Answer: 96
Step-by-step explanation:
Ok, lines a and b are parallel.
We can separate this problem in two cases:
Case 1: 2 vertex in line a, and one vertex in line b.
Here we use the relation:
"In a group of N elements, the total combinations of sets of K elements is given by"
[tex]C = \frac{N!}{(N - K)!*K!}[/tex]
Here, the total number of points in the line is N, and K is the ones that we select to make the vertices of the triangle.
Then if we have two vertices in line a, we have:
N = 6, K = 2
[tex]C = \frac{6!}{4!*2!} = \frac{6*5}{2} = 3*5 = 15[/tex]
And the other vertex can be on any of the four points on the line b, so the total number of triangles is:
C = 15*4 = 60.
But we still have the case 2, where we have 2 vertices on line b, and one on line a.
First, the combination for the two vertices in line b is:
We use N = 4 and K = 2.
[tex]C = \frac{4!}{2!*2!} = \frac{4*3}{2} = 6[/tex]
And the other vertice of the triangle can be on any of the 6 points in line a, so the total number of triangles that we can make in this case is:
C = 6*6 = 36
Then, putting together the two cases, we have a total of:
60 + 36 = 96 different triangles
What shape best describes the cross-section cut at an angle to the base of a right rectangular prism? Trapezoid Parallelogram Square Rectangle
Answer:
Parallelogram
Step-by-step explanation:
Answer:
Parallelogram
Step-by-step explanation
F(x)=0.5x^2-2 and g(x)=8x^3+2
Answer:
(f*g)(x) = 4x⁵ - 16x³ + x² - 4
Step-by-step explanation:
To find (f*g)(x), you need to multiply f(x) with g(x). Use FOIL to multiply.
f(x) = 0.5x² - 2
g(x) = 8x³ + 2
(f*g)(x) = (0.5x² - 2)(8x³ + 2)
(f*g)(x) = 4x⁵ + x² - 16x³ - 4
(f*g)(x) = 4x⁵ - 16x³ + x² - 4
3/v=2/4? i need help plz
Answer:
v = 6
Step-by-step explanation:
3/v = 2/4
We can use cross products to solve
2v = 3*4
2v = 12
Divide each side by 2
2v/2 = 12/2
v =6
Answer:
v=6
Step-by-step explanation:
If this is making them equal, then you should know that 2/4 is 1/2 , so you could just multiply 3 by both the 1 and the 2 in 1/2 and 1 times 3 is 3 which is what we have and 2 times 3 is 6 which is v.
Which statement best explains why the sine of an acute angle is equal to the cosine of the angles complement
Answer:
Option (B)
Step-by-step explanation:
From the figure attached,
ΔABC is a right triangle.
Cosine and Sine ratios from the given triangle will be,
SinA = [tex]\frac{\text{Opposite side}}{Hypotenuse}[/tex]
= [tex]\frac{a}{c}[/tex]
CosB = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{a}{c}[/tex]
Therefore, both the ratios (Sine and Cosine) will be equal as [tex]\frac{a}{c}[/tex]
Option (B) will be the correct option.
A researcher wants to use a confidence interval to estimate the proportion of college students in his state who plan to vote in the 2020 presidential election. He plans to randomly sample 120 college students, and plans to construct a 95% or 99% confidence interval. Which of these confidence intervals will be wider, and why
Answer:
99% confidence interval will be wider because as the level of confidence increase the width increases as well and the standard error decreases
Step-by-step explanation:
The confidence interval is directly proportional to the sample size hence the 99% confidence interval will be wider than the 95% confidence interval of the sample of 120 college students
using a 99% confidence interval gives a more accurate result than a 95% confidence because the standard error decreases with increase in confidence interval
Which statement about this figure is true ?
a. it has reflection al symmetry with one line of symmetry
b. it has no rotational symmetry
c. it has no rotational symmetry with an angle of rotation of 90 degrees
d. it has no reflectional symmetry
The statement that is true about the given figure, a limaçon, is c. It has no rotational symmetry, with an angle of rotation of 90 degrees.
Let's examine each option and explain why they are true or false:
a. It has reflectional symmetry with one line of symmetry: This option is false. To have reflectional symmetry with one line of symmetry, the figure must be identical on both sides when divided by a line. The given figure, a limaçon, does not exhibit this property.
b. It has no rotational symmetry: This option is true. Rotational symmetry means that the figure remains unchanged after rotation by certain angles. The limaçon does not have any rotational symmetry because it does not appear the same after any rotation.
c. It has no rotational symmetry, with an angle of rotation of 90 degrees: This option is true. A figure with rotational symmetry of 90 degrees would appear the same after a 90-degree rotation. However, the limacon does not exhibit this property.
d. It has no reflectional symmetry: This option is true. Reflectional symmetry requires the figure to have a line of symmetry dividing it into two identical halves. The limaçon does not possess such a line of symmetry.
Based on the explanations above, the correct statement is that the limaçon has no rotational symmetry with an angle of rotation of 90 degrees (option c).
Learn more about symmetry here:
https://brainly.com/question/32342060
#SPJ4
Use mathematical induction to prove the statement is true for all positive integers n. 8 + 16 + 24 + ... + 8n = 4n(n + 1)? Please show work
Answer:
The sum of the series is Sₙ = n/2 [2·a + (n - 1)·d] where a = 8 and d = 8, therefore 8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)
Step-by-step explanation:
The parameters given are;
8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)
The given series of numbers can be checked to find;
16 - 8 = 24 - 16 = 8
Therefore, the series of numbers is an arithmetic progression with first term = 8, and common difference = 8, we have;
The sum of n terms of an arithmetic progression, Sₙ, is given as follows;
Sₙ = n/2 [2·a + (n - 1)·d]
Where;
a = The first term of the series of numbers = 8
d = The common difference = 8
∴ Sₙ = n/2 × [2×8 + (n - 1)×8] = n [2×8/2 + (n - 1)×8/2] = n × [8 + (n - 1)×4]
Sₙ = n × [8 + (n - 1)×4] = n × [8 + 4·n - 4] = n × [8 - 4 + 4·n] = n × [4 + 4·n]
Sₙ =n × [4 + 4·n] = 4 × n×(n + 1) = 4·n·(n + 1).
Figure ABCD is a rectangle Find the value of x
Step-by-step explanation:
Since this is a rectangle these two equations for the length have to equal each other.
2x+4=7x-1
We now need to get all of the x's on one side and constant numbers on the other side.
add 1 to both sides and subtract 2x from both sides.
5=5x
divide 5 from both sides.
x=1
Two mechanics worked on a car. The first mechanic worked for hours, and the second mechanic worked for hours. Together they charged a total of . What was the rate charged per hour by each mechanic if the sum of the two rates was per hour?
Answer:
The rate charged by first mechanic per hour= x =$85
The rat charged by second mechanic per hour =y = $70
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1900. What was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?
Solution
Let
x= hourly rate of the first mechanic
y= hourly rate of the second mechanic
Derive two equations to solve for the two unknowns
10x + 15y = 1900 (1)
x + y = 155 (2)
From (2)
x + y = 155
x=155-y
Substitute x=155-y into (1)
10x + 15y = 1900
10(155-y) + 15y =1900
1550 -10y + 15y =1900
5y =1900-1550
5y=350
Divide both sides by 5
y= 70
Substitute y=70 into (2)
x + y = 155
x + (70) =155
x=155 - 70
= 85
x= 85
The rate charged by first mechanic per hour= x =$85
The rat charged by second mechanic per hour =y = $70
A toy box in the shape of a rectangular prism has a volume of 6,912 cubic inches. The base area of the toy box is 288 square inches. What is the height of the toy box?
Answer:
h= 24 inches
Step-by-step explanation:
(Volume)= (Base Area) * (Height)
6,912= 288h
h=
Some time ago , Keith's height and his nephew's height were at a ratio of 15:7. Then, Keiths height increased by 16% and his nephew,s height doubled. Keith is now 34 cm taller than his nephew, what is their total current height
Answer:
The answer is below
Step-by-step explanation:
The ratio of Keith's height and his nephew's height is 15:7. Let keith height be x cm and his nephews height be y cm.
[tex]\frac{x}{y}=\frac{15}{7} \\x=\frac{15}{7}y[/tex]
Keiths height increased by 16% , therefore Keith new height is (100% + 16%) × x = 1.16x
The nephew height is doubled, therefore his new height is 2y.
Given that Keith is now 34 cm taller than his nephew
1.16x = 2y + 34
but x = (15/7)y
[tex]1.16(\frac{15}{7} )y=2y+34\\\\\frac{87}{35} y=2y+34\\\\\frac{87}{35} y-2y=34\\\\\frac{17}{35}y=34\\ \\y=\frac{34*35}{17}\\ \\y=70\ cm[/tex]
The nephews new height = 2y = 2(70) = 140 cm
Keith new height = 2y + 34 = 140 + 34 = 174 cm
Their total current height = 140 cm + 174 cm = 314 cm
The function f(x) = 50(0.952)x, where x is the time in years, models a declining feral cat population. How many feral cats will there be in 9 years?
Work Shown:
f(x) = 50(0.952)^x
f(9) = 50(0.952)^9
f(9) = 32.1146016801717
f(9) = 32 approximately
Side note: the exponential function is in the form a*b^x with b = 1+r = 0.952, which solves to r = -0.048. The negative r value means we have a 4.8% decrease each year.
Another note: you don't even need to use math to answer this question. Note how 50 is the starting population and the population is declining. Only choice B has a value smaller than 50, so we can rule out the others right away.
Answer:
32
Step-by-step explanation:
The initial value of the population is f(0) = 50(0.952^0) = 50. If the population is declining, it must be less than 50 in 9 years. The only answer choice that is less than 50 is ...
about 32 feral cats
_____
You can evaluate f(9) to choose the same answer:
f(9) = 50(0.952^9) ≈ 32.114 ≈ 32
Which professionals most directly use geometry in their work? A. accountants B. astronomers C. judges D. pharmacists E. politicians\
Answer:
Astronomers directly use geometry in their work rather than accountants , judges, pharmacist and politicians.
They used geometry to measure velocity , direction, distance, relativity, momentum, and probability. They used it to look at objects in the sky with a telescope by setting a required angle to get a proper view .
But Accountants, judges, pharmacist and politicians are not in use of geometry directly or frequently.
Hence, Option 'B' is correct.
Step-by-step explanation:
Answer: b
Step-by-step explanation:
how do you find the area of an open cylinder... what is the Formula?? please help
Answer:
Cylinder has a formula
π×r²×h
so of it is open
π×r²×h - π×r²
Answer:
pls give brainiest
Step-by-step explanation:
A=2πr×h(r+h)
what’s the equation of line ?
y =__x + __
Answer:
y=3/4x-2
Step-by-step explanation:
two points from graph (0-2) and (8,4)
find slope m: y2-y1/x2-x1
m=4+2/8-0
m=6/8=3/4
x=0 then y=b=-2
y=3/4x-2
Help now for brainliest,5stars and thanks.Find the values of x in the range 0≤x≤180° for which 15sin^2 x+11cox-17=0
Answer:
[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]
Step-by-step explanation:
Given equation is:
[tex]15sin^2 x+11cosx-17=0[/tex]
To find:
Values of [tex]x[/tex] in the range [tex]0^\circ\leq x\leq180^\circ[/tex].
Solution:
First of all, let us recall one identity of square of sine and square of cosine.
Sum of square of sine of an angle and square of cosine of the same angle is equal to 1.
[tex]\bold{sin^2\theta+cos^2\theta=1}[/tex]
So
Putting [tex]sin^2x=1-cos^2x[/tex] in the given equation.
[tex]15(1-cos^2x)+11cosx-17=0\\\Rightarrow 15-15cos^2x+11cosx-17=0\\\Rightarrow -15cos^2x+11cosx-2=0\\\Rightarrow 15cos^2x-11cosx+2=0\\\Rightarrow 15cos^2x-5cosx-6cosx+2=0\\\Rightarrow 5cosx(3cosx-1)-2(3cosx-1)=0\\\Rightarrow (5cosx-2)(3cosx-1)=0\\\Rightarrow cosx=\dfrac{2}{5}, \dfrac{1}{3}[/tex]
So, in the range [tex]0^\circ\leq x\leq180^\circ[/tex]
[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]
85 POINTS! PLEASE HELP! Explain how to write an equation parallel to the equation y = 2x + 3 and the new line also includes the ordered pair (1,-2).
Answer:
[tex]\huge\boxed{\sf y = 2x -4}[/tex]
Step-by-step explanation:
The given equation is:
y = 2x + 3
Where Slope = m = 2 , Y-intercept = b = 3
Parallel lines have equal slopes
So, Slope of new line = m = 2
Now, Finding y-intercept:
Given Point = (x,y) = (1,-2)
So, x = 1 , y = -2
Putting m, x and y in standard form of equation to get b:
[tex]\sf y = mx+b[/tex]
[tex]\sf -2 = (2)(1) + b\\-2 = 2 + b\\[/tex]
Subtracting 2 to both sides
[tex]\sf b = -2-2\\[/tex]
b = -4
So, the standard form og equation for the new line is :
[tex]\sf y = mx+b[/tex]
[tex]\sf y = 2x -4[/tex]
Answer:
y = 2x - 4
Step-by-step explanation:
the problem is called (slope-intercept form)
the equation of the line is y = mx + b
the equation of a line is given as y = 2x + 3
slope = 2
b = y-intercept is where the line crosses the y-axis = 3
so point (x1, y1) = (1, -2)
by using the equation.
y = mx + b
-2 = 2 (1) + b
-2 -2 = b
therefore b = -4
writing the new equation using the slope intercept form
y = mx + b would be y = 2x + 4
so the equation parallel to the equation y = 2x + 3 is y = 2x - 4
Use the substitution method to solve the system of equations. Choose the correct ordered pair.
Answer:
b
Step-by-step explanation:
Answer:
The answer is D or (10,-9)
Step-by-step explanation:
Since y is already given (and you have to use the substitution method) substitute y into one of the equations. So you should have something like this:
-2x+11=3x+21
After that merely solve for x which should get you x=10. After you get your x value plug 10 in either (of the original) equation and your y value should be -9. For example if you chose y=-2x+11 you should have y= -2(10)+11. In the end your answer should be (10,-9).
If you want to check your work merely plug your answer into both equations (ex: -9=-2(10)+11 --> -9=-9), therefore you know your answer is correct).
Hope this helped!
can you solve;
3/7+5/21
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\frac{3}{7}+\frac{5}{21}[/tex]
[tex]= \frac{3}{7}+\frac{5}{21}[/tex]
[tex]= \frac{9}{21}+\frac{5}{21}[/tex]
[tex]= \frac{9 + 5}{21}[/tex]
[tex]= \frac{14}{21}[/tex]
[tex]= \frac{2}{3}[/tex] (Decimal: 0.666667)
Answer : [tex]\boxed{\frac{2}{3} }[/tex] (Decimal: 0.666667)
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Elena drank 3 liters of water yesterday. Jada drank 3⁄4 times as much water as Elena. Lin drank twice as much water as Jada. Did Lin drink more or less water than Elena? Group of answer choices
Answer:
Lin drank more water
Step-by-step explanation:
Given
Elena = 3 litres
Jada = ¾ of Elena
Lin = 2 times of Jada
Required
Determine if Lin drank more or less water than Elena
First, we have to get the actual amount of water Jada drank.
Jada = ¾ of Elena
Substitute 3 litres of Elena
[tex]Jada = \¾ * 3 litres[/tex]
[tex]Jada = 9/4 litres[/tex]
[tex]Jada = 2\¼\ litres[/tex]
Lin = 2 * Jada
Substitute 2¼ litres for Jada
[tex]Lin = 2 * 2\¼\ litres[/tex]
[tex]Lin = 2 * 9/4 litres[/tex]
[tex]Lin = 9/2 litres[/tex]
[tex]Lin = 4\frac{1}{2} litres[/tex]
Recall that Elena drank 3 litres
Comparing 3 Litres to [tex]4\frac{1}{2}[/tex] litres, we can conclude that Lin drank more water.
Solve for b. -11b+7 = 40 b=
Answer:
B= -3
Step-by-step explanation:
Move the terms that do not contain b to the right then solve. Hope this helps!
Answer:
[tex]\large \boxed{{b=-3}}[/tex]
Step-by-step explanation:
[tex]-11b +7=40[/tex]
Subtract 7 from both sides.
[tex]-11b +7-7=40-7[/tex]
[tex]-11b=33[/tex]
Divide both sides by -11.
[tex]\displaystyle \frac{-11b}{-11} =\frac{33}{-11}[/tex]
[tex]b=-3[/tex]
In the Rhombus, m<3=80. Find m<2
160
80
50
40
==============================================
Explanation:
The diagonal cuts the rhombus into two congruent isosceles triangles. We know they are isosceles because the non-diagonal sides are equal in length (since all four sides of a rhombus are the same length).
Let x be the measure of angle 1. This is one base angle. The other base angle is also x as well. The third angle of the bottom triangle is angle 3, which is given to us at 80 degrees. For any triangle the three angles always add to 180.
x+x+80 = 180
2x+80 = 180
2x = 180-80
2x = 100
x = 100/2
x = 50
Angle 1 is therefore 50 degrees.
Angle 2 is also 50 degrees because angles 1 and 2 are congruent alternate interior angles. Any rhombus is a parallelogram (but not the other way around) so the top and bottom lines of the rhombus are parallel, allowing the alternate interior angles to be congruent.
Answer:
m<2 = m<1 = 50°
Step-by-step explanation:
In a Rhombus, Diagonals intersect at 90° as well bisect angles.
Therefore, in a triangle formed by <1, 90° at the diagonal intersection and angle bisection of <3 = 40°.
m<1 = m<2 = 50°
A business has $25,000 to spend on training sessions for its employees. It wants 45 of its employees to attend. The business wants to send as many employees as it can to a technology training. The technology training costs $1,000 per person. The customer service training costs $500 per person. Create a system of equations that models how many of each type of training the business should purchase. 1,000x + 500y = 45 x + y = 25,000 1,000x + 500y = 25,000 x + y = 45 1,000x + y = 45 x + 500y = 25,000 x + 500y = 45 1,000x + y = 25,000
Answer: [tex]x+y=45\\\\1000 x + 500y = $2500[/tex]
Step-by-step explanation:
Let x = Number of employees taking technology training
y= Number of employees taking customer service training
Given, The technology training costs $1,000 per person. The customer service training costs $500 per person.
Total cost = 1000 x + 500y
Since, Total cost = $25,000 and total employee to attend training= 45 .
That means , the required equations are:
[tex]x+y=45\\\\1000 x + 500y = $2500[/tex]
Answer:
1,000x + 500y = 45
x + y =45
Step-by-step explanation:
So that means answer b is the correct answer, also I took the test.
I need help pppppppllssssssssss
Answer:
y=x-1
Step-by-step explanation:
el deposito de gasolina en una estacion de servicio alcanza para 5 dias si se venden 1400 galones diarios ¿cuantos galones diarios deben venderse para que el deposito cura 7 dias?
Answer:
u should put this also in English then type it in so it will translate
what is the value of digit 9 in 3.45×0.27×0.3 ?
Answer:
[tex]\boxed{\pink{0.27945}}[/tex]
Step-by-step explanation:
[tex]3.45 \times 0.27 \\ = 0.9315 \times 0.3 \\ = 0.27945[/tex]
Answer: thousandths place
Step-by-step explanation:
↓
3.45 x 0.27 x 0.3 = 0.27945
The place values to the right of the decimal point are:
one to the right (2): tenths
two to the right (7): hundredths
three to the right (9): thousandths
four to the right (4): ten thousandths
five to the right (5): hundred thousandths
I need help pls will give you five stars and a big thank you comrade
Answer:
B, f(x) = ( x+2) ^2(x-1) (x+3)
Step-by-step explanation:
Looking at the x- intercepts, the line passes at 2, -1, and 3, so B is you answer (:
Explain what each of them is.
Answer:
What are natural numbers?the positive integers or whole numbers include 1, 2, 3, and etc. sometimes zero.
What are whole numbers?Whole numbers are 0, 1, 2, 3, 4, 5, 6. Whole numbers include positive integers along with 0.
17, 99, 267, 8107 and 999999999 are examples of whole numbers.
What are rational numbers?A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333
What are irrational numbers?A real number that can NOT be made by dividing two integers (an integer has no fractional part). "Irrational" means "no ratio", so it isn't a rational number.
Example: π is an irrational number.
What are real numbers?The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2.
Included within the irrationals are the transcendental numbers, such as π
the sum of three consecutive numbers is 276. What is the smallest of these intengers?
Answer:
91
Step-by-step explanation:
Let x be the smallest one:
● x is the first number
● x+1 is the second number
● x+2 is the third number
The sum of these numbers is 276
● x+(x+1)+(x+2) =276
● x+x+1+x+2 = 276
● 3x + 3 = 276
Substract 3 from both sides:
● 3x+3-3 = 276-3
● 3x = 273
Divide both sides by 3
● (3x)/3 = 273/3
● x = 91
So the smallest one is 91
please i need help asap lol
A baseball league is holding registration for both a men's league and a women's league. Only a total of 546 players can register, and each team consists of exactly 13 players. If 25 women's teams have already registered, which inequality could be used to find m, the number of men's teams that can register? A. 25(13) + 13m 546 C. 25(13 + 13m) 546
Answer:
546 - 25 x 13 (divided by) 13
546 - (25 x 13) / 13
Step-by-step explanation:
25 x 13 = 325
546 - 325 = 221
221 / 13 = 17
17 mens teams can register.
Answer:
[tex]25(13)+13m\leq 546[/tex]
A
Step-by-step explanation:
Each team can only consists of thirteen players. Therefore, by letting w represent the number of women's teams and m the number of men's teams, the total number of players is represented by the equation:
[tex]13w+13m[/tex]
The total number of players cannot surpass 546. In other words, it must be less than or equal to. Therefore:
[tex]13w+13m\leq 546[/tex]
We are given that that 25 women's teams have already signed up. To find out the possible number of men's teams that can sign up, we can substitute 25 for w and then solve for m.
Therefore:
[tex]25(13)+13m\leq 546[/tex]
In conclusion, the answer is A.
