Answers
Answer:
[tex]243.2cm^{2}[/tex]
Step-by-step explanation:
Step 1: Understand what this shape is constructed out of
2 Congruent Trapezoid
2 Congruent Rectangles
1 Small Rectangle
1 Large Rectangle
Step 2: Find the surface area of the shapes
Area of 2 Trapezoids =[tex](\frac{a+b}{2}h)2=(\frac{4+6}{2}2.8)2=(\frac{10}{2}2.8)2=((5)}(2.8))2= (11.6)(2)=23.2cm^{2}[/tex]
Area of 2 Rectangles = [tex](3)(10)(2)=(60)(2)=120cm^{2}[/tex]
Area of Smaller Rectangle = [tex](4)(10)=40cm^{2}[/tex]
Area of Larger Rectangle = [tex](6)(10)=60cm^{2}[/tex]
Step 3: Add the surface areas up
[tex]23.2cm^{2} +120cm^{2} +40cm^{2} +60^{2} =243.2cm^{2}[/tex]
Therefore the surface area of the Trapezoidal Prism is [tex]243.2cm^{2}[/tex]
Related Questions
Please help me with this
Answers
verifying, by putting [tex] \theta=60^{\circ}[/tex]
LHS≠RHS
hence the question is FALSE
What is the answer to (6/7)/(12/21) = 4/x Algebra plz help
Answers
Answer:
(6/7)/(12/21) = 4/x
the first part of the expression :
when divide fraction: turn the sign from ÷ to × and flip the second fraction
(6/7)×(21/12)=4/x
126/84=4/x ( simplify the fraction 126/84)
GCF of 126 and 84 is 42 ( 126/48=3 and 84/42=2)
3/2=4/x ( cross multiplication ( butterfly)
1.5=4/x
1.5x=4
x=4/1.5=2.6666.......
I promise i will mark as brainiest
Answers
Answer:
The answer is option BStep-by-step explanation:
The question above means that how many numbers can divide 2003 with a remainder of 23
That means all the numbers are less than 2003
The number of numbers that have this property are only
22 numbersHope this helps you
after allowing 5 percent discount on the marked price of a radio 10 percent vat is charged on it , then its price became rs 1672 .how much amount was given in the discount
Answers
Answer:
Hi, there!!!
The solutions in pictures will help you.
Best of luck....
PLS HELP ME ANSWER THIS QUESTION I DONT UNDERSTAND IT I WILL GIVE BRAINLIST AND A THANK YOU!!!!
Answers
Answer:
x=150°
Step-by-step explanation:
Using the vertical angle theorem, you can infer that AEC and DEB are in fact the same angle, 20°, and the same goes for FED and CEG, both 130°.
So, x spans AEC and CEG so is 20° + 130° = 150°
PLEASE ANSWER QUICKLY
Answers
Answer:
Hi ! Answers given in the pictures below
Step-by-step explanation:
how many 6-digit numbers can be created using8, 0, 1, 3, 7, and 5 if each number is used only once?
Answers
Answer:
600 numbers
Step-by-step explanation:
For six-digit numbers, we need to use all digits 8,0,1,3,7,5 each once.
However, 0 cannot be used as the first digit, because it would make a 5-digit number.
Therefore
there are 5 choices for the first digit (exclude 0)
there are 5 choices for the first digit (include 0)
there are 4 choices for the first digit
there are 3 choices for the first digit
there are 2 choices for the first digit
there are 1 choices for the first digit
for a total of 5*5*4*3*2*1 = 600 numbers
Terri graphed a system of linear inequalities. Which ordered pairs are a part of the solution set for this system of linear inequalities? Select two that apply.
(-1, 5)
(2, -4)
(7, -1)
(4, 6)
(5, 2)
Answers
Answer: (2, -4) and (7, -1)
Step-by-step explanation:
Ok, the solutions of the system of inequalities are all the points that lie on the blue shaded part of the graph or in the solid line.
So, in order to see if the points are solutions of the system, then you need to locate the point in the graph and see if it is inside the shaded region or in the solid line (only in the segment that "touches" the shaded region).
Now, we want to find the equation of the solid line, we can see that it passes through the points (0, 6) and (6, 0)
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then, in this case, the slope is:
a = (0 - 6)/(6 - 0) = -1.
And to find the value of b, we have that when x = 0, y = 6.
y = 6 = -1*0 + b
6 = b
The equation is:
y = -1*x + 6
(-1, 5) is not in the blue region nor in the solid line, so this is not a solution.
(7, - 1) this point is near the solid line, let's test it:
y(7) = -1*7 + 6 = -1
So the point (7, -1) is on the solid line, and is the other solution of the system.
Simplify 2√28 - 3√63
Answers
Answer:
[tex]-5\sqrt{7}[/tex]
Step-by-step explanation:
2√28 - 3√63
4√7 - 9√7
- 5√7
Answer:
- 5√7
Step-by-step explanation:
without actually calculating the cubes find the value of each of the following (-28)^3+(12)^3+(16)^3
Answers
Answer:
-16128
Step-by-step explanation:
This expression can be calculated by algebraic means, whose process is described below:
1) [tex](-28)^{3}+(12)^{3}+(16)^{3}[/tex] Given.
2) [tex](-12-16)^{3} + (12)^{3}+(16)^{3}[/tex] Definition of addition.
3) [tex](-12)^{3} + 3\cdot (-12)^{2}\cdot (-16)+3\cdot (-12)\cdot (-16)^{2}+(-16)^{3}+(12)^{3}+(16)^{3}[/tex] Cubic perfect binomial.
4) [tex](12)^{3}+[(-1)\cdot (12)]^{3}+(16)^{3} + [(-1)\cdot (16)]^{3}+3 \cdot (-12)^{2}\cdot (-16) + 3\cdot (-12)\cdot (-16)^{2}[/tex] Commutative property/[tex](-x)\cdot y = -x\cdot y[/tex]
5) [tex](12)^{3} + (-1)^{3}\cdot (12)^{3} + 16^{3} +(-1)^{3}\cdot (16)^{3} + (-3)\cdot [(-12)^{2}\cdot (16) +(-16)^{2}\cdot (12)][/tex] Distributive property/[tex](-x)\cdot y = -x\cdot y[/tex]/[tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]
6) [tex](12)^{3} + [-(12)^{3}]+(16)^{3} + [-(16)^{3}]+ (-3)\cdot [(-12)^{2}\cdot (16)+(-16)^{2}\cdot (12)][/tex] [tex](-x)\cdot y = -x\cdot y[/tex]
7) [tex](-3)\cdot [(-12)^{2}\cdot (16) + (-16)^{2}\cdot (12)][/tex] Existence of the additive inverse/Modulative property for addition.
8) [tex](-3) \cdot [(12)^{2}\cdot (16)+(16^{2})\cdot (12)][/tex] [tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]/[tex](-x)\cdot (-y) = x\cdot y[/tex]
9) [tex](-3)\cdot (12)\cdot (16)\cdot (12+16)[/tex] Distributive property.
10) [tex]-16128[/tex] [tex](-x)\cdot y = -x\cdot y[/tex]/Definition of sum/Definition of multiplication/Result
For a quadratic function y = ax² + bx + c, suppose the constants a, b, and c are consecutive terms of a geometric sequence. Show that the function does not cut the x axis.
Answers
Hello, because of the geometric sequence we can say that:
[tex]\alpha = \dfrac{b}{a}=\dfrac{c}{b}\\\\\dfrac{c}{a}=\dfrac{c*b}{a*b}=\dfrac{c}{b}\dfrac{b}{a}=\alpha^2\\\\\text{So the equation becomes.}\\\\ax^2+bx+c=0<=>x^2+\dfrac{b}{a}x+\dfrac{c}{a}=0\\\\<=>x^2+\alpha x+ \alpha^2=0\\\\\Delta=b^2-4ac = \alpha^2-4\alpha^2=-3\alpha^2 < 0[/tex]
So there is no real root, so the function does not cut the x axis.
Thank you
For the given quadratic function, the x-axis is not cut by the function because there is no true root.
What is a quadratic function?To determine values for various parameters, quadratic functions are employed in a variety of scientific and engineering disciplines. A parabola is used to graphically illustrate them. The orientation of the curve is defined by the highest degree factor.
As per provided data in question,
α = b/a = c/b
c/a = (c × b)/(a × b) = (c/b) (b/a) = α²
For the equation,
ax² + bx + c = 0
x² + b/a(x) + c/a = 0
⇒ x² + ax + α² =0
Δ = b² - 4 ac = α² - 4α²
Δ = -3α² < 0, which means that no real root is there.
To know more about quadratic functions:
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divide 1725 by 102 show work please
Answers
Answer:
16.91176471
Step-by-step explanation:
1725÷102
= 16.91176471
can someone explain mean and median to me?
Answers
Answer:
Mean is obtained by adding of all of the term values by the number of terms in a given set of data. Mean is also called "average".
Median on the other hand is the arrangement of numerical data in chronological order from least to greatest and finding the middle number from that arranged set of data.
Evaluate the expression below for x =4 and y = 5.
x2 + 3(x + y)
When x = 4 and y = 5, x2 + 3(x + y)= |
(Type an integer or a decimal.)
Answers
Answer:
positive 35
Step-by-step explanation:
x2 + 3(x + y) given
4(2) + 3(4+5) problem
4(2) + 3(9)
8 + 27= 35
A researcher says to the respondents in a poll, “Eating too many sugary foods leads to cavities. Would you rather have soda or water served with your meal?” Is this a valid question to ask of sample respondents?
A. Yes, the more information provided by a researcher the better. Respondents can now give an informed opinion and the results will be more accurate.
B. No, the wording of the question makes respondents more likely to say water, even if they may actually prefer soda at a meal.
C. No, a researcher cannot ask people for preferences because they may not answer honestly. The researcher should observe people and record their beverage selections to insure accurate responses.
D. Yes, the researcher is simply stating a fact: eating sugary foods does lead to cavities. It is okay for a researcher to state facts in asking questions of respondents.
Answers
The correct answer is B. No, the wording of the question makes respondents more likely to say water, even if they may actually prefer soda at a meal.
Explanation:
One important factor when designing questions in research is to avoid any language that might influence the answers of respondents. This recommendation was not followed in the question "Eating too many sugary foods leads to cavities. Would you rather have soda or water served with your meal?" because mentioning sugary foods, which includes soda, leads to cavities will make respondents consider soda is negative and they are more likely to choose water. This implies the wording in the question influences respondents and introduces bias, which is inappropriate. Thus, the correct answer is B.
A circular hall has a hemispherical roof.
The greatest height is equal to the
inner diameter. If the capacity of
the hals is
the
floor is.
43510 m^3
then
area
of the
Answers
Answer:
Area=1,288.88m²
Step-by-step explanation:
A circular hall(big room) has a hemispherical roof.The greatest height is equal to the inner diameter.Find the area of the floor,given that the capacity of the hall is 43510 cubic meter
Solution
let
diameter = D
radius,r = D/2
Greatest height = D
height of cylindrical part (h)= D-r = r
radius of cylindrical part = r
area of floor = πr²
volume = volume of cylindrical part + volume of hemispherical part
= πr²h + 2/3 πr³
Recall h=r
volume = πr³ + 2/3 πr³
43510=5/3πr³
Make r the subject
r=3√(43510*3)/5π
=3√(130,530/15.7
=3√8,314.01
=20.26
Area of floor = πr²
=3.14*(20.26)²
=3.14*410.47
=1,288.88m²
EXAMPLE 10 Show that the points (a, a),(-a, - a) and (-3a, 3a) are the vertices of an equilateral triangle. Also find its area.
Answers
Answer:
The triangle is not equilateral.
Step-by-step explanation:
Distance formula:
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Distance from (a, a) to (-a, -a):
[tex] d_1 = \sqrt{(-a - a)^2 + (-a - a)^2} [/tex]
[tex] d_1 = \sqrt{(-2a)^2 + (-2a)^2} [/tex]
[tex] d_1 = \sqrt{8a^2} [/tex]
Distance from (-a, -a) to (-3a, 3a):
[tex] d_2 = \sqrt{(-3a - (-a))^2 + (3a - (-a))^2} [/tex]
[tex] d_2 = \sqrt{(-2a)^2 + (4a)^2} [/tex]
[tex] d_2 = \sqrt{20a^2} [/tex]
Distance from (-3a, 3a) to (a, a):
[tex]d_3 = \sqrt{(-3a - a)^2 + (3a - a)^2}[/tex]
[tex]d_3 = \sqrt{(-4a)^2 + (2a)^2}[/tex]
[tex]d_3 = \sqrt{20a^2}[/tex]
The three sides do not have the same length, so the triangle is not equilateral.
Dr. Green has to multiply the weight of the team's bug spray bottles, 7 x 90 grams. To solve this, he writes out the equation 7 x 9 x 10. Why does this strategy work?
Answers
Because 9 × 10 equals 90
Then 7×90=7×9×10
What is this used for and how do i use it..?
Answers
you have to solve each one to get your answer and I think that your answer will be inside the circle
Answer:
This is called the Unit Circle. It is used in trigonometry. It had a radius of 1.
It helps you when using the trig function of sin cos and tan.
Hope this helps!!!!
Step-by-step explanation:
Find the value of x to the nearest degree.
A. 35
B. 28
C. 51
D. 55
Answers
Answer:
A
Step-by-step explanation:
First, we are already given the sides adjacent and opposite to ∠x. Therefore, we can use the tangent function. Recall that:
[tex]\tan(x)=opp/adj[/tex]
The opposite side is 20 while the adjacent side is 14.
Plug in the numbers. Use a calculator:
[tex]\tan(x)=20/14=10/7\\x=\tan^{-1}(10/7)\\x\approx55.0080\textdegree\approx55\textdegree[/tex]
Edits: Improved Answer. Removed Wrong Answer.
Answer:
55
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan x = 20/14
Taking the inverse tan of each side
tan ^-1 tan x = tan ^ -1 (20/14)
x =55.0079798
To the nearest degree
x = 55
The perimeter of an isosceles triangle is 32 inches. If the base is longer than half of the two other equal sides by 2 inches, find the length of all sides of this triangle.
Write as a equation.
Answers
Answer:
Step-by-step explanation:
Let equal sides of an isosceles triangle = a inches
Base = [tex]\frac{1}{2}a+2[/tex] inches
Perimeter = 32 inches
a + a + [tex]\frac{1}{2}a+2[/tex] = 32
[tex]2a + \frac{1}{2}a+2 = 32\\\\\frac{2a*2}{1*2}+\frac{1}{2}a+2=32\\\\\frac{4a}{2}+\frac{1}{2}a+2=32\\\\\frac{5}{2}a+2 = 32\\\\[/tex]
Subtract 2 from both sides
[tex]\frac{5}{2}a=32-2\\\\\frac{5}{2}a=30\\\\a=30*\frac{2}{5}\\\\a=6*2[/tex]
a = 12 inches
base = [tex]\frac{1}{2}*12+2[/tex]
= 6 + 2
Base = 8 inches
I need to know this fairly soon pleaseee
Answers
Answer:
m<PQT= 94°
Step-by-step explanation:
If line QS bisect <PQR
m<PQS = m < SQR
7x-6= 4x+15
7x-4x= 15+6
3x= 21
X= 21/3
X= 7
m<PQS= 7x-6
m<PQS= 7(7)-6
m<PQS= 49-6
m<PQS= 43°
m<PQS= m<SQR
<mSQR=43°
m<PQR= m<PQS + m < SQR
m<PQR=43+43
m<PQR= 86°
BUT
m<PQR= m<TQW
m<PQT= m<RQW
m<PQR+m<TQW +m<PQT+ m<RQW
= 360°
Let m<TQW= x
86+86+x+x= 360
2x+172= 360
2x= 188
X= 94°
m<PQT= 94°
Select the equivalent expression.
Answers
C, because we multiply the exponents to get the answer.
Answer:
C
Step-by-step explanation:
Using the rule of exponents
[tex](a^{m}b^{n}) ^{p}[/tex] = [tex]a^{mp}[/tex] × [tex]a^{np}[/tex]
Thus
[tex](7^{2}5^{6})^4[/tex]
= [tex]7^{2.4}[/tex] × [tex]5^{6.4}[/tex]
= [tex]7^{8}[/tex] × [tex]5^{24}[/tex] → C
simplify the equation. (5xE2 - 3x) - (5xE2 - 3x+1)
Answers
Answer:
[tex]\huge \boxed{\mathrm{-1}}[/tex]
Step-by-step explanation:
[tex](5xe^2 - 3x) - (5xe^2 - 3x+1)[/tex]
Distribute negative sign.
[tex]5xe^2 - 3x- 5xe^2 +3x-1[/tex]
Combine like terms.
[tex]0xe^2 +0x-1[/tex]
[tex]0-1=-1[/tex]
what is the coefficient of the variable in the expression 4-3x
Answers
As per the question,
We have to find what's the coefficient.
Let's start to seperate the expression.
Here,
x is the variable,
4 is a number.
-3 is also a number.
4, -3x
The number with x here is -3 in (-3x) as the coefficient is (-3) in the given equation.
Answer:
Hey there!
Rearrange the expression to: -3x+4
The coefficient would be -3.
Let me know if this helps :)
Thomas loves tomatoes. He plans to fill the container shown below with soil to grow his own tomato
plants. The dimensions of the container are shown in inches.
umi
ndo
20 in
geo
10 in-
How much soil will the container hold?
Either enter an exact answer in terms of or use 3.14 for .
inches?
Answers
Given that
Height of container is 20 inches .Radius of base is 10 inches .To Find
Volume of container .Formula
Volume of cylinder is πr²hSolution
→ Volume = πr²h
Using π as 3.14
→ 3.14 × 10 × 10 × 20 = Volume
→ 314 × 20 = Volume
→ 6280 inches² is the holding capacity of the container.
Answer:
6280
Step-by-step explanation:
this is correct on khan academy
Please answer this question now
Answers
Answer:
m∠C = 102°
Step-by-step explanation:
This is is a cyclic quadrilateral
• The sum of opposite angles in a cyclic quadrilateral is equal to 180°
m∠D + m∠B = 180°
m∠B = 180° - m∠D
m∠B = 180° - 80°
m∠B = 100°
If you look at the above diagram properly, you will notice there are are angles outside the circle. We refer to this an exterior or external angles in a cyclic quadrilateral
• Note that m∠B is Opposite the exterior angle m∠CDA
Hence,
m∠CDA = 2 × m∠B
m∠CDA = 2 × 100°
m∠CDA = 200°
• m∠CDA = m∠CD + m∠DA
m∠DA = m∠CDA - m∠CD
m∠DA = 200° - 116°
m∠DA = 84°
• Another external angle we need to find is m∠DAB
m∠DAB = m∠DA + m∠AB
We know that m∠DA = 84°, therefore,
m∠DAB = 84° + 120°
m∠DAB = 204°
• The final step is to solve for m∠C
m∠DAB is Opposite m∠C
Hence
m∠C = 1/2 × m∠DAB
m∠C = 1/2 × 204
m∠C = 102°
What transformation of the parent function f(x) is made to get f(3x)?
Answers
Answer: Vertically shifting it by 3
The transformation of a function is horizontally shrink by a factor of 3 .
What is a horizontal shrink?We can apply horizontal shrink to a function by multiplying its input values by a scale factor, a, where 0 < 1/a < 1.Let’s go ahead and look at how f(x) = x2 will be affected by a scale factor of 1/2 and 1/3.
Below is a graph of the data.As we have expected, the graph stretches by a factor of 2 and 3. This is true for all horizontal stretches. The graph only stretches away from the y-axis when we horizontally stretch a graph.Horizontal stretch on other functions will exhibit similar properties. Let’s say we have f(x) = |x|, if this function’s graph is to be stretched horizontally to attain g(x), the new function’s expression can be expressed as |1/3 ∙ x| = |x/3|.How do you horizontally shrink by a factor of 3 ?
If g(x) = 3f (x): For any given input, the output of g is three times the output of f, so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.Learn more about Transformation on :
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Why is it important to consider scale when graphing inequalities?
Answers
Answer:
Because to get a straight line you need a scale. Otherwise you will not be able to graph a straight line.
Hope this helps:)
choose the answer based on the most efficient method. if the first step in the equation " -9 + x = 5x - 7" is subtract x, what should the next step be
Answers
Answer:
add 7 to both sides
Step-by-step explanation:
This is so because we are trying to solve the equation by seperating the variables from the real numbers. So as they remove all variables from the left side of the equation, we should remove any remaining numbers that are on the right side of the equation.
Hope this helps!
