Answer/Step-by-step explanation:
1. To find the area of the shaded region, you'd find the area of the white rectangular shape, next, find the area of the whole triangular shape, then find the difference of their areas to get the area of the shaded region. Thus, the formula to use would be:
Area of shaded region = area of triangle - area of rectangle
Area of shaded region = ½*base*height - length*width
1. a. Volume of triangular prism = area of triangular base * height of prism
Volume of triangular prism = ½bh * H
Where,
b = 6 m
h = 4 m
H = 8 m
Substitute
Volume of prism = ½*6*4*8
Volume of prism = 96 m³
b. Volume of sphere = ⁴/3πr³
Where,
r = 9 cm
Substitute
Volume = ⁴/3*π*9³
Volume = ⁴/3*π*729
Volume ≈ 3,053.6 cm³ (nearest tenth)
2. Use Pythagorean theorem to find the height of the cone
radius of the cone (r) = ½(16) = 8 cm
Slant height (l) = 11 cm
height (h) = ?
Using Pythagorean theorem, we have:
h = √(l² - r²)
Substitute
h = √(11² - 8²)
h = √(57)
h ≈ 7.5 cm (nearest tenth)
b. Volume of the cone = ⅓πr²h
where,
r = 8 cm
h = 7.5 cm
Volume = ⅓*π*8²*7.5
Volume = 502.7 cm³ (nearest tenth)
Ryan rented a truck for one day. There was a base fee of $16.99, and there was an additional charge of 74 cents for each mile driven. Ryan had to pay $133.17 when he returned the truck. For how many miles did he drive the truck?
Answer:
157 miles
Step-by-step explanation:
total cost = flat fee + cost per mile * miles
133.17 = 16.99 + .74 * m
Subtract 16.99 from each side
116.18 = .74m
Divide each side by .74
116.18 / .74 = .74m/.74
157 = m
This table shows the relationship of the total number of pieces of fruit to the number of bananas.
Why is StartFraction 6 Over 5 EndFraction not equivalent to Three-halves?
Given:
The table that shows the relationship of the total number of pieces of fruit to the number of bananas.
To find:
Why is [tex]\dfrac{6}{5}[/tex] not equivalent to [tex]\dfrac{3}{2}[/tex].
Solution:
If a, b, c are real numbers, then
[tex]\dfrac{a}{b}=\dfrac{a\times c}{b\times c}[/tex]
The given fraction is [tex]\dfrac{3}{2}[/tex]. It can be written as:
[tex]\dfrac{3\times 2}{2\times 2}=\dfrac{6}{4}[/tex]
The number 3 is multiplied by 2 to get 6. So, the 2 should also be multiplied by 2. The ratio should be [tex]\dfrac{6}{4}[/tex], not [tex]\dfrac{6}{5}[/tex].
Therefore, the correct option is A.
An acute angle of a right triangle measures 30°, and the length of the triangle's hypotenuse is 10 ft. Find the missing angle measure and side lengths.
Answer:
missing angle <60 and side lengths 5, 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
we understand from the given information that the triangle in question is a special right triangle
and since this is a special triangle the side lengths follows :
the side length that sees <90 is represented by 2x
the side length that sees <60 is represented by x[tex]\sqrt{3}[/tex]
and the side length that sees <30 is represented by x
2x = 10 so x = 5 and x[tex]\sqrt{3}[/tex] = 5[tex]\sqrt{3}[/tex]
What is the rate of change of the amount earned with respect to hours worked for this function?
A) 1/13 hours per dollar
B) 2/5 hours per dollar
C) 3 dollars per hour
D) 13 dollars per hour
The rate of change of the amount earned with respect to hours worked for this function is D. 13 dollars per hour.
What is rate of change?The rate of change for the point defined on the graph can be deduced by calculating the ratio of the difference between the two coordinate points given, similar to calculating the gradient or slope :
Point a = (5, 65) = (x₂, y₂)
Point b = (2, 26) = (x₁, y₁)
Calculating the gradient or slope :
Rate of change = (y₂ - y₁) / (x₂ - x₁)
Rate of change = (65 - 26) / (5 - 2)
Rate of change = 39 / 3
Rate= 13 dollars per hour
Learn more about rate of change on:
https://brainly.com/question/8728504
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Complete question
The graph shows the amount of money Miguel earns after working x hours. What is the rate of change of the amount earned with respect to hours worked for this function? hours per dollar hours per dollar 3 dollars per hour 13 dollars per hour
Which are the solutions of x2 = -7x – 8?
Ž
17 7
4
+
17
4
-
글
그를
+
ZIA
+
V 17
4
4
7 - 17 7 + /17
-
-7 - V 17 -7 + v17 .
2
Answer:
( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
Step-by-step explanation:
x^2 = - 7x - 8
x^2 + 7x + 8 = 0
Here,
a = 1
b = 7
c = 8
D = b^2 - 4ac
= 7^2 - 4 ( 1 ) ( 8 )
= 49 - 32
D = 17
x = - b ± √D / 2a
= - 7 ± √17 / 2 ( 1 )
x = ( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
HELP PLEASE HURRY
THANKS
Answer:
Step-by-step explanation:
A running track has two semi-circular ends with radius 27m and two straights of length 90.6m as shown.
Calculate the total distance around the track rounded to 1 DP.
Answer:
350.85
Step-by-step explanation:
90.6*2 = 181.2
27*2 = 54 (diameter)
54*pi = 169.646003294
169.646003294 + 181.2 = 350.846003294
350.846003294 = 350.85
first answer gets marked brainliest!!!
Answer:
in neighbourhood q the total number of people in the nine families I higher than that in neighbourhood s because of we add up the number of people in the families in neighbourhood q we get a total of 35 yet we have a total of only 27 people in the nine families in neighbourhood s
hope that helps ❤
Travis makes and sells fishing lures. He
has 56 fishing lures that he is putting into
boxes. Each box can hold 5 fishing lures.
How many boxes can Travis fill
completely?
The polygons in each pair are similar. Find the missing side length
Answer:
24 is the answer because 18/3=6 6x4 is 24
what is 8/9 divided 2/3
Answer:
4/3
Step-by-step explanation:
8/9 ÷ 2/3
Copy dot flip
8/9 * 3/2
Rewriting
8/2 * 3/9
4 * 1/3
4/3
What is the answer I need help ASAP be truthful
Answer:
your closest number should be A
Answer:
A.√99
Step-by-step explanation:
10^2 = 100
Or vise versa √100 = 10
The closest number to 100 is 99
So √99 is closest to 10
Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x-4
h(x) = 3/4x
h(x) = 1/4x
Answer:
Let the inverse of f(x) be h(x):
[tex]{ \tt{h(x) = \frac{1}{4x} }}[/tex]
Please help me with this, i need help
Answer:
woa
i n
Step-by-step explanation:
The length of a rectangle is three times the width. The area of the rectangle is 108 sq. inches what’s the triangles width?
Answer:ÑÑÑÑÑÑÑÑÑññÑÑÑÑññññññÑÑÑÑÑÑÑÑÑñÑÑÑÑññ
Step-by-step explanation:
How much water should be added to 90ml of 45 percent acid solution to dilute it to 25 percent acid solution
Answer:
72 ml
Step-by-step explanation:
Let
x = amount of water that should be added
45% acid solution = 45/100 = 0.45
25% acid solution = 25/100 = 0.25
The equation is
90(0.45) = 0.25(x + 90)
40.5 = 0.25x + 22.5
40.5 - 22.5 = 0.25x
18 = 0.25x
Divide both sides by 0.25
x = 18/0.25
= 72
x = 72 ml
The probability that Dan buys a sandwich is 0.2.
The probability that Dan gets the bus is 0.9.
Assuming the events are independent, what is the probability that Dan buys a sandwich
and gets the bus?
Answer:
0.18
Step-by-step explanation:
Find the probability that both independent events occur by multiplying the individual probabilities by each other:
0.2(0.9)
= 0.18
So, the probability is 0.18
Which is the correct form of the partial fraction decomposition for the expression StartFraction 4 x cubed + 3 x squared Over (x + 1) squared (x squared + 7) squared EndFraction?
Given:
The expression is:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]
To find:
The correct form of the partial fraction decomposition for the given expression.
Solution:
We have,
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]
By partial fraction decomposition, it can be written as:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{A}{x+1}+\dfrac{B}{(x+1)^2}+\dfrac{Cx+D}{x^2+7}[/tex] ...(i)
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B}{(x+1)^2(x^2+7)}[/tex]
[tex]4x^3+3x^2=(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B[/tex]
[tex]4x^3+3x^2=x^3A+x^3C+x^2A+x^2B+2x^2C+x^2D+7xA+xC+2xD+7A+7B+D[/tex]
[tex]4x^3+3x^2=x^3(A+C)+x^2(A+B+2C+D)+x(7A+C+2D)+7A+7B+D[/tex]
On comparing both sides, we get
[tex]A+C=4[/tex]
[tex]A+B+2C+D=3[/tex]
[tex]7A+C+2D=0[/tex]
[tex]7A+7B+D=0[/tex]
On solving these equations, we get
[tex]A=\dfrac{23}{32},B=-\dfrac{1}{8},C=\dfrac{105}{32},D=-\dfrac{133}{32}[/tex]
Substituting these values in (i), we get
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]
Therefore, the required partial fraction decomposition is:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]
Answer:
A on Edg
Step-by-step explanation:
got it right
I NEEDDDD D HELPPPPP!!!
Answer:
70 degrees
Step-by-step explanation:
there are multiple ways, as all the trigonometric functions are related.
let's try it this way :
consider the missing side to be the radius of a circle.
then 41 would be the cos value of the angle (multiplied by that radius, of course).
so, let's calculate the missing side per Pythagoras
c² = a² + b² = 113² + 41² = 12769 + 1681 = 14450
c = 120.21
and now
41 = cos(?) × 120.21
cos(?) = 41/120.21 = 0.341...
? = 70.0576... ≈ 70 degrees
Answer:
70°
Step-by-step explanation:
tangent θ = (opposite side / adjacent side)
tangent θ = (113 / 41)
θ = arctan (113 / 41)
θ = 70.0576°
*Note: "arctan" is the same as "inverse tangent"
**Note: "soh-cah-toa" (and "cho-sha-cao" for sec, csc, & cot) is an easy mnemonic device to remember the trig functions (sin, cos, & tan) and their relations to the sides of a given angle.
You just decided to open a savings account and went to the bank and made an initial deposit. You decide to save another set amount each month. Without any interest being paid, the equation =20+50
represents the amount of money,
y
, in your savings account after
m
months. Select what the slope and y-intercept represent in this problem.
(Choose 2)
Answer:
Options (1) and (4)
Step-by-step explanation:
Given equation for the deposit in the saving account is,
y = 20x + 50
Here, y = Amount of money in the account
20 = money added in the account every month
50 = Initial deposit
By comparing this equation with the slope-intercept form of the equation of a line,
y = mx + b
Here, slope m = money added in the account every month
And b = y-intercept
Therefore, Options (1) and (4) will be the answer.
Help pleas like please ASAP
Answer:
(x+9)(x+5)
Step-by-step explanation:
find 2 numbers that add to 14 and multiply to 45
convert into power notation -1/81
Answer:
-1/9^2 is the power notation for your questions
Step-by-step explanations
On an electricity bill of $40.80, Mrs.
Miller pays only $38.76 because she pays
before a certain date. What percent
discount is Mrs. Miller allowed?
Answer:
100%_$40.80
? × _$38.76
Step-by-step explanation:
100%×$38.76÷$40.80=95%
Answer:
40.80
Step-by-step explanation:
Kasey has three pieces of wood that measure 9 inches, 12 inches, and 21 inches. Can she make a right triangle
with the three pieces of wood (without cutting or overlapping)?
Answer: No
Step-by-step explanation:
Add 2 sides together. If the sum of greater than the length of the 3rd side for all 3 options it can form a right triangle if it doesn’t than it can’t:
9 + 12 = 21 which is not greater than the 3rd side length of 21 so this cannot form a right triangle.
The cars of a circular Ferris wheel at an amusement park are equally spaced about the wheel's circumference. They are numbered consecutively beginning with 1. The cars numbered 14 and 30 lie on opposite ends of a diameter. How many cars are on the Ferris wheel?
Answer:
32 cars
Step-by-step explanation:
we know that 14 and 30 lie on opposite sides of the ferris wheel, so we need to calculate how many cars are inbetween car number 14 and carn number 30. since each car is numbered starting from 1, we know that the cars do not skip any numbers. after counting, we know that there are 16 cars inbetween car number 14 and car number 30. since there are 2 sides of a circle we have to double our number by 2. so 16×2 is 32
Math step-by-step:
30-14=16
16×2=32
Please help me with this
Answer:
A
Step-by-step explanation:
The function f(x) = One-sixth (two-fifths) Superscript x is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?
Answer:
[tex](-3,4/375)[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{1}{6}(\frac{2}{5})^x[/tex]
Reflection: Across y-axis
Required
The ordered pair on g(x)
The rule of reflection across y-axis is:
[tex](x,y) = (-x,y)[/tex]
So, we have:
[tex]g(x) = f(-x)[/tex]
f(-x) is:
[tex]f(-x) = \frac{1}{6}(\frac{2}{5})^{-x[/tex]
Recall that:
[tex]g(x) = f(-x)[/tex]
Hence:
[tex]g(x) = \frac{1}{6}(\frac{2}{5})^{-x[/tex]
From the options (missing in the question), the ordered pair is:
[tex](-3,4/375)[/tex]
To check this, we have:
[tex]g(x) = \frac{1}{6}(\frac{2}{5})^{-x[/tex]
[tex]g(-3) = \frac{1}{6}(\frac{2}{5})^{--3[/tex]
[tex]g(-3) = \frac{1}{6}(\frac{2}{5})^{3[/tex]
Expand
[tex]g(-3) = \frac{1}{6}(\frac{8}{125})[/tex]
Simplify
[tex]g(-3) = \frac{1}{3}(\frac{4}{125})[/tex]
Open bracket
[tex]g(-3) = \frac{4}{375}[/tex]
Titus works at a hotel. Part of his job is to keep the complimentary pitcher of water at least half full and always with ice. When he starts his shift, the water level shows 8 gallons, or 128 cups of water. As the shift progresses, he records the level of the water every 10 minutes. After 2 hours, he uses a regression calculator to compute an equation for the decrease in water. His equation is W –0.414t + 129.549, where t is the number of minutes and W is the level of water. According to the equation, after about how many minutes would the water level be less than or equal to 64 cups?
Answer:
Step-by-step explanation:
If we are looking for how long it will take the level to be less than or equal to 64 cups, we are solving an inequality as opposed to an equation. It would look like this:
-.414t + 129.549 ≤ 64 We subtract 129.549 from both sides to get
-.414t ≤ -65.549 and then divide by -.414. But because we are dividing by a negative number we need to change the way the inequality is pointing:
t ≥ 158.3 minutes which is about 2.6 hours
Answer:
t ≥ 158.33, or rounded, t ≥ 160.
Explanation:
The equation we're given is
W = -0.414t + 129.549, which an be written as
-0.414t + 129.549 = W.
We are asked to find the amount of time it would take for the water level to be less than or equal to 64 cups. Plugging this information in, we have:
-0.414t + 129.549 ≤ 64
To solve this, we first cancel 129.549 by subtracting from both sides:
-0.414t + 129.549 - 129.549 ≤ 64 - 129.549
-0.414t ≤ -65.549
Now divide both sides by -0.414:
-0.414t/-0.414 ≤ -65.549/-0.414
t ≥ 158.33
(When we multiply or divide both sides of an inequality by a negative number, we must flip the inequality symbol)
C and D are complementary angles. Which of the following measures cannot be true
Om C= 30° and m D = 60°
Om C= 60° and m2D = 30°
Om C= 65° and m D = 35°
Om C = 55° and m D = 35°
Answer:
C= 65° and m D = 35°
this cannot be true
Step-by-step explanation:
a complementary angle adds up to 90°
65°+35°=100
90° =/= 100°
What value of x will make the equation true?
(Square Root of 5) (square root of 5)=x
Answer:
(2.236067978)(2.236067978)
=5 ans.
If this is incorrect forgive me
I hope this will help you
stay safe