The solutions to the given quadratic equation are (3+√5)/2 and (3-√5)/2.
What is the quadratic formula?Quadratic formula is the simplest way to find the roots of a quadratic equation.
The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.
The given quadratic equation is x²-3x+1=0.
By comparing x²-3x+1=0 with ax²+bx+c=0, we get a=1, b=-3 and c=1.
Now, x= [3±√((-3)² - 4×1×1)]/2×1
= [3±√(9-4)]/2
= (3±√5)/2
So, the solutions to the given equation are (3+√5)/2 and (3-√5)/2.
Therefore, the solutions to the equation are (3+√5)/2 and (3-√5)/2.
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Angle D and Angle F are supplementary. The measure of Angle D is (3x + 5), and the measure of angle F is (2x). What is the measure of Angle D? (It’s not asking for x)
Step-by-step explanation:
Two angles are called suplementary when their measures add to 180 degrees.
D+F= 180
3x+5+2x= 180
5x+5=180
5x= 175
x= 35°
angle D = 3x+5= 3(35)+5= 110°
A preschool has a student to teacher ratio of 5:2 The total number of students and teachers was 56 last year and is 70 this year How many students and teachers were there for each of the two years
Answer:
Step-by-step explanation:
Student : teacher = 5 : 2
Number of students = 5x
Number of teachers = 2x
Last year:
Last year Total = 56
5x+ 2x = 56
7x = 56
x = 56/7
x = 8
Number of students = 5*8 = 40
Number of teachers = 2*8 = 16
This year:Total = 70
5x + 2x = 70
7x = 70
x = 70/7
x = 10
Number of students = 5*10 = 50
Number of teachers = 2*10 = 20
At East Coast Dogs, 9 of the last 18 customers wanted mustard on their hot dogs. Considering this data, how many of the next 8 customers would you expect to want mustard?
Answer:
9
Step-by-step explanation:
because the paragraph is telling you 9 of the 18 customers want mustard on their hot dog so the paragraph is telling you de answer
Answer:
57
Step-by-step explanation:
First, write the experimental probability as a fraction in simplest form.
P(mustard)
=
mustard
total
=
mustard
mustard+other
=
30
30+10
=
30
40
=
3
4
The experimental probability is
3
4
.
We can predict the outcome of the second set of trials by assuming that the ratio will be the same as in the first set of trials. Write a proportion by setting the two ratios equal to each other, then solve.
3
4
=
n
76
3
4
(476)
=
n
76
(476) Multiply both sides by (476)
376
= 4n Simplify
228
= 4n Simplify
57
= n Divide both sides by 4
You would expect 57 of the next 76 customers to want mustard.
What is 26 - 16? Can anyone tell me?
Answer:
10
Step-by-step explanation:
Answer:
26 - 16=10 is your answer
A taxi travels for 30 minutes at a speed of 28 mph. Calculate how far it travles.
Answer:
14 m
Step-by-step explanation:
Speed = 28 mph
Time = 30 minutes = 30/60 = 1/2 hour
Distance = speed * time
= 28 * [tex]\frac{1}{2}[/tex]
= 14 m
Answer:
14 miles
Step-by-step explanation:
Roberta earns $262.50 per week. She works 30 hours per week. How much does she earn per hour
Answer:
292.5
Step-by-step explanation:
Roberta earns $262.50 per week so i added 262.50 and 30 and got 292.5
Ian bought a can of soup to give to his friend.(Ian is cheap) Now he wants to wrap the entire soup can. If the can has a circular base with a diameter of 4 inches and a height of 6 inches, how much wrapping paper will Ian need?
Answer:10inches
Step-by-step explanation:
PMark for Review
5 The Raven Club sold tickets to the local fall festival. On day one, they sold 50 child tickets and 75 adult
tickets and the total was $525. On day two, they sold 45 child tickets and 65 adult tickets and the total
was $460. What was the cost of the adult tickets?
Answer:
Y = 6
Step-by-step explanation:
On the first day of ticket sales the school sold 3 adult ticket and 8 student tickets for a total of $72. The school took in $152 on the second day by selling 7 adult tickets and 16 student tickets. How much is a student ticket?
Day 1: 3x + 7y = 72
Day 2: 7x + 16y = 152
This becomes a system of equations.
3x+8y=72
3x+8y+−8y=72+−8y (Add -8y to both sides)
3x=−8y+72
3x/3 = −(8y+72)/3
X = (-8/3) y + 24
Substitute (-8/3) y + 24 for x in7x+16y=152:
7(-8/3 y + 24) + 16y = 152
-8/3 y + 168 = 152 (Simplify both sides of the equation)
-8/3 y + 168 − 168 = 152 + (−168) (Add -168 to both sides)
-8/3 y = -16
(-8/3 y)/(-8/3 y) = -16/ -8/3 y (Divide both sides by (-8)/3)
y = 6
The locations of Mr. Zavala's house (3, 2) and office (6, 11) are mapped on the coordinate plane below.
his daughter school is 2/3 the distance from his house to his office and lies on the segment shown. What are the coordinates of the school?
Answer: (5,8)
Step-by-step explanation:
2. Which expression is equivalent to 11-4x118?
A.
121-32
B.
11-32
C.
114
D.
1214
find the value of x
7x+2=16
The perimeter of a square is 66.8 cm. What is the side length of the square?
A) What is the equation that models this situation?
B) Use the equation to find the side length of the square.
Answer:
b
Step-by-step explanation:
The measure of EFH is twice the measure of GFH. What is the
degree measure of GFH?
HELP PLEASE I NEED HELP ASAP IM TIMED
Answer:
30 degree's
Step-by-step explanation:
Becuase the rule is GFH(2)+EFH
And GFH+EFH+90 the only solution is 30 and 60.
a model plane has a scale of 1 in: 2 ft. if the real plane is 12 ft tall then how tall is the model plane.
Answer:
6ft tall
Step-by-step explanation:
Given we know that the scale is 1 in 2ft.
Using this information we know we could divide 12/2=6. We also know that we could multiply 2×6=12. Therefore, we know that the model plane is 6ft tall.
I hope this helps!
The top of a building is a cone 10 meters tall with a radius of 4 meters at the base. Round to the nearest hundredth.
Answer:
V = 167.55 m³
Step-by-step explanation:
Given that,
The height of a cone, h = 10 m
Radius of the cone, r = 4 m
It can be assumed to find the volume of the cone. Th formula for the volume of a cone is given by :
[tex]V=\dfrac{1}{3}\pi r^2 h\\\\V=\dfrac{1}{3}\pi \times (4)^2\times 10\\\\V=167.55\ m^3[/tex]
So, the required volume is 167.55 m³.
PLEASE ANSWER THIS ASAP!!!!
Answer:
300
Step-by-step explanation:
→ First substitute the biggest number into it
45% of 300 =
→ Do 45 × 300
13500
→ Divide answer by 100
135
→ Therefore 45% of 300 = 135
what is the distance between (0, -2) and (9, 10) ? please show your work so i can understand thank you
Given:
The two points are (0, -2) and (9, 10).
To find:
The distance between the given points.
Solution:
Distance between the two points is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the above distance formula, the distance between given points is
[tex]d=\sqrt{(9-0)^2+(10-(-2))^2}[/tex]
[tex]d=\sqrt{(9)^2+(10+2)^2}[/tex]
[tex]d=\sqrt{81+(12)^2}[/tex]
On further simplification, we get
[tex]d=\sqrt{81+144}[/tex]
[tex]d=\sqrt{225}[/tex]
[tex]d=15[/tex]
Therefore, the distance between the given points (0,-2) and (9,10) is 15 units.
How would you simplify the expression represented by the diagram below? Four figures. The first consists of 4 squares each labeled 1. The second consists of 2 rectangles each labeled c. The third consists of 2 squares each labeled 1. The fourth consists of one rectangle labeled c.
Based on the description of the diagram, we get simplified expression is 6 + 3c.
Describe Algebraic Expression?An algebraic expression is a mathematical phrase that consists of variables, constants, and arithmetic operations (such as addition, subtraction, multiplication, and division), as well as exponentiation and roots. These expressions are used to represent mathematical relationships and formulas in a concise and standardized way.
Based on the description of the diagram, we can simplify the expression as follows:
There are 4 squares labeled 1, so their total value is 4.
There are 2 rectangles labeled c, so their total value is 2c.
There are 2 squares labeled 1, so their total value is 2.
There is 1 rectangle labeled c, so its value is c.
Therefore, the expression represented by the diagram simplifies to:
4 + 2c + 2 + c
6 + 3c
So the simplified expression is:
6 + 3c.
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Write the equation of the line in slope-intercept form that passes through the following points:
(-5, 6) and (-2, 1)
a) Slope:
b) Y-Intercept:
c) Equation in Slope Intercept Form:
Answer:
the slope is -1 2/3
The y-intercept is -1.4
The equation in y = mx + b form is
y = –5/3x - 2 1/3
Step-by-step explanation:
-x + 6y = -8
x-6y=8
Answer:
inifinitely many solutions
Step-by-step explanation:
HELP!!!!!!!If a 0.27 cm long crystal appears to be 13.5 cm long under a
microscope, what is the power of the microscope?
Answer:
50 times magnification
Step-by-step explanation:
13.5/0.27
What is the mean?
-9 -9 -3 -6 -7
Answer:
-6.8
Step-by-step explanation:
To find the mean, you add all the numbers together, then divide that number by the amount of numbers there were, so:
-9 + -9 + -3 + -6 + -7 = -34
-34/5 = -6.8
Yoooo, if you gave me brainliest that would be pretty pog. Because as it turns out, only a small percentage of the people I answer actually give me brainliest. I'm trying to get Virtuoso by the end of the day, and you giving me brainliest would really help out. Also while you're at it leave a thanks and a 5-star rating to help boost this answer in the brainly algorithm.
Mhanifa please help! This is due in 1 hour! I will mark brainliest! Random answers will be reported
Answer:
m∠M = 33°Step-by-step explanation:
Given
ΔXYZ ≅ ΔMNLCorresponding angles are congruent:
∠X≅∠Mm∠X = m∠Mm∠X = 33° ⇒ m∠M = 33°given: y is the midpoint of xz
prove: xy = 1/2xz
Answer:
yes im pretty sure that is correct
SHOPPING Ramos went to a pizza shop and spent half of
his money on lunch. If Ramos had $4.50 left after lunch,
how much money did he have originally?
EE
THE
HELSE
TELEP
Help i need it quick
Keylina used 8 cups of chocolate chips to make 4 batches of muffins. Which of the following rates represent the cups of chocolate chips per batch of muffins?
2 cup per batch.
8 ÷ 4 = 2
Find y. Simplify completely.
y=√9+√25
3+5
=8
division is addition
What does to solve the equation x - 2 = 9 (hint: you would need to subtract 2) form both sides of the equation am I correct?
Answer:
I think the answer to X = 11.
Step-by-step explanation:
X - 2 = 9, correct?
11 - 2 = 9.
I hope this can help! Please correct me
if i got it wrong. :D
please help ..............
Answer:
3/1
Step-by-step explanation:
Line is passing through the points (0, 0) and (1, 3)
Slope of the line
[tex] = \frac{3 - 0}{1 - 0} \\ \\ = \frac{3}{1}[/tex]
which statement correctly describes the rage of change between hours studied and corresponding test scores of the two students?
A. Jake’s test scores increased by 1 point more than Howie’s test scores for each hour studied.
B. Jake’s test scores increased by 3 points more than Howie’s test scores for each hour studied.
C. Howie’s test scores increased by 1 point more than Jake’s test scores for each hour studied.
D. Howie’s test scores increased by 3 points more than Jake’s test scores for each hour studied.
Answer:
A. is ur answer
Step-by-step explanation:
the rate of change for Jack is 7 points increased for each additional hour studied and the rate of change for Howie is 6 points increased per hour so 7-6 is equal to 1.
hope this helps <3