6x + x/2
Which algebraic expression best represents this word phrase?
The sum of six times a number and the quotient of that number and two
in the right triangle ABC mc=90, a=4, and sinA=1/2. what is the length of the hypotenuse?
Answer:
The length of the hypotenuse is 8 units
Step-by-step explanation:
Recall the notation SOH CAH TOA. This means that in aright angled triangle,
Sin A = a/c where a is the length of the opposite side and c is the length of the hypotenuse.
Given that sinA=1/2 and a = 4, the hypotenuse c
sin A = 4/c
1/2 = 4/c
cross multiply
c * 1 = 4 * 2
c = 8 units
An open tank is to be constructed with a square base of side x metres with four rectangular sides. The tank is to have a capacity of 108m^3. Determine the least amount of sheet metal from which the tank can be made?
Answer: roughly 151.81788 square meters of metal
=====================================================
Explanation:
The base is a square with side lengths x, so its area is x*x = x^2
Let h be the height of the tank. We have four identical wall panels that have area of xh square meters. The four walls lead to a lateral surface area of 4xh. Overall, the entire tank requires x^2+4xh square meters of metal. We're ignoring the top since the tank is open.
-----------
Let's set up a volume equation and then isolate h.
volume = length*width*height
108 = x*x*h
108 = x^2*h
x^2*h = 108
h = 108/(x^2)
-----------
Plug that into the expression we found at the end of the first section.
x^2+4xh
x^2+4x(180/(x^2))
x^2+(720/x)
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Depending on what class you're in, the next step here will vary. If you are in calculus, then use the derivative to determine that the local min happens at approximately (7.11379, 151.81788)
If you're not in calculus, then use your graphing calculator's "min" feature to locate the lowest point on the f(x) = x^2+(720/x) curve.
This lowest point tells us what x must be to make x^2+(720/x) to be as small as possible, where x > 0.
In this context, it means that if the square base has sides approximately 7.11379 meters, then you'll need roughly 151.81788 square meters of metal to form the open tank. This is the least amount of metal required to build such a tank, and that will have a volume of 108 cubic meters.
Pls help school is almost over
Answer:
correct answer is c
Step-by-step explanation:
2.44x10^-3
What is the area of the triangle ?
A) 64
B) 56
C) 48
D) 112
Answer:
[tex]\text{B) }56\:\mathrm{cm^2}[/tex]
Step-by-step explanation:
The area of a triangle with height [tex]h[/tex] and base [tex]b[/tex] is given by [tex]A=\frac{1}{2}bh[/tex]. By definition, the base and the height must intersect at a 90 degree angle. Therefore, the diagram gives a base of 14 cm and a height of 8 cm. Substituting these values, we get:
[tex]A=\frac{1}{2}\cdot 8\cdot 14=\boxed{\text{B) }56\:\mathrm{cm^2}}[/tex]
help please anyone ??
An earthquake with a rating of 6.5 is
considered a major earthquake that can
cause damage over a large area.
Answer:
it is not considered a major earthquake, for it to be considered a major earthquake it has to have a rating of 8.0 or higher
HELP PLZ ALMOST DONE!!!
Answer:
A = 30 inches^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2)h where b1 and b2 are the lengths of the bases
A = 1/2 ( 10+5) * 4
A = 1/2 (15)*4
A = 30 inches^2
Answer:
Area of trapezoid is 30 inches ².
Step-by-step explanation:
Question :-A trapezoid having length of Base ¹ and Base ² are 10 in. and 5 in. and it's height is 4 in. Find the area of trapezoid.
Solution :-Area of trapezoid is given by
= 1/2 × ( B¹ + B² ) × h
Where, B¹ = 10 in.
B ² = 5 in.
h = 4 in.
substitute the values
Area = 1 / 2 × ( 10 in × 5 in ) × 4 in
multiplying the values
Area = 1 / 2 × 15 in. × 4 in
Area = 1 / 2 × 60 in ².
Area = 30 in².
Hence, Area of trapezoid is 30 inches ².
Simplify the expression 35e^9/5e^8
[tex] \frac{35e {}^{9} }{5 {e}^{8} } \ \\ \\ \frac{7e {}^{9} }{e {}^{8} } \\ \\ \\ = 7e[/tex]
Step By Step Explanation:
Reduce: Reduce the fraction with 5Simplify: Simplify the expressionAlternate Forms:
19.02797☆彡HannaHELPPPPP!!!
Jack and Joey went to the store to buy candy. Jack bought 5 Hershey bars and 2 packs of
starbursts for $12. Joey bought 3 Hershey bars and 4 packs of starbursts for $13.50. Let x equal the cost of one Hershey bar and y equal the cost of one pack of starbursts.
8a) Write a system of equations that describes the situation above.
8b) using the equations from part a, determine the cost of one Hershey bat and the cost of one pack of starburst in dollars and cents
Answer:
5x + 2y = 12
3x + 4y = 13.50
One Hersey bar = 1.5
One pack of Starburst = 2.25
Step-by-step explanation:
Let :
Cost of one Hersey bar = x
Cost of one pack of Starburst = y
System of equation :
For Jack :
5x + 2y = 12 - - - (1)
For Joey :
3x + 4y = 13.50 - - - (2)
To determine the cost per Hersey bar and pack of Starburst
5x + 2y = 12 - - - (1)
3x + 4y = 13.50 - - (2)
Multiply (1) by 3 and (2) by 5
15x + 6y = 36 - - - (3)
15x + 20y = 67.50 - - - (4)
Subtract (4) from (3)
-14y = - 31.50
y = 31.50 / 14
y = 2.25
Using (1)
5x + 2y = 12
Put y = 2.25
5x + 2(2.25) = 12
5x + 4.50 = 12
5x = 12 - 4.50
5x = 7.50
x = 1.5
the perimeter of a rectangular painting is 304 CM. If the width of the paint is 63 cm what is the length
Answer:
The PERIMETER P is the distance around the rectangle.
Let's call the width of the rectangle W and the length of the rectangle L.
As you go around the edge there two equal lengths and two equal widths.
The formula for the perimeter of a rectangle is P=2*L+2*W.
P=2L%2B2W
Substitute 290 for P and 62 for the width.
290=2L%2B2%2862%29
Solve for L.
290=2L%2B2%2862%29
290=2L%2B124
290-124=2L
2L=166
L=83
The equation L=83 means that the length is 83 cm.
CHECK your work.
2(62)+2(83) = 124+166 = 290cm.
The length of the rectangle is 83cm.
In order to help decide when and where to advertise, an outdoor equipment repair company decided to pull invoices and tally what types of power tools were repaired. There were twenty-five power tools repaired that month. What is the level of measurement for the data
Answer:
The answer is "nominal, qualitative".
Step-by-step explanation:
The information available is not numerically structured in a form name.
The measuring level is therefore nominal. Qualitative information is also called, which can be seen but not measured. Thus data given is qualitative.
A drone is originally priced at 110$. The online retailer gives a discount and the drone is now $88 . enter the percentage discount for the cost of the drone.
Answer:
20%
Step-by-step explanation:
Decrease in amount = original - new amount
Decrease in amount = 110 - 88 = $22
Decrease % = decrease/original x 100%
= 22/110 x 100%
= 20%
Dave wants to build a rectangular screened-in porch that is 20 feet long, and it will extend 6 feet out from the backside of his house.
Dave sketches a scale drawing of the porch. Choose a reasonable size and scale for Dave’s drawing of the porch. How should Dave label the dimensions of the model?
Answer:
Scale of the drawing would be 20/12 inch and 0.6 (6/12) inch
Step-by-step explanation:
For most of the residential buildings an scale of 1 inch = 12 feet can be used to draw the residential units.
In that case the scale of the drawing would be 20/12 inch and 0.6 (6/12) inch
Dave should label the dimensions in inches
The running back for the Bulldogs football team carried the ball 7 times for a total loss of 8 3/4 yards. Find
the average change in field position on each run. Enter the average change as a simplified mixed number.
The average change in field position on each run was
yards.
Answer:
-1 1/4 yards
Step-by-step explanation:
7 carries
-8.75 yards total yardage
-.8.75 / 7 = -1.25 yards average per carry
In mixed number ? -1 1/4 yards
Which expression has a value of 24?
A 12+16÷(4+2)×2
B (12+16)÷4+2×2
C. 12+16÷(4+2×2)
D. 12+(16÷4+2)×2
Answer:
the last one
Step-by-step explanation:
12+(16/4+2)2
12+(4+2)2
12+6*2
12+12
24
Answer:
D
Step-by-step explanation:
A. 17.33
B. 11
C. 14
D. 24
Find the missing length indicated. Hey can someone help me out?
Answer:
C) 6
by-step explanation:
Triangle D E F is shown. Angle E F D is a right angle. The length of E F is 24 and the length of D F is 7.
Which trigonometric ratios are correct for triangle DEF? Select three options.
sin(D) = StartFraction 24 Over 25 EndFraction
cos(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 24 Over 7 EndFraction
sin(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 7 Over 24 EndFraction
Answer:
Sin(E) = 7/25
Sin(D) = 24/25
Tan(D)= 24/7
Step-by-step explanation:
Sin=opp/hyp
Tan=opp/adj
Cos=adj/hyp
The trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
How to determine the trigonometric ratios?The given parameters are:
EF = 24
DF = 7
Start by calculating the length DE using:
DE²= EF² + DF²
So, we have:
DE²= 24² + 7²
Take the square root of both sides
DE= 25
The sine of the angles is calculated using:
sin(Ф) = opp/hyp
So, we have:
sin(E) = 7/25
sin(D) = 24/25
The tangent of the angles is calculated using:
tan(Ф) = opp/adj
So, we have:
tan(D)= 24/7
Hence, the trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
Read more about trigonometric ratios at:
https://brainly.com/question/11967894
HELP!!! PLEASE!!!!!!!!!!
please help picture included
Match the verbal expression (term) with its algebraic expression (definition). Match Term Definition Some number A) a = 2 increased by two A variable decreased B) b + 2 by two Product of an C) y2 unknown value and two D) X - 2 Quotient of some number and two An unknown value E) 22 squared
9514 1404 393
Answer:
B, D, E, A, C
Step-by-step explanation:
The main idea here is to use your English comprehension skill to determine the meaning of the phrase, then use your math understanding to write it in symbols. Turning off your brain at the sight of a "word problem" will not be productive.
The wording "some number" or "a variable" or "unknown value" all refer to a variable, typically represented by a single letter. Letters commonly use are {a, b, c, x, y, z}, but variables are not restricted to that set (nor to single letters, nor lower case letters).
In most cases, the math expression is a direct translation of the English expression using the usual math symbols. Values are generally increased by addition, decreased by subtraction, squared using an exponent of 2. A product is the result of multiplication, and a quotient is the result of division.
Top-to-bottom, the boxes on the left will be filled with B, D, E, A, C.
Cual es la ecuación de la recta dado su pendiente m=2 y p(2,3)
Answer:
y=2x-1
Step-by-step explanation:
How many centimeters are there in 3 meters?
A. 100 cm
B. 200 cm
C. 300 cm
D. 400 cm
Answer:
Step-by-step explanation:
c
A rectangle has a length of 12.6 m and a width of 6.3 m. A similar rectangle has a width of 2.1 m. What is the length of the similar rectangle?
Step-by-step explanation:
Please see the photo for the method
Answer this as soon as possible please!!!!!
A books storevhad 30816 exercise books which were packed in cartons, each carton contains 24exercise books.The mass of an empty carton was 2kg and full was 12kg."what was the total mass of each empty carton, what was the total mass of the books alone?"
Step-by-step explanation:
the total mass of each empty carton
1284×2568kg
the total mass of books alone
30816×10=12840kg
Randi bought a wallet for $8.33. She paid with a $20 bill. Which of the following could be the change she received?
A. 1 $10 bill, 1 $1 bill, 2 quarters, 1 dime, 1 nickel, and 2 pennies
B. 1 $10 bill, 1 $1 bill, 2 quarters, 1 dime, 2 nickels, and 2 pennies
C. 1 $10 bill, 1 $1 bill, 3 quarters, 1 dime, 1 nickel, and 2 pennies
D. 1 $10 bill, 1 $1 bill, 2 quarters, 2 dimes, 1 nickel, and 2 pennies
Answer:
A.
Step-by-step explanation:
She would receive $11.67
A is the correct math
24)
Evaluate:
(-4) - (-16) + (-10) - (-1) - (14) + (11)
Answer:
I think its 0.
Step-by-step explanation:
Double negatives make a positive, add the like terms. Hope this helps
If 81 is added to a number the result is 39 less than three times the number
let x =the number
Step-by-step explanation:
81+x=3x-39
group like terms
81+39=3x-x
120=2x
120/2=2x/2
60=x
therefore x =60
Answer:
60
Step-by-step explanation:
number is represented as x.
81 is added to a number is
81 + x
39 less than three times the number
3x - 39
So
81 + x = 3x - 39
Solve for x.
81 + x = 3x - 39 Add 39 to each side so 39 cancels on the right.
81 + x + 39 = 3x - 39 + 39
81 + x + 39 = 3x
81 + 39 + x = 3x
120 + x = 3x Subtract x from each side.
120 + x - x = 3x - x
120 = 3x - x
120 = 2x Divide each side by 2
120/2 = 2x/2
120/2 = x
60 = x
Given that ABCD is a rectangle, find the total area of the figure below. Round your answer to the nearest tenth.
Options
18 ft²
20.25 ft²
21.5 ft²
22.5 ft²
Answer:
C
Step-by-step explanation:
The Isosceles Trapezoid is part of an Isosceles triange with a 32° vertex angle. What is the measure of an acute base angle of the trapezoid?
Answer:
[tex]b = 74^o[/tex] --- acute base
Step-by-step explanation:
Given
See attachment for the figure
Required
The acute base angle of the trapezoid
From the question, the isosceles triangle and the trapezoid share the same base.
Represent the base angle with b.
So:
[tex]b + b + 32^o = 180^o[/tex] --- angles in a triangle
[tex]2b = 180^o-32^o[/tex]
[tex]2b = 148^o[/tex]
Divide by 2
[tex]b = 74^o[/tex]
Please answer this, its one of my homework questions
Answer:
4^4=4^3*4=64*4=256
4^6=4^5*4=1024*4=4096
Step-by-step explanation:
Answer:
4^4 = 256
4^6 = 4,096