Question 4 of 10
Solve (x-4)²2 = 5.
OA. x=-4± √5
OB. x=5± √√4
OC. x=9 and x = -1
OD. x=4± √5
Step-by-step explanation:
Solve the following equation for x.
10 = 2 – 4(ar – 3)
OA. -
a
OB.
Oc.
OD.
5
a
The equation for the (x-4)²2 is 5. x=4± √5. Hence, option D is correct.
What is a quadratic equation?Due to the fact that they contain two or more algebraic terms, quadratic equations fall within the category of polynomial equations. It must equal 0 in order to solve a quadratic equation. There can be zero, one, or two (true) solutions to a quadratic equation.
To solve the equation (x - 4)² = 5, we can start by taking the square root of both sides:
√[(x - 4)²] = ±√5
This gives us two possible equations:
x - 4 = √5 or x - 4 = -√5
Now it can add 4 to both sides of each equation:
x = 4 + √5 or x = 4 - √5
So the solutions to the equation (x - 4)² = 5 are x = 4 + √5 and x = 4 - √5.
Thus, option D is correct.
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The given equation is wrong, the correct equation is given below-
(x-4)²2 = 5.
10 The length of a piece of wood is 294 cm when truncated to the nearest centimetre. Complete the error interval for the length of the piece of wood.
The error interval for the length of the piece of wood is 293.5 ≤ length < 294.5
What is Error Interval ?Error Interval can be defined as the limit of Accuracy when a number has been truncated.
It is given that the length of the piece of wood is 294 cm truncated to the nearest centimeter.
To determine the error interval for the length of the piece of wood
length ≥ 293.5
length < 294.5
293.5 ≤ length < 294.5
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Which equation can be solved by using this system of equations?
StartLayout Enlarged left-brace 1st Row y = 3 x Superscript 5 Baseline minus 5 x cubed + 2 x squared minus 10 x + 4 2nd Row y = 4 x Superscript 4 Baseline + 6 x cubed minus 11 EndLayout
The equation that can be solved using the system of equations is 4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4
How to determine the equation?The correct formats of the equations are:
y = 3x^5 - 5x^3 + 2x^2 - 10x + 4
y = 4x^4 + 6x^3 - 11
To determine the equation, we substitute 4x^4 + 6x^3 - 11 for y in the first equation.
So, we have:
4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4
Hence, the equation that can be solved using the system of equations is 4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4
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Select the correct answer.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
12x^9y^4 / 6x^3y^2
[tex]2x^6y^2[/tex]The equivalent expression to the given expression is [tex]2x^6y^2[/tex] (option D)
How to determine the equivalent expression?An expression in mathematics is a fusion of numbers, variables, and operators that embodies a mathematical entity. Expressions possess the ability to symbolize magnitudes, functions, and connections, exhibiting versatility and finesse.
Expressions are used in many different areas of mathematics. They are used to represent quantities, functions, and relationships.
To determine the given expression, lets start:
[tex](12x^9y^4)/(6x^3y^2)[/tex]
= [tex](12/6) x^(^9^-^3^) y^(^4^-^2^)[/tex]
= [tex]2x^6y^2[/tex]
Therefore, the equivalent expression to [tex](12x^9y^4)/(6x^3y^2)[/tex] is [tex]2x^6y^2[/tex]
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A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam. Find, using vectors, the tension in the cables.
The tension in the cable is given by the newton's first law will be 163.622 N.
What is newton's first law?The summation of the force is equal to zero.
The formula is given as
ΣF = 0
Where m is the mass of the body and a is the acceleration.
A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam.
Then the tension in the cable will be
Let T be the tension in the cable.
T sin 29° + T sin 53° – 210 = 0
On simplifying, we have
T (sin 29° + sin 53°) = 210
T = 163.622 N
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What is the answer to 2/5 - 1/3?
Work Shown:
2/5 - 1/3
6/15 - 5/15
(6-5)/15
1/15
Here are two ways to check the answer:
Type 2/5 - 1/3 into your calculator to get roughly 0.06667. The 6's actually repeat forever, but of course the calculator rounds at some point. You should notice that 1/15 has the same decimal value. Therefore 2/5 - 1/3 = 1/15Type (2/5-1/3) - (1/15) into your calculator. You should get zero or very close to it. I'm using the fact that if A = B, then A-B = 0.Hi Student!
Looking at the problem statement and them just asking for us to determine the difference between two numbers seems like an easy task. The first thing that we must do is to find a common denominator so we subtract them otherwise we can not since the denominators are different.
The denominators of the fractions are 5 and 3 and we know that they both multiply up to 15 so that can be our common denominator.
Convert to common denominator
[tex]\frac{2}{5}-\frac{1}{3}[/tex][tex]\frac{2*3}{5*3}-\frac{1*5}{3*5}[/tex][tex]\frac{2*3}{15}-\frac{1*5}{15}[/tex][tex]\frac{6}{15}-\frac{5}{15}[/tex]Subtract
[tex]\frac{6}{15}-\frac{5}{15}[/tex][tex]\frac{6-5}{15}[/tex][tex]\frac{1}{15}[/tex]Therefore, the final answer to the question asking the difference between 2/5 and 1/3 would be 1/15.
Prove (1+tanx)/(1+cotx)=tanx by algebra
[tex]\text{L.H.S}\\\\=\dfrac{1+\tan x}{ 1+ \cot x}\\\\\\=\dfrac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\dfrac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) \times \dfrac{\tan x}{1+ \tan x}\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
10. rhombus abcd has vertices at a(-2, 7), b(8, 7), c(2, -1), and d (-8, -1).
determine the area of abcd.
Answer: 80
Step-by-step explanation:
We can use the formula [tex]A=\frac{d_{1}d_{2}}{2}[/tex], where [tex]d_{1}, d_{2}[/tex] are the lengths of the diagonals.
By the distance formula,
[tex]AC=\sqrt{(-2-2)^{2}+(-1-7)^{2}}=\sqrt{16+64}=4\sqrt{5}\\BD=\sqrt{(-8-8)^{2}+(-1-7)^{2}}=\sqrt{256+64}=8\sqrt{5}[/tex]
So, the area is [tex]\frac{(4\sqrt{5})(8\sqrt{5})}{2}=\boxed{80}[/tex]
1.1 How many grams of can of apple pie filling Chantel is going to use in the Apple (2) Cinnamon Cake.
The number of grams of canned apple that Chantel needs for her apple-cinnamon cake is about 1400 grams.
How to calculate the amount of canned apple that Chantel needs?To know the amount of canned apple that Chantel needs for her apple and cinnamon cake recipe, we must review the amount of apple that she needs for the filling of her cake.
According to the basic recipe to make this cake, we need 6 to 8 apples. Taking into account that each apple weighs about 200g, we can infer that Chantel is going to use about 1400g of canned apple as shown below.
On average we need 7 apples.
6 + 8 = 1414 ÷ 2 = 7Each apple weighs 200g, so 7 apples would be 1400g.
7 × 200g = 1400gBased on the above, Chantel needs 1400g of canned apple.
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A tractor costs $20000 and depreciates in value by 15% per year. how much will the tractor be worth after 5 years?
Answer:
$ 8874.11 after 5 years
Step-by-step explanation:
Each year it is worth 85 % of its value
20 000 ( .85)^5 = 8874.11
A box contains 50 batteries, of which 10 are dead and 5 are weak. Suppose you select batteries at random from the box and set them aside for recycling if they are dead or weak. If the first battery you select is dead and the second one is weak, what is the probability that the next battery you select will be weak?
Find a number that is 45% greater than 90
Answer:
130.5Step-by-step explanation:
the number that is 45% greater than 90 is :
[tex]90+90\times \frac{45}{100} = 90 + 40.5 = 130.5[/tex]
HELP ME PLSSS
A rectangle has a height of 4 and a width of x² + 3x + 2.
Express the area of the entire rectangle.
The area of the entire rectangle is 4x² + 12x + 8
How to determine the area of the entire rectangle?The given parameters are:
height = 4
Width = x² + 3x + 2
The area of the rectangle is:
Area = Width * Height
So, we have:
Area = (x² + 3x + 2) * 4
Expand
Area = 4x² + 12x + 8
Hence, the area of the entire rectangle is 4x² + 12x + 8
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5. Find the value of x so that lines s and t are parallel.
(7x - 20)°
(4x + 16)
The value of x so that lines s and t are parallel is 12
How to find angles involving parallel lines?The angle are alternate exterior angles.
Therefore, alternate exterior angle theorem states that when two parallel lines are intersected by a transversal, then the exterior angles formed on either side of the transversal are equal.
Hence,
7x - 20 = 4x + 16
7x - 4x= 16 + 20
3x = 36
x = 36 / 3
x = 12
Therefore, the value of x is 12.
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You are packing for a road trip and you buy snack packages (same size, same weight) for the trip. you buy 6 potato chips, 5 doritos, and 3 corn curls. you put them in a bag and mix them up. during the trip, you reach into the bag and pull out two packages at random, one at a time. draw a tree and calculate the probability of each outcome. use p for potato chips, d for doritos, and c for corn curls. what is the probability of picking two snacks of the same type?
The probability of picking two snacks of the same type is 0.308.
How to calculate the probability?The probability of picking 2 potato will be:
= 6/14 × 5/13
= 0.429 × 0.385
= 0.165
The probability of picking 2 doritos will be:
= 5/14 × 4/13
= 0.357 × 0.308
= 0.110
The probability of picking 2 corn curls will be:
= 3/14 × 2/13
= 0.214 × 0.154
= 0.033
Therefore, the probability of picking two snacks of the same type will be:
= 0.165 + 0.110 + 0.033
= 0.308
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In the given figure, if y = 30, find (i) x (ii) z and (iii) u
Answer:
u=30
x=150
z=150
y=30
Step-by-step explanation:
u=y [ being vertically opposite angle]
x+u=180[ being linear pair]
x+30=180
x=180-30
x=150
z=x[being vertically opposite angle]
z=150
y=u[ being voa]
Answer:
=40°
Step-by-step explanation:
Sorry that's all I know
^keep safe^
What is the area of the rhombus in simplest radical form? The figure is not drawn to scale.
0162 √3
0162
081 √6
018 √3
The area of the Rhombus is 162√3 sq.unit , Option A is the correct answer.
What is a Rhombus ?A rhombus is a polygon , which has four equal sides , its diagonal bisect each other at 90 degree.
Let x be the half of the other diagonal.
tan 60 = x / 9
x = 9 tan 60
x = 9√3
Area of the Rhombus = (d1 * d2 /2 )
d1 and d2 are the length of the diagonal.
Area of the Rhombus = (9*2)(2 *9√3)/2
Area of the Rhombus =162√3 sq.unit
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John is buying a new car. The value of one car he is considering is $20,000. The value of the car as it ages can be modeled by the
function v= 20, 000 (0. 84), where t is the number of years from the time of purchase. One of the factors John is using to make his decision is
the value of the car over time until it reaches half its original value. What values of domain are reasonable for the given function in this
context?
O
A. all real numbers greater than or equal to 0 and less than 4
O B. all real numbers greater than or equal to 0
O
C. all real numbers greater than or equal to 10,000 and less than or equal to 20,000
O
D. all real numbers greater than or equal to 0 and less than 2.8
Answer:
all real numbers greater than or equal to 10,000 and less than or equal to 20,000
Step-by-step explanation:
ye
Where did he even get the 5 and the -1?
Answer:
the arrows and dots show where
Hey there!
Look at your graph… then look at your points (the green dots) and it should be there.
Your x-values are across (just think of its saying “East” and ”West”) & your y-values are up and down (just think of it as “North” and “South”)
So, based on that that information:
ANSWER:
Your x-value would be: -1 because the point landed on it whereas the y-value would be: 5 because the point landed on it.
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What is the value of n?
38°
Answer: 247 the Answer
Find the midpoint of A and B where A has coordinates (8, 2)
and B has coordinates (3,8).
Answer:
(5.5, 5 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = A (8, 2 ) and (x₂, y₂ ) = B (3, 8 ) , then
midpoint = ( [tex]\frac{8+3}{2}[/tex] , [tex]\frac{2+8}{2}[/tex] ) = ( [tex]\frac{11}{2}[/tex] , [tex]\frac{10}{2}[/tex] ) = (5.5, 5 )
The coordinates of A,B,C are(6,3),(-3,5),(4,-2) respectively and P(x,y) is any point,prove that∆PBC/∆ABC=x+y-2/7
The solution to the coordinates of A,B,C as (6,3),(-3,5),(4,-2) and the prove that ∆PBC/∆ABC=x+y-2/7 is given in the image attached.
What is coordinates?This is known to be that which is created by two part that are known to give the latitude and longitude position of a person or place.
Therefore, The solution to the coordinates of A,B,C as (6,3),(-3,5),(4,-2) and the prove that ∆PBC/∆ABC=x+y-2/7 is given in the image attached.
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If f(x) = x2 2x 3, what is the average rate of change of f(x) over the interval [-4, 6]?
Answer:
see the attachment photo!
What is the recursive rule for the sequence?
Answer:
2nd option
Step-by-step explanation:
the recursive rule is
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d ( d is the common difference )
use the explicit rule to find a₁ and d
a₁ = 48 - 11(1) = 48 - 11 = 37
a₂ = 48 - 11(2) = 48 - 22 = 26
then
d = a₂ - a₁ = 26 - 37 = - 11
recursive rule is then
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 11
a₁ = 37
solve the equation for a? z=mab. a)a=z+mb b)a=z-mb c)a= mb/z d)a=z/mb
Answer:
a = z/mb
Step-by-step explanation:
Given:
[tex]\displaystyle \large{z=mab}[/tex]
To solve for a, divide both sides by the variables mb to isolate a-term.
[tex]\displaystyle \large{\dfrac{z}{mb}=\dfrac{mab}{mb}}[/tex]
Simplify the expression and we finally have solved for a-term.
[tex]\displaystyle \large{\dfrac{z}{mb}=a}\\\\\displaystyle \large{a=\dfrac{z}{mb}}[/tex]
Therefore, the answer to this question is a = z/mb.
Please let me know if you have any questions regarding my answer or explanation!
One angle of a right-angled triangle is 60 grades . Find the other angle in degree.
Answer:
30°
Step-by-step explanation:
This right triangle has :
right angle (90°)One angle of 60°=========================================================
Solving :
We know the angle sum of a triangle is 180°.
⇒ x + 90° + 60° = 180°
⇒ x + 150° = 180°
⇒ x = 30°
We know the angle sum of a triangle is 180° so
x + 90° +60°= 180°
x + 150°= 180°
⇒x = 30°
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. Construct Arguments Based on the survey data below, a marketing team for an airline concludes that someone between 18 and 24 years of age is more likely never to have flown on a commercial airliner than someone 25 years or older. Do you agree with this conclusion? Justify your answer.
The marketing team conclusion that someone between 18 and 24 years of age is more likely never to have flown on a commercial airliner than someone 25 years or older is true based on the percentage.
How to compute the percentage?The percentage for someone between 18 and 24 years of age to have flown on a commercial airline will be:
= 216/279 × 100.
= 77.4%
The percentage for someone that is 25 years older to have flown will be:
= 2210/2988 × 100
= 74%
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What is the common ratio for this geometric sequence?
16, 8, 4, 2, ...
Determine the value of "a" for which g(h(a)) = 13
Answer:
a = 6
Step-by-step explanation:
g(x) = 5x - 2
h(x) = √(x + 3)
g(h(x)) = 5[tex]\sqrt{x+3}[/tex] - 2
g(h(a)) = 5[tex]\sqrt{a+3}[/tex] - 2
5[tex]\sqrt{a+3}[/tex] - 2 = 13
5[tex]\sqrt{a+3}[/tex] = 15
[tex]\sqrt{a+3}[/tex] = 3
( [tex]\sqrt{a+3}[/tex] )² = 3²
a + 3 = 9
a = 6
A data set is represented by the box-and-whisker plot below.
A box plot has 5 data descriptions. The correct option is 87 and 132.
How does a boxplot show the data points?A box plot has 5 data descriptions.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called the second quartile.The last line of the box shows the third quartile.Since each quartile of the box-and-whisker plot represents 25% of the data. Therefore, values between which there are 3 quartiles present will represent 75% of the data.
Hence, the correct option is 87 and 132.
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