The solution to the quadratic equation 6x² + 6 = 12x is x = 1
How to determine the solutions?The quadratic equation is given as:
6x² + 6 = 12x
Equate the equation to 0
6x² - 12x + 6 = 0
Expand the equation
6x² - 6x - 6x + 6 = 0
Factorize the expression
6x(x - 1) - 6(x - 1) = 0
Factor out x - 1
(6x - 6)(x - 1) = 0
Split
6x - 6 = 0 or x - 1 = 0
Solve for x in both instance
x = 1 or x = 1
Hence, the solution to the quadratic equation 6x² + 6 = 12x is x = 1
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V-125 - 5 X 32
[tex]3 \sqrt{ - 125} - 5 \times {3}^{2} [/tex]
Simplify the following and show all your workings
Answer:
Because of the order of operations, we start the equation backwards because exponents are what we prioritize here.
[tex]3^2 = 9\\\\9 * 5 = 45\\\\\sqrt{-125} = -11.1803399\\\\45 - -11.1803399 = 56.1803399\\\\56.1803399 * 3 = \boxed{168.54}[/tex] Result rounded to 2 DP
A surveyor measures the angle of elevation at 20° for a point 5 miles away what is the vertical change in elevation from the point where the surveyor is standing to the point 5 miles away???
help please
Step-by-step explanation:
there are just some big words trying to confuse you.
it just means that there is a right-angled triangle :
there is the point on the ground, where the surveyor is standing.
then there is the elevated point up there, where the surveyor was measuring the angle to.
and then there is the point on the ground directly under this elevated point. at this point in the ground we have the right angle (90°).
this height of the elevated point above this ground point is what we are looking for, and it is one leg of the right-angled triangle.
the ground distance from the surveyor to the ground point under the elevated point is 5 miles and the second leg.
the direct line of sight from the surveyor to the elevated point is inclined up by 20°, and is the Hypotenuse (baseline opposite of the 90° angle) of the triangle.
remembering that the sum of all angles in a triangle is always 180°, we also know the angle at the elevated point :
180 - 90 - 20 = 70°
now we are using the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where the sides are always opposite to their associated angles.
so, we have in our triangle
height/sin(20) = 5/sin(70)
height = 5×sin(20)/sin(70) = 1.819851171... miles
so, the elevated point is 1.819851171... miles above the elevation of the surveyor.
How many right angles are on this shape?
Explanation:
The term "right angle" is another way of saying "90 degree angle".
Such angles are marked as squares. Usually there are tiny square symbols inside the angle to be very clear that we have 90 degree angles. Some diagrams may not do this, and simply imply that anything that looks like a square 90 degree angle actually is one.
With this in mind, the angles that fit the description are angles J and M at the bottom of the figure. Therefore, there are 2 right angles in this shape.
Side note: This figure is a trapezoid because it has exactly one set of parallel sides KJ and LM.
The roof of braeden's house is shaped like a parallelogram. The base of the roof is 12m and the area is 114 cm square. Choose a number and unit to make this statement true.
Draw polygon abcdef in this coordinate plane, given its vertices a=(-2,-3), b=(0,-3), c=(0,1), d=(3,1), e=(3,3), f=(-2,3)
The polygon abcdef in the coordinate plane shown with area of 18 square units.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
We have vertices for the polygon:
a=(-2,-3), b=(0,-3), c=(0,1), d=(3,1), e=(3,3), f=(-2,3)
After marking the coordinates on the coordinate plane and connecting the lines, we will get a polygon.
We can find the area of the shape:
Area of the shape = 18 square units
Thus, the polygon abcdef in the coordinate plane shown with area of 18 square units.
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NEED HELP ASAP 100 POINTS AND BRAINLIEST FOR THE CORRECT ANSWER!!!
Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences.
g(x)=3x+2
f(x)=|x-4|+2
As it's already graphed their inetresection point is solution for both functions
Red one is g(x) as it's linearOther one is f(x) as it's modulusThe solution is (1,5)
Answer:
(1, 5)
Step-by-step explanation:
The solution to the system of equations would be where the lines of the two intersect. The point of intersection (based on the graph) is :
(1, 5)Nine balls, each marked with a number from 1 to 9, are placed in a bag and one ball is taken at random. What is the probability that the number on the ball is multiple of 2?
A.1/9
B.2/9
C.4/9
D.1
Total balls=sample space=9
Multiples of 2
{2,4,6,8}Total multiples=4
Probability
4/9Option C
Hello, the answer should be [tex]\frac{4}{9}[/tex], C option.
First, let's define the numbers that are a multiple of 2 from the balls we have.
2468Then, we will calculate our probability. To do this correctly, we must divide the amount of expected states into the amount of all the states.
Expected numbers: 2-4-6-8
All numbers: 1-2-3-4-5-6-7-8-9
[tex]P=\frac{{2,4,6,8}}{1,2,3,4,5,6,7,8,9} =\frac{4}{9}[/tex]
Good luck! If you have any questions, then feel free to ask in comments!
A new truck can travel 350 miles on 25 gallons of gas. How far can it travel on 60 gallons of gas? What is the car's gas milage?
6th grade middle school
ANSWER:
The MPG is 1/14. The car can travel 840 miles with 60 gal. of gas.
The scale factor for ΔABC to ΔMNL is:
Answer:
2
Step-by-step explanation:
The scale factor shows the proportion of a number to another one
The side lengths for triangle ABC: 12-4-2
The side lengths for triangle LMN: 6-2-1
if we write them as fractions
12/6 = 2
4/2 = 2
2/1 = 2 so the answer is in third option.
Expand to write an equivalent expression
-1/4 (-8x + 12y)
The equivalent expression on expanding -1/4 (-8x + 12y) is 2x - 3y
Expansion of expressionExpansion of expression can be carried out using the distributive rule a shown:
A(B + C) = AB + AC
Note that A is distributed over B and C
Given the expression
-1/4 (-8x + 12y)
-1/4(-8x) - 1/4(12y)
2x - 3y
Hence the equivalent expression on expanding -1/4 (-8x + 12y) is 2x - 3y
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An extension cord 6 yards long costs $8.46. What is the price per foot? There are 3 feet in 1 yard.
Submit
The extension cord is an illustration of unit rates, and the price per foot is $0.47 per foot
How to determine the price per foot?The given parameters are:
Length = 6 yards
Cost = $8.46
Convert the length from yard to feet.
So, we have:
Length = 6 feet * 3
This gives
Length= 18 feet
The price per foot is then calculated using:
Rate = Cost/Length
This gives
Rate = 8.46/18
Evaluate
Rate = 0.47
Hence, the price per foot is $0.47 per foot
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Evaluate
-
b
2a
when a = 4 and b = -3.
Answer:
=24
Step-by-step explanation:
Correct Q:
-b•2a
Ans:
Put the values.=+3*2•4
=24
According to the fundamental theorem of algebra, which polynomial function has exactly 6 roots? f (x) = 5 x superscript 4 baseline 10 x squared 2 f (x) = 5 x superscript 5 baseline 3 x superscript 4 baseline 12 x cubed 7 x squared minus 2 x 15 f (x) = 6 x superscript 5 baseline x cubed minus 4 x squared x minus 5 f (x) = 7 x superscript 6 baseline 3 x cubed 12
The polynomial with 6 roots is the one of degree 6, so the correct option is:
[tex]f(x) = 7x^6 + 3x^2 + 12[/tex]
Which polynomial function has 6 roots?
You need to remember that if p(x) is a polynomial of degree N, then it has N roots (such that some of these N roots may be equal or not).
Then we just need to find the polynomial of degree 6. (Remember that the degree represents the maximum exponent of the polynomial).
In this case, the only one of degree 6 is:
[tex]f(x) = 7x^6 + 3x^2 + 12[/tex]
Which is the last option.
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Answer:
The answer is D
Step-by-step explanation:
I took the test
Suppose a normal distribution has a mean of 26 and a standard deviation of 4. What is the probability that a data value is between 28 and 35? Round your answer to the nearest tenth of a percent.
A. 29.6%
B. 23.6%
C. 27.6%
D. 25.6%
Using the normal distribution, it is found that the probability that a data value is between 28 and 35 is given by:
A. 29.6%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Researching the problem on the internet, the mean and the standard deviation are given by:
[tex]\mu = 26, \sigma = 4[/tex].
As a proportion, the probability that a data value is between 28 and 35 is the p-value of Z when X = 35 subtracted by the p-value of Z when X = 28, hence:
X = 35:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 26}{4}[/tex]
Z = 2.25
Z = 2.25 has a p-value of 0.988.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 26}{4}[/tex]
Z = 0.5
Z = 0.5 has a p-value of 0.692.
0.988 - 0.692 = 0.296 = 29.6%, which means that option A is correct.
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GIVING BRAINLIEST!!!!!
Answer:
23.33
Step-by-step explanation:
The sum of the internal angles of a triangle is 180°, which is given by The Angle Sum Property of Triangles.
⇒ 3x - 17 + 2x + 5 + x + 52 = 180
⇒ 6x + 40 = 180
⇒ 6x = 140
⇒ x = 140/6
⇒ x = 70/3
⇒ x = 23.33
Answer: x = 23.333
In any triangle, all the three angles will ALWAYS add up to 180°. According to that:
▪ 180° = <a + <b + <c
(2x + 5) + (3x - 17) + (x + 52) = 180
2x + 5 + 3x - 17 + x + 52 = 180
Rearrange according to like terms
2x + 3x + x + 52 - 17 + 5 = 180
6x + 40 = 180
Now we'll find the value of x
6x = 180 - 40
x = 140/6
By cross cancellation we get
x = 70/3
You could change it into decimal as well
x = 23.333 answer
therefore, the third option that says 23.33 is correct.
Hope that helps...
Please answer ASAP! I will give you brain L. #8
Answer:
AC = [tex]3\sqrt{3}[/tex]
BC = [tex]6\sqrt{3}[/tex]
Step-by-step explanation:
AC is [tex]x\sqrt{3}[/tex] and x = 3 so [tex]3\sqrt{3}[/tex] and it [tex]=3\sqrt{3}[/tex]
BC is [tex]2x[/tex] and x = 3 so [tex]2(3\sqrt{3}) = 6\sqrt{3}[/tex]
Hopefully this was what you wanted, and is correct!
Vince is cutting fabric strips for a project. He needs fabric strips that are 1212 inches wide. He cut his first fabric strip too wide. His percent error was 5%. How wide did Vince cut the fabric strip?
Answer:
13.125 inches wide
Step-by-step explanation:
5% more than 12.5 which is 12 1/2 as a decimal, equals 13.125 inches.
Multiply your needed fabric width (12.5 or 12 1/2) by (1 + %/percent you're increasing it by) to equal the width you cut instead:
[tex]12.5(1+5) = 12.5(1.05) = 13.125[/tex]
I need help to find the slope of graph.
Answer:
slope m = - [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
Does anybody want to help with math?
2a(-5a^8b+a^2-12ab)
Ty :D
Answer: 18a4 - 6a3b - 5a2b4 - 45a2b2 + 36ab2 - 12ab + 3b
———————————————————————————————-
3
Step-by-step explanation:
Determine the equation for the line of best fit to represent the data.
Answer:
d
Step-by-step explanation:
Deremine the general solution of sin 2x - 4cos2x
Answer:
[tex]x=\frac{1}{2}\left(\tan^{-1}{4}+\pi k\right)[/tex], where k is any integer
Step-by-step explanation:
Let's start by getting all the trig functions on one side and all the constants on the other. We can do this by dividing both sides by [tex]\cos{2x}[/tex]:
[tex]\dfrac{\sin{2x}}{\cos{2x}}=4[/tex]
This ratio looks familiar! It just so happens that the tangent function is defined as the ratio of sine to cosine. In our case:
[tex]\dfrac{\sin{2x}}{\cos{2x}}=\tan{2x}[/tex]
Substituting this back into our equation, we have [tex]\tan{2x}=4[/tex]. We can unwrap the 2x by applying the inverse tangent function to both sides, giving us [tex]2x=\tan^{-1}{4[/tex]. Note, this specific solution only accounts for values of 2x between 0 and 2π radians. To make it general, we can add the term πk to the end of the right side, where k is any integer. We use π as a coefficient because the tangent function has a period of π radians, and it repeats its values every period.
Finally, we divide both sides of the equation by 2 to isolate x, giving us
[tex]2x=\tan^{-1}{4}+\pi k\\x=\frac{1}{2}\left(\tan^{-1}{4}+\pi k\right)[/tex]
What is the area of this figure? PLS ANSWER
Answer:
42 units ^2
Step-by-step explanation:
Break in to a top triangle a middle rectangle and a bottom triangle
area = 1/2 7 *2 + 4 * 7 1/2 * 2 * 7 = 42 units ^2
ASAP!!! PLEASE HELP & EXPLAIN.
Answer:
B
Step-by-step explanation:
the domain of a graph consists of all the input values shown on the x-axis.
so because the only parts shown on the x axis are 6 and -6 that is the answer!
hope this helps!
4 of 8
Given that y = 6 cm and 0 = 32", work out I rounded to 1 DP.
x =
Answer:
[tex]x=3.18[/tex] [tex]cm[/tex]
Explanation:
[tex]x=3.18[/tex] [tex]cm[/tex]
Substitute [tex]y=6 cm[/tex] into [tex]\frac{}{AC} =y:\frac{}{AC} =6cm[/tex]
Substitute [tex]0=32[/tex] into ∠[tex]CAB=0:[/tex] ∠[tex]CAB=32^o[/tex]
sinA=leg opposite ∠A/hypotenuse : [tex]sin(CAB)=\frac{\frac{}{BC} }{\frac{}{AC} }[/tex]
Substitute [tex]\frac{}{BC} =x,\frac{}{AC}=6cm,[/tex] ∠[tex]CAB=32^o[/tex]
into sin(∠[tex]CAB[/tex]) [tex]=\frac{\frac{}{BC} }{\frac{}{AC} }:sin(32^o)=\frac{x}{6}[/tex]
Calculate [tex]sin(32^o)=\frac{x}{6} :x=3.18cm[/tex]
María y Sara se preparan para una competencia de atletismo. María recorre tres octavas partes de la distancia total de la competencia y Sara las dos quintas partes.
¿Qué fracción representa el total de la distancia recorrida por las dos atletas?
A.
140
B.
640
C.
2440
D.
3140
Answer:
D. 31/40
Step-by-step explanation:
3/8 + 2/5 =
15/40 + 16/40 =
31/40
Which expression is equivalent to (3√x^2)^6
Step-by-step explanation:
[tex] = {(3 \sqrt{ {x}^{2} } )}^{6} [/tex]
[tex] = {(3 {x}^{ \frac{2}{2} } )}^{6} [/tex]
[tex] = {(3x)}^{6} [/tex]
[tex] = {3}^{6} {x}^{6} [/tex]
[tex] = 729 {x}^{6} [/tex]
====================================
[tex]\large \sf \underline{Problem:}[/tex]
Which expression is equivalent to (3√x^2)^6
====================================
[tex]\large \sf \underline{Answer:}[/tex]
The answer is x⁴
====================================
[tex]\large \sf \underline{Explanation:}[/tex]
[tex]( \sqrt[3] {x}^{2} )⁶ \: {The \: cube \: root \: of \: x² \: is \: x^(2/3)} (x^(2/3))⁶ {Now, \: simply \: multiply \: 2/3 \: by \: 6 \: to \: get \: 4.}[/tex]
x⁴
[tex]( \sqrt[3] {x}^{2} )⁶ \: is \: equivalent \: to \: x⁴[/tex]
====================================
Which expression can you use that is equivalent to 5x - 2 ( 15 - x )
Answer:
7x - 30
Step-by-step explanation:
5x -2(15-x)
Distribute -2 to the parenthesis
= 5x -30 +2x
Combine like terms
7x-30
jorge makes fruit snacks for his friends. He uses 1 1/2 apples to make 3 fruit snacks.
How many apples does jorge need to make 1 fruit snack
Answer:
Jorge needs 1/2 apple to make the snack.
Solve the system with
elimination.
x - y = 10
3x - 2y = 25
Answer:
Step-by-step explanation:
{x,y}={5,-5}
29. Having a large enclosed space has advantages, but it can be more expensive to heat and cool. Assume an air conditioner uses about 4 BTUs/cubic foot each hour (a BTU is a measure of energy). How many BTUs will the air conditioner need to produce each hour to cool the structures? Hint: Multiply the enclosed space by the number of BTUs needed per cubic foot. (3 points)
1: Cylinder
2: Pyramid
3: Dome
The BTU required by the air conditioner/hour to cool the following structures is given as:
Cylinder: 4*π r² h (Where h is height, and r is the radius);Pyramid: 4 (lwh/3) (Where l is the length, w - the width, and h, the height;Dome: 4 * (4/3 πr³)What is the explanation for the above?It is to be noted that the BTU required to cool per cubic foot of space is 4BTUs.
Since we are not given the dimensions of the structures, the required constant is thus, multiplied by the volume of the structures whose equations have been given above.
Note that:
Volume translates to enclosed space; and
BTU means British Thermal Unit.
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