1,2 cause of the o and y axis
The vertex is where the parabola changes directions, or in simpler terms, at the parabolas lowest point. Unless the parabola is upside down, then the vertex is where the highest point is.
The acid of symmetry is the line where the parabola can be divided evenly. This is almost always where the vertex is, except it continues on.
The y-intercept is where the parabola intersects with the y-axis.
I’ve answered the question below in the picture (my graph is not to scale but the answers are correct for yours)
Hope this helped and good luck!!
A cab rider from your home to the airport cost $23.47. If you want to tip the cab driver close to 10 percent of the fare, how much should you tip?
For this case we must make a rule of three:
23.47 ----------------> 100%
x -----------------------> 10%
Where the variable "x" represents the tip rate.
[tex]x = \frac {10 * 23.47} {100}\\x = 2,347[/tex]
Thus, the tip should be 2,347 dollars.
Answer:
$ 2,347
Craig has a building block in the shape of a rectangular pyramid. A net of which is shown below.
If a measures 12 cm, b measures 6 cm, and d measures 13 cm, what is the surface area of the rectangular pyramid?
A. 183 sq cm
B. 936 sq cm
C. 516 sq cm
D. 294 sq cm
Answer:
the answer is D: 294 sq. cm
Step-by-step explanation:
first you want to split the net into 4 triangles and 1 rectangle
a = 12 cm
b = 6 cm
d = 13 cm
calculate the surface area of the pyramid...
1st find the area of the rectangle base
Rectangle base area
b x a = (6 cm) (12 cm)
= 72 sq. cm
next find the area of the triangle on the left
Left triangle
1/2(b)(d) = 1/2 (6 cm)(13 cm)
= 1/2 (78 sq cm)
= 39 sq. cm
Since all the triangles are congruent (same), you will need to multiply by 2 to get the combined area of the triangle on the left and on the right.
Area of left & right triangles
= 2 (39 sq. cm)
= 78 sq. cm
Find the area of the triangle on the bottom
Bottom triangle area = 1/2 (a)(a)
= 1/2 (12 cm) (12 cm)
= 1/2 (144 sq. cm)
= 72 sq. cm
Since the bottom of the triangle is congruent to the top triangle, multiply that by 2 to get a combined area of the triangle on the bottom and top
Area of top & bottom triangles
2 (72 sq. cm) = 144 sq. cm
Finally...add the area of the 4 triangles to the area of the rectangular base
72 + 78 + 144 = 294 sq. cm
Answer:
D
Step-by-step explanation:
Fun fact: During your life you can produce enough saliva for 2 swimming pools! :O 0.0 :D
PLZ HELP IM ON A TIMELINE HURRY
Answer:
5 x 5, 2 raised to the fifth power, 25
6 x 6 x 6, six cubed, 216
1/5 2, one fifth cubed, 1/5
62, 6 x 6, 36
hope this helped please give me the brainliest answer?
Have a good day ma dude!!! <3
HELP ASAP!
Mr. Ray had $400. He spent 2/5 of it on a vacuum cleaner and 1/4 of the remainder on a fan. How much money did he have left?
WILL MARK AS BRAINLEST
and also remember to add ur step by step exclamation.
Answer:
180
Step-by-step explanation:
Ok first lets find out what 1/5 of 400 dollars is: 400/5= 80
So 1/5 of 400 is 80, now lets see what 2/5 is= 80 * 2= 160
Then subtract: 400 - 160= 240
we have 240 left. If he spent 1/4 of that on a vacuum cleaner then we have to: 240/4=60
He spent 60 dollars, now to find the remaining we must subtract: 240-60=180
Hope this helped ;)
So 2/5 is 0.4
0.4 of 400=160
400-160=240
240 is the remainder(what is left)
He used 1/4
1/4=0.25
240*1/4 =60
So 240-60=180
So your answer is: Mr.Ray will have $180 left.
Simplify the variable expression by evaluating it's numerical part m-8+143-5 and how did get m
m - 8 + 143 - 5
Answer: m + 130
Final answer:
To simplify the expression m - 8 + 143 - 5, combine the numerical parts to get 130, then the simplified expression is m + 130.
Explanation:
To simplify the variable expression m - 8 + 143 - 5, you must combine the numerical parts of the expression and keep the variable part as is. The numerical parts are -8, +143, and -5.
First, simplify the numerical parts by addition and subtraction:
143 - 8 - 5 = 130.
Next, keep the variable m in the expression, so the simplified form of the expression is:
m + 130
This is straightforward numerical evaluation, where units are not involved and thus can be worked out easily without mathematical complexity.
Which expression has a value of 36?
A. 9/12 x 48
B. 6/7 x 21
C. 10/13 x 39
D. 3/7 x 42
The expression that has a value of 36 is A. 9/12 x 48
Which expression has a value of 36?
From the question, we have the following parameters that can be used in our computation:
A. 9/12 x 48
B. 6/7 x 21
C. 10/13 x 39
D. 3/7 x 42
Evaluating the expressions, we have
A. 9/12 x 48 = 36
B. 6/7 x 21 = 18
C. 10/13 x 39 = 30
D. 3/7 x 42 = 18
Hence, the expression that has a value of 36 is A. 9/12 x 48
What is the value of x in the equation -x =4 -3x +6?
A. 5
B. 10
C. -5
D. -10
Worth 10 points
Answer:
A.5
Step-by-step explanation:
-x = 4 - 3x + 6
-x+3x = 4 + 6
2x =10
x=5
what is the value of p in the proportion below
20/6=p/12
Answer: 40
Step-by-step explanation:
the numbers were doubled
Answer:
40
Step-by-step explanation:
Plz help me with this
Answer: [tex]\bold{y=sin(4x)+3}[/tex]
Step-by-step explanation:
[tex]\text{The standard form of a sine equation is: y=A cos(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]
The given information is:
A (amplitude) = 1[tex]Period\bigg(\dfrac{2\pi}{B}\bigg)=\dfrac{\pi}{2}}\qquad \implies B=4[/tex]D (Vertical shift) = +3[tex]\implies \large\boxed{y=sin(4x)+3}[/tex]
That one particular store the sale price S is always 75% of it displayed price do you write in equation that shows how to calculate S and D find the sale price if displayed price is $85
Step-by-step explanation:
displayed price=100%=85
selling price=75% of the displayed price
discount=,25%
Final answer:
To find the amount of sales tax on a $85 jacket with a 7.5% sales tax, convert the percentage to 0.075 and multiply by $85, resulting in a tax of $6.375. Add this to the original price for a total of $91.38.
Explanation:
To calculate the amount of sales tax for an item, you must first convert the percentage to a decimal and then multiply it by the item's displayed price. For the example of a jacket priced at $85 with a 7.5% sales tax, you would use the following equation:
Amount of sales tax = price × rate of sales tax
First, convert 7.5% to a decimal by dividing by 100, which gives us 0.075. Then, multiply $85 by 0.075:
$85 × 0.075 = $6.375
Therefore, the sales tax is $6.375. To find the total cost of the jacket including the sales tax, you simply add the amount of the sales tax to the displayed price:
Total cost = displayed price + sales tax
Total cost = $85 + $6.375 = $91.375
Since the total cost usually needs to be rounded to the nearest cent, the final total cost of the jacket would be $91.38.
Caroline knows the height and the required volume of a cone-shaped vase she’s designing. Which formula can she use to determine the radius of the vase?
Answer:
Option B. [tex]r=\sqrt{\frac{3V}{\pi h}}[/tex]
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
Solve for the radius r
That means-----> isolate the variable r
Multiply by 3 both sides
[tex]3V=\pi r^{2} h[/tex]
Divide by [tex](\pi h)[/tex] both sides
[tex]r^{2}=\frac{3V}{\pi h}[/tex]
square root both sides
[tex]r=\sqrt{\frac{3V}{\pi h}}[/tex]
If Caroline knows the height and the required volume of a cone-shaped vase, the formula she can use to determine the radius of the vase is: [tex]\mathbf{r = \sqrt{\frac{3V}{\pi h} } }[/tex]
What is the Volume of a Cone?Volume of cone (V) = 1/3πr²h
radius = r; height of cone = h
Having the height (h) and volume (V), find r:
1/3πr²h = V
(πr²h)/3 = V
πr²h = 3V
Divide both sides by πh
r² = 3V/πh
Take the square root of both sides
[tex]\mathbf{r = \sqrt{\frac{3V}{\pi h} } }[/tex]
Therefore, if Caroline knows the height and the required volume of a cone-shaped vase, the formula she can use to determine the radius of the vase is: [tex]\mathbf{r = \sqrt{\frac{3V}{\pi h} } }[/tex]
Learn more about the volume of a cone on:
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Back side lateral area and surface area
This is a regular pyramid. A regular pyramid is a right pyramid whose base is a regular polygon and whose apex is directly above the centre of the base. The lateral surface area is the sum of the areas of all the lateral faces while the surface area is the sum of all the lateral faces plus its base. In this exercise, the base is a square so this is also a square pyramid. Next, we have:
LATERAL SURFACE AREA:
For the lateral sides, we have four identical triangles, so the area of a triangle can be found as:
[tex]A=\frac{bh}{2} \\ \\ Where: \\ \\ b:base \\ \\ h:height[/tex]
and the lateral surface will be four times this value:
[tex]S_{L}=4A[/tex]
The base of the triangle is the same as the base of the square. So:
[tex]b=9yd[/tex].
On the other hand, the height of the triangle is the slant height of the pyramid, which is:
[tex]h=10yd[/tex]
So the area of a triangle is:
[tex]A=\frac{(9)(10)}{2} \\ \\ A=45yd^2[/tex]
Therefore:
[tex]S_{L}=4(45)\\ \\ \boxed{S_{L}=180yd^2}[/tex]
SURFACE AREA:
The surface area can be found as:
[tex]S=S_{L}+A_{b} \\ \\ Where: \\ \\ A_{b}: Area \ of \ the \ base \\ \\ S_{L}: Lateral \ surface[/tex]
Calculating the area of the base, which is a square, we have:
[tex]A_{b}=b^2 \\ \\ A_{b}=9^2 \\ \\ A_{b}=81yd^2[/tex]
Therefore:
[tex]S=180+81 \\ \\ \boxed{261yd^2}[/tex]
8. Find the lateral and surface area.In this case, we have another similar pyramid compared to the previous one, but we are given the height of the pyramid and we'll name it [tex]H[/tex] in capital letter. We know that the area of a triangle is:
[tex]A=\frac{bh}{2} \\ \\ Where: \\ \\ b:base \\ \\ h:height[/tex]
and the lateral surface will be:
[tex]S_{L}=4A[/tex]
To find [tex]h[/tex], which is the slant height of the pyramid, we need to use the Pythagorean theorem. Next, it is true that:
[tex]h=\sqrt{\left(\frac{b}{2}\right)^2+H^2} \\ \\ b=14 \\ H=12 \\ \\ h=\sqrt{\left(\frac{14}{2}\right)^2+12^2} \therefore h=\sqrt{193}[/tex]
So the area of a triangle is:
[tex]A=\frac{(14)(\sqrt{193})}{2} \\ \\ A=7\sqrt{193}ft^2[/tex]
Therefore:
[tex]S_{L}=4(7\sqrt{193})\\ \\ S_{L}=28\sqrt{193}ft^2 \approx 388.9884[/tex]
Rounding to the nearest tenth:
[tex]\boxed{S_{L}=389.0ft^2}[/tex]
SURFACE AREA:
We know that the surface area can be found as:
[tex]S=S_{L}+A_{b} \\ \\ Where: \\ \\ A_{b}: Area \ of \ the \ base \\ \\ S_{L}: Lateral \ surface[/tex]
Calculating the area of the base, which is a square, we have:
[tex]A_{b}=b^2 \\ \\ A_{b}=14^2 \\ \\ A_{b}=196ft^2[/tex]
Therefore:
[tex]S=28\sqrt{193}+196 \\ \\ S \approx 584.9884ft^2[/tex]
Rounding to the nearest tenth:
[tex]\boxed{S=585ft^2}[/tex]
9. Lateral surface area.Here Patrick is making a paper model of castle. He has a net, so he can fold it to build up a pyramid. That's amazing, right? Well, recall that for a pyramid like that the lateral surface area is the area of the lateral faces, that are all triangles. Thus, for a triangle:
[tex]A=\frac{bh}{2} \\ \\ Where: \\ \\ h: \ slant \ height \ of \ the \ pyramid \\ \\ b: base \ of \ the \ pyramid[/tex]
The slant height of the pyramid is [tex]h=20cm[/tex] because this is the same height of the triangle. On the other hand, the base is [tex]b=15cm[/tex]. So:
[tex]A=\frac{15(20)}{2} \\ \\ h=150cm^2[/tex]
Next the lateral surface area is:
[tex]S_{L}=4(150) \\ \\ \boxed{S_{L}=150cm^2}[/tex]
________________
THE OTHER ANSWERS HAVE BEEN ATTACHED BELOW.What is the solution to this system of equations? -3x+5y=-2 3x+7y=26
Answer: the first answer
.... Please mark branliest!!
Answer:
solution is (4,2)
Step-by-step explanation:
[tex]-3x+5y=-2[/tex]
[tex]3x+7y=26[/tex]
To solve for x and y , we use elimination method.
we add both equations.
[tex]-3x+5y=-2[/tex]
[tex]3x+7y=26[/tex]
---------------------------------
[tex]12y=24[/tex]
Divide both sides by 12
y=2
Now we find out x
[tex]-3x+5y=-2[/tex]
[tex]-3x+5(2)=-2[/tex]
[tex]-3x+10=-2[/tex]
Subtract 10 from both sides
[tex]-3x=-12[/tex]
Divide by -3 on both sides
x=4
So, solution is (4,2)
Here's an easy one for you! Change £x to pence.
Answer:
£x = 100x pence
Step-by-step explanation:
£1 = 100 pence
£x = 100x pence
Answer:
100x pence
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
We know that £1 = 100 pence so from this knowledge we can
£x = 100 p
I need help with this question on USA Test Prep
Answer choice C, 1.5 x 3= 4.5
your correct answer would be c. 3
Someone plz explain!
Answer:
18° and 72°
Step-by-step explanation:
Complimentary angles form 90°
We have an angle (x) 4 times larger than the other (y).
Well actually, a system of equations isn't required, so forget about x and y, just divide 90 by 5. This gives you 18, one of the angle's measurements is 18°. Multiply 18 by 4 and get 72. The other angle's measurement is 72°.
what is the value of x?
•4
•4√3
•8
•8√3
Answer:
4√3Step-by-step explanation:
Look at the picture.
We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
Therefore we have the equation:
[tex]x=\dfrac{8\sqrt3}{2}\\\\x=4\sqrt3[/tex]
A- 43
B- 48
C- 37
D- 24
A circle has 360°
Each percent of a circle represents 3.6°
Faucets contributed to 12% of the used water.
12 * 3.6° = 43.2°
A machine can pack a 3ft. by 2ft. by 1ft. carton with styrofoam “peanuts” in 7.5 seconds. How long would it take to fill a carton that measures 4ft by 6ft by 6ft? Possible answers: 180 sec, 45 sec, 20 sec, or 75 sec?
The answer is 180 seconds. The reason for this is that the second carton is 24 times the volume of the first one; so, the time taken to pack the container would be 24 times longer. This means that the answer would be found by the equation 7.5 * 24 which is evaluated to 180 seconds
To find out how long it would take to fill the larger carton, you can use the ratio of the volumes of the two cartons and the time it takes to fill the smaller carton. The formula to calculate the volume of a rectangular prism (like a carton) is:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
First, we calculate the volume of the original carton:
\[ \text{Original Carton Volume} = 3 \text{ ft} \times 2 \text{ ft} \times 1 \text{ ft} = 6 \text{ cubic feet} \]
Next, we calculate the volume of the new larger carton:
\[ \text{New Carton Volume} = 4 \text{ ft} \times 6 \text{ ft} \times 6 \text{ ft} = 144 \text{ cubic feet} \]
Now, you can find out how much bigger the new carton is compared to the original carton by taking the ratio of the volumes:
\[ \text{Volume Ratio} = \frac{\text{New Carton Volume}}{\text{Original Carton Volume}} = \frac{144}{6} = 24 \]
This ratio means the new carton is 24 times larger in volume than the original carton.
Given that it takes 7.5 seconds to fill the original carton, you can now calculate the time it would take to fill the new carton by multiplying the original time by the volume ratio:
\[ \text{Time to fill new carton} = \text{Original Time} \times \text{Volume Ratio} = 7.5 \text{ sec} \times 24 = 180 \text{ sec} \]
Therefore, it would take 180 seconds to fill the carton that measures 4ft by 6ft by 6ft.
In triangle XYZ, angle Z is a right angle. If sinX = 3/4, find tan Y.
ANSWER
[tex]{ \tan(y) } = \frac{ \sqrt{7} }{3}[/tex]
EXPLANATION
If
[tex] \sin(X )= \frac{3}{4} [/tex]
[tex] \sin(X )= \frac{opposite}{hypotenuse} [/tex]
This implies that the opposite is 3 units and the hypotenuse is 4 units.
We now find the adjacent side using the Pythagoras Theorem.
[tex] {a}^{2} + {o}^{2} = {h}^{2} [/tex]
[tex] {a}^{2} + {3}^{2} = {4}^{2} [/tex]
[tex]{a}^{2} + 9 =16[/tex]
[tex] {a}^{2} =16 - 9[/tex]
[tex]{a}^{2} = 7[/tex]
[tex]{a}= \sqrt{7} [/tex]
[tex] { \tan(y) } = \frac{opposite}{adjacent} [/tex]
The side opposite to Y is √7 and the side adjacent to Y is 3.
[tex] { \tan(y) } = \frac{ \sqrt{7} }{3} [/tex]
two times a number plus 8 is the same as 20 minus the number
Answer:
2x+8=20-x
Step-by-step explanation:
if it is an equation you are asking that will be it
2x + 8=20 - x
That is the equation. As you are reading the sentence try writing down exactly what it says. “2 times a number” We know that “times” means multiply, but what are we multiplying. It says to multiply 2 and a number, but we don’t know that number so we call it “x.” Then, it says “plus 8” or add 8. From that information we should come up with the expression 2x + 8. Then, it states “is the same as” which basically means equal to or =. Finally, it states “20 minus the number.” We subtract 20 and the number which can be shown as 20 - x.
All together the equation is written as 2x + 8=20 - x
We can simply do this by writing exactly what the sentence states in the order that it is written.
The function below describes the population of caribou in a tundra, where f(t) represents the number of caribou, in hundreds, and t represents the time, in years.
f(t)=1.8(1.2)^t
Initially, the tundra has _____ caribou, and every ____ , the number of caribou increases by a factor of ____ .
Answer:
Initially, the tundra has 180 caribou, and every year , the number of caribou increases by a factor of 1.2 .
Step-by-step explanation:
"Initially" generally means "when t=0." Put 0 where t is in the function and evaluate it:
f(0) = 1.8(1.2)^0 = 1.8(1) = 1.8 . . . . . hundreds
1.8 hundreds is 1.8×100 = 180.
__
t is in years, so the simplest choice for the second blank in the statement is "year".
__
The exponent of 1.2 is t, which means that 1.2 is a factor of the expression the number of times specified by t.
for t=0, f(0) = 1.8
for t=1, f(1) = 1.8(1.2)
for t=2, f(2) = 1.8(1.2)(1.2)
for t=3, f(3) = 1.8(1.2)(1.2)(1.2)
Perhaps you can see that every year, the number increases by a factor of 1.2.
_____
You could put "3 years" in the second blank, then the third blank would be 1.2³ = 1.728. While correct, it is probably not what is expected by your answer checker.
Answer:
180
1 year
1.2
Step-by-step explanation:
got it correct on edmentum
8 * 4.9999a(345.5 x .98)^9
Answer:
Step-by-step explanation:
Always do what is inside the brackets first.
345.5 * 0.98 = 338.59
Now raise this to the 9th power.
338.58^9 = 5.8488*10^22
You are now finished with the brackets.
8*4.9999a = 39.9992a
Now multiply by 5.84 * 10^22
2.3395 * 10^24
need help asap. !!!
3.5
3
4.5
4.2
Answer:
B
Step-by-step explanation:
Since the line segment JK is tangent to the circle C, it creates a 90° angle at the point of intersection.
This means that we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
Plug in the values given.
[tex]24^2+b^2=28^2 \\ \\ 576+b^2=784 \\ \\ b^2=208 \\ \\ b=\sqrt{208} \\ \\ b=14.4[/tex]
The answer would be B I think
Both circles have the same center. The circumference of the inner circle is 77.872 centimeters. What is the area of the shaded region?
Answer:
The area of the shaded region is [tex]875.68\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the large circle minus the area of the inner circle
step 1
Find the radius of the inner circle
we know that
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=77.872\ cm[/tex]
substitute and solve for r
[tex]77.872=2(3.14)r[/tex]
[tex]r=77.872/[2(3.14)]=12.4\ cm[/tex]
step 2
Find the radius of the large circle
[tex]r=12.4+8.4=20.8\ cm[/tex]
step 3
Find the area of the shaded region
[tex]A=(3.14)[20.8^{2} -12.4^{2}]= 875.68\ cm^{2}[/tex]
The area of the shaded region is: 875.60 square centimeters
What is the area of the shaded region?The formula for the circumference of a circle is:
C = 2πr
where:
C is Circumference
r is radius
We are told the the circumference of the inner circle is 77.872 cm
Thus:
2πr = 77.872
r = 77.872/2π
r = 12.39 cm
Total radius of larger circle = 12.39 + 8.4 = 20.79 cm
Area of larger circle = π * 20.79²
Area of larger circle = 1357.87 cm²
Area of smaller circle is: π * 12.39²
Area of smaller circle is: 482.27 cm²
The area of the shaded region = 1357.87 cm² - 482.27 cm²
The area of the shaded region = 875.60 square centimeters
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Plsssssssss helpppppp asapasap!
Answer:
Step-by-step explanation:
-8
Answer: First option.
Step-by-step explanation:
We need to remember that:
[tex]\sqrt[n]{a^n}=a[/tex]
[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]
And, according to the Power of a power property we know that:
[tex](a^m)^n=a^{(mn)}[/tex]
Knowing this, we can descompose 32 into its prime factors:
[tex]32=2*2*2*2*2=2^5[/tex]
Then we can rewrite the expression as:
[tex]=\sqrt[5]{(-32)^3}\\\\=\sqrt[5]{(-2^5)^3}[/tex]
Finally, simplifying the expression, we get:
[tex]=\sqrt[5]{(-2)^{15}}\\\\=(-2)^3\\\\=-8[/tex]
This matches with the first option.
How to find the area of a polygon
The method of calculating the area of a polygon depends on the type of polygon. Rectangles and triangles have straightforward calculations, however complex polygons might need to be divided into simpler figures. Certain figures such as circles and ellipses have unique formulas.
Explanation:Calculating the area of a polygon depends on the type of polygon. For simple regular polygons like a rectangle, area can be found by length x width, for triangles it's base x height / 2. In particular complex polygons, the shape might need to be divided into simpler shapes, and the areas calculated separately.
For a circle, the area A = πr², where r is the radius. If you're trying to find the area of an ellipse, it can be calculated by A = πab, with a and b being half the long and short axis respectively.
The process to determine the area of a frequency polygon is little complex. First, the range of each class interval must be determined, and then multiplied by the frequency of that interval, with these values then being added together.
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To find the area of a polygon, you can divide it into smaller shapes with known area and add them up. Alternatively, you can use the formula for the area of a regular polygon.
Explanation:To find the area of a polygon, you can use different formulas depending on the type of polygon. One general method is to divide the polygon into smaller shapes whose area you know how to calculate, such as triangles or rectangles, and then add up the areas of those shapes. For example, to find the area of a rectangle, you multiply its length by its width.
Another method is to use the formula for the area of a regular polygon, which is given by the formula: Area = 1/2 * ap, where 'a' is the apothem (the distance from the center of the polygon to the middle of one of its sides) and 'p' is the perimeter of the polygon.
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A rectangular prism was sliced parallel to one of its faces resulting in a 4 x 8 cross-section. Which could have been the dimensions of the prism?
A. 2 x 4 x 2
B. 4 x 8 x 3
C. 2 x 2 x 2
D. 8 x 2 x 2
Answer:
Option B. 4 x 8 x 3
Step-by-step explanation:
we know that
If the resulting cross-section is a rectangular figure with dimensions of 4x8
then
one of the dimensions of the prism must be 4 and another of the dimensions of the prism must be 8
You invest $5,175 in a stock plan. It increases 9% the first year then loses 5% of its value the second year. What is your gain compared to your original investment?
A. 183.71
B. 195.65
C. 201.14
D. 185.21
Answer:
A. 183.71
Step-by-step explanation:
Original investment in stock plan = $5175
Increase in the first year of investment in stock plan = 9% of $5175
= 0.09 ( $5175)
= $465.75
then new value of investment in stock plan = $5175 + $465.75 = $5640.75
Loss in the investment of stock plan = 5% of $5640.75
= 0.05 ( $5640.75)
= $282.0375
then new value of investment in stock plan = $5640.75 - $282.0375 = $5358.7125
Now let's find difference between latest value and the original value of investment
$5358.7125 - $5175 = $183.7125
Hence choice A. 183.71 is correct.
Solve for p.
2(p + 1) = 18
Answer:
p = 8
Step-by-step explanation:
Subtract 18 from behind the equal sign to cancel it out. This leaves you with 2(p+1)- 18= 0.
Next you'll need to pull out the terms to work with the beginning of the problem. 2(p+1)- 18= 0 would turn into 2p - 16 = 2(p - 8).
This would leave you with 2= 0, but that's not true so continue on to the variable.
So p - 8= 0 making the answer p = 8