The x term has a coefficient of 4. Take half of this to get 2, then square it to get 4. This is the value we add to both sides to get x^2+4x+4 = 5. Note how x^2+4x+4 factors into (x+2)^2
---------
Another example: Let's say we started with x^2+6x = 1. To complete the square, we need to add 9 to both sides. I start with 6 (the x coefficient) and cut that in half to get 3, then I squared that to get 9. So we add 9 to both sides getting x^2+6x+9 = 10 which becomes (x+3)^2 = 10
The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.
What is Quadratic equation?In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no ax^2 term.
For example
Examples of quadratic equations are: 6x² + 11x – 35 = 0, 2x² – 4x – 2 = 0, 2x² – 64 = 0, x² – 16 = 0, x² – 7x = 0, 2x² + 8x = 0 etc.
Given :
x²+4x=1
as, the x has coefficient 4.
so half the coefficient of x and add and subtract the square of the remaining.
x²+4x + 2 ² - 2² =1
Now, make the whole square term
x²+4x + 2 ² - 4 - 1=0
( x + 2)² -5= 0
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Please help with 2 and 3 for maths
Answer:2-4=
Step-by-step explanation:y-16-(-42)
y-16+16
y-32
y-16-(-22)
y-16+4
y-20
y-16-(02)
y-16
y-16-(42)
y-0
Answer:
The answer is 2-4
Step-by-step explanation:
The sum of 4 consecutive integers is 130 what is the third number in the sequence
PLZ HELP!!!
Answer:
33
Step-by-step explanation:
We can write an equation:
x+x+1+x+2+x+3=130
x represents the smallest number of the consecutive integers
By the way, an example of consecutive would be 2, 3, 4, 5 or 10, 11, 12, 13
We can combine like terms from our equation:
4x+6=130
4x=124
x=31
The smallest number is 31. The second number would be 31+1=32, which means the third number is 33!
Hope this helps! :) :)
Answer:
[tex]\huge\boxed{3rd\ number = 33}[/tex]
Step-by-step explanation:
Let the consecutive numbers(Coming one after another) be x, x+1, a+2 and x+3
So,
x+x+1+x+2+x+3 = 130
4x + 6 = 130
Subtracting 6 to both sides
4x = 130-6
4x = 124
Dividing both sides by 4
x = 32
So,
1st number = x = 31
2nd Number = x+1 = 31+1 = 32
3rd number = x+2 = 31+2 = 33
4th number = x+3 = 31+3 = 34
Find the surface area of the square pyramid shown below.
Answer:
179.38 sq.units
Step-by-step explanation:
answer is in the pic
Phillip deposited $5,670 into a savings account 19 years ago. The account has an interest rate of 4.1% and the balance is currently $12,356.04. How often does the
interest compound?
Answer:
$12165.97
Step-by-step explanation:
100 + 4.1 = 104.1%
104.1% = 1.041
$5670 x 1.041^19 = $12165.97
Answer:
daily
Step-by-step explanation:
To answer this try plugging in each type of compund: daily, monthly, quarterly, and annually.
5670(1+0.041/365)^(365*19)
= 12356.04
365= daily
so your answer would be that the interest compounds daily.
Determine whether the lines given by the vector equations r1=2i+3j+k+s(4i−k) and r2=2i+3j+k+t(2i+2j+k) intersect. If they intersect, give the coordinates of their point of intersection.
They do. the initial point is same in both lines.
formally,
[tex] \vec{r_1}=(2\hat i+3 \hat j+\hat k)+s(4\hat i-\hat k)[/tex]
$\vec{r_2}=(2\hat i +3 \hat j +\hat k)+t(2\hat i+2\hat j +\hat k)$
if they intersect then $\begin{vmatrix} 4 & 0 & -1 \\ 2 & 2 & 1 \\ (2-2) & (3-3) & (1-1) \end{vmatrix}=0$
(which obviously is zero)
You buy a new computer for $1,500. The value of the computer decreases by 6%
every year. How much is the computer worth after 4 years?
$999.80
$1,171.05
$1,008.50
$1,225.35
Answer:
$1171.05
Step-by-step explanation:
1500 × (1-(6 / 100))⁴
Answer:
Hey there!
Each year, the computer is (100-6), or 94% of it's original value.
Thus, we have:
Original: 1500
First year: 1500(0.94)
Second year: 1500(0.94)(0.94)
Third year: 1500(0.94)(0.94)(0.94)
Fourth year: 1500(0.94)(0.94)(0.94)(0.94)
Fourth year: 1171 dollars.
Hope this helps :)
help could u guys add an explanation on how u got the answer too? thanks!
Answer:
15
Step-by-step explanation:
f(x) = x^2+1
f(2) = 2^2+1 = 4+1 = 5
g(x) = 3x+1
g(3) = 3(3)+1 = 9+1 = 10
f(2)+g(3) = 5+10 =15
Answer:
15
Step-by-step explanation:
I'm just guessing though.
what is the equation
Answer: -12 - 3 = -15
Explanation:
We start at -12 which goes in the first box.
Moving to the left 3 units means we subtract off 3, so that's why 3 goes in the second box.
The arrow is pointing at -15 as the final destination, which goes in the final third box.
Can someone please help with questions 4 and 5 and explain it to me I’ll appreciate!
Answer for number 4:
4. It will take them 3.5 hours on the fourth day.
Alright, so this is a multistep problem.
1. We need to calculate how many miles they have already traveled.
In order to do that, we multiply the number of hours by the average speed on each day.
- On day 1, they drove 5 hours at an average of 70 mph. 5 * 70 = 350, so they drove 350 miles on the first day.
- On day 2, they drove 7 hours at an average of 65 mph. 7 * 65 = 455, so they drove 455 miles on the second day.
- 350 miles + 455 miles = 805 miles, so they've driven 805 miles so far.
2. We need to figure out how far they have left to travel.
They started out with 1,050 miles, so they've got 245 miles left. 1,050 - 805 = 245.
3. We need to figure out how many hours they've got left to drive.
On the third day, they drive at an average speed of 70 mph, and they've got 245 miles left. to find the amount of time they need to drive, we divide the distance by the speed.
245 miles ÷ 70 mph = 3.5 hours. Therefore, it will take them 3.5 hours to reach their friend's home.
Answer For Number 5:
10 gallons of water will leak out in 30 hours.
This question involves unit rates.
1. We need to figure out how much water leaks out per hour.
- Since 7 gallons of water will leak out in 21 hours, we divide the amount of water by the amount of time it took for it to leak out. The answer will be how much water leaks out in an hour.
- 7 gallons ÷ 21 hours = 1/3 gallon of water. Now we have our unit rate. Every hour, 1/3 gallon of water leaks out.
2. We need to figure out how much water will leak out in 30 hours.
- Since we know how much water leaks out in 1 hour, we can easily figure out how much water leaks out in 30 hours. All we need to do is multiply how much water leaks out in one hour by 30!
- 1/3 gallon * 30 hours = 10 gallons of water.
Therefore, 10 gallons of water will leak out in 30 hours.
I hope this helps!
Let X, Y, and Z be points such that [tex]\frac{XZ}{XY} = \frac{ZY}{XY} = \frac{1}{2}.[/tex] If Y = (1, 7), Z = (-1, -7), then what is the sum of the coordinates of $X$?
Answer:
1
Step-by-step explanation:
1
Simplify (−3c3w5)3. −9c6w8 −9c9w15 −27c6w8 −27c9w15
Answer:
-6723cw
Step by Step:
(-3c * 3w * 5) * 3 - 9c * 6w* 8 - 9c * 9w * 15 - 27c * 6w * 8 - 27c * 9w * 15
Can someone do this?
Need Help ASAP!!!!!!!!!!!!!!!!
If In a = 2, In b = 3, and Inc = 5, evaluate the following:
(a) In
(b) In V63c4a-2
(c)
In(a+b-3)
In(be)"
3
(d)
Answer:
-20/343
Step-by-step explanation:
Mr. Blake's biology class is divided into three secrions. The same test is given to each section. The table above shows both the lowest score and the range of scores on this rest for each section
What is the overall range of all scores in all three sections?
Answer:
25
Step-by-step explanation:
The overall range of all scores in all three sections is 25.
What is Average?In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
Given:
The range of 3 sections is 28, 25 and 22.
So, the overall range of all scores in all three sections
= (28+ 25+ 22)/ 3
= 75/3
= 25
Hence, the overall range of all scores in all three sections is 25.
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d) Use your knowledge of scale drawings and image sizes to fill in the missing
information in the table. (3 points)
Empire State Building
Original
Image
Actual Height
(in feet)
1,450
1,450
1,450
Reduced
Image
Model Height
(in blocks)
145
1
1
Scale Factor
25
50
Answer:
Your table is filled in below.
Step-by-step explanation:
The scale factor is the ratio of image size to original size. In part (d), the image height is "blocks" while the original height is "feet". So, the units of the scale factor are "blocks/ft".
Sometimes a scale factor has units, like this, and sometimes it is expressed as a pure number. A map scale factor might be the pure number ratio 1 : 62500, or it could also be expressed with units as 1 in : 1 mile.*
__
* actually, these are slightly different scales. 1:62500 is about 0.98643 inches per mile.
Answer: Image
Step-by-step explanation:
took the test
How are you? Heres the question of the day! 138 + 76 x 94 =
Answer:
7282
Step-by-step explanation:
To answer this use PEMDAS
First, we need to multiply: 76 x 94 = 7144
Then we add: 7144 + 138 = 7282
Answer:
[tex]\boxed{7282}[/tex]Step-by-step explanation:
Using PEMDAS rule:
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
Now, let's solve:
[tex] \mathsf{138 + 76 \times 94}[/tex]
Multiply the numbers
[tex] \mathsf{ = 138 + 7144}[/tex]
Add the numbers
[tex] \mathsf{7282}[/tex]
Hope I helped!
Best regards!
If -1< y< 0, which of the following has the greatest value?
Answer:
[tex]\boxed{\sf B}[/tex]
Step-by-step explanation:
-1 < y < 0
The value of y is negative.
Let’s take the number -0.5.
(-0.5)² = 0.25
1 - (-0.5) = 1.5
1 + (-0.5) = 0.5
2(-0.5) = -1
The greatest value is 1.5.
The answer is 1 - y.
Of a group of boys and girls at Central Middle School’s after-school party, 15 girls left early to play in a volleyball game. The ratio of boys to girls then remaining was 2 to 1. Later, 45 boys left for a football game. The ratio of girls to boys was then 5 to 1. How many students attended the party?
Answer:
90
Step-by-step explanation:
Let g and b represent the number of girls and boys attending, respectively.
After 15 girls left, the ratio of boys to girls was ...
b/(g -15) = 2/1
b = 2g -30 . . . . . multiply by (g-15)
__
After 45 boys left, the ratio of girls to boys was ...
(g -15)/(b -45) = 5/1
g -15 = 5b -225 . . . . . . multiply by (b-45)
g = 5b -210
Using the latter to substitute into the former, we have ...
b = 2(5b -210) -30
450 = 9b . . . . . add 450-b
50 = b . . . . . . 50 boys attended
g = 5(50) -210 = 40 . . . . . 40 girls attended
The number of students who attended the party was 50 +40 = 90.
_____
Check
After 15 girls left, the ratio of boys to girls was 50/25 = 2/1.
After 45 boys left, the ratio of girls to boys was 25/5 = 5/1.
Answer:
let b = original number of boys
let g = original number of girls
:
Of a group of boys and girls at Central Middle School's after-school party, 15 girls left early to play in a volleyball game.
The ratio of boys to girls then remaining was 2 to 1.
b%2F%28%28g-15%29%29 = 2%2F1
Cross multiply
b = 2(g-15)
b = 2g - 30
:
Later, 45 boys left for a football game. The ratio of girls to boys was then 5 to 1.
%28%28g-15%29%29%2F%28%28b-45%29%29 = 5%2F1
cross multiply
g - 15 = 5(b-45)
g - 15 = 5b - 225
g = 5b - 225 + 15
g = 5b - 210
Replace b with (2g-30)
g = 5(2g-30) - 210
g = 10g - 150 - 210
g = 10g - 360
360 = 10g - g
360 = 9g
g = 360/9
g = 40 girls originally
find b
b = 2(40) - 30
b = 50 boys originally
" How many students attended the party?"
40 + 50 = 90 students
PLEASE NEED HELP ASAP!!!!!!! WILL GIVE BRAINLY!!!!!! what are the domain, range, and asymptote of h(x)=(0.5)^x-9
Answer:
[tex]\mathrm{Domain\:of\:}\:0.5^x-9\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Range\:of\:}0.5^x-9:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>-9\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-9,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Asymptotes\:of}\:0.5^x-9:\quad \mathrm{Horizontal}:\:y=-9[/tex]
Step-by-step explanation:
Domain:
The function has no undefined points nor domain constraints. Therefore, the domain is
[tex]...-\infty \:<x<\infty \:[/tex]
Definition: The domain of a function is the set of input or argument values for which the function is real and defined.
_________________________________________________
Range:
[tex]\mathrm{The\:range\:of\:an\:exponential\:function\:of\:the\:form}\:c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k\\k=-9[/tex]
[tex]f\left(x\right)>-9[/tex]
Definition: The set of values of the dependent variable for which a function is defined.
_________________________________________________
Asymptotes:
[tex]\mathrm{Vertical\:asymptotes\:of\:}0.5^x-9:\quad \mathrm{None}\\\mathrm{Horizontal\:Asymptotes\:of\:}0.5^x-9:\quad y=-9\\\mathrm{Horizontal}:\:y=-9x^{2}[/tex]
The figure shows a parallogram inside a rectangle outline: What is the area of a parallogram? (1/25) (11/25) (3/25) (4/25)
Answer:(3/25)
Step-by-step explanation: just had this question
Which data set could be represented by the box plot shown below?
Answer:
16
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Type the expressions as radicals
y3/5
Answer:
[tex]\sqrt[5]{y^3}[/tex]
Step-by-step explanation:
[tex]y^{3/5}[/tex] is simply [tex]\sqrt[5]{y^3}[/tex]
Add.
8/9+2/3+1/6
11/18
11/15
1 13/18
1 2/9
Answer:
1 13/18
Step-by-step explanation:
Get a common denominator of 18
8/9+2/3+1/6
8/9 *2/2 + 2/3 *6/6 + 1/6 *3/3
16/18 + 12/18 + 3/18
31/18
18/18+13/18
1 13/18
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{The Lowest Common Denominator (LCD) of these fraction is: \bf 18}[/tex]
[tex]\mathsf{\dfrac{8}{9}+\dfrac{2}{3}+ \dfrac{1}{6}}\\\\\mathsf{= \dfrac{8\times2}{9\times2}+\dfrac{2\times6}{3\times6}+ \dfrac{1\times3}{6\times3}}\\\\\mathsf{8\times2=\bf 16}\\\mathsf{2\times6=\bf 12}\\\mathsf{1\times3 = \bf 3}\\\\\mathsf{9\times2=\bf 18}\\\mathsf{3\times6= \bf 18}\\\mathsf{6\times3 = \bf 18}\\\\\mathsf{\dfrac{16 + 12 + 3}{18}}\\\\\mathsf{16+12+3}\\\mathsf{= 28 + 3}\\\mathsf{=\bf 31}\\\\\\\mathsf{ = \bf 1 \dfrac{13}{18}}\\\\\\\boxed{\huge\textsf{Answer: \boxed{\mathsf{1 \dfrac{13}{18}}}}}}[/tex] ☑
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Help ASAP please and thanks
PLEASE HEEELPPP 15 POINTS PLESSEE
NEED HELP PLEASE
A football is kicked at 40 yards away from a goal post that is 10 feet high. Its path is modeled by y = -0.03x 2 + 1.6x, where x is the horizontal distance in yards traveled by the football and y is the corresponding height above the ground in feet.
Does the football go over the goal post? How far above or below the goal post is the football? Use two or more complete sentences to explain your answers. (Hint: The unit conversion is built into the given function.)
Answer:
It goes over the goal post by 6 feet
Step-by-step explanation:
The football will be at the same x position as the goal when x = 40. When x = 40, y = -0.03 * 40² + 1.6 * 40 = 16. The height of the goal post can be represented by the equation y = 10. Since 16 > 10, the football goes over the goal post by 16 - 10 = 6 feet.
determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x-4y=-5 8x+6y=-5 show full work please and thank you
A building casts a 33-m shadow when the sun is at an angle of 27° the vertical. How tall is the building to the
nearest meter? How far is it from the top of the building to the tip of the shadow?
Answer:
1. EF = 65m
2. DF = 73m
Step-by-step explanation:
1. EF = height of the building = h = 33 / tan 27 = 65m
2. DF = sqrt (65² + 33²) = 73m
The building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.
From the triangle DEF, we find the value of EF by using tan function.
tan function is a ratio of opposite side and adjacent side.
tan(27)= 33/FE
0.5095 = 33/FE
Apply cross multiplication:
FE=33/0.5095
FE=64.76
Now DF is the hypotenuse, we find it by using pythagoras theorem.
DF²=DE²+EF²
DF²=33²+64.76²
DF²=1089+4193.85
DF²=5282.85
Take square root on both sides:
DF=72.68
In a triangle the the sum of three angles is 180 degrees.
∠D + 27 +90 =180
∠D + 117 =180
Subtract 117 from both sides:
∠D =63 degrees.
Hence, the building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.
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A bag contains red, white, and blue marbles. If 1/4 of the marbles are red and 2/3
of the marbles are white, what fractional part of the marbles are blue?
Answer: 1/12
Step-by-step explanation: 1/4=3/12. 2/3=8/12. 3/12+8/12=11/12. The remaining 1/12 is blue.