This oblique triangular prism has a volume of 63 cm.
What is the area of the base of the prism?
Answers
Answer:
its 10.5 cm
Step-by-step explanation:
its what I got off of khan
The base area of the oblique triangular prism is 10.5 square cm
How to determine the base area?The volume is given as:
Volume = 63 cubic cm
The height of the prism is:
Height = 6 cm
The base area of the prism is then calculated using:
Area = Volume/Height
So, we have:
Area = 63/6
Evaluate
Area = 10.5
Hence, the base area of the triangular prism is 10.5 square cm
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Related Questions
After heating up in a teapot, a cup of hot water is poured at a temperature of 210°F. The cup sits to cool in a room at a temperature of 70° F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below: T = T. + (To - Tale To = the temperature surrounding the object To = the initial temperature of the object t = the time in minutes T= the temperature of the object after t minutes k = decay constant The cup of water reaches the temperature of 197°F after 1.5 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes. Enter only the final temperature into the input box.
Answers
Newton's Law of Cooling:
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}[/tex]
[tex]T(t) =[/tex] Temperature given at a time
[tex]t =[/tex] Time
[tex]T_{s} =[/tex] Surrounding temperature
[tex]T_{o}=[/tex] Initial temperature
[tex]e =[/tex] Constant (Euler's number) ≈ 2.72
[tex]k =[/tex] Constant
Using this information, find the value of [tex]k[/tex], to the nearest thousandth, then use the resulting equation to determine the temperature of the water cup after 4 minutes.
First, plug in the given values in the equation and solve for [tex]k[/tex]:
[tex]T(t) =[/tex] 197°, [tex]t =[/tex] 1.5 minutes, [tex]T_{s} =[/tex] 70° and [tex]T_{o}=[/tex] 210°
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\197=70+(210-70)e^{-1.5k} \\197 -70 = (140)e^{-1.5k} \\127 =(140)e^{-1.5k}\\\frac{127}{140}=e^{-1.5k} \\ln(\frac{127}{140})=-1.5k\\-0.097=-1.5k\\0.0649 = k[/tex]
[tex]k[/tex] ≈ [tex]0.065[/tex]
Let the temperature of the water cup after [tex]t = 4[/tex] minutes be [tex]T(t) = x[/tex]
Now, let's plug the new time and [tex]k[/tex] constant in the equation and solve for [tex]x[/tex]:
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\\\\x=70+(210-70})e^{-0.065*4}\\\\x=70+(140})e^{-0.26}, -0.26=-\frac{26}{100}=-\frac{13}{50} \\[/tex]
[tex]x=70+(140})e^{-\frac{13}{50}}\\\\[/tex]
[tex]x=70+(140})e^{\frac{1}{\frac{13}{50}}\\\\\\[/tex]
[tex]x=70+e^{\frac{140}{\frac{13}{50}}\\\\\\[/tex]
[tex]x=70+{\frac{140}{\sqrt[50]{e^{13}}}\\[/tex]
[tex]x = 70 +\frac{140}{1.3} \\x=70+107.947\\[/tex]
[tex]x=177.95[/tex] ≈ [tex]178[/tex]
Temperature of water after 4 minutes is 178°
sorry if there's any misspelling or wrong step but I hope my answer is correct ':3
Evaluate the expression for the given value of x.
−7x + 6 for x = −7
Answers
Answer:
[tex]\Huge \boxed{\mathrm{55}}[/tex]
Step-by-step explanation:
[tex]-7x + 6[/tex]
Put x as -7 and evaluate the expression.
[tex]-7(-7)+6 \\\\\\ 49+6 \\\\\\ 55[/tex]
Which expression represents the measure of segment RS? A.7x – 3 B.7x + 5 C.x + 5 D.x – 3
Answers
Answer:
D) x-3
Step-by-step explanation:
(4x+1)-(3x-4)=
4x-3x+1-4=
x-3
Find the sum of (4x^3+2x) + (8x^3+4)
Answers
solve the equation (2^2x +2) (2^3x -7)= 2^25
Answers
Answer:
[tex]\Huge \boxed{x=6}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex](2^{2x +2}) (2^{3x -7})= 2^{25}[/tex]
When multiplying same bases, add the exponents.
[tex](2^{2x +2+3x -7})= 2^{25}[/tex]
[tex](2^{5x -5})= 2^{25}[/tex]
Cancelling the same bases from both sides.
[tex]5x-5=25[/tex]
Adding 5 to both sides.
[tex]5x=30[/tex]
Dividing both sides by 5.
[tex]x=6[/tex]
[tex]\rule[225]{225}{2}[/tex]
90 POINTS PLEASE HELP Describe the three main trigonometry functions, their ratios and reciprocal functions.
Answers
Answer and Step-by-step explanation:
There are three reciprocal trigonometric functions
making a total of six including cosine, sine, and tangent.
→The reciprocal cosine function is secant: sec(Ф)=1/cos(Ф).
→The reciprocal sine function is cosecant, csc(Ф)=1/sin(Ф).
→The reciprocal tangent function is cotangent, expressed two ways: cot(Ф)=1/tan(Ф) or cot(Ф)=cos(Ф)/sin(Ф).
We've already learned the basic trig ratios:
sin(A) = a/c
cos(B) = b/c
tan(C) = a/b
But there are three more ratios to think about:
→Instead of a/c, we can consider c/a
→Instead of b/c, we can consider c/b
→Instead of a/b, we can consider b/a
These new ratios are the reciprocal trigonometric ratios, and we’re about to learn their names.
The cosecant (csc)
The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.
sin(A) = opp / hyp = a/c
csc(A) = hyp / opp = c/a
The secant (sec)
The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.
cos(A) = adj/hyp = b/c
sec(A) = hyp/adj = c/b
The cotangent (cot)
The cotangent is the reciprocal of the tangent. It is the ratio of the adjacent side to the opposite side in a right triangle.
tan(A) = opp/adj = a/b
cot(A) =adj/opp = b/c
For what value of a is a(2x+3)=9x+15+x an identity?
Answers
Answer:
Expand the left side, group like terms on both sides, and get
(2a)x + 3a = 10x + 15
To be true for all x, equate like terms from both sides and get
2a = 10
3a = 15
Solution: a = 5
You can test the answer.
Step-by-step explanation:
Expand the left side, group like terms on both sides, and get
(2a)x + 3a = 10x + 15
To be true for all x, equate like terms from both sides and get
2a = 10
3a = 15
Solution: a = 5
You can test the answer.
what is 5/13 rounded to the nearest tenth
Answers
Answer:
5 thirteenth ti the nearest tenth Is .6
Answer:
0.4
Step-by-step explanation:
First make it a decimal:
5/13 (divide)
0.38 (round)
So you get 0.4
solve the given equation: 2 x ( x + 3 ) − 6 ( x + 3 ) = 0 2 x ( x + 3 ) - 6 ( x + 3 ) = 0
Answers
Answer:
x = 3 or x = -3
Step-by-step explanation:
Solve for x over the real numbers:
2 x (x + 3) - 6 (x + 3) = 0
Expand out terms of the left hand side:
2 x^2 - 18 = 0
2 x^2 - 18 = 2 (x^2 - 9):
2 (x^2 - 9) = 0
Divide both sides by 2:
x^2 - 9 = 0
x = (0 ± sqrt(0^2 - 4 (-9)))/2 = ( ± sqrt(36))/2:
x = sqrt(36)/2 or x = (-sqrt(36))/2
sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = 6/2 or x = (-6)/2
6/2 = 3:
x = 3 or x = (-6)/2
(-6)/2 = -3:
Answer: x = 3 or x = -3
How to graph the function (4,32) on a graph that only goes up to 8?
Answers
Answer:
Well make sure your answer is correct. If it’s correct extend your graph.
Step-by-step explanation:
A map has a scale of 6 in. = 8 mi. If you measured the distance between two cities to be 25 in. On the map, how many miles would it actually be?
Answers
Answer:
33 2/6 miles
Step-by-step explanation:
So we know that every 6 inches equals 8 miles. To find one mile, we would divide both sides by 8, so every 6/8 of an inch is 1 mile. if the two cities are 25 in apart on a map, that means that we can first do 6*4:8*4 for the ease of it to get 24 inches and 32 miles. So so far it's already 32 miles. Then we have to calculate the leftover one inch. To find out how many miles one inch is, we can divide both sides by 6, so one inch=8/6 of a mile.
So then we add 32+8/6=33 2/6
Tell me if that works for you
Every natural number is an integer. True or false?
Answers
Answer:
yes every natural number is integer
because intezer is collection of positive and negative numbers....
Answer:
Step-by-step explanation:
Hello friend!!!
It's TRUE
Natural numbers are the range of numbers from 1 to infinite.
Integers are made up of positive as well as negative numbers.
Since natural numbers are positive numbers, they are also integers.
Hope this helps
plz mark as brainliest!!!!!
What are the roots of the equation 9x^2 + 54x +82 = 0 in simplest a + bi form?
Answers
Answer:
The roots are
[tex]x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i \\ [/tex]Step-by-step explanation:
9x² + 54x + 82 = 0
Using the quadratic formula
That's
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]From the question
a = 9 , b = 54 , c = 82
Substitute the values into the above formula and solve
That's
[tex]x = \frac{ - 54\pm \sqrt{ {54}^{2} - 4(9)(82)} }{2(9)} \\ x = \frac{ - 54\pm \sqrt{2916 - 2952} }{18} \\ x = \frac{ - 54\pm \sqrt{ - 36} }{18} \\ x = \frac{ - 54\pm 6i}{18} [/tex]Separate the real and imaginary parts
That's
[tex]x = - \frac{54}{18} \pm \frac{6}{18} \: i \\ x = - 3\pm \frac{1}{3} i[/tex]We have the final answer as
[tex]x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i \\ [/tex]Hope this helps you
help me with this please! I haven’t found the solution since 11:30 am
Answers
Answer:
PT = 22
Step-by-step explanation:
Given that T is the midpoint of PQ, then
PT = TQ , substitute values
5x + 2 = 7x - 6 ( subtract 5x from both sides )
2 = 2x - 6 ( add 6 to both sides )
8 = 2x ( divide both sides by 2 )
4 = x
Thus
PT = 5x + 2 = 5(4) + 2 = 20 + 2 = 22
A new top-selling DVD is marked 20% off at Discount DVD, where it normally sells for $29.90. The same disc sells for $28.60 at Value Video, where you have a coupon for 15% off anything in the store. Where would you buy the DVD? Explain how you decided and be sure to include work to support your answer.
Answers
Answer:
You would buy the DVD at Discount DVD.
Step-by-step explanation:
To decide where to buy the DVD, you have to determine the price at each store after the discount is applied.
-Discount DVD: $29.90*0.2=$5.98
$29.90-$5.98=$23.92
-Value Video: $28.60*0.15=$4.29
$28.60-$4.29=$24.31
According to this, you would buy the DVD at Discount DVD because it is where you will get the lower price.
4 solutions for z<-6
Answers
Answer:
-7, -8, -9, -10
Step-by-step explanation:
Is this actually the whole problem? If so, the answer is anything less than -6. z < -6 includes all the numbers less than -6, so that would include -7, -8, -1000, -6.000001, etc.; you get what I mean. This would NOT include -6, though, because z is less than, not equal to, -6.
You can visualize it on a number line. If every value that could possibly equal z had a dot on it, you would see an infinite number of dots starting from -6 and going left to infinity. Like: <-------------o, if o was -6.
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Can a translation, a reflection, or a rotation of a figure ever result in an image with
a different size or shape? Explain.
Answers
Answer:
no, it will always be the same size and image just in a different placement.
Step-by-step explanation:
No, a translation, a reflection, or a rotation of a figure never results in an image with a different size or shape.
What is a translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.
Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.
Hence, a translation, a reflection, or a rotation of a figure never results in an image with a different size or shape.
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100 milk cartons were put out for breakfast, After breakfast, there were 40 milk cartons left. What is the ratio of milk cartons drunk to total milk cartons put out?
Answers
Answer:
The ratio of milk cartons drunk to total milk cartons put out= 3 : 5
Step-by-step explanation:
Total milk cartons put out for breakfast=100
Milk cartons left after breakfast=40
Total milk cartons drunk during breakfast = Total milk cartons put out for breakfast - Milk cartons left after breakfast
=100 - 40
=60
Total milk cartons drunk during breakfast = 60
What is the ratio of milk cartons drunk to total milk cartons put out?
Total milk cartons drunk during breakfast : Total milk cartons put out for breakfast
= 60 : 100
=3 : 5
The ratio of milk cartons drunk to total milk cartons put out= 3 : 5
How many solutions does the equation −4a + 4a + 3 = 8 have?
Answers
Answer:
none
Step-by-step explanation:
Answer:
It does not have any solution because 3 is not equal to 8
What's the only place in this world who's Fahrenheit and Celsius degrees can be equal?
Answers
Antarctica , I think
Step-by-step explanation:
Please help, find what X is. 42 - X = 29
Answers
Answer:
X = 13
Step-by-step explanation:
42 - X = 29
Subtract 42 from each side
42-42 - X = 29-42
-X = -13
Multiply each side by -1
X = 13
Which function describes this table of values?
Answers
Answer:
[tex]y=\frac{4}{5}x[/tex]
Step-by-step explanation:
Equations in the given options are linear, so the table given represent a linear function.
Let the equation of the linear function is,
y = mx + b
Since this equation passes through (0, 0),
0 = m(0) + b
b = 0
Therefore, equation of the line will be,
y = mx
Slope of the line passing through (10, 8) and (5, 4),
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{8-4}{10-5}[/tex]
= [tex]\frac{4}{5}[/tex]
Therefore, equation of the line will be,
[tex]y=\frac{4}{5}x[/tex]
Option (2) will be the answer.
what digit is in the hundredths place 132.054
Answers
Answer:
5
Step-by-step explanation:
0 is 10ths 5 is 100ths
1-1 Relations and Functions The following list details the numbers of tickets sold for a talent show: grade 9: 22; grade 10: 32; grade 11: 41; and grade 12: 30. What are the domain and range of this relation? A. domain: {22, 32, 41, 30}; range: {9, 10, 11, 12} B. domain: {9, 22, 10, 32}; range: {11, 41, 12, 30} C. domain: {9, 10, 11, 12}; range: {22, 32, 41, 30} D. domain: {11, 41, 12, 30}; range: {9, 22, 10, 32}
Answers
Answer:
[tex]Domain = \{9, 10, 11, 12\}[/tex]
[tex]Range = \{22, 32, 41, 30\}[/tex]
Step-by-step explanation:
Given
Grade 9: 22
Grade 10: 32
Grade 11: 41
Grade 12: 30
Required
Determine the domain and the range
The domain and range of a function is represented as thus (x,y)
From the given parameters;
[tex](x,y) = (Grade\ 9, 22), (Grade\ 10, 32) (Grade\ 11, 41), (Grade\ 12, 30)[/tex]
Remove "Grade" to represent as only digits
[tex](x,y) = (9, 22), (10, 32), (11, 41), (12, 30)[/tex]
Split to x and y values:
Where x = domain and y = range
[tex]Domain = \{9, 10, 11, 12\}[/tex]
[tex]Range = \{22, 32, 41, 30\}[/tex]
So, from the list of given options; option C answers the question.
Please answer this question for me please!!! Today I got headaching questions from other subjects and my mind has stopped!☠️ Question number 7, 13, and 16 please!!! It's worth 20 points!!!
Answers
Answer:
7a) 5/8 cup
7b) 4 3/8 cup
Step-by-step explanation:
a) Divide 1 1/4 by 2:
Do this by putting the 1 into the fraction and then convert to 8th
1 1/4 = 5/4 = 10/8
(10/8)/2 = 5/8
b) 3 1/2 * 1 1/4 = 7/2 * 5/4 = 7*5/(2*4) = 35/8 = 4 3/8
Solve the equation for u.
Uw + uq=r
Answers
Answer:
u = [tex]\frac{r}{w+q}[/tex]
Step-by-step explanation:
Given
uw + uq = r ← factor out u from each term on the left side
u(w + q) = r ← divide both sides by (w + q)
u = [tex]\frac{r}{w+q}[/tex]
The equation uw + uq = r is solved for u will be written as u = r / (w + q).
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
uw + uq = r
Simplify the equation for u, then the equation will be written as,
uw + uq = r
u(w + q) = r
u = r / (w + q)
The equation uw + uq = r is solved for u will be written as u = r / (w + q).
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Answer the two please 1. A monopoly playing board is in the shape of a square.The sides measure 19 inches. What is the area of the monopoly board? Use the golf scores below to answer quest 2 72,75,82 75,72,74 2. What is the median golf score? A.74.5 B.74 C.75.5 D.75
Answers
When I take half of my number and add two, I get twenty-four. What is my number?
Answers
in the adjoining figure, ABC is a right-angled triangle, where
B = 90°, AB = 3 cm and AC
3V2 cm, find the size of ®.
Answers
Answer:
the value of theta i 45°
Michael solved this inequality as shown: Step 1: -6(x + 3) + 10 < -2 Step 2: -6x − 18 + 10 < -2 Step 3: -6x − 8 < -2 Step 4: -6x < 6 Step 5: x > -1 What property justifies the work shown between step 3 and step 4? A. transitive property B. division property of inequality C. distribution property D. addition property of inequality
Answers
Answer:
D. addition property of inequalityStep-by-step explanation:
Given the step 3 and 4 of the solution Step 3: -6x − 8 < -2 Step 4: -6x < 6
From step 3;
-6x − 8 < -2
Michael got the step 4 by adding 8 to both sides of the inequality as shown;
-6x − 8 + 8 < -2 + 8
-6x < 6 (Step 4)
Since Michael added 8 to both sides of the inequality, the property that justifies the transition from step 3 to step 4 is the addition property of inequality. Addition property is the property that adds an integer to both sides of an inequality without altering the inequality sign and also retaining the inequality equation.