Answer -
a+1/a = 3 -----(1)
a²+1/a² = 7
By doing square of equation 1
(a+1/a)² = 9
a²+1/a²+ 2 ×a × 1/a = 9 using (a+b)²=a²+b²+2ab
a²+1/a²+2=9
a² + 1/a² = 9-2
a²+1/a²= 7 Ans.
can i have some super quick help? subject is stretching and reflecting quadratic functions
#1
Passes through
(-1,4)y=x² passes through (-1,1)
Stepped 4 times
y=4x²#2
First make a negative as parabola is opening downwards.
y=-x²Passes through (1,-2)
y=-x² passes through (1,-1)
So
final graph
y=-2x²Answer:
a) Stretched parallel to the y-axis by a scale factor of 5
b) Stretched parallel to the y-axis by a scale factor of 5/2 and reflected in the x-axis.
Step-by-step explanation:
Transformation
y = a f(x)
The graph of a f(x) is f(x) stretched parallel to the y-axis (vertically) by a factor of a.If a < 0, the graph is also reflected in the x-axisPart (a)[tex]\textsf{Parent function}:\quad y=x^2[/tex]
[tex]\textsf{Transformed function}:\quad y=5x^2[/tex]
Transformation: Stretched parallel to the y-axis by a scale factor of 5.
Part (b)
[tex]\textsf{Parent function}:\quad y=x^2[/tex]
[tex]\textsf{Transformed function}:\quad y=-\dfrac{5}{2}x^2[/tex]
Stretched parallel to the y-axis by a scale factor of 5/2 and reflected in the x-axis.
A triangle has one angle that measures 56° and one angle that measures 63º.
The measure of the triangle's third angle is degrees.
The solution is
An equation is shown below:
5(2x − 3) = 5
Part A: How many solutions does this equation have? (4 points)
Part B: What are the solutions to this equation? Show your work. (6 points)
Your answer:
Answer:
this equation has 1 answer
Step-by-step explanation:
x = 2
A total of 133 million square miles of the Earth's surface are covered in water. The ratio of the area covered in water to the area of land is 7/3. Find the area of land on Earth.
URGENT! Whoever gets first correct answer is brainliest
Answer:
57 million square milesStep-by-step explanation:
Let the area of water is w and area of land is l.
Their ratio is:
w/l = 7/3or
133 / l = 7/3Find the value of l
l = 133*3/7l = 57 million square milesLet that be x
133/x=7/37x=399x=399/7x=57M mi²
One angle of a rhombus measures 110, and the shorter diagonal is 4 inches long. How long is the side of the rhombus?
side of rhombus: 2.44 inch
Use the sine rule:
[tex]\sf \dfrac{sin(A)}{a} = \dfrac{sin(B)}{b}[/tex]
============= Let the side be "b"
[tex]\rightarrow \sf \dfrac{sin(110)}{4} = \dfrac{sin(35)}{b}[/tex]
[tex]\rightarrow \sf b = \dfrac{sin(35)*4}{sin(110)}[/tex]
[tex]\rightarrow \sf b = 2.441549178[/tex]
[tex]\rightarrow \sf b =2.44 \ in[/tex]
Answer:
3.5 in (nearest tenth)
Step-by-step explanation:
Properties of a rhombus:
Quadrilateral (four sides & four interior angles)Parallelogram (opposite sides are parallel)All sides are equal in lengthOpposite angles are equal in measureDiagonals bisect each other at right anglesInterior angles sum to 360°Adjacent angles are supplementary (sum to 180°)Diagonals bisect interior anglesTherefore, a rhombus is made up of 4 congruent right triangles.
** see attached diagram **
To find the side length of the rhombus, we need to calculate the hypotenuse of the right triangle.
As the shorter diagonal is 4 in, the base of the right triangle is 2 in
The angles that measure 110° are the angles by the shorter diagonal. Therefore, the base angle of the right triangle is 55°
Using cos trig ratio:
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuseGiven:
[tex]\theta[/tex] = 55°A = 2H = x[tex]\implies \sf \cos(55^{\circ})=\dfrac{2}{x}[/tex]
[tex]\implies \sf x=\dfrac{2}{\cos(55^{\circ})}[/tex]
[tex]\implies \sf x=3.486893591...[/tex]
Therefore, the side of the rhombus is 3.5 in (nearest tenth)
How do the charges compare when two objects are charged through friction? The objects become oppositely charged and have equal amounts of charge. The objects become positively charged and have equal amounts of charge. The objects become negatively charged and have different amounts of charge. The objects become oppositely charged and have different amounts of charge.
Answer:
If both objects started with no charge, they would carry opposite charges of the same magnitude after rubbing.
Step-by-step explanation:
When one insulator is rubbed against another, some electrons on one insulator might travel to the surface of the other insulator. Electrons are neither lost nor created in this process- they are just moved from one surface to the other.
Let the two insulators in this question be denoted as [tex]A[/tex] and [tex]B[/tex]. Assume that both insulators were initially not charged.
Let [tex]{\rm e}[/tex] denote the fundamental charge. Each electron carries a negative charge of [tex](-1\; {\rm e})[/tex]. Assume that [tex]n[/tex] electrons are moved from insulator [tex]A\![/tex] to insulator [tex]B\![/tex]:
Insulator [tex]A\!\![/tex] would now have [tex]n\![/tex] fewer electrons than it used to do. Thus, the charge on insulator [tex]A\![/tex] would have been reduced by [tex]n \times (-1\; {\rm e})[/tex]. Since insulator [tex]A[/tex] started with no charge, it would now carry a charge of [tex]0 - n \times (-1 \; {\rm e}) = n\; {\rm e}[/tex].Insulator [tex]B[/tex] would now have [tex]n[/tex] more electrons than it used to do. The charge on insulator [tex]B\![/tex] would have increased by [tex]n \times (-1\; {\rm e})[/tex]. Since insulator [tex]B[/tex] started with no charge, it would now carry a charge of [tex]0 + n\times (-1\; {\rm e}) = (-n\; {\rm e})[/tex].In other words, the insulator that lost some electrons (which are negatively charged) now carries less negative charge and becomes positively charged. In contrast, the insulator that gained some electrons now carries more negatively charge becomes negatively charged.
The amount of electrons on the two objects combined stays unchanged. Thus, the amount of charge one insulator lost is equal to what the other insulator gained. Therefore, the sign of the charge on the two insulators would be different, but the magnitude (absolute value) of the charge would be equal.
Therefore, the two objects would be oppositely charged, with the magnitude of the charge on them being equal.
Can U Guys Tell Me The Angle And Type?
Answer:
The angle is 90°, and the type of angle is a right angle.
Step-by-step explanation:
That is a right angle, the little box and the straight lines indicate that is one. A right angle will always be 90°.
12 times a number, x, minus 5 is ninety-one
x=8
Solution:First, multiply 12 times x, like so:12xNow, subtract 5:12x-5This expression is equivalent to 91:12x-5=91Now, add 5 to both sides:12x=91+512x+96x=8Hope it helps.
Do comment if you have any query.
[tex]12x-5 = 91\\\\\implies 12x = 91+5\\\\\implies 12x = 96 \\\\\implies x= \dfrac{96}{12}\\\\\implies x = 8[/tex]
solve for x :)
i’m not sure how to solve this it’s from geometry lesson 10.2
Step-by-step explanation:
Angle of a circle = 360
x + 90 + 84 + 16 = 360
x + 190 = 360
x = 170°
Which of the following ordered pairs is represented by a point located on the x-axis?
(-3, -3)
( - 6,6)
(5,0)
(0,5)
Answer:
(5,0)
Step-by-step explanation:
The # 5 is on the x axis and there is no value for the y since it is 0. This means that this ordered pair will be located on the x-axis.
order of operation 3×5+4×2-3
[tex]3\times 5 +4 \times 2- 3\\\\=15+8-3\\\\=12+8\\\\=20[/tex]
a rectangular prism has length x, width x/2 and height x/3. Which expression represents the volume of the prism?
Answer:
x^3 / 6
Step-by-step explanation:
Multiply the three dimensions to get the volume
x * x/2 * x/3 =
The expression represents the volume of the prism that will be, x³/6. The expression is obtained by finding the volume of the rectangular prism for the given data.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that, the length is x, width x/2, and height is x/3.
The volume of the rectangular prism is the product of the length, width, and height.
V= length × width × height
V=x × x/2 × x/3
Apply the multiplication operation in the fraction
Simply multiply the numerators to obtain the product's numerator and the denominators to obtain the product's denominator in order to multiply two fractions.
V=x³/6
Thus, the expression represents the volume of the prism that will be, x³/6. The expression is obtained by finding the volume of the rectangular prism for the given data.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ2
Pls help me
Pls show your answer pls and thank you
Answer:
DWest I think
Step-by-step explanation:
I dont really know if this is right so pls forgive me if this is wrong.
100 POINTS!!! Please help ^^ it’s urgent!!
Answer:
x=1 y=4
Step-by-step explanation:
5x+y=9
10x-7y=-18
-35x-7y=-63
-45x=-45
x=1
y=4
(10)-(28)=18
Brainliest would be appreciated
Answer:
x=1 y=4
Step-by-step explanation:
a
20 characters or more
Answer:
2 (y-value increase as x-value also increase)
Step-by-step explanation:
Lets look at the graph! when x is 7, y is 4. and when x is 9, y is 5 which is proving that they BOTH increase
Consider the line – 2x - 5y= 2.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Slope of a perpendicular line:
Answer:
Step-by-step explanation:
What is the value of k? G(x)=f(x+k)
Answer:
K=6
Step-by-step explanation:
I hope this answer is right
need this answer ASAP 20 points as reward
Simplify. Write the answer with positive exponents only.
x3 x5
x3 x5 =
Answer:
1/x^2
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x5" was replaced by "x^5". 1 more similar replacement(s).
Step 1:
Simplify x^3 / x^5
Dividing exponential expressions :
x^3 divided by x^5 = x ^ (3-5) = x^(-2) = 1/x^2
True or false? Based only on the given information, it is guaranteed that
AD = BD
A
D
Given: ADI AC
DBI CB
ACE BC
B
O A. True
B. False
Answer:
True
Step-by-step explanation:
The triangles are both right triangles, meaning they can be used with pythagorean theorem. If the triangles CAD and CBD share the same "hypotenuse" (CD), and they have a pair of congruent sides, they other pair of sides must be able to fit into the pythagorean theorem/
Its a multiple choice, HELP IM BEGGING
Answer:
B)
E)
Step-by-step explanation:
translation Dilation
M(x,y) ——————>M”(x”,y”)=(x+5,y+8) ——————> M’(x’,y’)=(3x”,3y”)
S(-5,-8) ——————>S”(x”,y”)=(0,0) ——————> S’(x’,y’)=(0,0)
R(-7,-6) ——————>R”(x”,y”)=(-2,2) ——————> R’(x’,y’)=(-6,6)
Q(-8,-10) ——————>Q”(x”,y”)=(-3,-2) ——————> Q’(x’,y’)=(-9,-6)
solve x/9 + 1/3 = -4/3
The solution is x = ?
Answer:
x = - 15
Step-by-step explanation:
[tex]\frac{x}{9}[/tex] + [tex]\frac{1}{3}[/tex] = - [tex]\frac{4}{3}[/tex] ( multiply through by 9 to clear the fractions )
x + 3 = - 12 ( subtract 3 from both sides )
x = - 15
Answer:
Solve for x by simplifying both sides of the equation, then isolating the variable.
x=−15
More help if you can! I desperately need to pass this one class
Answer:
volume of cuboid = lbh = 8.2 ft x 9.4 ft x 10.7 ft
= 824.8 ft^3
or 22,4:58:53 AM
Watch help video
Cooper gave out a survey to some students in his school about their favorite color.
tudents could choose between red and blue. 129 of those surveyed said their favorite
color was red. 57% of the students surveyed said their favorite color was blue. How
many students were surveyed in total?
Answer:
300 students were surveyed.
Step-by-step explanation:
Well, we know that 57% of students like blue, so that leaves 43% who like red. By simply dividing 129 by 43, we get 3, so know we can conclude that 1% is equal to 3 students. Knowing this, we can multiply 3 by 57 to get 171. Adding these up, we get 300, and we can verify this, by simply finding the difference between 57 and 43, which is 14. Now that we also know that 1% is equal to 3 students, we can multiply 14 by 3, to get 42, which is also the difference between 171 and 129.
give the missing angle
Answer:
60°, 115°, 65°Step-by-step explanation:
Angles a and 60°, also c and 65° are alternate interior angles and therefore are equal:
a = 60°c = 65°Angles b and 65° form a linear pair, so they sum to 180°
b + 65° = 180°b = 180° - 65°b = 115°Answer:
a = 60°
b = 115°
c = 65°
Step-by-step explanation:
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent (same).
Therefore, a = 60° and c = 65°
Angles on a straight line sum to 180°
⇒ b + 65° = 180°
Subtracting 65° from both sides:
⇒ b + 65° - 65° = 180° - 65°
⇒ b = 115°
Solve this system of linear equations. Separate
the x- and y-values with a comma.
18x - 7y = -17
3x - 3y = -12
Enter the correct answer.
Answer:
-> (x,y) => (1,5)
x = 1y = 5Step-by-step explanation:
Let's solve your system by elimination.
18x−7y=−17;3x−3y=−12
Multiply the second equation by -6, then add the equations together.
(18x−7y=−17)
−6(3x−3y=−12)
Becomes:
18x−7y=−17
−18x+18y=72
Add these equations to eliminate x:
11y=55
Then solve 11y=55for y:
11y=55
11y/11 = 55/11
(Divide both sides by 11)
y=5
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
18x−7y=−17
Substitute5foryin18x−7y=−17:
18x−(7)(5)=−17
18x−35=−17(Simplify both sides of the equation)
18x−35+35=−17+35(Add 35 to both sides)
18x=18
18x/18 = 18/18
(Divide both sides by 18)
x=1
a group of 10 people are ordering pizza. each person wants 2 slices and each pizza has 5 slices. how many pizzas should thay order
Answer:4
Step-by-step explanation:
2 slices each ten people times them together 20 slices .4 pizzas*5slices=20
A $299.99 grill was discounted 25% for a labor day sale. When the sale ended, the sale price increased 25%. How much is the grill now?
Find the slope and the equation for the line passing through the points: (-3,0) and (-1,2)
Answer:
slope: 1equation: y = x +3Step-by-step explanation:
The slope of the line between two points can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (2 -0)/(-1 -(-3)) = 2/2
m = 1 . . . . . the slope of the line is 1
__
The value of the y-intercept can be found by solving the slope-intercept equation for b.
y = mx +b
b = y -mx
b = (0) -(1)(-3) = 3 . . . . . using point (x, y) = (-3, 0)
The equation of the line with slope 1 and y-intercept 3 can be written as ...
y = x +3
Express 0.10190 as a fraction.