Answers
Answer:
[tex]\fbox{ Option D ➫ \: 416 \: cm²}[/tex]
Step by step explanation:
Given:
height of prism h = 18 cm
length of base of triangle b = 10cm
height of triangle h' = 2 cm
side A of triangle = 5 cm
side B of triangle = 7 cm
To find:
Surface area of prism = ?
Solution:
[tex]Area \: of \: base \: triangle = \: \frac{1}{2}\cdot{b}{h'} \\ Area \: of \: base \: triangle = \frac{1} {\not2}\cdot{10} \times \not{2} \\ Area \: of \: base \: triangle = 10 \: {cm}^{2} [/tex]
[tex] \fbox{Area \: of \: base \: triangle \: (B) = 10 \: cm²}[/tex]
[tex]Perimeter \: of \: base \: triangle = Side A + Side B + base b \\ Perimeter \: of \: base \: triangle = 5 + 7 + 10 \: cm \\ Perimeter \: of \: base \: triangle = 22 \: cm[/tex]
[tex] \fbox{Perimeter \: of \: base \: triangle (p) \: = 22 \: cm}[/tex]
[tex]Surface \: area \: of \: prism = 2B+ \: ph \\ Surface \: area \: of \: prism = 2 \times 10+ \: 22 \times 18 \\ Surface \: area \: of \: prism = 20 + 396\\ Surface \: area \: of \: prism = 416 \: {cm}^{2} [/tex]
[tex]\fbox{Surface \: area \: of \: prism = 416 \: cm²}[/tex]
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Answer:
D. 416 cm²
Step-by-step explanation:
Let S be the surface area of the prism
B be the area of the base of the prism
A be the lateral area of the prism
_______
formula :
S = 2B + A
__________
The base is a triangle ,then B the area of the base :
[tex]B=\frac{10 \times 2}{2}=10 \mathrm{~cm}^{2}[/tex]
_______
formula :
A = (Perimeter of the base) × (the height of the prism)
__________
then ,
[tex]\begin{aligned}A &=(10+5+7) \times 18 \\&=22 \times 18 \\&=396cm^2\end{aligned}[/tex]
Conclusion:
[tex]\begin{aligned}S &=2 B+A \\&=2 \times(10)+396 \\&=20+396 \\&=416 \mathrm{~cm}^{2}\end{aligned}[/tex]
Related Questions
how do you simplify (y+z)^3
Answers
Answer: y3+3y2z+3yz2+z3
Step-by-step explanation:
(y+z)3
=(y+z)*(y+z)*(y+z)
=(y+z)(y2+2yz+z2)
=(y)(y2)+(y)(2yz)+(y)(z2)+(z)(y2)+(z)(2yz)+(z)(z2)
=y3+2y2z+yz2+y2z+2yz2+z3
=y3+3y2z+3yz2+z3
Tori made a scale drawing of an Italian
restaurant. The restaurant's kitchen is 2
millimeters long in the drawing. The actual
kitchen is 16 meters long. What scale did Tori
use for the drawing?
1 millimeter :
meters
Answers
Step-by-step explanation:
2mm : 16m
so to get 1mm you need to divide 16 by 2
16/2 is 8 therefore
1mm : 8m
1 millimeter represents 8 meters in real life
hope that helps :)
Keisha is jogging from her house to school. Her school is 4 1/2 miles from her house. She has gone 3/8 miles so far. How many miles does Keisha still have to jog?
Answers
4.125 miles still to jog
Explanation:
Check out the work I’ve attach
Hope it helps, Let me know if you have any other questions!
Have a nice rest do your day :)
Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much.
Answers
Answer:
1 pound of peanuts cost 3 dollars
1 pound of wallnuts costs 2 dollars
Step-by-step explanation:
24/6=4
12/6=2
4 + (x + y) = (4 + x) + y =
what are the properties?
Answers
Answer:
Distributive
Step-by-step explanation:
PLEASE HELP what is the remainder if 3⁷³ is divided by five please and BRAINLIEST
Answers
Answer:
3
Step-by-step explanation:
3^1 = 3, 3^2 = 9, 3^3 =27, 3^4 =81,
3^5 = 243, etc. We see that the last digits of the powers of 3 are 3, 9, 7, and 1. If we continue this pattern, the last digit of 3^73 is 3. So if 3^73 is divided by 5, the remainder is 3.
which statement about the transformation is true? A. the unshaded octagon is a reflection because it is a flip over a diagonal line B. the unshaded octagon is a dilation because it is smaller than the shaded octagon C. the unshaded octagon is a horizontal translation because it is directly to the left of the shaded octagon D. the unshaded octagon is a vertical translation because it is directly under the shaded octagon
Answers
If you draw a diagonal line going down and crossing the origin, you can see that the figure reflects over that line. It’s like a mirror.
It is not the case for horizontal reflection because then it had to be reflected to the left of y-axis and it is not vertical reflection because then it would reflect below the x-axis
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER. What is the value of X in simplest radical form?
X=_____
Answers
Answer:
X=97
Step-by-step explanation:
The formula for the Pythagorean Theorem is:
[tex]\sqrt{a^2+b^2}=c[/tex]
Now,
A=65
B=72
72x72=5184
65x65=4225
4225+5184=9409
Last,
Take the square root of 9409.
The square root is 97.
Therefore, the hypotenuse is 97.
To check, use the equation:
[tex]a^2+b^2=c^2[/tex]
A=65
B=72
C=97
72x72=5184
65x65=4225
97x97=9409
5184+4225=9409
9409=9409
Therefore, the missing side, which is the hypotenuse, is 97.
Answer:
97
Step-by-step explanation:
Given:
Opposite = 65Adjacent = 72Hypotenuse = xDefinition:
Opposite is a perpendicular/vertical side.Adjacent is a horizontal side, by adding opposite and adjacent together, you have formed a right angle.Hypotenuse is the longest side of all which is the side that’s opposite of the right angle.To find:
Value of xPythagorean Theorem:
[tex]\displaystyle \large{a^2+b^2=c^2}[/tex]
Determine:
a = oppositeb = adjacentc = hypotenuseNote:
a and b can swap each other so you can determine a = adjacent and b = opposite instead of a = opposite and b = adjacent. This is because of addition property.The exception is value of c - ‘c’ cannot be changed and must be hypotenuse.Therefore, substitute given information in:
[tex]\displaystyle \large{65^2+72^2=x^2}[/tex]
Evaluate:
[tex]\displaystyle \large{4225+5184=x^2}\\\displaystyle \large{9409=x^2}[/tex]
Square Root both sides:
[tex]\displaystyle \large{\sqrt{9409} = \sqrt{x^2}}[/tex]
Cancel the squared x, add plus-minus:
[tex]\displaystyle \large{\pm \sqrt{9409} = x}[/tex]
Simplify the surd:
[tex]\displaystyle \large{\pm 97 = x}[/tex]
However, side length is a scalar value so it cannot be negative nor have negative values. Therefore:
[tex]\displaystyle \large{x=97}[/tex]
Hence, the value of x is 97
A straight boardwalk is being built over a
circular wetlands area, so that it divides
the area in half. A hiking path goes around
the outside. The boardwalk is 50 m long.
How long is the hiking path that goes
around the wetlands?
Answers
Answer:
157 if youre going by 3.14
157.08 if youre going by π
Step-by-step explanation:
you want to find the circumference
circumference is 2πr
the radius id 50/2=25, because radius is half of the diameter (the diameter is the length across a circle
2 * 3.141 * 25 = 157
The length of the path that goes around the outside of the circle stands at 157.08 meters.
What is a circle?A circle stands as a curve traced out by a point moving in a plane so that its distance from a given point exists constant; alternatively, it stands for the shape created by all points in a plane that exists at a set distance from a given point, the center.
Given that the boardwalk divides the circle area into two halves, and exists straight with a length of 50 meters. Thus, the straight Boardwalk exists within the length of the diameter of the circle.
Now, the perimeter of the circle exists the length of the path that goes around the outside.
Thus, the perimeter of the circle stands,
Perimeter = π × Diameter
= π × 50 meters
= 157.07963 meters ≈ 157.08 meters
Thus, the length of the path that goes around the outside of the circle exists 157.08 meters.
To learn more about the circle
https://brainly.com/question/23580895
#SPJ2
Carlos has 8 dollars and 48 cents. Alissa has 4 dollars and 14 cents. How much money does Carlos need
To give Alissa so that each of them has the same amount of money?
Answers
Answer:
.2 dollars and 17 cents
Step-by-step explanation:
Carlos has 8dollars and 48 cents --->8+0.48=8.48
Alissa has 4dollars and 14 cents--->4+0.14=4.14 let
x--->amount of money that Carlos needs to give Alissa
The linear equation that represents this situation is 8.48-x=4.14+x
solve for x2x=8.48-4.14
2x=4.34
x=2.17
therefore,the amount of money is 2 dollars and 17 cents.
thank you
by Angel osei
rectangular floor is 8 yd long and 3 yd wide. what is the area in square feet?
Answers
Answer:
216 square feet
Step-by-step explanation:
First we must convert both dimensions to feet. 1 yd = 3 feet
8 yd = 24 feet and 3 yd = 9 feet
We got the yd by multiplying by 3 to get the number of fett.
Area of a rectangle = base * height
24 feet * 9 feet = 216 square feet
I need help please give explanation and thank you
Answers
Area of triangle = 0.5(width*height )
SOMEONE PLEASE HELP!!!! ILL GIVE BRAINLIEST
Answers
Answer:
Your Answer is A.
Step-by-step explanation:
Looking at the picture the LM is the original and wants to translate it to L'M'.
So Right 5 and 2 up.
Answer:
A
Step-by-step explanation:
LM is 5 units away from LM'
LM is 2 units down from LM'
BRAINLIEST please if this helped!How many different ways can the letters of grade be arranged?
( I have to use permutation to solve please and thank you )
Answers
Explanation:
Assuming you want to arrange the letters of "grade", then we have 5 unique letters. That gives 5! = 5*4*3*2*1 = 120 different permutations. Order matters. The exclamation mark means factorial. It means we start at 5 and count our way down to 1, multiplying along the way.
In other words, we have 5 choices for the first slot, then 4 choices for the next slot, and so on. We count down because we cannot reuse any previously selected letter.
Alternatively, you can use the nPr permutation formula
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
where n = 5 and r = 5 since we have 5 letters to pick from and 5 slots to fill.
Answer:
120 ways
Step-by-step explanation:
The given word is :
GRADEIt has five letters⇒ Any of the 5 letters can be in each place
⇒ 5! ways is the number
⇒ 5 x 4 x 3 x 2 x 1
⇒ 20 x 6
⇒ 120 ways
Identify the indicated angles as Adjacent, vertical, linear, or complimentary
Answers
Select the two values of x that are roots of this equation.
x² + 34-3=0
. A. X=
-3+2/3
2
B. X=
-3-3
N
I X =
C. x.-3+27
=
1/21
2
O
D. *= -3-V21
=
2
Answers
Answer:
A. x=3 2.3
B . x=8
C. x=i do not know.
D. x=26
Step-by-step explanation:
A. -3+2/3=2
-3+2/3=-2 1/3
-2 1/3+3 2/3.=2
B. -3-3n=1
-3-3=-6n
-6n+8=1
C i do not understand.
D. -3-v21=2
21√5
Decimal Form:
1.0796532
or -24=2
-24+26=2
Write an equation in slope-intercept form of the line shown.
An equation is
Answers
Answer:
Slope-intercept Form: y = 3/4*x -2
Step-by-step explanation:
From looking at the graph we can get out slopes which is rise/run and y-intercept.
m = 3/4 and b = -2
Slope-intercept Form: y = 3/4*x -2
If the teacher wants to show work you would have to use a point-slope form using those two points to solve m. Then using a point and slope plug that into the point-slope form and make it into slope-intercept form.
Find the area of the shape.
Answers
a) Write an expression to represent the amount of money you
should have in the following situation.
Angela has $29 in her wallet. She gets paid $19 per hour and she
worked 8 hours last week and 6 hours this week. Then her friend
friend Tom borrowed $58.
b) How much money does Angela have left ?
PLEASE ANSWER THIS. I have an assignment due soon :((
Answers
Answer: $237
Step-by-step explanation:
Angela: 29 + 19(6 + 8) - 58
= -29 + 19(14) = -29 + 266 = $237
Find the unit vector in the direction of (6, 7).
Write your answer in component form.
Do not approximate any numbers in your answer.
Answers
Answer:
<(6/√85),(7/√85>
Step-by-step explanation:
Let vector o = 6i + 7j,
The magnitude, | o | = √(6²+7²) = √85
Unit vector, ô = (6i + 7j)/√85
= (6/√85)i + (7/√85)j
In component form, ô = <(6/√85),(7/√85>
Answer the Graph based Question I will make Brainliest + 50 points
Answers
Answer:
Here is the answerStep-by-step explanation:
Brainlest me please
#a
Take one coordinate and solve
(-3,5)So
y=x²-k5=(-3)²-k5=9-kk=9-5k=4Take another
(-2,0)So
y=x²-k0=(-2)²-k4-k=0k=4Hence k=4
#b
Graph attached
#c
Turn to vertex form
y=x²-4y=(x-0)²-4Compare to vertex form
y=a(x-h)²+kSo
Vertex(h,k)=(0,-4)#d
At no intervals of x the graph decreases negatively
Because
a is positive (+1) parabola is opening upwards#d
y=4-k²y=2²-k²y=(2+k)(2-k)So if y be 0
x intercepts are
(-2,0) and (2,0)Zeros are
-2 and 2For which values of x is the expression undefined x-8/x-5
Answers
Answer:
(x+10 (3x-45) is the answer of the question so easy
Answer:
x = 5
Step-by-step explanation:
Any number over 0 is undefined. Given that, the values of x that make this expression undefined make the denominator equal to 0
x - 5 = 0
x = 5
I hope this helps!
help please!!!!!!!! please be correct
Answers
Answer:
Step-by-step explanation:
the answer is 66. To find the third angle subtract 80 and 34 by 180.
A rectangle has a width of 3.5 inches and a length of x inches. If the diagonal of the rectangle is 12.5 inches, what is the value of x?
Answers
Answer:
12.0
Step-by-step explanation:
we solve using the pythagorean theorem.
sqrt of (12.5^2 - 3.5^2)
answer is 12
rounded of to the nearest tenth is 12.0
PLS HELP FAST!!! NO LINKS
Answers
Answer:
Im 98% sure its the first one
Step-by-step explanation:
John's water bill this month was $19.67 . Looking at the water bill, it says he used exactly 10,000 gallons of water. How much does he pay per gallon of water used?
Answers
Answer:
0.001967 per gallon
Step-by-step explanation:
19.67/10000 = 0.001967
terry had his car repaired ace auto. he was charged $40 per hour of labor plus 200 for parts. his total bill for the repair before tax was $380. how many hours of labor was terry charged for? write an equation
Answers
Answer:
380 = 40h +200 (equation)
4 1/2 hours (solution)
Step-by-step explanation:
The total cost is the sum of labor cost and parts cost. The labor cost depends on the number of hours.
__
An equation describing Terry's charges might be ...
total = labor cost + parts cost
380 = 40h +200 . . . . . . labor was $40 per hour for each of h hours
180 = 40h . . . . . . subtract 200
4.5 = h . . . . . . divide by 40
Terry was charged for 4 1/2 hours of labor.
Hello, pls help. Ty!
[tex] [/tex]
Answers
Answer:
See below ↓↓↓
Step-by-step explanation:
Question #1
line DE is the segment bisector as it bisects the line segment ACQuestion #2
A bisector divides a line in halfSo, AB = 1/2ACAB = 1/2 x 20 = 10 cmQuestion #3
Similarly, it divides the line in half in this case as wellBC = 1/2AC or AC = 2BCAC = 2 x 7 = 14 cmWrite an equation in point-slope form for the line that passes through the points (f, g) and (h,j).
Answers
Point-slope form is a form of a linear equation: [tex]y-y_1=m(x-x_1)[/tex]
[tex](x_1,y_1)[/tex] is a point that falls on the linem is the slope of the lineTo write an equation in point-slope form:
Calculate the slope of the line by solving for mPlug m into the general equationPlug a point that falls on the line in the general equation as [tex](x_1,y_1)[/tex]Solving the QuestionWe're given:
The line passes through the points (f,g) and (h,j)Solve for the slope (m):
[tex]y-y_1=m(x-x_1)[/tex]
⇒ Plug in the point (f,g) as (x,y):
[tex]g-y_1=m(f-x_1)[/tex]
⇒ Plug in the point (h,j) as (x₁,y₁):
[tex]g-j=m(f-h)[/tex]
⇒ Isolate m by dividing both sides by (f-h):
[tex]\dfrac{g-j}{f-h}=m[/tex]
⇒ Therefore, the slope of the line is [tex]\dfrac{g-j}{f-h}[/tex].
Plug the slope into the general equation:
[tex]y-y_1=\dfrac{g-j}{f-h}(x-x_1)[/tex]
Plug one of the points, (f,g) or (h,j) into the equation as (x₁,y₁):
[tex]y-j=\dfrac{g-j}{f-h}(x-h)[/tex]
AnswerThere can be multiple answers for this question, depending on what we consider to be (x,y) and what we consider to be (x₁,y₁). This is one of the possible answers, for (f,g) is (x,y) and (h,j) is (x₁,y₁):
[tex]y-j=\dfrac{g-j}{f-h}(x-h)[/tex]
Find the sum of the interior angle measures of a 14-gon.
The sum is___ degrees.
Answers
Step-by-step explanation:
the sum of interior angles in a triangle is 180°.
the sum of interior angles of a polygon, is the product of the number of triangles in the polygon (that can be created from a single vertex or corner via lines to all other corners) and 180°.
so, in reality, the number of triangles in each polygon is two less than the number of sides (because the lines to the 2 neighboring corners are sides and do not create triangles).
so the formula for the sum of all interior angles is
(n - 2) × 180
with n being the number of sides of the polygon.
in our case
(14 - 2) × 180 = 12×180 = 2160°
