The Euler's formula relates the vertices, faces and the edges of a polyhedron.
The correct option is (e) [tex]V = 6[/tex] [tex]E = 10[/tex] [tex]F = 6[/tex] [tex]6- 10 + 6 = 2[/tex]
First, we count the number of faces. This is the flat parts of the shape.
The attached shape has 6 flat surfaces.
So:
[tex]F = 6[/tex]
Next, we count the number of edges. This is where two faces meet.
The attached shape has 10 edges;
So:
[tex]E = 10[/tex]
Lastly, we count the number of vertices. This is where two edges meet.
The attached shape has 6 vertices.
So:
[tex]V = 6[/tex]
Using Euler's formula, we have:
[tex]V - E + F = 2[/tex]
Substitute values for V, E and F
[tex]6- 10 + 6 = 2[/tex]
[tex]2 = 2[/tex]
Hence, the polyhedron has 6 vertices, 10 edges and 6 faces
Read more vertices, edges, and faces at:
https://brainly.com/question/23347978
The table shows values for a quadratie function
What is the average rate of change for this function for the interval from 1
Please see
Pic
Answer:
B
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 1, 3 ] , then
f(3) = 18 ← value of y when x = 3
f(1) = 2 ← value of y when x = 1
Then
average rate of change = [tex]\frac{18-2}{3-1}[/tex] = [tex]\frac{16}{2}[/tex] = 8 → B
Identify one similarity and one difference between the graph of 2x + 4 and the graph of y= -1/2x + 4
Answer:
Similarity: Both graphs have same y-intercepts.
Difference: Graph 2x + 4 has a slope of 2 while the graphic -½x + 4 has a slope of -½
Step-by-step explanation:
[tex]{ \sf{y = mx + b}}[/tex]
m is the slope
b is the y-intercept
Write the quadratic expressions in the numerator and the
denominator in factored form
4x^2-14x+6/
X^3-7x^2+12x
I have to give 2 Ans form my question so sorry
PLEASE HELP WILL MARK BRAINLIEST!!!! You work for a consumer advocate agency and want to find the mean repair
cost of a washing machine. As part of your study, you randomly select 40
repair costs and find the mean to be $120.00. The sample standard deviation
is $17.50. The 99% confidence interval for the population mean repair cost is? A.(112.86, 127.14) B.(114.58, 125.42) C. (115.43, 124.57) D. (111.57, 128.43)
Answer:
The correct answer is - A.(112.86, 127.14)
Step-by-step explanation:
Given:
mean = $120
sd = $17.50
n = 40
Solution:
Confidence interval for a populationcan be express as mean +/- margin of error (E)
degree of freedom = n-1 = 40-1 = 39
confidence level (C) = 99% = 0.01
significance level = 1 - C = 1 - 0.01 = 0.99 = 99%
by margin of error E = t×sd/√n = 2.58*17.50/√40
= 2.58*2.76
= 7.138 or 7.14
then the lower limit of mean = mean - E = 120 - 7.14 = $112.86
and, the upper limit of population mean = mean + E = 120 + 7.14 = $127.14
The tens digits of a certain two-digit number is 1/3 of the units digit. When the digits are reversed, the new number exceed twice the original number by 2 more than the sum of the digits. Find the original number.
Answer:
The orginal number is 26.
Step-by-step explanation:
So the units digit can be 3 6 or 9
The tens digit can be 1 2 or 3
So the original number can be 13
31 = 2*13+ (1+3) + 2
31 =? 26 + 4 + 2
This doesn't work. The right side is 32
26
62 = 2*26 + 8 + 2
62 = 52 + 8 + 2
This is your answer.
3 and 9 won't work because 39 is odd and so is 93. The result has to be even.
Value of the boat after 3 years?
after each year it's 83% of it's value from last year (100%-17%=83%)
the function in 19000 * (0.83) ^x
3 will be filled in for x
19000 * (0.83) ^3= 10863.953
$10863.95
Answer:
$10,863.95
Step-by-step explanation:
y = 19,000[tex](.83)^{t}[/tex]
y = 19,000[tex](.83)^{3}[/tex]
y =$10,863.95
Geometry, please answer question ASAP
Answer:
D
Step-by-step explanation:
The median goes from the vertex to the midpoint of the opposite side, so
LN = NM , that is
3x - 7 = 5 ( add 7 to both sides )
3x = 12 ( divide both sides by 3 )
x = 4
Then
KL = 2x + 3 = 2(4) + 3 = 8 + 3 = 11 → D
PLZZZZ HELPPPPPP!!!!!!!!!!!
Answer:
5/8 boxes
Step-by-step explanation:
1/3 ⋅ 1 7/8 = ?
1/3 ⋅ 15/8 = 15/24
15/24 = 5/8
5/8 boxes
Find the ordered pair $(s,t)$ that satisfies the system
\begin{align*}
\dfrac{s}{2} + 5t &= 3,\\
3t - 6s &= 9.
\end{align*}
Answer:
[tex]\left(\dfrac{8}{7} , \ \dfrac{17}{35} \right)[/tex]
Step-by-step explanation:
The given system of equations is presented as follows;
[tex]\dfrac{s}{2} + 5 \cdot t = 3[/tex]
3·t - 6·s = 9
Making t the subject of both equations, gives;
In the first equation; t = (3 - s/2)/5
In the second equation; t = (9 + 6·s)/3
Equating both values of t to find the the values that satisfies both equations, gives;
(3 - s/2)/5 = (9 + 6·s)/3
3 × (3 - s/2) = 5 × (9 + 6·s)
9 - (3/2)·s = 45 + 30·s
45 - 9 = (30 + (3/2))·s
36 = (63/2)·s
s = 36/(63/2) = 8/7
t = (3 - s/2)/5
∴ t = (3 - (8/7)/2)/5 = 17/35
Therefore, the ordered pair is (8/7, 17/35)
Mr. Ellington has a total of 32 students in his class , The ratio of girls to boys is 3:5, how many girls are in Mr . Ellington's class ?
Add the ratio: 3 + 5 = 8
Divide total students by that:
32/8 = 4
The ratio for girls is 3, multiply the 4 by 3:
4 x 3 = 12
There are 12 girls
Answer:
12
Step-by-step explanation:
If the ratio of girls to boys is 3:5, that means that for every 8 total students, 3 would be girls and 5 would be boys. Therefore 3/8 of the students are girls and 5/8 are boys. If 3/8 are girls, then:
[tex]\frac{3}{8}[/tex] of 32
= [tex]\frac{3}{8} * 32[/tex]
[tex]=\frac{3 * 32}{8} \\= \frac{96}{8} \\= 12[/tex]
There are 12 girls.
Independent Practice
Find the first, fourth, and eighth terms of the sequence.
an=0.5 · 3n−1a subscript n baseline equals 0.5 times 3 superscript n minus 1 baseline
A.
0.667; 4.5; 364.5
B.
3; 0.375; 0.0234375
C.
0.5; 13.5; 1093.5
D.
0.5; 121.5; 280.5
Answer:
C.
0.5; 13.5; 1093.5
Step-by-step explanation:
Help anyone can help me do the question,I will mark brainlest.
Answer:
a) 30
b)600pi
Step-by-step explanation:
For the first questions, since the arc is 240°, the area of the sector and circumference will be 240/360 or 2/3 of the total of the circles'. Therefore 125.6 x 3/2 is the circumference, which is 188.4. When we divide this by 6.28, we get 30
Now, since the area is pi r^2 where we know that r=30, we get 900pi as the area of the whole thing, however since the sector is 2/3 of the whole circle, 2/3 x 900pi = 600pi
I need help plz help
We know
[tex]\boxed{\sf cos\Theta=\dfrac{b}{h}}[/tex]
[tex]\\ \sf\longmapsto cos22=\dfrac{x}{47}[/tex]
[tex]\\ \sf\longmapsto 0.9=\dfrac{x}{47}[/tex]
[tex]\\ \sf\longmapsto x=47(0.9)[/tex]
[tex]\\ \sf\longmapsto x=42.3[/tex]
Rhombus LMNO is shown with its diagonals.
Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.
Angle MNO measures 112°. What is the measure of angle LMN?
Answer:
hope this help
Step-by-step explanation:
Answer:
90
51
10
Step-by-step explanation:
Check if -2 is the solution of equation 2 – x = 4x + 3
Answer:
7x the answer i think
Step-by-step explanation:
Answer:
[tex]\boxed {\boxed {\sf -2 \ is \ not \ a \ solution}}[/tex]
Step-by-step explanation:
We are asked to check is -2 is the solution of the following equation.
[tex]2-x= 4x+3[/tex]
We must substitute -2 in for x and solve both sides of the equation. If the two sides are equal, then -2 is the solution.
[tex]2- (-2) = 4(-2)+3[/tex]
Solve both sides of the equation according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Let's start with the left side.
[tex]2+2= 4(-2)+3 \\[/tex]
[tex]4= 4(-2)+3[/tex]
Now solve the right side. Remember to multiply first.
[tex]4= -8+3[/tex]
[tex]4= -5[/tex]
[tex]4\neq -5[/tex]
4 is not equal to -5, so -2 is not the solution for this equation.
Item 1 Which fraction is equivalent to 3.47? 3_23/50 3_47/100 3_12/25 I don't know.
Answer: 3 and 47/100
Step-by-step explanation:
A person walks away from a pulley pulling a rope slung over it. The rope is being held at a height 10 feet below the pulley. Suppose that the weight at the opposite end of the rope is rising at 4 feet per second. At what rate is the person walking when s/he is 20 feet from being directly under the pulley
The image of this question is missing and so i have attached it.
Answer:
dd/dt = 4.47 ft/s
Step-by-step explanation:
From the image attached, let's denote the following;
d = horizontal distance beneath pulley
h = height of pulley
l = diagonal from the pulley to the head of the person
v = velocity of rope rising
Using pythagoras theorem;
l² = d² + h²
Differentiating with respect to time and considering h = c^(te) gives;
2l(dl/dt) = 2d(dd/dt)
We are given;
d = 20 ft
h = 10 ft
v = 4 ft/s
We know that velocity in this case is change in diagonal distance with time. Thus;
v = dl/dt = 4 ft/s
From earlier, we saw that;
2l(dl/dt) = 2d(dd/dt)
Thus, reducing it gives
(dl/dt)(l/d) = dd/dt
Now, l² = d² + h²
l = √(d² + h²)
Also, v = dl/dt = 4
Thus;
4(√(d² + h²))/d = dd/dt
4(√(20² + 10²))/20 = dd/dt
dd/dt = 4.47 ft/s
20) solve:
[tex] {8}^{2} + 2 = [/tex]
21) solve:
[tex]4(2x + 5y = [/tex]
22) simplify the expression
[tex]4( {2}^{2} + 30) - 4 = [/tex]
Match the answers……………..
9 in 8956 = 900
9 in 95675 = 90000
9 = 9 in 124569
9 in 68795 = 90
90000 = 9 in 2549652.........
hope it helps...
What is the reminder? Help
Answer:
6
Step-by-step explanations:
The remainder is what is left over after dividing whatever from d. So if you add one to d, then the remainder would increase from 5 to 6.
Hope this helps.
Please help me. if I don’t complete my course I’m getting sent back to my parents house, and I need to complete this course
This is similar polygons, and the lessons I get don’t help
see attached photo, please help asap!!!
Answer:
3.398
Step-by-step explanation:
log(10) 2500 = log(10) (5^2*10^2) = log(10) 5^2 + log(10) 10^2 = 2*log(10) 5 + 2=3.398
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need help asap pls !
Answer:
L={∅}
Step-by-step explanation:
Answer hurry which one 1 2 3 or 4?
Answer:
Option: 1Step-by-step explanation:
Let,
Footprints that Adele will find be = f
So, Footprints that Yumiko finds = 2f = f + f
Since,
As given that,
Yumiko finds 16 Footprints so it will be,
2f = f + f = 16
And,
f = 16 / 2
= 8
Which is half of Footprints found by Yumiko.
So the bar model 1 represents it correct.
Answer:
option 1
Step-by-step explanation:
i did the quiz
A plank 6m long leans against a vertical wall so that the foot of the plank is 4m away from the wall. A lizard climbs 2m up the plank. Calculate the horizontal distance between the lizard and the wall.
Answer: [tex]\dfrac{8}{3}\ m[/tex]
Step-by-step explanation:
Given
Length of the plank is [tex]6\ m[/tex]
Foot of the flank is [tex]4\ m[/tex] away from the wall
Lizard climbs 2 m up the wall
from the figure, the two triangles are similar
[tex]\therefore \dfrac{2}{6}=\dfrac{x}{4}\\\\\Rightarrow x=4\times \dfrac{2}{6}\\\\\Rightarrow x=\dfrac{4}{3}\ m[/tex]
So, the distance from the wall is
[tex]\Rightarrow 4-x\\\\\Rightarrow 4-\dfrac{4}{3}\\\\\Rightarrow \dfrac{8}{3}\ m[/tex]
Triangle ABC is a right triangle.
Triangle A B C. Angle A is x degrees, B is 90 degrees, C is (x minus 10) degrees. The exterior angle to angle C is (2 x + 40) degrees.
Which equations can be used to find the value of x? Check all that apply.
x + 90 + (x minus 10) = 180
x + 90 + (2 x + 40) = 180
2 x + 80 = 180
x + 90 = 2 x + 40
(x minus 10) + 90 = 2 x + 40
Answer:
x + 90 + (x minus 10)= 180° can be used to find the value of x.
Answer:
A) X+90+ (x-10) - 180
C) 2x+80 = 180
D) x+90 = 2x+40
Step-by-step explanation:
#What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?
Discriminant = b2 – 4ac
–8
4
8
16
Answer:
16
Step-by-step explanation:
the quadratic equation –3 = –x2 + 2x can be changed into :
x²-2x-3= 0
a=1, b= -2 , and c = -3
so, the discriminant = (-2)²-4(1)(-3)
= 4 + 12 = 16
using appropriate properties , find 7/5 × 5/12 − 3/12 × 7/5 − 1/15
Answer:
[tex] \frac{1}{6} [/tex]
Step-by-step explanation:
[tex] \frac{7}{5} \times \frac{5}{12} - \frac{3}{12} \times \frac{7}{5} - \frac{1}{15} = \frac{7}{5} ( \frac{5}{12} - \frac{3}{12} ) - \frac{1}{15} = \frac{7}{5} \times \frac{1}{6} - \frac{1}{15} = \frac{7}{30} - \frac{2}{30} = \frac{5}{30} = \frac{1}{6} [/tex]
Monica makes tomato sauce with the plants she grows in her garden. She uses 3 basil leaves in her sauce for every 8 tomatoes. She is making a big batch of sauce with 32 tomatoes from her garden.
Answer: 12 Basil leaves
Step-by-step explanation:
Given
Monica uses 3 basil leaves for every 8 tomatoes
For 32 tomatoes she needs
[tex]\Rightarrow 3\ \text{basil leaves}\equiv8\ \text{Tomatoes}\\\\\Rightarrow 4\times 3\ \text{basil leaves}\equiv4\times 8\ \text{Tomatoes}\\\\\Rightarrow 12\ \text{basil leaves}\equiv 32\ \text{Tomatoes}[/tex]
Thus, she needs 12 basil leaves.
