To find the solutions of quadratic equation, there are two ways to do which are:
FactorizeQuadratic FormulaStep 1
- Factor the expression.
To factor the expression, refer below:
[tex] \displaystyle \large{ (x - a)(x - b) = {x}^{2} - bx - ax + ab}[/tex]
For bx and ax, both can be common-factored. Therefore
[tex] \displaystyle \large{ (x - a)(x - b) = {x}^{2} - (b + a)x + ab}[/tex]
From the above, we conclude that:
The middle term is b+aThe last term is a×bThus, we have to find two numbers that satisfy a+b and a×bFrom the expression, 30 comes from 5×6 and when 5-6 = -1. Therefore, a can be 5 and b can be 6.
[tex] \displaystyle \large{{x}^{2} - x - 30 = (x + 5)(x - 6)}[/tex]
Because in the middle term, it is -x which is negative, we have to let the highest number become negative.
From the factored expression:
The middle term = 5x + (-6x) = -xThe last term = 5 × (-6) = -30Then we replace the standard equation with factored form.
[tex] \displaystyle \large{ (x + 5)(x - 6) = 0}[/tex]
For this part, we solve like a linear equation where we isolate x. Just think you are solving two linear equations!
Hence
[tex] \displaystyle \large{ x = - 5, 6}[/tex]
Therefore, the solutions are x = -5, 6.
Brent needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle?
Two right triangles are attached along their longest side. The smaller triangle has height 6 cm and base 2 cm. The height of the larger triangle is 9 cm and its base is 5 cm.
4.5 cm2
8.5 cm2
16.5 cm2
33.0 cm2
9514 1404 393
Answer:
(c) 16.5 cm^2
Step-by-step explanation:
The area of each triangle is given by the formula ...
A = 1/2bh
Smaller triangle area = (1/2)(2 cm)(6 cm) = 6 cm^2
Larger triangle area = (1/2)(5 cm)(9 cm) = 22.5 cm^2
The difference in area is ...
22.5 cm^2 -6 cm^2 = 16.5 cm^2
The sum of 5 abd twice a number
Answer:
5+2x
Step-by-step explanation:
Find the area of the triangle.
A. 19.2 yd²
B. 9.3 yd²
C. 8.5 yd²
D. 17.1 yd²
Answer:
8.5 yd sq.
Step-by-step explanation:
[tex]area \: of \: triangle = \frac{1}{2} \times \sin(156) \times 6 \times 7 \\ = 0.41 \times 21 \\ = 8.5[/tex]
Jenna has
131
131131 dog biscuits. She wants to give them as gifts to each of her
4
44 poodles.
Hi! I'm happy to help!
To solve for how many biscuits each poodle gets, we have to split or divide the amount of biscuits by the amount of poodles. (We will use division)
131,131,131÷444
295,340.3851... rounded to 295,340
So, each poodle will receive 295,340 dog biscuits. (A LOT)
I hope this was helpful, keep learning! :D
the eleventh term of an A.P 25 and its first term -3 find its common difference
Determine the simple interest. The rate is an annual rate. Assume 360 days in a year.
p = $390, r=6.25%, t = 2.75 years
HERE
The simple interest is $0
(Round to the nearest cent as needed.)
9514 1404 393
Answer:
$67.03
Step-by-step explanation:
The interest formula is ...
I = Prt
Using the given values, we have ...
I = $390·0.0625·2.75 = $67.03125 ≈ $67.03
The simple interest is $67.03.
_____
Additional comment
Here, the time period is given in years. The number of days per year is only relevant if the time period is given as a number of days or other sub-unit of a year.
Find LCM for the following usin devision method
a. 200
Answer:
l.c.m of 100,150,200
Step-by-step explanation:
What is the difference?
2x+5 3x+ 5 X+ 1
x² – 3x X² – 9x x²-g
Answer:
(x + 5)(x + 2) / (x³ - 9x)
Step-by-step explanation:
We need to find a common denominator.
factor each denominator
x² - 3x = x(x - 3)
x³ - 9x = x(x² - 9) = x(x + 3)(x - 3)
x² - 9 = (x + 3)(x - 3)
As the factors of the first and third denominators are subsets of the second, the second is the LCD. This immediately eliminates the last two options as possible solutions.
Now we multiply each term by the missing factor over itself (1)
(2x + 5)(x + 3) - (3x + 5) - (x + 1)(x)]
(x² - 3x)(x + 3) (x³ - 9x) (x² - 9)(x)
[(2x² + 11x + 15) - (3x + 5) - (x² + x)] / (x³ - 9x)
[2x² + 11x + 15 - 3x - 5 - x² - x] / (x³ - 9x)
(x² + 7x + 10) / (x³ - 9x)
(x + 5)(x + 2) / (x³ - 9x)
I will mark brainliest!!
Answer:
Fareed
Step-by-step explanation:
All the other people have complications that won't let them be on every floor, but Fareed can.
What’s equivalent to this
Answer:
a^(m-n)
Step-by-step explanation:
We have
a^m / a^n
Exponent rules state that
a^m / a^n = a^(m-n)
36. What number shows a temperature of 9° below zero?
Answer:
-9*
Step-by-step explanation:
1. anything below zero is negative
2.if you say a positive temperature such as this example (9) then say below zero it is is always going to be a negative temperature
A temperature of 9° below zero is represented by the number -9.
The negative sign indicates that the temperature is below zero on the Celsius or Fahrenheit scale. It means that the actual temperature is 9 degrees lower than the freezing point of water. For example, if the freezing point is 0°C, a temperature of -9°C would indicate that it is 9 degrees below freezing.
Similarly, on the Fahrenheit scale, a temperature of -9°F would indicate that it is 9 degrees below the freezing point of 32°F. Negative temperatures signify colder conditions than the reference point of zero degrees.
Therefore, a temperature of 9° below zero is represented by the number -9.
Learn more about temperature here
https://brainly.com/question/12800812
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evaluate the expression when b=5
Answer:
8. 10
11. 10
Step-by-step explanation:
put 5 instead of b
8. (15 - b)
= (15-5)
= (10)
11. b +b
= 5 +5
= 10
Solve the system using a matrix.
3x -y + 2z =7
6x -10y + 3z =12
x – y + 4z = 9
([?],[ ], [ ] )
Give your answer as an ordered triple.
Answer:
(1, 0, 2)
Step-by-step explanation:
[3 -1 2 | 7 ]
|6 -10 3 | 12|
[1 -1 4 | 9 ]
To the first row, add -3 times the values of the third row
To the second row, add -6 times the values of the third row
[0 2 -10 | -20 ]
|0 -4 -21 | -42 |
[1 -1 4 | 9 ]
To the second row, add 2 times the values in the first row
[0 2 -10 | -20 ]
|0 0 -41 | -82 |
[1 -1 4 | 9 ]
z = -82 / -41
z = 2
2y - 10(2) = -20
y = 0
x - 0 + 4(2) = 9
x = 1
Find the place value of 7 in 374596
Answer:
It is tens
Step-by-step explanation:
3 » ones
[tex]{ \boxed{ \sf{7 \: » \: tens}}}[/tex]
4 » hundreds
5 » thousands
9 » ten thousands
6 » hundred thousands
What is the y-intercept of the graph of the equation ?
Answer:
Step-by-step explanation:
It is the point where the graph passes through the y-axis.
So if it passes through the point where y = 2, the y-intercept is (0, 2) - note the x coordinate is 0 at this point.
If we are asked to find the y-intercept of the graph of the equation y = 3x - 4
we put x = 0 and work out y as follows:
y = 3(0) - 4 = 0 - 4
y = -4
so the y-intercept is (0, -4).
If TU = 13x − 1, UV = 6x − 2, and TV = 18x + 15, what is TV?
Answer:
303
Step-by-step explanation:
13x + 1 + 6x - 2 = 18x + 15
19x - 1 = 18x + 15
19x = 18x + 16
x = 16
18(16)+ 15
288 + 15
303
(root 5ab2) where a =5 and b= 2
sorry pls ignore this answer
but I think it's 10
[tex]\\ \sf\longmapsto \sqrt{5 {ab}^{2} } \\ \\ \sf\longmapsto \sqrt{5 \times 5 \times {2}^{2} } \\ \\ \sf\longmapsto \sqrt{25 \times 4 } \\ \\ \sf\longmapsto \sqrt{100} \\ \\ \sf\longmapsto 10[/tex]
Suppose y varies inversely with x, and y = -1 when x = 6. What inverse variation equation relates x and y?
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
a. y = 6/x
b. y = -12x
c. y= -6x
d. y= -6/x
Answer:
[tex]\displaystyle \text{d. }y=\frac{-6}{x}[/tex]
Step-by-step explanation:
If two values [tex]x[/tex] and [tex]y[/tex] are inversely proportional, their product is always some maintained constant (the product of [tex]x[/tex] and [tex]y[/tex] is always maintained). This way, if one goes up, the other must go down by the same extent. By definition, this represents an inversely proportional relationship.
Therefore, we can simply find this constant by multiplying the given values of [tex]x[/tex] and [tex]y[/tex]:
[tex]xy=k,\\6\cdot (-1)=-6[/tex]
The constant [tex]-6[/tex] must be maintained as the product of [tex]x[/tex] and [tex]y[/tex] for all values of [tex]x[/tex] and [tex]y[/tex] for them to be inversely proportional. Thus, we have the equation:
[tex]xy=-6[/tex]
Divide both sides by [tex]x[/tex] to isolate [tex]y[/tex]:
[tex]\boxed{y=\frac{-6}{x}}[/tex]
Answer:
d. [tex]\displaystyle y = \frac{-6}{x}[/tex]
Step-by-step explanation:
The fastest way to do this is to simply plug in whatever the exercise gave to you into each answer choise to figure out which one fits the best.
I am joyous to assist you at any time.
What is the smallest number that has both 8 and 9 as a
factor?
A 72
B 36
C 54
D 48
Answer:
A
Step-by-step explanation:
8 and 9 can go in 72.
Look for the LCM of 72
Answer:
72
Step-by-step explanation:
72 has both 8 and 9 as its factors from the alternatives
Apart from 72,
the available options does not have both 8 and 9 being its factors.
jordan drank 36 ounces of water today , how many cups of water did he drink ?
a. 4.5 cups
b. 9 cups
c. 18 cups
d. 288 cups
answer asapppp 2 .
Answer:
jordan drinks 4.5 cup of water
Black Cab Taxi charges a $4.95 flat rate for a ride in the cab. In addition to that, they charge $0.49 per mile. Katie has no more than $20 to spend on a ride. At most, how many miles can Katie travel without exceeding her spending limit?
Answer:
30 miles.
Step-by-step explanation:
.5x + 5 > 20
x = 30
Please give brainliest if this helped you!
Round this number to the nearest 100,000
927,545
Answer:
900,000
Step-by-step explanation:
rounding is quite simple, the number 927,545, like all numbers, has different number places/values. the number 9 is in the 100,000th place and to round you look at the number in the place to the right of it which is 2. the number 2 is is less than 5 so it can't raise the number 9 to a ten. because of this, it reduces all of the other numbers to 0. leaving you with the number 900,000
PLEASE HELP!!!
Which graph represents the solution set of this inequality?
10c + 5 ≤ 45
Answer:
B
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
c ≤ 4
Interval Notation:
( − ∞ , 4]
What type of angle is it
Answer:
acute
Step-by-step explanation:
Angles between 0 and less than 90 are acute
A 90 degree angle is right
Greater than 90 and less than 180 is obtuse
180 degree angles are straight
45 degrees is less than 90 so it is acute
Answer: acute
Step-by-step explanation: if angle is between 0 and 90 degrees, it is acute
50 Points to correct answer!!!
what is the average rate of change from 2 to 9 of the function represented by the graph?
Answer:
-3/7
Step-by-step explanation:
It is asking to find the slope of the secant line going through points (2,f(2)) and (9,f(9)).
We must find f(2) by looking at the curve at x=2. We should see that y=2 there so f(2)=2.
We must find f(9) by looking at the curve at x=9. We should see that y=-1 there so f(9)=-1.
The slope of a line is calculated by finding the ratio of the change of y to the change of x.
(-1-2)/(9-2)
(-3)/(7)
-3/7
3 3/5 divided by 1/6?
Answer:
10.8
Step-by-step explanation:
3 3/5 divided by 1/6
(3(3/5))/(1/6)
(9/5)/(1/6)
54/5
10(4/5)
10.8
There are 21 red apples and 18 green apples. What is the ratio of green to red apples?
Answer:
A possible can be 7 red apples for every 6 green apples.
Step-by-step explanation:
21 and 18 have a common factor of 3. 21/3 =7 and 18/3=6. So the answer can be 7 red apples for every 6 green apples. Hope this helps
A prisoner is planning to escape from prison! The prison s gate consists of horizontal and vertical bars that are spaced one unit apart so the area of each hole between the bars is 1 x 1. The prisoner manages to remove certain bars to make some bigger holes. Determine the area of the largest hole in the gate after the bars are removed in java
Answer:
2
Step-by-step explanation:
HLP HLP HLP HLP 10 10 10
Answer:
B. [tex]4^{6}[/tex] ÷ [tex]5^{6}[/tex]
Step-by-step explanation:
its a formula
Help??????? Please please help me please
Answer:
17 +158 *55 /45
Step-by-step explanation:
maaf kalo salah