2 .
5.) 6/12 = (6/6) / (12/x)
1/2 = 1 / (12/x)
1/2 = x/12
2x = 12
x = 6.
6.) 3 / 15 = (3 /x) /(15 / 3)
3/15 = (3/x) / 5
3/15 = 3/5x
15x = 15× 3
x =3.
7.) 175/250 = (x/25) / (250/25)
taking LHS
175/250 = 7/ 10
Solve RHS
(x/25) / (250/25)
(x/25) / (10) = x/250
x/250 = 7/10
x = 175.
8.) 28 /56 = (28/28) / (x/28)
28/56 = 1/ (x/28)
28 / 56 = 28 /x
x =56 .
9.) 14/16 =(14/x) / (x/2)
14/16 = 14/x × 2/x
14 /16 = 28 /x²
1 /16 = 2/ x²
x² =32 .
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A'BC' is a dilation of ABC.
If the center of dilation was (0,0), what was the scale factor used to create the dilation?
I’m literally sobbing- I have no clue what this question means
Answer:4
Step-by-step explanation:
dilation
In a plane, a transformation in which each point on the image lies on the same line as the corresponding point on the preimage and a fixed point called the center of dilation; the ratio between the distance from the center of dilation to a point on the image and the distance from the center of dilation to the corresponding point on the preimage remains constant.
PLS HELP WILL GIVE 30 POINTS
Write a quadratic function in standard form whose graph has the given characteristics.
passes through (- 8,0), (- 6, -16), and (2,0).
Answer: [tex]y=x^2 +6x-16[/tex]
Step-by-step explanation:
From the roots, the equation in factored form is [tex]y=a(x-2)(x+8)[/tex]. Substituting in the coordinates (-6, -16),
[tex]-16=a(-6-2)(-6+8)\\\\-16=-16a\\\\a=1[/tex]
So, the equation is [tex]y=(x-2)(x+8)[/tex], which expands to [tex]x^2 +6x-16[/tex].
Which of these has the same value as 45/8? Which of these has the same value as 45/8?
6 5/8
8 5/8
5 5/8
7 5/8
Answer: 5 5/8
Step-by-step explanation:
6 5/8= 6*8= 48 48+5=53 53/8
8 5/8= 8*8=64 64+5=69 69/8
5 5/8= 5*8=40 40+5=45 45/8
7 5/8= 7*8=56 56+5=61 61/8
Which of the following mass values is equal to 40,000 grams?
A. 40 kilograms
OB. 40 milligrams
OC. 4 kilograms
OD. 4,000 megagrams
Answer:
A
Step-by-step explanation:
1 kilogram is equal to 1000 grams, so 40000 grams is 40 kilos.
Sally had 256 dollars to spend on 7 books. After
buying them she had 11 dollars. How much did each book cost ?
in a class 60% of the total number of student are boys and there are 14 girls how many students are there in class
Answer:
14 girls divided by their percentage 0.4 the result will be
35 students
Select the correct answer from each drop-down menu. How many solutions does each polynomial have? Equation Number of Solutions y = - 6 x − 9 y = 2 x 5 − x 4 + 2 x 3 − 6 x 2 + 2 x + 4 y = - 4 x 3 − 10 x 2 + 7 x + 5
Answer:
1
5
3
in order
Step-by-step explanation:
First, note that the degree of a polynomial is the value of the highest exponent in the polynomial
There will be as many solutions as there are degrees
1. - 6x − 9y = 2 has degree 1 since x == x¹ so 1 solution
2. [tex]2x^5-x^4+2x^3-6x^2+2x\:+\:4=0[/tex] has degree 5 so 5 solutions
3. [tex]-4x^3 - 10x^2+7x+5[/tex] has degree 3 so 3 solutions
Two whole numbers have their first common multiple as 6,what is their 4th and 8th common multiple
Answer:
24, 48
Step-by-step explanation:
The 4th common multiple is 6(4)=24.
The 8th common multiple is 6(8)=48.
I WILL GIVE YOU 80 POINTS BUT I NEED IT TODAY ONLY NEED TO ANSWER SIX AND SEVEN
The volume of a right rectangular prism is found by multiplying the length of the base by the width of the base by the height of the prism. A right rectangular prism has a volume of 30 cubic inches. If the height of the prism is 6i inches, what is the area of the base of the prism?
If the height and volume of the prism are 6 inches and 30 cubic inches. Then the base area of the prism is 5 square inches.
What is a rectangular prism?
A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.
The volume of a right rectangular prism is found by multiplying the length of the base by the width of the base by the height of the prism.
A right rectangular prism has a volume of 30 cubic inches.
If the height of the prism is 6 inches. Then the base area of the prism will be
The volume is given as
Volume = Base area × Height
We know
Volume = 30
Height = 6
Then the base area will be
30 = Area × 6
Area = 5
An equation of a line through (-2, 8) which is parallel to the line y = 4 x + 4 has slope:
The slope of the line that is parallel to the given equation is 4
Slope of a lineFrom the question, we are to determine the slope of the equation that is parallel to the given line
The given line is
y = 4x + 4
First, we will determine the slope of the given line
By comparing with the slope-intercept form of the equation of a straight line,
y = mx + b
Where m is the slope
and b is the y-intercept
By comparison,
m = 4
Thus,
The slope of the line is 4
NOTE: If two lines are parallel, their slopes are equal
Hence, the slope is 4
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Which statements about the system are true? Select two options.y= 1/3x-4 3y-x= -7 The system has one solution. U The system consists of parallel lines, Both lines have the same slope. Both lines have the same y-intercept. The equations represent the same line.
Answer:
The system consists
Step-by-step explanation:
Help me solve this I’ll give u vbucks
Answer:
49
Step-by-step explanation:
You first simplify (1/7)^2 which is 7^2 then you get 49.
Answer:
49
Step-by-step explanation:
did it
Question 15 The length is : A rectangular room is 1.9 times as long as it is wide, and its perimeter is 29 meters. Find the dimension of the room. > meters. Submit Question 0/1 pt100 Deta Question Help: Message instructor meters and the width is
The length of rectangular room is 9.5 meter.
The width of rectangular room is 5 meter.
What is Perimeter of rectangular?
The perimeter of a rectangle is two time the sum of length and width of rectangle.
Given that;
The perimeter of rectangular room = 29 meter
The length of rectangular room is 1.9 times as long as it is wide.
Now, Let the width of rectangular room = x
Then Length of rectangular room = 1.9x
Since, Perimeter of rectangular room = 2 ( length + width)
⇒ 29 = 2 (1.9x + x)
⇒ 29 = 2 * 2.9x
⇒ x = 5
Hence, The length of rectangular room = 1.9x
= 1.9 * 5
= 9.5 meter
The width of rectangular room is = x
= 5 meter.
So, The length of rectangular room is 9.5 meter.
The width of rectangular room is 5 meter.
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Given h(x) = 5x-1, find h(-4)
Step-by-step explanation:
h(-4) = 5(-4) - 1
= -20 - 1
= -21.
Answer:
-21 is correct
Step-by-step explanation:
Harriet wants to buy items worth $248.50. She is using a store coupon for 25 percent off her purchases. She has to pay 5 percent sales tax. Calculate the total cost of the items
Answer:$195.70
Step-by-step explanation:
Starting price is : $248.50
Price with 25% off :
$248.50 x ( 1 - 0.25 ) = $248.50 x 0.75 = $186.375
After that she has to pay 5 % sales tax:
$186.375 x 1.05 = $195.70
Answer:
The total cost of the items is $195.70.
Suppose that you drink a 20 oz. bottle of Dr. Pepper with both lunch and dinner every day. If so, you’re adding 250 calories to each meal.
A. How many extra calories are you consuming per year compared to just drinking water, which has no calories?
B. A general rule of thumb is that an average-sized person expends about 100 calories for each mile walked. How many miles would you have to walk over the course of a year to burn off all the calories you’re getting from your daily Dr. Pepper?
The extra calories that you are consuming per year is 182,500 calories.
The number of miles that you should walk to burn the extra calories is 1,825 miles.
How many extra calories are you consuming?You are consuming 20 oz of Dr. Pepper each meal. You take Dr. Pepper twice in a day. To determine the total extra calories that is being consumed, multiply the calories consumed per month by the number of times in a day you consume Dr. Pepper and by the number of days in a week.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers. The sign used to represent multiplication is ×.
Extra calories consumed in a year = calories per meal x 2 x number of days in a year
250 x 2 x 365 = 182,500 calories
In order to determine the number of miles you have to walk to lose the extra calories, divide the extra calories by the calories lost per mile
Number of miles to walk = 182,500 / 100 = 1825 miles
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1. There are 15 apples in a basket. 7 of these are green. The rest of them are red.
a. What is the ratio of green apples to red apples?
Answer:
there are 7 green apples to 8 red apples, or it can be said as 7/8.
Step-by-step explanation:
15 - 7 = 8. This leaves 8 apples left, making these ones red.
Which of the graphs below shows correctly plotted points for the following line?
y=3−2x
Select the correct answer below:
Four plotted points on a coordinate plane.
A coordinate plane has a horizontal x-axis and a vertical y-axis. Four labeled points are plotted at left-parenthesis negative 1 comma 1 right-parenthesis, left-parenthesis 0 comma 3 right-parenthesis, left-parenthesis 1 comma 5 right-parenthesis, and left-parenthesis 2 comma 7 right-parenthesis.
Four plotted points on a coordinate plane.
A coordinate plane has a horizontal x-axis and a vertical y-axis. Four points are plotted at left-parenthesis negative 1 comma 5 right-parenthesis, left-parenthesis 0 comma 3 right-parenthesis, left-parenthesis 1 comma 1 right-parenthesis, and left-parenthesis 2 comma negative 1 right-parenthesis.
4 points are plotted
A coordinate plane has a horizontal x-axis and a vertical y-axis. Four points are labeled at left-parenthesis negative 1 comma negative 5 right-parenthesis, left-parenthesis 0 comma negative 2 right-parenthesis, left-parenthesis 1 comma 1 right-parenthesis, and left-parenthesis 2 comma 4 right-parenthesis.
Four plotted points on a coordinate plane.
A coordinate plane has a horizontal x-axis and a vertical y-axis. Four points are plotted at left-parenthesis negative 1 comma 2 right-parenthesis, left-parenthesis 0 comma 3 right-parenthesis, left-parenthesis 1 comma 4 right-parenthesis, and left-parenthesis 2 comma 5 right-parenthesis.
Four plotted points on a coordinate plane.
The graph that correctly plots the line y=3−2x is option B which is:
Four plotted points on a coordinate plane.
A coordinate plane has a horizontal x-axis and a vertical y-axis. Four points are plotted at left-parenthesis negative 1 comma 5 right-parenthesis, left-parenthesis 0 comma 3 right-parenthesis, left-parenthesis 1 comma 1 right-parenthesis, and left-parenthesis 2 comma negative 1 right-parenthesis.
How to find the plotted pointswe use the given equation to get the points by substituting the values of x given, to get the values of y as follows
y = 3 - 2x
for x = -1
y = 3 - 2 ( -1 )
y = 3 - ( -2 )
y = 3 + 2
y = 5
( -1, 5 )
y = 3 - 2x
for x = 0
y = 3 - 2 (0 )
y = 3 - 0
y = 3
( 0, 3 )
y = 3 - 2x
for x = 1
y = 3 - 2 ( 1 )
y = 3 - ( 2 )
y = 3 - 2
y = 1
( 1, 1 )
y = 3 - 2x
for x = 2
y = 3 - 2 ( 2 )
y = 3 - ( 4 )
y = 3 - 4
y = -1
( 2, -1 )
( -1, 5 ), ( 0, 3 ), ( 1, 1 ), and ( 2, -1 ) These represents the points in the second option hence the correct answer.
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The shelf life of a battery produced by one major company is known to be normally distributed with a mean life of 3.5 years and a standard deviation of 0.75 years. What percent of batteries last between 1.25 and 5.75 years?
The percentage of batteries that last between 1.25 and 5.75 years will be 99.73%.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
One significant manufacturer's batteries are known to have a shelf life that is regularly distributed, with an average life of 3.5 years and a standard deviation of 0.75 years.
The value of the z-score will be
z = (1.25 - 3.5) / 0.75, (5.75 - 3.5) / 0.75
z = -3, 3
The percentage of batteries that last between 1.25 and 5.75 years will be
P(1.25 < x < 5.75) = P(- 3 < z < 3) x 100
P(1.25 < x < 5.75) = 0.9973 x 100
P(1.25 < x < 5.75) = 99.73%
The percentage of batteries that last between 1.25 and 5.75 years will be 99.73%.
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A square on a coordinate plane has one vortex at (-0.5, -2) and a perimeter of 10 units. If all the vertices are located in quadrant III, what are the coordinates of the other three vertices
Answer:
Step-by-step explanation:
each side of square=10/4=2.5
because all the vertices are in quarter |||
so all the coordinates are negative.
x coordinate=-0.5-2.5=-3
y coordinate=-2-2.5=-4.5
all the coordinates are (-3,-2) ,(-0.5,-2)
and (-3,-4.5),(-0.5,-4.5)
a +x = b
solve for x?
What is your name? Answer this question and I will vote you as brainliest
Answer:
Jade Howey
Step-by-step explanation:
Answer:
Maria
Step-by-step explanation:
yodjdjdjdkdkdjekrnrjr
At the time of her grandson's birth, a grandmother deposits $9000 in an account that pays 8% compounded monthly What will be the value of the account at the child's twenty- first birthday, assuming that no other deposits or withdrawals are made during this period ?
The value of the account is $47226.73.
The compound interest formula is equal to
A = P( 1 + r/n )^{nt}
where A is the Final Investment Value, P is the Principal amount of money that is to be invested, r is the rate of interest, t is the Number of Time Periods, and n is the number of times interest is compounded per year.
Now, we have:
t = 21 years
Principal amount, P = $9000
Rate, r = 8% = 0.08 and
n = 12 as a year has 12 months.
Substituting these values in the formula,
[tex]A = P( 1 + \frac{r}{n} )^{nt}[/tex]
A = 9000 × ( 1 + 0.08/12)²⁵²
A = 9000 × ( 1 + 0.0066)²⁵²
A = 9000 × ( 1.0066)²⁵²
A = 9000 × 5.247
A = 47226.73
The value of the account will be $47226.73.
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A number added to -19 is -21
x= -19 +21
-19-21 = x
-19 + x = -21
x -21 = -19
Answer:
(c) -19 + x = -21
Step-by-step explanation:
You want the mathematical expression equivalent to the English sentence "a number added to -19 is -21."
ExpressionsAddition is written using the math plus symbol (+).
The English word "is" usually signifies sameness or equality, expressed using the math equal sign (=).
The variable x is often used to represent "a number."
When a number is added to -19, we start with -19, then, using the plus symbol, we add x:
"a number added to -19" ⇒ -19 + x
"is" ⇒ =
"-21" ⇒ -21
So, the translated description is ...
-19 + x = -21
Find the value of x in the triangle shown below
The value of x from the triangle is 12
How to determine the valueGiven the sides as;
Hypotenuse = 15opposite = xAdjacent = 9Using the Pythagorean theorem
Hypotenuse square = opposite square + adjacent square
Substitute the value, we have;
15² = x ² + 9²²
Find the squares
225= x² + 81
collect like terms
225 - 81 = x²
144 = x²
Take the square root of both sides
x √144
x = 12
Thus, the value of x from the triangle is 12
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A STORY OF UNITS
Lesson 16 Homework Helper 4.1
Name
Lesson 16 Homework 4.1
•Said
Sanchez
1. Zachary's final project for a college course took a semester to write and had 95,234 words. Zachary wrote
35,295 words the first month and 19,240 words the second month.
Date
a. Round each value to the nearest ten thousand to estimate how many words Zachary wrote during the
remaining part of the semester.
In the remaining part of the semester, Zachery wrote an average of 10,000 words per month to complete his final project for the course.
We are given that Zachery has to write a total of 95,234 words.
Total words to be written = 95,234 words.
Words already written in the first month = 35,295 words.
Words already written in the second month = 19,240 words.
Words written in total = 35,295 words + 19,240 words.
= 54,535 words
Words left for writing = 95,234 words - 54,535 words
= 39,699 words
months left = 4
Average Words written in remaining month = 39,699 words / 4
= 9924.75 words.
= 10,000 words.
Therefore, in the remaining part of the semester, Zachery wrote an average of 10,000 words per month to complete his final project for the course.
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