1(t) = 12(t) (2,2,4) +t(2,4,6) and Ia(t) = 12(t) (2,2,4) +t(2,4,6) represents the same line, as they are both equivalent to 12(t)(2,2,4) + t(2,4,6). So Option A is correct.
The equation of a line in 3-dimensional space can be represented in the form "r(t) = a + tb" where "r(t)" is a vector that represents any point on the line, "a" is a vector that represents a point on the line, and "b" is a vector that represents the direction of the line.
The given equations are:
1(t) = 12(t) (2,2,4) +t(2,4,6)
Ia(t) = 12(t) (2,2,4) +t(2,4,6)
As we can see that both equations are identical to equation 12(t) (2,2,4) +t(2,4,6) thus these three equations represent the same line.
The other given options B, C, and D are not equivalent to each other or to the original equation, thus they do not represent the same line.
To learn more about equations:
https://brainly.com/question/2972832
#SPJ4
PLS HELP MY WHOLE GRADE IS DEPENDING ON THIS QUESTION
A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the
wall is 6 feet.
What is the area A of the table after it is cut in half?
Give your answer in terms of pi.
А=____feet2
Answer:
4.5π ft.^2
Step-by-step explanation:
Please see the attached image.
The area of a circle is the radius of the circle squared times pi.
The diameter of the round top is 6.
The radius of a circle is equal to half the diameter, so 6/2=3.
Knowing the radius of the table is 3, we can find the area by doing
3^2π=9π
9π is the area of the table, so to get half of that, simply divide by 2.
9π/2=4.5π
Answer: 4.5π ft.^2
Answer:
14.1 ft^2 or In terms of pi: A = (1/2)(π)(3 ft)^2 = (9/2)π ft%2
Step-by-step explanation:
We're talking about a semicircle here. "semi-" indicates "half."
Here the cut edge along the wall is 6 ft, so the radius of the semicircle is half that, or 3 ft.
The area of the semicircle is A = (1/2)(pi)(3 ft)^2 = 14.1 ft^2
In terms of pi: A = (1/2)(π)(3 ft)^2 = (9/2)π ft%2
The number of acres in a landfill is given by the function A=3000e−0. 05t, where t is measured in years. How many acres will the landfill have after 9 years? (Round to the nearest acre. )
Is this exponential growth or decay?
A function A = 3000 e^(-0. 05t) is an exponential decay function.
And the landfill after 9 years = 1912.8 acres
From given information, the number of acres in a landfill is given by the function A = 3000 e^(-0. 05t), where t is measured in years.
To find: the landfill after 9 years
Substitute t = 9 years in above function.
A = 3000 × e^(-0. 05t)
A = 3000 × e^(-0.05 × 9)
A = 3000 × e^(-0.45)
A = 3000 × 0.6376
A = 1912.8 .............(1)
Substitute t = 9 years in given function.
A = 3000 e^(-0. 05t)
A = 3000 × e^(-0.05 × 0)
A = 3000 × e^(0)
A = 3000 × 1
A = 3000
This means, initially a landfill was 3000 acres.
From (1) we can observe that after 9 years, the landfill is 1912.8 acres.
A landfill has been reduced.
So, a function is exponential decay function.
Learn more about the function here:
https://brainly.com/question/28193995
#SPJ4
A dealer gained a 10 percent profit by selling an article for birr 330.00 what was the original price of the article
Answer:
300
Step-by-step explanation:
330/110
=3=value of 1%
3*100
=300
or
x=(330*100)/110
=300
x=
Length=
Width=
WILL GIVE BRAINLIEST + 5 star
Answer:
x = 20
Length = 20ft
Width = 12ft
Step-by-step explanation:
A = 240
x^2 - 8x = 240
x^2 - 8x - 240 = 0
x^2 - 20x + 12x - 240 = 0
x(x-20) + 12(x-20) = 0
(x+12)(x-20) = 0
x = 20
x = -12 (which we discard since x is a length)
So the dimensions are 20ft and 20-8 = 12ft
How do you make an XY graph in Excel?
Select the data for which you want to create a chart slope . Click INSERT > Recommended Charts. On the Recommended Charts tab, scroll through the list of charts that Excel recommends for your data
When you find the chart you like, click it > OK.
The formula for a horizontal line at y=4 is as follows: There is no slope. 4.0 is the y-intercept.
What are the Slope and intercepts ?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.
To know more about Slope please click here
brainly.com/question/29265771
#SPJ4
50 POINTS!!!! urgent!!!!!!
Mary is collecting cup cakes for the school fair. She will make 12 cupcakes to start it off. She plans to collect 24 cupcakes each
day from her surrounding neighborhood for the next 3 days. If you model this word problem for Mary as y=mx+b then match the
corrects pairs.
a. 12
b. 84
c. 3
d. 24
1. m
2. y
3. x
4. b
Since the problem is about linear equation in the form of y = mx + b, initial number represents the value of b = 12, the number of days represents the value of x = 3, the daily collection of cupcakes represent the slope m = 24, then the value of y is:
y = 24*3 + 12 = 72 + 12 = 84So the matching pairs are:
a ⇔ 4, b ⇔ 2,c ⇔ 3,d ⇔ 1 .A water sprinkler sends water out in a Circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 1,133.54 Square feet? used 3.14 for pi.
The sprinkler can spread water ____ Feet away
Answer: 38 feet
Step-by-step explanation:
make an equation that satisfies the above statement.
make it [tex]3.14(r)^{2} = 1133.54^{2}\\=> r^{2} = \frac{1133.54}{3.14} \\=> 361 = r^2\\=> r = \sqrt[]{361} \\=> 19[/tex]therefore 19 is the radius and the diameter is the answer which is 38
Which tatement correctly compare the meaure of center of the data in the dot plot
A statement that correctly compares the measures of center in the two sets of data is: Both the mean and median are greater for Plot A than for Plot B.
The correct answer is an option (A)
Consider plot A.
The data value represented on the dot plot:
3, 4, 4, 5, 5, 6, 6, 7, 7, 10
Using the formula of mean, the mean of Plot A would be:
mean = (3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 7 + 10) / 10
mean = 57/10
mean = 5.7
The middle value of the data is: 5, 6
So, the median is:
Median = (5 + 6)/2
= 11/2
= 5.5
Consider plot B.
The data value represented on the dot plot:
3, 4, 4, 5, 5, 5, 6, 6, 6, 7
mean = (3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7)/10
mean = 51/10
mean = 5.1
The middle value of the data is: 5, 6
So, the median is:
Median = (5 + 5)/2
= 5
Hence, both the mean and median are greater for Plot A than for Plot B.
Learn more about the dot plot here:
https://brainly.com/question/22746300
#SPJ4
The complete question is:
Which statement correctly compares the measures of center in the two sets of data? Both the mean and median are greater for Plot A than for Plot B. Both the mean and median are greater for Plot B than for Plot A. Plot A has a greater median than Plot B, but Plot B has a greater mean. Plot B has a greater median than Plot A, but Plot A has a greater mean.
Is 0 in a closed interval?
So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.
In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers
the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).
Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.
Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff.
So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.
To learn more about intervals:
https://brainly.com/question/13708942
#SPJ4
May someone please help me with this :) I have to find the value of x
Answer:
the answer is 50 are you trying to find the answer
What are the 7 steps in problem solving examples?
The 7 stepd in problem-solving examples are:
Step 1: Read through the problem
Step 2: Draw diagram
Step 3: Assign variable to each unknown
Step 4: Translate information into an equation
Step 5: Check the equation
Step 6: Use algebra rules to solve the equations
Step 7: Check the final answer.
We know that the word problems are required to translate the real world problem into mathematical terms.
Everything mentioned in the word problem is important.
The seven necessary steps in problem solving examples:
Step 1: Read the problem throughly
Step 2: Draw picture / diagram / arrow diagram related to example
Step 3: Assign an alphabate to each unknown value
Step 4: Translate information into an equation
Step 5: Check the types equation
Step 6: solve the equations using algebra rules
Step 7: Check the final answer.
Learn more about problem here:
https://brainly.com/question/28165310
#SPJ4
if f(x)= mx+ c , f (1)=5 and f(-2)=-1
Answer:
[tex]y = 2x + 3[/tex]
Step-by-step explanation:
We can find the slope.
[tex] \frac{ 5 + 1}{1 + 2 } = 2[/tex]
so m is 2
[tex]y = 2x + c[/tex]
Plug one the equations in to find c.
[tex] - 1 = 2( - 2) + c[/tex]
[tex] - 1 = - 4 + c[/tex]
[tex]3 = c[/tex]
so the equation is
[tex]y = 2x + 3[/tex]
Can someone tell me what this is?
Answer:
there's one solution bc the lines have one point in common
Please help! No links please! Will give brainliest to correct person!!
Answer:
About 50.14 Centimeters
Step-by-step explanation:
The formula for the volume of a cylinder is:
[tex]\pi(r^2)h[/tex]
Now, let's plug in the values. (We'll use 3.14 for pi.)
[tex]3.14(r^2)76 = 600,000[/tex]
All we do now, is solve for r. Divide 76 on both sides...
[tex]3.14(r^2) = 7894.74[/tex]
Divide 3.14 on both sides...
[tex]r^2 = 2514.25[/tex]
Lastly, find the square root on both sides.
[tex]\sqrt{r^2} = \sqrt{2514.25}[/tex]
[tex]r = 50.14[/tex]
Therefore, the r, or the radius, is around 50.14 centimeters. Hope this helps!
Please help!!!!!!!!!!!
Answer:
9/4 *(x-2)
Step-by-step explanation:
Replace xa and y in the given function then solve for y
A certain psychological test measures empathy and
emotional intelligence. The score, S, of a randomly
selected senior student at a large university has a mean
of 123 and a standard deviation of 29. The score, F, of a
randomly selected first-year student at a large university
has a mean of 104 and a standard deviation of 34.
Suppose we randomly select one senior student and one
first-year student. We can consider Sand F to be
independent random variables.
As per the given standard deviation, the probability that the first-year student shows a higher emotional intelligence test score in a randomly selected senior/first-year pair is 0.72
Here we have given that the score, S, of a randomly selected senior student at a large university has a mean of 123 and a standard deviation of 29.
And the score, F, of a randomly selected first-year student at a large university has a mean of 104 and a standard deviation of 34.
Then the probability is calculated as,
=> 123/104
=> 1.182
Where as the based on the standard deviation, the value is calculated as
=> 29/34
=> 0.852
Then the total probability of the given situation is calculated as,
=> 0.852/1.182
=> 0.72
To know more about Standard deviation here.
https://brainly.com/question/16555520
#SPJ4
What are the 3 names of angles?
Angles are classified into three. They are acute angles, obtuse angle and right angle.
Therefore the three names of angles are - acute angles, obtuse angle and right angle.
Acute angles are angles that measure less than 90 degrees. They are smaller than a right angle and are often described as "sharp."
Right angles are angles that measure exactly 90 degrees. They are often represented by a square corner or the letter "L" shape.
Obtuse angles are angles that measure greater than 90 degrees but less than 180 degrees. They are larger than a right angle and are often described as "blunt."
To know more on angles
https://brainly.com/question/19247815
#SPJ4
Miranda is buying yarn so she can crochet scarves for her family. She likes the Furry Fibers brand best. At the store, she finds a 7-ounce roll of Furry Fibers yarn for $8. 33 and a 16-ounce roll for $18. 72. Which size roll is the better value?
The size roll which is the better value is $1.17 per ounce.
To determine which size roll is the better value, we need to compare the price per ounce of each roll.
To find the price per ounce of the 7-ounce roll, we divide the total cost by the number of ounces: $8.33 ÷ 7 ounces = $1.19 per ounce.
To find the price per ounce of the 16-ounce roll, we divide the total cost by the number of ounces: $18.72 ÷ 16 ounces = $1.17 per ounce.
Since $1.17 per ounce is less than $1.19 per ounce, the 16-ounce roll is the better value. It is cheaper per ounce than the 7-ounce roll.
Learn more about unit price or unit cost and shopping here: https://brainly.com/question/14286952
#SPJ4
1. Combine the like like terms
14 + 8x + 2y -5x - 2
Answer:
12 + 3x + 2y
Step-by-step explanation:
14 + 8x + 2y -5x - 2
14 + -2 + 8x -5x + 2y
12 + 3x + 2y
Answer:
3x + 2y + 12
Step-by-step explanation:
In the photo.
I'll mark you the brainliest
plzzzz help asap❤❤
if x+y+z=1 and 1/x+1/y+1/z=0
what is x²+y²+z²=?
A) 0
B) 1
C) 2
D) 3
and please tell me why?
find the volume of the given solid. bounded by the planes z = x, y = x, x + y = 5 and z = 0
The volume of the solid given is 125/24 and is constrained by the planes z = x, y = x, x + y = 5, and z = 0.
what is volume ?The capacity of an object is expressed in terms of volume. The quantity of space a three-dimensional item takes up can also be referred to as volume. It is sometimes referred to as the vessel's "capacity" or "volume." infant milk bottle with milliliter measuring indications and juice bottle with a 1 liter capacity.
Given
The bounds for z are 0 ≤ z ≤ x.
The bounds in the xy-plane are x ≤ y ≤ 5 - x and x in [0, 5/2]
So, V = ∫∫ (x - 0) dA
= ∫(x = 0 to 5/2) ∫(y = x to 5 - x) x dy dx
= ∫(x = 0 to 5/2) x (5 - 2x) dx
= ∫(x = 0 to 5/2) (5x - 2x^2) dx
= (5x^2/2 - 2x^3/3) {for x = 0 to 5/2}
= 125/24.
The volume of the solid given is 125/24 and is constrained by the planes z = x, y = x, x + y = 5, and z = 0.
To know more about volume visit :-
https://brainly.com/question/13338592
#SPJ1
HELp meh with this question it very hard
Answer:
AB = 7 cmStep-by-step explanation:
Use the law of cosines to find the side AB:
[tex]AB = \sqrt{(x + 3)^2+x^2-2x(x+3)cos (60)} =[/tex] [tex]\sqrt{x^2+6x+9+x^2-x^2-3x} = \sqrt{x^2+3x+9}[/tex]Use the Heron's area formula next:
[tex]A = \sqrt{s(s - a)(s-b)(s-c)}[/tex], where s- semi perimeters = 1/2[x + x + 3 + [tex]\sqrt{x^2+3x+9}[/tex]) = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex])s - a = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex] - 2x - 6) = 1/2 ([tex]\sqrt{x^2+3x+9 }[/tex] - 3)s - b = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex] - 2x) = 1/2 ([tex]\sqrt{x^2+3x+9}[/tex] + 3)s - c = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex] - 2[tex]\sqrt{x^2+3x+9}[/tex]) = 1/2 (2x + 3 - [tex]\sqrt{x^2+3x+9}[/tex])Now
(s - a)(s - b) = 1/4 [(x²+3x+9) - 9] = 1/4 (x² + 3x)s(s - c) = 1/4 [(2x + 3)² - (x² + 3x + 9)] = 1/4 (3x²+ 9x) = 3/4(x² + 3x)Next
A² = 3/16(x² + 3x)(x² + 3x)300 = 3/16(x² + 3x)²1600 = (x² + 3x)²x² + 3x = 40Substitute this into the first equation:
[tex]AB = \sqrt{40 + 9} = 7 cm[/tex]Answer:
AB = 7 cm
Step-by-step explanation:
Sine Rule for Area
[tex]\sf Area =\dfrac{1}{2}ab \sin C[/tex]
where:
a, b and c are the sides opposite angles A, B and Ca and b are the sides and C is the included angleGiven:
Area = √(300) cm²a = (x + 3) cmb = x cmC = 60°Substitute the given values into the formula and solve for x:
[tex]\begin{aligned} \sf Area & = \dfrac{1}{2}ab \sin C \\\\\implies \sqrt{300} & = \dfrac{1}{2}(x+3)x \sin 60^{\circ}\\\\\sqrt{300} & = \dfrac{\sqrt{3}}{4}(x+3)x\\\\\dfrac{4\sqrt{300}}{\sqrt{3}} & = x^2+3x\\\\40 & = x^2+3x\\\\x^2+3x-40 & = 0\\\\ (x-5)(x+8)& = 0\\\\ \implies x & = 5, -8\end{aligned}[/tex]
As length is positive, x = 5 only.
Substitute the found value of x into the expressions for the side lengths:
a = 5 + 3 = 8 cmb = 5 cmCosine rule
[tex]c^2=a^2+b^2-2ab \cos C[/tex]
(where a, b and c are the sides and C is the angle opposite side c)
Substitute the found values into the formula and solve for AB:
[tex]\begin{aligned}c^2 & =a^2+b^2-2ab \cos C\\\implies AB^2 & =8^2+5^2-2(8)(5) \cos 60^{\circ}\\AB^2 & =89-40\\AB^2 & =49\\AB & =\sqrt{49}\\AB & = \pm 7\end{aligned}[/tex]
As length is positive, AB = 7 cm.
Learn more about the sine rule for area here:
https://brainly.com/question/27088353
Solve the system of linear equations using the matrix method.
What do X and Y equal?
Answer:
The matrix method is basically making the matrix in the picture equal to
{1 0 = x}
{0 1 = y}
To do this you must multiply reciprocals and add opposites to make 2x = 1, 7y = 0, 3x = 0, and -12y = 1.
I used the simple way of solving linear equations:
3(2x + 7y = 48)
-2(3x - 12y = 27)
6x + 21y = 144
-6x + 24y = -42
45y/45 = 102/45
y = 34/15 or 2.26667
Plug in y-value to get x-value:
2x + 7(34/15) = 48
- 7(34/15) -7(34/15)
2x = 482/15
2x/2 = 482/15/2
x = 241/15 or 16.06667
Which statement is true?
Answer: (d)
Step-by-step explanation:
For option (a)
[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}[/tex]
for the same exponent, numbers multiply keeping exponent the same.
for option (b)
[tex]a\sqrt[n]{x} +b\sqrt[n]{y} =\left(a+b\right)\sqrt[n]{x}[/tex]
for option (c)
[tex]\Rightarrow \dfrac{\sqrt[m]{x} }{\sqrt[m]{y} }=\sqrt[m]{\dfrac{x}{y}}[/tex]
for option (d)
exponent multiplies
[tex]\therefore \left(\sqrt[m]{x^a} \right)^b=\sqrt[m]{x^{ab}}[/tex]
option (d) is correct
Helppppppp
1. Which of the following equations are written in proper slope-intercept form?
y = -x + 9
4y = 2x - 1
x + y = 10
3x + 7y = 0
Answer:
a. y = -x + 9
Step-by-step explanation:
slope-intercept form is
y = mx + b
so of the options, only option a follows slope-intercept form.
hope this helps!
What is the value of x in the system of equations shown below?
5x + 4y = 1
y = 1 - 3
There are 20 pennies in a jar. If 16% of the coins in the jar are pennies, how many coins are in the jar?
Answer:
125 coins
Step-by-step explanation
realized that 25 coins would be 20% of the amount of coins in the jar. Multiply 5 on both and you see that 125 coins is 100% the amount that is in the jar.
hope this helps :)
reply If you need a more proper explanation.
The number of coins in the jar are 125 coins.
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. It is denoted using the symbol "%".
We know that 16% of the coins in the jar are pennies. Let's represent the total number of coins in the jar as "x".
Then, we can set up the following equation:
0.16x = 20
Solving for "x", we can divide both sides by 0.16:
x = 20/0.16
x = 125
Therefore, there are 125 coins in the jar.
To know more about Percentage check:
https://brainly.com/question/29306119
#SPJ3
For the rhombus below, find the measures
Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.
what is rhombus ?A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal. A rhombus also has equal-length sides and diagonals that are at right angles to one another. The term "rhombus" can also refer to a diamond or rhombus. A rhombus has equal opposite angles. At a 90° angle, the diagonals split in half. 180 degrees is the sum of adjacent angles.
given
There is a line that passes through the parallel line; the alternate interior angles are 3 and 39.
The alternative interior angles are similar, hence Angle 3 = 39.
Since the upper left triangle is a triangle, angles 3, 4, and the center angle all add up to 180 degrees. The angle in the middle is 90 degrees. hence, we may locate angle 4.
angle 4=51.
Since Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.
To know more about rhombus visit :-
https://brainly.com/question/27870968
#SPJ1
please help please please please please
Explanation is[tex]^{}[/tex] in a file
bit.[tex]^{}[/tex]ly/3gVQKw3
Find the area of the shaded region in terms of pi.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let’s find the area of the circle.
A = 3.14(7)^2 = 153.86
Now the area of the square:
14•14=196
Now we find the area of the shaded region:
196 - 153.86 = 42.14
the shaded region is 42.14 cm