Answer:
16.81
Step-by-step explanation:
Given:
Number = 4.1
Find:
Square of the given number
Computation:
[4.1]²
⇒ [4.1] × [4.1]
⇒ 16.81
If Janine square 4.1 by assuming (round off) 4 as an integer number then gets 16, which means Janine's estimate would be considered appropriate.
In a dessert, the ratio of the number of ounces of dark chocolate used to the number of ounces of white chocolate used is 8 : 5 How many ounces of dark chocolate are used for every 1 ounce of white chocolate used to make the dessert ?
Answer:
1.6 ounces
Step-by-step explanation:
Divide the ratio by 5 to get the number of ounces of dark chocolate used for 1 ounce of white chocolate, since 5/5 = 1
8/5 = 1.6
5/5 = 1
The new ratio is 1.6 : 1
This means that 1.6 ounces of dark chocolate are used for every 1 ounce of white chocolate
Consider the system of quadratic equations \begin{align*} y &=3x^2 - 5x, \\ y &= 2x^2 - x - c, \end{align*}where $c$ is a real number. (a) For what value(s) of $c$ will the system have exactly one solution $(x,y)?$ (b) For what value(s) of $c$ will the system have more than one real solution? (c) For what value(s) of $c$ will the system have no real solutions? Solutions to the quadratics are $(x,y)$ pairs. Your answers will be in terms of $c,$ but make sure you address both $x$ and $y$ for each part.
Hello, we need to solve this system, c being a real number.
[tex]\begin{cases}y &= 3x^2-5x\\y &= 2x^2-x-c\end{cases}[/tex]
y=y, right? So, it comes.
[tex]3x^2-5x=2x^2-x-c\\\\3x^2-2x^2-5x+x+c=0\\\\\boxed{x^2-4x+c=0}[/tex]
We can compute the discriminant.
[tex]\Delta=b^2-4ac=4^2-4c=4(4-c)[/tex]
If the discriminant is 0, there is 1 solution.
It means for [tex]4(4-c)=0 <=> 4-c=0 <=> \boxed{c=4}[/tex]
And the solution is
[tex]x_2=x_1=\dfrac{4}{2}=2[/tex]
If the discriminant is > 0, there are 2 real solutions.
It means 4(4-c) > 0 <=> 4-c > 0 <=> [tex]\boxed{c<4}[/tex]
And the solution are
[tex]x_1=\dfrac{4-\sqrt{4(4-c)}}{2}=\dfrac{4-2\sqrt{4-c}}{2}=2-\sqrt{4-c}\\\\x_2=2+\sqrt{4-c}[/tex]
If the discriminant is < 0, there are no real solutions.
It means 4(4-c) < 0 <=> 4-c < 0 <=> [tex]\boxed{c>4}[/tex]
There are no real solutions and the complex solutions are
[tex]x_1=\dfrac{4-\sqrt{4(4-c)}}{2}=\dfrac{4-2\sqrt{i^2(c-4)}}{2}=2-\sqrt{c-4}\cdot i\\\\x_2=2+\sqrt{c-4}\cdot i[/tex]
Thank you.
Brendan's dog has a mass of 25,700 grams. What is the dog's mass in milligrams? Show your work.
Answer:
25700000
Step-by-step explanation:
1,000 miligrams in a gram so 25700*1000 = 25700000
f(x)= (1,2) (3, -4) (-5, -8)
Answer: y= 156
Step-by-step explanation:
y= 12(3-4) (-5 -8)
A set of 9 numbers has a mean of 20. What additional number must be included in this set to create a new set with a mean that is 4 less than the mean of the original set?
Greetings from Brasil...
The average for a set of 9 elements will be
(A + B + C + D + E + F + G + H + I) ÷ 9 = 20
Let's make (A + B + C + D + E + F + G + H + I) like S
(I chose S to remember a sum)
Let us think.....
S ÷ 9 = 20
S = 20 × 9
S = 180
So, (A + B + C + D + E + F + G + H + I) = 180
According to the statement, we will include a number (element J) in the sum to obtain a mean of (20 - 4), that is:
(A + B + C + D + E + F + G + H + I + J) ÷ 10 = (20 - 4)as seen above, (A + B + C + D + E + F + G + H + I) = 180, then
(180 + J) ÷ 10 = 16
(180 + J) = 160
J = 160 - 180
J = - 20So, including the number - 20 (minus 20) in the original mean we will obtain a new mean whose result will be 16
2 which of the following is a perfect cube
a) 400 -
D. 3375–
C 8000 -
Answer:
8000 is a perfect cube but 3375 can be also but i m a little sure that 8000 is a perfect cube
Solve log x = 4.
Ox=4
O x = 40
Ox= 1,000
Ox= 10,000
Hi there! :)
Answer:
[tex]\huge\boxed{x = 10,000}[/tex]
Given:
[tex]logx = 4[/tex]
The given expression is a logarithm with a base of 10, therefore we can rewrite this as:
[tex]10^{4} = x[/tex]
Evaluate:
[tex]x = 10,000[/tex]
7 > x/4, solve for x, simplify
Answer:
28 > x
Step-by-step explanation:
Step 1: Solve the inequality
[tex]7 > \frac{x}{4}\\28 > x[/tex]
Therefore x is any value smaller than 28
Answer:
[tex]\huge\boxed{x<28}[/tex]
Step-by-step explanation:
[tex]7 > \frac{x}{4}\\\\7*4>\frac{x}{4}*\frac{4}{x}\\\\28>x\\\\\boxed{x<28}[/tex]
Point M is the midpoint between points A and B. If A(-7, 2) and B(-1,-4)
find the location of M.
Answer:
M(-4, -1)
Step-by-step explanation:
M = (A +B)/2
M = ((-7, 2) +(-1, -4))/2 = (-8, -2)/2 = (-4, -1)
The location of M is (-4, -1).
If f(x) = 2x +3, what is f(-3)? Show work.
A)-3/
B) -4
C) -5
D-6
Answer:
f(-3) = -3
Step-by-step explanation:
f(x) = 2x +3
Let x = -3
f(-3) = 2*-3 +3
= -6+3
= -3
Answer:
-3
Step-by-step explanation:
1. Subsitute x for -3
2. multiply 2(-3) = -6
3. add -6 +3
4. f(-3) is -3
How many dots are there at t minutes? Solve the problems by your preferred method. Your
solution should indicate how many dots will be in the pattern at 3 minutes, 100 minutes,
and t minutes. Be sure to show how your solution relates to the picture and how you
arrived at your solution.
The image to the question is missing, but I found a matching image, which is attached to this solution
Answer:
3 minutes = 13 dots
100 minutes = 401 dots
t minutes = 4(t) + 1 dots
Step-by-step explanation:
From the image, the following can be noticed:
time (Mins) dots
0 1
1 5
2 9
The pattern gotten from this progression is that, if the time is multiplied by 4, and the result added to one, the result will be the number of dots.
hence, when the time is 0 minutes:
0 × 4 = 0
0 + 1 = 1 ( 1 dot)
when the time is 1 minute
1 × 4 = 4
4 + 1 = 5 (5 dots)
when the time is 2 minutes
2 × 4 = 8
8 + 1 = 9 ( 9 dots)
Therefore,
when the time = 3 minutes
3 × 4 = 12
12 + 1 = 13 dots
at 100 minutes:
100 × 4 = 400
400 + 1 = 401 dots
at t miutes
t × 4 = 4t
4t + 1 = number of dots
Therefore number of dots at t minutes = 4(t) + 1
Suppose the test scores of students in a class are normally distributed with a mean of 86 and a standard deviation of 4. What is the z-score for a student that scored 76 on a test? A.−4 .−2.5 C.2.5 D.4
Answer:
-2.5
Step-by-step explanation:
Here in this question, we are interested in calculating the z-score for a student that had a particular mark at the test
To calculate the z-score, we need to use a mathematical formula
Mathematically;
z-score = (x - mean)/SD
From the question;
x = 76
mean = 86
standard deviation SD = 4
Plugging these values in the equation, we have;
z-score = (76-86)/4 = -10/4 = -2.5
A bike rental company charges a $10 fee
plus $5 per hour. Sofia has $25 to spend.
Which inequality could you use to find x,
the number of hours Sofia could rent a
bike?
Answer:
10 + 5x ≤ 25
Step-by-step explanation:
There are a total of 84 people, lions, and giraffes at the zoo. Cassie visits the
zoo and counts 282 total legs. If you were to double the number of people,
that is equivalent to tripling the number of lions. How many of each are at the
zoo?
Answer:
14 giraffes, 28 people and 42 lions
Step-by-step explanation:
you add how many legs for all 3 x1
add this you have a total 14
double that is 28 triple that is 42
total 84
x+5=5+x is an example of what property?
Answer: Commutative Property
Step-by-step explanation: In Picture.
10 = 7 - m*
It says solve & check solution. Can someone help asap
Answer:
see explanation
Step-by-step explanation:
Given
10 = 7 - m ( subtract 3 from both sides )
3 = - m ( multiply both sides by - 1 )
- 3 = m , or
m = - 3
As a check
Substitute m = - 3 into the right side of the equation and if equal to the left side then it is the solution
7 - m = 7 - (- 3) = 7 + 3 = 10 = left side
Thus m = - 3 is the solution to the equation
Perpendicular to y = 6x + 2; passing through the point (3,5).
Answer:
Step-by-step explanation:
y = 6x + 2
Slope = 6
A line perpendicular to this would have a negative reciprocal slope = [tex]-\frac{1}{6}[/tex]
To solve for the y-intercept, plug the coordinates given into the question.
y = mx + b
5 =[tex]-\frac{1}{6}[/tex] (3) + b
5 = [tex]-\frac{3}{6}[/tex] + b
5 = [tex]-\frac{1}{2}[/tex] + b
b = 5 + [tex]\frac{1}{2}[/tex]
b = [tex]\frac{11}{2}[/tex] or 5 [tex]\frac{1}{2}[/tex]
So, your new slope-intercept line equation is
y = [tex]-\frac{1}{6}[/tex]x + 5 [tex]\frac{1}{2}[/tex]
I would really appreciate it if you would please mark me brainliest!
Have a blessed day!
Solve. 10. On weekdays, Kiki walks 2 miles in the morning and I mile in the evening. On Saturdays, she walks 4 miles. Place parentheses in the expression to represent the number of miles Kiki walks each week. 5x 2 + 1 + 4 USING GROUPING SYMBOLS (C)
Answer:
The parenthesis should be placed as shown:
5 x (2+1) + 4
Step-by-step explanation:
What Kiki walks every week day is : 2 miles + 1 mile = (2+1)
since this is done 5 times per week (on weekdays) to obtain the total walked on weekdays, you multiply this by 5: 5 x (2+1)
and we need to add to this what Kiki walks on Saturdays (4 miles){
5 x (2+1) + 4
Please solve, 7(2-2x)= -13-5x
Answer:
[tex]x=3[/tex]
Step-by-step explanation:
We can try and isolate x on one side of the equation to find its value.
First let's apply the distributive property on the left side and get a simpler equation.
[tex]7(2-2x)=-13-5x\\\\14-14x = -13-5x[/tex]
Now, to simplify this down, we can add 5x to both sides.
[tex]14-14x + 5x = -13-5x + 5x\\\\14-9x=-13[/tex]
Now we can add 13 to both sides:
[tex]14-9x+13=-13+13\\\\27-9x=0[/tex]
Now we subtract 27 from both sides:
[tex]27-9x-27=0-27\\\\-9x=-27[/tex]
And finally we divide both sides by -9.
[tex]-9x\div-9=-27\div-9\\\\x=3[/tex]
Hope this helped!
Answer:
[tex]\Huge \boxed{x=3}[/tex]
Step-by-step explanation:
[tex]7(2-2x)= -13-5x[/tex]
Expanding brackets.
[tex]14-14x= -13-5x[/tex]
Adding 5x and -14 to both sides.
[tex]-14x+5x=-13-14[/tex]
[tex]-9x=-27[/tex]
Dividing both sides by -9.
[tex]x=3[/tex]
Find The area of each square. Input each area then click them
Answer:
see below
Step-by-step explanation:
Area 1 = 3 x 3 = 9 m²
Area 2 = 4 x 4 = 16 m²
Area 3 = 5 x 5 = 25 m²
The areas are 16 unit², 9 unit² and 25 unit² respectively.
What is Surface Area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. Square units are used to measure it as well.
As per the given diagram:
We are given 3 squares, and we have to find out the area of each square.
The area of a square is given by a², where a is the length of the side of the square.
For area of the square with length of the side, 4 units.
A = (4)² unit² = 16 unit²
For area of the square with length of the side, 3 units.
A = (3)² unit² = 9 unit²
For area of the square with length of the side, 5 units.
A = (5)² unit² = 25 unit²
The areas are 16 unit², 9 unit² and 25 unit² respectively.
Hence, The areas are 16 unit², 9 unit² and 25 unit² respectively.
To learn more about surface area, click:
brainly.com/question/29298005
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How do you simplify 4/42
Answer:
4/42 = 2/21 when simplified down
Step-by-step explanation:
Cancel the common factor: 2
=2/21
Answer:
2/21Step-by-step explanation:
[tex]\frac{4}{42}\\\\\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{2}{21}\\\\\left(\mathrm{Decimal:\quad }\:0.09523 \right)[/tex]
If y varies inversely as x, and y = 6 when x = 24, find x when y = 18
Answer:
x = 8
Step-by-step explanation:
Standard form for inverse variation:
y = k/x
We now use the given information to find k.
y = 6 when x = 24
6 = k/24
k = 6 * 24
k = 144
The equation for this inverse relation is
y = 144/x
For y = 18, we get
18 = 144/x
18x = 144
x = 144/18
x = 8
Answer:
x = 8Step-by-step explanation:
To find the value of x when y = 18 we must first find the relationship between them.
The statement
y varies inversely as x is written as
[tex]y \: \: \alpha \: \: \frac{k}{x} [/tex]where k is the constant of proportionality
From the question when
y = 6
x = 24
Substitute the values into the above equation
That's
[tex]6 = \frac{k}{24} [/tex]Cross multiply
That's
k = 24(6)
k = 144
So the formula for the variation is
[tex]y = \frac{144}{x} [/tex]When
y = 18
[tex]18 = \frac{144}{x} [/tex]Cross multiply
18x = 144
Divide both sides by 18
x = 8Hope this helps you
Caren held 260 of the shares for herself and sold the rest in equal amounts to six investors. How many shares does each investor own? If the business fails and leaves $65,000 in debt, for how much would each investor be liable
Answer:
40 shares each and $3,000 each
Step-by-step explanation:
The computation is shown below:
For the number of shares
Since there are total of 500 shares out of which 260 shares are held by Caren so the remaining shares left is
= 500 shares - 260 shares
= 240 shares
And, there are 6 investors
So the number of shares owned by each investor is
[tex]= \frac{240}{6}[/tex]
= 40 shares
Now the value of the shares held by each inventory is
[tex]= 40 shares \times \$75[/tex]
= $3,000
Total debt is $65,000
So, the liability per share is
[tex]= \frac{\$65,000}{500}[/tex]
= $130
And each investor holds 40 shares
So, each investor is liable for
[tex]= \$130 \times 40\ shares[/tex]
= $5,200
As we can see that the value of the shares is less than the amount liable by each investor
So each investor is liable for $3,000
And, the liability of Caren is
[tex]= 260\ shares \times \$75[/tex]
= $19,500
AB is parallel to CD. EG = FG ˆ AEG = 110° ˆ Calculate the size of DGH.
Opposite exterior angles are congruent.
DGH = AEG
DGH = 110
Simplify: 7 - 3(2x - 5) - 4x
Answer:
[tex]\Huge \boxed{2(-5x+11)}[/tex]
Step-by-step explanation:
[tex]7 - 3(2x - 5) - 4x[/tex]
Expanding brackets.
[tex]7-6x+15-4x[/tex]
Grouping like terms.
[tex](-6x-4x)+(7+15)[/tex]
Combining like terms.
[tex]-10x + 22[/tex]
Factoring the expression.
[tex]2(-5x+11)[/tex]
PLEASE HELP ME ASAP!!! ILL MARK BRIANLIEST AND GIVE EXTRA POINTS1. When writing a linear equation for a word problem, what are some things to keep in mind or some keywords to watch out for? What do those keywords mean/ why should you watch out for those things?
Answer:
Some keywords include "starting amount," you should look out for this because it will be the y-intercept for the equation. Another keyword may be "daily" or "monthly" or "yearly," which would be the coefficient of x, or the amount that y increases with an increase of 1 in x.
pls mark brainliest :)
The linear function that models the population of rainbow smelt is y1 = −19.76x + 227, where x = the years since 1990 and y1 = the number of rainbow smelt. The linear function that models the population of bloater fish is y2 =
The linear function that models the population of bloater fish is y2= -92.57x + 1, 052
The linear equation that determines when the two populations were equal is
-19.76x + 227 = -92.57x + 1052
The solution is x= 11.33 years
Simplity (a+(-a) ) + b
Answer:
Hey there!
(a+(-a))+b
a-a+b
b
Let me know if this helps :)
Answer:
b // (a-a)+b
Step-by-step explanation:
(a+(-a)) +b
(a-a)+b
b
Find the volume of a cylinder that has a diameter of 12 in. and a height of 15 in
Answer:
[tex] \sf{ \boxed{ \bold{1697.14}}}[/tex]Step-by-step explanation:
Given,
diameter ( d ) = 12 in
height ( h ) = 15 in
finding the radius of a cylinder
Radius is just half of diameter.
Radius ( r ) = 12 / 2 = 6 in
finding the volume of a cylinder having radius of 6 in and height of 15 in
Volume of a cylinder = [tex] \sf{\pi \: {r}^{2} h}[/tex]
⇒[tex] \sf{ \frac{22}{7} \times {6}^{2} \times 15}[/tex]
⇒[tex] \sf{ \frac{22}{7} \times 36 \times 15}[/tex]
⇒[tex] \sf{1697.14} \: in[/tex]
Hope I helped!
Best regards!!
Answer: 1697.1[tex]in^{3}[/tex]
Step-by-step explanation:
diameter= 12
radius= [tex]\frac{diameter}{2}[/tex] = [tex]\frac{12}{2}[/tex] = 6
height = 15
volume =π[tex]r^{2}[/tex]h
[tex]\frac{22}{7} X 6^{2} X 15[/tex] =1697.1[tex]in^{3}[/tex]
Identify each polynomial as either a monomial binomial or trinomial. Then state the degree and leading coefficient.
1) 4x^5 + 2
Name?
Degree?
Leading Coefficient?
2) - 4x + 7x^3-11
Name?
Degree?
Leading Coefficient?
3) 18x^5y^3z
Name?
Degree?
Leading Coefficient?
Answer with explanation:
Monomial = Polynomial with one term. Binomial = Polynomial with two terms.Trinomial = Polynomial with three terms.Degree - highest power of variableLeading coefficient - Coefficient of the variable or variables with highest power.[tex]1)\ \ 4x^5 + 2[/tex]
Name = Binomial (as it has two terms)
Degree= 5 (power of x)
Leading Coefficient = 4 (coefficient of [tex]x^5[/tex])
[tex]2)\ \ - 4x + 7x^3-11[/tex]
Name = trinomial (as it has 3 terms)
Degree = 3 (highest power of x)
Leading Coefficien= 7 ( coefficient of [tex]x^3[/tex])
[tex]3)\ \ 18x^5y^3z[/tex]
Name= Monomial (as it has 1 term)
Degree= 5+3+1= 9 [Addition of power of all variables]
Leading Coefficient = 18