US_
Diagram NOT
accurately draw
(x + 1)cm
(3 - x) cm
(2x + 5) cm
The diagram shows a cuboid of volume V cm3
(a) Show that V = 15 + 16x - x (squared) - 2x (cubed)
Answers
Answer:
Step-by-step explanation:
Length of the cuboid = ((2x + 5) cm
Width of the cuboid = (3 - x) cm
Height of the cuboid = (2x + 5) cm
Since, volume of the cuboid = Length × Width × Height
= (2x + 5)(3 - x)(x + 1)
= [2x(3 - x) + 5(3 - x)](x + 1)
= (6x - 2x² + 15 - 5x)(x + 1)
= (-2x² + x + 15)(x + 1)
= x(-2x² + x + 15) + 1(-2x² + x + 15)
= -2x³ + x² + 15x - 2x² + x + 15
= -2x³ - x² + 16x + 15
≈ 15 + 16x - x² - 2x³
Related Questions
The vertices of a triangle are (-1,3) (6,3) and (-1,-4)
Find the area of the triangle
Please show all workings
Answers
Answer:
24.5 unit²
Step-by-step explanation:
Area of ∆
= ½ | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |
= ½ | (-1)(3 -(-4)) + 6(-4 -3) + (-1)(3 - 3) |
= ½ | -7 - 42 |
= ½ | - 49 |
= ½ (49)
= 24.5 unit²
Method 2:
Let the vertices are A, B and C. Using distance formula:
AB = √(-1-6)² + (3-3)² = 7
BC = √(-6-1)² + (-4-3)² = 7√2
AC = √(-1-(-1))² + (4-(-3))² = 7
Semi-perimeter = (7+7+7√2)/2
= (14+7√2)/2
Using herons formula:
Area = √s(s - a)(s - b)(s - c)
here,
s = semi-perimeter = (14 + 7√2)/2
s - a = S - AB = (14+7√2)/2 - 7 = (7 + √2)/2
s - b = (14+7√2)/2 - 7√2 = (14 - 7√2)/2
s - c = (14+7√2)/2 - 7 = (7 + √2)/2
Hence, on solving for area using herons formula, area = 49/2 = 24.5 unit²
Answer:
24.5
Step-by-step explanation:
To find the area with the coordinates provided:
(-1,3), (6,3), (-1,-4)
First we count the units that are inside the triangle which is area.
[tex]\frac{49}{2}[/tex]
So we know that there are [tex]\frac{49}{2}[/tex] units and then we divide 49 by 2 which gets you 24.5.
49 ÷ 2 = 24.5
The answer is 24.5 units.
what is the logarithmic form for
[tex]2 { }^{x - 4} = 32[/tex]
Answers
Answer:
[tex]2^x-4=32\quad :\quad x=\frac{2\ln \left(6\right)}{\ln \left(2\right)}\quad \left(\mathrm{Decimal}:\quad x=5.16992\dots \right)\\\\2^x-4=32 \\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\2^x-4+4=32+4\\\mathrm{Simplify}\\2^x=36\\\\apply exponential rule\\x\ln \left(2\right)=\ln \left(36\right)\\x\ln \left(2\right)=\ln \left(36\right)\\x=\frac{2\ln \left(6\right)}{\ln \left(2\right)}[/tex]
hope it helps:)
find the value of given expression
[tex] \sqrt{24 \times 24} [/tex]
Answers
Answer:
24 is the answers for the question
Answer:
the answer is 24 ........
The graph below is an example of which type of function?
a. quadratic
b. linear
c. cubic
d. square root
Answers
Answer:
i think its c
Step-by-step explanation:
its not a or b
Answer:
C. cubic
Step-by-step explanation:
Correct on Edge 2021!!!
Which comparison of the two equations is accurate?
Equation A: sqrt (x^2+3x-6) = sqrt (x+2)
Equation B: ^3 sqrt (x^2+3x-6) = sqrt (x+2)
O Both equations have different solutions because the square root of a number is not the same as the cube root of a number
O Both equations result in different equations after eliminating the radicals, so they have the different solutions
O Both equations have the same potential solutions, but equation A might have extraneous solutions
O Both equations have the same potential solutions, but equation B might have extraneous solutions
Answers
Answer:C
Step-by-step explanation:
i took it on edge2021
Answer:
The answer is C.
O Both equations have the same potential solutions, but equation A might have extraneous solutions
Step-by-step explanation:
I just took the quiz on edge.
Stephanie and Jill share a reward of $65 in a ratio of 1:4. How much does Stephanie
get?
Answers
Answer:
Step-by-step explanation:
Each part is equal to 65/(1+4)=$13
Since Stephanie only got 1 part, she got $13.
Consider a system of two linear equations in two variables. If the graphs of the equations are not the same line, is it possible for the system to have infinitely many solutions. Explain.
Answers
Answer:
No
Step-by-step explanation:
Solutions to systems of equations are points at which the lines of the equations intersect. Knowing this, only equations representing the same line would have infinitely many solutions because they would intersect at every one of each other's points - they're the exact same line. Therefore, if they are not the same line, they would not intersect at each and every point, and would not have infinitely many solutions.
What function should you choose if you want to make a copy of a digital image file to back it up? Save Copy Save As All of the above Question 7(Multiple Choice Worth 2
Answers
Answer:
What function should you choose if you want to make a copy of a digital image file to back it up? Save Copy Save As All of the above Question 7(Multiple Choice Worth 2
Step-by-step explanation:
If you read 98 pages of a book in one week. What is his unit rate of pages read per day
Answers
Answer: 14 pages a day
Step-by-step explanation:
98 / 7 = 14
Answer: 14 pages read per day.
Step-by-step explanation:
98/7= 14
Hope this helps!
In ΔGHI, g = 27 cm, i = 35 cm and ∠I=63°. Find all possible values of ∠G, to the nearest degree.
Answers
Answer:43
Step-by-step explanation:
A tree 10 meters high casts a 17.3 meter shadow. Find the angle of elevation to the sun
Answers
30.03 degrees
Step-by-step explanation:
You have labeled this diagram correctly.
The trig function that links the side opposite the angle x and the length of the shadow is the tangent function.
Here, tan x = (opposite side) / (adjacent side) = (10 m) / (17.3 m), or 0.578.
Starting from tan x = 0.578, use the inverse tangent function to find the angle, first in radians and then in degrees:
arctan 0.578 = 0.524 radians
Converting this to degrees yields 30.03 degrees. This is the angle of elevation of the sun from the horizontal, from the point where the observer is standing.
?.?.?.?.??.?..?.?.???..?..?
Answers
Answer:
82
Step-by-step explanation:
Sides AB and BC are equal, which means angle BAC and BCA have the same measure, as stated in the base angles theorem. Angle BAC is 49 degrees, so angle BCA must also be 49 degrees. The sum of all angles in a triangle is 180 degrees, so angles BAC, BCA, and CBA will add up to 180. Write this in an equation:
BAC+BCA+CBA=180
BAC and BCA both measure 49 degrees:
49+49+CBA=180
Solve for CBA
CBA=180-49-49
CBA=82
lmk if i made any errors, hope this helps :)
A city library selects a random sample of 1,250 of its patrons and finds that the 90% confidence interval for the
proportion of those who have read an e-book in the previous 12 months is (0.71, 0.75).
Calculate the point estimate and margin of error for the given confidence interval.
Enter both values to 2 decimal places.
The point estimate =
The margin of error =
Answers
Answer:
point estimate: .73
margin of error: .02
Step-by-step explanation:
correct on edg
Simplify. (4 w + 3) – 2 w + 7
Answers
Answer:
Apply the distributive property.
4
w
+
4
⋅
−
2
−
2
(
2
w
+
7
)
Multiply
4
by
−
2
.
4
w
−
8
−
2
(
2
w
+
7
)
Apply the distributive property.
4
w
−
8
−
2
(
2
w
)
−
2
⋅
7
Multiply
2
by
−
2
.
4
w
−
8
−
4
w
−
2
⋅
7
Multiply
−
2
by
7
.
4
w
−
8
−
4
w
−
14
Step-by-step explanation:
Here you go!!
Answer:
2W + 10
Step-by-step explanation:
Eliminate redundant parentheses
(4w +3) - 2w + 7
4w + 3 - 3w + 7
add the numbers
4w + 3 - 2w + 7
4w + 10- 2w
Combine like terms
4w + 10 - 2w
2w + 10
solution
2w + 10
Which angles are vertical angles?
2 and 4
1 and 5
2 and 5
2 and 3
Answers
Jesse bought a car for $25,000. The car depreciates approximately 10% of its value each year. What will the car be worth in 5 years?
Answers
Answer:
$12,500
Step-by-step explanation:
I got this answer by first taking the purchase price of the car and multiplying it by .10 to see what ten percent of the price was and I got $2,500. Then I took and multiplied 2,500 by 5 years and go 12,500. Then I subtracted 12,500 from the original purchase price to get $12,500. Meaning that the value of the care has decreased by half of the purchase price.
HOPE THIS HELPS!
Solve for x = [?]
2x+ 20
3x + 15
2x + 20
Answers
Answer:
x=29
Step-by-step explanation:
3x+15+2x+20=180
3x+2x+15+20=180
5x+35=180
5x=180-35
5x=145
x=145/5
x=29
A bag of skittles contains only red, yellow, and green colors. The respective ratios are 1:3:5 for those three colors. If there are a total of 36 skittles in the bag, how many of each skittles red, yellow, and green are in the bag?
Answers
Answer:
Red skittles = 4 skittles
Yellow skittles = 12 skittles
Green skittles = 20 skittles
Step-by-step explanation:
A bag of skittles contains only red, yellow, and green colors.
The respective ratios are 1:3:5 for those three colors.
We have
red: yellow: green
1:3:5
The sum of the proportion = 1 + 3+ 5 = 9
If there are a total of 36 skittles in the bag, how many of each skittles red, yellow, and green are in the bag?
Hence,
Number of red skittles is calculated as:
1/9 × 36 skittles
= 4 skittles
Number of yellow skittles is calculated as:
3/9 × 36 skittles
= 12 skittles
Number of green skittles is calculated as:
5/9 × 36 skittles
= 20 skittles
Therefore, the number of
Red skittles = 4 skittles
Yellow skittles = 12 skittles
Green skittles = 20 skittles
Plz hellppp I don’t understanddddd
Answers
Then you can add 4 to both sides then you get H=2
100 POINTS, MAHNIFIA PLEASE ANSWER!
SCAMMERS WILL NOT BE TOLERATED!
Answers
Answer:
- 3.4(21) = - 71.4
(- 2.3)(- 7.9) = 18.17
9.24 ÷ - 7 = -1.32
(- 8.5) ÷ (- 3.4) = 2.5
- 6.85 ÷ 0.5 = - 13.7
Which figure shows a reflection of pre-image ABC over the y-axis?
Two right triangles graphed on a grid. Right triangle A B C, with right angle C, is in Quadrant One. Right triangle A-prime, B-prime, C-prime, with right angle C-prime, is in Quadrant Two. The coordinates of triangle A B C are A (one, one), B (three, four), and C (three, one). The coordinates of triangle A-prime, B-prime, C-prime are A-prime (negative one, one), B-prime (negative three, four), and C-prime (negative three, one).
Two right triangles graphed on a grid. Right triangle A B C, with right angle C, is in Quadrant One. Right triangle A-prime, B-prime, C-prime, with right angle C-prime, is in Quadrant Three. The coordinates of triangle A B C are A (one, one), B (three, four), and C (three, one). The coordinates of triangle A-prime, B-prime, C-prime are A-prime (negative one, negative one), B-prime (negative three, negative four), and C-prime (negative three, negative one).
Two right triangles graphed on a grid. Right triangle A B C, with right angle C, is in Quadrant One. Right triangle A-prime, B-prime, C-prime, with right angle C-prime, is in Quadrant Four. The coordinates of triangle A B C are A (one, one), B (three, four), and C (three, one). The coordinates of triangle A-prime, B-prime, C-prime are A-prime (one, negative one), B-prime (three, negative four), and C-prime (three, negative one).
Answers
The figure that shows a reflection of pre-image ABC over the y-axis is the third figure.
How to depict the figure?From the complete information, the triangle ABC is reflected over the y axis.
The vertices of the triangle are A(1, 1), B(3, 4) and C(3, 1). The vertices of the images are A(1, 1) = A'(-1, 1). B(3, 4) = B(-3, 4) ans C(3, 1) = C'(-3, 1).
In conclusion, the figure that shows a reflection of pre-image ABC over the y-axis is the third figure.
Learn more about reflection on:
https://brainly.com/question/3643476
How long will it take to accumulate $1200
in an account, if you begin with $1000 and
the account pays 6% compounded
monthly?
Answers
Answer:
it will take 4 months
Step-by-step explanation:
help pls i need help
Answers
Answer:
The second and third one
Step-by-step explanation:
According to the statement, numbers between 4 and 5 is 4.1 - 4.9
But it is doubled so it is 8.2 - 9.8
These numbers are greater than 8 and less than 9
These numbers are also greater than 9 and less than 10
find the mean of the set of data. round to the nearest 10th if necessary.
9.9, 10.8, 10.8, 6.2, 10.8, 7.2
Answers
Answer:
The mean of the data set is 9.3 rounded to the nearest tenth
Step-by-step explanation:
First you add them all together: 9.9 + 10.8 + 10.8 + 6.2 + 10.8 + 7.2 = 55.7
Then you divide it by how many numbers there are which is 6 in this situation:
55.7 ÷ 6 = 9.28333333333. but if we round it to the nearest tenth we get 9.3
So the answer is 9.3
The circumference of the base of the cone is 8.5pi inches. What is the volume of the cone in terms of ne? Round to the nearest hundredth. Enter
your answer in the box.
15 in.
IT in
3
Answers
Answer:
8.93h in³
Step-by-step explanation:
The circumference of the base of the cone is 8.5pi inches. What is the volume of the cone in terms of ne? Round to the nearest hundredth. Enter
Step 1
We find the radius of the cone
Base area = 8.5 π inches
Radius = √Area/π
Radius = √8.5 π /π
Radius = √8.5
Radius of the cone = 2.9154759474 inches
Approximately = 2.92 inches
Step 2
We find the volume of the cone
= πr²h/3
Height is not given, so we find in terms of h
= π × 2.92² × h/3
= 8.9288252005h in³
Approximately = 8.93h in³
The
Tell which number is greater. 50%, 13/25 HELP MEEEE
Answers
Answer:
13/25
Step-by-step explanation:
if you put it in decimal the fraction is greater
Answer:
13/25 is larger then 50%
Step-by-step explanation:
13/25=52%
50%=12.5/25
write the equation of the circle given a center of (1,3) and a point on the circle at (-2,7)
Answers
Answer:
Ecuación estándar de un círculo
(x−2)2+(y−2)2=25
Forma general de la ecuación de un círculo
x2−4x+y2−4y−17=0
Ecuaciones paramétricas de un círculo
x=5cosθ+2y=5sinθ+2
Step-by-step explanation:
Ecuación Estándar de un Círculo
La ecuación estándar de un círculo con el centro en (x_0, y_0) y radio r es
(x^2-x_0) + (y^2-y_0)=r^2
Ecuaciones Paramétricas de un Círculo
Las ecuaciones paramétricas de un círculo con el centro en (x_0, y_0) y radio r son
x=r cos \theta + x_0\\y=r sin \theta + y_0
Ecuación General de un Círculo
La ecuación general de un círculo con el centro en (x_0, y_0) y radio r es
x^2+ax+y^2+by+c=0,
donde
a=-2x_0\\b=-2y_0\\c=x^2_0+y^2_0-r^2
find the value of given expression
[tex] \sqrt{213 \times 213} [/tex]
Answers
Answer:
213 Answer ..............
Answer:
√{213×213}=√213²=±213 is your answer
Someone please help me?
Answers
Answer:
31.7 degrees (A)
Step-by-step explanation:
90 degrees (the whole angle) - 58.3 degrees = 31.7 degrees
the angles are complementary
they add up to 90 degrees
brainliest plz
Answer:
31.7
Step-by-step explanation:
pls mark brainliest
58.3 + 31.7 is 90
What is the volume of the rectangular prism below? Use the formula V = lwh. 4 ft 4 ft 8 ft
Answers
Answer:
V=128
Step-by-step explanation:
Answer:
V =128ft^3
Step-by-step explanation:
V=lwh=4*4*8=128