Answer:
The value of x is 2 or -2.
Step-by-step explanation:
Consider the provided equation.
[tex]3x^2= 12[/tex]
We need to solve the above equation for x.
Divide 3 from both the sides.
[tex]\frac{3x^2}{3}=\frac{12}{3}[/tex]
[tex]x^2=4[/tex]
Square root both the sides.
[tex]x=\pm \sqrt{4}[/tex]
[tex]x=\pm 2[/tex]
Hence the value of x is 2 or -2.
The solution to the equation [tex]3x^2 = 12[/tex] is [tex]x = \pm2[/tex], which is [tex]x = 2[/tex] and [tex]x = -2.[/tex]
To solve the equation [tex]3x^2 = 12[/tex] algebraically:
Divide both sides of the equation by 3 to isolate the [tex]x^2[/tex] term:
[tex]\frac{3x^2}{3}=\frac{12}{3}[/tex]
[tex]x^2 = 4[/tex]
Take the square root of both sides to solve for x:
[tex]\sqrt{x^2}=\sqrt{4}[/tex]
[tex]x = \pm2[/tex]
Hence, the solutions to the equation [tex]3x^2 = 12[/tex] are [tex]x = 2[/tex] and [tex]x = -2.[/tex]
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ6
Use the remainder theorem to divide 5x^2+9x-2 by x+3. what is the remainder?
A)16
B)-44
C)-20
D)40
Answer:
A)16
Step-by-step explanation:
Given
f(x)=5x^2+9x-2
Remainder theorem states that when f(x) is divided by x-a then the remainder can be calculated by calculating f(a).
Now Using the remainder theorem to divide 5x^2+9x-2 by x+3 to find the remainder:
f(x)=5x^2+9x-2
f(-3) = 5(-3)^2 +9(-3) -2
=5(9) - 27 -2
= 45-29
= 16 !
the line passing through point (2, 2) and perpendicular to the line whose equation is y = x
Answer:
[tex]y=-x+4[/tex]
Step-by-step explanation:
We want to find the equation of the line passing through (2,2) and perpendicular to the line with equation y=x.
The given line y=x has slope n=1.
The line that is perpendicular to this line has slope m=-1
The equation is given by the formula;
[tex]y-y_1=m(x-x_1)[/tex]
we plug in the slope and the point to get;
[tex]y-2=-1(x-2)[/tex]
[tex]y-2=-x+2[/tex]
[tex]y=-x+2+2[/tex]
The required equation is
[tex]y=-x+4[/tex]
what is 6.4r−7−2.9 simplified
The simplified expression is 3.5r - 7.
To simplify the expression 6.4r - 7 - 2.9r, first, combine like terms by subtracting the coefficients of 'r'.
This yields (6.4 - 2.9)r. Simplifying the coefficients gives 3.5r. Then, subtract 7. Therefore, the simplified expression is 3.5r - 7.
This means that when you distribute the 'r', you multiply it by 3.5, then subtract 7 from the result.
The simplified expression is 3.5r - 7.
Complete question :- Simplify 6.4r - 7 - 2.9r.
Find the missing measurements for the rectangle when the area equals 216 and the perimeter equals 66
[tex]\bf \stackrel{\textit{perimeter of a rectangle}}{P=2(L+w)}~~ \begin{cases} L=length\\ w=width\\ \cline{1-1} P=66 \end{cases}\implies 66=2(L+w) \\\\\\ 33=L+w\implies \boxed{33-w=L} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of a rectangle}}{A=Lw}\qquad \implies 216=Lw\implies 216=(33-w)w \\\\\\ 216=33w-w^2\implies w^2-33w+216=0 \\\\\\ (w-24)(w-9)=0\implies w= \begin{cases} 24\\ 9 \end{cases}[/tex]
now, both values are valid, so if "w" is either one, "L" is the other.
Find the value of each variable
Answer:
The correct answer is option C
a = 10√3, b = 5√3, c = 15 and d = 5
Step-by-step explanation:
Points to remember
The angles of a right angled triangle, 30°, 60° and 90° then sides are in the ratio, 1: √3 : 2
To find the value of variables
From the figure we can see 2 right angled triangle with angle 30, 60 and 90
we get, d= 5 then b = 5√3
b = 5√3 the c = 5√3 * √3 = 15
and a = 2 * 5√3 = 10√3
Therefore the correct answer is option C
a = 10√3, b = 5√3, c = 15 and d = 5
Answer:
d.[tex]a=10\sqrt3,b=5\sqrt3,c=15,d=5[/tex]
Step-by-step explanation:
We have to find the value of each variable.
[tex]\frac{P}{H}=sin\theta[/tex]
[tex]\frac{b}{10}=sin 60^{\circ}[/tex]
[tex]\frac{b}{10}=\frac}\sqrt3}{2}[/tex]
[tex]b=10\times \frac{\sqrt3}{2}=5\sqrt3[/tex]
[tex]\frac{d}{10}=cos 60^{\circ}[/tex] ([tex]cos\theta=\frac{base}{hypotenuse}[/tex])
[tex]d=\frac{1}{2}\times 10=5[/tex]
[tex]\frac{b}{a}=sin30^{\circ}[/tex]
[tex]\frac{5\sqrt3}{a}=\frac{1}{2}[/tex]
[tex]a=10\sqrt3[/tex]
[tex]\frac{b}{c}}=tan 30^{\circ}[/tex] ([tex]tan\theta=\frac{p}{b}[/tex])
[tex]\frac{5\sqrt3}{c}=\frac{1}{\sqrt3}[/tex]
[tex]c=5\sqrt3\times \sqrt3=15[/tex]
[tex]a=10\sqrt3,b=5\sqrt3,c=15,d=5[/tex]
Hence, option d is true.
In the fall you charge people $8 for going to their house to pick fruits, then $5 for every hour you pick. If you make $28 one day, how many hours did you spend picking?
Answer: 4 hours
Step-by-step explanation: 20-8=20
20/5= 4hours
What is the completely factored form of x4 + 8x2 – 9?
ANSWER
[tex] ( {x}^{2} + 9)({x} - 1)(x + 1)[/tex]
EXPLANATION
The given function is
[tex] {x}^{4} + 8 {x}^{2} - 9[/tex]
Split the middle term
[tex] {x}^{4} + 9 {x}^{2} - {x}^{2} - 9[/tex]
Factor by grouping;
[tex]{x}^{2} ( {x}^{2} + 9) -1 ({x}^{2} + 9)[/tex]
Factor further to get:
[tex] ( {x}^{2} + 9)({x}^{2} - 1)[/tex]
Apply difference of two squares to get:
[tex] ( {x}^{2} + 9)({x} - 1)(x + 1)[/tex]
Answer:
[tex](x^2+9)(x-1)(x+1)[/tex]
Step-by-step explanation:
We would need to let u = x^2 and use middle term factorization first. let's do this:
if u = x^2, then x^4 + 8x^2 – 9 would be
u^2+8u-9
Middle term factorization of this is:
(u+9)(u-1)
now replacing back u = x^2:
(x^2+9)(x^2-1)
Using the formula a^2 - b^2 = (a+b)(a-b), we can write (x^2 - 1) as (x+1)(x-1).
So, the final factored form is: (x^2+9)(x-1)(x+1)
!!need answer asap!!
solve for x
Answer:
X= 0, X=-3, X=1
Step-by-step explanation:
given that (-4,-4) is on the graph of f(x), find the corresponding point for the function 1/2 f(x)
Answer:
(-4, -2)
Step-by-step explanation:
The x-coordinate would stay the same, but the y-coordinate would be halved. Thus, the corresponding point would be (-4, -2).
What is the slope of the line that contains the points (-1,2) and (3,3)?
Answer:
1/4
Step-by-step explanation:
To find the slope of a line from two points we use
m = (y2-y1)/(x2-x1)
m = (3-2)/ (3--1)
= (3-2)/(3+1)
=1/4
Step-by-step explanation:
A(-1,2) and B(3,3) then AB=(4,1).
Normal vector
n=(-1,4)
Our line contains point A(-1,2) and has normal vector n=(-1,4) is
[tex](d) : - 1(x + 1) + 4(y - 2) = 0[/tex]
[tex](d ): - x - 1 + 4y - 8 = 0[/tex]
[tex](d) : - x + 4y - 9 = 0[/tex]
Use the diagram below to answer questions 1-3
Answer:
1.) ∠GAC and ∠CAF are complementary and acute angles
2.) 27°
3.) m∠CAG+m∠GAD=180°
Step-by-step explanation:
2.) because you solve for x:
63°+x°=90°
x= 27°
an original piece of artwork is 3 feet by 2.5 feet. A reprint of the artwork is 6 inches by 5 inches. Are the pieces similiar? If so, what is the ration of their corresponding side lengths?
Answer:
Yes
Explaination:
They are similar and the ratio is still the same. The artwork's shape didn't change we just resized it by multiplyting its length and width by 2.
Karen has $800 to open a checking account. She wants an account with the lowest fees. She only writes about five checks per month and her employer has direct deposit. She does not plan on using the ATM or online banking.
Answer:
account c
Step-by-step explanation:
took on quiz 100%
Answer: C. Account C
Step-by-step explanation:
A trapezoid has based of 15 inches and 7 inches. It’s height is 6 inches. What equation can I use to find the area?
Answer:
A=1/2 h(b1+b2)
Step-by-step explanation:
h being the height and b1 being base one and b2 being base two
Please help I don’t know which one it is
Substitute all values for x and y into their placement
y<1-6x
(1)<1-6(-1)
1<7
The coordinate pair is (-1,1)
Identify the corresponding word problem given in the inequality x less than or equal to 4.50
Answer:
[tex]\boxed{x \leq 4.50}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rrcl}\textbf{Words:} & \text{x} & \text{less than or equal to} & \text{4.50}\\\textbf{Symbols:} & x & \leq & 4.50\\\end{array}[/tex]
Answer:
Step-by-step explanation:
the product of a number and -6 is at least 24. Write an inequality and solve the problem
Answer:
-6x ≥ 24
x = ≤ 4
Step-by-step explanation:
Number = x
The product of the number and -6.
-6x
The product is at least 24.
-6x ≥ 24
Solve the problem
-6x ≥ 24
Divide by -6 and we change the sign
x = ≤ 4
Answer:
Step-by-step explanation:
Type the correct answer in each box. A circle is centered at the point (-7, -1) and passes through the point (8, 7). The radius of the circle is units. The point (-15, ) lies on this circle.
Answer:
r = 17 units
Step-by-step explanation:
The radius is the distance from the centre (- 7, - 1) to the point on the circle
(8, 7)
Use the distance formula to calculate the radius (r)
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 7, - 1) and (x₂, y₂ ) = (8, 7)
r = [tex]\sqrt{(8+7)^2+(7+1)^2}[/tex]
= [tex]\sqrt{15^2+8^2}[/tex]
= [tex]\sqrt{225+64}[/tex]
= [tex]\sqrt{289}[/tex] = 17 units
The probability that Yuri will make a free throw is 0.3. The probability that he will make two consecutive free throws is _______. The probability that he will make the first and not the second in two free throws is _______. The probability that he will make neither of the two free throws is _______.
Answer:
1. 0.09
2. 0.21
3. 0.49
Step-by-step explanation:
If the probability that Yuri will make a free throw is 0.3, then the probability that Yuri will not make a free throw is 1-0.3=0.7.
1. The probability that Yuri will make two consecutive free throws is
[tex]0.3\cdot 0.3=0.09[/tex]
2. The probability that he will make the first and not the second in two free throws is
[tex]0.3\cdot 0.7=0.21[/tex]
3. The probability that he will make neither of the two free throws is
[tex]0.7\cdot 0.7=0.49[/tex]
Answer:
0.78
Step-by-step explanation:
Divide: 5/18
need help ASAP algebra 2 please !!!
Answer:
The answer is D.
Step-by-step explanation:
This is because the first part of the expression is the conjugate and youre given -5. The second part of the expression is the imaginary part and youre given 4i.
Answer:
C
Step-by-step explanation:
Given a complex number in the form
a + bi then the conjugate is a - bi
Note the real part remains unchanged while the sign of the imaginary part is negated.
Given
- 5 + 4i then the conjugate is - 5 - 4i → C
A rectangular prism is 6 inches long, 3 inches wide, and 2 inches high. What is its volume?
72 in. 3
11 in. 3
36 in. 3
22 in. 3
This may be what you're looking for:
Answer:
36 in.³
Step-by-step explanation:
volume = length × width × height
volume = 6 in. × 3 in. × 2 in.
volume = 36 in.³
An office supply store has five different packages of thumb tacks. Which is the best deal available on thumb tacks at this office supply?
Barry buys a package of pasta for $2.39 and a jar of tomato sauce for $3.09. He uses a $0.75 coupon and a $0.50 coupon.
Answer:$4.23
Step-by-step explanation:
Answer:
4.23 is the answer if its wrong let me know what mistakes i made
What is the value of the expression?
tan π/6
Exact Form: √3/3
Decimal Form: 0.57735026
sorry if i got it wrong, i tried my best on this :)
The value of the expression tan π/6 is √3/3 or approximately 0.5774.
The value of the expression tan π/6 is √3/3 or approximately 0.5774.
To find this value, we can remember that tan θ = sin θ / cos θ. So, tan(π/6) = sin(π/6) / cos(π/6).
Thus, tan(π/6) = (√3/2) / (1/2) = √3/3.
Please help and thank you
Answer:
survey
Step-by-step explanation:
because she wants to know the opinions of the girls
Hi!
I think it would be a survey because then the people would give their opinions, which is what she wants.
Hope this helps!
Match the vocabulary word to its correct definition,
1. absolute value
2. continuous function
3. step function
4. piecewise-defined function
function whose graph has no breaks
function whose output equals input for non-negative numbers, and whose output is the opposite of a negative input
function defined on different intervals by different domain rules
function whose graph consists of horizontal line segments
Answer:
function defined on different intervals by different domain rules
hope it helps
The terms absolute value, continuous function, step function, and piecewise-defined function are matched with their respective definitions: the absolute value measures distance from zero, a continuous function has a graph without breaks, a step function has a graph with horizontal steps, and a piecewise-defined function has different rules for different intervals.
Matching Vocabulary to Definitions
Let's match each mathematical term to its correct definition:
Absolute value - This is the function whose output equals the input for non-negative numbers, and whose output is the opposite of a negative input. It can be thought of as the distance from zero on the number line, regardless of direction.
Continuous function - A function whose graph has no breaks is known as continuous. It means you can draw the function without lifting your pen off the paper, indicating it has no jumps or holes.
Step function - Such a function has a graph that consists of horizontal line segments. The value of the function changes in 'steps' rather than smoothly.
Piecewise-defined function - When a function is defined on different intervals by different domain rules, it is known as a piecewise-defined function. It's like having multiple functions strung together each applicable to different parts of the domain.
A spinner is numbered from 1 through 10 with each number equally likely to occur. What is the probability of obtaining a number less than 3 or greater than 8 in a single spin?
Answer:
[tex]P = 0.4[/tex]
Step-by-step explanation:
If each number X has the same probability of occur then the probability for each number is:
[tex]P = \frac{1}{10}[/tex]
Note that X is a discrete random variable, and the probability of obtaining an X number is independent for each trial.
So the probability that X is less than 3 is:
[tex]P (X <3) = P (1) + P (2)[/tex]
But [tex]P (1) = P (2) = \frac{1}{10}[/tex]
So:
[tex]P (X <3) = P (1) + P (2) = \frac{2}{10} = \frac{1}{5}[/tex]
Also
[tex]P (X> 8) = P (9) + P (10) = \frac{1}{10} = \frac{1}{5}[/tex]
Finally
[tex]P (X <3\ or\ X> 8) = \frac{1}{5} +\frac{1}{5} = \frac{2}{5} = 0.4[/tex]
uwu pls help :''( i may cry if you don't
Combine the like terms to create an equivalent expression:
−4q−(−8q)+10
1.So, what you do is remove the () from -8q.
2. Time -8q by one and it equals -8q.
3. Combined -4q and -8q, that equals -12q
4. Once you combine them create the equation which will be -12q+10 And that’s your answer because you can’t combine the 10 with any other number because -12q has a q. Hope this helps. And I’m sorry if I’m wrong >_<4q + 10 is the equivalent expression of −4q−(−8q)+10
What is an algebraic expression?An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. For instance, the algebraic formula 3x² + 2xy + c
Given
-4q - (-8q ) + 10
using BODMAS
-4q + 8q +10
4q + 10
To know more about algebraic expression refer to :
https://brainly.com/question/19864285
#SPJ2
The system of equations y=-1/2 x + 4 and y= 2x - 1 is shown on the graph below According to the graph what is the solution to this system of equations?
Answer:
the answer is where the 2 points intersect... A. (2,3)
Step-by-step explanation:
Answer:
The correct option is A.
Step-by-step explanation:
The given system of equations is
[tex]y=-\frac{1}{2}x+4[/tex]
[tex]y=2x-1[/tex]
All the points on a line is are the solutions of the equation of line.
From the graph it is clear that the lines intersect each other at point (2,3). It means both the lines passes through the point (2,3) and point (2,3) is the solution of given system of equations.
Since (2,3) is the solution of given system of equations, therefore the correct option is A.
Luna had $50 when she got to the carnival.After riding 12 rides, she had $26 left. What was the price of each ride?which equation could be used to represent this situation?
Answer:
I'm not sure but I believe it's 50-12p=26
Step-by-step explanation:
Answer:
The third box: (50-12p=26)
Step-by-step explanation:
50-12p=26
-12p=26-50
-12p=-24
p=2
The price of each ride was $2.
Since the other answers gave you a negative, it would not have given you thr right answer.