Answer:
In order to go from the first point to the second, we need to rise from 4 to 7, i.e. by 3. We also need to run from -4 to -2, i.e. by 2. Therefore the slope is 32 .
Step-by-step explanation:
If using the method of completing the square to solve the quadratic equation
x²-10x – 15 = 0, which number would have to be added to "complete the
square"?
Answer:
For quadratic equations that cannot be solved by factorising, we use a method which can solve ALL quadratic equations called completing the square. We use this later when studying circles in plane analytic geometry.
Completing the square comes from considering the special formulas that we met in Square of a sum and square of a difference earlier:
(x + y)2 = x2 + 2xy + y2 (Square of a sum)
(x − y)2 = x2 − 2xy + y2 (Square of a difference)
To find the roots of a quadratic equation in the form:
\displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax
2
+bx+c=0,
follow these steps:
(i) If a does not equal \displaystyle{1}1, divide each side by a (so that the coefficient of the x2 is \displaystyle{1}1).
(ii) Rewrite the equation with the constant term on the right side.
(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.
(iv) Write the left side as a square and simplify the right side.
(v) Equate and solve.
Example 1
Find the roots of x2 + 10x − 4 = 0 using completing the square method.
Answer
Example 2
Solve 4x2 + x = 3 by completing the square.
Answer
Exercises
Solve the following quadratic equations by completing the square
Q1. \displaystyle{2}{s}^{2}+{5}{s}={3}2s
2
+5s=3Answer
Q2. \displaystyle{3}{x}^{2}={3}-{4}{x}3x
2
=3−4xAnswer
Q3. \displaystyle{9}{v}^{2}-{6}{v}-{2}={0}9v
2
−6v−2=0Answer
Q4. \displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax
2
+bx+c=0Answer
1. Solving Quadratic Equations by Factoring
3. The Quadratic Formula
Find the slope for the line that runs through points (2, 5) and (-3, 7)
Answer:
-0.4
Step-by-step explanation:
to solve use the formula m=y2-y1/x2-x1
What is six and eighty-seven thousandths
Answer:
6.087
Step-by-step explanation:
0.000
^ones
^tenths
^hundredths
^thousandths
Answer:
depends how u want ur answer... :|
6.087
6 and 870
Hope that helps! :)
Step-by-step explanation:
what's HCF/GCD of 144 and 0 ?
Answer:
144 =4
=>144=2×2×2×3×3
OK
OK i know this only
enjoy your day
The radius of a circle is 2 inches. What is the circle's area?
r=2 in
Use 3.14 for a
square inches
Answer:
12.56 in.
Step-by-step explanation:
A=Pi*R to the 2nd power
A=3.14*2 to the 2nd power
A=3.14*4
A=12.56
Let me know if im wrong
Area of the circle is 12.56 square units which has radius 2 inches.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that radius of a circle is 2 inches.
We need to find the area of circle.
Radius= 2 inches.
π=3.14
We know that area of circle=πr²
Area of circle=3.142×2²
=3.142×4
=12.56 square inches.
Hence, area of the circle is 12.56 square units which has radius 2 inches.
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Your family has a second car that takes 1 gallon per 25 miles and has 10 gallons to start. Write an equation, identify the y intercept and slope. Please help !
Answer:
Let's use the slope-intercept form of the equation of a line describe the slope and the y-intercept:
y = mx + b where m=slope and b=y-intercept
A machine paints 360 toy boats in 45 MINUTES. Write the expression that represents the unit rate per HOUR
Answer:
480 toy boats per hour
Step-by-step explanation:
1. Divide 360 by 45 to find unit rate per MINUTE.
360 / 45 = 8
2. One hour = 60 minutes, so multiply 8 and 60.
8 * 60 = 480
Find the volume of a cylinder below . The formula for the volume of a cylinder is . The radius of the circle is represented by r and h stands for the height of the cylinder. use 3.14 for pu and round your answers to the nearest tenth
Answer:
The volume of the cylinder V = 942 cm³
Step-by-step explanation:
Step(i):-
Given that the graph
The height of the cylinder (h) = 12cm
The diameter of the cylinder d = 10cm
The radius of the cylinder
d = 2r
r = [tex]\frac{10}{2}[/tex]
r = 5 cm
Step(ii):-
The Volume of the cylinder
V = π r² h
V = π (5)²(12)
V = 300π cubic centimeter
V = 300 × 3.14
V = 942 cm³
Final answer:-
Volume of the cylinder V = 942 cm³
Donna packs 14 pounds of nuts in bags . Each bag has 1/4 pound of nuts Which equation shows the number of bags Donna packed with all the nuts
Answer:
Step-by-step explanation:
Where are the equations to choose from?
14 pounds × (1 bag)/(¼ pound) = 56 bags
30 POINTS!!!!! What is the domain for each function below?
Picture included below!
-For the 1st equation, the options are the greater than/equal to symbol and the less than/equal to symbol, and then 3, -3, and 0.
-For the 2nd equation, the options are the greater than/equal to symbol and the less than/equal to symbol, and 0 and 3.
The domain is the set of input values for which the function is real and defined.
Find non negative values for the radicals.
For y = sqrt(3-x) if x is greater than the 3 the value under the square root would be negative which would result in a non real number.
The answer needs to be x <= 3 ( less than or equal to)
For y = sqrt(3x), if x is less than 0, the number under the sqrt root would be negative resulting in a non real number.
The answer is x >= 0 ( greater than or equal to)
The ratio of coretta's weight to Justin's weight is 3:4. If corretta gains 5 pounds the ratio of their weights will be 4:5. How much does Justin weigh?
Answer:
100 pounds
Step-by-step explanation:
Amjed has 223 cards in his trading card collection. Latif has
8.741 cards in his trading card collection. Using the orders of
magnitude, about how many times more trading cards does Latif
have than Amjed?
Answer:
The orders of magnitude are numbers of the form:
10^n
where n can be any integer number.
So we can write something like:
"A is n orders of magnitude above B
Now we have the quantities:
Amjed cards = 223
Latif cards = 8741
We want to find how many times more trading cards does Latif have than Amjed.
Then we need to look at the quotient between the number of cards of Latif and Amjed.
8741/223 = 39.2
Now we need to approximate this to the nearest 10^n number.
(..., 0.1, 1, 10, 100, 1000, ...)
The nearest one to 39.2 is 10.
So we can say that Latif's collection is 10.
and 10 = 10^1
then n = 1
Then we can say that Latif's collection is one order of magnitude above Amjed's collection.
The graph shows depth of water in a tank over time.
Calculate the rate at which the depth is decreasing.
Give your answer as a decimal.
PLEASE HELP ASAP!!!
x+10> 20 or x+12< 3. Help please!!!
Answer:
x < -9 or x > 10.
Step-by-step explanation:
x + 10 > 20
x > 10.
x + 12 < 3
x < -9.
Ian's car can go 93 miles on 3 gallons of gas. During a drive, last weekend, Ian used 8 gallons of gas. How far did Ian drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas used.
Answer:248
Step-by-step explanation:
First you need to find the unit rate by dividing 93 by 3 which would be 31 then take that number (which is how many miles for one gallon) and multiply it by 8 which would get you 248( if you need this as an equation here 93\3= 31 31*8 = 248). If they gave you the distance instead you would have had to divide by 31 instead of using multiplication. Hope this helps!
Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 2626 thousand dollars and 2 22 thousand dollars, respectively. Suppose we select one of these cars at random. Let X = X=X, equals the sale price (in thousands of dollars) for the selected car.
Complete question :
Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 thousand dollars and 2 thousand dollars, respectively. Suppose we select one of these cars at random. Let X represent the sale price (in thousands of dollars) for the selected car.1. Find P(26< X<30) You may round your answer to two decimal places
Answer:
0.48
Step-by-step explanation:
Mean, m = 26000 ; Standard deviation, s = 2000
P(x < x)
Zscore = (x - m) / s
P(26< X<30) ;
P[(26 - 26 / 2) < (30 - 26) / 2)]
P[(0 < Z < 2)]
P(Z < 2) - P(Z <0)
Using a z table of z calculator, we can obtain the probabilties of the Z value :
0.97725 - 0.5
= 0.47725
= 0.48 ( 2 decimal places)
HELP MEEEEEE PICKING BRAINLIEST!!!
Answer:
2 kg cashews
6 kg pecans
Step-by-step explanation:
System of Equations:
c + p = 8
8c + 7p = 8(7.25)
let c = 8-p
8(8-p) + 7p = 58
64 - 8p + 7p = 58
-p = -6
p = 6
solve 1.9(2x + 1) = 22x + 13
the answer is: x= -111/182
Answer:
x= -0.60989010989
Step-by-step explanation:
A man walks 5m due south and then 12m due East. Find his distance from the starting point.
Answer: 13 m
Step-by-step explanation:
distance from starting point = root{(5)^2 + (12)^2 }
=root{ 25 + 144}
= 13
Answer:
13 mStep-by-step explanation:
Between south direction and east direction we have right angle, so we can use Pythagorean theorem:
a² + b² = c²
a = 5 m
b = 12 m
c = the distance
[tex]5^2+12^2=c^2\\\\c^2=25+144\\\\c^2=169\\\\c=\sqrt{169}=13\,m[/tex]
Marcus borrowed 9000 from his bank to buy a car. The bank charged him a simple interest rate of 1.25%. By the time he paid back the money he had pad a total of 9281.25. How long did it take Marcus to pay back the money?
Answer:
2.5 years
Step-by-step explanation:
Given data
P=9000
r= 1.25%
A= 9281.25
The simple interest expression is given as
A=P(1+rt)
substitute
9281.25= 9000(1+0.0125*t)
9281.25=9000+112.5t
collect like terms
9281.25-9000=112.5t
281.25= 112.5t
t= 281.25/112.5
t= 2.5
Hence the time is 2.5 years
write a polynomial in standard form that represents the area of the shaded region
Answer:
x^2-3x+36
Step-by-step explanation:
No question, just whoever needs free answers.
Answer this and get free answers for a bit.
Now what's 2+2?
Answer:
4 lol
Step-by-step explanation:
Answer:
Step-by-step explanation:
The area of a rectangular room is 240 square feet. The width is 12 feet. What is the length?
Answer:
20 ft
A=wl
l=A/W=240/12=20ft
In the figure, shown, AD, CE, and FB intersect at point F. Find the value of x.
Answer:
8
Step-by-step explanation:
∡AB + ∡BC + ∡CD = 180°
∡CD = ∡AE
∡AB + ∡BC + ∡AE = 180°
(8x + 6)° + (6x + 2)° + (7x + 4)° = 180°
8x + 6 + 6x + 2 + 7x + 4 = 180
21x + 12 = 180
21x = 180 - 12
21x = 168
x = 8
Help please!!!!!!!!!!!!!!!!!! marking brainliest for correct answer!!!!!!!!!!!
Step-by-step explanation:
angle 2 = 49
angle 1 = 131
angle 3 = 112
plz mark my answer as brainlist.hope this will be helpful to you ☺️.
What percent is 50% of 50% of x? Please help.
25% is 50% of 50.
Explaination is on the picture.
50% of 100 is 50.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
Let x be a number such that
50% of x is 50
This forms an equation in one variable which can be solved by transposition.
[tex]50/100\times x = 50[/tex]
x/2=50
On multiplying 2 both sides,
[tex]X/2\times 2 =50\times 2[/tex]
X=100
Thus, 50% of 100 is 50.
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Correct question:
50% of what is 50.
Find the distance between
(5 , 1 ) and ( 3 ,6)
Answer:
Step-by-step explanation:
[tex]\sqrt{(6-1)^{2}+(3-5)^{2} }[/tex]=[tex]\sqrt{29}[/tex]
=5.39(correct to nearest hundredth)
The composite score range for the ACT is:
A. 20 to 85
B. 1 to 98
C. 1 to 50
D. 1 to 36.
The composite score range for the ACT is D) 1 to 36.
The composite score range for the ACT (American College Testing) is the total score achieved by an individual after taking all four sections of the ACT, which include English, math, reading, and science. The composite score ranges from 1 to 36, with 36 being the highest possible score.
The ACT score is used by colleges and universities in the United States to assess the readiness of a student to enter college. A high composite score indicates that the student has the skills and knowledge needed to succeed in college-level courses. Therefore, the correct answer is D) 1 to 36.
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40 kişinin katıldığı bir davete 5 evli çift daha
katılırsa, davete katılan erkeklerin sayısı, ka-
dınların sayısının 2 katından 13 eksik oluyor.
Buna göre, son durumda davete kaç erkek-
katılmıştır?
a) 30 D) 29 C) 26
D) 24
sen türksün be ne işin var senin burada
(1,5) with a slope of -2
Answer:
y = -2x + 7 is the equation if that's what you are asking for.
answer:
Linear equation :
y= -2x +7
Step-by-step explanation: