Answer:
23
Step-by-step explanation:
-The length of the cubes side is (x-5) and the total surface area is 1944 sq units.
-We apply the formula for surface area and equate to solve for x:
[tex]A=6s^2\\\\1944=6(x-5)^2\\\\324=(x-5)^2\\\\324=x^2-10x+25[/tex]
#Equate to zero as below:
[tex]324=x^2-10x+25\\\\x^2-10x+25-324=0\\\\x^2-10x-299=0\\\\\# Quadratic \ Formula:\\\\x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\=\frac{10\pm\sqrt{(-10)^2-4(1\times-299)}}{2\times1}\\\\x_1=23, \ \ \ x_2=-13[/tex]
length dimensions are always positive.
Hence, the value of x is 23
Can someone please help me ?
Answer:
B. π(3/2)²h
(27/4)π cubic inches
Step-by-step explanation:
A. The formula for the volume of a cylinder is ...
V = πr²h
The radius (r) is half the diameter, so for a diameter of 3 inches, the radius is 3/2 inches. When this is put into the formula, the volume is ...
V = π(3/2)²h . . . . . . matches choice B
__
B. When h=3, the volume evaluates to ...
V = π(9/4)(3) = (27/4)π . . . . cubic inches
the ratio 6:12 in its simplest form
Answer:
1:2
Step-by-step explanation:
÷ by 6 both 6 and 12
you will receive 1:2 is the simplest form.
Aiden has $15.00 on his copy card. Each time he uses the card to make a photocopy, $0.06 is deducted from his card. Aiden wants to be sure that there will be at least $5.00 left on his card when he is finished. The inequality below relates x, the number of copies he can make, with his copy card balance.
15 minus 0.06 x greater-than-or-equal-to 5
What is the maximum number of copies Aiden can make?
60
83
166
250
Answer:
166
Step-by-step explanation: 0.06 times 166 equals 9.96 and Aiden wants at least 5 dollars left so 166 is the answer
The sum of a number and seven is the same as double the number increased by three.
Answer:
Not true
Step-by-step explanation:
n+7 = 2n+3
Final answer:
The student's algebra problem is solved by setting up the equation x + 7 = 2x + 3, where x is the unknown number, and using algebraic manipulations to find that x equals four.
Explanation:
The student's question pertains to an algebraic expression where a number and seven have a sum that's equivalent to double the number increased by three. To express this situation mathematically, we could set up the equation x + 7 = 2x + 3, where x represents the unknown number. To solve for x, we start by subtracting x from both sides of the equation, leading to 7 = x + 3. Then, we subtract 3 from both sides to isolate x on one side, resulting in 4 = x. Therefore, the number we are looking for is four.
The properties of numbers, such as the commutative property of addition which states that A + B = B + A, apply to this equation. This principle indicates that the order in which you add numbers does not affect the sum, a foundational concept taught across various arithmetic and algebra contexts in mathematics.
The product of the areas of two rectangular rugs is 84. If each of the dimensions is a prime number, what are the four dimensions? PLEASE help FAST!!!!
A.) 2,3,3,7
b.) 3,3,4,7
C.)2,2,3,3
D.)2,2,3,7
Final answer:
The correct dimensions for the two rectangular rugs, given that the product of their areas is 84 and each dimension is a prime number, are 2, 3, 3, and 7. Option : A) 2, 3, 3, 7 is correct answer .
Explanation:
The student's question is about finding the four dimensions of two rectangular rugs given that the product of their areas is 84 and each dimension is a prime number. We can break down the number 84 into its prime factors which are 2, 2, 3, and 7. Because dimensions must be prime numbers and since the only way to multiply four factors to get 84 is to pair them as (2 x 3) and (2 x 7), the dimensions of the rectangles are 2, 3, 2, and 7. However, since we know that the dimensions of the rugs must also be lengths, and lengths cannot be repeated for the same rug, it follows that the correct option must list each length only once.
Therefore, the four dimensions cannot be 2, 3, 2, and 7 since this would imply one rug has dimensions 2 x 2 which would not yield a prime number length for one side. Looking at the options given, the only set of dimensions that fulfill the criteria of being prime numbers and not repeating any length for the same rug is 2, 3, 3, and 7. Thus, the correct answer is: A) 2, 3, 3, 7.
The four dimensions of the rectangular rugs are 2, 2, 3, and 7. Hence, the correct option is D.
The four dimensions of the rectangular rugs are 2, 2, 3, and 7.
To find the dimensions, we need to factorize 84, which is 2 x 2 x 3 x 7 = 2^2 x 3 x 7.
Therefore, the dimensions are 2, 2, 3, and 7, which are all prime numbers.
what is the value of the expression?
-13 - (-9)
Answer:
Its
C my dude
Step-by-step explanation:
.
In Scott’s backyard, he has a windmill that makes 5 ¾ of a turn every hour. How many turns does it make for 1 ½ hours?
Answer: 8 5/8 turns
Step-by-step explanation:
Hi, to answer this question we have to simply to multiply the number of turns that the windmill makes per hour (5 3/4) by the time asked (1 ½ hours).
Mathematically speaking:
5 3/4 x 1 1/2 = (5x4+3)/4 x (1x2+1)/2 = 23/4 x 3/2= 69/8 or 8 5/8 (mixed form)
In conclusion, the windmill makes 8 5/8 turns in 1 1/2 hours.
Find the distance between point K and point L.
Answer:
(-8,0) is the answer
Step-by-step explanation:
x,y = (-8,0)
or
x/y = -8/0
We use x,y = 8,0 if the relationship if it was between L and K
The question states '' between point K and point L'' so it becomes -8,0 for x,y relationship.
Have attached trigonometry word doc for some guidance with picture memory trigonometry non related for someone to print out.
Hope the above helped.
How many variable terms are in the expression 3x to the 3rd power y + 5x to the 2nd power + y + 9? (Input a numeric value only.)
Answer: 2
[tex]3x^3y+5x^2+y+9[/tex]
Which number is rational and a real number, but not an integer?
A. Square root 2
B. There is no such number
C. -5
D. 5/7
Answer:
D. 5/7
Step-by-step explanation:
5/7 is real because it can be plotted on a number line,
Its rational because it can be written as a fraction of 2 integers
But it is not an integer
Help plzzzz I need help
Answer:
1. 425,328 -> 425,330
2. 105,025 -> 105,030
3. 45,527 -> 45,530
4. 35,478 -> 35,480
5. 212,369 -> 212,370
Step-by-step explanation:
000,000 the underlined number is the tens place. In order for the tens place to round up the ones place must be 5 or above. If the ones place is lower than 5 you round down to the nearest tens.
In Example:
333,389 you would round up to 333,390 because of the 9 in the ones place.
Now, 333,333 you would round down to 333,330 because of the 3 in the ones place
what is x²-22x-40=0
Student council at school would like to hold an end of the school year event for the eighth grade students they would like to know what’s students enjoy doing but do not have time to poll everybody Provide a suggestion for them to implement that would be unbiased
One unbiased suggestion is to create an online survey with a variety of activity options and allow students to anonymously vote for their preferences.
To ensure an unbiased approach in determining the activities for the end-of-the-school-year event, the student council can implement an online survey. This method allows all eighth-grade students to participate anonymously, eliminating potential biases based on social dynamics or peer pressure.
The survey should include a range of activity options, including both indoor and outdoor activities, sports, games, arts and crafts, and any other activities that may appeal to a diverse group of students. Additionally, students should have the option to suggest their own activity ideas to ensure that all interests are represented.
To further promote fairness, the survey should be distributed widely to all eighth-grade students through school email, online platforms, or even paper flyers if necessary. The survey should clearly state the purpose of gathering feedback and reassure students that their responses will be kept confidential.
After collecting responses, the student council can analyze the data to identify the most popular activity choices among students. This data-driven approach ensures that the end-of-the-school-year event reflects the interests and preferences of the majority of eighth-grade students, promoting inclusivity and fairness.
Overall, implementing an online survey provides an unbiased and transparent method for gathering feedback and making decisions about the event, ultimately enhancing the experience for all students involved.
Find the solution to the system of equations.y=-7x+3 y=-x-3
Answer:
x = 1; y = -4
Step-by-step explanation:
y = -7x + 3
y = -x - 3
since y = y then -7x + 3 = -x - 3
-7x + 3 = -x - 3
- 7x + 6 = -x (Because we add 3 to both sides)
x = 7x - 6 (Multiply both sides by -1)
-6x = -6 (Subtract 7x from each side)
x = 1
Answer:
7/3
Step-by-step explanation:
-3=-7x+3y
y=7/3+3y
7/3x-1
3x+3/7
=7/3
in ABC, AD is the angle bisector of /_BAC.
What is BD?
Enter your answer as a decimal,
? in.
Answer:
1.8
Step-by-step explanation:
ADC is a right angled triangle. So is ADB.
For right angled triangle ADC,
[tex] {ad}^{2} + {dc}^{2} = {ac}^{2} \\ {x}^{2} + {3}^{2} = {4}^{2} \\ {x}^{2} + 9 = 16 \\ {x}^{2} = 16 - 9 = 7 \\ x = \sqrt{7} [/tex]
For right angled triangle ADB,
[tex] {ad}^{2} + {db}^{2} = {ab}^{2} \\ 7 + {y}^{2} = {3.2}^{2} \\ 7 + {y}^{2} = 10.24 \\ {y}^{2} = 10.24 - 7 \\ {y}^{2} = 3.24 \\ y = \sqrt{3.24} \\ y = 1.8[/tex]
the answer to - 9 b = 27
Answer:
b= -3
Step-by-step explanation:
To solve, we must isolate the variable, b
-9b=27
Divide both sides by -9 to "reverse" the multiplication being done to b
b= -3
Find the value of x in the figure.
A. 3
C. 6
B. 7
D. 5
Answer:
A. 3
Step-by-step explanation:
since the missing angle adds up to 90° when added to 66°, first you would subtract 66 from 90
[tex]90-66=24[/tex]
set that number equal to [tex]8x[/tex] and solve for [tex]x[/tex]
[tex]8x=24[/tex]
[tex]x=3[/tex]
Find the missing length of the triangle (I need a step by step answer please)
Answer:
c = 12.5
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem (a^2 + b^2 = c^2)
lets say 10 = a and 7.5 = b (this is because they are the legs of the triangle and variables a and b represent the legs of the triangle)
plug into the Pythagorean theorem.
10^2 + 7.5^2 = c^2
simplify (here you just square 10 and 7.5)
100 + 56.25 = c^2
simplify
156.25 = c^2
simplify
(here you get the square root of 156.25 and c^2, the positive square root of 156.25 is 12.5 and the square root of c^2 is c)
12.5 = c
Answer: 12.5
Step-by-step explanation: the pythagorean theorem is used to solve this equation theorem is (a x a) + (b x b) = (c x c) this is also called squaring
first substitute them in : (10 x 10) + (7.5 x 7.5) = (c x c)
then multiply 10 x 10 = 100 and 7.5 x 7.5 = 56.25 then substitute again
100 + 56.25 = (c x c) then add
156.25 = (c x c) then calculate the square root of 156.25 which is 12.5
hope this helps mark me brainliest if it helped
If BCDE is a rhombus, find the measure of
Answer:
GDE=47°
DGE=90°
so DEG=180°-137°=25°
Answer:
43°
Step-by-step explanation:
Every triangle adds up to 180.
Since it is a rhombus, the central angle is 90.
180 - 90 = 90
90 - 47 = 43
What is the mean rainfall for the three towns in January to the nearest centimeter?
Answer:
I think its 3.0
Step-by-step explanation:
Subtract:
79 – 33
Question 10 options:
A)
–46
B)
46
C)
112
D)
–112
Answer:
it's answer is B 46
As 79 -33 = 46
Answer:
B) 46
Step-by-step explanation:
79 - 33 =
= + 46
WILL GIVE BRAINLIEST!!!
Solve the system using substitution.
-x-y=4
3x-4y=-13
A. (-1,3)
B. (3,-1)
C. (-3,1)
D. (1,-3)
Answer:
C. (-3, 1)
Step-by-step explanation:
[tex] - x + y = 4 \\ \therefore \: y = x + 4...(1) \\ \& \: 3x - 4y = - 13....(2) \\ substituting \: y = x + 4 \: in \: equation \: (2) \\ 3x - 4(x + 4) = - 13 \\ 3x - 4x - 16 = - 13 \\ - x = 16 - 13 \\ - x = 3 \\ \huge \red{ \boxed{x = - 3}} \\ plug \: x = - 3 \: in \: equation \: (1) \\ y = - 3 + 4 \\ \huge \purple{ \boxed{y = 1}} \\ \\ \orange{ \boxed{ \bold {\therefore \: (x, \: \: y) = ( - 3, \: \: 1)} }}[/tex]
29 is what percent of 80?
Answer:36.25%
Step-by-step explanation: 29 divided by 80 = .3625
Then convert to a percentage by moving the decimal two spaces to the right =36.25
Answer:
36.25 %
Step-by-step explanation:
Is means equals and of means multiply
Let P be the percent
29 = P * 80
Divide each side by 90
29/80 = P 80/80
.3625 = P
Changing from decimal form to percent form
36.35% = P
Which equation can be used to find 42 x 51?
(40 x 50) + (2 x 1) = 2,000 + 2
(4 x 5) + (2 1) = 20 + 2
(4 x 5) + (4 x 1) + (2 5) + (2 1) = 20 + 4 + 10 + 2
(40 x 50) + (40 x 1) + (2 x 50) + (2 x 1) = 2,000 + 40 + 100 + 2
Answer:
(40 x 50) + (40 x 1) + (2 x 50) + (2 x 1) = 2,000 + 40 + 100 + 2
The equation can be used to find 42 x 51 will be (40 x 50) + (40 x 1) + (2 x 50) + (2 x 1) = 2,000 + 40 + 100 + 2. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 42 x 51
Simplify the expression, then we have
⇒ 42 x 51
⇒ (40 + 2) x (50 + 1)
⇒ 40 x 50 + 40 x 1 + 50 x 2 + 2 x 1
⇒ 2,000 + 40 + 100 + 2
⇒ 2,142
The equation can be used to find 42 x 51 will be (40 x 50) + (40 x 1) + (2 x 50) + (2 x 1) = 2,000 + 40 + 100 + 2. Then the correct option is D.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
How many solutions does this system have? 2 x- 4 y = 8. x + y = 7.
Answer:
One solution: (6,1)
Step-by-step explanation:
2 x- 4 y = 8
x - 2y = 4
x = 4 + 2y
x + y = 7
4 + 2y + y = 7
3y = 3
y = 1
x = 4 + 2(1)
x = 6
One solution: (6,1)
Answer:
2 x- 4 y = 8
x + y = 7
y= 7-x-----------(1)
2 x- 4 y = 8
on substitution
=>2x -4(7-x)= 8
=>2x -28+4x = 8
=>6x= 36
=>x= 6
From (1)
y= 7-6= 1
Therefore, the system have 1 solution
(6,1)
Decide whether ▱ABCD with vertices A(−2,3), B(2,3), C(2,−1), and D(−2,−1) is a rectangle, a rhombus, or a square. Select all names that apply.
rectangle
rhombus
square
Answer:
it is a rectangle, rhombus, and a square
Step-by-step explanation:
when you graph it out, they all have equal sides and they have congruent angles
z=-302+19.3i?????????
Answer:
I don;t know what the question is but I know that z is an imaginary number.
Step-by-step explanation:
z=-302+19.3i
that means that it doesn't represent an actual number but is imaginary.
An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, and its square is −25.
Old man Jenkins left 1/2 of his money to his grandkids and 1/2 of that amount to his kids. He left 1/6 to his wife and the remaining $1000 to his tiger. How much did he leave altogether?
Answer:
12000
Step-by-step explanation:
Jenkins had x dollars
He left 1/2 of that to his grandkids
He has x-1/2x = 1/x
He leaves 1/2 of that to his kids
1/2*1/2 x = 1/4x to his kids
His wife gets 1/6x
The rest is 1000
The total is
grand kids + kids + wife + 1000
1/2 x + 1/4x + 1/6x + 1000
He started with x
1/2 x + 1/4x + 1/6x + 1000 =x
Multiply each side by 12 to get rid of the fractions
12(1/2 x + 1/4x + 1/6x + 1000) =x*12
6x+3x +2x +12000= 12x
Combine like terms
11x +12000 = 12x
Subtract 11x from each side
11x-11x +12000 = 12x-11x
12000=x
Since he started with x, he left 12000 dollars
Answer:
$12,000
Step-by-step explanation:
Let total be X
X - ½X = remaining after giving to grand kids
½(X/2) = ¼X remaining after giving to children
¼X - ⅙X = (3X - 2X)/12 = X/12 after giving to wife
X/12 = 1000
X = 12,000
need help will give brainist
Answer:
11. x=15 , 12. x=-16, 13 x is greater than or equal to 15 , 14 x=-3 , 15 x=-3, 16 x=15/2 , 17 x is greater than is equal to -4, 18: x is greater than -11
Step-by-step explanation:
11. 4x+15=75
subtract 15
4x=60
divide
x=15
12. 2x = -32 (subtract 13 from each side)
divide
x=-16
13. multiply each side by
-3/2
x is greater than or equal to 15
14. -3x -18 + 5 = -4
isolate x
-3x=9
x=-3
15. -5x-30 +5=-10
isolate x
-5x = 15
x= -3
16. 2x + 16 = 6x - 14
isolate x
4x = 30
x= 15/2
17 isolate x
x is greater than is equal to -4
18. isolate x
x is greater than -11
Hope it will help u.....
Expand: In (4a)^3
- 3 In 4 + In a
- 3 In 4 - 3 In a
- 3 In 4 + 3 In a
Answer:
3 ln 4 + 3 lna
Step-by-step explanation:
In (4a)^3
We know that ln x^y = y ln x
3 ln (4a)
We also know that ln (xy) = ln x + ln y
3( ln 4 + ln a)
3 ln 4 + 3 lna
Answer:
3 ln 4 + 3 lna
Step-by-step explanation: