Answer:
There are no real solutions to the quadratic equation 5a² - 6a + 10 = 0.
Step-by-step explanation:
We can determine the number of real solutions to a quadratic equation according to the value of its determinant, which is written with the capital letter D.
If pa² + qa + r = 0 and p > 1.
Thus, D = q² - 4pr.
If D > 0, then the equation has 2 real solutions.
If D = 0, then the equation has 1 real solution.
If D < 0, then the equation has 0 real solutions.
We can deduce D from the equation 5a² - 6a + 10 = 0 by writing the following:
p = 5
q = -6
r = 10
D = q² - 4pr
D = (-6)² - 4(5)(10)
D = 36 - 200
D = -164
D < 0
Since the determinant is negative, the equation 5a² - 6a + 10 = 0 has zero real solutions.
I hope this helps! Sorry if my English didn't really help with having a clearer explanation.
Carlos' school is selling tickets to a spring musical. On the first day of ticket sales the school
sold 6 adult tickets and 12 student tickets for a total of $204. The school took in $79 on the
second day by selling 5 adult tickets and 3 student tickets. What is the price each of one adult
ticket and one student ticket?
Answer:
Adult ticket = $8
Student ticket = $13
Step-by-step explanation:
Hi, to answer this we have to write a system of equations (sales equations)
6x + 12y =204 (first day)
5x +3y =79 (second day)
Where x is the price of each adult ticket and y is the price of each student ticket.
If we multiply the second equation by 4 , and subtract the first equation to the second equation:
20x +12y =316
-
6x + 12y =204
___________
14x = 112
Solving for x:
x =112/14
x = 8
Substituting x=8 on any equation:
5x +3y =79
5(8)+3y =79
40+3y =79
3y =79-40
3y = 39
y =39/3
y = 13
What is the surface area of a cone with a radius of 3 cm and a length of 8 cm
Answer: surface area = 108.8 sq. cm
Step-by-step explanation:
A=πr(r+√h2+r2)
Answer:
108.8cm^2
Step-by-step explanation:
Surface Area
A = πr(r+ √h2+r2)
A= π3 * (3 +1/3) √64 + 9 (+ 3) = sqroot 17 +3 = 20 + (3 x 4) = π32
A= 108.7
Volume
V=πr2h/3
V= π9*8 = π72/3 = 226.28/3
V= 72.4cm^3
Additional
The cone has a radius of 3cm and height of 8cm, find total surface area of the cone.
To begin with we need to find slant height of the cone, which is determined by using Pythagoras, since the cross section is a right triangle.
l2 = h2 + r2
l2 = 64 + 9
l = √(73)
l = 8.54 cm
And the total surface area of the cone is:
SA = πr2 + πrl
SA = π · r · (r + l)
SA = π · 3 · (3 + 8.54)
SA = π x 3 . 11.54
SA = 9.42477796077 x 11.54 = 108.76 cm2
SA = 108.8cm^2
Write the equation of the line with the following characteristics.
a)Parallel to y=7x+2 through the point (0,0)
b)Slope of 2 through the point (0,−3)
c)A horizontal line through the point (0,3)
d)A vertical line through the point (−2,0)
PLZZZZ HELP VERY URGENT
Answer:
y = 7x
y = 2x -3
y = 3
x = -2
Step-by-step explanation:
Slope-intercept form: y= mx+bParallel lines have same slopea)Parallel to y=7x+2 through the point (0,0)
This line will have a form:
y= 7x + bConsidering the given point of (0,0), to find the value of b:
0= 7*0+b ⇒ b =0The line is:
y = 7xb)Slope of 2 through the point (0,−3)
Solving as above:
y= 2x + b-3 = 2*0 + b ⇒ b = -3y = 2x -3c)A horizontal line through the point (0,3)
A horizontal line will have constant value for y for any value of x:
y = 3d)A vertical line through the point (−2,0)
A vertical line will have constant value of x for any value of y:
x= -2solve for x in 4x-4/x+4=10
Answer:
-22/3 =x
Step-by-step explanation:
(4x-4) /(x+4) = 10
Multiply each side by (x+4)
(4x-4) /(x+4) * (x+4) = 10 * (x+4)
(4x-4) = 10 * (x+4)
Distribute
4x-4 = 10x+40
Subtract 4x from each side
4x-4-4x = 10-4x+40
-4 = 6x+40
subtract 40 from each side
-4 -40 = 6x+40-40
-44 = 6x
Divide each side by 6
-44/6 = -6x/6
-22/3 =x
Answer:
x = -22/3
Step-by-step explanation:
4x - 4 / x + 4 = 10
=> 4x - 4 = 10(x + 4)
=> 4x - 4 = 10x + 40
=> 4x - 10x = 40 + 4
=> -6x = 44
=> x = -44/6
=> x = -22/3
a bus travels at a speed of 80km per hour . what is the distance it travels by 15 mins.
Answer:
The bus will travel 20km within 15 minutes
Step-by-step explanation:
Answer: 20 km
Step-by-step explanation:
Distance = speed / time
To change a decimal to a fraction we route write the digit to the left or to the right of the decimal point over the appropriate power of 10
Answer:
The digit goes to the right of the decimal point
Step-by-step explanation:
If you had [tex]\frac{1}{10}[/tex], you would convert that to 0.1, which is equivalent to the fraction form. The one goes on the right of the decimal point.
The first two terms of a geometric sequence are a1 = 1 and a2 = 3. Find a4, the fourth term of the sequence. Question 1 options: A) 81 B) 27 C) 243 D) 9
Answer:
B)
Step-by-step explanation:
Common ratio = a2/a1 = 3/1 = 3
[tex]a_{n}=ar^{n-1}\\\\a_{4}=1*3^3\\\\ = 27[/tex]
PLEASE HELP ME! WILL MARK BRAINLIEST! I WILL REPORT ABSURD AND INCORRECT ANSWERS!
2. Suppose, 11 numbers are given. When each of them was increased by 1, the sum of their squares did not change. Once again each number is increased by 1. Does the sum of squares change this time, and if so, by how much?
4. Several points were marked on a line after which a point was added between any two neighboring points. This operation was repeated 2 more times, and as a result, there were 65 points on the straight line. How many points were there in the beginning?
Hello, please consider the following.
PART 2
Let's note [tex](x_i)_{1\leq i\leq 11}[/tex] the 11 numbers.
We can write the following
[tex]x_1^2+...+x_{11}^2=(x_1+1)^2+...+(x_{11}+1)^2\\\\=x_1^2+...+x_{11}^2+2(x_1+...+x_{11})+11\\\\\text{So } 2(x_1+...+x_{11})+11 = 0\\\\(x_1+2)^2+...+(x_{11}+2)^2=x_1^2+...+x_{11}^2+4(x_1+...+x_{11})+4*11\\\\\text{As we know that }2(x_1+...+x_{11})+11 = 0\\4(x_1+...+x_{11})+4*11=-11*2+4*11=22[/tex]
So the sum of squares changes by
[tex]\boxed{ \ 22 \ }[/tex]
PART 4
Let's say that we have n points at the beginning.
We will add n-1 points the first time, we will get n + n - 1 = 2n -1 points.
And then, the second time we add 2n - 1 - 1 points and we get
2n - 1 +2n - 2 = 4n - 3.
Finally, we do it a last time, we add 4n - 3 - 1 points and we get 4n - 3 + 4n - 4 points = 8n - 7 and it must be 65.
So, 8n -7 = 65 <=> 8n = 65+7=72 <=> n = 72/8=9
[tex]\boxed{= \ 9}[/tex]
Thank you
help me please i need it !
Answer:
A
Step-by-step explanation:
There is 2 of the same number on the Y
Which phrase describes the algebraic expression B2+7?
the product of 8 and 7 more than a number
the quotient of 8 and 7
8 times the sum of a number and 7
8 times a number plus 7
Answer:
8 times a number plus 7
Step-by-step explanation:
I need help with this question
-30(E+H=50)
-30E-30H=-1500
30E+60H=1950
(add the 2 equations)
0E+30H=450
H=15
(plug H into first equation)
E+15=50
E=35
Can someone help me on these two questions?
Answer:
1. 88 degrees
2. x=8
Step-by-step explanation:
1.
In a hexagon, all of the interior angles must add up to 720 degrees. Therefore:
x+125+120+95+120+172=720
x=88
2.
Since opposite sides of a parallelogram are equal:
2x=x+8
x=3x-16
Let's go with the first equation.
2x=x+8
Subtract x from both sides:
x=8
You can plug this into the second equation to ensure it works:
3(8)-16=8
24-16=8
8=8
Hope this helps!
Answer:
1. 88
2. 48
Step-by-step explanation:
1. The total of the inner angles of the hexagon is 720
95+120+120+172+125=632
720-632=88
2. 2x=x+8
x=8
If we put all the x's in place and add them, the result is: 48
Solve the equation 12 + 2x = 16
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
[tex]12 + 2x = 16[/tex]
[tex]2x=16-12[/tex]
[tex]2x=4[/tex]
[tex]x=2[/tex]
Which expressions are equivalent to -90-60w
Answer:
Two algebraic expressions are equivalent if they always lead to the same result when you evaluate them, no matter what values you substitute for the variables. For example, if you substitute x := 3 in x + x + 4, then you get 3 + 3 + 4, which works out to 10; and if you substitute it in 2x + 4, then you get 2(3) + 4, which also works out to 10.
Step-by-step explanation:
Three dressers are placed side by side one dresser is 2 feet 9 inches wide , another is 2 feet 7 inches wide , and the third 3 feet 11 inches wide . How wide are they combined
Answer:
18 feet 3 inches
Step-by-step explanation:
4 feet 7 inches + 6 feet 11 inches + 6 feet 9 inches =
10 feet 18 inches + 6 feet 9 inches =
16 feet 27 inches =18 feet 3 inches
Answer: 9.25 Feet
Step-by-step explanation:
Step 1: Take all the feet add them together = 7Ft or 84 inches
Step 2: Now add all the inches together to = 27 inches
Step 3: Add 27 + 84 = 111
Step 4: Divide that by 12 cause 1 foot = 12 inches
Step 5: should equal 9.25 :)
A man measured his height and found 5.7 feet. However, after he carefully measured his height a second time, he found his real height to be 5 feet.What is the percent error the man made the first time he measured his height?
Answer:
percentage error = 12.28%
Step-by-step explanation:
5 x 0.14 = 0.7
5 x 1.14 = 5.7
as increase is not the same as error decrease.
We use the same numbers 12.28% = 0.1228.
5.7 x 0.1228 = 0.69996 = 12.28%
5.7 - 0.69996 = 5.00004 foot. As decrease.
And find it is correct.
His error therefore was 12.28% out.
As we work the first numbers 5.7 and can only x by a number to see 5ft
We take 5.7 x 0.1228 and find 0.69996 when taken from 5.7 ft. is unmistakably 5 foot. (5.00004) ft.
Answer:
14%
Step-by-step explanation:
percent error = (experimental measure - real measure)/(real measure) * 100%
percent error = (5.7 ft - 5 ft)/(5 ft) * 100%
percent error = (0.7 ft)/(5 ft) * 100%
percent error = 0.14 * 100%
percent error = 14%
Lines a and b are parallel. If the slope of line a is 3 , what is the slope of line b?
A. -3
B. -1/3
C. 1/3
D. 3
Answer:
D.
Step-by-step explanation:
They are parallel and therefore has the same slope.
If (x – 13) is one factor of x^2– 9x – 52, the other factor is
Lt. Bartlett spent 2 hours doing push ups, 1 hour doing sprints, and 1.5 hours benching 400 lbs. What percentage of time was spent sprinting? please explain how you get the answer, I want to understand on my own and math is a struggle for me.
If Lt. Bartlett spent 2 hours doing push ups, 1 hour doing sprints, and 1.5 hours benching 400 lbs, the percentage of time he spent sprinting is 22.2%.
What is Percentage?Percentage is simply number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
Given that;
Time spent on push ups = 2 hoursTime spent on sprints = 1 hoursTime spent on benching = 1.5 hoursPercentage of time spent sprinting P = ?First we determine the total time.
T = tPUSHUPS + tSPRINT + t BENCHING
T = 2hrs + 1hr + 1.5hrs
T = 4.5hrs
Now, percentage of time spent sprinting P will be;
Percentage = ( Part / Whole ) × 100%
Percentage = ( tSPRINT / Total time ) × 100%
P = ( 1hr / 4.5hr ) × 100%
P = ( 0.2222 ) × 100%
P = 22.2%
Therefore, if Lt. Bartlett spent 2 hours doing push ups, 1 hour doing sprints, and 1.5 hours benching 400 lbs, the percentage of time he spent sprinting is 22.2%.
Learn more about Percentages here: brainly.com/question/24159063
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Angie has a box that is 3/4 of a foot long What fraction is equal to the length, in feet, of the box?
A. 6/12
B. 8/12
C. 9/12
D. 11/12
EXPLAIN AS WELL WHY YOU PICK THAT ANSWER!
Answer:
C.
3 x 3 = 9
4 x 3 = 12
3/3 = 1 so it is equal
3/4 = 9/12
Step-by-step explanation:
Find the coordinates of the image.
Answer:3,-7
Step-by-step explanation:
11. Britney wants to bake at most 0 loaves of bread for a bake sale.
She wants to make banana bread that sells for $1.25 each and
nut bread that sells for $1.50 each and make at least $24 in sales.
Write a system of inequalities for the given situation and
the inequalities.
Answer:
Look at the attachment
Simplify the ratio 9/12 by dividing both the numerator and denominator by the greatest common factor of 3
A) 1/4
B) 1/2
C) 3/4
D) 4/3
Answer:
Option C
Step-by-step explanation:
9/3=3
12/3=4
so, the answer is 3/4
Option C
Answer:
Think of it as 9 / 3 = 3
12 / 3 = 4
so it is 3/4. The ratio is equal because 3/3 = 1 so you are dividing by 1
Hope this helps
Step-by-step explanation:
PLSSSSS HELPPPP!!! A data set has a mean of 72 and a standard deviation of 3.5. The z-score for a data point is -1.2. What is the data point?
Answer:
D. The data point is 2.5 standard deviations away from 0.5.
Step-by-step explanation:
Z-score is the measure of how many number of standard deviations, the data point, is away from the mean. It also measures how many standard deviations below or above the population mean, a raw score is.
Given, a set of data has a mean (μ) of 0.5 and a standard deviation (σ) of 0.01 with a data point of the set has a z-score of 2.5.
i.e the data point is 2.5 standard deviations away from the mean 0.5.
Hope this helped!
The sum of three numbers is 16. The sum of twice the first number, 5 times the second number, and 6 times the third number is 85. The difference between 4 times the first number and the second number is negative 3. Find the three numbers.
Answer:
1, 7, 8Step-by-step explanation:
x, y, z - numbers to find
The difference between 4 times the first number and the second number is negative 3:
4x - y = -3
- y = -3 - 4x
y = 3 + 4x
The sum of three numbers is 16:
x + y + z = 16
x + 4x + 3 + z = 16
5x + z = 13
z = 13 - 5x
The sum of twice the first number, 5 times the second number, and 6 times the third number is 85:
2x + 5y + 6z = 85
2x + 5(3 + 4x) + 6(13-5x) = 85
2x + 15 + 20x + 78 - 30x = 85
-8x + 93 = 85
-8x = -8
x = 1
y = 3 + 4•1 = 7
z = 13 - 5•1 = 8
Veryfying:
1 + 7 + 8 = 16
2•1 + 5•7 + 6•8 = 2 + 35 + 48 = 85
Which of the following relations represents a function?
O A. {(1, 1), (1, 2), (1,3)}
O B. {(1, 1), (2, 1), (3, 1)}
O C. {(1, 1), (2, 2), (3, 3)}
O D. Both B and C.
OPTION NUMBER D IS CORRECT
D.Both B and C.
Step-by-step explanation:
function is the relation from set A to B such that every element of set A(domain) should have only 1 image in Set B(co domain).
5. Which of the following linear functions has a graph which passes through points (−5,−2) and (−3,0)?
options:
A. f(x) = x – 3
B. f(x) = x + 3
C. f(x) = –x + 3
D. f(x) = –x – 3
Answer:
[tex]f(x) = x + 3[/tex]
Step-by-step explanation:
Given
Points (−5,−2) and (−3,0)
Required
Find a linear function that passes through the given points
The question implies that we solve for the equation for the line;
First, the slope of the line must be calculated;
This is calculated as thus:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where [tex](x_1,y_1) = (-5,-2)\ and\ (x_2,y_2) = (-3,0)[/tex]
So, [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes
[tex]m = \frac{0 - (-2)}{-3 - (-5)}[/tex]
[tex]m = \frac{0 + 2}{-3 + 5}[/tex]
[tex]m = \frac{2}{2}[/tex]
[tex]m = 1[/tex]
The equation of the line can then be calculated using any of the given points;
Using
[tex]m = \frac{y - y_1}{x - x_1}[/tex]
[tex]Where\ (x_1,y_1) = (-5,-2)\ and\ m =1[/tex]
We have
[tex]1 = \frac{y-(-2)}{x-(-5)}[/tex]
[tex]1 = \frac{y+2}{x+5}[/tex]
Multiply both sides by x + 5
[tex](x+5)*1 = \frac{y+2}{x+5} * (x+5)[/tex]
[tex]x + 5 = y + 2[/tex]
Subtract 2 from both sides
[tex]x + 5 - 2 = y + 2 - 2[/tex]
[tex]x + 3 = y[/tex]
[tex]y = x + 3[/tex]
Replace y with f(x)
[tex]f(x) = x + 3[/tex]
Hence, from the list of given options; Option B is correct
Answer: B. f(x) = x + 3
Step-by-step explanation:
does anyone know the answer to this ?
Answer:
the horse walked 20 feet away i think
Step-by-step explanation:
i say this because it shows an arrow from a horse to the 20 square feet
Answer:
Step-by-step explanation:
it is a three quarter circle with radius=7.1 ft
reqd. area=3/4 πr²
=3/4×π×7.1²
≈3/4×3.14×7.1²
≈118.72 ft²
The difference between two numbers is 28. The first number is three times the other number. What are the numbers? A. 14 and 42 B. 26 and 42 C. 14 and 14 D. 15 and 43
Answer: the answer is A
Step-by-step explanation:
1st:subtract 42-14=28(the difference)
2nd: divide 42÷14=3
describe to a friend how to graph a point at (2,5)
Answer:
So to start, the first number in the set is usually on the x axis. The x axis is the line going to the right. You go two ticks on there. Next is the second number, so what you do is just go up 5 ticks from there andd there ya go, you graphed it!
Um, I'm not very good at explaining but I hope that makes sense haha. I don't really understand the point of marking brainliest, but if you want you can mark mine it
Taking 1 cm = 1 unit we draw the x-axis and y-axis and plot (2,5) at a distance of 2 from x-axis and distance of 5 from y-axis.
What are the co-ordinates of a point in a graph?A point has two inputs namely the x-coordinate and y-coordinate. The x-coordinate and y-coordinate is the perpendicular distance from y axis and x axis respectively.
Given point is (2,5)
Plot x=2 at a perpendicular distance from y axis measured along positive x axis
plot y=5 at a perpendicular distance from x axis measured along positive y axis
and we get the required point.
The point (2,5) is plotted in the graph attached with the answer.
Learn more about co-ordinates here:
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