Answer:
The volume of the box would be 6x³+33x²+54x+27.
Step-by-step explanation:
The new dimensions of the box would be (x+3), (2x+3), and (3x+3). Since the volume of a rectangular prism are calculated by multiplying the length, width, and depth, we can just multiply all three of these dimensions together to come up with the answer.
Using foil on the first two terms originally you get (x+3)×(2x+3)= 2x²+3x+6x+9 which can be simplified to 2x²+9x+9.
Then you multiply this equation by (3x+3). (2x²+9x+9)×(3x+3)= 6x³+6x²+27x²+27x+27x+27 which can be simplified to 6x³+33x²+54x+27.
Answer:
6x³+33x²+54x+27
Step-by-step explanation:
dimensions are now:
x+3, 2x+3, 3x+3
Volume
V=lwhV= (x+3)(2x+3)(3x+3)= 3(x+1)(x+3)(2x+3)= 3( x² + 4x+3)(2x+3)= 3(2x³+11x²+18x+9)=6x³+33x²+54x+27Which reslts only in a horizontal compression of y=1/x by a factor of 6?
Answer:
y=1/6x
Step-by-step explanation:
y=1/x
the rule for horizontal compression is f(k.x) since we have the equation of y=1/x and k=6 then y=1/6x
Can anyone help me with this?
Answer:
Yes it is 7 cuz it has the equation of 3-5a
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Plug in -3 as a
h(-3) = (3+15)/3
h(-3) = 18/3
h(-3) = 6
What is the probability of selecting a boy or a blonde-haired person from 12 girls, 5 of whom have blonde-haired and 15 boys, 6 of whom have blonde-haired
Answer: 20/27
Step-by-step explanation:
So it is non- mutually exclusive;
Let B for the boys and H for the blond hair.
P(B) = 15/27; P(H) 11/27; P(B and H) = 6/27
Then, we have,
P(B or H) = 15/27 + 11/27 - 6/27
P(B or H) = 20/27
Therefore, the probability of selecting a boy or a blond-haired person is 20/27.
Solve for s.
6 − 4s = –8 − 6s
s =
Step-by-step explanation:
6 - 4s = - 8 - 6s
Bringing like terms on one side
-4s + 6s = - 8 - 6
2s = - 14
S = - 14/2
S = - 7
HELP FAST! A cat spies a bird sitting at the top of a 32 foot pole. If the angle of elevation from the cat to the bird is 47°, then the cat is __________ feet from the base of the flagpole. Select one:
a. 29.880
b. 29.890
c. 29.820
d. 29.800
e. 29.840
Answer:
e. 29.840
Step-by-step explanation:
The cat, the floor and the foot pole form the shape of a right angled triangle.
The opposite is the height of the foot pole = 32 ft
The adjacent is the distance of the cat from the base of the foot pole.
The hypotenuse is the direct distance of the cat from the bird.
The angle of elevation, x, is 47°
To find the distance of the cat from the foot of the foot pole, we can use to TAN part of the trigonometric function SOHCAHTOA:
tan(x) = opposite / adjacent
=> tan(47) = 32 / adj
adj = 32 / tan(47)
adj = 29.840 ft
Therefore, the cat is 29.840 feet from the base of the foot pole.
pls help for brainliest
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πr^2 = area
Half the diameter to get the radius
Substitute the values in:
area = 3.142 x (7)^2
area = 153.958 cm^2
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Answer:
153.958cm^2
Step-by-step explanation:
r=d/2=14/2=7cm
A=πr^2
A=3.142×7^2
A=3.142×49cm^2
A=153.958cm^2
What is the sum of the greatest and least numbers below: \[8\frac15, \qquad -8\frac25, \qquad -\frac{26}{3}, \qquad -\frac{54}7, \qquad \frac{53}{6}.\]
Answer:
[tex]\dfrac{47}{42} \ \ \ \ \ OR \ \ \ \ 1.1[/tex]
Step-by-step explanation:
The objective of this question is to find the sum of the greatest and least numbers below:
[tex]\[8\frac15, \qquad -8\frac25, \qquad -\frac{26}{3}, \qquad -\frac{54}7, \qquad \frac{53}{6}.\][/tex]
To do this ; we will need to find the decimal component of each of them and equate them on a number line before summing the greatest and least numbers.
[tex]8 \frac{1}{5} = \dfrac{8*5+1}{5} \\ \\ = \dfrac{41}{5} \\ \\ = 8.2[/tex]
[tex]-8 \frac{2}{5} =- \dfrac{8*5+2}{5} \\ \\ =- \dfrac{42}{5} \\ \\ = -8.4[/tex]
[tex]-\dfrac{26}{3}= - 8.7[/tex]
[tex]-\dfrac{54}{7} = - 7.7[/tex]
[tex]\dfrac{53}{6}= 8.8[/tex]
Thus; the above decimal component of the fractions given are :
8.2, -8.4, -8.7 , -7.7 and 8.8
We are to find the sum of the greatest and the smallest number ; on a number line; we will realize that the positive side is greater than the negative side , As such the greatest number from the positive side will be 8.8 and the smallest number will be -7.7
The sum of 8.8 + ( -7.7 ) = 8.8 - 7.7
= 1.1
i.e
[tex]\dfrac{53}{6} + (- \dfrac{54}{7} )[/tex]
[tex]\dfrac{53}{6} - \dfrac{54}{7}[/tex]
[tex]\dfrac{53}{6} - \dfrac{54}{7} = \dfrac{53*7 - 6*54}{42} \\ \\ = \dfrac{47}{42} \\ \\ = 1.1[/tex]
Answer:
47/42Step-by-step explanation:
Malik decides that he wants a good result on the state math test. He plans to study for at least 45 minutes three nights per week. Which expression represents Malik's study goal for each week?
Answer:
[tex]135<t_{minutes}\:<315[/tex]
Step-by-step explanation:
Malik's goal is a minimum total of 135 (45 x 3) minutes per week, in three session of 45 minutes.
Notice that it is at least.
So He can do sessions from 3 , 4, 5, 6 up to 7 nights per week
Hence, we can write his goals in minutes per week:
[tex]G_{w}=3*45<t_{minutes}<7*45\\G_{w}=135<t_{minutes}<315[/tex]
May I Please Get Help For Number 5
Answer:
$ 60
Step-by-step explanation:
p(x) = 7x + 25
f(1) = 2.1² + 3 = 5
p(f(1)) = p(5) = 7 . 5 + 25 = 35 + 25 = 60
so he get $ 60 for 5 hours work with tips
PLEASE HELP ASAP MATH
Answer:
3. 324+432=756 in cubed
4. 2100+7200=9300 yd cubed
rewrite the expression in the form 2n
Answer:
two times a number
Step-by-step explanation:
the shapes below are drawn on a centimeter grid, show that the triangle and the square have the same area.
Answer:
Area_square = 4 cm2
Area_triangle = 4 cm2
Step-by-step explanation:
The first thing to do is calculate the area of both figures.
The area of the square is given by:
Area_square = side * side
The side of the square is 2 cm, so:
Area_square = 2 * 2 = 4 cm2
The area of the triangle is given by:
Area_triangle = base * height / 2
The base is 2 cm, and the height is 4 cm, so we have:
Area_triangle = 2 * 4 / 2 = 4 cm2
So we have that Area_square = Area_triangle = 4 cm2
The amount of money that Tom had in his pension fund n 2016 was E55 000. Dis plans involve him putting $8 200 in his fund every year for the next 15 years. How much will Tom have in the pension fund in 2031?
Answer:
$178,000
Check my explanation for further details
Step-by-step explanation:
$8200 in his pension fund for 15 years
=8200×15
=$123,000
By 2031
Tom will have a total of $55 000+$123,000
=$178,000
If by saying E55,000 you mean 55,000 Euro
Then,
$62,174.99=E55000
$62,174.99+$123,000
=$185,174.99
Tom can do a job in 4 hours while Sam can do it in 6 hours. How many hours would it take to complete this job if they work together?
Answer:
12/5hours=2.4 hours
Step-by-step explanation:
Sam:6hours
Tom:4hours
This is a rate problem
Sam's rate is one job completed in 6 hours which is 1/6
Tom's rate is one job completed in 4 hours which is 1/4
Together, they could complete 1/4+1/6 of the job in y hours
We are trying to find the rate at which Sam and Tom could complete the job together, or one job in x days, for a rate of 1/y
1/4+1/6=1/y
The least common denominator is 12y
Multiplying through by the LCD which gives:
12y(1/4)+ 12y (1/6)= 12y (1/y)
3y + 2y=12
5y = 12
y=12/5 hours=2.4hours
Therefore it will take 12/5 hours or 2.4 hours to complete the job if they work together
The Arc de Triomphe measures 50 m in height. You are asked to make a replica model in art class using a scale of 1:275. What should the height of your model be in millimeters?
Answer:
180 millimeters.
Step-by-step explanation:
To find the height of the replica, a ratio can be set up:
[tex]\frac{x}{50}= \frac{1}{275}[/tex]
Cross multiply:
[tex]275x = 50[/tex]
Divide both sides by '275:
x≈0.18 meters
Convert 'meters' to 'millimeters' by multiplying by a thousand:
0.18 × 1000 = 180 millimeters.
i dont know which two chose
If cos0 =1/3
then sin0=?
Answer:
sin θ = +/- (2√2)/3
Step-by-step explanation:
cos θ = 1/3
cos²θ + sin²θ = 1
(1/3)² + sin²θ = 1
sin²θ = 1 - 1/9
√(sin²θ) = +/-√(8/9)
sin θ = +/- (2√2)/3
What is the value of 3/10 to the third power
Answer:
[tex]\frac{27}{1000}[/tex]
Step-by-step explanation:
=> [tex](\frac{3}{10} ) ^3[/tex]
=> [tex]\frac{(3)^3}{(10)^3}[/tex]
=> [tex]\frac{27}{1000}[/tex]
Answer:
It's 0.003.
Step-by-step explanation:
50 POINTS!
You have $10,000 to invest, and three different funds from which to choose. The municipal bond fund has a 7% return, the local bank's CDs have an 8% return, and the high‐risk account has an expected (hoped‐for) 12% return. To minimize risk, you decide not to invest any more than $2,000 in the high‐risk account. For tax reasons, you need to invest at least three times as much in the municipal bonds as in the bank CDs. Assuming the year‐end yields are as expected, what are the optimal investment amounts?
Answer:
Optimal investment amount = $300
Step-by-step explanation:
discount = x
original price = 10,000
discount% = 7%
x/10,000 = 7/100
x · 100 = 7 · 10,000
100x = 70,000
100x/100 = 70,000/100
x = 700
discount = x
original price = 10,000
discount% = 8%
x/10,000 = 8/100
x · 100 = 8 · 10,000
100x = 80,000
100x/100 = 80,000/100
x = 800
discount = x
original price = 10,000
discount% = 12%
x/10,000 = 12/100
x · 100 = 12 · 10,000
100x = 120,000
100x/100 = 120,000/100
x = 1,200
So:
$1,200 - $800 - $700 = $300
We max out the high return investment, $2000 for 12%.
We have $8000 left to invest and we want to put as much in CDs at 8% as possible. Let's call b the bond investment and c the CD investment. We have
b ≥ 3c
Since munis have the lower return we want as many CDs as possible. So we choose:
b = 3c
b + c = 8000
3c + c = 8000
4c = 8000
c = 2000
That leaves b=3c=6000 for bonds.
Answer: $6000 in bonds, $2000 in CDs, $2000 in high-risk.
4.7 - 2.3 = 4.7 + (-2.3) =
Answer:
2.4
General Formulas and Concepts:
Math
Base 10 Decimal SystemPre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
4.7 - 2.3
Step 2: Evaluate
Subtract
2.4
Answer:
2.4
Step-by-step explanation:
PLEASE HELP! Shalini found the sum of the measures of the interior angles of the triangle to be 175°. She knows the sum is supposed to be 180°. What was Shalini’s error? m∠A = 45° m∠B = 85° m∠C = 45° Shalini did not add the sum of the 3 angles correctly.
Answer:
its c
Step-by-step explanation:
because i said
Answer:
c is the correct option
Step-by-step explanation:
what is the LCM of x^2+5 and x^2+10x+25?
Answer:
(x+5)²(x²+5)
Step-by-step explanation:
Given two functions x²+5 and x²+10x+25, to get their Lowest common factor, we need to to first factorize x²+10x+25
On factorising we have:
x²+5x+5x+25
= x(x+5) +5(x+5
= (x+5)(x+5)
= (x+5)²
The LCM can be calculated as thus
| x²+5, (x+5)²
x+5| x²+5, (x+5)
x+5| x²+5, 1
x²+5| 1, 1
The factors of both equation are x+5 × x+5 × x²+5
The LCM will be the product of the three functions i.e
(x+5)²(x²+5)
This hives the required expression.
The triangles shown below must be congruent.
45°
45-
12
45°
45°
12
O A. True
B. False
Answer: True
Step-by-step explanation: The angles given are the same AND the side given us the same. The triangle has been reflected, but the reflection is still congruent.
The two triangles given are congruent according to the ASA congruence rule.
What is ASA congruence rule ?Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.
Check whether the triangles are congruent :The given triangles are both right angled triangles.
The side 12 units is the included side between the angles 45° and 90° in both the triangles. This is the required condition for ASA congruence rule.
Hence we can say that the triangles are congruent according to the ASA congruence rule. The answer is A.True.
Learn more about congruence of triangles here:
brainly.com/question/36879
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Round 3.44570830811 to the nearest hundred-thousandth,
Answer:
3.44571
Step-by-step explanation:
look at the number to the right of the decimal. if the number is higher than or is 5 round the number up, but if the number is less than 5 it will stay the same.
The number after rounding off to nearest hundred-thousandth or 5 decimal places will be -
3.44571
We have the following number - 3.44570830811
We have to round it of nearest hundred-thousandth or 5 decimal places.
What are Rounding numbers?Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. For example - 53 rounded to the nearest ten is 50.
According to the question, we have the following number -
3.44570830811
Rounding it off One by one until we get 5 digits after decimal -
R1 - 3.44570830811
R2 - 3.4457083081
R3 - 3.445708308
R4 - 3.44570831
R5 - 3.44570831
R6 - 3.4457083
R7 - 3.445708
R8 - 3.44571
Hence, the number after rounding off to nearest hundred-thousandth or 5 decimal places will be -
3.44571
To solve more questions on Rounding Numbers, visit the link below-
brainly.com/question/17284779
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The low temperature during 4 days in September was 21°C, 21°C, 19°C and 19°C. What was the mean temperature?
Answer:
Step-by-step explanation:
The Answer is 20.
1: First, add up all the temperatures that has been provided, 21 + 21 + 19 + 19. It should give you 80.
2: Divide 80 by how many temperatures has been shown. There were 4 temperatures shown, so 80/4 = 20. Hope this helps you!
Which of the following is a secant on the circle below
Answer:
RT is more appropriate, though even SU could be called a secant.
Step-by-step explanation:
Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
- 18y = 1
Step-by-step explanation:
Adding the 2 equations term by term on both sides gives
(- 5x + 5x) + (- 9y - 9y) = (3 - 2), that is
0 + (- 18y) = 1
- 18y = 1
3
7
10
Which expression has a negative value?
O 2+12
(-3)(-8)
10-(-18)
-35-5
Wakandi telur
Answer:
-35 - 5
Step-by-step explanation:
2 + 12 = 14, which is positive
(-3) * (-8) = 24, which is positive
10 - (-18) = 10 + 18 = 28, which is positive
-35 - 5 = -40, which is negative
Answer:
[tex]-35-5[/tex]
Step-by-step explanation:
[tex]2+12=14[/tex]
The result is a positive value.
[tex]-3 \times -8=24[/tex]
The result is a positive value.
[tex]10-(-8)\\10+8=18[/tex]
The result is a positive value.
[tex]-35-5=-40[/tex]
The result is a negative value.
Find the 7th term of the geometric sequence with a3= -45 and a5= -405
Answer:
Step-by-step explanation:
let a be the first term and r be common ratio.
[tex]a_{3}=ar^2=-45\\a_{5}=ar^4=-405\\divide\\\frac{ar^4}{ar^2} =\frac{-405}{-45} =9\\r^2=9\\r=\pm3\\9a=-45\\a=-5\\a_{7}=ar^{7-1}=ar^6=ar^4 \times r^2=-405 \times 9=-3645[/tex]
What is M and C for the line Y=X-6?
Answer:
Step-by-step explanation:
Equation of line: y = mx + c
y = x - 6
Slope m = 1
y-intercept c = -6
Answer:
m = 1
c = -6
Step-by-step explanation:
Formula for a line is y = mx+c
m = gradient
c = intercept.
Here:
m = 1
c = -6
Hope this helps
Good Luck
