The corresponding roots of the quadratic equations are given.
What are Quadratic Equations?Quadratic expressions are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
1. x² = 49
Find the square root.
x = ±√49 = ±7
2. x² - 27 = 0
x² = 27 = 9 × 3
x = √27 = √(9×3) = √9 × √3 = ±3√3
3. 3x² - 36 = 0
3x² = 36
Divide 3 on both sides.
x² = 12
x = √12 = √(4 × 3) = ±2√3
4. 9x² = 0
x = 0
5. 5x² - 15 = 0
5x² = 15
x² = 3
x = ±√3
6. 2x² - 144 = 0
2x² = 144
x² = 72
x = √72 = √(36 × 2) = ±6√2
7. (x + 3)² = 9
x + 3 = √9
x + 3 = ±3
x = 3 - 3 = 0 and x = -3 - 3 = -6
8. 4x² - 100 = 0
4x² = 100
x² = 25
x = ±√5
9. 5x² = 40
x² = 8
x = √8 = √(4 × 2) = ±2√2
10. 3x² - 12 = 0
3x² = 12
x² = 4
x = ±2
11. (x - 5)² = 121
x - 5 = √121
x - 5 = ±11
x = 11 + 5 = 16 or x = -11 + 5 = -6
Hence the solutions are found.
Learn more about Quadratic Equations here :
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You pay $80 for a game system. The monthly rental fee for games
is m dollars. Your cost for the year is $188. Using the equation
12m + 80 = 188, how much is your monthly fee?
Answer: 9
Step-by-step explanation:
12m + 80 = 188
-80 - 80
12m = 108
12m = 108
12 12
m = 9
plzzz help!!
Order the following from greatest to least.
Answer:
I think the answer is C
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
122%=122% 49/29=169% 26/15=173%, 1.98=198%
joyce is y years old.she is 10 years older than peter . what will be the sum oftheir ages ij 5 years time?
Employees at a company are given £800 to spend on items for the office.
They decide to buy a coffee machine and as many bean bags as possible.
Bean bags cost £40 with an offer of "Buy at least 10 get 10% off the price."
The coffee machine costs £310.
How much will they have left over from the £800?
Answer:51273.816238
Step-by-step explanation:
Answer:
they have 490 to buy bean bags
If there is no discount, the amount they can buy is 490/40=12,25>10, so they will get a discount
call the bean bag is X we have: X*40*(100%-10%) ≤ 490
⇒X≤13,6
they can buy at most 13 bag and they will have left 490-40*13*90%=22
Step-by-step explanation:
A rental car agency charges $220 per week plus $0.15 per mile to rent a car. How many miles can you travel in one week for $340?
The number of miles you can travel in one week for $340 is ?.
Answer:
800 miles
Step-by-step explanation:
You would make the equation .15x+ $200 and put that equal to 340 to get the equation:
.15x+$200=340
-$200 (subtract the like term first)
.15x=120
.15x over 120
Your answer comes out to be x=800.
What is the sample space for a spinner with four equal sections, numbered 1 to 4?
A. 1, 2, 3, 4
B. 4-1. 4-2. 4-3. 4-4
C. 1-1,1-2, 1-3, 1-4
D. 1, 2, 3, 4, 5
PLEASE HELP
Answer:
A. 1, 2, 3, 4
Step-by-step explanation:
I. When sample space means all possible case could happend.
In this case we have 4 equal sections numbered 1 to 4.
So from 1st section to 4th sections could happend fairly.
That makes 1, 2, 3, 4 is the right answer.
Hope that help :)
Which of the following is an even function?
Of(x) = (x - 1)2
O f(x) = 8x
Of(x) = x2 - x
O f(x) = 7
Answer:
f(x) = 7
Step-by-step explanation:
In an even function of x, all powers of x are even (2, 4, 6, etc.).
In this case we have f(x) = 7, or 7x^0, which is an even function because the power (0) of x is even.
Help pls I’ll mark as brainliest!!
(d) 2 and 3 because they each have three terms.
Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern lighthouse and N 21o E from the southern lighthouse, how much closer is the closest lighthouse to the boat than the lighthouse furthest away? The northern lighthouse is 51.3 miles closer than the southern lighthouse. The northern lighthouse is 24.4 miles closer than the southern lighthouse. The northern lighthouse is 79.9 miles closer than the southern lighthouse. The northern lighthouse is 17.0 miles closer than the southern lighthouse.
Answer:
The northern lighthouse is approximately [tex]24.4\; \rm mi[/tex] closer to the boat than the southern lighthouse.
Step-by-step explanation:
Refer to the diagram attached. Denote the northern lighthouse as [tex]\rm N[/tex], the southern lighthouse as [tex]\rm S[/tex], and the boat as [tex]\rm B[/tex]. These three points would form a triangle.
It is given that two of the angles of this triangle measure [tex]40^{\circ}[/tex] (northern lighthouse, [tex]\angle {\rm N}[/tex]) and [tex]21^{\circ}[/tex] (southern lighthouse [tex]\angle {\rm S}[/tex]), respectively. The three angles of any triangle add up to [tex]180^{\circ}[/tex]. Therefore, the third angle of this triangle would measure [tex]180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}[/tex] (boat [tex]\angle {\rm B}[/tex].)
It is also given that the length between the two lighthouses (length of [tex]\rm NS[/tex]) is [tex]75\; \rm mi[/tex].
By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, [tex]\angle {\rm B}[/tex] is opposite to side [tex]\rm NS[/tex], whereas [tex]\angle {\rm S}[/tex] is opposite to side [tex]{\rm NB}[/tex]. Therefore:
[tex]\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}[/tex].
Substitute in the known measurements:
[tex]\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}[/tex].
Rearrange and solve for the length of [tex]\rm NB[/tex]:
[tex]\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}[/tex].
(Round to at least one more decimal places than the values in the choices.)
Likewise, with [tex]\angle {\rm N}[/tex] is opposite to side [tex]{\rm SB}[/tex], the following would also hold:
[tex]\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}[/tex].
[tex]\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}[/tex].
[tex]\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}[/tex].
In other words, the distance between the northern lighthouse and the boat is approximately [tex]30.73\; \rm mi[/tex], whereas the distance between the southern lighthouse and the boat is approximately [tex]55.12\; \rm mi[/tex]. Hence the conclusion.
BRAINLIEST ASAP!!!!!!!!!! Please someone help
Tìm giá trị nhỏ nhất của hàm số: y = cos 2x + 4cos x - 3
Answer:
upp7fpfpzfpufpufpufpufpu
Step-by-step explanation:
uxcicicovovovovovvNC coordinatorby McKnight
Can someone please help me
The last option; intersecting, but not perpendicular
If anything is wrong and the answer to x-coordinate of vertex
Answer:
................hfgmehshshdhdjwieir
Which statement about the function y = −14x − 2 is true?
Answer:
slope is -14
X int. X is at 1/7
y int. y is at -2
Step-by-step explanation:
If you graph it you will see.
whats x+10<6 as a inequality sign?
Answer:
x < -4
Step-by-step explanation:
x + 10 < 6
-10 < -10
x < -4
The first one to answer gets brainy
I need these ASAP………..
Step-by-step explanation:
1) 3x - 4 = 86 + 24
→ 3x - 4 = 110
→ 3x = 110 + 4 = 114
→ x = 114/3 = 38
therefore, value of x is 38.
2) -10x = 30 + 90
→ -10x = 120
→ x = 120/10 = 12
→ x = 12
therefore, value of x is 12.
3) -8x + 23 + 51 = 130
→ -8x + 74 = 130
→ -8x = 130 - 74
→ -8x = 56
→ x = 56/8
→ x = 7
therefore, value of x is 7.
4) -9 + 2x = 59 + 90
→ -9 + 2x = 149
→ 2x = 149 + 9
→ 2x = 158
→ x = 158/2 = 79
→ x = 79
therefore, value of x is 79.
hope this answer helps you dear...take care !
What is the time on this clock?
Answer:
11:53 ish.
Step-by-step explanation:
Dave ran 10km in 40 minutes. He rested for 5 minutes then ran a further 8 km in 35 minutes.Work out his average speed for the whole journey. (Give your answer in km/h)
Answer:
27/2 km/hr
Step-by-step explanation:
8/x = 2x+1 Solve this pls
(calculus) please help! will mark brainliest!
Hello friend,
The answer to your question is attached in the image uploaded by me. Please refer them.
✍️ By Benjemin ☺️
2 complementary angles are in the ratio 3:6. Find the angles
Answer:
The angles are 60°, and 30°
Step-by-step explanation:
Complementary angles add up to 90°
3 = 6 = 9
90/9 = 10
10 * 3 = 30
10 * 6 = 60
-Chetan K
Can someone pls help me
Pls get it right.
Using Pythagorean theorem
[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]
[tex]\\ \sf\longmapsto P^2=8^2-(4\sqrt{3})^2[/tex]
[tex]\\ \sf\longmapsto P^2=64-48[/tex]
[tex]\\ \sf\longmapsto P^2=16[/tex]
[tex]\\ \sf\longmapsto P=4[/tex]
________
[tex] \: [/tex]
a² = c² - b²
a² = 8² - (4√3)²
a² = 64 - 48
a² = 16
a = √16
a = 4
I NEED HELP
Line a and line c are perpendicular and m<26 = (5x+7). Find the value of x.
Answer in fraction form = 83/5
Answer in decimal form = 16.6
==================================================
Explanation:
All eight angles shown are 90 degrees since lines a and c are perpendicular to each other. Perpendicular lines form right angles.
Set 5x+7 equal to 90 and solve for x
5x+7 = 90
5x = 90-7
5x = 83
x = 83/5 is the fraction form of the answer
x = 16.6 is the decimal form of the answer
Answer:
83/5 = 16.6
Step-by-step explanation:
5x+7 = 90
5x = 90-7 subtract 7 from both sides.
5x = 83
x = 83/5 = 16.6
PLEASE PLEASE HELP WILL GIVE BRAINIEST AND ALOT OF POINTS PLEASE SHOW WORK TOO
a rectangle has a width of 1.75x+6.8 and a length of -3.5y - 2.7, find the perimeter
Answer:
3.5x + 13.6 - 7y -5.4
Step-by-step explanation:
Perimeter is equal to 2 times the sum of the length and width
2(1.75x+6.8-3.5y-2.7) = 3.5x + 13.6 - 7y -5.4
A building is 240 feet tall. On a scale drawing, 1/4 inch = 10 feet. What is the height of the building in the scale drawing?
15 in
9 in
60 in
13 in
Help Pleaseee
Answer:
60 in = 240 ft
Step-by-step explanation:
240/4 = 60
—
15 x 4 = 60
9 x 4 = 36
60 x 4 = 240
13 x 4 = 52
HEEELP PLEASE
A company prepares a graph of its profit forecast. The annual budget predicts monthly income of at least $5000 more than expenditures.
What inequality models this situation?
Let x represent the expenditures in dollars for a given month and let y represent the income in dollars for the same month.
Express your answer as an inequality in slope-intercept form.
Answer:
that's he
ard
Step-by-step explanation:
sole it your seldf fast ⏩ fast food in advance of my head I can you e d f 3
Multifactorial factor: 5x^3-3x^2+3x
Answer: There are two solutions how to get the answer the factor solution and the factor by groupings solution.
Step-by-step explanation:
THE FACTOR SOLUTION
factor x out of 5x^3-3x^2 3x
X(5x^2 - 3x +3)
FACTOR BY GROUPINGS
Group of factors out the greatest common factor (GCF) then combined
X(5x^2 - 3x + 3)
I HOPE IT HELP YOU :)
Pls Help
Use slope-intercept form, y = mx + b, to find the value for the y-intercept (b) of a line that has a slope of 6 and passes through the point (3, –5).
b=
a. -23
b. -14
c. 21
d. 33
What is the new equation written in slope-intercept form?
a. y=6x-23
b. y=6x-14
c. y=6x+21
d. y=6x+33
Answer:
y-intercept: -23
y = 6x - 23
Step-by-step explanation:
Slope: 6
Point (3, -5)
y-intercept: -5 - (6)(3) = - 5 - 18 = - 23
At 1 pm one day the temperature inside a freezer was -20°C
The freezer broke down.
The temperature inside the freezer went up by 4°C every hour after 1pm.
At what time did the temperature inside the freezer reach 0°C?
Answer:
6 p.m.
Step-by-step explanation: