Answer:
Rectangular Cuboid
Step-by-step explanation:
A rectangular cuboid has 4 faces that are rectangles and 2 faces that are squares. Since a square is a rectangle, this shape is technically built of 6 rectangles and is creates a 3-dimensional shape. Hence, we have the prism, rectangular cuboid.
Evaluate each limit. Give exact answers.
Answer:
Given that 1 and 4 are vertical asymtotes we have;
(a) -∞
(b) +∞
(c) +∞
(d) -∞
Step-by-step explanation:
(a) For the function;
[tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]
We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)
Therefore, as the function approaches 4 from the left [lim (x → 4⁻)] gives;
[tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(3.999 - 1)\cdot (3.999 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(2.999)\cdot (-0.001)} \right )[/tex][tex]=- \infty[/tex]
(b) Similarly, we have;
[tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]
We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)
Therefore, as the function approaches 4 from the right [lim (x → 4⁺)] gives;
[tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(4.0001 - 1)\cdot (4.0001 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(3.0001)\cdot (0.0001)} \right )[/tex][tex]= +\infty[/tex]
(c)
[tex]\lim_{x\rightarrow 1^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{x^{2}-5\cdot x+4} \right )[/tex]
We have the denominator given by the expression, x² - 5·x + 4 which can be factorized as (x - 4)(x - 1)
Therefore, as the function approaches 1 from the left [lim (x → 1⁻)] gives;
[tex]\lim_{x\rightarrow 1 ^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(x - 1)\cdot (x - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 1^{-}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(0.999 - 1)\cdot (0.999 - 4)} \right )[/tex] [tex]\lim_{x\rightarrow 4^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(-0.001)\cdot (-3.001)} \right )[/tex][tex]=+ \infty[/tex]
(d) As the function approaches 1 from the right [lim (x → 1⁺)]
We have;
[tex]\lim_{x\rightarrow 1^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(1.0001 - 1)\cdot (1.0001 - 4)} \right )[/tex]= [tex]\lim_{x\rightarrow 1^{+}}\left (\dfrac{2\cdot x^{2}+13\cdot x+20}{(0.0001)\cdot (-2.999)} \right ) =- \infty[/tex]
3x2 +x=10 what’s the answer?
Answer:
Step-by-step explanation:
3 × 2 + x = 10
6 + x = 10
x = 10 -6
x = 4
Step-by-step explanation:
so 3 x 2 is 6
6 add x is 6x
6x = 10
divide by 6 or 10 on both sides to get ur answer
hope this helps
i would appreciate it if u could heart my answer and give it 5 stars or maybe even give it brainliest pls i beg u thx !!!!! : )
Inspired by election season, Evan decided to run for class president. He earned 80% of the votes in his class. If he earned 24 votes, how many students were in his class? ( with a explanation on how you got the answer)
Answer:
30 students (30 total voters)
Step-by-step explanation:
Let s represent the number of students in the class. Evan earned 80% of these votes, which came to 24 votes. Symbolically, we have:
24 votes
0.80s = 24 votes. Therefore, s = total number of voters = ---------------- = 30 voters 0.8
The total number of students (voters) in his class was 30.
Answer:
It is 30.
Step-by-step explanation:
A Roman statue is three times as old as a Florentine statue. One hundred years from now the Roman statue will be twice as old as the Florentine statue. How old is the Roman statue?
Answer:
300 years
I hope this helps!
Kendra was given this system of equations. Negative 3 x + 7 y = negative 15. Negative 2 x minus 7 y = 5. Kendra’s work is shown in the table. Where, if anywhere, did Kendra first make a mistake? Steps Kendra’s Work Step 1 Negative 3 x + 7 y = negative 15. Negative 2 x minus 7 y = 5. Negative 5 x = negative 10. Step 2 Negative 5 x = negative 10. x = 2. Step 3 Negative 3 (2) + 7 y = negative 15. Negative 6 + 7 y = negative 15. 7 y = negative 9. y = Negative StartFraction 9 Over 7 EndFraction = negative 1 and StartFraction 2 Over 7 EndFraction step 1 step 2 step 3 no mistake
Answer:
i dont think Kendra made a mistake
Step-by-step explanation:
Given:
Kendra was given this system of equations.
-3x+7y=-15 and -2x-7y=5.
TO FIND :
The steps in Kendra’s work where did she make a mistake.
SOLUTION :
Kendra's work :
Step 1 :
Given equations are
-3x+7y=-15
and
-2x-7y=-15
Step 2:
Adding the equations (1) and (2) we get
-5 x = -10.
x=-10/-5
x = 2.
Step 3:
Substitute the value of x in the equation (1) we have,
-3(2)+7y=-15
-6+7y=-15
7y=-15+6
7y=-9
y=-9/7
y=-1 2/7
From Kendra's worked steps she made no mistake.
Hope this helps, if it did, please give brainliest, it will help me a lot :)
Have a good day :)
Graph: y = |x + 2| + 1
Answer:
[tex]x = y - 3 [/tex]
[tex]x = - (y + 1) y \geqslant 1[/tex]
Hope this is correct and helpful
Step-by-step explanation:
I suppose that this is the graph
HAVE A GOOD DAY!
is this right? i’ll give brainliest :)
It is.
[tex]x-10 \geq 0\\\\x \geq 10\\\\\\-5 +n< -6\\\\n < 5-6\\\\n< -1[/tex]
Answer:
Correctomundo!
Step-by-step explanation:
For x-10 > 0:
1. Add 10 to both sides. x- 10 + 10 > 0 + 10
x > 10
For -5 + n < -6:
1. Simplify both sides of the inequality. n - 5 < -6
2. Add 5 to both sides. n - 5 + 5 < -6 + 5
n < -1
:)
The baker makes54 biscuits in the morning. Then he makes 26 more in the afternoon.
Answer:
80 biscuits
Step-by-step explanation:
The question is not a whole question so I am just assuming that the question is how many biscuits were baked the whole day
Hope this helps :)
The lengths of the sides of a triangle are in the ratio of 6:6:5. The perimeter of the triangle
is 34 centimeters. Find the length of each side of the triangle.
Hello!
Answer:
12 cm, 12 cm, 10 cm.
Step-by-step explanation:
Given:
Perimeter, or P = 34 cm
Ratio of sides = 6 : 6 : 5
To find the length of each side, we can use a variable in the ratio to find the perimeter:
34 = 6x + 6x + 5x
Combine like terms:
34 = 17x
Solve for x:
34/17 = 17x/17; x = 2
Plug in this value of "x" into each expression for the side-lengths:
6(2) = 12 cm
6(2) = 12 cm
5(2) = 10 cm
Therefore, the lengths of each side of the triangle are 12 cm, 12 cm, 10 cm.
Hope this helped you! :)
Answer:
12, 12 and 10 cm.
Step-by-step explanation:
6 + 6 + 5 = 17
So one side = 6/17 * 34 = 12 cm
One other side is also 12 cm
The third side = 5/17 * 34 = 10 cm.
FIRST GETS BRAINLLESTIf you spin the spinner below 80 times, which of the following outcomes are reasonable? Select all that apply. A) Lands on blue 43 times B) Lands on yellow 8 times C) Lands on red 33 times D) Lands on red 62 times
Answer:
A, B, C
Step-by-step explanation:
Answer:
A) Lands on blue 43 times
B) Lands on yellow 8 times
C) Lands on red 33 times
Step-by-step explanation:
Blue is 1/2 of the spinner so theoretically is should be landed on 1/2 of the time which is 40/80 but experimentally, it can differ slightly. Using this same logic, it can be applied to yellow and red. Yellow is 1/8 of the spinner so it should be landed on about 10 out of the 80 times. Red is 3/8 of the spinner so it should be landed on approximately 30 out of 80 times.
Five test scores have a mean (average score) of 90, a median (middle score) of 91 and a mode (most frequent score) of 94. Find the sum of the two lowest test scores.
Answer:
171 points.
Step-by-step explanation:
If five test scores have a mean of 90, all the scores added together will be 5 * 90 = 450.
The middle score is 91, so the other four scores added together will be 450 - 91 = 359.
The mode is higher than the median, so we can assume that the highest two numbers are the same: 94. 94 * 2 = 188. 359 - 188 = 171.
That means that the sum of the two lowest test scores is 171 points.
Hope this helps!
Answer:
The sum of the two lowest test scores is 171.
Step-by-step explanation:
We see that there are 5 test scores, so the median ( middle score ) was not taken to be the average of the two middle scores. It is an element present in the set of five test scores. The mode of course has to be present in the set, but multiple times. If we can figure out how many times this mode is present in the set, it would help us.
As 91 is the middle value, there has to be two above 91. Therefore, as 94 appears the most frequent, is must appear twice.
Now another key thing we need here is the sum of all 5 numbers. Given a mean of 90, 90 [tex]*[/tex] 5 = the sum of all 5 numbers = 450. Therefore, the sum of the two lowest test scores should be = 450 - 94 - 94 - 91 = 171 - which is our solution.
How many pounds of candy that sells for $0.81 per Ib must be mixed with candy that sells for $1.27 per Ib to obtain 8 lb of a mixture that should sell for $0.92 per lb?
1. $0.81-per-lb candy: _____ lb?
Answer:
should I ans?
Step-by-step explanation:
mayb not...coz idu
ASAP PLZZZ Find the area of the shaded polygons:
Step-by-step explanation:
You can use the Pick's theorem:
[tex]A=i+\dfrac{b}{2}-1[/tex]
where
i - number of lattice points in the interior located in the polygon
b - number of lattice points on the boundary placed on the polygon's perimeter
[tex]1.\\i= 5;\ b=12\\\\A=5+\dfrac{12}{2}-1=5+6-1=10\\\\2.\\i=3;\ b=4\\\\A=3+\dfrac{4}{2}-1=3+2-1=4\\\\3.\\i=5;\ b=10\\\\A=5+\dfrac{10}{2}-1=5+5-1=9[/tex]
Answer:
Of course, the Pick's theorem is the way to solve this question, but consider:
Another approach is using topography:
Gauss's Area Calculation Formula:
[tex]$A=\frac{1}{2} \sum_{i=1}^{n} (x_{i} \cdot y_{i+1}-y_{i} \cdot x_{i+1})$[/tex]
Taking the purple one:
We have 6 points. I will name them:
[tex]A(0, 4);B(0, 0);C(1, 1);D(4, 0);E(4, 4);F(1, 2);[/tex]
[tex]$D=\begin{vmatrix}0& 0& 1 & 4& 4 & 1 & 0\\ 4& 0 & 1 & 0& 4 & 2 & 4 \end{vmatrix}$[/tex]
[tex]D=28-8=20[/tex]
[tex]$A=\frac{20}{2} =10$[/tex]
2) If Mike fell from (0.35) to (20, 0), determine the slope of his fall.
Answer:
-7/4.
Step-by-step explanation:
I'll take it to mean (0, 35)
The slope = (y2-y1)/(x2-x1)
= (0-35)/ (20-0)
= -35/20
= -7/4.
if (x + y) + (2(x + y) + 3) = 9, what is x + y??
A. 3-1
B. -3 + 1
c. -3-1
D 3 + 1
E. 9-31
Answer:
[tex]\boxed{\mathrm{Option \ A}}[/tex]
Step-by-step explanation:
=> [tex](x+y)+(2(x+y)+3)=9[/tex]
Solving the bracket
=> [tex]x+y+2x+2y+3 = 9[/tex]
=> [tex]3x+3y = 9-3[/tex]
=> [tex]3(x+y) = 6[/tex]
Dividing both sides by 3
=> [tex]x+y = 2[/tex]
A) 3 - 1 = 2 ← (Correct Answer)
B) -3+1 = -2
C) -3-1 = -4
D) 3+1 = 4
E) 9-31 = -22
Using every digit from 0−9 exactly once, make two five-digit numbers such that their sum is as large as possible. What is the sum?
Answer:
97,531+86,420=183,951
Step-by-step explanation:
Answer:
183,951
Step-by-step explanation:
Each of the 5 digit numbers would have to start with the two largest digits (9&8). The next two digits would have to be the next two largest digits (7&6). Continuing that pattern, we get:
97531+86420=183,951
The radius of a circle is three units. What is the diameter of the circle?
Answer:
6 units
Step-by-step explanation:
3x2=6
Answer: 6 units
Step-by-step explanation: The diameter of a circle which is a cord that passes through the center is always 2 times the radius.
So if we know that the radius of pour circle is 3 units,
we can simply multiply 2 by 3 to get 6 units.
So the diameter is 6 units.
Question 1 - Part A
Maria is bringing her sick dog Pedro in for a series of appointments at the
veterinary clinic. Her total cost over the course of treatment will be $150 for testsand medicine plus $30 per appointment, a.
Part A
Write an equation to show the total cost, t, she will owe.
Part C
what will be maria’s total discounted cost if pedro’s treatment requires three veterinary appointments?
Answer:
A and C
Step-by-step explanation:
Part A
150+30x, x being the amount of visits she takes
Part C
150+30(3)
150+90
240
$240
Complete the point-slope equation of the line through ( − 1 , − 10 )and (5 , 2) y-2 =?
Answer:
y - 2 = 3(x - 5).
Step-by-step explanation:
We need to find the slope of the line.
[2 - (-10)] / [5 - (-1)] = (2 + 10) / (5 + 1) = 12 / 6 = 2 / 1 = 2
So, y1 = 2, x1 = 5, and m = 2.
y - 2 = 3(x - 5)
Hope this helps!
The formula for point slope is written as y - y1 = m(x -x1)
You are given y - 2 = ?
Since the 2 form the point (5,2) is the y1 value, then the 5 is equal to x1
The formula becomes: y-2 = m(x-5)
Now solve for the slope, which is the change in y over the change in x:
Slope = -10 - 2 / -1 - 5 = -12/-4 = 3
Now replace m to get y-2 = 3(x-5)
What is the answer of 4(b+3) when b is 6?
Answer:
36
Step-by-step explanation:
Well first if b is 6 we plug that into the following.
4(b+3)
To,
4(6+3)
6+3 is 9 and 9*4 is 36.
Answer:
36
Step-by-step explanation:
4(6+3)
4(9)
36
One number is 5 more than 4 times another their sum is 20
Answer:
3, 17
Step-by-step explanation:
1st number = x
2nd number = 4x+5
x+4x+5=20
5x=15
x=3
1st number = 3
2nd number = 4(3)+5=12+5=17
The area of rhombus ABCD is 120 square units. AE = 12 and BD = x – 2. What is the value of x and the length of segment BD?
Answer:
its a
Step-by-step explanation:
Answer:
X=12 BD=10
Step-by-step explanation:
See Above
HELPPPP PLEASEEE I DONT WANNA GOT TO GRANNYS HOUSE
Answer:
15
Step-by-step explanation:
f(5) = (5)^2 - 2(5) = 25 - 10 = 15
solve please 3y^4t^-2/11y^-4
Answer:
[tex] \dfrac{3y^8}{11t^2} [/tex]
Step-by-step explanation:
[tex]\dfrac{3y^4t^{-2}}{11y^{-4}} =[/tex]
[tex] = \dfrac{3y^{4 - (-4)}}{11t^2} [/tex]
[tex] = \dfrac{3y^8}{11t^2} [/tex]
Diego cut 7 smaller boards of equal length from a board that is 9 and one-third feet long. How long is each of the 7 smaller boards? Four-thirds StartFraction 7 over 9 EndFraction StartFraction 9 over 7 EndFraction Three-fourths
Answer:
9 over 7 end fraction three-fourths
Step-by-step explanation:
The length of the 7 smaller boards will be ''Four-thirds'' (4/3 feet).
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Diego cut 7 smaller boards of equal length from a board that is 9 1/3 feet long.
Now,
Since, Diego cut 7 smaller boards of equal length from a board that is 9 and one-third feet long.
So, The length of the 7 smaller boards = 9 1/3 ÷ 7
= 28/3 ÷ 7
= 28/3 × 1/7
= 4/3 feet
Thus, The length of the 7 smaller boards will be ''Four-thirds'' (4/3 feet).
Learn more about the divide visit:
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what is 3^3/2 equal to?
Answer:
D. 2^3/2
Explanation:
3 3/2
= ²√3³
= ²√27
Hope this helped! :D
Answer:
The answer is D
Step-by-step explanation:
hope this helps ^_^
One day the temperature was 72°F. That night, the temperature was 44°F. What number represents the change in temperature?
Answer:
28°F
Step-by-step explanation:
We can find the change in temperature by subtracting 44 from 72:
72 - 44 = 28
So, the change in temperature was 28°F
A shipping box has dimensions as shown in the diagram. The red, dashed line represents the longest length of item that will fit inside the box. What is the length of the longest item that will fit inside the shipping box? Enter the correct answer in the box by replacing the values of m and n.
Answer:
26.8 in
Step-by-step explanation:
The red dashed line is the hypotenuse of the right triangle with one leg equal to 24 inches and the other leg equal to 12 inches. Its length is given by the Pythagorean theorem:
space diagonal = √(24^2 +12^2) = √(720) = 12√5
space diagonal ≈ 26.83 . . . inches
The length of the longest item that will fit in the box is about 26.83 inches.
Which word phrase could represent the algebraic expression 2p + 3 where p represents Sam's age?
Answer:
1. 3 + 4x
2. 8/ x-y
3. X/2y
4. Four times a number m
5 let m represent months
30 + 12m
Box A contains 5 dark chocolates and
10 milk chocolates. Box B contains 12
dark chocolates and 12 milk chocolates.
Craig picks a box at random and then
takes out one chocolate at random.
What is the probability that he gets a dark
chocolate?
% (1 d.p.)