Answers
Answer:
The correct option is;
a. 12 pie cm
Step-by-step explanation:
Cavalieri's principle states that if the cross-sectional area of two or more figures of the same altitude are the same at each level of the figures, then the volumes of the figures are also the same;
Given that the base area of the square based prism and the cylinder are the same, and that the square based prism and the cylinder have equal height of 4 cm, then by Cavalieri's principle, their volumes are the same
The volume of the square based prism = 452 cm³
Therefore, the volume of the cylinder (of equal base area) = 452 cm³
The formula for the volume of square based prism = Area of base × Height
∴ The volume of square based prism, 452 cm³ = Area of base × 4 cm
Which gives;
Area of the base of the square based prism = 452/4 = 113 cm²
The area of the base of the cylinder [tex]A_c[/tex] = The area of the base of the square based prism = 113 cm²
The area of the base of the cylinder,[tex]A_c[/tex] is given by the following equation;
[tex]A_c[/tex] = π×r² = 113 cm²
r = √(113/π) = √35.97 ≈ √36 = 6 cm
The circumference of the base of the cylinder,[tex]C_c[/tex] is given by the following equation
[tex]C_c[/tex] = 2×π×r ≈ 2×π×6 = 12×π cm
The correct option is 12 pie cm.
Related Questions
I need hellp please its my last chance to become a senior please someone
Answers
Answer:
d= 6
r= 6/2
r=3
V= π. r². h
V= π . 3². 14
V= π. 9 . 14
V= π 126 cm³
V= 126 π cm³ (π not in number)
hope it helps^°^
Answer:if you use the formula it is 126 pi cm cubed
The answer is c
Step-by-step explanation:
AB =
Round your answer to the nearest hundredth.
B
?
2
25°
С
A
Answers
Answer:
? = 4.73
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opp / hyp
sin 25 = 2 / ?
? sin 25 = 2
? = 2 / sin 25
? =4.732403166
To the nearest hundredth
? = 4.73
Your mother has left you in charge of the annual family yard sale. Before she leaves you to your entrepreneurial abilities, she explains that she has made the job easy for you: everything costs either $1.50 or $3.50. She asks you to keep track of how many of each type of item is sold, and you make a list, but it gets lost sometime throughout the day. Just before she’s supposed to get home, you realize that all you know is that there were 150 items to start with (your mom counted) and you have 41 items left. Also, you know that you made $227.50. Write a system of equations that you could solve to figure out how many of each type of item you sold.
A) x + y = 109
(1.5)x + 227.50 = (3.5)y
B) x + y = 109
(3.5)x + 227.50 = (1.5)y
C) x + y = 41
(1.5)x + 227.50 = (3.5)y
D) x + y = 109
(1.5)x + (3.5)y = 227.50
E) x + y = 150
(1.5)x + (3.5)y = 227.50
F) x + y = $3.50
(1.5)x + (3.5)y = 227.50
Answers
Answer:
[tex]D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50[/tex]
Step-by-step explanation:
Let the items sold with price $1.5 = [tex]x[/tex]
Let the items sold with price $3.5 = [tex]y[/tex]
Initially, total number of items = 150
Items left at the end of the day = 41
So, number of items sold throughout the day = Total number of items - Number of items left
Number of Items sold = 150 - 41 = 109
So, the first equation can be written as:
[tex]\bold{x+y = 109} ....... (1)[/tex]
Now, let us calculate the sales done by each item.
Sales from item with price $1.5 = Number of items sold [tex]\times[/tex] price of each item
= (1.5)[tex]x[/tex]
Sales from item with price $3.5 = Number of items sold [tex]\times[/tex] price of each item
= (3.5)[tex]y[/tex]
Total sales = [tex]\bold{(1.5)x+(3.5)y = 227.50} ....... (2)[/tex]
So, the correct answer is:
[tex]D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50[/tex]
PLEASE HELP
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square.
Answers
Answer:
perimeter is 4 sqrt(29) + 4pi cm
area is 40 + 8pi cm^2
Step-by-step explanation:
We have a semicircle and a triangle
First the semicircle with diameter 8
A = 1/2 pi r^2 for a semicircle
r = d/2 = 8/2 =4
A = 1/2 pi ( 4)^2
=1/2 pi *16
= 8pi
Now the triangle with base 8 and height 10
A = 1/2 bh
=1/2 8*10
= 40
Add the areas together
A = 40 + 8pi cm^2
Now the perimeter
We have 1/2 of the circumference
1/2 C =1/2 pi *d
= 1/2 pi 8
= 4pi
Now we need to find the length of the hypotenuse of the right triangles
using the pythagorean theorem
a^2+b^2 = c^2
The base is 4 ( 1/2 of the diameter) and the height is 10
4^2 + 10 ^2 = c^2
16 + 100 = c^2
116 = c^2
sqrt(116) = c
2 sqrt(29) = c
Each hypotenuse is the same so we have
hypotenuse + hypotenuse + 1/2 circumference
2 sqrt(29) + 2 sqrt(29) + 4 pi
4 sqrt(29) + 4pi cm
Step-by-step explanation:
First we need to deal with the half circle. The radius of this circle is 4, because the diameter is 8. The formula for the circumference of a circle is 2piR.
2pi4 so the perimeter for the half circle would be 8pi/2.
The area of that half circle would be piR^2 so 16pi/2.
Now moving on the triangle part, we need to find the hypotenuse side of AC. We will use the pythagoram theorem. 4^2+10^2=C^2
16+100=C^2
116=C^2
C=sqrt(116)
making the perimeter of this triangle 2×sqrt(116)
The area of this triangle is 8×10=80, than divided by 2 which is equal to 40.
We than just need to add up the perimeters and areas for both the half circle and triangle.
The area would be equal to 8pi+40
The perimeter would be equal to 4pi+4(sqrt(29))
1. Suzette ran and biked for a total of 80 miles in 9 hours. Her average running speed was 5 miles per hour (mph) and her average biking speed was 12 mph. Let x = total hours Suzette ran. Let y = total hours Suzette biked. Use substitution to solve for x and y. Show your work. Check your solution. (a) How many hours did Suzette run? (b) How many hours did she bike?
Answers
Answer:
a) Suzette ran for 4 hours
b) Suzette biked for 5 hours
Step-by-step explanation:
Speed is rate of distance traveled, it is the ratio of distance traveled to time taken. It is given by:
Speed = distance / time
The total distance ran and biked by Suzette (d) = 80 miles, while the total time ran and biked by Suzette (t) = 9 hours.
For running:
Her speed was 5 miles per hour, let the total hours Suzette ran be x and the total distance she ran be p, hence since Speed = distance / time, therefore:
5 = p / x
p = 5x
For biking:
Her speed was 12 miles per hour, let the total hours Suzette ran be y and the total distance she ran be q, hence since Speed = distance / time, therefore:
12 = q / y
q = 12y
The total distance ran and biked by Suzette (d) = Distance biked + distance ran
d = p + q
80 = p + q
80 = 5x + 12y (1)
The total time taken to run and bike by Suzette (t) = time spent to bike + time spent to run
t = x + y
9 = x + y (2)
Solving equation 1 and equation 2, multiply equation 2 by 5 and subtract from equation 1:
7y = 35
y = 35/7
y = 5 hours
Put y = 5 in equation 2:
9 = x + 5
x = 9 -5
x = 4 hours
a) Suzette ran for 4 hours
b) Suzette biked for 5 hours
Complete the square to transform the expression x2 - 2x - 2 into the form a(x - h)2 + k
Answers
Answer:
A
Step-by-step explanation:
Find the vertex form of the quadratic function below.
y = x^2 - 4x + 3
This quadratic equation is in the form y = a{x^2} + bx + cy=ax
2
+bx+c. However, I need to rewrite it using some algebraic steps in order to make it look like this…
y = a(x - h)^2 + k
This is the vertex form of the quadratic function where \left( {h,k} \right)(h,k) is the vertex or the “center” of the quadratic function or the parabola.
Before I start, I realize that a = 1a=1. Therefore, I can immediately apply the “completing the square” steps.
STEP 1: Identify the coefficient of the linear term of the quadratic function. That is the number attached to the xx-term.
STEP 2: I will take that number, divide it by 22 and square it (or raise to the power 22).
STEP 3: The output in step #2 will be added and subtracted on the same side of the equation to keep it balanced.
Think About It: If I add 44 on the right side of the equation, then I am technically changing the original meaning of the equation. So to keep it unchanged, I must subtract the same value that I added on the same side of the equation.
STEP 4: Now, express the trinomial inside the parenthesis as a square of a binomial, and simplify the outside constants.
After simplifying, it is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)
2
+k where the vertex \left( {h,k} \right)(h,k) is \left( {2, - 1} \right)(2,−1).
Visually, the graph of this quadratic function is a parabola with a minimum at the point \left( {2, - 1} \right)(2,−1). Since the value of “aa” is positive, a = 1a=1, then the parabola opens in upward direction.
Example 2: Find the vertex form of the quadratic function below.
The approach to this problem is slightly different because the value of “aa” does not equal to 11, a \ne 1a
=1. The first step is to factor out the coefficient 22 between the terms with xx-variables only.
STEP 1: Factor out 22 only to the terms with variable xx.
STEP 2: Identify the coefficient of the xx-term or linear term.
STEP 3: Take that number, divide it by 22, and square.
STEP 4: Now, I will take the output {9 \over 4}
4
9
and add it inside the parenthesis.
By adding {9 \over 4}
4
9
inside the parenthesis, I am actually adding 2\left( {{9 \over 4}} \right) = {9 \over 2}2(
4
9
)=
2
9
to the entire equation.
Why multiply by 22 to get the “true” value added to the entire equation? Remember, I factored out 22 in the beginning. So for us to find the real value added to the entire equation, we need to multiply the number added inside the parenthesis by the number that was factored out.
STEP 5: Since I added {9 \over 2}
2
9
to the equation, then I should subtract the entire equation by {9 \over 2}
2
9
also to compensate for it.
STEP 6: Finally, express the trinomial inside the parenthesis as the square of binomial and then simplify the outside constants. Be careful combining the fractions.
It is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)
2
+k where the vertex \left( {h,k} \right)(h,k) is \left( {{{ - \,3} \over 2},{{ - 11} \over 2}} \right)(
2
−3
,
2
−11
).
Example 3: Find the vertex form of the quadratic function below.
Solution:
Factor out - \,3−3 among the xx-terms.
The coefficient of the linear term inside the parenthesis is - \,1−1. Divide it by 22 and square it. Add that value inside the parenthesis. Now, figure out how to make the original equation the same. Since we added {1 \over 4}
4
1
inside the parenthesis and we factored out - \,3−3 in the beginning, that means - \,3\left( {{1 \over 4}} \right) = {{ - \,3} \over 4}−3(
4
1
)=
4
−3
is the value that we subtracted from the entire equation. To compensate, we must add {3 \over 4}
4
3
outside the parenthesis.
Therefore, the vertex \left( {h,k} \right)(h,k) is \left( {{1 \over 2},{{11} \over 4}} \right)(
2
1
,
4
11
).
Example 4: Find the vertex form of the quadratic function below.
y = 5x^2 + 15x - 5
Solution:
Factor out 55 among the xx-terms. Identify the coefficient of the linear term inside the parenthesis which is 33. Divide it by 22 and square to get {9 \over 4}
4
9
.
Add {9 \over 4}
4
9
inside the parenthesis. Since we factored out 55 in the first step, that means 5\left( {{9 \over 4}} \right) = {{45} \over 4}5(
4
9
)=
4
45
is the number that we need to subtract to keep the equation unchanged.
Express the trinomial as a square of binomial, and combine the constants to get the final answer.
Therefore, the vertex \left( {h,k} \right)(h,k) is {{ - \,3} \over 2},{{ - \,65} \over 4}
2
−3
,
4
−65
.
Answer:
(x - 1 )^2 - 3
Step-by-step explanation:
( x - 1 )^2 + ( -3)
x^2 - 2x + 1 - 3
x^2 - 2x - 2
Will give Brainliest, Please show work.
Answers
Answer:
Hi, there!!
Hope you mean the answers in the solution.
Hope it helps...
Answer:
Step-by-step explanation:
7)
JKLM is a isosceles trapezium.
KL // JM
∠K + ∠J = 180 {Co interior angles}
50 +∠J = 180
∠J = 180 - 50
∠J = 130
As it is isosceles, non parallel sides KJ = LM &
∠L = ∠K
∠L = 50
∠M = ∠J
∠M = 130
8)JKLM is a isosceles trapezium.
KL // JM
∠K + ∠J = 180 {Co interior angles}
100 +∠J = 180
∠J = 180 - 100
∠J = 80
As it is isosceles, non parallel sides KJ = LM &
∠L = ∠K
∠L = 100
∠M = ∠J
∠M = 80
Which of the following best describes the graph shown below?
16
A1
1
14
O A This is the graph of a linear function
B. This is the graph of a one-to-one function
C. This is the graph of a function, but it is not one to one
D. This is not the graph of a function
Answers
The vertical line test helps us see that we have a function. Note how it is not possible to draw a single straight line through more than one point on the curve. Any x input leads to exactly one y output. This graph passes the vertical line test. Therefore it is a function.
The function is not one-to-one because the graph fails the horizontal line test. Here it is possible to draw a single straight horizontal line through more than one point on the curve. The horizontal line through y = 2 is one example of many where the graph fails the horizontal line test, meaning the function is not one-to-one.
The term "one-to-one" means that each y value only pairs up with one x value. Here we have something like y = 2 pair up with multiple x values at the same time. This concept is useful when it comes to determining inverse functions.
20. A pool holds 1440 cubic feet of water, the city charges $1.75 per cubic meter of water used.
How much will it cost to fill the pool?
Answers
Answer:Conversion units
Step-by-step explanation: 1 ft^3= 0.028m^3 .: 1440ft^3=40.776m^3, so $1.75x40.776=$71.358~ $71.36.:
Answer:
$71.36
Step-by-step explanation:
1 foot = 0.3048 metros
1 cubic feet = (0.3048metros)³ = 0.02932 cubic meters (aprox.)
1440 cubic feet = 1440*0.02932 = 40.7763 m
$1.75 por cubic meter:
1.75*40.7763 = $71.36
Consider the following system of equations: y=2x−2 6x+3y=2 The graph of these equations consists of two lines that: 1. intersect at more than one point. 2. intersect in an infinite number of points. 3. intersect at exactly one point. 4. do not intersect.
Answers
Answer:
3. Intersect at exactly one point. ( (2/3), (-2/3) )
Step-by-step explanation:
To make the comparison of these lines easier, let's rewrite the 2nd equation into slope-intercept form, as the 1st equation is in slope-intercept form.
[1] y = 2x - 2
---------------------
[2] 6x + 3y = 2 ==> 3y = 2 - 6x ==> y = -2x + (2/3)
[2] y = -2x + (2/3)
So now that we have both equations in slope-intercept form, we can see that the two equations are both linear, have different slopes, and have different y-intercepts.
Since these equations have both different slopes and different y-intercepts, we know that the lines will cross at least one point. We can confirm that the lines only cross at a single point using the fact that both equations are linear, meaning there will only be one point of crossing. To find that point, we can simply set the equations equal to each other.
y = 2x - 2
y = -2x + (2/3)
2x - 2 = -2x + (2/3)
4x = (8/3)
x = (8/12) = (2/3)
And plug this x value back into one of the equations:
y = 2x - 2
y = 2(2/3) - 2
y = (4/3) - (6/3)
y = (-2/3)
Thus these lines only cross at the point ( (2/3), (-2/3) ).
Cheers.
Answer:
I don't understand the question
I need help asap!!!
Answers
how do you solve 2m-10=44+8m
Answers
Answer:
m = -9
Step-by-step explanation:
2m-10=44+8m
Subtract 2m from each side
2m-2m-10=44+8m-2m
-10 = 44+6m
Subtract 44 from each side
-10-44 = 44-44+6m
-54 = 6m
Divide by 6
-54/6 = 6m/6
-9 = m
Answer:
solve by solving the salvation for equation don't be a slave get educated from what's gave
What the relation of 1/c=1/c1+1/c2 hence find c
Answers
[tex]\frac 1c=\frac1{c_1}+\frac1{c_2} [/tex]
$\frac1c=\frac{c_1+c_2}{c_1c_2}$
$\implies c=\frac{c_1c_2}{c_1+c_2}$
PLEaSE HELP!!!!!! will give brainliest to first answer
Answers
Answer:
The coordinates of A'C'S'T' are;
A'(-7, 2)
C'(-9, -1)
S'(-7, -4)
T'(-5, -1)
The correct option is;
B
Step-by-step explanation:
The coordinates of the given quadrilateral are;
A(-3, 1)
C(-5, -2)
S(-3, -5)
T(-1, -2)
The required transformation is T₍₋₄, ₁₎ which is equivalent to a movement of 4 units in the leftward direction and 1 unit upward
Therefore, we have;
A(-3, 1) + T₍₋₄, ₁₎ = A'(-7, 2)
C(-5, -2) + T₍₋₄, ₁₎ = C'(-9, -1)
S(-3, -5) + T₍₋₄, ₁₎ = S'(-7, -4)
T(-1, -2) + T₍₋₄, ₁₎ = T'(-5, -1)
Therefore, the correct option is B
3/4a−16=2/3a+14 PLEASE I NEED THIS QUICK and if you explain the steps that would be geat:) Thank youuuuuuu
Answers
Answer:
360
Step-by-step explanation:
3/4a - 16 = 2/3a + 14 ⇒ collect like terms 3/4a - 2/3a = 14 + 16 ⇒ bring the fractions to same denominator9/12a - 8/12a = 30 ⇒ simplify fraction1/12a = 30 ⇒ multiply both sides by 12a = 30*12a = 360 ⇒ answerprove tan(theta/2)=sin theta/1+cos theta for theta in quadrant 1 by filling in the calculations and reasons. PLEASE HELP!!!!
Answers
Answer:
See explanation
Step-by-step explanation:
We have to prove the identity
[tex]tan(\frac{\Theta }{2})=\frac{sin\Theta}{1+cos\Theta }[/tex]
We will take right hand side of the identity
[tex]\frac{sin\Theta}{1+cos\Theta}=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{1+[2cos^{2}(\frac{\Theta }{2})-1]}[/tex]
[tex]=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{2cos^{2}(\frac{\Theta }{2})}=\frac{sin(\frac{\Theta }{2})}{cos(\frac{\Theta }{2})}[/tex]
[tex]=tan(\frac{\Theta }{2})[/tex] [ Tan θ will be positive since θ lies in 1st quadrant ]
The graph below shows Roy's distance from his office (y), in miles, after a certain amount of time (x), in minutes: Graph titled Roys Distance Vs Time shows 0 to 10 on x and y axes at increments of 1.The label on x axis is time in minutes and that on y axis is Distance from Office in miles. Lines are joined at the ordered pairs 0, 0 and 1, 1 and 2, 2 and 3, 3 and 4, 4 and 5, 4 and 6, 4 and 7, 4.5 and 7.5, 5 and 8, 6. Four students described Roy's motion, as shown in the table below: Student Description Peter He drives a car at a constant speed for 4 minutes, then stops at a crossing for 6 minutes, and finally drives at a variable speed for the next 2 minutes. Shane He drives a car at a constant speed for 4 minutes, then stops at a crossing for 2 minutes, and finally drives at a variable speed for the next 8 minutes. Jamie He drives a car at a constant speed for 4 minutes, then stops at a crossing for 6 minutes, and finally drives at a variable speed for the next 8 minutes. Felix He drives a car at a constant speed for 4 minutes, then stops at a crossing for 2 minutes, and finally drives at a variable speed for the next 2 minutes. Which student most accurately described Roy's motion? Peter Shane Jamie Felix
Answers
Answer:
Felix
Step-by-step explanation:
The graph contains 3 segments,
first one is for the first 4minutes,
second one is for the next 2 minutes (standing still)
third one is for the last 2 minutes.
Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end. (e.g., from 4 to 6 is 2 minutes).
The student that most accurately described Roy's motion is Felix.
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
We need to find the student that most accurately described Roy's motion.
Here we can see that the graph contains 3 segments, first one is for the first 4 minutes, Second one is for the next 2 minutes (standing still) and the third one is for the last 2 minutes.
Now, Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end.
Therefore, the student that most accurately described Roy's motion is Felix.
Learn more about finding the graphed function here:
https://brainly.com/question/27330212
#SPJ5
State whether the given measurements determine zero, one, or two triangles. A = 58°, a = 25, b = 28
Answers
Answer:
1
Step-by-step explanation:
I believe it is 1. Just picture or draw a diagram of the constraints. Don't quote me on this though...
Answer:
Step-by-step explanation:
apply sine formula
[tex]\frac{a}{sin ~A} =\frac{b}{sin~B} \\\frac{25}{sin~58} =\frac{28}{sin ~B} \\sin~B=\frac{28}{25} \times sin~58\\B=sin^{-1} (\frac{28}{25} \times sin ~58)=71.77 \approx 72 ^\circ[/tex]
so third angle=180-(58+72)=180-130=50°
∠C=50°
[tex]cos ~C=\frac{a^2+b^2-c^2}{2ab} \\or ~2abcos~C=a^2+b^2-c^2\\2*25*28*cos ~50=25^2+28^2-c^2\\c^2=625+784-1400 *cos~50\\c^2=1409-899.90\\c^2=509.1\\c=\sqrt{509.1} \approx 22.56 \approx 22.6[/tex]
so one triangle is formed.
The equation of line WX is 2x + y = −5. What is the equation of a line perpendicular to line WX in slope-intercept form that contains point (−1, −2)?
Answers
Answer: [tex]y=\dfrac12x-\dfrac{3}{4}[/tex]
Step-by-step explanation:
Given, The equation of line WX is 2x + y = −5.
It can be written as [tex]y=-2x-5[/tex] comparing it with slope-intercept form y=mx+c, where m is slope and c is y-intercept, we have
slope of WX = -2
Product of slopes of two perpendicular lines is -1.
So, (slope of WX) × (slope of perpendicular to WX)=-1
[tex]-2\times\text{slope of WX}=-1\\\\\Rightarrow\ \text{slope of WX}=\dfrac{1}{2}[/tex]
Equation of a line passes through (a,b) and has slope m:
[tex]y-b=m(x-a)[/tex]
Equation of a line perpendicular to WX contains point (−1, −2) and has slope [tex]=\dfrac12[/tex]
[tex]y-(-2)=\dfrac{1}{2}(x-(-1))\\\\\Rightarrow\ y+2=\dfrac12(x+1)\\\\\Rightarrow\ y+2=\dfrac12x+\dfrac12\\\\\Rightarrow\ y=\dfrac12x+\dfrac12-2\\\\\Rightarrow\ y=\dfrac12x-\dfrac{3}{4}[/tex]
Equation of a line perpendicular to line WX in slope-intercept form that contains point (−1, −2) [tex]:y=\dfrac12x-\dfrac{3}{4}[/tex]
Given the equations of a straight line f(x) (in slope-intercept form) and a parabola g(x) (in standard form), describe how to determine the number of intersection points, without finding the coordinates of such points. Do not give an example.
Answers
Answer:
Step-by-step explanation:
Hello, when you try to find the intersection point(s) you need to solve a system like this one
[tex]\begin{cases} y&= m * x + p }\\ y &= a*x^2 +b*x+c }\end{cases}[/tex]
So, you come up with a polynomial equation like.
[tex]ax^2+bx+c=mx+p\\\\ax^2+(b-m)x+c-p=0[/tex]
And then, we can estimate the discriminant.
[tex]\Delta=(b-m)^2-4*a*(c-p)[/tex]
If [tex]\Delta<0[/tex] there is no real solution, no intersection point.
If [tex]\Delta=0[/tex] there is one intersection point.
If [tex]\Delta>0[/tex] there are two real solutions, so two intersection points.
Hope this helps.
Cam’s tent (shown below) is a triangular prism.
Find the surface are, including the floor of his tent
PLEASE HELP
Answers
Answer:
21.4 m²
Step-by-step explanation:
To find the surface area of this whole triangular prism, we have to look at the bases (the triangles), find their surface area, then look at the sides (the rectangles) and find theirs.
Let's start with the triangles. The area of any triangle is [tex]\frac{bh}{2}[/tex]. The base of this triangle is 2m (because there are 2 one meters) and the height is 1.7m.
[tex]\frac{2\cdot1.7}{2} = \frac{3.4}{2} = 1.7[/tex]
So the area of one of these triangles is 1.7m. Multiplying this by two, because there are two triangles in this prism:
[tex]1.7\cdot2=3.4[/tex]
Now let's find the area of the sides.
The side lengths are 2 and 3, so
[tex]2\cdot3=6[/tex], and there are 3 sides (including the bottom/floor) so [tex]6\cdot3=18[/tex].
Now we add.
[tex]18+3.4=21.4[/tex] m².
Hope this helped!
Answer: 21.4 square meters^2
Step-by-step explanation:
Shaquira is baking cookies to put in packages for a fundraiser. Shaquira has made 86 8686 chocolate chip cookies and 42 4242 sugar cookies. Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies. What is the greatest number of identical packages that Shaquira can make?
Answers
Answer: 2
Step-by-step explanation:
Given: Shaquira has made 86 chocolate chip cookies and 42 sugar cookies.
Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.
Now, the greatest number of identical packages that Shaquira can make= GCD of 86 and 42
Prime factorization of 86 and 42:
86 = 2 ×43
42 = 2 × 3 × 7
GCD of 86 and 42 = 2 [GCD = greatest common factor]
Hence, the greatest number of identical packages that Shaquira can make =2
How do u simplify each expression by combining like terms?
Answers
Answer:
1. 8y - 9y = -1y
( 8 - 9 = -1)
3. 8a - 6 +a - 1
( i have showed the like terms here)
8a - 1a= 7a
-6 - 1 = -7
7a - 7
5. -x - 2 + 15x
( i have showed the like terms here)
-x + 15x = 14x
(x = 1)
14x + 2
7. 8d - 4 - d - 2
( i have showed the like terms here)
8d - d = 7d
-4 -2 = -6
7d - 6
8. 9a + 8 - 2a - 3 - 5a
( i have showed the like terms here)
9a - 2a - 5a = 2a
8 - 3= 5
2a + 5
Two co-interior angles
formed between the
two parallel lines are in the ratio of 11.7.
Find the measures
of angles
Answers
Answer:
110° and 70°
Step-by-step explanation:
The angles are supplementary, thus sum to 180°
sum the parts of the ratio, 11 + 7 = 18
divide 180° by 18 to find the value of one part of the ratio
180° ÷ 18 = 10° ← value of 1 part of the ratio
Thus
11 parts = 11× 10° = 110°
7 parts = 7 × 10° = 70°
The angles are 110° and 70°
X-5y=-15x−5y=−15x, minus, 5, y, equals, minus, 15 Complete the missing value in the solution to the equation. (-5,(−5,left parenthesis, minus, 5, comma ))
Answers
Answer:
The missing value is 2. The coordinate will be (-5, 2)Step-by-step explanation:
The question is not properly written. Find the correct question below.
If x – 5y = -15 . Complete the missing value in the solution to the equation (-5, ____)
Let the coordinate of the variables be (x, y). Comparing the coordinates (x, y) with the given coordinate (-5, __), we will discover that x = -5. To get the y coordinate, we will substitute x = -5 into the given expression as shown;
If x – 5y = -15
-5 - 5y = -15
Adding 5 both sides
-5-5y+5 = -15+5
-5y = -10
Dividing both sides by -5;
-5y/-5 = -10/-5
y = 2
Hence the missing value in the solution of the equation is 2. The coordinate will be (-5, 2)
Answer:
2
Step-by-step explanation:
I did the khan :)
Use the discriminant to determine the number of real solutions to the equation. −8m^2+2m=0
Answers
Answer:
discriminant is b²-4ac
= 2²-4(-8)(0)
= 0
one solution
hope this helps :)
I need help fast please
Answers
Answer:
Difference : 4th option
Step-by-step explanation:
The first thing we want to do here is to factor the expression x² + 3x + 2. This will help us if it is similar to the factored expression " ( x + 2 )( x + 1 ). " The denominators will be the same, and hence we can combine the fractions.
x² + 3x + 2 - Break the expression into groups,
( x² + x ) + ( 2x + 2 ) - Factor x from x² + x and 2 from 2x + 2,
x( x + 1 ) + 2( x + 2 ) - Group,
( x + 2 )( x + 1 )
This is the same as the denominator of the other fraction, and therefore we can combine the fractions.
x - 1 / ( x + 2 )( x + 1 )
As you can see this is not any of the options present, as we have not expanded ( x + 2 )( x + 1 ). Remember previously that ( x + 2 )( x + 1 ) = x² + 3x + 2. Hence our solution is x - 1 / x² + 3x + 2, or option d.
SAVINGS ACCOUNT Demetrius deposits $120 into his account. One week later, he withdraws $36. Write an addition expression to represent this situation. How much higher or lower is the amount in his account after these two transactions?
Answers
Answer:
+$120 - $36
Higher by $84
Step-by-step explanation:
Addition expression is an equation without the equals to sign
$120 - $36
When the first expression was made, the account was higher by $120
After the second transaction, the account would be higher by $120 - $36 = $84
PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answers
Answer:
last option
Step-by-step explanation:
Let's call the original angle x° and the radius of the circle y. The area of the original sector would be x / 360 * πy². The new angle, which is a 40% increase from x, can be represented as 1.4x so the area of the new sector is 1.4x / 360 * πy². Now, to find the corresponding change, we can calculate 1.4x / 360 * πy² ÷ x / 360 * πy² = (1.4x / 360 * πy²) * (360 * πy² / x). 360 * πy² cancels out so we're left with 1.4x / x which becomes 1.4, signifying that the area of the sector increases by 40%.
Find the vertex of f(x)= x^2+ 6x + 36
Pls help soon
Answers
Answer:
vertex(-3,27)
Step-by-step explanation:
f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)
V(h,k)
h=-b/2a=-6/2=-3
k=f(-3)=3²+6(-3)+36
f(-3)=9-18+36=27
vertex(-3,27)
