The solid triangular prism shown below is made from metal . The prism is melted down and the metal is used to create a solid cube. Find the side length of the cube. For the triangle, the base is 9cm, Height is 4cm, and Length is 12cm.
Answer:
6 cm
Step-by-step explanation:
Given :
base is 9cm, Height is 4cm, and Length is 12cm.
Volume of triangular prism :
V = 1/2 * base * height * length
V = 1/2 * 9 * 4 * 12
V = 9 * 2 * 12
V = 216 cm³
Volume of a cube = a³
Where , a = side length
If 216cm³ is melted to form a cube
Then ;
a = 216^1/3
a = 6 cm
In the diagram below of triangle UVW, X is a midpoint of UV and Y is a
midpoint of VW. If mZXYV = 7x + 21, and mZUWY = 91 – 7x,
what is the measure of ZXY?
V
X
Y
U
W
Given:
In triangle UVW, X is the midpoint of UV and Y is the midpoint of VW.
[tex]m\angle XYV=7x+21[/tex]
[tex]m\angle UWY=91-7x[/tex]
To find:
The measure of angle XYV.
Solution:
Since X is the midpoint of UV and Y is the midpoint of VW, therefore XY is the mid-segment of the triangle UVW and parallel to the base of the triangle, i.e., UW.
If a transversal line intersect two parallel lines, then the corresponding angles are congruent and their measures are equal.
[tex]\angle XYV \cong \angle UWY[/tex] [Corresponding angle]
[tex]m\angle XYV=m\angle UWY[/tex]
[tex]7x+21=91-7x[/tex]
We need to solve this equation for x.
[tex]7x+7x=91-21[/tex]
[tex]14x=70[/tex]
[tex]x=\dfrac{70}{14}[/tex]
[tex]x=5[/tex]
Now,
[tex]m\angle XYV=7x+21[/tex]
[tex]m\angle XYV=7(5)+21[/tex]
[tex]m\angle XYV=35+21[/tex]
[tex]m\angle XYV=56[/tex]
Therefore, the measure of angle XYV is 56 degrees.
which expression is equivalent to 6x*3 + 3y*2 - 5x*3 + 2y*2
Answer:
3x + 10y
Step-by-step explanation:
Calculate: (6x*3)+(3y*2)-(5x*3)+(2y*2) = 18x + 6y - 15x + 4y
Collect Like Terms: 18x + 6y - 15x + 4y = 3x +10y
Solution: 3x + 10y
y = x2 – 14x + 23
y = - 3x + 5
Answer:
let first equation be y=x^2-14x+23
second equation be y=-3x+5
now substitute the vale of y in equation second
y=-3x+5
x^2-14x+23=-3x+5
x^2-14x+3x=5-23
x^2-11x=-18
x^2-11x+18=0
x^2-(9+2)x+18=0
x^2-9x-2x+18=0
x(x-9)-2(x-9)=0
(x-2)(x-9)=0
either x-2=0 Or, x-9=0
x-2=0
x=0+2
x=2
x-9=0
x=0+9
x=9
therefore x=2,9
Step-by-step explanation:
-
Answer:
(2, - 1 ) and (9, - 22 )
Step-by-step explanation:
Given the 2 equations
y = x² - 14x + 23 → (1)
y = - 3x + 5 → (2)
Substitute y = x² - 14x + 23 into (2)
x² - 14x + 23 = - 3x + 5 ( subtract - 3x + 5 from both sides )
x² - 11x + 18 = 0 ← in standard form
(x - 2)(x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 9 = 0 ⇒ x = 9
Substitute these values into (2) for corresponding values of y
x = 2 : y = - 3(2) + 5 = - 6 + 5 = - 1 ⇒ (2, - 1 )
x = 9 : y = - 3(9) + 5 = - 27 + 5 = - 22 ⇒ (9, - 22 )
sushmila is buying Mehdi supplies
Answer:
3(p - 5) + 2s should be the correct answer!
Step-by-step explanation:
3 henna powder, and you get $5 off each henna powder so equation is 3(p - 5)
2 bottle so, 2s
add them up and get the answer
Anyways, hope this helped!
A school uses the function p(t)=t2−20t+175 to model the profit (in dollars) expected in a weekend when the tickets are sold at a certain price, t, to the school musical go on sale a. Write an equation to find out the prices at which the school would earn $100 in profit from the school musical each weekend. b. Find out at what prices the tickets should be sold at to make a $100 profit each weekend. SHOW ALL WORK.
Answer:
[tex](a)\ t^2 - 20t + 75= 0[/tex]
[tex](b)[/tex] [tex]t = 5; t -=15[/tex]
Step-by-step explanation:
Given
[tex]p(t) = t^2 - 20t + 175[/tex]
Solving (a): Equation when profit = 100.
This implies that:
[tex]p(t) =100[/tex]
So, we have:
[tex]100 = t^2 - 20t + 175[/tex]
Rewrite as:
[tex]t^2 - 20t + 175 - 100 = 0[/tex]
[tex]t^2 - 20t + 75= 0[/tex]
Solving (b): Calculate t, in (a)
In a, we have:
[tex]t^2 - 20t + 75= 0[/tex]
Expand
[tex]t^2 - 15t -5t + 75= 0[/tex]
Factorize
[tex]t(t - 15) -5(t - 15)= 0[/tex]
Factor out t - 15
[tex](t - 5)(t - 15)= 0[/tex]
Split
[tex]t - 5 = 0; t - 15 =0[/tex]
Solve
[tex]t = 5; t -=15[/tex]
The prices are $5 and $15, respectively
pleaseeeeee helppppppppp
Answer:
Supplement = 4°
other angle = 176°
Step-by-step explanation:
44x + x = 180°
45x = 180°
x = 4
Since the supplement = x
and we now that x = 4
The supplement = 4°
180° - 4° = 44(4)
176°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
On Sunday, the wind chill temperature reached −36 °F. On Monday, the wind chill temperature only reached 1 4 of Sunday's wind chill temperature. What was the lowest wind chill temperature on Monday? A −144 °F B −36 1 4 °F C −9 °F D −40 °F
Answer:
(A) -9 °F
Step-by-step explanation:
On Sunday, the wind chill temperature reached - 36 °F. On Monday, the wind chill
temperature only reached¼ of Sunday's wind chill temperature. What was the
lowest wind chill temperature on Monday? (A) -9 °F (B) -36¼°F (C) -40 °F (D) -144 °F
Sunday temperature = - 36 °F
Monday temperature = ¼ of Sunday's wind chill temperature
Monday = 1/4 of - 36 °F
= 1/4 * -36 °F
= (1 * -36)/4 °F
= -36/4 °F
= -9 °F
Monday temperature = -9 °F
The correct answer is (A) -9 °F
PLEASE HELPPPP I NEED THIS FASTTTTT
Answer:
[tex]there \: are \: 8 \: values \\ = \frac{8}{17} \times 100\% \\ = 47\%[/tex]
write a liner equation that passes through the point (2, -9) and has a slope of -5
Answer:
y=-5x-9
Step-by-step explanation:
a cylindrical pipe made of metal 3 m long is 3 cm if the internal radius of the pipe is 10 cm what is the volume of metal used in making the pipe
Answer:
857.766cm^3
Step-by-step explanation:
Given data
Lenght = 3m
Internal radius r = 3m
External radius R= 10m
Volume of pipe= πr^2h
Volume of metal= External - Internal
Volume= πR^2h-πr^2h
Volume= πh(R^2-r^2)
Volume= 3.142*3(10^2-3^2)
Volume= 3.142*3(100-9)
Volume= 9.426*(91)
Volume= 857.766cm^3
Hence the volume of the metal is 857.766cm^3
Which of the following choices is NOT one of the six tenses of verbs?
past participle
future perfect
future
present perfect
Answer:
past participle
Step-by-step explanation:
all of the other ones are correct
3. Which of the following is not equal to sin(270°)?
(1) cos(180)
(3) -sin (90)
(2) - cos(0)
(4) sin(360)
Find sec 0, sin 0, and tan 0, where is the angle shown in the figure.
Give exact values, not decimal approximations.
Answer:
Secθ = 11 / 9.22 or sec33°
Sinθ = 6 / 11 or Sin33°
Tanθ = 6 / 9.22 or Tan33°
θ = 33°
Step-by-step explanation:
Given:
Hypotenuse = 11 unit
Perpendicular = 6 unit
Find:
Secθ
Sinθ
Tanθ
Computation:
Base = √Hypotenuse² - Perpendicular²
Base = √11² - 6²
Base = √121 - 36
Base = √85
Base = 9.22 unit (Approx.)
Secθ = Hypotenuse / Base
Secθ = 11 / 9.22 or sec33°
Sinθ = Perpendicular / Hypotenuse
Sinθ = 6 / 11 or Sin33°
Tanθ = Perpendicular / Base
Tanθ = 6 / 9.22 or Tan33°
So value of θ = 33°
PLEASE HELP I HAVE A C ALREADY I NEED TO GET THIS RIGHT PLEASE
You want to estimate the number of students in your school who support extra funding for the science club. You survey the first 13 students who arrive at a science class.
Determine whether the sample is biased or unbiased.
Answer:
BRO I HAVE THE SAME QUESTION FOR MY TEST....
ITS BIASED IM REALLLLY SURE
Step-by-step explanation:
Find (-5) when f(x) = x^2 + 2x + 5
Answer:
Value of F(x) when x = -5 is 20
Step-by-step explanation:
Given equation;
f(x) = x² + 2x + 5
f(x) = f(-5)
Find:
Value of F(x) when x = -5
Computation:
Given function;
f(x) = x² + 2x + 5
By putting value of x in given function
f(-5) = (-5)² + 2(-5) + 5
f(-5) = (-5 x -5) + 2(-5) + 5
f(-5) = (25) - 10 + 5
f(-5) = (25) - 5
f(-5) = 20
Value of F(x) when x = -5 is 20
Given that f(x) = 3x - 2, g(x) = x2 + 3x and h(x) = 4.2^x
Help plz math question. EXPLAIN HOW YOU GOT THE ANSWER. 30 PTS btw thx if u help
Answer:
256
Step-by-step explanation:
4^4^4 = 4^(4^4) = 4^256
so written in base 4, there will be 256 zeroes after a 1.
This translates to approximately 154 digits in decimal.
Just like 2^2^2 = 2^4
there will be four zeroes after a 1.
2^2^2=2^(2^2) = 2^4 = 16 = 10000 (16 in base 2).
If someone vapes for every 15 minutes in a total of 16 hours how many times would they vape in those 16 hours
Answer:
64 times
Step-by-step explanation:
There are 4 sessions of 15 minutes in an hour. Meaning that a person would vape 4 times in an hour. 4 * 16 = 64. A person vapes 64 times in 16 hours. o-o dont vape kids.
Answer and Step-by-step explanation:
We are given the ratio of 1 vape every 15 minutes. We need to convert the time to hours, then multiply the hours by 16.
1 : 15
We know that there are 60 minutes in 1 hour, so we need to multiply 15 by 4 to get 60.
15 × 4 = 60
We also need to multiply 1 by 4, so that the result will be a multiple of the beginning number and so that we didn't get random numbers from somewhere.
1 × 4 = 4
Now we have the ratio 4 : 60, which means that the person vapes 4 times every 60 minutes, or every hour. But since we turned the minutes into an hour, this turns the 60 into a 1. 4 : 1
Now, we have to multiply 4 and 1 by 16 to get the amount of vapes done in 16 hours.
4 × 16 = 64
1 × 16 = 16
So, we have the ratio 64 : 16
This means that the person smokes 64 times in the 16 hours.
#teamtrees #PAW (Plant And Water)
which elevation is higher 8 feet below sea level or 13 feet below sea level
Answer: 8 feet below sea level is higher
Step-by-step explanation:
hey! please help i’ll give brainliest
Answer:
C
Step-by-step explanation:
"grow or develop in a healthy or vigorous way, especially as the result of a particularly favorable environment."
Answer:
C.
hope this helps
have a good day :)
Step-by-step explanation:
helppppp meeeee plz i'll give brainliest!!!
Answer:
1
Step-by-step explanation:
2m + 4 = 6
2m = 6 - 4
2m = 2
m = 1
the answer is one.. ....
I NEED HELP PLEASE PLEASE IN ALGEBRA!
Answer:
what is question?
Step-by-step explanation:
seth put $500 in his savings account, which earns a earns a simple interest rate of 4%
A. use the simple interest equation ( I=Prt ) to find out how much interest seth earns after 6 years.
B. now find out how much interest seth wold earn if he were to earn 7% compound interest for 6 years
Someone help me out :)
Answer: sorry i dont know this
Step-by-step explanation:
Find the value of x that makes ABCD a parallelogram.
D
с
X + 40°
70°
70°
X + 40°
А
B
O A. x = 40°
B. x = 50°
O c. x = 70°
O D. x = 30°
HELPPP MEEE PLSSS ASAPPPP !!!!!
The value of x that makes ABCD a parallelogram is C. x = 70°.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal.
Given that ABCD is a parallelogram.
We know that opposite angles of a parallelogram are equal.
It is already given.
Also, adjacent angles of a parallelogram is equal to 180°.
So,
x + 40 + 70 = 180
x + 110 = 180
x = 180 - 110
x = 70
Hence the correct option is C. x = 70°.
To learn more about Parallelograms, click here :
https://brainly.com/question/11220936
#SPJ7
Why did the robber take a bath
Answer:
To make a "clean getaway"
Step-by-step explanation:
haha, nice one :D
The diameter of a foot ball is 12cm ?find itsvolume
Answer:
288 [tex]\pi[/tex] cm³
Step-by-step explanation:
diameter = 12 cm
radius = diameter/ 2
= 12/ 2
= 6 cm
volume of a sphere = 4/ 3 × [tex]\pi[/tex] × (6)³
= 4/ 3 × [tex]\pi[/tex] × 216
= ( 864 [tex]\pi[/tex])/ 3
= 288 [tex]\pi[/tex] cm³
PLS HELP LOLZ <33
tasha is putting money into a savings account with a simple interest rate of 4% per year. if she initially deposits $6,000, then how much will her investment be worth at the end of six year
Answer: tasha's investment will be worth $1,440
Step-by-step explanation:
4%= 4/100= 0.04
PRT=6,000*0.04*6= $1,440
How how how how how how answers plz
9514 1404 393
Answer:
a) 540°
b) 720°
c) 900°
d) 1440°
Step-by-step explanation:
The total measure of internal angles of a convex polygon is given by the formula ...
sum of angles = 180°(n -2) . . . . for an n-sided polygon
So, you count the sides, subtract 2, and multiply that result by 180°.
__
a) 180°(5 -2) = 540°
b) 180°(6 -2) = 720°
c) 180°(7 -2) = 900°
d) 180°(10 -2) = 1440°
please help i have an exam next week and im really stuck on this
Answer:
Area = 96 square cm
Step-by-step explanation:
Area of the figure = (2 x Area of triangles) + Area of square
[tex]Area \ of \ triangle = \frac{1}{2} \times base \ height = \frac{1}{2} \times 8\times 4 = 16cm^2\\\\Area \ of \ square = side \times side = 8 \times 8 = 64cm^2[/tex]
Therefore, [tex]Area \ of \ the\ figure = (2 \times 16) + 64 = 32 + 64 = 96cm^2[/tex]