Answer:
There are 108900 different committees can be formed
Step-by-step explanation:
* Lets explain the combination
- We can solve this problem using the combination
- Combination is the number of ways in which some objects can be
chosen from a set of objects
-To calculate combinations, we will use the formula nCr = n!/r! × (n - r)!
where n represents the total number of items, and r represents the
number of items being chosen at a time
- The value of n! is n × (n - 1) × (n - 2) × (n - 3) × ............ × 1
* Lets solve the problem
- There are 12 men and 12 women
- We need to form a committee consists of 3 men and 4 women
- Lets find nCr for the men and nCr for the women and multiply the
both answers
∵ nCr = n!/r! × (n - r)!
∵ There are 12 men we want to chose 3 of them
∴ n = 12 and r = 3
∴ nCr = 12C3
∵ 12C3 = 12!/[3!(12 - 3)!] = 220
* There are 220 ways to chose 3 men from 12
∵ There are 12 women we want to chose 4 of them
∴ n = 12 and r = 4
∴ nCr = 12C4
∵ 12C4 = 12!/[4!(12 - 4)!] = 495
* There are 495 ways to chose 4 women from 12
∴ The number of ways to form different committee of 3 men and 4
women = 220 × 495 = 108900
* There are 108900 different committees can be formed
Any line with a slope of zero is parallel to the
O y-axis
O x-axis
O line y = x
Answer:
x-axis
Step-by-step explanation:
A line with a slope of zero has the same y-value everywhere, so is parallel to the line y=0, the x-axis.
Answer:
x- axis
Step-by-step explanation:
We are given that any line whose slope is zero.
We have to find the line with a slope of zero is parallel to which axis.
We know that when any line is parallel to x- axis
It means y does not change with
Therefore, [tex]\frac{dy}{dx}=0[/tex]
Slope of a line which is parallel to x- axis is zero because y does not vary with x.
But when a line parallel to y - axis then slope of that line is undefined.
When line y=x
Then , [tex]\frac{dy}{dx}=1\neq 0[/tex]
Hence, any line with slope of zero is parallel to the x- axis.
Answer:x- axis.
Which inequality statement best represents the graph?
Answer:
Step-by-step explanation:
If you have choices, you really should list them.
Here is the graph for y = (x + 0.25)(x - 1.75) which will look like yours. There are all sorts of variations that are possible, but at least I could reproduce a similar looking graph.
The figure below is a right rectangular prism. which expression represents the volume of the prism?
Answer: The expression (equation/formula) for the volume of a:
" right rectangular prism " ; is represented by:
____________________________________________________
→ " V = L * w * h " ;
____________________________________________________
in which: all the dimensions are in the same "units of measurement" (or converted to the same "units of measurement" ;
and in which:
" V " is the "volume" of the right rectangular prism; in the "cubic units" ; or written as: "units³ " ; or, [insert the particular units used}^ ³ " ;
→ that is, [units] raised to the "3rd [third] power" ; assuming these units are the same same "fundamental units of measurement" as the "other 2 (two) values in the expression".
If we are given no specific units of measurement whatsoever, then we use the generic term, "units" as the "units of measurement" ; and we express the "volume; "V" ; of a "right rectangular prism" as: " units ³ " ; or "cubic units" ;
in our answer— if we are asked to solve for the:
"volume; "V"; of a "right rectangular prism" ;
_________________________________________________
and in which:
"L" represents the "length" of a "right rectangular prism" ;
"w" represents the "width" of a "right rectangular prism" ;
"h" represents the "height" of a "right rectangular prism" .
_________________________________________________
To given an example:
Say we have a "right rectangular prism" ; with the given measurements:
width , "w" : w = 2 units;
length, "L" : L = 3 units ;
height, "h" : h = 8 units.
_________________________________________________
We are asked to "find the volume " ; of this "right recentangular prism" .
The formula for the volume; "V" ; of this "right rectangular prism" ;
is:
_________________________________________________
→ Volume = Length * width * height ;
that is:
→ V = L * w * h ;
Solve for the volume; "V" .
_________________________________________________
→ V = L * w * h ; Now plug in the values given:
→ V = (3 units) * (2 units) * (8 units) ;
= 3 * 2 * 8 * (units) * (units) * (units) ;
= 3 * 2 * 8 * units ³ ;
= 48 units ³ .
_________________________________________________
Hope this answer— and explanation—is helpful to you!
Wishing you the best in your academic pursuits
— and within the "Brainly" community!
_________________________________________________
Answer: A
Step-by-step explanation:
Which situation represents a proportional relationship? A) The cost of a taxi cab ride of $2.00 per mile with an initial fee of $3.00. B) The height of a tree that grows 1 foot a month with a starting height of 4 feet. C) The number of pounds of dirt in a wheelbarrow with each 5 pound shoveled scoop of dirt. D) The cost of a gym membership with a cost of $22.00 per month and a one time sign-up fee of $50.00.
Answer:
I think the answer is (c)
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The only one that doesn't require the initial part, since the initial part should be 0, in order, for a relationship to be proportional is answer C.
A) Initial fee of $3 (we need the initial to be 0).
B) Initial height of 4 ft (we need the initial to be 0).
C) I see nothing about a starting or initial so far this is it!
D) Initial fee is 50 dollars (we need the initial to be 0).
using the distributive property write numerical expression that is equivalent to 25+10
Answer:
5(5 + 2).
Step-by-step explanation:
5 is a factor of 25 and 10 so :
15 + 10 = 5(5 + 2).
For this case we have that by definition, the distributive property establishes:
[tex]a (b + c) = ab + ac[/tex]
Then, using the above definition, we must write an expression equivalent to:
[tex]25 + 10[/tex]:
The largest integer that divides both numbers without leaving residue is 5, then:
[tex]5 (5 + 2) = 5 * 5 + 5 * 2 = 25 + 10[/tex]
Answer:
[tex]5 (5 + 2)[/tex]
Which sentence demonstrates the multiplicative identity?
1/2 • 2= 1
1/2• 1= 1/2
1/2 + 0 = 1/2
Answer:
1/2 • 1 = 1/2
Step-by-step explanation:
It shows that anything multiplied by 1 is itself.
Answer:
1/2· 1= 1/2
Step-by-step explanation:
When multiplying by 1, you will get the same number.
NEED HELP QUICK
What is the mean of this set: {2, 6, 7, 9, 9, 9}?
6
7
8
9
The mean of a dataset if given by the sum of the elements divided by the number of elements:
[tex]M = \dfrac{2+6+7+9+9+9}{6} = \dfrac{42}{6}=7[/tex]
B. 7
Explanation:The mean (also known as the average) is found by adding all of the numbers in the set together, then dividing the result by how many numbers are in the set.
First, add the numbers together. [tex]2+6+7+9+9+9=42[/tex]
Finally, divide that by the amount of numbers in the set. [tex]\frac{42}{6}=7[/tex]
find the length of wire required to fence a rectangle field with three round, whose length and breadth are 150 m and 80m respectively
Answer:
1380 meters
Step-by-step explanation:
perimeter of a rectangle :2(l+b)
2(150 +80)
2(230)
460 meters of wire for one round
for three rounds :3×460=
1380 meters
Which three pairs of measurements are possible side length for the triangle?
Answer:
A, B, E, F
Step-by-step explanation:
In a 30-60-90 triangle, the hypotenuse is twice the length of the short leg.
That makes choice E possible.
In a 30-60-90 triangle, the long leg is sqrt(3) times the length of the short leg.
That makes choices A, B, and F possible.
Answer:
First option.
Option 5.
Option 6.
Step-by-step explanation:
The formula for a 30-60-90 triangle is this:
1) Side opposite to 30 will be value [tex]a[/tex].
2) Side opposite to 60 will be value [tex]a\sqrt{3}[/tex].
3) Hypotenuse will be [tex]2a[/tex].
So let's look and see:
First option: [tex]AB=4[/tex] and [tex]BC=4\sqrt{3}[/tex]
AB is opposite of the angle with 30 degree measurement.
BC is opposite of the angle with 60 degree measurement.
So [tex]a=4[/tex] here.
So the side opposite of 60 using the formula should be [tex]4 \sqrt{3}[/tex] which it is here.
So first option looks good.
Second option: [tex]BC=2\sqrt{3}[/tex] and [tex]AC=2[/tex].
We aren't given the side opposite to 30.
AC is the hypotenuse so 2a=2 which means the side opposite to 30 is a=2/2=1.
This means using the formula that the side opposite to 60 will be [tex]1\sqrt{3}=\sqrt{3}[/tex] but we don't have that.
So not option 2.
Third option: [tex]AB=3[/tex] and [tex]AC=3\sqrt{3}[/tex]
AB is the side opposite of 30, so we have [tex]a=3[/tex]
AC is the hypotenuse so that side should be [tex]2a=6[/tex] and it isn't.
Option 3 is not working.
Fourth option: [tex]BC=10[/tex] and [tex]AC=4\sqrt{3}[/tex]
So we have that [tex]2a=4\sqrt{3}[/tex] which means [tex]a=2\sqrt{3}[/tex] and so [tex]a\sqrt{3}=2\sqrt{3}\sqrt{3}=2(3)=6[/tex] but that is a contradiction because we have this value should be 10.
Not option 4.
Option 5: [tex]AB=7[/tex] and [tex]AC=14[/tex]
So we have [tex]a=7[/tex] and [tex]2a=14[/tex] so this looks good.
Option 6: [tex]AB=11[/tex] and [tex]BC=11\sqrt{3}[/tex]
[tex]a=11[/tex] so [tex]a\sqrt{3}=11\sqrt{3}[/tex] which is what we have.
Option 6 works.
Approximate area under the curve f(x) =-x^2+2x+4 from x=0 to x=3 by using summation notation with six rectangles and use the the right endpoint value for x to calculate the height
Answer:
Summation notation:
[tex]\frac{1}{2}\sum_{k=1}^6f((.5k))[/tex]
or after using your function part:
[tex]\frac{1}{2}\sum_{k=1}^6(-(.5k)^2+2(.5k)+4)[/tex]
After evaluating you get 11.125 square units.
Step-by-step explanation:
The width of each rectangle is the same so we want to take the distance from x=0 to x=3 and divide by 6 since we want 6 equal base lengths for our rectangles.
The distance between x=0 and x=3 is (3-0)=3.
We want to divide that length of 3 units by 6 which gives a length of a half per each base length.
We are doing right endpoint value so I'm going to stat at x=3. The first rectangle will be drawn to the height of f(3).
The next right endpoint is x=3-1/2=5/2=2.5, and the second rectangle will have a height of f(2.5).
The next will be at x=2.5-.5=2, and the third rectangle will have a height of f(2).
The fourth rectangle will have a height of f(2-.5)=f(1.5).
The fifth one will have a height of f(1.5-.5)=f(1).
The last one because it is the sixth one will have a height of f(1-.5)=f(.5).
So to find the area of a rectangle you do base*time.
So we just need to evaluate:
[tex]\frac{1}{2}f(3)+\frac{1}{2}f(2.5)+\frac{1}{2}f(2)+\frac{1}{2}f(1.5)+\frac{1}{2}f(1)+\frac{1}{2}f(.5)[/tex]
or by factoring out the 1/2 part:
[tex]\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))[/tex]
To find f(3) replace x in -x^2+2x+4 with 3:
-3^2+2(3)+4
-9+6+4
1
To find f(2.5) replace x in -x^2+2x+4 with 2.5:
-2.5^2+2(2.5)+4
-6.25+5+4
2.75
To find f(2) replace x in -x^2+2x+4 with 2:
-2^2+2(2)+4
-4+4+4
4
To find (1.5) replace x in -x^2+2x+4 with 1.5:
-1.5^2+2(1.5)+4
-2.25+3+4
4.75
To find f(1) replace x in -x^2+2x+4 with 1:
-1^2+2(1)+4
-1+2+4
5
To find f(.5) replace x in -x^2+2x+4 with .5:
-.5^2+2(.5)+4
-.25+1+4
4.75
Now let's add those heights. After we obtain this sum we multiply by 1/2 and we have our approximate area:
[tex]\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))[/tex]
[tex]\frac{1}{2}(1+2.75+4+4.75+5+4.75)[/tex]
[tex]\frac{1}{2}(22.25)[/tex]
[tex]11.125[/tex]
Okay now if you wanted the summation notation for:
[tex]\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))[/tex]
is it
[tex]\frac{1}{2}\sum_{k=1}^{6}(f(.5+.5(k-1)))[/tex]
or after simplifying a bit:
[tex]\frac{1}{2}\sum_{k=1}^6 f((.5+.5k-.5))[/tex]
[tex]\frac{1}{2}\sum_{k=1}^6f((.5k))[/tex]
If you are wondering how I obtain the .5+.5(k-1):
I realize that 3,2.5,2,1.5,1,.5 is an arithmetic sequence with first term .5 if you the sequence from right to left (instead of left to right) and it is going up by .5 (reading from right to left.)
Solve for x
X^2+6x+9=20
Answer:
x = 1.47 or x = -7.47
Step-by-step explanation:
x²+6x+9=20
This is a quadratic equation
x²+6x+9-20=0
x²+6x-11=0
Step 1 : Write the quadratic formula
x = -b±√b²-4(a)(c)
2a
Step 2 : Substitute values in the formula
a = 1
b = 6
c = -11
x = -6±√6²-4(1)(-11)
2(1)
x = -6±√80
2
x = -3 + 2√5 or x = -3 - 2√5
x = 1.47 or x = -7.47
!!
Answer:
x=1.472 or x=-7.472
Step-by-step explanation:
Lets begin by rearranging the equation into the format ax²+bx+c=0
The equation will be:
x²+6x+9-20=0
x²+6x-11=0
We shall use the quadratic formula to solve the equation.
x=[-b±√(b²-4ac)]/2a
=[-6±√(6²-4×1×-11)]/2
=[-6±√80]/2
=[-6±8.944]2
x= Either (-6+8.944)/2 or x= (-6-8.944)/2
Solving for x in each case gives:
x=1.472 or x=-7.472
Add the following lengths: 4'9" + 7"
Answer:
5'4"
Step-by-step explanation:
In terms of height, the apostrophe ( ' ) stands for feet and the quotation mark ( " ) stands for inches.
Your first term includes 4 feet and 9 inches. There are 12 inches in a foot, so we can simplify this as being 57 (48+9) inches.
Your second term includes 7 inches.
Add your two terms (57 and 7) together, and you have 64 inches.
Again, there are 12 inches in a foot, so to convert 64 inches to feet, count how many times you can put 12 into 64 without surpassing 64.
12 / 24 / 36 / 48 / 60
This will result in 5 times, so you have 5 feet and 4 inches left over.
Subtract the sum of _36/11 and 49/22 from the sum of 33/8 and _19/4.
Answer:37/88
Step-by-step explanation:
Sum of -36/11&49/22=- 1,1/22
Sum of 33/8&-19/4=- 5/8
-5/8-(-1,1/22)=37/88
A class used cars and vans to go on a field trip because of the buses were already in use the use 12 vehicles to go on the trip each car holds for students in each van holds 11 students if 83 students went on the trip and how many of each type of vehicle did the class use
Please answer
Answer:5 vans 7 cars
Step-by-step explanation:
c=cars v=vans
c+v= 12
c =( 12-v)
11v + 4(12-v) = 83
11v + 48-4v = 83
7v = 35
v= 5
c = 12-5 c = 7
7 cars x 4 students = 28 students
5 vans x 11 students = 55 students
55+28 = 83 students
Explain why the two sets are equivalent.
A={The letters in the word SEAT}
B={The letters in the word TASTE}
A. The two sets are not equivalent because set A has 4 letters and set B has 5.
B. Both sets contain the same elements.
C. Both sets contain objects.
D. Both sets contain letters.
Answer:
B. Both sets contain the same elements.
Step-by-step explanation:
Given:
A={The letters in the word SEAT}
B={The letters in the word TASTE}
Writing the sets in elements form
A = {S,E,A,T}
B={A,S,T,E} => the letter T appears two times but the repeating elements are written only once.
Hence, both sets contain the same letters.
Therefore, the correct answer is:
B. Both sets contain the same elements ..
About what percentage of Guadalupe's payments so far have gone to paying
interest?
Answer: C. 96% -------- APEX :D
help please also thank you so much if you do
Answer:
Step-by-step explanation:
100 cm = 1 meter
200 cm = 2 meters
100 cm = 1 meter
150 cm = 150 / 100 = 1.5 meters.
1 meter = 100 cm
6.5 meters = 6.5 * 100 = 6500 cm
1 km = 1000 meters.
5 km = 5 * 1000 meters = 5000 meters.
1 meter = 100 cm
1.68 m = 100 * 1.68
1.68 m = 168 cm
1 km = 1000 meters.
8.25 km = 8.25 * 1000 m = 8250 meters.
what is 144^1/2=12 written in logarithmic form
Answer:
[tex]\log_{144}(12)=\frac{1}{2}[/tex]
Step-by-step explanation:
First step identify the base. The base is 144.
The exponent is the logarithm.
The number not mentioned is the one that goes inside.
In other words [tex]a^x=b[/tex] is equivalent to [tex]log_a(b)=x[/tex]
There are some restrictions on what a and b can be.
You read [tex]log_a(b)=x[/tex] as log base a of b equals x
x is the exponent
a is the base
So we have log base 144 of 12 equals 1/2
[tex]\log_{144}(12)=\frac{1}{2}[/tex]
What is the slope of the line?
y + 1 = 3 (x - 4)
A. 1/3
B. -4/3
C. -3/4
D. 3
Answer:
D. 3
Step-by-step explanation:
In the Point-Slope Formula, y - y₁ = m(x - x₁), m represents the rate of change [slope], which in this case is 3.
I am joyous to assist you anytime.
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The slope of the line y + 1 = 3 (x - 4) is 3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line y + 1 = 3 (x - 4)
y + 1 = 3 (x - 4)
Subtract 1 on both sides.
y = 3(x - 4) - 1
y = 3x - 12 -1
y = 3x - 13
This is in the form of y = mx + c
Now,
Slope = m
m = 3
Thus,
The slope of the line y + 1 = 3 (x - 4) is 3.
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ2
what is the point-slope form of the equation for the line with a slope of -2 that passes through the point (4,-6)
Answer: y+6=-2(x-4)
Step-by-step explanation:
Point slope form: Y-y1=m(x-x1)
Answer:
[tex]y+6=-2(x-4)[/tex]
Step-by-step explanation:
Point-slope form of a line is [tex]y-y_1=m(x-x_1)[/tex] where the slope is [tex]m[/tex] and [tex](x_1,y_1)[/tex] is a point on the line.
We know both of those things so we have enough information without doing any math to do this problem. You just got to plug in.
So replace [tex]m[/tex] with -2, [tex]x_1[/tex] with 4, and [tex]y_1[/tex] with -6.
Like so:
[tex]y-(-6)=-2(x-4)[/tex].
You can simplify a little:
[tex]y+6=-2(x-4)[/tex].
suppose a figure is located in Quadrant l. which of the following sequences will result in an image that is located in Quadrant lll?
Answer:
Step-by-step explanation:
A will.
Suppose the object is placed on (5,4)
If you rotate it 180o counterclockwise, the point will become (-5,-4) (both x and y will change signs.)
Moving one unit down will still leave you in quadrant III.
If you start in another quadrant, this answer will not be correct. If the point started out in quadrant 2, rotating it 180o counterclockwise will put you in quad 4. For example
Object Start: (-2,3) Starts in quad 2
Image found: (- -2, - 3) = (2, - 3) which is in quad 4.
Find the value of m<3-m<1.
A. 20°
B. 50°
C. 90
D. 120°
Answer:
B. 50°
Step-by-step explanation:
70° and m<1 are Complementary Angles, meaning they add up to 90°, so, m<1 is 20°. Now, m<3 is also 70° because they are Alternative Angles, meaning that they are reflexive. Now you can perform your deduction:
70 - 20 = 50
I am joyous to assist you anytime.
In a museum, Nick is looking at a famous painting through a mirror at an angle of 58 degrees Find the angle the painting makes with the mirror. Also, find m
here's your answer
The angle of incidence of the painting is 58°, one property of mirrors is angle of incidence = angle of reflection. Therefore angle of reflection the painting makes with the mirror is 58°.
HOPE IT HELPS....
Answer:
58 degree
Step-by-step explanation:
We know that in mirror angle of incident equal to the angle of reflection.Here angle between reflected ray and mirror is 58 degree (let angle of reflection ). Therefore the angle of incident (angle between painting and mirror) must be 58 degree.
Hence the angle of the painting with the mirror =58 degree.
The graph shows Melissa's heart rate in beats per minute be) during the tirst few minutes other cool down after
jogging
Melissa's Heart Rate
Heart Rate -
Answer:
The domain is {1,2,3,4,5}
The range is {150,135,120,105,90}
Step-by-step explanation:
Domain is the set of x-values (x axis) and Range is the set of y-values (y axis).
Now if you look at the relation (points given), you can see the 5 points corresponds to 1,2,3,4, adn 5 in the x axis (minutes). So this is the domain - 1,2,3,4,5.
If we look at the y-axis (Heart Rate) , the values corresponding to 1,2,3,4,and 5 are 150, 135, 120, 105, and 90. These are the range.
Hence the last choice is the correct answer.
Answer: Domain = {1,2,3,4,5}
Range = {150,135, 120,105, 90}
Step-by-step explanation:
We know that,
Domain : Set of all input values .
Range : Set of output values.
In a graph, x values are the input values and y values are output values.
Given : The graph shows Melissa's heart rate in beats per minute be) during the first few minutes other cool down after jogging .
In the graph, number of minutes are shown by x-values and heart rate are shown by y-values.
Thus from graph, Domain = {1,2,3,4,5}
Range = {150,135, 120,105, 90}
If you travel 90 miles in 1 ½ hours, what distances would you travel if you drove 6 hours?
Answer:
360 miles
Step-by-step explanation:
If you travel 90 miles in 1 ½ hours, it will take 360 miles if you drove 6 hours.
All you have to do is, multiply 1 ½ until you get to 6.
The easiest way is:
1 ½ = 90 miles
1 ½ (90 miles) x 2 = 3 or 180 miles
3 (180 miles) x 2 = 6 or 360
Therefore, 6 hours = 360 miles.
Final answer:
This detailed answer explains how to calculate distances based on speed and time using a specific formula.
Explanation:
The question is about calculating distances traveled based on time and speed.
To find the distance, use the formula: distance = speed × time.
Given 90 miles in 1 ½ hours, first find the speed: 90 miles ÷ 1.5 hours = 60 miles/hour.
Then for 6 hours of travel: distance = 60 miles/hour × 6 hours = 360 miles.
If two cylinder are similar and the ratio between the lengths of their edges is 4;3 what is the ratio of their volumes
Answer:
64 : 27
Step-by-step explanation:
Given 2 similar figures with
ratio of lengths = a : b, then
ratio of volumes = a³ : b³
For 2 cylinders with ratio of lengths = 4 : 3, then
ratio of volumes = 4³ : 3³ = 64 : 27
Answer:
Its 64:27
Step-by-step explanation:
What is the value of x in the equation 3/4(1/4x+8)-(1/2x+2)=3/8(4-x)-1/4x ?
Answer: x = 24
Step-by-step explanation:
3/4 (x/4 + 8) - x/2 +2 = 3/8 (4-x) - x/4
3x/16 + 6 - x = 3/2 - 3x/8 - x/4
collect like term
3x/16 - x+ 3x/8 +x/4 = 3/2 -6
3x-16x+6x +4x / 16 = 3-12 / 2
-3x/16 = -9/2
cross multiply
-6x = -144
Divide bothside by -6
-6x/-6 = -144/6
x = 24
Sure, let's solve the equation:
\[ \frac{3}{4}\left(\frac{1}{4}x + 8\right) - \left(\frac{1}{2}x + 2\right) = \frac{3}{8}(4 - x) - \frac{1}{4}x \]
First, distribute the fractions across the terms inside the parentheses:
\[ \frac{3}{4} \cdot \frac{1}{4}x + \frac{3}{4} \cdot 8 - \frac{1}{2}x - 2 = \frac{3}{8} \cdot 4 - \frac{3}{8} \cdot x - \frac{1}{4}x \]
[Simplify the terms]:
\[ \frac{3}{16}x + 6 - \frac{1}{2}x - 2 = \frac{3}{2} - \left(\frac{3}{8} + \frac{1}{4}\right)x \]
Now, combine like terms:
\[ \frac{3}{16}x - \frac{8}{16}x + 4 = \frac{3}{2} - \frac{3}{8}x - \frac{2}{8}x \]
\[ -\frac{5}{16}x + 4 = \frac{3}{2} - \frac{5}{8}x \]
Next, we want to solve for \( x \), so we'll move all the \( x \)-terms to one side and the constants to the other side:
\[ -\frac{5}{16}x + \frac{5}{8}x = \frac{3}{2} - 4 \]
Convert \( \frac{5}{8} \) to a fraction with a denominator of 16:
\[ -\frac{5}{16}x + \frac{10}{16}x = \frac{6}{4} - \frac{16}{4} \]
Combine like terms again:
\[ \frac{5}{16}x = -\frac{10}{4} \]
\[ \frac{5}{16}x = -2.5 \]
Finally, solve for \( x \):
\[ x = \frac{-2.5}{\frac{5}{16}} \]
\[ x = -2.5 \cdot \frac{16}{5} \]
\[ x = -2.5 \cdot 3.2 \]
\[ x = -8 \]
So the solution for \( x \) in the given equation is \( x = -8 \).
- the following functions.
f = {(-4,1),(5, 1), (1, -1)}
and
8 = {(5, 1), (1,4)}
2: Find (f + g)(1).
Answer:
(f+g)(1)
equals
3
Step-by-step explanation:
(f+g)(1) is f(1)+g(1).
f(1) means what y corresponds to x=1 so f(1)=-1.
g(1) means what y corresponds to x=1 so g(1)=4.
So (f+g)(1)=f(1)+g(1)=-1+4=3.
The Rangers won 5 of their first 8 games. At this rate,how many games should the Rangers win out of 56 games? F. 28 games. G. 32 games. H. 35 games. I. 37 games.
Answer: H. 35 games
Step-by-step explanation: Set up a proportion.
5/8 = X/56
Cross multiply.
5 x 56 = 280
8 x X = 8x
The cross multiplied equation will be 280=8x.
Divide by 8 in order to isolate x.
x=35
They will win 35 games.
Answer:
The answer is H. 35 games
What is the equation of the following line written in slope-intercept form?
Answer:
[tex]y=-\frac{3}{2}x - 9/2[/tex]
Step-by-step explanation:
The slope - intercept equation is
[tex]y = mx + b[/tex]
where m = slope
and b = intercept
The line intercepts the y axis in -9/2, so b = -9/2
To calculate the slope we can take two points where the line passes:
p1= (-3, 0)
p2=(-1, -3)
the slope will be a fraction with the numerator being the difference in the y coordinates and the denominator the difference in the x coordinates
[tex]m=\frac{-3-0}{-1-(-3)}=\frac{-3}{2}[/tex]
replacing the values for m and b in the slope - intercept equation:
[tex]y=-\frac{3}{2}x - 9/2[/tex]