Answers
Answer:
D
Step-by-step explanation:
We will solve the equation by using quadratic formula.
x= (-b ± √(b^2-4ac))/2a
The standard form of quadratic equation is:
ax^2+bx+c=0
So by comparing with the standard form, we get:
a=1
b= -4
c=18
Putting the values in the formula
x= (-(-4)± √((-4)^2-4(1)(18)))/2(1)
x = (4± √(16-72))/2
x = (4± √(-56))/2
The minus sign in square root will introduce the imaginary symbol.
x = (4± √(14*4*(-1)))/2
The minus 1 can be replace by the imaginary i => i^2 = -1
x = (4± √(14*2^2*i^2 ))/2
The terms with squares can be brought out of the square root
So,
x = (4± 2i√14)/2
Taking 2 as common
x = (2(2± i√(14)))/2
x = 2± i√14
Related Questions
the two figures are similar
Answers
Answer:
Part a) [tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]
Part b) The dilation is an enlargement, because the sides of the image are larger than the sides of the original figure.(the scale factor is greater than 1)
Part c) The scale factor is [tex]3[/tex]
Step-by-step explanation:
Part a) Write the similarity statement
we know that
If two figures are similar, then the ratio of its corresponding sides is equal
so
[tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]
substitute the values
[tex]\frac{9}{27}=\frac{12}{36} =\frac{15}{45}[/tex]
[tex]\frac{1}{3}=\frac{1}{3} =\frac{1}{3}[/tex] ----> is true
therefore
the figures are similar
Part b) The dilation is an enlargement, because the sides of the image are larger than the sides of the original figure. (the scale factor is greater than 1)
Part c) we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z------> the scale factor
x-----> corresponding side of the image
y------> corresponding side of the original figure
so
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=A'B'=27\ units[/tex]
[tex]y=AB=9\ units[/tex]
substitute
[tex]z=\frac{27}{9}=3[/tex]
The scale factor is greater than 1
therefore
Is an enlargement
Solve this questions beow
Answers
Answer:
140 ft²
Step-by-step explanation:
The figure is composed of a rectangle and a triangle
note triangle has a base = 16 - 12 = 4 ft
Area = area of rectangle + area of triangle
= (16 × 8) + ([tex]\frac{1}{2}[/tex] × 4 × 6)
= 128 + 12
= 140 ft²
Rewrite 0.01 as a power of 10
Answers
Here is your answer
B) [tex]\huge{10}^{-2}[/tex]
REASON:
0.01
=1/100
=1/
[tex] {10}^{2} [/tex]
=
[tex] {10}^{ - 2} [/tex]
HOPE IT IS USEFUL
Answer: 10 to the negative second power
Step-by-step explanation: To write 0.01 as a power of 10, first notice that 0.01 is a decimal which means that the exponent on our power of 10 will be negative.
To determine the value of the exponent, count the number of places we would need to move the decimal point in order to get 1.0.
In this problem, we would need to move the decimal point 2 places to get 1.0 which means that the exponent on our power of 10 will b -2.
Therefore, 0.01 can be written as 10 to the negative 2nd power.
Please help ASAP! Which answer is the correct one?
a survey asked 60 students if they play an instrument and if they are in band
1.- 35 students play and instrument
2.- 30 students are in band
3.- 30 students are not in band.
which table shows these dates correctly entered in a two way frequency table?
Answers
Answer:
A
Step-by-step explanation:
B doesn't work because you can have people who are in a band and not in a band at the same time, which is showing in the first spot
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
Number of students asked in a survey = 60
Number of students who play an instrument = 35
Number of students who are in band = 30
Number of students who are not in band = 30
So, the two way frequency table would be :
Play instrument Not play instrument Total
In band 30 0 30
Not in band 5 25 30
Total 35 25 60
Hence, option 'a' is correct.
What is the value of 8 exponent 3+5x when x=12
Answers
Hey there!
When x=12 the equation would look like this: 3 + 5 * 12
Therefore, the answer is 63
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
‼️20 Points‼️
John drew the line of best fit on the scatter plot. What is the equation of this line of best fit in slope-intercept form?
A) Y=2x + 6/5
B) Y=5/6x + 2
C) Y= 2x + 5/6
D) Y= 6/5x + 2
Answers
Answer:
D
Step-by-step explanation:
the slope is 12/10 which simplifies to 6/5 and the y intercept is 2
PLEASE HELP ASAP. I need help with this problem, I've gotten two answers: 60 and 90 but I can't figure out which one it is. Please help with this and show work so I can understand how to do it, 30 points and thank you very much.
Answers
Find the ratio of the known sides.
6/4 = 1.5
The larger triangle is 1.5 times larger than the smaller one.
Area is in square units, so to find the area of the larger triangle square the ratio and multiply that by the area of the known triangle.
1.5^2 x 40 = 90 square cm.
The probability of giving birth to a boy is 1/2. What is the probability that a family with 5 children will have at least 2 boys?
a)about 81.3%
b)about 76.9%
c)about 62.5%
d)about 90.3%
Answers
Answer:
0.78
Step-by-step explanation:
"The probability that a family with 5 children will have at least 2 boys" is equivalent to the complement 1 - P(family will have 1 or 0 boys).
We can use a calculator with statistical functions built in to calculate this probability. The function needed is for binomial probability: binom(n, p, x).
P(family will have 1 or 0 boys) = binomcdf(5, 0.5, {0, 1} ) produces two results: one the probab. of having 0 boys and one the probab. of having 1 boy: 0.03125 and 0.1875. We add these together, obtaining 0.21875.
Then we subtract this result from 1 to obtain The probability that a family with 5 children will have at least 2 boys: 1 - 0.21875 = 0.78125, which may be reasonably rounded off to 0.78.
Answer:
81.3%.
Step-by-step explanation:
This is Binomial probability.
Prob( Getting 1 boy) = 5C1 (1/2)^5
= 0.156
Prob ( Getting all girls = 5C5 (1/2)^5
= .031.
So Prob( at least 2 boys = 1 - (0.156 + 0.031)
= 0.813
= 81.3%.
solve the system of equations using subsitutions. x-4y=111 and 2y-x=-7
Answers
Answer:
[tex]\frac{x}{4}-\frac{111}{4}\\x=2y+7[/tex]
I'm pretty sure this is correct!
Answer:
(- 97, - 52)
Step-by-step explanation:
given the 2 equations
x - 4y = 111 → (1)
2y - x = - 7 → (2)
Rearrange (1) expressing x in terms of y by adding 4y to both sides
x = 111 + 4y → (3)
Substitute x = 111 + 4y into (2)
2y - (111 + 4y ) = - 7 ← distribute and simplify left side
2y - 111 - 4y = - 7
- 2y - 111 = - 7 ( add 111 to both sides )
- 2y = 104 ( divide both sides by - 2 )
y = - 52
Substitute y = - 52 into (3) for corresponding value of x
x = 111 + 4(- 52) = 111 - 208 = -97
Solution is ( - 97, - 52 )
Chris is packing toy boxes that are cubes with 4 inch-sides into a crate. The crate is 3 feet wide by 3 feet long by 2 feet tall. How many toy boxes can Chris pack into the crate?
Answers
Answer:
[tex]486\ toy\ boxes[/tex]
Step-by-step explanation:
we know that
[tex]1\ ft=12\ in[/tex]
step 1
Convert the dimensions of the boxes to feet
[tex]4\ in=4/12=(1/3)\ ft[/tex]
step 2
Find the volume of the toy boxes
[tex]V=b^{3}[/tex]
[tex]V=(1/3)^{3}=(1/27)\ ft^{3}[/tex]
step 3
Find the volume of the crate
[tex]V=LWH[/tex]
[tex]V=(3)(3)(2)=18\ ft^{3}[/tex]
step 4
Divide the volume of the crate by the volume of the toy boxes to find the number of toy boxes
[tex]\frac{18}{(1/27)}= 486\ toy\ boxes[/tex]
Suppose we want to choose 2 objects, without replacement, from the 5 objects pencil, eraser, desk, chair, and lamp. (a)How many ways can this be done, if the order of the choices matters? (b)How many ways can this be done, if the order of the choices does not matter?
Answers
Answer:
a) 20 ways
b) 10 ways
Step-by-step explanation:
When the order of selection/choice matters, we use Permutations to find the number of ways and if the order of selection/choice does not matter, we use Combinations to find the number of ways.
Part a)
We have to chose 2 objects from a group of 5 objects and order of choice matters. This is a problem of permutations, so we have to find 5P2
General formula of permutations of n objects taken r at time is:
[tex]nPr=\frac{n!}{(n-r)!}[/tex]
Using the value of n=5 and r=2, we get:
[tex]5P2=\frac{5!}{(5-2)!} =20[/tex]
Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice matters.
Part b)
Order of choice does not matter in this case, so we will use combinations to find the number of ways of choosing 2 objects from a group of 5 objects which is represented by 5C2.
The general formula of combinations of n objects taken r at a time is:
[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]
Using the value of n=5 and r=2, we get:
[tex]5C2=\frac{5!}{2!(5-2)!} =10[/tex]
Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice does not matters.
Answer:
20
10
Step-by-step explanation:
just took the test
PLEASE HELP ME!
Please simplify this equation.
(-4a^2) (2a^-3)^-4
The options are:
A. a^14 divided by -4
B. 1 divided by -4a^10
C. -4a^10
D. -64a^14
By the way, when the symbol, ^, is behind a number, it means that the number in front of it is an exponent.
Answers
Answer:
A. a^14 divided by -4Step-by-step explanation:
[tex](-4a^2)(2a^{-3})^{-4}\qquad\text{use}\ (xy)^n=x^ny^n\ \text{and}\ (x^n)^m=x^{nm}\\\\=(-4a^2)\bigg(2^{-4}a^{(-3)(-4)}\bigg)\qquad\text{use}\ 4=2^2\\\\=(-2^2a^2)(2^{-4}a^{12})\\\\=-(2^2)(2^{-4})(a^2a^{12})\qquad\text{use}\ x^nx^m=x^{n+m}\\\\=-2^{2+(-4)}a^{2+12}\\\\=-2^{-2}a^{14}\qquad\text{use}\ x^{-n}=\dfrac{1}{x^n}\\\\=-\dfrac{1}{2^2}a^{14}\\\\=-\dfrac{a^{14}}{4}[/tex]
How much profit does she make
Answers
evaluate the expression 2x/y for x= -28 and y =-7
Answers
[tex] \frac{2x}{y} \: x = - 28 \: y = - 7[/tex]
[tex]2( - 28) \div ( - 7)[/tex]
[tex] \frac{ - 56}{ - 7} [/tex]
[tex] = 8[/tex]
The simplification of the given expression for x= -28 and y =-7 is 8.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The given expression is 2x/y.
Substiute the given values;
x= -28 and y =-7
Then, 2x / y = 2(-28) / -7
= -56 / -7
= 8
Hence, the simplification of the given expression for x= -28 and y =-7 is 8.
Learn more about simplification;
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identify a transformation of the function f(x) = √x by observing the equation of the function g(x) = √x-2
Answers
Answer:
g(x) is the image of f(x) after translated horizontally 2 units to the right
Step-by-step explanation:
∵ f(x) = √x
∵ g(x) = √(x - 2)
∴ The x-coordinate of f(x) becomes (x - 2)
∴ f(x) translated horizontally 2 units to the right
Maria earns a 15% commission on her car sales. How much commission would Mariabearn on a sale of $23,000?
Answers
Answer:
$3,450
Step-by-step explanation:
As Maria earns 15% commission, a car sale of $23,000 would lead to a $3,450 commission. This can be achieved by multiplying .15 (15% translated into a decimal) to the total car sale of $23,000.
x = commission
x = 23,000 * (.15) = 3,450
Final answer:
Maria would earn a commission of $3,450 on a sale of a car priced at $23,000, calculated by multiplying the sale amount by her 15% commission rate.
Explanation:
Maria earns a 15% commission on her car sales. If she sells a car for $23,000, her commission is calculated by multiplying the total sale amount by the commission rate. To find the commission, use the following formula:
Commission = Sale Amount × Commission Rate
Commission = $23,000 × 0.15
Commission = $3,450
Therefore, Maria would earn a commission of $3,450 on a sale of $23,000.
9...................
Answers
For this case we must evaluate the following expression:
[tex]\sqrt [4] {16}[/tex]
We have by definition of properties of powers and roots that:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
On the other hand, we can rewrite the 16 as:
[tex]16 = 2 * 2 * 2 * 2 = 2 ^ 4[/tex]
So:
[tex]\sqrt [4] {16} = \sqrt [4] {2 ^ 4} = 2 ^ {\frac {4} {4}} = 2 ^ 1 = 2[/tex]
ANswer:
Option D
How would u convert 3 yards 2 feet into inches
Answers
a yard = 3 feet, a foot =12 in, so 3 yardsx3 feet would be 9 feet, plus the 2 other feet, would be 11, times 12 inches, would be 132 inches.
Answer:
The correct answer is 3 yards 2 feet = 132 inches
Step-by-step explanation:
Points to remember
1 Yard = 3 foot
1 foot = 12 inches
It is given that, 3 yards 2 feet we have to convert it into inches.
To convert into inches
3 yards to feet
we have, 1 Yard = 3 foot
3 yards = 3 * 3 = 9 feet
3 yards 2 feet = 9 feet + 2 feet = 11 feet
11 feet to inches
1 foot = 12 inches
11 feet = 11 * 12 = 132 inches
What is 0.47058824 rounded to nearest tenth
Answers
Answer:
0.5
Step-by-step explanation:
0.47058824
the 4 is in the tenths place
the 7 makes it turn to a 5
the answer would be 0.5 :)
pleasssssssss heeeelllllpppppp!!!! Bethany attached two cubes side by side.
What is the volume of the entire figure?
36 in 3
74 in 3
468 in 3
720 in 3
Answers
Answer:
468
Step-by-step explanation:
The volume of a cube is V = s³. Fin the volume of each cube separately and add together for the volume all together.
The small cube has side length 5 so V = 5³ = 125.
The large cube has side length 7 since 12 - 5 = 7. So V = 7³ = 343.
Together the volume is 125 + 343 = 468
Answer:
468
Step-by-step explanation:
Solve the equation 9b2 + 30b + 25 =0
Answers
Answer:
C. b = -5/3
Step-by-step explanation:
9b2 + 30b + 25 =0
(3b)^2 + 30b +(5)^2 = 0 <---perfect square
(3b + 5)^2 = 0
(3b + 5) = 0
3b = -5
b = -5/3
Answer
C. b = -5/3
Answer:
C. b = -5/3
Step-by-step explanation:
9b² + 30b + 25 = 0
We can factor: two numbers that add up to 30 and its' product is 225: 15 & 15.
So we have 9b² + 15b + 15b + 25 = 0.
We can change this to (3b + 5) (3b + 5), or (3b + 5)².
This means there is only one solution: 3b + 5 = 0.
This can be turned into 3b = -5 -> b = -5/3.
Víctor saves $11 every week.Which expression represents the amount of money,in dollars,Victor Will save in w weeks?
Answers
Answer:
11*w=x
Step-by-step explanation:
x= the amount of money he will have after w weeks
so, 11 times the amount of weeks will give you the amount he has after any number of weeks
When Danny gets wild l, his mom tells him to do laps around the block. His block is 66 yards wide and 80 yards long. How many yards are in one lap around Danny's block?
Answers
Answer:
292
Step-by-step explanation:
The block is a rectangle with 80 yd length and 66 yd width. We need the perimeter of the block, which is the perimeter of the rectangle.
P = 2L + 2W
P = 2(80 yd) + 2(66 yd)
P = 160 yd + 132 yd
P = 292 yd
To calculate the distance of one lap around Danny's rectangular block (66 yards wide and 80 yards long), we find the perimeter, which is 292 yards.
The question asks about finding the distance Danny must run when doing a lap around his block, which is shaped as a rectangle. To find the distance around a rectangular path, we calculate the perimeter. The formula for the perimeter of a rectangle is 2 * (length + width). Given that the block is 66 yards wide and 80 yards long, the perimeter is 2 *(66 + 80) yards.
First, we add the length and width: 66 + 80 = 146 yards. Then, we multiply by 2: 2 * 146 = 292 yards. Therefore, one lap around Danny's block is 292 yards.
Plz help!!!!!!!!!!!!!
Answers
Answer: The correct answer is -2,5/2 which is the last answer.
Step-by-step explanation:
* Hopefully the work below helps:)Mark me the brainliest:)!!
Answer: [tex]\bold{\{-2, \dfrac{5}{2}\}}[/tex]
Step-by-step explanation:
2x² - x - 10 = 0
Replace -x with 4x - 5x and factor using Grouping Method:
2x² + 4x -5x - 10 = 0
2x(x + 2) -5(x + 2) = 0
(2x - 5) (x + 2) = 0
2x - 5 = 0 and x + 2 = 0
2x = 5 and x = -2
x = 5/2
2x^2 -19x + 35 =0
Factor
Answers
Answer:
(-x+7) (-2x+5) are the factor of 2x²-19x+35=0
help!!!!!!!!!!!!!!.........
Answers
there is no help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
For this case we must resolve the following expression:
[tex]9 ^ {\sqrt {3}}[/tex]
We have to, by definition:
[tex]\sqrt {3} = 1.732050808[/tex]
So:
[tex]9 ^ {1.732050808} =[/tex]
Evaluating in a calculator we have to:
[tex]9 ^ {1.732050808} = 44.95691576[/tex]
Rounding the obtained expression:
[tex]9 ^ {\sqrt {3}} = 44.9569[/tex]
Answer:
Option C
Can someone please help me with math???
Answers
D. [tex]24 - 2d[/tex]
EXPLANATION
Marjorie bought a total of 24 bottles of juice.
If she opens and drinks 2 bottles each day, then
at the end of the first day,the number of unopened bottles will be;
[tex] = 24 - 2(1) = 22[/tex]
at the end of the second day,the number of unopened bottles will be;
[tex] = 24 -2 (2) = 20[/tex]
at the end of the third day,the number of unopened bottles will be;
[tex] = 24 - 2(3) = 18[/tex]
At the end of d days,the number of unopened bottles will be;
[tex] = 24 - 2(d)[/tex]
[tex] = 24 - 2d[/tex]
The correct choice is D
Which situation could NOT represent a proportional relationship? A) The cost of purchasing candy bars at a price of $1.25 per candy bar. B) The number of cookies produced in a factory at a rate of 1,000 cookies per hour. C) The cost of transporting an automobile for a charge of $1.00 per mile with a pick-up fee of $100. D) The cost of a field trip to a museum for a group of high school students at a cost of $10.00 per student.
Answers
Answer:
Option C. The cost of transporting an automobile for a charge of $1.00 per mile with a pick-up fee of $100
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
verify each case
case A) The cost of purchasing candy bars at a price of $1.25 per candy bar.
Let
y------> the cost
x----> the number of candy bars
The linear equation that represent the situation is
y=1.25x -------> represent a proportional relationship
case B) The number of cookies produced in a factory at a rate of 1,000 cookies per hour
Let
y------> the number of cookies
x----> the number of hours
The linear equation that represent the situation is
y=1,000x -------> represent a proportional relationship
case C) The cost of transporting an automobile for a charge of $1.00 per mile with a pick-up fee of $100
Let
y------> the cost
x----> the number of miles
The linear equation that represent the situation is
y=x+100 -------> not represent a proportional relationship
case D) The cost of a field trip to a museum for a group of high school students at a cost of $10.00 per student
Let
y------> the cost
x----> the number of students
The linear equation that represent the situation is
y=10x -------> represent a proportional relationship
Answer: The answer is B.
Which functions are exponential function
( select all that apply )
Answers
Answer:
Step-by-step explanation:
The first and the last of these functions are exponential functions. Such functions can be recognized by the constant base and variable exponent found in each: 3^x, (5)^x, in this particular problem.
5x^2 is not an expo function because the base is not constant; this is called a power function.
the exponential function is f(x) = 3^x and 3(5)^x. Therefore, option a and d both are the correct answer.
The correct answers are f(x) = 3^x (choice A) and f(x) = 3(5) (choice D) for exponential functions, then it means you're considering a constant function (f(x) = 3(5)) as a simple form of an exponential function where the base is 3 and the exponent is 5.
This is a valid interpretation, but typically exponential functions are written as f(x) = a^x, where 'a' is a constant, and 'x' is the variable in the exponent.
In this case, if you're considering f(x) = 3(5) as an exponential function, it represents a specific case with a constant exponent.
So, both A and D can be considered as exponential functions depending on the context of the question.
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PLZ HELP (40 POINTS)
3 QUESTIONS
Answers
Answer:
first one is D
second is B
third is B
Step-by-step explanation: