A cuboid with a volume of 924 cm' has dimensions
4 cm, (x + 1) cm and (x + 11) cm.
Show clearly that x2 + 12x – 220 = 0
Solve the equation by factorisation, making sure you show the factorisation.
State both values of x on the same line.
Finally, find the dimensions of the cuboid, writing all three on one line.
Answer:
4cm, 11cm, 21cm
Step-by-step explanation:
4(x + 1)(x + 11)
4(x ^ 2 + 12x + 44)
x ^ 2 + 12x + 11 = 231
x ^ 2 + 12x + 11 - 231 = 0
x ^ 2 + 12x - 220 = 0
(x - 10)(x + 22) = 0
x = 10 and x = - 22
4cm , 11cm , 21cm
Hope it helps you xx
Answer:
Dimensions = 4cm, 11cm and 21 cm.
Step-by-step explanation:
x2 + 12x - 220 = 0
x2 + 22x - 10x - 220
= x(x+22) -10(x+22)
=(x+22)(x-10)
x + 22= 0
-22 -22
x = -22 (x cant be negative so this is wrong)
x-10 = 0
+10 +10
x = 10 (positive so its correct)
4 , (10+1), (10+11)
= 4, 11, 21 cm.
Isabella took a taxi from her house to the airport. The taxi company charged a pick-
up fee of $4.70 plus $2.25 per mile. The total fare was $58.70, not including the tip.
Write and solve an equation which can be used to determine , the number of miles in the taxi ride.
Answer:
Equation: 2.25x+4.7=58.70
Answer: x = 24x=24
Hope this helps
Please help please no links please please anything helps
Answer:
140
Step-by-step explanation:
Possibly i'm not that great at math but this might be the answer.
WILL GIVE BRAINLIEST IF YOU HELP ME
Answer:
D. Point S
Step-by-step explanation
The opposite of -5.5 is 5.5, therefore since Point S is at 5.5 on the number line, the answer is D.
how is finding 8x3/4 similar to finding 3/4 of 8
Answer: your answer would be 6
8*3=24/4 and 24/4=6
Step-by-step explanation: Hope this help :D
Answer:
Because in order to find 3/4 of 8, you must solve for 8 * 3/4.
A helpful tip is that "of" is one of the giveaways of a multiplication problem. Others include but are not limited to, "multiply, " "product," "by," "times," "area," "twice," "double," "thrice," "triple," and "quadruple."
I would appreciate Brainliest, but no worries.
Help fast it’s for a test I do t wanna fail!!
Answer:
it is decreasing by 1/2 half every number to get the next answer is 6
Step-by-step explanation:
what adds to 3 and multiplies to -70
Julio spent $52.43 on batteries. If they cost $7.49/pack, how many packs did he buy?
Answer:
7
Step-by-step explanation:
52.43 ÷7.74=7
There is a 30% probability of
hail. What is the probability
that it will NOT hail?
Answer:
70% probability
Step-by-step explanation:
100% probability
-30% probability
=70% probability
Olaf wants to buy a guitar that costs $600. He makes $3 per day. How many days will it take Olaf to save enough money to buy the guitar
Answer:
200 days
Step-by-step explanation:
600/3 = 200
Answer:
200 days
Step-by-step explanation:
Simple: You divide the cost of the guitar by the amount he gets paid per day. Hope this helps :)
1. A company has $6582 to give out in bonuses. An amount is to be given out equally to each of the 32 employees.
(a) A manager, Jake, reasoned that since 32 goes into 64 twice, each employee will get about $2000. Is his estimate correct? Why or why not?
(b) How much will each employee receive, rounded to the nearest whole dollar? Leave the remainder undivided. Show your work.
Answer:
Answer:
A) His estimate is incorrect, since he has increased a figure to the amount that each employee would receive.
B) Rounded to the nearest dollar, each employee would receive $ 209.
Step-by-step explanation:
Since a company has $ 6582 to give out in bonuses, and an amount is to be given out equally to each of the 32 employees, and A) a manager, Jake reasoned that since 32 goes into 64 twice, each employee will get about $ 2000 , to determine if his estimate is correct, and B) determine how much will each employee receive, rounded to the nearest whole dollar, the following calculations must be performed:
A)
2000 x 32 = 64000
200 x 32 = 6400
Therefore, his estimate is incorrect, since he has increased a figure to the amount that each employee would receive.
B)
6582/32 = X
208.68 = X
Therefore, rounded to the nearest dollar, each employee would receive $ 209.
Decide which of the following quantities can be represented by a positive number and which can be represented by a negative number. Give an example of a quantity with the opposite sign in the same situation
Answer:
Step-by-step explanation:
a +
b -
c +
d -
e -
positive, Negative , Positive, Negative, Negative.
What is Number System?A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner.
The given sentences are
(A) Tylers puppy gained 5 pounds.
This we can take as a positive number. Because here the value is increasing. whenever we use gained means it is positive.
Tylers puppy lost 5 pounds is the negative number.
(b) The aquarium leaked two pounds of water
This we can take as a Negative number. Because here the value is decreased. whenever we use leaked means it is negative.
The aquarium added with two pounds of water is a positive.
(c) Andrew received a gift of $10.
This we can take as a positive number. Because here the value is increasing. whenever we use received means it is positive.
Andrew gifted a gift of $10.
This we can take as a Negative number. Because here the value is decreased. whenever we use gifted means it is negative.
(d) Kiran gave a gift of $10
This we can take as a Negative number. Because here the value is decreased. whenever we use gave means it is negative.
Kiran received a gift of $10 is positive.
(e) A climber descended 550 feet.
This we can take as a Negative number. Because here the value is decreased. whenever we use descended means it is negative.
Hence positive, Negative , Positive, Negative, Negative,.
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what is the shortest distance from the surface xy+15x+z2=209 to the origin ?
We can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.
Given the equation of the surface is xy + 15x + z^2 = 209.
Let's determine the shortest distance from the surface to the origin.
The shortest distance between the surface and the origin is given by the perpendicular distance, which can be calculated as follows:
Firstly, we need to determine the gradient of the surface, which is the vector normal to the surface.
For this purpose, we need to write the surface equation in the standard form, which is:xy + 15x + z^2 = 209 xy + 15x + (0)z^2 - 209 = 0 (the coefficients of x, y, and z are a, b, and c).
The gradient of the surface is given by the vector: ∇f = (a, b, c) = (y + 15, x, 2z) at the point P(x, y, z), which is a point on the surface.
Here, the normal vector is ∇f = (y + 15, x, 2z).
Now, let's consider a point A on the surface which is closest to the origin.
Let the coordinates of A be (a, b, c).
Therefore, the position vector of A is given by: OA = ai + bj + ck.
The direction of the position vector is in the direction of the normal vector, and therefore: OA is parallel to ∇f.
Thus, we can write: OA = λ∇f = λ(y + 15)i + λxj + 2λzkWhere λ is a scalar.
Since A lies on the surface, we have: a*b + 15a + c^2 = 209.
We also know that OA passes through the origin.
Therefore, the position vector of A is perpendicular to the direction vector OA.
This gives us: OA·OA = 0⟹ (ai + bj + ck)·(λ(y + 15)i + λxj + 2λzk) = 0
Simplifying this equation gives us:aλ(y + 15) + bλx + c(2λz) = 0
Also, we know that OA passes through the origin.
Therefore, the magnitude of OA is equal to the distance of A from the origin.
Hence, we can write: |OA| = √(a^2 + b^2 + c^2)
The value of λ can be obtained from the equation: aλ(y + 15) + bλx + c(2λz) = 0orλ = -2cz / (b + a(y + 15))
Substituting this value of λ in OA, we get: OA = λ(y + 15)i + λxj + 2λzk= -2cz/(b + a(y + 15)) (y + 15)i - 2cz/(b + a(y + 15)) xj - 4cz^2/(b + a(y + 15))k
Substituting this value of λ in |OA|, we get: |OA| = √[(2cz/(b + a(y + 15)))^2 + (2cz/(b + a(y + 15)))^2 + (4cz^2/(b + a(y + 15)))^2] = 2cz√[(y + 15)^2 + x^2 + 4z^2] / |b + a(y + 15)|
The distance of the point A from the origin is |OA|, which is minimized when the denominator is maximized. The denominator is given by |b + a(y + 15)|.
Thus, we have to maximize the denominator with respect to a and b. The condition for maximum value of the denominator is obtained by differentiating the denominator with respect to a and b separately and equating it to zero. The values of a and b obtained from these equations are substituted in the equation a*b + 15a + c^2 = 209 to obtain the coordinates of the point A, which is closest to the origin.
Hence, we can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.
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What is the difference of 506 and 297
Answer:
209
Step-by-step explanation:
subtract
Answer:
209
Step-by-step explanation:
subtraction bro
What is the area of the figure? I give brainliest! :)
Answer: I think it is 142
Step-by-step explanation:
91 + 51 = 142
The following quadrilateral is a parallelogram. Solve for x, y, and z.
Answer:
Angle X = 73 degrees, Angle Z = 34 degrees, and Angle Y = 146 degrees
You earn $18 for watching three cars how much do you earn to Washing 2 cars
Answer:
$12
Step-by-step explanation:
3 cars divide that by $18 and u get $6 per car. multiply that by two cars nd you get $12.
Please help I’m really need the help (NO LINKS ) (NO LYING ) PART 2 again again again
Answer:
Step-by-step explanation: i wont tell you the answer but ill thell you how to do it,soo the strat is to count where the line is as a different part then u just add em
example 1:41.6
8-4=4x4=16
8x3.2=25.6
16+25.6=41.6
:)
Answer:
A. 15
B. 25.6
C. 41.6
three numbers are in A.P. the difference between the first and the last is 8 and the product of these two is 20. find the numbers
9514 1404 393
Answer:
10 and 2
Step-by-step explanation:
Essentially, you're being asked to find factors of 20 that have difference of 8. 20 can be factored as ...
20 = 20×1 = 10×2 = 5×4
The factors 10 and 2 have a difference of 8.
The numbers are 10 and 2.
The zeros of a parabola are -5 and -3. The point (0, 60) is on the graph as represented by the equation.
60=a(0+5)(0+3)
What is the value of a?
−7.5
−4
4
7.5
plz be right its a massive grade
Answer:
C is the Correct answer and luck on the massive grade
Find the equation (in terms of x ) of the line through the points ( − 5 , 4 ) and ( 4 , 0 ) . Express your answer in slope-intercept form
Answer:
Equation = 4x + 9y = 16Step-by-step explanation:
co-ordinate = (-5.4) & (4,0)
slope(m) = (y² - y¹) / (x² - x¹)
slope(m) = (0-4) / (4+5)
slope(m) = -4 / 9
Equation,
y = mx + c
y - 0 = -4/9 (x - 4)
9y = -4x + 16
4x + 9y = 16
Rectangular prism l 2/3, h 3/5 w 4/7 what is volume?
Answer:
Step-by-step explanation:
volume= width X height X length
volume= 4/7 X 3/5 X 2/3
volume= 0.23
) Which expressions show the total area of the tiny house in square feet? Choose ALL that apply. 36x + 24 24x + 36 2.(12 + 3) 12(2x + 3)
Answer:
24x+36 and 12(2x+3)
Step-by-step explanation:
I just did it
Jacqueline is ordering pizzas for a party. Each pizza is cut into 12 slices. Jacqueline wants to have enough pizza so each person can have 4 slices. 16 people will be at the party. If Jacqueline buys 7 pizzas, how many extra slices will be left over after each guest eats 4 slices?
Answer:
20
Step-by-step explanation:
Just write down the answer.
While standing on a pier, Lynette saw a balloon floating 20 feet above her and a fish swimming 4 feet below the surface of the water.
Let 0 represent the water surface, and let the positive side of 0 represent position above the surface. Which number sentence correctly compares the distances of the balloon and the fish to the surface of the water?
A. |-4| < |20|
B. |-4| > |20|
C. |4| < |20|
D. |4| > |-20|
Answer:
I'd go with A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
geometry math plz help
Answer:
1. mCD is equal to 84 degrees.
2. I believe that RPT would be equal to approximately 51 feet. I think I am right, but I am not 100% sure. I used formula though.
Step-by-step explanation:
1. In order to find the measure of CD, you would find the measure of AD and CD, because they add to 180, and from there you can take the answer, which will be the x value, and plug it back into measure CD's equation.
1. Add the equations of mAD and mCD and set them equal to 180, because together on the graph they add to 180 degrees, which is a semi-circle.
19x-49+5x+37=180
24x-12=180
2. Solve.
24x-12=180
24x=168
x=7
3. Plug x back into mCD and find the answer!
19(7)-49=84
mCD= 84 degrees!
2. Arc Length Formula
2[tex]\pi[/tex]r degrees/360
2pi (14) 208/360≈51
I’ll give brainliest
Find the area of the smaller sector.
Round to the nearest tenth.
500
7 1371
Area = [? ]ft2
Answer:
22.2
Step-by-step explanation:
Hello There!
This is the sector area formula
[tex]A=\frac{0}{360} (\pi r^2)[/tex]
where 0 = sector angle
and r = radius
The given sector has a measure of 50 degrees and a radius of 7.13
Knowing this information we plug it into the formula
[tex]A=\frac{50}{360} (\pi 7.13^2)\\\frac{50}{360} =0.1388888889\\7.13^2=50.8369\\50.8369\pi =159.7088316\\159.7088316*0.1388888889=22.18178216[/tex]
so we can conclude that the area of the sector is 22.18178216 ft²
finally we round to the nearest tenth
and get that the answer is 22.2
The following data points represent the number of puppies in each litter at Port's Pup Rescue.
Sort the data from least to greatest.
11
14
7
2
9
6
2
Find the median number of puppies.
puppies
My
D. Write an original equation and solve.
Eight fewer than twice the sum of x and 4 is 10.
Answer:
2(x+4) - 8 = 10
Step-by-step explanation:
the sum of x and 4: x+4
twice the sum of x and 4: 2(x+4)
eight fewer than twice the sum of x and 4: 2(x+4) - 8
eight fewer than twice the sum of x and 4 is 10: 2(x+4) - 8 = 10
Jacob's family takes the train to the city. The sign below shows information about the cost of train tickets. Jacob's family buys 2 adult tickets and 3 child tickets.
How much does it cost Jacob's family to take the train into the city?
Train Fare One-Way Adult $7 Child $6
It costs Jacob's family $
32
to take the train into the city.
You got it!
Jacob’s father pays for the tickets with $5 bills. He receives $3 in change. How many $5 bills does Jacob’s father use to pay for the tickets?
Answer:
it cost Jacob family $32 and he used 7 $5 bill to pay
Step-by-step explanation:
2 × 7 = 14
3 × 6 = 18
18 + 14 = 32
5x - 32 = 3
5x = 32 + 3
5x = 35
x = 35 ÷ 5
x = 7