Find the lateral area for the prism. L.A. =
Find the total area for the prism. T.A. =
Answers
LA=[area of the two triangles]+[area of the lateral rectangles]
hypotenuse of the triangle will be given by Pythagorean:
c^2=a^2+b^2
c^2=6^2+4^2
c^2=52
c=sqrt52
c=7.211'
thus the lateral area will be:
L.A=2[1/2*4*6]+[6*8]+[8*7.211]
L.A=24+48+57.69
L.A=129.69 in^2
The total are will be given by:
T.A=L.A+base area
base area=length*width
=4*8
=32 in^2
thus;
T.A=32+129.69
T.A=161.69 in^2
Answer:
Part 1) [tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]
Part 2) [tex]TA=(104+16\sqrt{13})\ in^{2}[/tex]
Step-by-step explanation:
Part 1) Find the lateral area of the prism
we know that
The lateral area of the prism is equal to
[tex]LA=Ph[/tex]
where
P is the perimeter of the base
h is the height of the prism
Applying the Pythagoras Theorem
Find the hypotenuse of the triangle
[tex]c^{2}=4^{2}+6^{2}\\ \\c^{2}=52\\ \\c=2\sqrt{13}\ in[/tex]
Find the perimeter of triangle
[tex]P=4+6+2\sqrt{13}=(10+2\sqrt{13})\ in[/tex]
Find the lateral area
[tex]LA=Ph[/tex]
we have
[tex]P=(10+2\sqrt{13})\ in[/tex]
[tex]h=8\ in[/tex]
substitutes
[tex]LA=(10+2\sqrt{13})*8=(80+16\sqrt{13})\ in^{2}[/tex]
Part 2) Find the total area of the prism
we know that
The total area of the prism is equal to
[tex]TA=LA+2B[/tex]
where
LA is the lateral area of the prism
B is the area of the base of the prism
Find the area of the base B
The area of the base is equal to the area of the triangle
[tex]B=\frac{1}{2}bh[/tex]
substitute
[tex]B=\frac{1}{2}(6)(4)=12\ in^{2}[/tex]
Find the total area of the prism
[tex]TA=LA+2B[/tex]
we have
[tex]B=12\ in^{2}[/tex]
[tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]
substitute
[tex]TA=(80+16\sqrt{13})+2(12)=(104+16\sqrt{13})\ in^{2}[/tex]
Related Questions
I NEEED HELPOPOP!!!!
PLEASE ASSIT ME FOR TWO MATH QUESTIONS
Answers
The only function in B has an inverse which is also a function (one x must have only 0 or 1 image (y)) for the first picture
Answer D for the second picture.
Answer B
what level of measurement is qualitative? Nominal? Ordinal? Interval? Or ration?
Answers
It is the only level of measurement which is only qualitative, whereas ordinal can be either qualitative or quantitative (depending on data), and interval and ratio can only be quantitative.
The term qualitative refers to the fact that non-numerical entries are used, meaning there are no numbers, and the word nominal refers to the Latin word for nouns, or words, which is why that is the correct answer. The rest of the options use numbers, but nominal doesn't.
what is the degree of 12x^4-8x+4x^2-3
Answers
4th degree
Answer:
The degree of [tex]12x^4-8x+4x^2-3[/tex] is 4.
Step-by-step explanation:
The given polynomial is [tex]12x^4-8x+4x^2-3[/tex]
This polynomial is of one variable which is x. Hence, the degree of the polynomial is the highest exponent.
For the given polynomial, the highest exponent is 4.
Therefore, the degree of [tex]12x^4-8x+4x^2-3[/tex] is 4.
He nine ring wraiths want to fly from barad-dur to rivendell. rivendell is directly north of barad-dur. the dark tower reports that the wind is coming from the west at 68 miles per hour. in order to travel in a straight line, the ring wraiths decide to head northwest. at what speed should they fly (omit units)?
Answers
This problem is better understood with a given figure. Assuming that the flight is in a perfect northwest direction such that the angle is 45°, therefore I believe I have the correct figure to simulate the situation (see attached).
Now we are asked to find for the value of the hypotenuse (flight speed) given the angle and the side opposite to the angle. In this case, we use the sin function:
sin θ = opposite side / hypotenuse
sin 45 = 68 miles per hr / flight
flight = 68 miles per hr / sin 45
flight = 96.17 miles per hr
A baseball team has won 13 out of 18 games they played this session. How many additional games must the team win in a row to raise its winning percentage to 80%?
A) 7
B) 14
C) 5
D) 24
Answers
What is the equation of a line that has a slope of -5 and passes through the point (0, 2)?
Answers
Find all solutions to the equation in the interval [0, 2π). cos 2x - cos x = 0
Answers
cos 2x-cosx=0
cos 2x=cosx
but:
cos 2x+1=2(cos^2x)
thereore;
from:
cos 2x=cos x
adding 1 on both sides we get:
cos 2x+1=cos x+1
2(cos^2x)=cosx+1
suppose;
cos x=a
thus;
2a^2=a+1
a^2-1/2a-1/2=0
solving the above quadratic we get:
a=-0.5 and a=1
when a=-0.5
cosx=-0.5
x=120=2/3π
when x=1
cos x=1
x=0
the answer is:
x=0 or x=2/3π
Answer:
The other answer is correct here except it is missing the answer 4pi/3
other wise its correct. The answers are 0, 2pi/3, and 4pi/3
Step-by-step explanation:
see previous answer
Determine the distance between a(-1, 2,3) and b(4,-5, 6) to the nearest tenth
Answers
the distance between A(-1, 2,3) and B(4,-5, 6)
AB= √((4-(-1)²+(-5-2)² + (6 - 3 ) ²) =√(25 +49 +9) = √83 ≅ 9.11
If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?
m∠A = 15° and m∠C = 35°
m∠A + m∠B = 155°
m∠A + m∠C = 60°
m∠A = 20° and m∠C = 30°.
Answers
all angles in a triangle add to 180
so
if the angles are m∠A, m∠B, m∠C, then
either m∠A=m∠B or m∠B=m∠C or m∠A=m∠C
anyway
so if we assume that vertex B is the one that has a twin then
130+130+?=180
260+?=180
?=-80
false, we can't have a negative angle measure
so 130 must be the odd one
?+?+130=180
2?+130=180
2?=50
?=25
so
m∠A=m∠C=25°
let's test the 2nd answer choice
m∠A+m∠B=25+130=155, yep
test 3rd
m∠A+m∠C=25+25=50≠60, nope
not 3rd one
so answer is 2nd statement
m∠A + m∠B = 155°
Which of the following equations describes the graph shown?
A.) y = x+2
B.) y = -x - 2
C.) y = x - 2
D.) y = -x + 2
Answers
Answer: The correct option is (D) y = -x + 2.
Step-by-step explanation: We are to select the correct equation that describes the given graph.
We can see that the graph is a straight line passing through the points (0, 2) and (1, 1).
So, the slope of the line will be
[tex]m=\dfrac{2-1}{0-1}=-1.[/tex]
Therefore, the equation of the line with slope m = -1 and passing through the point (0, 2) is given by
[tex]y-2=m(x-0)\\\\\Rightarrow y-2=-1\times x\\\\\Rightarrow y-2=-x\\\\\Rightarrow y=-x+2.[/tex]
Hence, the equation that describes the graph is y = -x + 2.
Thus, (D) is the correct option.
Find the prime factors of each of the following numbers. a. 25 b. 38 c. 36 d. 285 e. 650 f. 1,740
Answers
You have to try all prime numbers less or equal than the sqrt(number).
Example: 285, sqrt(285) =16.88194301613413
Try all below 16: 2, 3, 5, 7, 11 and 13:
285 / 3 = 95, 95 / 5 = 19 (19 is prime, end),
285 = 3*5*19, the prime factors are 3, 5 and 19
25 = 5*5
38=2*19
36 = 2^2 * 3^2, so 2 and 3.
That's why I let you do the last one
Answer:
The prime factors are:
a. 5 and 5 (5 × 5 = 25)
b. 2 and 19 (2 × 19 = 38)
c. 2, 2, 3, and 3 (2 × 2 × 3 × 3 = 36)
d. 3, 5, and 19 (3 × 5× 19 = 285)
e. 2, 5, 5, and 13 (2 × 5 × 5 × 13 = 650)
f. 2, 2, 3, 5, and 29 (2 × 2 × 3 × 5 × 29 = 1,740)
Step-by-step explanation:
straight from Penn
Margie and four friends are eating lunch at a restaurant. The total bill is $52.50 before tax and tip. Margie has a coupon good for $10off their total purchase. If sales tax of 6 percent is collected on the discount amount, what is the total cost after tax?
Answers
has a $ 10 off coupon..
52.50 - 10 = 42.50...this is the discount amount
has a 6% sales tax
0.06(42.50) = 2.55...this is the sales tax
for a total of : 42.50 + 2.55 = 45.05 <==
what are the roots of the polynomial equation x3-7x=6x-12? Use a graphing calculator and a system of equations.
Answers
x3-7x-6x+12=0
x3-13x+12=0
(x-1)(x2+x-12)=0
Calculate delta of the second bracket:
delta = 1+4*12=49
sqrt(delta)=sqrt(49)=7
x_1=(-1-7)/2=-4
x_2=(-1+7)/2=3
(x-1)(x+4)(x-3)=0
Answear:
Roots: x=1, x=-4, x=3.
The roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial equation:
x³ - 7x = 6x - 12
[tex]\rm x^3-7x+12=6x[/tex]
x³ - 13x + 2 = 0
(x - 1)(x -3)(x + 4) = 0
x = 1, 3, -4
Thus, the roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.
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What is the equation of the line that is parallel to the line y = x + 4 and passes through the point (6, 5)?
Answers
y-5=x-6
y=x-1 is parallel to y=x+4
Match the pairs of values of f(x) and g(x) with the corresponding values of h(x) if h(x) = f(x) ÷ g(x).
Screenshot of the tiles below
(Please help)
Answers
2)f(x)/g(x)=x^2-4x+3/x-3=x+1
3)f(x)/g(x)=x^2+4x-5/x-1=x+5
4)f(x)/g(x)=x^2-16/x-4=x+4
The We have given that the pairs of values of f(x) and g(x) with the corresponding values of h(x) s given below.
(x^2-9)/(x-3)
x^2-4x+3/x-3
x^2+4x-5/x-1
x^2-16/x-4
We have to match the pairs of values of f(x) and g(x) with the corresponding values of h(x) if h(x) = f(x) ÷ g(x).
What is the function?A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
1)f(x)/g(x)=(x^2-9)/(x-3)=x+3
2)f(x)/g(x)=x^2-4x+3/x-3=x+1
3)f(x)/g(x)=x^2+4x-5/x-1=x+5
4)f(x)/g(x)=x^2-16/x-4=x+4
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PLEASE HELP ASAP 20 POINTS PLUS BRAINIEST!
Find the greatest possible error for each measurement.
3 ft
a.
1 ft
b.
1/2 ft
c.
1/4 c
d.
1/6 c
Answers
the greatest possible error when measuring in feet is 1/2 foot
answer is B
Which polynomial is a perfect square trinomial?
A. 36x²-18x-9
B. 4a²-28a-49
C. 25b²-40b+16
D. 4x²-6x+9
Answers
because of how the multiples of 25 are 5 and 5 and the multiples of 16 can be -4,-4...
5*-4+5*-4=-40
(5x-4)²= ((5²)x²-40x+(-4²))=25x²-40+16
//Brief explanation
Using a discriminant (b^2 - 4ac), for a perfect square the discriminant = 0.
For A the discriminant is >0 (1620)
For B the discriminant is >0 (1568)
For C the discriminant = 0
For D the discriminant is < 0 (-108)
What is the value of 35+20/5-4*7
11
49
245
35
Hellllpp :)
Answers
= 35 + 4 - 28 = 11
The answer is 11
35 + 20/5 - 4×7 =
35 + 4 - 28 =
39 - 28 =
11
A hyperbola centered at the origin has a vertex at (3, 0) and a focus of the hyperbola is located at (9, 0). What are the equations of the directrices?
x = ±
Answers
To find the equations of the directrices for a hyperbola centered at the origin with a vertex at (3, 0) and a focus at (9, 0), we use the formula x = ±a/e. The hyperbola's directrices are x = ± 1.
Explanation:The student asked about the equations of the directrices for a hyperbola that is centered at the origin, with a vertex at (3, 0) and a focus at (9, 0). A hyperbola has two directrices, and each is a line that is perpendicular to the transverse axis and equidistant from the center as the foci are, but on the opposite side. The equation of a directrix can be found using the formula x = ±a/e, where 'a' is the distance from the center to the vertex and 'e' is the eccentricity, which is the ratio of the distance from the center to a focus (c) over 'a'.
In this case, the hyperbola is aligned along the x-axis. Given a vertex at (3, 0), it implies that 'a' is equal to 3. Since the focus is at (9, 0), it suggests 'c' is equal to 9. The eccentricity 'e' can be found by e = c/a, which is 9/3 = 3. Using the directrix formula x = ±a/e, the two directrices of the hyperbola would be x = ±(3/3), which simplifies to x = ± 1.
PLEASE HELP!!! Evaluate Show your work.
Answers
sqrt (7x)(sqrt (x) - 7sqrt (7)) =
sqrt (7x) * sqrt (x) - sqrt (7x) * 7sqrt (7)
now if you have two things multiplied by each other and they are both under the sqrt sign then we can multiply them by each other But we have to leave them under the sqrt sign. so this becomes:
sqrt (7x * x) - 7sqrt (7x *7) =
sqrt (7x^2) - 7sqrt (7^2 *x)
in the first sqrt we have x^2 And in the second we have 7^2. The sqrt of anything squared is the same number without the square. So sqrt (x^2) becomes x and sqrt(7^2) becomes 7. So now we have:
x * sqrt (7) - 7 * 7sqrt (x) =
xsqrt (7) - 49sqrt (x)
Answer:
[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
Step-by-step explanation:
Given: [tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]
Simplify the expression.
[tex]\Rightarrow \sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]
Distribute [tex]\sqrt{7x}[/tex] over parentheses
[tex]\Rightarrow \sqrt{7x}\cdot\sqrt{x}-\sqrt{7x}\cdot7\sqrt{7}[/tex]
[tex]\Rightarrow \sqrt{7x^2}-7\sqrt{7^2x}[/tex]
square term take out from square root
[tex]\Rightarrow x\sqrt{7}-7\cdot 7\sqrt{x}[/tex]
[tex]\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
In the triangle below, determine the value of a.
Answers
a=14tan42°
a≈12.61 (to the nearest hundredth of a unit)
Use tangent to find the opposite to the adjacent side (14) from the angle (in this case a).
a = 14*tan(42°) = 14*0,9 = 12,6 (approssimatively)
the square has a radius of 3 square root 2 what is the apothem?
Answers
The apothem of the square is equal to half the length of a side of the square, which can be calculated by doubling the radius. In this case, the apothem is 3√2.
Explanation:The apothem of a square is a line segment drawn from the center of the square to any side of the square, perpendicular to that side. The apothem is equal to half the length of a side of the square.
Given that the square has a radius of 3√2, we can determine the length of a side of the square by doubling the radius. So, the length of a side is 2 * 3√2 = 6√2.
Therefore, the apothem of the square is half the length of a side, which is (6√2)/2 = 3√2.
During a recent snowstorm in red hook ny Jaime notice that there were 4 inches of snow on the ground at 3:00p.m and there were 6 inches of snow on the ground at 7:00p.m. If she were to graph these data what does the slope of the line connecting these two point represent in the context of this problem
Answers
If 35% of a natural area is to be developed, leaving 500 acres untouched, how many acres are to be developed?
Answers
Answer:
Area to be developed = 269.23 acres
Step-by-step explanation:
Let there is A acres natural area to be developed.
If 35% of A acres is developed then untouched area will be (100 - 35 = 65%)
Now it has been given in the question that 65% of A (untouched area) = 500 acres
[tex]A.\frac{65}{100}=500[/tex]
[tex]A=\frac{500}{0.65}=769.23[/tex]
So area of the natural field = 769.23 acres
Now 35% of the natural area which is to be developed = A×35%
[tex]=769.23.\frac{35}{100}=(769.23)(.35)=269.23[/tex]
Area of the natural area to be developed is 269.23 acres
The number of acres that are to be developed is 269 acres.
Number of acresUsing this formula
Number of acres=(Number of acres untouched/(100%-Percentage of natural area)×Percentage of natural area
Let plug in the formula
Number of acres=500 acres/(100%-35%)×35%
Number of acres=(500 acres/65%)×35%
Number of acres=769.23×35%
Number of acres=269 acres
Inconclusion the number of acres that are to be developed is 269 acres.
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What is the polygon being rotated to create the brown quilt block pattern?
Answers
Answer with explanation:
The pre image which is in blue color is parallelogram.
There are four blue parallelograms here,congruent to each other,each one of them when rotated by certain angle ,gives parallelogram in brown color.
When we rotate a polygon,after rotation neither the shape nor the size of polygon changes.The two shapes are congruent to each other.
→The Polygon being rotated to create the brown quilt block pattern is
Option C: Parallelogram
Solve 152x = 36. Round to the nearest ten-thousandth.
A. 0.6616
B. 2.6466
C. 1.7509
D. 1.9091
Answers
Since no one was getting the the answer that is on the assignment I plugged the problem into an algebra calculator, and got A 0.6616
Help Please!!!!!!
f(x)=5x^2+9x−4
g(x)=−8x^2−3x−4
Find (f+g)(x)
My Options Are...:
a. 3x^2+6x−8
b. −3x^3+6x^2−8x
c. −3x^4+6x^2−8
d. −3x^2+6x−8
Answers
Combine like terms
f+g(x)=-3x^2+6x-8
Final answer: D
Write cos 53 degrees in terms of sine.
Answers
cos(53) = sin(90 - 53)
cos(53) = sin(37)
The value of cos 53 degrees in terms of sine is,
⇒ sin 37 degree
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
We have to given that;
⇒ cos 53 degree
Hence, We can change it into sine as;
⇒ cos 53 degree
⇒ sin (90 - 53)
⇒ sin 37 degree
Thus, The value of cos 53 degrees in terms of sine is,
⇒ sin 37 degree
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Find the missing factor x(y+6)-5(y+6)( ) (y+6)
Answers
We are given the equation:
x (y + 6) – 5 (y + 6) ---> 1
We are to look for the missing factor in the equation: (_) (y + 6) from the given values.
Knowing the rules of the polynomial multiplicity, we can have an idea that the given equation can also be written in the form of:
(x – 5) (y + 6) ---> 2
wherein the whole factor (y + 6) was simply distributed to the values in the factor (x – 5). To prove that equations 1 and 2 are equal:
x (y + 6) – 5 (y + 6) = (x – 5) (y + 6)
Expanding:
x y + 6 x - 5 y – 30 = x y + 6 x – 5 y – 30 (EQUAL!)
Therefore our missing factor is:
(x – 5)
Fill in the missing term in the equation. x/x^2-4x+4-x/x^2-3x+2=?/(x-2)^2(x-1)
Answers
----------------- - --------------------
x^2 -4x + 4 x^2-3x+2
x x
= ---------------- - --------------------
(x -2)^2 (x - 2)(x - 1)
x (x-1) - x(x +2)
= ----------------------------
(x -2)^2 (x - 1)
x^2 -x -x^2 - 2x
= --------------------------
(x -2)^2 (x - 1)
-3x
= -----------------------
(x -2)^2 (x - 1)
answer
missing term in the equation: -3x
Answer:
The missing term is x.
Step-by-step explanation:
Given expression is,
[tex]\frac{x}{x^2-4x+4}-\frac{x}{x^2-3x+2}------(1)[/tex]
Since, [tex]x^2-4x+4=(x)^2-2\times (2x)+(2)^2[/tex]
[tex]\implies x^2-4x+4=(x-2)^2------(2)[/tex] ( (a-b)² = a² - 2ab + b² )
Now, [tex]x^2-3x+2=x^2-2x-x+2[/tex] ( By middle term splitting )
[tex]=x(x-2)-1(x-2)[/tex]
[tex]\implies x^2-3x+2=(x-1)(x-2)------(3)[/tex]
From equation (1), (2) and (3),
[tex]\frac{x}{x^2-4x+4}-\frac{x}{x^2-3x+2}=\frac{x}{(x-2)^2}-\frac{x}{(x-2)(x-1)}[/tex]
[tex]=\frac{x(x-1)-x(x-2)}{(x-2)^2(x-1)}[/tex]
[tex]=\frac{x(x-1-x+2)}{(x-2)^2(x-1)}[/tex]
[tex]=\frac{x(1)}{(x-2)^2(x-1)}[/tex]
[tex]=\frac{x}{(x-2)^2(x-1)}[/tex]
Hence, the missing term in the equation is x.