Answer:
x ≈ - 5.32, x ≈ 1.32
Step-by-step explanation:
x² + 4x - 7 = 0 ( add 7 to both sides )
x² + 4x = 7
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(2)x + 4 = 7 + 4
(x + 2)² = 11 ( take the square root of both sides )
x + 2 = ± [tex]\sqrt{11}[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\sqrt{11}[/tex]
Thus
x = - 2 - [tex]\sqrt{11}[/tex] ≈ - 5.32 ( to 2 dec. places )
x = - 2 + [tex]\sqrt{11}[/tex] ≈ 1.32 ( to 2 dec. places )
Answer:
x = -5.32, x = 1.32
Step-by-step explanation:
Ok. So to use the Complete the Square method, you divide the middle value by 2 and then square the number you get. This will give:
[tex](x^{2} + 4x + (\frac{4}{2}) ^2) - (\frac{4}{2}) ^2 -7 = 0[/tex]
[tex](x^{2} + 4x + 4) - 4 -7 = 0[/tex]
[tex](x^{2} + 4x + 4) - 11 = 0[/tex]
[tex](x^{2} + 4x + 4) = 11[/tex] (now factor the left side)
[tex](x + 2)(x + 2) = 11[/tex]
[tex](x + 2)^{2} = 11[/tex] (now square root both sides)
[tex]\sqrt{(x + 2)^{2}} = \sqrt{11}[/tex]
[tex]x + 2 = \sqrt{11}[/tex]
[tex]x = - 2 +/- \sqrt{11}[/tex] (+/- = plus or minus)
x = -5.32, x = 1.32
What is the measure of the third angle
58
a right triangle is 90 degrees so you subtract 32 from 90 to find the remainder
Answer:
The third angle is 58 degrees
Step-by-step explanation:
In a triangle all three angles add up to 180 degrees. If you know two sides, add them up then subtract the sum from 180. This will leave you with the last angle measurement.
In a right triangle we always know there is one angle that has a measure of 90 degrees. So now we know two angles 90 and 32.
90 + 32 = 122
180 - 122 = 58
solve the equation
2(h-8) - h=h - 16
A h = 8
B h= -8
C h = infinitely many solutions
D h = no solution
Answer:
2(h-8)-h=h-16
2(h-8)=h+h-16
2(h-8)=2h-16
2(h-8)=2(h-8)
h-8=h-8
h-h=8-8
0=0 so their can be infinite value of h.
hence c is correct
we can put in place of anything but answer will be zero.
Answer:
C h= infinitely many solutions
Step-by-step explanation:
when you replace h with any number it is true
say h= 3
2(3-8) - h = h-16
2(-5) - 3 = 3 - 16
-10 - 3 = -13
-13 = -13
using distributive property:
2h-16-h = h-16
combine like terms
h-16=h-16
it is the same expression on both sides of the equal sign
hope that helps!
3. Bond energy is the energy
a. absorbed as a molecule forms.
b. change as atoms get closer together.
C. required to break a chemical bond and form separate, neutral
atoms.
d. of two covalently bonded atoms.
What is f(1/2)? (1 over 2)
Sammie read at the rate of 25 pages per hour. Alex read at the rate of 1/2 of a pages per minute. Who was reading faster? By how many pages per hour faster?
Answer:
Alex is reading faster by 5 more pages per hour.
Step-by-step explanation:
Alex's rate of reading is 1/2 pages per minute, or 1 page every 2 minutes. To convert his rate to pages per hour, we can divide 60 (minutes in an hour) by 2 (minutes it takes Alex to read a page) which is equal to 30 (pages read in an hour). Therefore, Alex is reading at 30 pages an hour and reading 5 more pages an hour than Sammie.
The sales tax for an item was $36.90 and it cost $410 before tax. Find the sales tax rate. Write your answer as a percentage.
Answer:
36.90/410 = 0.09
0.09 X 100 = 9%
PLEASE HELP DUE TMRW!
A furniture company buys chairs at wholesale price of $48. They mark
up the price so they make a 30% profit. How much will one chair sell for?
Answer:
i dont know just trying to get pionts haha sorry rihana
Step-by-step explanation:
How many dots would be in Figure 17?
Answer:
306
Step-by-step explanation:
PLEASE HELP!! I just need help with b-d!
Answer:
b) The slope of line is 20
c) The equation in slope-intercept form is: [tex]\mathbf{y=20x}[/tex]
d) i) she would have travelled 1480 m after 74 s
ii) It will take 125 s to travel 2.5 km
Step-by-step explanation:
Part b: Slope of Line
Slope of line can be found using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table we can take any two points and find the slope.
Looking at the graph, the time is x-axis and distance is y-axis
Let we take (0,0) and (8,160)
So, we have: [tex]x_1=0, y_1=0, x_2=8, y_2=160[/tex]
Now finding Slope:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{160-0}{8-0} \\Slope=\frac{160}{8}\\Slope=20[/tex]
So, the slope of line is 20
Part c) Find the equation in slope-intercept form
The general equation of slope-intercept form is: [tex]y=mx+b[/tex] where m is slope and b is y-intercept
We have found slope, m = 20
We need to find y-intercept.
y-intercept can be found by putting x-axis (time) equal to zero and check what the y-axis (distance) is:
So, when x =0, y=0
So, y-intercept = 0
The equation will be:
[tex]y=mx+b\\y=20x+0\\y=20x[/tex]
The equation in slope-intercept form is: [tex]\mathbf{y=20x}[/tex]
Part d)
Part i) How far will she have travelled after 74 s
We are given time (x) = 74 s
We need to find distance i.e. y:
Using the equation: [tex]\mathbf{y=20x}[/tex]
Put x = 74
[tex]y=20x\\y=20(74)\\y=1480[/tex]
So, she would have travelled 1480 m after 74 s
Part ii) How long will it take to travel 2.5 km
We are given distance (y) = 2.5 km
We need to find time i.e. x:
Using the equation: [tex]\mathbf{y=20x}[/tex]
Since distance is given in meters but here it is in km
So converting 2.5 km into m
We know that 1 km = 1000m
So, 2.5 km = 2500 m
Now finding time:
[tex]y=20x\\2500=20(x)\\x=\frac{2500}{20}\\x=125[/tex]
So, It will take 125 s to travel 2.5 km
Which pair of points have -3 as the y-coordinate
A. Points C and G
B. Points F and E
C. Points B and D
D. Points B and L
I NEED THIS NOW PLEASEE
How can I calculate the zeros of x^3+3x^2-4?
I know the answers (x1= -2 and x2= 1) but I need to show why these are the zeros.
Answer:
x = 2
x = -1
A store advertises 15% off an item that regularly sells for $300
what is the price of the item?
For this problem, we're finding the percent of 300. To do that we:
1. Multiply 300 by 15.
300 x 15 = 4500
2. Divide 4500 by 100. (% = 100)
4500 / 100 = 45
Therefore, the unit price is 45. But we're not done. We need to subtract 45 by 300.
300 - 45 = 255
Now, our answer is 255 and the unit price is 45.
Let me know of any questions!
What is the value of |a-b|?
Answer:
|3+2|=5
Step-by-step explanation:
2x+1=5
2x+=-5
x=2
x=-3
a= -3, b=2
find f(-10) f(x)=7x-5
Answer:
f(-10) = -75Step-by-step explanation:
F(x) is simply another way of saying y. We are given the x value of -10. We can substitute this in for x and find y.
f(-10) = 7(-10) - 5
f(-10) = -70 - 5
f(-10) = -75
Answer:
Rewrite the equation in term of
x
and
y
.
f
(
x
)
=
2
x
2
−
7
x
+
5
Rewrite the equation in vertex form.
Tap for fewer steps...
Complete the square for
2
x
2
−
7
x
+
5
.
Tap for more steps...
2
(
x
−
7
4
)
2
−
9
8
Set
y
equal to the new right side.
y
=
2
(
x
−
7
4
)
2
−
9
8
Use the vertex form,
y
=
a
(
x
−
h
)
2
+
k
, to determine the values of
a
,
h
, and
k
.
a
=
2
h
=
7
4
k
=
−
9
8
Find the vertex
(
h
,
k
)
.
(
7
4
,
−
9
8
)
Step-by-step explanation:
The radius of the circle on a basketball court is 6 feet. What are the approximate
circumference and area of the circle?
Circumference: 37.7 feet
Area: 113.0 square feet
Circumference: 18.8 feet
Area: 37.7 square feet
Circumference: 18.8 feet
Area: 113.0 square feet
Circumference: 12.0 feet
Area: 18.8 square feet
Answer:
C= 37.69ft
A= 113.09ft
Step-by-step explanation:
Circumference=
=37.69
Area=
Area = pi * 6 ^2
Area =113.09
Simplify the expression (2−3i) (5+i) by distributing. Express your answer in a+bi form, Step by Step.
Answer:
13-13i
Step-by-step explanation:
2(5+i)-3i(5+i)
10+2i-15i-3i²
10-13i+3
13-13i
what is the formula to calculate velocity?
Answer:
Velocity (v) is a vector quantity that measures displacement (or change in position, Δs) over the change in time (Δt), represented by the equation v = Δs/Δt. Speed (or rate, r) is a scalar quantity that measures the distance traveled (d) over the change in time (Δt), represented by the equation r = d/Δt.
here is a picture.
I hope this helps.
Your friend claims that a triangle with side lengths of a, b, and c will have half the area of a triangle with side lengths of 2a, 2b, and 2c. Is your friend correct?
Answer:
My friend is wrong since, the area of the triangle with sides a, b, c is one-quarter the area of triangle with sides 2a, 2b, 2c
Step-by-step explanation:
Using herons formula, the area of the first triangle with sides a, b, c is A = √[s(s -a)(s - b)(s -c)] where s = (a + b + c)/2.
So, A = √[(a + b + c)/2((a + b + c)/2 - a)((a + b + c)/2 - b)((a + b + c)/2 - c)]
= √[(a + b + c)/2((b + c - a)/2)((a - b + c)/2)((a + b - c)/2)]
= 1/4√[(a + b + c)(b + c - a)(a - b + c)(a + b - c)].
For the triangle with sides 2a, 2b, 2c, the area is A' = √[s'(s' - 2a)(s' - 2b)(s' -c)] where s' = (2a + 2b + 2c)/2 = a + b + c.
So, A' = √[(a + b + c)((a + b + c) - 2a)((a + b + c) - 2b)((a + b + c) - 2c)]
= √[(a + b + c)((b + c - a)(a - b + c)(a + b - c)]
= √[(a + b + c)(b + c - a)(a - b + c)(a + b - c)].
Since A = 1/4√[(a + b + c)(b + c - a)(a - b + c)(a + b - c)]. and A' = √[(a + b + c)(b + c - a)(a - b + c)(a + b - c)] ⇒ A = A'/4
So, the area of the triangle with sides a, b, c is one-quarter the area of triangle with sides 2a, 2b, 2c. So, my friend is wrong.
The Ferrer family is taking a vacation. During their vacation they will drive a total of 686 miles per hour. Which equation best describes how many, m, miles are left after driving, h, hours?
Help me do 1/6+1/4 make sure the demonator is the same
______________________________
1.) Find the LCF of 6 and 4: [tex]6,4=12[/tex]
- We do this because in order to add these, they must have the same denominator. So you must find the LCF, (Least Common Factor) of 6 and 4.
2.) Convert the fractions to have the same denominator: [tex]\frac{1}{6}=\frac{2}{12}[/tex] [tex]\frac{1}{4}=\frac{3}{12}[/tex]
- [tex]\frac{1}{6}[/tex] changes to [tex]\frac{2}{12}[/tex] by multiplying the numerator and denominator by 2. And [tex]\frac{1}{4}[/tex] changes to [tex]\frac{3}{12}[/tex] because you multiply the numerator and denominator by 3.
3.) Add the numerators: [tex]2+3=5[/tex]
- Since both fractions have the same denominator all you have to do is add the numerators together.
______________________________
Please help I’ll give u 5 points
Answer:
1/2cup
as if 3and1/2cup is divided into 4people then in every one will get half cup.
Answer:
Each person gets [tex]\frac{7}{8}[/tex] cup of pudding.
Step-by-step explanation:
The problem is essentially asking;
[tex]3\frac{1}{2}[/tex] ÷ 4
(4 because the pudding has to be divided amongst Regina and her 3 friends, hence 4 people)
To divide fractions, first one has to convert from improper fractions to mixed numbers;
[tex]\frac{7}{2}[/tex] ÷ 4
Next, one has to reciprocate the second fraction, since the second number is an integer, one simply has to put the number as the denominator, and set the numerator to 1.
[tex]\frac{7}{2}[/tex] * [tex]\frac{1}{4}[/tex]
Now, one has to perform the multiplication, simply multiply the numerators and denominators together (there is no way of simplifying in this problem);
[tex]\frac{7}{8}[/tex]
Each person gets [tex]\frac{7}{8}[/tex] cup of pudding.
30 POINTS PLEASE HELP ME OUT
A scuba diver descends 80 feet, rises 25 feet, descends 12 feet, and then
rises 52 feet where he will do a safety stop for five minutes before surfac-
ing. At what depth did he do his safety stop?
Answer: That would be 15ft
What is the domain and range?
Answer:
The domain D = {0, 1, 2, 3, 4, 5}
The range R = {3, 4}
Step-by-step explanation:
Given the ordered pairs or points on the graph
{(0, 4), (1, 4), (2, 4), (3, 3), (4, 3), (5, 3)}
We know that the domain of the function is the set of input or arguments for which the function is real and defined.
In other words,
Domain refers to all the possible sets of input values on the x-axis.It means the set of all the x-coordinates of the given points or ordered pairs on a graph will be the domain.
Thus,
The domain D = {0, 1, 2, 3, 4, 5}
Determining the range:
We also know that range is the set of values of the dependent variable for which a function is defined.
In other words,
Range refers to all the possible sets of output values on the y-axis.It means the set of all the y-coordinates of the given points or ordered pairs on a graph will be the range.
Thus,
The range R = {3, 4}
Note: Please note that the duplicated elements in the range are written only once.
BRAINLIEST! URGENT! If you can answer this, please help. If you can explain how you got that answer, I will mark you Brainliest.
Answer:
[tex]\mathrm{A.\:}x+2y=a[/tex]
Step-by-step explanation:
In standard form [tex]ax+by=c[/tex], any point the line passes through will make the inequality true. We can simply use any point given to find the equation of the line:
We can write the following system of equations from two points from the table:
[tex]\begin{cases}d\cdot3a+e\cdot(-a)=f\cdot a\\d\cdot5a+e\cdot(-2a)=f\cdot a\end{cases}[/tex]
Solving, we get:
For [tex]a \notin 0[/tex],
[tex]d=1,\\e=2,\\f=1[/tex]
Therefore, our equation is:
[tex]dx+ey=fa,\\1x+2y=1a,\\\fbox{$x+2y=a$}[/tex].
What is the cost in dollars of each large envelope
Answer:
there isn't enough information but I believe it is $1.42
Step-by-step explanation:
Answer:
$1.42
Step-by-step explanation:
wheres the work?
can someone help me please? find the value of each variable..
Answer:
x = 4, y = 3
Step-by-step explanation:
plz answer asap!!!!!!!!!!!!!!!!!!!!!!
Answer:
It can be represented by the expression 2r, or “two times the radius.” So if you know a circle's radius, you can multiply it by 2 to find the diameter; this also means that if you know a circle's diameter, you can divide by 2 to find the radius. Find the diameter of the circle.
Step-by-step explanation:
you'r welcome :)
Find x given Circle P.
PLEASE HELP !!!
Answer:
360 - 60 = 300
x = 300
Step-by-step explanation:
Algebraically find the vertex of the function f(x) = x2 – 6x + 16.