Answer:
[tex]x_1=3+2\sqrt{6}[/tex]
[tex]x_2=3-2\sqrt{6}[/tex]
Step-by-step explanation
[tex]\rule{100mm}{0.5mm}[/tex]
[tex]x^2-6x=15[/tex]
[tex]x^2-6x+\left(\dfrac{6}{2}\right)^2-\left(\dfrac{6}{2}\right)^2=15[/tex]
[tex]x^2-6x+3^2=15+3^2[/tex]
[tex]x^2-6x+9=15+9[/tex]
[tex](x-3)^2=24[/tex]
[tex]\sqrt{(x-3)^2} =\sqrt{24}[/tex]
[tex]x-3=\pm2\sqrt{6}[/tex]
[tex]\red{\boxed{x_1=3+2\sqrt{6}}}[/tex]
[tex]\red{\boxed{x_2=3-2\sqrt{6}}}[/tex]
[tex]\rule {100mm}{0.5mm}[/tex]
For the function y =[tex]3x^{2}[/tex]– 2x + 5, what is the output if the input is 4?
A) 9
B) 21
C) 45
C) 51
ill give brainly to first correct answer
Answer:
C
Step-by-step explanation:
The input is the value of x. Substitute x = 4 into y for output
y = 3(4)² - 2(4) + 5 = 3(16) - 8 + 5 = 48 - 8 + 5 = 45
Thus the output is 45 → C
PLZ HELP I TRIED LIKE 20 TIMES AND GOT IT WRONG
Answer:
(5نغنفنفتغن6نغنص7
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54ىكللعغص3تةوعخو
Iggy wants to purchase a six-cylinder sports car that costs $15,690. The dealer is offering either a $3,500 instant rebate or 20%-off discount. Which incentive should Iggy use to pay the lowest price for the car?
Step 1: Find the price after rebate.
$12,190
$12,490
$13,190
$12,552
The numbers 22 and 35 are relatively prime. TrueFalse
Answer: True
Step-by-step explanation:
Answer:
False They are coprime numbersStep-by-step explanation:
I hope it helps ❤❤A rectangular auditorium seats 1855 people. The number of seats in each row exceeds the number of rows by 18. Find the number of seats in each row.
Answer:
53 seats per row
Step-by-step explanation:
Given that:
Capacity = 1855
Let number of rows = x
Hence, Number of seats per row = x + 18
The Area of auditorium = capacity
Area of rectangle = Length * width
1855 = x * (x + 18)
1855 = x² + 18x
x² + 18x - 1855 = 0
x² + 53x - 35x - 1855 = 0
x(x + 53) - 35(x + 53) = 0
(x - 35) = 0 or (x +53) = 0
x = 35 or x = - 53
Hence x = 35 ; (x can't be negative)
Number of seats per row = 35 + 18 = 53
Using a quadratic equation cal
I.Write the algebraic expressions for the following statements:
1. The sum of a and b subtracted from 5.
2. A number added to half of itself.
3. 2 less than 2times of x.
4. Product of numbers m and n added to 7.
5. One-third of the sum p and q subtracted from the product of p and q.
6. A number a multiplied by itself.
Answer:
1. 5 - (a+b)
2. n + 0.5n = 1.5 n
3. 2x - 2
4. 7 + mn
5. pq - (p+q)/3
6. a*a = a^2
Step-by-step explanation:
There are 9 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible?
jackie rode his bike 20 miles per hour for 1 1/2 hours. how far did he ride?
Answer:
30 miles.
Step-by-step explanation:
To calculate distance traveled, you multiply the miles per hour by the number of miles. In this problem, it is 20 times 1.5 or 20 times 1 1/2. This equals 30 miles per hour.
parallel lines, transversal, and algebra really need help
Answer:
1. 58 = 5x-2, 60 = 5x, x = 12
2. 134 = 16x+22, 112 = 16x, x = 7
3. 125 = 7x-1, 126 = 7x, x = 18
4. 133+9x+2 = 180, 9x=45, x=6
5. 8x-77 = 3x+38, 5x = 115, x=23
6. 11x-47 = 6x-2, 5x = 45, x=9
7. 13x-21 = 5x+75, 8x = 96, x=12
8. 5x+3+9x-33 = 180, 14x = 210, x=15
9. 8x-31 = 6x+3, 2x = 34, x=17
5y+35+6(17)+3 = 180, 5y = 40, y = 8
10. 29x-3+15x+7 = 180, 44x = 176, x=4
13y-17+15(4)+7 = 180, 13y = 130, y=10
1. x = 12
2. x = 7
3. x = 18
4. x = 5
5. x = 23
6. x = 9
7. x = 12
8. x = 15
9. x = 17; y = 8
10. x = 4; y = 10
To find the value of each missing variable(s), we would need to apply our knowledge of algebra. However, recall the following rules of angles in parallel lines:
corresponding angles are congruent (i.e. equal to each other)vertically opposite angles are congruent alternate angles are congruent same-side interior angles are supplementary (i.e. sum up to give 180°alternate exterior angles are congruent.Let's solve the given problems as shown below given that line l is parallel to line m:
1. [tex]58 = (5x - 2)[/tex] (corresponding angles)
solve for x
[tex]58 = 5x - 2\\58 + 2 = 5x - 2 +2[/tex] (addition property of equality)
[tex]60 = 5x \\\frac{60}{5} = \frac{5x}{5}[/tex](division property of equality)
[tex]12 = x\\x = 12[/tex]
2. [tex]134 = 16x+22[/tex] (alternate exterior angles)
[tex]\\134 - 22 = 16x +22-22[/tex] (subtraction property of equality)
[tex]134 - 22 = 16x +22-22\\112 = 16x\\\frac{112}{16} = \frac{16x}{16}[/tex](division property of equality)
[tex]7 = x\\x = 7[/tex]
3. [tex]7x - 1 = 125[/tex] (alternate angles)
[tex]7x - 1 + 1 = 125 + 1\\7x = 126\\\frac{7x}{7} = \frac{126}{7} \\x = 18[/tex]
4. [tex](9x+2) + 133 = 180[/tex] (same-side interior angles)
[tex]9x+2 + 133 = 180\\9x + 135 = 180\\9x + 135 - 135 = 180 - 135\\9x = 45\\\frac{9x}{9} = \frac{45}{9} \\x = 5[/tex]
5. [tex]3x+38 = 8x-77[/tex] (alternate exterior angles)
[tex]77 + 38 = 8x - 3x\\115 = 5x\\\frac{115}{5} = \frac{5x}{5} \\23 = x\\x = 23[/tex]
6. [tex]6x-2 = 11x-47[/tex] (corresponding angles)
[tex]6x-2 = 11x-47\\47 - 2 = 11x - 6x\\45 = 5x\\x = 9[/tex]
7. [tex]5x+75 = 13x - 21[/tex] (alternate angles)
[tex]5x+75 = 13x - 21\\21 + 75 = 13x - 5x\\96 = 8x\\12 = x\\x = 12[/tex]
8. [tex](5x+3)+(9x-33)= 180[/tex] (same-side interior angles)
[tex]5x+3+9x-33= 180\\14x - 30 = 180\\14x - 30 + 30 = 180 + 30\\14x = 210\\x = 15[/tex]
9. [tex]8x-31 = 6x+3[/tex] (alternate angles)
[tex]8x - 6x = 31 + 3\\2x = 34\\x = 17[/tex]
Solve for y
[tex](5y + 35) + (6x + 3) = 180[/tex] (same-side interior angles)
[tex]5y + 35 + 6x + 3 = 180\\[/tex]
Plug in the value of x
[tex]5y + 35 + 6(17) + 3 = 180\\5y + 35 + 102 + 3 = 180\\5y + 140 = 180\\5y = 180 - 140\\5y = 40\\y = 8[/tex]
10. [tex](29x-3)+(15x+7) = 180[/tex](supplementary angles)
Solve for y
[tex]13y - 17 = 29x - 3[/tex] (alternate exterior angles)
Plug in the value of x
[tex]13y - 17 = 29(4) - 3\\13y - 17 = 116 - 3\\13y - 17 = 113\\13y = 113 + 17\\13y = 130\\y = 10\\[/tex]
Learn more about parallel lines here:
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How many baby's does it take to paint a wall
Answer:
12 I think?
Step-by-step explanation:
The answer to the famous joke is "It depends on how hard you throw them." It's important to note that this joke is dark humor and can be considered offensive or inappropriate.
It plays on a shocking and insensitive idea, which is why it's not suitable for all audiences. Jokes like this should be used with extreme caution, as they can cause discomfort or distress to others.
Humor should be inclusive and respectful of everyone's feelings and sensitivities. While jokes can be a form of entertainment, it's essential to choose them wisely and be mindful of their potential impact on others. In most social settings, it's best to avoid jokes that involve sensitive subjects or potentially harmful content.
To know more about dark humor, click here.
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------------The given question is incomplete, the complete question is:
"What is the answer to the famous joke, "How many babies does it take to paint a wall?"---------------
a company dyes two sizes of rugs a small rug requires 8 hours for dyeing and a medium-sized rug requires 12 hours of dyeing the dryers have to make at least 22 guys ansld that must do it in less than 240 hours let x equal small rugs abd u equal medium rugs state a possible ordered pair solution for the system of inequalities justify mathematically using both inequalities
Answer:
C says 8x+12y, but D says 12x+8y, instead of 8x and 12y. The correct answer is C, I guess
Step-by-step explanation:
Let x=small rugs and y=medium rugs. It takes 8 hours to dye a small rug, so you would write 8x. It takes 12 hours to dye a small rug, so you would write 12y. Those two would need to be added together. The dyer needs to dye at least 22 rugs in 240 hours, so you would need a less than or = to sign.
I'm not sure which choice has the line beneath, indicating that the sign is a "less than or equal to" sign, but the answer is gonna be either C or D.
8x+12y≤240, or 12y+8x≤240
State whether the equation represents a linear or a nonlinear function. Explain y=7(x--8)
Answer: Is this for nine grade
Step-by-step explanation:
Complete the proof!!!
Answer:
The correct options are;
1. Definition of supplementary angles
2. m∠1 + m∠2 = m∠1 + m∠3
3. m∠2 = m∠3
4. Definition of congruent angles
Step-by-step explanation:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠1 and ∠2 are supplementary [tex]{}[/tex] Given
∠1 and ∠3 are supplementary [tex]{}[/tex]
2. m∠1 + m∠2 = 180° [tex]{}[/tex] (1) Definition of supplementary angles
m∠1 + m∠3 = 180°
3. (2) m∠1 + m∠2 = m∠1 + m∠3 [tex]{}[/tex] Transitive Property
4. (3) m∠2 = m∠3 [tex]{}[/tex] Subtraction property of equality
5. ∠2 ≅ ∠3 [tex]{}[/tex] (4) Definition of congruent angles
Given that angles ∠1 and ∠2 are supplementary, we have, ∠1 + ∠2 = 180°
Given that angles ∠1 and ∠3 are also supplementary, we also have, ∠1 + ∠3 = 180°
∴ ∠1 + ∠2 = 180° = ∠1 + ∠3
∠1 + ∠2 = ∠1 + ∠3
∠1 + ∠2 - ∠1 = ∠1 + ∠3 - ∠1
∴ ∠2 = ∠3
∴ ∠2 ≅ ∠3, by definition of congruent angles.
A customer opens a checking account and a savings account at a bank. They will deposit a maximum of $600, some in the checking account and some in the savings account. (They might not deposit all of it and keep some of the money as cash.)
Write an inequality to describe the constraints. Specify what each variable represents.
Write the inequality
Answer:
x +y [tex]\leq \\[/tex] 600
Step-by-step explanation:
plz help i will mark you as brainlist
Answer:
C. Six is to the left of the zero and negative six is to the right.
Step-by-step explanation:
Simple, think of a number line and zero is in the middle, to the left there is positive numbers, like six, and to the right there is negative six.
Determine if this is a function or not based on the graph
O yes
O no
Answer:
yes
Step-by-step explanation:
brainiest plz
Find two consecutive whole numbers that the square root of 85 lies between.
9514 1404 393
Answer:
9, 10
Step-by-step explanation:
It helps if you're familiar with the squares of small integers.
9^2 = 81
(√85)^2 = 85
10^2 = 100
The square root of 85 lies between 9 and 10.
_____
Of course, you can find this answer using your calculator:
√85 ≈ 9.2195, a number between 9 and 10
Find the value of x please
Step-by-step explanation:
In isoceles triangle two sides are equal and two angles are equal.
Then,
∠R = ∠T = (5x-40)°
Then,
∠RTS + ∠STU = 180° (bcoz it lies on a straight line)
(5x-40) ° + 5x = 180°
10x = 220°
x = 22°
Therefore,
Option A is correct✔
consider the following equation x+4/x-6+3/2x+5=7 What are the constraints on x? Select all that apply.
if anyone knows pls help!!! will give the brainliest!!
Answer:
I think A would be the right answer.
Answer:
A)
Step-by-step explanation:
V: y = -4; H: x = -6
hope it helps!
confused on this plz help real quick
Im sorry i cant help but if it lets you try to copy paste the question onto whatever you can
A three-and-a-half foot stick is cut into two pieces. One piece is
1.65 ft long. How long is the other piece?
Answer:
1.4
Step-by-step explanation:
3.05 is the length of the stick and 1.65 is one part if the stick si we subtract 1.65 from 3.05 to find the length of the other piece
-22 = -11h what does H equal??
Answer:
h = 2
Step-by-step explanation:
-22 = -11h
/-11 /-11
2 = h
hope this helps
Answer:
[tex]h=2[/tex]
Step-by-step explanation:
STEP 1: Rewrite the equation as [tex]-11h=-22[/tex].
[tex]-11h=-22[/tex]
STEP 2: Divide each term by [tex]-11[/tex] and simplify.
[tex]h=2[/tex]
Urgent, please help.
The width of a rectangle is a whole number of centimetres.
The length of the rectangle is 7cm longer than the width.
The perimeter of the rectangle is less than 152cm.
Find the greatest possible width of the rectangle.
I will give whoever answers this 50 points please it’s desperate.
According to the perimeter of the rectangle, it is found that it's greatest possible width is of 34 cm.
What is the perimeter of a rectangle?The perimeter of a rectangle of length l and width w is given by:
[tex]P = 2(l + w)[/tex]
In this problem, the length of the rectangle is 7cm longer than the width, hence l = 7 + w. Considering that the perimeter is less than 152 cm:
[tex]2(l + w) < 152[/tex]
[tex]l + w < 76[/tex]
[tex]7 + w + w < 76[/tex]
[tex]2w < 69[/tex]
[tex]w < 34.5[/tex]
Rounding, it's it's greatest possible width is of 34 cm.
More can be learned about the perimeter of a rectangle at https://brainly.com/question/10489198
Which is greater: 6/30 or 12/40
Answer:
12/40
Step-by-step explanation:
match the denominators so have 6/30 be multiplies with 40/40 and 12/40 multiplied with 30/30
6/30(40/40) = 240/1200
12/40(30/30) = 360/1200
As we can see, 360/1200 is bigger than 240/1200, therefore 12/40 is bigger
Answer: [tex]\frac{12}{40}[/tex]
Step-by-step explanation:
Hey there!
-If we were to simplify [tex]\frac{6}{30}[/tex] we would be able to simplify it to [tex]\frac{1}{5}[/tex].
-Multiply [tex]\frac{6}{30}[/tex] by 100 and you get 20 .
-Now compare that with [tex]\frac{3}{10}[/tex] which is [tex]\frac{12}{40}[/tex] simplified.
-Multiply [tex]\frac{12}{40}[/tex] by 100 and you get 30.
-We can now tell that [tex]\frac{12}{40}[/tex] is greater than [tex]\frac{6}{30}[/tex].
~I hope I helped :)~
what is the distance between piont S (3 -2) and point T (-5, -2)
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Choose ASA, SAA, or neither
to describe this figure.
A
B
ASA
SAA
neither
Answer:
SAA
Step-by-step explanation:
there is a side, and vertical angles equal eachother so it would be SAA
Suppose it takes John 45 minutes to run 4 miles. How long would it take him to run 4 kilometers? Round your answer to the nearest minute
Answer:
28 minutes
Step-by-step explanation:
4 miles = 45 minutes
4 kilometers = (m) minutes
45 ÷ 4= 11.25
4 kilos= 2.48548 miles
2.48548 x 11.25= 27.96165
m = 28 minutes
- I hope this helps have a great day
John will covers 4 km distance in 28 minutes.
What is Rate of change?
A rate is anything that can be measured over time. Common rates include velocity (which is the rate of distance traveled), power (rate of work being done), etc. All these have one thing in common which is that they are all divided by the amount of time it took to obtain a certain measurement.
Here, it is given that John takes 45 minutes to run 4 miles and is known that :
1 mile ≈ 1.61 km
that is for,
4 mile ≈ 6.44 km
John covers 6.44 km in 45 minutes, John will cover 4 km in :
6.44 km ⇒ 45 minutes
1 km ⇒ 45/6.44 minutes
4 km ⇒ 4 x (45/6.44) minutes ≈ 28 minutes
Therefore, John will covers 4 km distance in 28 minutes.
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really confused on this! help is appreciated!!
Is this a function?
nah buddy
Step-by-step explanation: