Answer:
Exact form: x= -1 ± √2
Decimal Form: x= 0.41421356..., -2.41421356...
Step-by-step explanation:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros) replace with 0 and solve for x.
L2) In a class of 27 students, there are 13 male students and 14 female students. What is the probability of randomly choosing 2 male students for class representatives?
Of the 50 students in the sixth grade, 16 are girls. What percent are girls?
Answer:
Step-by-step explanation:
That is (16/50) * 100
= 16 * 100/50
= 16 *2
= 32%.
Answer: 32%
Step-by-step explanation:
put it into a fraction, 16/50 then multiply by 2 to get 32/100 now you can turn that into a percent to get 32%
4.
Rectangle MATH was translated 7 units to the left and 4 urlits down to create rectangle M'ATH'. Which rule describes this transformation?
The rectangle MATH is translated by using the transformation rule P'(x, y) = (x - 7, y - 4) to create the rectangle M'A'T'H'.
What is the resulting rule transformation for the translation of a rectangle?
In this problem we have the case of a rectangle, a geometric locus, that is translated both horizontally (7 units to the left) and vertically (4 units down). Vectorially speaking, a translation is represented by the following vector sum:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original point.P'(x, y) - Resulting point.T(x, y) - Translation vector.If we know that P(x, y) = (x, y) and T(x, y) = (- 7, - 4), then the transformation rule is derived below:
P'(x, y) = (x, y) + (- 7, - 4)
P'(x, y) = (x - 7, y - 4)
The rectangle MATH is translated by making use the transformation rule P'(x, y) = (x - 7, y - 4).
To learn more on transformation rules: https://brainly.com/question/28722842
#SPJ1
Help -crys- "pacman traveled 18 feet every 6 seconds. pacman's distance is proportional to time. (im not in high school im in middle school i dont know why it says that)
Constant of Proportionality
k=___
Based on the distance that Pacman traveled for every 6 seconds, and the distance being proportional to time, the Constant of Proportionality is 3.
How to find the constant of proportionality?The Constant of Proportionality shows how the quantity of a variable increases of decreases as the quantity of another related variable increases or decreases as well.
In the distance traveled by Pacman, the constant of proportionality can be found by the formula:
= Distance traveled / Time traveled
= 18 feet / 6 seconds
= 3 feet per second
Find out more on the constant of proportionality at https://brainly.com/question/28413384
#SPJ1
A bakery made 9 cakes using 3 bags of flour. The bakery uses the same relationship between cakes made and the amount of flour used to make all their cakes.
Which table of values shows the relationship between the number of cakes the bakery makes and the number of bags of flour the bakery uses?
The table of values showing the relationship between the number of cakes the bakery makes and the number of bags of four the bakery uses is:
Cakes | 3 6 9 12 15
Bags of flour| 1 2 3 4 5
A bakery made 9 cakes using 3 bags of flour.
We can introduce a relation between the number of cakes and the bags of flour in the form of a ratio.
Then, cakes : bags of flour = 9 : 3
We can simplify this ratio into 3:1.
So the ratio between the number of cakes and bags of flour = 3:1
We take values for number of bags of flour from 1 to 5 and found the corresponding values for number of cakes using the ratio 3:1.
For each value of number of bags of flour, we just needed to multiply 3 with it to get the number of cakes made.
So using this relationship between cakes made and the amount of flour used to make all their cakes, we can makes table with values:
Cakes | 3 6 9 12 15
Bags of flour| 1 2 3 4 5
Learn more about ratio at https://brainly.com/question/2914376
#SPJ1
Round to the nearest dollar $6.34
a large water tank holds 800 gallons of water . it is losing water at the rate shown in the table. PLEASE HELP- I CAN'T FIND ANY ANSWER FOR THIS ANYWHERE
The slope of equation is -80 and the equation of a line is y=-80x+800.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, a large water tank holds 800 gallons of water.
From the table, we have (0, 800) and (1, 720)
Here, slope m=(720-800)/(1-0)
m= -80
Substitute m=-80 and (x, y)=(0, 800) in y=mx+c, we get
800=-80(0)+c
c=800
Substitute m=-80 and c=800 in y=mx+c, we get
y=-80x+800
Therefore, the slope of equation is -80 and the equation of a line is y=-80x+800.
To learn more about the the equation of a line visit:
https://brainly.com/question/2564656.
#SPJ2
suppose that kellogg believes that the average weight for a box of frosted flakes is 18 ounces. as part of a quality control effort, they sample 30 boxes and find that the mean of those 30 boxes is 18.2 ounces. historical records show that the standard deviation of the filling process is 0.32 ounces. how likely is it for the sample mean to have been 18.2 ounces or larger if the actual mean is 18 ounces and the standard deviation of the filling process is 0.32 ounces? round your answer to four decimal places.
Answer:
18.34
Step-by-step explanation:
18.2
0.32 so
18.2+0.32=18.34
Three less than the product of 7 and half a number
MATHEMATICALLY THIS CAN BE WRITTEN AS
Let that number =x
[tex] \frac{1}{2} (x) \times 7 - 3 \\ = \frac{x}{2} (7) - 3 = \\ = \frac{7x}{2} - 3[/tex]
Erin and her dad share an intense love of baseball. every weekend, they go to the batting cages to practice hitting. erin's dad buys tokens for her to use in the batting cage. there is a proportional relationship between the number of tokens erin uses, x, and the number of pitches thrown by the pitching machine, y. x (tokens) y (pitches) 1 14 2 28 3 42 7 98 write an equation for the relationship between x and y. simplify any fractions.
The relationship between x and y is given by Y=14*X;
Relationship between the number of tokens Erin uses, x, and the number of pitches thrown by the pitching machine, y. x (tokens) y (pitches) 1 14 2 28 3 42 7 98
by, observing the given data we say that;
x is proportional to y so, the general equation is given by
x ∝ y so, by removing the proportionality sign we get y=k*x;
now using given x and y we put in this equation to get the value of k; then by substituting the value of k in this equation we get our required equation.
so, putting x=1 and y=14 we get k=14;
and, putting x=2 and y=28 we get k=14;
and putting x=3 and y =42 we get k=14;
similarly, the last data satisfy the equation.
By putting k =14 in the equation we get, Y=14*X
thus, Y=14*X is our required answer.
also, we solve this problem by using the equation of line concept;
Learn more about the equation of line concept here: https://brainly.com/question/5717349
#SPJ4
-k-(-8k+7)
what is the answer
Answer:
7k-7
Step-by-step explanation:
[tex]-k-(-8k+7) \\ \\ =-k+8k-7 \\ \\ =7k-7[/tex]
What is the slope equation for (7,5) and (2,-5)
Answer:
2
Step-by-step explanation:
To find the slope, m, you use the equation:
[tex]m \: = \frac{y2 - y1}{x2 - x1} [/tex]
From our question, (x1 = 7, y1 = 5) ; ( x2 = 2, y2 = -5)
Substitute the values into the equation:
[tex]m \: = \frac{ - 5 - 5}{2 - 7} \\ = 2[/tex]
The slope, m is therefore 2
State a true conclusion.
1) If Bis between A and C, then AB+ BC = AC.
2) Qis between Rand S.
Conclusion:
Both conclusion are correct and the second conclusion is RS = RQ + QS.
What is a midpoint of line segment?The midpoint is halfway between the two end points, Its x value is halfway between the two x values. Its y value is halfway between the two y values.
Given that,
Part 1, If B is between A and C then AB + BC = AC
Then, we need to find the conclusion in Part 2 if Q is between R and S.
The required conclusion can be find out by using the concept of deductive reasoning.
Deductive reasoning involves a pattern which is followed in one argument and by following the same pattern we reach to a conclusion for some other argument.
Now, If we see in Part 1 if B is between A and C then the length of line segment AC is equal to sum of its mid segments AB and BC
⇒ AB + BC = AC
Similarly, if Q is between R and S, then the length of line segment RS is equal to sum of its mid segments RQ and QS
⇒ RS = RQ + QS
Hence, The required Conclusion is RS = RQ + QS.
To learn more about midpoint of a line segment from the given link:
https://brainly.com/question/3047271
#SPJ9
Make x the subject of the following equation:
[tex] \sqrt{4x} = 3a - y \\ \sqrt{4} \times \sqrt{x} = 3a - y \\ 2 \sqrt{x} = 3a - y \\ \frac{2 \sqrt{x} }{2} = \frac{3a}{2} - \frac{y}{2} \\ \sqrt{x} = \frac{3a}{2} - \frac{y}{2} \\ ( { \sqrt{x} })^{2} = {( \frac{3a}{2} - \frac{y}{2} })^{2} \\ x = ( \frac{3a}{2} - \frac{y}{2} ) ^{2} [/tex]
ATTACHED IS THE SOLUTION
Jenny spend 24 days at grandmas house last summer. Her sister spent 3/8 of that time at grandmas. How many days did jennys sister spend at grandmas house last summer
Thus, we have
[tex]\frac{3}{8}\times24=\frac{3\times24}{8}=3\times3=9\text{ days}[/tex]Therefore Jenny's sister spent 9 days
the right choice is B
Joaquin works at a loading dock. He has been asked to load 30 trucks today, and so far he has finished loading 12. Name the numerator and denominator of the fraction that represents the number of trucks that he has loaded out of the total needing to be loaded .
Answer:
first choice in the image.
numerator: 12
denominator: 30
Step-by-step explanation:
"Name the numerator and denominator of the fraction that represents the number of trucks that he has loaded out of the total needing to be loaded"
so numerator = "number of trucks that he has loaded"
and denominator = "total needing to be loaded"
Joaquin was asked to load 30 trucks today. So his/her total would be 30.
thus the denominator is 30.
Joaquin has finished loading 12 already, which means he/she has loaded 12. so, the numerator is 12.
Write the equation of the line that passes through points (-2,0) and (3,4) in point-slope form.
Answer:
y-0 = [tex]\frac{4}{5}[/tex](x +2)
or
y - 4 = [tex]\frac{4}{5}[/tex](x -3)
These both mean the same thing.
Step-by-step explanation:
First, we have to find the slope. The slope is the change in y over the change in x.
Our y's are 4 and 0 and your x's are 3 and -2
[tex]\frac{4-0}{3- - 2}[/tex] = [tex]\frac{4-0}{3+2}[/tex] = [tex]\frac{4}{5}[/tex]
Now that we have the slope, we can use either point to write the eqation.
If we use point (-2,0)
The equation is
y - [tex]y_{1}[/tex] == m(x -[tex]x_{1}[/tex]
y - 0 = [tex]\frac{4}{5}[/tex] (x - -2)
y - 0 = [tex]\frac{4}{5}[/tex](x +2)
If we use the point (3,4)
y-4 = [tex]\frac{4}{5}[/tex](x -3)
Ella needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3 hours and charged her $61 for parts. The total was $226. Write and solve an equation which can be used to determine x, the cost of the labor per hour.
Answer:
x = 55
Step-by-step explanation:
61+3×X=226
61+3x=226-61
3x=165
x= 165/3
x= 55
Work out the area of the triangle (my drawing is bad it isn’t a 90° angle)
The area of the given triangle in the diagram is 11.83[tex]cm^{2}[/tex]
Given triangle ABC. Let AB=x, BC=y, CA=z
We use Heron's formula when asked to find the area of a triangle and the measures of the sides are given only. According to Heron's formula,
Area of a triangle[tex]=\sqrt{s(s-x)(s-y)(s-z)}[/tex] where s is the semi-perimeter of the triangle given by [tex]s=\frac{x+y+z}{2}[/tex] and x,y,z are the measures of the three sides of the triangle
According to the diagram of the triangle AB=x=8 cm, BC=y=3 cm,
CA= z= 9 cm
∴Semi-perimeter [tex]s=\frac{8+3+9}{2}=10 cm[/tex]
∴Area of the triangle[tex]=\sqrt{10(10-8)(10-3)(10-9)}=\sqrt{10*2*7*1}=2\sqrt{35}=11.83 cm^{2}[/tex]
Therefore the area of the triangle ABC is 11.83[tex]cm^{2}[/tex]
To know more about Heron's Formula:
brainly.com/question/22391198
#SPJ4
when light strikes the surface of a medium such as water or glass, its intensity decreases with depth. the beer-lambert-bouguer law states that the percentage of decrease is the same for each additional unit of depth. in a certain lake, intensity decreases about 85% for each additional meter of depth. (a) explain why intensity i is an exponential function of depth d in meters. intensity i is an exponential function of depth since i increases by a decreasing percentage as a function of depth. intensity i is an exponential function of depth since i decreases by an increasing percentage as a function of depth. intensity i is an exponential function of depth since i decreases by a decreasing percentage as a function of depth. intensity i is an exponential function of depth since i decreases by a constant percentage as a function of depth. intensity i is an exponential function of depth since i increases by an increasing percentage as a function of depth. (b) use a formula to express intensity i as an exponential function of d. (use i0 to denote the initial intensity.) i(d)
Increasing
decreasing
concave up
concave down
Answer:
won't that be concave up?
Please help!
In the diagram of triangle ABD shown below, point C is located on BD such that AB is congruent AC and AC DC. I
m/B=62°, what is the measure of angle ADC?
Step-by-step explanation:
follow the steps and apply the rules of geometry
How do I find x in this question?
Answer:120
Step-by-step explanation:
When it is flat it is 180 degree so
180=60+x
Minus 60 on both side
120=x
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the product. Write your answer as a mixed number in simplest form.
5 × 2 =
=
Answer: 9 755/9
Step-by-step explanation:
given- a statement
to find-evaluate
soulition-
4 2/9 x 2 4/9
38/9 x 22/9
836/81
9 755/9
help me please help me
Step-by-step explanation:
it is very similar to do the manual division of numbers.
5x² - 18x - 15 ÷ x - 4 =
so, we are starting on the left, dividing 5x² by x.
5x²/x = 5x
5x² - 18x - 15 ÷ x - 4 = 5x
then we multiply (x - 4) by 5x and subtract the result from the left part. and then we pull down the next term
5x² - 18x - 15 ÷ x - 4 = 5x
- 5x² -20x
---------------
0 2x - 15
and again, we take the left term and divide by x :
2x/x = 2
5x² - 18x - 15 ÷ x - 4 = 5x + 2
and again we multiply (x - 4) by 2 and subtract the result. and, if there still is one, we pull down the next term.
5x² - 18x - 15 ÷ x - 4 = 5x + 2
- 5x² -20x
---------------
0 2x - 15
- 2x - 8
--------------------
0 -7
there is no more term to pull down, so we are finished.
there is a remainder in the last line unequal to 0.
this becomes therefore -7/(x - 4).
so, the total result is
(5x² - 18x - 15) ÷ (x - 4) = 5x + 2 - 7/(x - 4)
2.
the same thing. we are now dividing the left terms by 3x, and then multiply that result every time with (3x - 2), subtract this abd pull the next term down until there is no more term to be pulled.
6x³ - 16x² + 17x - 6 ÷ 3x - 2 = 2x² - 4x + 3
- 6x³ - 4x²
---------------
0 -12x² + 17x
- -12x² + 8x
-----------------------
0 9x - 6
- 9x - 6
----------------------------
0 0
there is no remainder in the last line, so the result is
(6x³ - 16x² + 17x - 6) ÷ (3x - 2) = 2x² - 4x + 3
What is the Standard form of 70,000
Answer: 7x10 to the 4th
Step-by-step explanation:
What’s x-7-9=2-8x
Please I need it now
hope it's true.
yes
x-7-9=2-8x
-16-2 = -8x-x
x= 18/9
x= 2
If two dice are rolled at one time what's the probability of getting a sum less than or equal to 10
Answer
Step-by-step explanation:
When one dice is rolled, the total sample space = 6 When two dice is rolled, total sample space = 6*6=36 A) P(sum less than 9) = 1 - P(sum greater than or equal to 9) Sample outcomes for sum greater than or equal to 9 = {(3,6),(4,5),(5,4),(6,3),(4,6), (5,5),(6,4), (5,6), (6,5),(6,6)} P(sum greater than or equal to 9) = 10/36 = 5/18 or 0.2778 P(sum less than 9) = 1-5/18 = 13/18 or 0.7222 B)Sample outcomes for sum greater than or equal to 10 = {(4,6),(5,5),(6,4), (5,6),(6,5),(6,6)} P(sum greater than or equal to 10) = 6/36 = 1/6 or 0.1667 C) sample outcomes for event 3 on one die or both = {(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),(1,3),(2,3), (4,3),(5,3),(6,3)} P(3 on one die or both die) = 11/36 or 0.3056
Multi step equation: -8(2-3x)=104
What is 2.87 rounded to the nearst tenth