Answer:
(a - b)^2 = 49 - 4b^2 +2ab
Step-by-step explanation:
Given: a^2 + b^2 = 7b (assuming A is really “a”)
b^2 + (2b - a)^2 = 7^2
Find; (a - b)^2
Plan: Use Algebraic Manipulation
Start with b^2 + (2b - a)^2 = 7^2 =>
b^2 + 4b^2 - 4ab + a^2 = 49 by expanding the binomial.
a^2 + b^2 + 4b^2 - 4ab = 49 rearranging terms
a^2 + b^2 -2ab - 2ab + 4b^2 = 49 =>
a^2 - 2ab + b^2 = 49 - 4b^2 +2ab rearranging and subtracting 4b^2 and adding 2ab to both sides of the equation and by factoring a^2 - 2ab + b^2
(a - b)^2 = 49 - 4b^2 +2ab
Double Check: recalculated ✅ ✅
(a - b)^2 = 49 - 4b^2 +2ab
Help me pls it’s number 8, will give brainliest but quickly pls
Write each number in standard form.
Answer:
35010
.08190
- 137000
- .00060041
Step-by-step explanation:
positive exponents add zeros to end and move decimal place to right the amount of the exponent.
negative exponents add zeros to begininng and move decimal to the left.
Instructions: Find the slope of the line through the points (-13, 16) and (-13, 12). Make sure to simplify
fractions and enter your answers with a foward slash (i.e. "/"). If the slope is undefined enter "undefined.
Answer: undefined
Step-by-step explanation:
Using the slope formula: (y^2 - y^1)/(x^2 - x^1), we can fill in the points:
(12 - 16)/(-13 - - 13) = -4/0
We can’t have a denominator of zero, so this is undefined.
prove [tex](x+1)^{2}(x+2)=(x^3+3x+21x+1)[/tex] no files
Answer:
LHS ≠ RHS
Step-by-step explanation:
[tex]LHS =\\\\=(x+1)^2 (x + 2) \\\\=(x^2 + 2x + 1)(x+2)\\\\=x(x^2 + 2x + 1) + 2(x^2 + 2x + 1) \\\\=(x^3 + 2x^2 + x ) + ( 2x^2 + 4x + 2) \\\\=x^3 + 2x^2 + x + 2x^2 + 4x + 2 \\\\=x^3 + 4x^2 + 5x + 2[/tex]
Suman and Narayan riding bikes towards each other they are 480 Km apart. The speed of Narayan is 6km/hr faster than Suman. If both meet each other after 6hours find there speeds when both started at same time.
Answer:
Suman 37 km/hr
Narayan 43 km/hr
(extremely sorry if this is wrong!!)
Step-by-step explanation:
We can use the formula distance divided by time is speed.
480/6 = 80.
Their speeds must add up to 80 km/hour
Lets set suman as a variable, lets say s.
Narayan has a speed 6 more than suman so we say 6+s
6+s+s = 80
subtract 6 from both sides
s+s = 74
add like terms
s+s = 2s
2s = 74
divide both sides by 2.
74/2=37
s=37
Suman's speed is 37 km/hr.
Narayan's speed would be 6 more than Suman's so we do 6+37
which makes 43 km/hr
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 6.2 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 23 samples is 6.4 ppm with a standard deviation of 0.7. Assume the population is normally distributed. A level of significance of 0.02 will be used. State the null and alternative hypotheses.
Answer:
H0 : μ = 6.2
H1 : μ ≠ 6.2
Step-by-step explanation:
Population mean, μ = 6.2 ppm
The hypothesis :
Null, H0 : = The mean level of Ozone is normally 6.2 ppm ;
The alternative hypothesis is the researcher's claim that the current ozone level is not normal, that is it may be higher or lower than the normal value in ppm
Hence, the hypothesis could be written as :
H0 : μ = 6.2
H1 : μ ≠ 6.2
what is the area of a flower pot that have the shape of a semi circle and its diameter 2.8cm?
Step-by-step explanation:
The area of a circle = pi r^2
d = 2r Divide by 2 to get the radius
r = d/2
The diameter = 2.8 cm
r = d/2
r = 2.8/2
r = 1.4
The area of the circle = pi * r^1
The area of the circle = 3.14 * 1.4^2
The area of the circle = 6.1544
But you are working with a semic circle
The area of a semicircle is 1/2 that of a circle
Area of semicircle = 1/2 6.1544 = 3.0772 =3.08 when rounded
If G(X) = 3x+1, then G-1(1) is
Answer:
0
Step-by-step explanation:
To find the inverse, or [tex]G^{-1}[/tex] , we must switch G(x) and x, and then make G(x) [tex]G^{-1} (x)[/tex] as we are finding the inverse, and G(x) represents the starting equation.
[tex]x = 3G^{-1} (x)+1\\x -1 = 3G^{-1} (x)\\\\\frac{x-1}{3} = G^{-1} (x)\\[/tex]
The steps used here are that we firt subtracted 1 from both sides, and then divided 3 from both sides.
To find [tex]G^{-1} (1)[/tex], we simply plug 1 into x in the inverse function, so our answer is [tex]\frac{1-1}{3} =0[/tex]
A rectangle has a length that is 8 less than it’s width w the perimeter is 52 which equation can be used to determine length
Answer:
width?
8-W-52
2(w-8) +2w=52
(W-8)+W=52
2(8-W) +2w=52
Please help me it's urgent!
Answer:
consistent system, independent system, independent system, inconsistent system
Step-by-step explanation:
1) A system of linear equation with at least one solution is a consistent system.
2) A system of linear equation with exactly one solution that is called independent system
3) A system of linear equations with an infinite number of solution is a dependent system
4) A system of linear equations with no solution is a inconsistent system
Given StartLayout Enlarged left-brace First-row StartFraction x cubed minus 1 Over x squared minus 1 EndFraction, for x less-than 1 second row StartFraction 3 Over x minus 1 EndFraction, for x greater-than-or-equal-to 1 EndLayout. What is Limit of f (x) as x approaches 1 minus?
Negative three-halves
0
Three-halves
DNE
Answer:
Its C 3/2 just did the test
Step-by-step explanation:
The value of the [tex]\lim_{ x \rightarrow 1^-}f(x)[/tex] is ∞, since option (d) DNE.
What is function?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
How to evaluate the [tex]\lim_{ x \rightarrow 1^-}f(x)[/tex]?The given function is [tex]f(x)=\left\{\begin{array}{l}\frac{x^{3}-1}{x^{2}-1}, \text { for } x < 1 \\\frac{3}{x-1}, \text { for } x \geq 1\end{array}\right[/tex].
We need to evaluate the value of [tex]\lim_{ x \rightarrow {1^-}}f(x)[/tex].
So [tex]\lim_{ x \rightarrow {1^-}}f(x)=\lim_{ x \rightarrow {1}}(\frac{3}{x-1})[/tex]
[tex]=\frac{3}{1-1}[/tex]
[tex]=\frac{3}{0}[/tex]
= ∞
Hence the value of the function is ∞.
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which value is an import of the function?
-14
12
0
4
You throw a stone with a force of 55.1 N. It accelerates at 41.6 m/s2.
Find the mass of the stone in kg. Round your answer to 1 decimal place.
Answer:
Mass = 1.3 Kilograms.
Step-by-step explanation:
Given the following data;
Force = 55.1 N
Acceleration = 41.6 m/s²
To find the mass of the stone in kg;
Newton's Second Law of Motion states that the acceleration of a physical object is directly proportional to the net force acting on the physical object and inversely proportional to its mass.
Mathematically, it is given by the formula;
Force = mass * acceleration
Substituting into the formula, we have;
55.1 = mass * 41.6
[tex] Mass = \frac {55.1}{41.6} [/tex]
Mass = 1.3 Kilograms
Complete the square x2+6x+3
x^2 + 6x + 9
x^2 + 3x + 3x + 9
x ( x + 3 ) + 3 ( x + 3 )
( x + 3 ) ( x + 3 )
( x + 3 ) ^2
140 divided by 8960 please I need to know.
The value will be 64 when the number 8960 is divided by 140.
What is division?A procedure of dividing anything into equal halves is called division. It is one of the four fundamental operations in math. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given numbers are 8960 and 140. To calculate the quotient divide the number 8960 by 140.
The given number can be divided as below:-
140 ) 8960 ( 64
-840
___________
560
-560
___________
000
Therefore, the value will be 64 when the number 8960 is divided by 140.
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what is the circumference of a circle diameter of 6 feet?use 3.14 for n
Answer:
18.84 feet.
Step-by-step explanation:
The formula for the circumference of a circle is:
2Pi*radius
The radius would be half the diameter so 3.
2*3.14*3
The Tetrahedron Superyacht designed by Jonathan Schwinge is a regular tetrahedron with edges 20 m
long. The distance r from one corner to the center of the base (shown in the picture below) is 11.5 m.
pecial rig
What is the vertical height h of the tetrahedron?
Round your answer to the nearest tenth of a meter.
% 4 day
h
m
Answer:
16.36 the proof is in the picture
Step-by-step explanation:
9. How many perpendiculars can we draw to a line from a given point outside the line?
O A. 3
O B. 2.
O C.O
D. 1
Answer:
The answer is D. 1. You can form only 1 perpendicular line.
39.63+0.30=24.45+0.80
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{39.63 + 0.30 = 24.45 + 0.80}[/tex]
[tex]\large\textsf{39.63 + 0.30}[/tex]
[tex]= \boxed{\large\textsf{\bf 39.93}}\large\checkmark[/tex]
[tex]\large\textsf{24.45 + 0.80}[/tex]
[tex]=\boxed{\large\textsf{\bf 25.25}}[/tex]
[tex]\large\textsf{\bf 39.93 } \mathsf{\bf \neq }\large\textsf{ \bf 25.25}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \bf FALSE or NOT TRUE because 39.93 }\mathsf{\neq }\large\textsf{ \bf 25.25}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
if x4 + 1/x4 = 4 find the value of x2+1/x2
Answer:
Hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Answer:
Step-by-step explanation:
I think its 2
The length of a regulation soccer field is 110 meters. The diagonal length of the same soccer field is about 133.14 meters. About how wide is the regulation soccer field?
A. 23.14 meters
B. 243.14 meters
C. 172.7 meters
D. 75 meters
Answer:
D
Step-by-step explanation:
Imagine this as a right angle triangle, where the diagonal length is the hypotenuse, the length is one side, and the width is the other.
We can therefore use Pythagoras' Theorem (or Pythagorean Theorem) to solve. The formula for this is a²+b²=c², where c is the hypotenuse, and a and b are the sides.
We can input the values we know to this formula to get the width. This gives 110²+b²=133.14² or 12100+b²=17 726.2596.
From there subtracting 12100 from both sides gives b²=5626.2596.
Square rooting b isolates it, leaving b=75.0083969.
Since the value of the diagonal was approximate, this can be assumed the b is 75m.
**This content involves Pythagoras' Theorem/Pythagorean Theorem, which you may wish to revise. I'm always happy to help!
Juanita opens a savings account with $200. Each month, she deposits $25 into her account and does not withdraw any money from it. Write an equation in slope-intercept form of the total amount y in Juanita’s account after x months
Answer:
225 hahahahahahahhahahahhaha
Hahhahahahaha
The equation in slope-intercept form will be; y = 200- 25x
How to find the slope?Slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.
Thus, we get:
Slope = rise/ run
We have been given that Juanita opens a savings account with $200.
For Each month, she deposits $25 into her account and does not withdraw any money from it.
Therefore, the equation in slope-intercept form of the total amount y in Juanita’s account after x months is,
y = 200- 25x
Here the slope is - 25.
Hence, the equation in slope-intercept form will be; y = 200- 25x
Learn more about slope here:
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could someone help me with this please?
Put these numbers in order from greatest to least.
3/10, 0.6 and 0.7
An angle that measures between 90 and 180° is called?
Answer:
Obtuse AngleStep-by-step explanation:
An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees.
Using the following image, find GH given HI = 1 and GI =
= 9.
Answer:
8
Step-by-step explanation:
Answer:
[tex]{ \tt{GH =GI - HI }} \\ = 9 - 1 \\ GH = 8[/tex]
You have $9 and earn $0.75 for each cup of orange juice you sell. Write an equation that represents the total amount $A (in dollars) you have after selling $j cups of orange juice. $A
Answer:
I believe it's A = 0.75j + 9
Step-by-step explanation:
If x or j is the amount of cups of OJ you sell, and you earn $0.75 per cup.
0.75x
The b = 9 which adds to the total amount of money you have
0.75x+9
A is the total money you earn after you sell j cups.
I hope this helps!
What is the area please?
Answer:
104
Step-by-step explanation:
18 for the bottom section, 35 for the middle section, and 51 for the top triangle.
will mark brainliest if answered
Answer:
See below
Step-by-step explanation:
The vertex form of a parabola is y = a(x - h)^2 + k
If the leading coefficient is positive, the parabola opens upward, and (h, k) represents the vertex, or turning point.
1a. The leading coefficient is 4, which is positive, meaning the parabola opens upwards. From the vertex form, we can say the vertex(turning point) is (2, 7).
1b. The leading coefficient is -3, which is negative, meaning the parabola opens downwards. From the vertex form, we can say the vertex(turning point) is (-6, 4).
1c. The leading coefficient is -1, which is negative, meaning the parabola opens downwards. From the vertex form, we can say the vertex(turning point) is (-4, -3).
To write the vertex form of a parabola, we need to complete the square. A perfect square trinomial is in the form a^2 + 2ab + b^2. In these cases we are already given a^2 and 2ab.
2a. We can say x^2 corresponds to a^2 because it is a square and 2ab corresponds to 6x. From this, we can say a = x. Now, we can plug that in:
2ab = 6x
2(x)b = 6x
b = 3
Therefore, the last term b^2, is 3^2 or 9. We can add 9 and subtract nine to keep the equation equivalent:
y = x^2 + 6x + 9 - 9 - 2
Now, we can factor the square into (a + b)^2 and simplify:
y = (x + 3)^2 - 11
From this form, the vertex(turning point) will be (-3, -11). Since the leading coefficient is 1, which is positive, the parabola opens upwards, meaning the turning point is a minimum.
2b. We can say x^2 corresponds to a^2 because it is a square and 2ab corresponds to -2x. From this, we can say a = x. Now, we can plug that in:
2ab = -2x
2(x)b = -2x
b = -1
Therefore, the last term b^2, is (-1)^2 or 1. We can add 1 and subtract nine to keep the equation equivalent:
y = x^2 - 2x + 1 - 1 + 11
Now, we can factor the square into (a + b)^2 and simplify:
y = (x - 1)^2 + 10
From this form, the vertex(turning point) will be (1, 10). Since the leading coefficient is 1, which is positive, the parabola opens upwards, meaning the turning point is a minimum.
si alguien me ayuda en esta doy coronita
Answer: yuh Step-by-step explanation: yuh
Answer:
11/8, 7/4, 8/2
someone reported me
Math help please show work
Answer:
7 in
Step-by-step explanation:
Answer:
a = 7 in
Step-by-step explanation:
[tex]Area = \frac{a+b}{2} \times h\\\\26.25 = \frac{a + 10.5}{2} \times 3\\\\26.25 \times 2 = (a+ 10.5) \times 3\\\\52.5 = (A + 10.5) \times 3\\\\\frac{52.5}{3} = a + 10.5\\\\17.5 = a + 10.5\\\\a = 17.5 - 10.5 = 7[/tex]