Answer:
Choice D is correct
Step-by-step explanation:
We have been given the expression;
[tex]21\leq-3(x-4)<30[/tex]
The first step is to open the brackets using the distributive property;
-3(x-4) = -3x + 12
Now we have;
[tex]21\leq-3x+12<30\\\\21-12\leq-3x+12-12<30-12\\ \\9\leq-3x<18\\\\\frac{9}{-3}\geq x>\frac{18}{-3}\\\\-6<x\leq-3[/tex]
The equation of a line in slope intercept form is y=mc+b where m is the x-intercept. True or False?
Answer:
False
Step-by-step explanation:
First, there is no x in your equation. I think you meant y = mx + b.
Second, m is the slope, and b is the y-intercept.
Nandini needs more than 80 points to win a game. She has 64 points so far. Which inequality represents p, the number of points she still needs to win the game?
Step-by-step explanation:
80=64+P if its it's there
Answer: I think its B, p+64 > 80.
Step-by-step explanation: P is the points she needs and 64 is the points she already has. They need to be more than 80, so p+64 is greater than 80.
What is the right-hand limit of the function `f(x) = (x^2 + 2x - 3)/(x - 3)` as x approaches 2?
[tex]\displaystyle\\\lim_{x\to 2}\dfrac{x^2+2x-3}{x-3}=\dfrac{2^2+2\cdot2-3}{2-3}=\dfrac{5}{-1}=-5[/tex]
The right-hand limit of the function f(x) = (x^2 + 2x - 3)/(x - 3) as x approaches 2 is -5 after substitution of x = 2 into the function.
The question asks about the right-hand limit of the function f(x) = (x^2 + 2x - 3)/(x - 3) as x approaches 2. The first step in finding this limit is to simplify the function, if possible. In this case, we can factor the numerator to obtain (x - 1)(x + 3). However, since we are looking for a limit as x approaches 2, the denominator x - 3 will not be zero, and the expression does not need further simplification for this purpose. We then substitute x = 2 directly into the simplified function and find the limit.
So, the right-hand limit as x approaches 2 is simply f(2) = ((2)^2 + 2*2 - 3)/(2 - 3) = (4 + 4 - 3)/(-1) = 5/(-1) = -5.
Evaluate the following expression. Round your answer to two decimal places Log7^e
A. 0.43
B. 1.47
C. 0.51
D. 1.95
The value of the given expression [tex]\log_{7} e[/tex] will be 0.51, i.e. option C.
What is expression ?Expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
We have,
[tex]\log_{7} e[/tex]
So,
Using the log rule,
On solving we get,
[tex]\log_{7} e =0.51[/tex]
So,
This the value of the given expression.
Hence, we can say that the value of the given expression [tex]\log_{7} e[/tex] will be 0.51, i.e. option C.
To know more about expression click here
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Final answer:
The given expression Log₇^eA can be simplified and evaluated to approximately 0.43 when rounded to two decimal places.
Explanation:
Logarithms:
The expression Log₇^eA can be rewritten as Log₇(e). Applying the change of base formula to convert it to a common logarithm form, Log₇(e) = ln(e) / ln(7). Since ln(e) = 1, the result is approximately 0.43, rounded to two decimal places.
Could anyone help me find the answer to this algebric equation. it needs to be written in mixed expression (x^2-5x+7)/(x-9)
Answer:
see explanation
Step-by-step explanation:
One way to divide is to use the denominator as a factor in the numerator
Consider the numerator
x(x - 9) + 9x - 5x + 7
= x(x - 9) + 4x - 7
= x(x - 9) + 4(x - 9) + 36 + 7
= x(x - 9) + 4(x - 9) + 43
quotient = x + 4, remainder = 43
Hence
[tex]\frac{x^2-5x+7}{x-9}[/tex] = x + 4 + [tex]\frac{43}{x-9}[/tex]
What is the area of the trapezoid?
16 square units
24 square units
32 square units
36 square units
Answer:
Second option.
Step-by-step explanation:
You can use the formula for calculate the area of a trapezoid. This is:
[tex]A_{(trapezoid)}=\frac{h}{2}(B+b)[/tex]
Where "B" is the larger base, "b" is the minor base and "h" is the height.
You can identify in the figure that:
[tex]B=8units\\b=4units\\h=4units[/tex]
Then you can substitute values into the formula, getting that the area of the trapezoid is:
[tex]A_{(trapezoid)}=\frac{4units}{2}(8units+4units)[/tex]
[tex]A_{(trapezoid)}=24units^2[/tex]
Answer: 24 units or answer b
Step-by-step explanation:
Please HELPP!!! Solve the system of equations.
y= 2x
y= x^2 - 15
[tex]y=2x\\y=x^2-15\\\\x^2-15=2x\\x^2-2x-15=0\\x^2-5x+3x-15=0\\x(x-5)+3(x-5)=0\\(x+3)(x-5)=0\\x=-3 \vee x=5\\\\y=2\cdot(-3) \vee y=2\cdot5\\y=-6 \vee y=10\\\\(x,y)\in\{(-3,-6),(5,10)\}[/tex]
Which of the following does the situation below best describe?
The enrollment at a high school does not change for 3 years in a row.
A. A relation that is not a function
B. A relation that is a function
C. The range of a function
D. The domain of a function
Answer:
B. A relation that is a function
Step-by-step explanation:
Answer:
B. A relation that is a function
Step-by-step explanation:
Let's see what a function is.
A function is a relation each different input has an output.
The given situation is " The enrollment at a high school does not change for 3 years in a row"
This means the consecutive years, the number of enrollment is the same.
Here each different years mapped with only one output. This is relation is a function.
This is classified as "a constant function" because three different inputs has the same output.
Therefore, the answer is B) A relation that is a function.
Which equation represents a line that passes through (4,3/4) and has a slope of 3/4
Answer:
The point-slope equation for a line that goes through the point (4, 1/3) with a slope of 3/4 is:
Choice B: [tex]\displaystyle y - \frac{1}{3} = \frac{3}{4}(x - 4)[/tex].
Step-by-step explanation:
This question gives
a point on the line, the slope (a.k.a. gradient) of the line.Consider the point-slope form of the equation of a line in a cartesian plane:
[tex]y - y_0 = m (x - x_0)[/tex],
where
[tex]x_0[/tex] and [tex]y_0[/tex] are the coordinates of the given point. The point on the line is [tex](x_0, y_0)[/tex].[tex]m[/tex] is the slope of the line.For this line:
The given point is [tex]\displaystyle (4,\; \frac{1}{3})[/tex] where [tex]x_0 = 4[/tex] and [tex]\displaystyle y_0 = \frac{1}{3}[/tex].The slope of the line: [tex]\displaystyle m = \frac{3}{4}[/tex].The point-slope equation of this line will be:
[tex]\displaystyle y - \frac{1}{3} = \frac{3}{4}(x - 4)[/tex].
Answer:
B.
Step-by-step explanation:
Got Correct On MyPath.
A grain silo is shown below: Grain silo formed by cylinder with radius 8 feet and height 172 feet and a half sphere on the top What is the volume of grain that could completely fill this silo, rounded to the nearest whole number? Use 22 over 7 for pi. (4 points) 34,597 ft3 11,532 ft3 35,669 ft3 2,146 ft3
Answer:
Third option: [tex]35,669 ft^3[/tex]
Step-by-step explanation:
You need to use the formula for calculate the volume of a cylinder:
[tex]V_c=\pi r^2h[/tex]
Where r is the radius (In this case is 8 feet) and h is the height (In this case is 172 feet).
The formula for calculate the volume of a half sphere is:
[tex]V_s= \frac{2}{3} \pi r^3[/tex]
Where r is the radius (In this case is 8 feet)
You need to add the volume of the cylinder and the volume of the half-sphere. Then the volume of grain that could completely fill this silo, rounded to the nearest whole number is (Remeber to use [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex]):
[tex]V=(\frac{22}{7}) (8ft)^2(172ft)+ (\frac{2}{3})(\frac{22}{7})(8ft)^3=35,669 ft^3[/tex]
Answer:
The correct answer is third option 35,669 feet³
Step-by-step explanation:
It is given that, Grain silo formed by cylinder with radius 8 feet and height 172 feet and a half sphere on the top
We have to find the volume of cylinder + volume of semi sphere
To find the volume of cylinder
Here r = 8 feet and f cylinder = πr²h
= (22/7) * 8² * 172
= 34596.57 ≈ 34597 feet³
To find the volume of hemisphere
here r = 8 feet
Volume of hemisphere = (2/3)πr³
= (2/3) * (22/7) * 8³
= 1072.76 ≈ 1073 feet³
To find the total volume
Total volume = volume of cylinder + volume of hemisphere
= 34597 + 1073
= 35,669 feet³
The correct answer is third option 35,669 feet³
A bakery offers a sale price of $2.90 for 4 muffins. What is the price per dozen?
Answer:
4 muffins are of $2.90
1 muffin is of 2.90/4 =0.725
1 dozen(12 muffens) 0.725x12=
Step-by-step explanation:
Answer:
8.70
Step-by-step explanation:
3 * 4 = 12.
12 = 1 dozen
So you have to multiply 2.90 * 3
The answer is 8.70
=======================
That's one way to do the problem. Here's another.
4 muffins = $2.90
12 muffins = x Cross multiply.
4x = 12*2.90
4x = 34.80 Divide by 4
4x/4 = 34.80/4 Do the division
x = $8.70
238·56+238·34+162·90
238(56)+238(34)+162(90)
=238(56+34) + 162(90)
=238(90) + 162(90)
=90(238+162)
=90(400)
=36000
For this case we must resolve the following expression:
[tex]238 (56) +238 (34) +162 (90) =[/tex]
We multiply term by term:
[tex]13328 + 8092 + 14580 =[/tex]
We add the terms:
[tex]13328 + 8092 + 14580 = 36000[/tex]
Finally, the answer is 36,000.
Answer:
[tex]238 (56) +238 (34) +162 (90) = 36,000.[/tex]
What is the solution to the linear equation?
4b + 6 = 2 - 6 + 4
0
b=-2
Ob=0
O b=4
6=6
0
Answer:
the solution of linear equation 4b + 6 = 2 - 6 + 4 is b = -2
Step-by-step explanation:
We need to solve the linear equation
4b + 6 = 2 - 6 +4
Adding constants
4b + 6 = 0
Adding -6 on both sides
4b + 6 -6 = 0 -6
4b = -6
Dividing with 4 on both sides
4b/4 = -6/4
b = -2
So, the solution of linear equation 4b + 6 = 2 - 6 + 4 is b = -2
Answer:
0
Step-by-step explanation:
Solve the system of equations.
4x+3y+6z=3
5x+5y+6z=5
6x+3y+6z=3
Answer:
C. [tex]x=0,\ y=1,\ z=0[/tex]
Step-by-step explanation:
Consider the system of three equations:
[tex]\left\{\begin{array}{l}4x+3y+6z=3\\5x+5y+6z=5\\6x+3y+6z=3\end{array}\right.[/tex]
Multiply the first equation by 5, the second equation by 4 and subtract them:
[tex]\left\{\begin{array}{r}4x+3y+6z=3\\-5y+6z=-5\\6x+3y+6z=3\end{array}\right.[/tex]
Multiply the first equation by 3, the second equation by 2 and subtract them:
[tex]\left\{\begin{array}{r}4x+3y+6z=3\\-5y+6z=-5\\3y+6z=3\end{array}\right.[/tex]
Multiply the second equation by 3, the third equation by 5 and add the second and the third equations:
[tex]\left\{\begin{array}{r}4x+3y+6z=3\\-5y+6z=-5\\48z=0\end{array}\right.[/tex]
Fro mthe third equation
[tex]z=0[/tex]
Substitute it into the second equation:
[tex]-5y+6\cdot 0=-5\\ \\-5y=-5\\ \\y=1[/tex]
Substitute y=1 and z=0 into the first equation:
[tex]4x+3\cdot 1+6\cdot 0=3\\ \\4x+3=3\\ \\4x=0\\ \\x=0[/tex]
The solution is
[tex]x=0,\ y=1,\ z=0[/tex]
Answer:
ageed its C
Step-by-step explanation:
Plz help 20 points answers please
Answer:
total=quantity*price per item on that row
New account balance=old account balance plus total on that row
Step-by-step explanation:
I won't do all of the rows but I will do a couple and explain to you how I got the answer and how you should too:
The total for each row is equal to that row's price per item times that row's quantity.
The amount balance is going to include previous account balance into it. So once you find the total for that row you will take previous account balance and add it to the previous account balance (We are doing adding instead of subtracting because the number we are getting is negative for the total.)
So example:
Second row total is 2(-45.25)=-90.50 so that is what we are adding to 2500.68 or we are subtracting 90.50 from 2500.68 giving us 2410.18
Third row total is 75(-1.39)=-104.25. Third row account balance is 2410.18-104.25=2305.93.
So again total=quantity*price per item on that row
New account balance=old account balance plus total on that row
If you want me to check your forth row to see if you are doing it right, I will.
Using the segment addition postulate, which is true?
AB + BC = AD
AB + BC = CD
BC + CD = AD
BC + CD = BD
Answer:
D
Step-by-step explanation:
For the segment addition postulate, two segments added together have to equal the third segment. In other words, if we added them together, the sum should be the first letter of the first line and the second letter of the second line.
BC + CD = BD
Two parallel lines are crossed by a transversal.
What is the value of x?
??!!!??!!!!!????
We can solve this problem by using the known value (115) to solve for the angle parallel to the equation.
To find the solve for the angle to the exact right of 115, subtract 115 from 180. This works because 115 and the unknown angle form to make a straight line, which is 180 degrees.
180-115=65
Now, since it is parallel, we know that 5x+5=65 degrees.
Solve the equation.
Subtract 5 on both sides.
5x=60
Divide both sides by 5 to isolate x.
5x=13
The value of x is 13.
Hope this helps!
multiply. (3.5x10^-5) (3x10^-10) express your answer in scientific notation.
Answer:
5.69034 × 1011
Step-by-step explanation:
Decimal
1234000000
Scientific Notation
1.234 x 10^9
×10^
9
1st Number
1.234
×10^
9
Operation
2nd Number
5.678
×10^
11
Write the point-slope form of the equation for a line that passes through (6, -1) with a slope of 2
ANSWER
[tex]y + 1=2(x-6)[/tex]
EXPLANATION
The point-slope form of a line is given by;
[tex]y-y_1=m(x-x_1)[/tex]
where
[tex]m = 2[/tex]
is the slope of the line and (6,-1) is point.
We substitute the point and the slope into the formula to obtain:
[tex]y + 1=2(x-6)[/tex]
Hence the b point slope form of the line with the given properties is
If nP3 /nC2 = 6, find the value of n
[tex]\dfrac{_nP_3}{_nC_2}=6\\\\\dfrac{\dfrac{n!}{(n-3)!}}{\dfrac{n!}{2!(n-2)!}}=6\\\\\dfrac{n!}{(n-3)!}\cdot \dfrac{2(n-2)!}{n!}=6\\\\2(n-2)=6\\\\2n-4=6\\\\2n=10\\\\n=5[/tex]
The value of n is 5
The formula to calculate permulation and combination are:
[tex]_nP_r = \frac{n!}{(n-r)!}\\\\\\_nC_r = \frac{n!}{r!(n-r)!}[/tex]
Putting in values we get:
[tex]_nP_3 = \frac{n!}{(n-3)!}\\\\\\_nC_2 = \frac{n!}{2!(n-2)!}[/tex]
Now we know that
[tex]\frac{_nP_3}{_nC_2} = 6[/tex]
So, putting in values we get:
[tex]\frac{\frac{n!}{(n-3)!}}{\frac{n!}{2!(n-2)!}} =6\\\\ \frac{n!}{(n-3)!} \times \frac{(n-2)! \times 2!}{ n!} = 6\\\\ \frac{1}{(n-3)!} \times (n-2)! \times 2! = 6\\\\ 2(n-2) = 6\\\\ n = 5[/tex]
Thus the value of n is 5.
What is the slope of the line shown below? (-1,8) and (2,-4)
Answer:
[tex]m = -4[/tex]
Step-by-step explanation:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
[tex]\frac{-4 - 8}{2-(-1)}[/tex]
[tex]-4 - 8 = -12\\ 2-(-1)=3[/tex]
[tex]\frac{-12}{3} = -4[/tex]
[tex]m = -4[/tex]
Answer:
M=-4
Step-by-step explanation:
The formula for the slope is:
m=[tex]\frac{y^{2} -y^{1} }{x^{2} -x^{1} }[/tex]
You have two points the first one would be: (-1,8)
So [tex]x^{1}= -1 y^{1}= 8 [/tex]
The second point is: (2,4)
So [tex]x^{2}= 2 y^{2}= 4 [/tex]
Now you just have to put the values inside the formula:
m=[tex]\frac{-4-8)}{2-(-1)}[/tex]
m=[tex]\frac{-12}{3}[/tex]
m=-4
Original Price:
Discount: 75%
Final Price: $85.99
Answer: $343.96
Step-by-step explanation:
x-0.75x=85.99
0.25x=85.99
Answer:
343.96
Step-by-step explanation:
The discount it 75%. That means we pay 25%
25% of the original price is 85.99
Let x be the original price
x*25% = 85.99
.25x = 85.99
Divide each side by .25
.25x/.25 = 85.99/.25
x =343.96
The original price is 343.96
what is the domain of f
Answer:
[ - 6 , 6 ]
Step-by-step explanation:
This is because the value of f(t) for x values only ranges from -6 to 6.
Please mark for Brainliest!! :D Thanks!!
For more questions or more information, please comment below!
Answer:
See attached!
Step-by-step explanation:
An air conditioning system can circulate 390 cubic feet of air per minute. How many cubic yards of air can it circulate per minute?
The air conditioning system can circulate approximately 14.44 cubic yards of air per minute.
To convert cubic feet to cubic yards, we need to know that there are 27 cubic feet in one cubic yard. Using this conversion factor, we can find the number of cubic yards of air that the air conditioning system can circulate per minute.
1. Start with the given value of 390 cubic feet per minute.
2. Divide this value by the conversion factor of 27 cubic feet per cubic yard:
390 cubic feet ÷ 27 cubic feet per cubic yard = 14.44 cubic yards
3. Rounding to the nearest hundredth, the air conditioning system can circulate approximately 14.44 cubic yards of air per minute.
In summary, the air conditioning system can circulate approximately 14.44 cubic yards of air per minute.
Find the volume of the specified cone. Use 3.14 for pi, and round your answer to the nearest whole number. Diameter = 3 cm, Height = 7 cm
Answer:
16 centimeters cubed
Step-by-step explanation:
Volume of cone is equal to 1/3 * pi * r^2 * h
We are using 3.14 for pi so I'm going to rewrite my formula for volume.
V=1/3 * 3.14 * r^2 * h
We are given diameter is 3 but we need the radius. We know the radius is half of the diameter so the radius is 1.5 since that is half of 3.
We are given the height is 7.
V=1/3 * 3.14 * 1.5^2 *7
Put into calculator
V=16.485
The whole number that this is closest to is .... 16
So
The Volume of the cone is approximately 16 centimeters cubed.
Answer: [tex]16\ cm^3[/tex]
Step-by-step explanation:
You can use this formula for calculate the volume of a cone:
[tex]V_{(cone)}=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height of the cone.
To find the radius, you need to divide the diameter by 2. Then:
[tex]r=\frac{3\ cm}{2}=1.5\ cm[/tex]
Knowing the radius and the height ([tex]h=7\ cm[/tex]), you can substitute them into the formula.
Therefore, the volume of the cone rounded to the nearest whole number is:
[tex]V_{(cone)}=\frac{1}{3}(3.14)(1.5\ cm)^2(7\ cm)\\\\V_{(cone})=16\ cm^3[/tex]
Harold has typed 14 more pages than Rebecca. Together they have
typed a total of 138 pages. How many pages have each of them typed?
Answer:
Harold typed 76, Rebecca typed 62
Step-by-step explanation:
It's Easy. For the first one, convert 1/5 and 2/3 to the like denominator of 15.
Therefore, you have 3/15 and 10/15. Add these to get 13/15. Now, find 13/15 of 60. To do this you will have to multiply 13 and 15 by 4 to get 52/60. Since the question asks you for how many are left, you subtract 52 from 60 to get 8.
And For the second one, first subtract 14 from 138. You have 124. Divide 124 by 2 to get 62. Then add 14 to Harold's total pages to get 76. 62 +76 = 138.
Transform the equation to isolate x:ax=bx + 1 how is the value of x related to the difference of a and b
Answer:
x = [tex]\frac{1}{a-b}[/tex]
Step-by-step explanation:
Given
ax = bx + 1
Collect the terms in x on the left side by subtracting bx from both sides
ax - bx = 1 ← factor out x from each term on the left side
x(a - b) = 1 ← divide both sides by (a - b)
x = [tex]\frac{1}{a-b}[/tex]
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27nft3. Which equation gives the volume of the sphere
Answer:
The volume of the sphere is [tex]V=18\pi\ ft^{3}[/tex]
Step-by-step explanation:
we know that
The volume of cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]V=27\pi\ ft^{3}[/tex]
substitute
[tex]27\pi=\pi r^{2}h[/tex]
simplify
[tex]27=r^{2}h[/tex]
Remember that
A sphere and a cylinder have the same radius and height
so
The height of cylinder is equal to the diameter of sphere
h=2r
substitute
[tex]27=r^{2}(2r)[/tex]
[tex]13.5=r^{3}[/tex] -----> equation A
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
substitute equation A in the formula of the volume of sphere
[tex]V=\frac{4}{3}\pi (13.5)[/tex]
[tex]V=18\pi\ ft^{3}[/tex]
Answer:
It's (A.) guys
Step-by-step explanation:
Find the missing value so that the two points have a slope of 3/2 (0,y) and (2,-2)
Answer:
y = -5
Step-by-step explanation:
To find the slope , we use
m = (y2-y1)/(x2-x1)
3/2 = (-2-y)/(2-0)
3/2 = (-2-y)/2
Since the denominators are the same, the numerators have to be the same
3 = -2-y
Add 2 to each side
3+2 = -2-y+2
5 = -y
Divide each side by -1
5/-1 = -y/-1
-5 = y
When you multiply by 0.01 the decimal point moves to the right or left
Answer:
The decimal point move to the left
Step-by-step explanation:
Let
x ----> a number
we know that
[tex]0.01=\frac{1}{100}[/tex]
When you multiply a number by 0.01 is equal to divide the number by 100
so
[tex]x*(0.01)=\frac{x}{100}[/tex]
therefore
The decimal point move to the left