Method used:-
Completing the square method.
Steps :-
[tex]( x - 1 ) ( x + 2 ) = - 2\\x^{2}+x-2=-2 \\x^{2}+x=-2+2 \\x^{2}+x=0[/tex]
Now, make the left hand side of the equation by adding the square of ½ to both sides of the equation.
[tex]x^{2}+x+\left(\frac{1}{2}\right)^{2}=\left(\frac{1}{2}\right)^{2} \\x^{2}+x+\frac{1}{4}=\frac{1}{4} \\\left(x+\frac{1}{2}\right)^{2}=\frac{1}{4} \\\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}} \\[/tex]
Simplify the equation. You'll get a +ve & -ve value.
[tex]x+\frac{1}{2}=\frac{1}{2} \\x+\frac{1}{2}=-\frac{1}{2}[/tex]
Simplify it further.
[tex]\boxed{\sf\:x=0}\\ \boxed{\sf\:x=-1 }[/tex]
The solutions are :-
x = 0 & x = -1
______
Hope it helps ⚜
compare. 2 1/4 and 3 /14
Answer:
[tex]\frac{1}{4}[/tex] is larger than [tex]\frac{3}{14}[/tex]
[tex]\frac{1*14}{4*14}[/tex] = [tex]\frac{14}{56}[/tex]
[tex]\frac{3*4}{14*4}[/tex] = [tex]\frac{12}{56}[/tex]
i cant tell if it is [tex]\frac{1}{4}[/tex] or 2 [tex]\frac{1}{4}[/tex]
but if it is 2 [tex]\frac{1}{4}[/tex] that mean this is a mixed number
and [tex]\frac{3}{14}[/tex] is a proper fraction
need help
a rectangular garden is 50m long and 45 m broad A path 2m wide is. running inside the garden . Calculate the cost of gravelling the path at rs 40 per square meter.....
Answer:
Rs. 14560
Hope you could get an idea from here.
Doubt clarification - use comment section.
In rectangle ABCD
L=50mB=45m[tex]\\ \sf{:}\longrightarrow Area=LB[/tex]
[tex]\\ \sf{:}\longrightarrow Area=50(45)[/tex]
[tex]\\ \sf{:}\longrightarrow Area=2250m^2[/tex]
In rectangle PQRS
L=50-2=48mB=45-2=43m[tex]\\ \sf{:}\longrightarrow Area=LB[/tex]
[tex]\\ \sf{:}\longrightarrow Area=48(43)[/tex]
[tex]\\ \sf{:}\longrightarrow Area=2064m^2[/tex]
Now
[tex]\\ \sf{:}\longrightarrow Area_{(Path)}=Area_{(ABCD)}-Area_{(PQRS)}[/tex]
[tex]\\ \sf{:}\longrightarrow Area_{(Path)}=2250-2064=186m^2[/tex]
Cost:-
[tex]\\ \sf{:}\longrightarrow 186(40)[/tex]
[tex]\\ \sf{:}\longrightarrow Rs 7440[/tex]
Sally is making 15 individual blueberry cheesecakes. How many pounds of blueberries will be in each cheesecake if 514 pounds of blueberries are divided equally among them?
Answer:
About 35 or 34.27 if you round to the tenths spot.
Step-by-step explanation:
514 divided by 15 is 34.27 once rounded.
The distance required for a car to stop is directly proportional to the
square of its velocity. If a car can stop in 112.5 meters at 15 kilometers
per hour, how many meters are needed to stop at 25 kilometers per hour?
Answer:
312.5 m
Step-by-step explanation:
let distance be d and velocity be v , then
d = kv² ← k is the constant of variation
To find k use the condition d = 112.5, v= 15
112.5 = k × 15² = 225k ( divide both sides by 225 )
0.5 = k
d = 0.5v² ← equation of variation
When v = 25 , then
d = 0.5 × 25² = 0.5 × 625 = 312.5 m
The total number of gallons of water in a tank, w, after t minutes is given in this table and the plot.
What is an equation showing the relationship between w and t?
Enter your answer by filling in the box to complete the equation.
w =
The equation showing the relationship between w and t is [tex]w = 4t[/tex]
From the table, we have the following points:
(0,0) and (1,4)
Start by calculating the slope (m)
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{4 -0}{1 -0}[/tex]
Simplify the numerator and the denominator
[tex]m = \frac{4}{1}[/tex]
Divide 4 by 1
[tex]m = 4[/tex]
The equation is then calculated as:
[tex]w = m(t - t_1) + w_1[/tex]
This gives
[tex]w = 4(t - 0) + 0[/tex]
Simplify
[tex]w = 4t[/tex]
Hence, the equation is [tex]w = 4t[/tex]
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The equation of a line is y = 12x - 3. Write the equation of a line parallel to this line.
Answer:
y=12x+3
Step-by-step explanation:
when parallel the slopes need to be the same but the y-intercept has to change
Can someone plz help me?
Answer:
A. 5(y+3) = 5(3+y)
Step-by-step explanation:
Lillian read 43 pages in 1 1/3 hours. At what rate, in pages per hour, did she read?
Answer:
hi
Step-by-step explanation:
Answer:
She reads one page in 1.40
help please???????????
Answer:
The answer is C. (a + -a = 0 )
Step-by-step explanation:
"The additive inverse of a number a is the number that, when added to a, yields zero"
If l || m, find the value of x
Answer: 9
Step-by-step explanation:
Answer:
9!
Step-by-step explanation:
what is 3x + 4y = 10
6x - 4y = 8
Answer:
x=2
y=1
Step-by-step explanation:
9x+0=18
so it's x=2
6=4y=10
so y=1
help me pls... ....
Step-by-step explanation:
A1
1 yard = 3 feet
1 foot = 12 inches
therefore,
100 yards = 100×3×12 inches = 3600 inches
A2
again, 1 yard = 3 feet
8 ft = 8/3 = 2.67 yards = 2 2/3 yards
A3
1 gallon = 8 pints
A4
1 liter = 1000 milliliters (remember, "mili" means 1/1000).
therefore,
2.2 liters = 2.2×1000 = 2200 milliliters
A5
again, 1 liter = 1000 milliliters
therefore
1 milliliter = 1/1000 liter
670 milliliters = 670 × 1/1000 liter = 670/1000 liter =
= 0.67 liter
B1
1 kg (kilogram) = 1000 grams ("kilo" means 1000).
we have 3 layers.
each layer weighs (cake plus icing)
1/2 kg + 100 g = 500 g + 100 g = 600 g
3 layers then weigh
3×600 g = 1800 g
the additional candle weighs 250 g.
so, the total is
1800 g + 250 g = 2050 g = 2.05 kg
B2
area is 110 m².
1 m = 100 cm ("centi" means 1/100).
and 1 m² is then 100×100 = 10000 cm².
so, the area in cm² is
110 × 10000 = 1,100,000 cm²
the top area of one brick = 10 × 20 = 200 cm²
so, we need
1,100,000 / 200 = 11,000 / 2 = 5500 bricks
A construction team is going to Guatemala to help a missionary build a church building. The construction team will be there for 24 days, which is 50% more days than they need to complete construction. How many days will they need to complete the church building
Answer:
72
Step-by-step explanation:
50% means ½ of the usual days,
if 50% = 24 days
then the usual day is 48 days
so, 48+24= 72
Please find the area...
f(x) = -4(x+2) what is f(4)
Answer:
-24
Step-by-step explanation:
f(4)= -4(x+2)
f(4)= -4(6)
f(4)= -24
Answer:
F(x)=-4(x+2)
0=-4-8
4x=-8
X=-2
So,-2×2
-4
Step-by-step explanation:
Have a great day!
Simplify.
(7⁴)²
(EXPONENT FORM ONLY)
f(x)=−2x^2+2x−20
Find f(−8)
Answer: -164
Step-by-step explanation:
Answer:-164
Step-by-step explanation:
−2(−8)
2
+2(−8)−20
Plug into each x-value
−
2
(
64
)
+
2
(
−
8
)
−
20
−2(64)+2(−8)−20
Square first
−
128
−
16
−
20
−128−16−20
Multiply
f
(
−
8
)
=
−
164
f(−8)=−164
Joseph removes 5/8 gallon of white paint from a can.
Then he adds 5/8 gallon of blue paint to the can.
Write and evaluate an addition expression to find
the overall increase or decrease in the amount of
paint in the can.
Create the expression from the data:
The gallon of paint begins as a whole: 8/8
Then he removes 5/8 gallons of paint from the can: - 5/8
Then he adds 5/8 of a different colored paint to the can: + 5/8
Now combine:
8 / 8 - 5 / 8 + 5 / 8 = 8/8
The paint can is full, then he removes an amount from the can. He then pours more paint into the can that is equal to the amount he originally removed. Therefore, the paint can remained full.
My question is in the attachment.
Answer:
5 and 25
Step-by-step explanation:
let the son's age be x then the father's age is x + 20
In 5 years
son = x + 5 and father = x + 20 + 5 = x + 25
Then
x + 25 = 3(x + 5) ← father is three times as old as son
x + 25 = 3x + 15 ( subtract x from both sides )
25 = 2x + 15 ( subtract 15 from both sides )
10 = 2x ( divide both sides by 2 )
5 = x and x + 20 = 5 + 20 = 25
si=on is 5 and father is 25
Answer:
The son is 5 and the father is 25.
Step-by-step explanation:
We can do this using Algebra.
Let the son be x years old.
Then the father's age is x + 20 years.
After 5 years the father's age is x + 25 and the son is x + 5 years.
So we can write the equation:
x + 25 = 3(x + 5)
x + 25 = 3x + 15
25 - 15 = 3x - x
10 = 2x
x = 5.
So the father's present age is 20 + 5 = 25 and the son is 5 years old.
Choose the linear equations.
Answer:
y = [tex]\frac{3}{3}[/tex]x - 5
y = 2x + 5
Step-by-step explanation:
In linear equations, both variables x and y must have the exponent of 1 (i.e. they cannot have a small number at the top-right). And they cannot be in the exponents (i.e. cannot be the small number at the top-right).
Ryan and Taylor are both saving money to buy new video game equipment. Ryan's savings plan can be modeled by the function s= 15m + 50 where m represents the number of months since Ryan started his plan, and s represents the amount of money saved in dollars. The table shown represents Taylor's savings plan.
Taylor's Savings Plan --- In the file (Picture).
a. Ryans rate of change is_________Taylor's rate of change.
b. Ryans starting balance is _________Taylor's starting balance.
a. Ryan's rate of change is $15 per month;
Taylor's rate of change is $20 per month
b. Ryan's starting balance is $50;
Taylor's starting balance is $25.
Recall:
A linear function is modelled by the equation, y = mx + b, where m is the rate of change and b is the initial value (starting value).Rate of change = change in y/change in xRyan's Savings Plan Function:
s = 15m + 50
Thus, the starting value (starting balance) modelled by this function is $50
The slope/rate of change is $15 per month
Taylor's Savings Plan:
Given the table, the starting value will be the amount saved (initial value) at 0 number of months.
Therefore, Taylor's starting balance is: $25Using (0, 25) and (1, 45) find the rate of change:
Rate of change = (45 - 25)/(1-0) = 20/1 = $20In summary:
a. Ryan's rate of change is $15 per month;
Taylor's rate of change is $20 per month
b. Ryan's starting balance is $50;
Taylor's starting balance is $25.
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Can i get some help :
Answer:
the second
Step-by-step explanation:
Answer:
0.9 + n = 5.2
Step-by-step explanation:
The lines represented by the equations y=x+5 and 2y-2x=10 are
The equations representing the lines, y=x+5 and 2y-2x=10, have the same slope, therefore the lines are parallel.
Recall:
Two lines that are parallel will have the same slope value.Two lines that are perpendicular to each other will have slopes that are negative reciprocal of each other.Equation representing a line in slope-intercept form is: y = mx + b, where m is the slope.Given:
y = x + 5
2y - 2x = 10
The slope of y = x + 5 is 1.
Rewrite 2y - 2x = 10 in slope-intercept form to determine its slope.
2y - 2x = 10
2y = 2x + 10
Divide both sides by 2y = x + 5
Thus, the slope of y = x + 5 (2y - 2x = 10) is also 1.
The equations representing the lines, y=x+5 and 2y-2x=10, have the same slope, therefore the lines are parallel.
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RS is the perpendicular bisector of TU. Find x and y
Answer:
x = 1
y = 30°
Step-by-step explanation:
is RS is ⊥ to TU then TS = US so we can use this equation to find 'x':
20x-3 = 5x+12
15x = 15
x = 1
we also know that RS intersecting with TU creates a 90° angle
if 3y = 90 then y = 30
In your own words, describe how to find the GCF for a set of numbers. Use the numbers 24 and 32 as an example. (PLS HELP ILL GIVE 100 points and brainlest also no links please, thanks)
Answer:
8Step-by-step explanation:
You need to factorize each number in the set:
24 = 2*2*2*332 = 2*2*2*2*2Common factors of both numbers are:
2*2*2 = 8GCF(24, 32) = 8
I need to know how to get the roots for example what is the root of 2 root 5
Answer:
Square roots are when you multiply the same number by itself like for example, the square root of 5 is 25, because 5*5=25
Step-by-step explanation:
The value of the root of 2√5 is approximately 2.116.
Here, we have,
To find the root of a number, you can use the concept of radicals.
The "root" refers to the inverse operation of raising a number to a power. For example, the square root (√) is the most common root, and it represents finding a number that, when squared, gives the original number.
To find the root of a number, such as the square root (√), you can use the following notation:
√(2 * √(5))
In this case, we have the square root of (2 times the square root of 5).
To simplify this expression further, we can break it down step by step:
Step 1: Simplify the square root of 5:
√(5) = 2.236 (approximately)
Step 2: Substitute the simplified value back into the original expression:
√(2 * 2.236)
Step 3: Simplify the expression:
√(4.472) = 2.116 (approximately)
Therefore, the root of 2√5 is approximately 2.116.
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if 3/15 is equivalent to 45/n. find n
Answer:
n = 225
Step-by-step explanation:
Multiply 15 by 15
Find the residual values, and use the graphing calculator tool to make a residual plot. A 4-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries negative 2. 7, negative 0. 9, 1. 1, 3. 2, 5. 4. The third column is labeled predicted with entries negative 2. 84, negative 0. 81, 1. 22, 3. 25, 5. 28. The fourth column is labeled residual value with all entries blank. Does the residual plot show that the line of best fit is appropriate for the data? No, the points are in a curved pattern. No, the points are evenly distributed about the x-axis. Yes, the points are in a linear pattern. Yes, the points have no pattern.
The residual of a regression is the difference between the actual value and the predicted value
The true statement about the residual plot is (c) Yes, the points are in a linear pattern
The entries are given as:
x Given Predicted Residual
1 -2.7 -2.84
2 -0.9 -0.81
3 1.1 1.22
4 3.2 3.25
5 5.4 5.28
The residual of a line of best fit is calculated using:
[tex]Residual = Actual - Predicted[/tex]
Using the entry headings, the formula would be:
[tex]Residual = Given - Predicted[/tex]
So, the residuals of the 5 entries are:
[tex]Residual_1 = -2.7 - -2.84 =0.14[/tex]
[tex]Residual_2 = -0.9 - -0.81 =-0.09[/tex]
[tex]Residual_3 = 1.1 - 1.22 =-0.12[/tex]
[tex]Residual_4 = 3.2 - 3.25 =-0.05[/tex]
[tex]Residual_4 = 5.4 - 5.28 =0.12[/tex]
So, the entries become:
x Given Predicted Residual
1 -2.7 -2.84 0.14
2 -0.9 -0.81 -0.09
3 1.1 1.22 -0.12
4 3.2 3.25 -0.05
5 5.4 5.28 0.12
See attachment for the residual plot.
From the plot, we can see that the points are in a linear pattern.
Hence, the true statement about the residual plot is (c)
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Is 6 a factor of the number 56 yes or no?
Answer:
No it is not a factor of 56
Answer:
No
Step-by-step explanation:
6,12,18,24,30,36,42,48,54,60
A motorcycle can travel 60 miles per gallon. Approximately how many gallons of fuel will the motorcycle need to travel 40 km? [1 mile = 1. 6 km] 0. 04 0. 08 0. 20 0. 42.
The motorcycle needs to travel 40 km, 0.42 gallons of fuel.
Given that,
A motorcycle can travel 60 miles per gallon.
We have to find,
How many gallons of fuel will the motorcycle need to travel 40 km?
According to the question,
The motorcycle travel 60 miles per gallon,
The motorcycle travels 40 km,
To convert it into kilometers 60 miles per gallon.
[tex]\rm 1 \ mile = 1.6\ k.m.\\\\60 \ miles \times 1.6 \ k.m. = 96 \ k.m.[/tex]
Therefore,
The gallons of fuel will the motorcycle need to travel 40 km is,
[tex]= \dfrac{96}{40}\\\\= 0.42[/tex]
Hence, The motorcycle needs to travel 40 km, 0.42 gallons of fuel.
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