The simplified expression is:
[tex]g(x)-f(x) = x^2-6x-1[/tex]
Solution:
Given that the expression is:
[tex]g(x) - f(x) = (x^2-x+3)-(5x+4)[/tex]
We have to simplify the expression
The expression can be simplified by combining the like terms
Like terms are terms that have the same variables and powers. The coefficients do not need to match
From given,
[tex]g(x) - f(x) = (x^2-x+3)-(5x+4)\\\\Remove\ the\ paranthesis\ and\ solve\\\\g(x) - f(x) = x^2-x+3-5x-4\\\\Combine\ the\ like\ terms\\\\g(x)-f(x) = x^2-x-5x+3-4\\\\Add\ the\ like\ terms\\\\g(x)-f(x) = x^2 -6x + 3 - 4\\\\Add\ the\ constants\\\\g(x)-f(x) = x^2 -6x -1[/tex]
Thus the expression is simplified
Please help meeeeeeeee
1 second = 2 megabytes
[tex]1\frac{1}{2}\ seconds=3\ megabytes[/tex]
2 seconds = 4 megabytes
Step-by-step explanation:
Given,
Time taken to download 5 megabytes = [tex]2\frac{1}{2}=\frac{5}{2}[/tex] seconds
[tex]\frac{5}{2}\ seconds = 5\ megabytes[/tex]
Multiplying both sides by [tex]\frac{2}{5}[/tex] to find unit rate
[tex]\frac{2}{5}*\frac{5}{2}\ second = \frac{2}{5}*5\\1\ second = 2\ megabytes[/tex]
1 second = 2 megabytes
[tex]1\frac{1}{2}\seconds = \frac{3}{2}\ seconds[/tex]
[tex]\frac{3}{2}\ seconds = \frac{3}{2}*2[/tex]
[tex]\frac{3}{2}\ seconds = 3\ megabytes[/tex]
[tex]1\frac{1}{2}\ seconds=3\ megabytes[/tex]
2 seconds = 2*2 megabytes
2 seconds = 4 megabytes
Keywords: fraction, multiplication
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Can someone help me please
Answer:
43.7 ft
Step-by-step explanation:
Radius of the semicircular garden is 8.5 ft .
Diameter = 8.5 × 2 = 17 ft
Circumference of the garden = [tex]\frac{1}{2}[/tex] × π × diameter = [tex]\frac{1}{2}[/tex] × π × 17 = 26.7 ft (rounded up to the nearest tenth of a foot)
Distance around the gardent = Circumference + diameter = 26.7 ft + 17 ft = 43.7 ft
There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.
What is the theoretical probability of randomly drawing a red marble?
20%
41.7%
62.5%
25%
Answer:
20%
Step-by-step explanation:
If there are 25 marbles in the bag and 5 of them are red then you just divide 25 by 5 which is 5 which is 1/5 the 25 witch 20%
Answer:
20%
Step-by-step explanation:
Nice seeing you a year later <3
1/4 10/9 simplify the complex fraction shown
Answer:
Step-by-step explanation:
[tex]\frac{1}{4}*\frac{10}{9}=\frac{1*5}{2*9}=\frac{5}{18}[/tex]
The simplified fraction is 9/40.
To simplify the complex fraction 1/4 over 10/9, you can multiply both the numerator and the denominator by the reciprocal of the denominator of the complex fraction, which is 9/10. This is sometimes referred to as the skillfully chosen factor. By doing so, you are simplifying the expression by getting rid of the complex fraction structure.
Here's the step-by-step simplification:
Multiply both the numerator (1/4) and the denominator (10/9) by 9/10.
Simplifying the numerator: (1/4) * (9/10) = 9/40.
Simplifying the denominator: (10/9) * (9/10) = 1 because the nines and tens cancel out.
Now you have a simple fraction: 9/40 over 1, which is just 9/40.
The simplified fraction is 9/40. When multiplying fractions, you multiply the top numbers and divide by the bottom numbers in the fractions.
H E L P ME OUT
According to the figure above the atmospheric pressure at an altitude of 22 kilometers is about:
Answer:
300mb
Step-by-step explanation:
We can read the atmospheric pressure at an altitude of 22 kilometers can be read by tracing directly from the graph.
22 kilometers is half way between 20 kilometers and 24 kilometers on the vertical axis.
The reading is shown in the attachment.
From the reading the atmospheric pressure is about 300mb
The correct answer is A
Which expression has the same GCF as 15x2 - 21x?
Answer:
12x^2-15x
Step-by-step explanation:
PLATO
The expression 12x²-15x has the same GCF as 15x² - 21x.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 15x²-21x
Let us find GCF of the given expression.
The GCF for a polynomial is the largest monomial that divides (is a factor of) each term of the polynomial
15x²-21x
3x(5x-7)
The GCF of 15x²-21x is 3x.
Now GCF of 18x²-24x, 6x(3x-4) is 6x
GCF of 12x²-15x, 3x(4x-4) is 3x
GCF of 15x²-21, 3(5x²-7) is 3
GCF of 12x²-18x, 6x(2x-3) is 6x
Hence, the expression 12x²-15x has the same GCF as 15x² - 21x.
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i don't btgcygljhbihlihnjknkl;n
Pls help!!
y = x + 2
2x - y = -4
Solve the system of equations using substitution.
A) (-2,-4)
B) (-2,0)
C) (-6,-4)
D) (-6,8)
E) (0,-2)
Answer:
B (-2, 0)
Step-by-step explanation:
put the first equation in for y in the second equation - watch the negative
2x - (x +2) = -4
2x - x -2 = -4
x = -2
plug this x back in to find y
y = -2 + 2 = 0
Answer:
B
Step-by-step explanation:
plug in the answers given into both equations to see if the statements true
y=x+2
0=(-2)+2
0=0
2x-y=-4
y=2x+4
0=2(-2)+4
0=0
7. Bobby buys 10 pounds seafood for $30. It
contains shrimp that sells for $5 per pound and
crawfish that sells $1 a pound. How many of each
kind were purchased in the mixture?
Answer:
5 pounds of shrimp and 5 pounds of crawfish were purchased in the mixture.
Step-by-step explanation:
We are given the following in the question:
Bobby buys 10 pounds seafood for $30.
Let x pounds of shrimp be purchased and y pounds of crawfish.
Thus, we can write,
[tex]x + y =10[/tex]
Cost of shrimp = $5 per pound
Cost of crawfish = $1 per pound
Total money spent = $30
Thus, we can write the equation,
[tex]5x + y = 30[/tex]
Solving the two equation by elimination method,
[tex]5x + y-(x+y) = 30-10\\4x = 20\\x = 5\\y = 10 - x = 10 - 5 = 5[/tex]
Thus, 5 pounds of shrimp and 5 pounds of crawfish were purchased in the mixture.
What is the mean of -15, -12,8, and 9?
Answer:
mean = -0.25
Step-by-step explanation:
Explanation:-
mean:- The sum of all the observations and then divided the number of observations and it is denoted by 'μ'
given data is -15 , -12 , 8 and 9
Given observations is '4' so n = 4
[tex]mean= \frac{-15-12+8+9 }{4}[/tex]
[tex]mean= \frac{-27+17}{4}[/tex]
[tex]mean = -0.25[/tex]
The mean of given data is - 0.25
The mean of -15, -12, 8, and 9 is calculated by summing the numbers to get -10 and then dividing by 4, leading to a mean of -2.5.
The mean of a set of numbers is calculated by summing up all the numbers and then dividing the total by the count of the numbers. In this case, to find the mean of -15, -12, 8, and 9, you would add these four numbers together and then divide by 4, because there are four numbers in this set.
The calculation would look like this:
(-15) + (-12) + 8 + 9 = -10
To find the mean, you would then divide -10 by the number of values in the set, which is 4:
Mean = -10 / 4 = -2.5
Therefore, the mean of the numbers -15, -12, 8, and 9 is -2.5.
Mrs. Webster wants to divide 6 pints of
water into 5-pint servings. How many
servings are possible? Explain how you
found your answer.
Answer:
18 servings each pint being 1/3 serving size that 3 servings per pint 3×6 =18
Someone pls help me find area pls
Factor each expression (6s + 18t + 3w)
Answer:
3(2s + 6t + w)
Step-by-step explanation:
Since the highest GCF is 3, I divided 6s, 18t, and 3w. This equals to 3(2s + 6t + w)
Answer:
3(2s+6t+w)
Step-by-step explanation:
Jordan paid $6.00 for 8 apples. How much did he pay per apple?
Answer:
Cost per Apple is $0.75
Step-by-step explanation:
Step 1: Divide cost by the apples
$6.00 / 8 = x
$0.75 = x
Cost per Apple is $0.75
Answer:
0.75
Step-by-step explanation:
Just divide $8.00 by $6.00
About how many cubic feet greater is the volume
of the Mega Moving Truck than the 2-bedroom
moving truck?
Mega Moving truck is 632.102 cubic feet greater than 2-bedroom moving truck.
Solution:
Volume of the mega moving truck = length × width × height
[tex]$=22 \frac{1}{4}\times7 \frac{7}{12}\times 8 \frac{5}{12}[/tex]
Convert mixed fraction into improper fraction.
[tex]$= \frac{22\times4+1}{4}\times \frac{7\times12+7}{12}\times \frac{8\times12+5}{12}[/tex]
[tex]$= \frac{89}{4}\times \frac{91}{12}\times \frac{101}{12}[/tex]
Volume of the mega moving truck = 1420.137 cubic ft
Volume of the 2-bedroom moving truck = length × width × height
[tex]$=14 \frac{1}{2}\times7 \frac{7}{12}\times 7\frac{1}{6}[/tex]
Convert mixed fraction into improper fraction.
[tex]$= \frac{14\times2+1}{2}\times \frac{7\times12+7}{12}\times \frac{7\times6+1}{6}[/tex]
[tex]$= \frac{29}{2}\times \frac{91}{12}\times \frac{43}{6}[/tex]
Volume of the 2-bedroom moving truck = 788.035 cubic ft
Difference between them = 1420.137 – 788.035
= 632.102 cubic ft
Hence Mega Moving truck is 632.102 cubic feet greater than 2-bedroom moving truck.
The areas of a figure and its transformed image are the same which transformation could NOT have been applied to the original figure to create the image ?
Answer: Dilation by a scale factor of 0.75
Step-by-step explanation:
What is the distance from the point (a, -b, -4) to the origin?
O V22-62-16 units
O V22-b2+16 units
O Va+b2+ 16 units
O
Va2 +62 - 16 units
Answer:
[tex]\sqrt{a^2+b^2+16}\text{ units}[/tex]
Step-by-step explanation:
The distance is found using the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]
Then the distance from the given point to the origin is ...
[tex]d=\sqrt{(a-0)^2+(-b-0)^2+(-4-0)^2}\\\\=\boxed{\sqrt{a^2+b^2+16}\ \dots\text{ units}}[/tex]
Rewrite 5a-(a-3b) in standard form.
Answer:
NOTE: Standard form is Ax+By=C
Distribute -1
5a -a +3b
Rewrite
5a +3b = -a
Multiply every term by -1 so -a will be positive
-5a -3b = a
Someone help me plzzzzz
Answer:
200
Step-by-step explanation:
200 × 33% = 66 so
200 is answer
Answer:
A) 200
Step-by-step explanation:
33% of x is 66
33/100 = 66/x
33x = 6600
x = 6600/33
x = 200
5x-3=21-x please someone answer
Answer:
X=4 Hope it helps Lol
Step-by-step explanation:
5*x-3-(21-x)=0
Step by step solution :
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
6x - 24 = 6 • (x - 4)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4
One solution was found :
x = 4
Answer:
X=4
Step-by-step explanation:
The first thing you would do is to make it so there is only x's on one side. To do this add the x on both sidesThis would make it so you have 6x-3=21Plus the 3 on both sides This would give you 6x=24Do 24÷6 giving you 4X=43. Solve the inequality –2(z + 5) + 20 > 6.
[tex]\boxed{-2\left(z+5\right)+20>6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:z<2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:2\right)\end{bmatrix}}[/tex]
Solution:
Given inequality is:
[tex]-2(z+5)+20>6[/tex]
We have to solve the given inequality
[tex]-2\left(z+5\right)+20>6\\\\\mathrm{Subtract\:}20\mathrm{\:from\:both\:sides}\\\\-2\left(z+5\right)+20-20>6-20\\\\\mathrm{Simplify}\\\\-2\left(z+5\right)>-14[/tex]
[tex]Multiply\ both\ sides\ by\ -1\ \left(reverse\:the\:inequality\right)[/tex]
Whenever we multiply or divide an inequality by a negative number, we must flip the inequality sign
[tex]\left(-2\left(z+5\right)\right)\left(-1\right)<\left(-14\right)\left(-1\right)\\\\\mathrm{Simplify}\\\\2\left(z+5\right)<14\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2\left(z+5\right)}{2}<\frac{14}{2}\\\\\mathrm{Simplify}\\\\z+5<7\\\\\mathrm{Subtract\:}5\mathrm{\:from\:both\:sides}\\\\z+5-5<7-5\\\\simplify\ the\ above\\\\\boxed{z < 2 }[/tex]
Thus the solution to inequality is:
[tex]-2\left(z+5\right)+20>6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:z<2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:2\right)\end{bmatrix}[/tex]
from the top of a barn 25 feet tall, you see a cat on the ground. The angle of depression to the cat is 40°. How many feet must the cat walk to reach the barn.
Answer:
21 feet (20.977)
Step-by-step explanation:
1. Draw a picture, it makes it much easier. Draw a right triangle with the vertical labeled 25 and the horizontal labeled X, then label the angle adjacent to the horizontal and hypotenuse 40°
2. Use tangent because X is opposite of 40 and 25 is adjacent to angle 40. the equation would be Tan40/1 = X/25
3. You then cross multiply to get 25Tan(40) = X
4 You then plug it into a calculator and get the full answer of 20.97749078, but I always round up to either 20.98 or 21 feet, whatever your teacher allows
160 students attended Music Night on Thursday night. The attendance on Friday was 120% of the attendance on Thursday night. The attendance on Saturday night was 75% of the attendance on Friday night. How many people attended Music Night on Friday night? How many people attended on Saturday night? What was the total attendance for the 3 nights?
Answer:
160+192+144=496
Step-by-step explanation:
120% of 160=Friday
75% of (1.2*160)=Sat
160=Thursday
Answer:
160+192+144=496
Step-by-step explanation:
120% of 160=Friday
75% of (1.2*160)=Sat
160=Thursday
Step-by-step explanation:
maggie weighs 105 lbs for her height and weight it is recommended that she be at least 120 lbs. and no more than 160 lbs. if she wanted to be in the middle of the healthy range how much weight should she gain?
Answer:
35 lbs
Step-by-step explanation:
because 160-120=40-5=35. sorry if wrong
Maggie wants to the middle of the healthy range weight 130lbs should she gain.
Given that,
Maggie weighs for her height = 105lbs
Recommended weight = 120lbs
Limit for weighs not more than = 160lbs
We have to find ;
If she wanted to be in the middle of the healthy range how much weight should she gain.
According to the question,
If she wanted to be in the middle of the healthy range = Limit for weighs not more than - Recommended weight
= 160lbs - 120lbs
= 40lbs
Then,
Recommended weight - limit for weighs not more than
= 120lbs - 105lbs
= 15lbs
Difference between the weight = 40-15 = 25lbs
Therefore ,
Maggie weighs for her height + Difference between the weight = 105lbs + 25lbs = 130lbs
Hence , Maggie wants to the middle of the healthy range weight 130lbs should she gain.
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BONUS: Name the restrictions, solve, & SHOW your check.
x + 1 = √(5x+11)
x = 5
Solution:
Given equation is [tex]x+1=\sqrt{5x+11}[/tex].
[tex]\Rightarrow x+1=\sqrt{5x+11}[/tex]
Squaring on both sides of the equation to remove the square root.
[tex]\Rightarrow (x+1)^2=(\sqrt{5x+11})^2[/tex]
[tex]\Rightarrow (x+1)^2=5x+11[/tex]
Using algebraic identity: [tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex]\Rightarrow x^2+2x(1)+1^2=5x+11[/tex]
[tex]\Rightarrow x^2+2x+1=5x+11[/tex]
Combine all terms in one side of the equation.
[tex]\Rightarrow x^2+2x+1-5x-11=0[/tex]
Arrange like terms together.
[tex]\Rightarrow x^2+2x-5x+1-11=0[/tex]
[tex]\Rightarrow x^2-3x-10=0[/tex]
Now solve by factorization.
[tex]\Rightarrow x^2-5x+2x-10=0[/tex]
[tex]\Rightarrow (x^2-5x)+(2x-10)=0[/tex]
Take common terms on left side of the term.
[tex]\Rightarrow x(x-5)+2(x-5)=0[/tex]
Now, take (x – 5) common on both terms.
[tex]\Rightarrow (x+2)(x-5)=0[/tex]
⇒ x + 2 = 0 (or) x – 5 = 0
⇒ x = –2 (or) x = 5
If we put x = –2 in the given equation,
[tex]-2+1=\sqrt{5(-2)+11}[/tex]
[tex]\Rightarrow-1=1[/tex]
It is false. So, x = –2 is not true.
If we put x = 5 in the given equation,
[tex]5+1=\sqrt{5\times5+11}[/tex]
[tex]5+1=\sqrt{36}[/tex]
[tex]\Rightarrow6=6[/tex]
It is true. So, x = 5 is true.
Hence x = 5 is the solution.
Question 2 of 10
2 Points
Assume that the lines De and my intersect as in the diagram below. Which
of the following statements are true?
Check all that apply.
O
A.
XAE and _DAY are vertical angles.
B. DĖ and are perpendicular.
c. XAE and DAY are complementary.
D. ZXAE and ZEAY form a linear pair.
SUBMIT
Answer:
XAE and EAY form a linear pair.
done
DE and XY are perpendicular.
XAE and DAY are vertical angles.
Step-by-step explanation:
This answer explains the mathematical concepts related to angles and lines i.e., vertical angles, perpendicular lines, complementary angles, and linear pair. Vertical angles are equivalent, perpendicular lines intersect at right angles, complementary angles sum to 90 degrees, and a linear pair of angles sum to 180 degrees.
Explanation:Without the actual diagram presented in your question, I can only provide some general insights into your question which is related to angles and lines. Firstly, vertical angles are the angles opposite each other when two lines intersect. They are always equal.
Secondly, two lines are perpendicular if they intersect at a right angle(90 degrees). In terms of angles, two angles are complementary when they add up to 90 degrees. Finally, a linear pair refers to two angles that are adjacent (share a common vertex and side but have no common interior points) and whose non-common sides are opposite rays, i.e., they add up to 180 degrees.
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How are the two functions f(x) = 0.7(6)x and g(x) = 0.7(6)–x related to each other?
Answer:
The sign of [tex]x[/tex] in [tex]g(x)[/tex] is opposite or negated. This is the only difference between [tex]f(x)[/tex] and [tex]g(x)[/tex], meaning it is a reflection through the y-axis.
Therefore, [tex]g(x)[/tex] will be the reflection of [tex]f(x)[/tex] through the y-axis.
Step-by-step explanation:
Considering the functions
f(x) = 0.7(6)xg(x) = 0.7(6)–xWe know that when we reflect a function through the y-axis, the x-coordinate gets opposite - negated.
Here, the sign of [tex]x[/tex] in [tex]g(x)[/tex] is opposite or negated. This is the only difference between [tex]f(x)[/tex] and [tex]g(x)[/tex], meaning it is a reflection through the y-axis.
Therefore, [tex]g(x)[/tex] will be the reflection of [tex]f(x)[/tex] through the y-axis.
Answer:
The sign of in is opposite or negated. This is the only difference between and , meaning it is a reflection through the y-axis.
Therefore, will be the reflection of through the y-axis.
Step-by-step explanation:
Considering the functions
f(x) = 0.7(6)x
g(x) = 0.7(6)–x
We know that when we reflect a function through the y-axis, the x-coordinate gets opposite - negated.
Here, the sign of in is opposite or negated. This is the only difference between and , meaning it is a reflection through the y-axis.
Therefore, will be the reflection of through the y-axis.
Kate can make 15 paper fortune tellers in 18 minutes. At this rate, how many paper fortune tellers can she make in 30 minutes?
Answer:
27 paper fortune tellers
Step-by-step explanation:
fortune tellers = time
3 = 6
6 = 9
9 = 12
12 = 15
15 = 18
18 = 21
21 = 24
24 = 27
27= 30
so 30 fortune tellers will be made in 30 minutes
hope this helps!!!
Answer:
Actually, it's 25 paper fortune tellers.
Step-by-step explanation:
15 = 18
15 divided by 3 = 18 divided by 3
5 = 6
5 x 5 = 6 x 5
25 = 30
Ming spent half of her weekly allowance aying mini golf. To earn more money her parents let her wash the car for $5. What is her weekly allowance if she ended with $9
Answer:
Her weekly allowance is $8.
Step-by-step explanation:
Let the weekly allowance of Ming is $x.
If she spends half of her weekly allowance playing mini-golf and to earn more money her parents let her wash the car for $5, then the remaining amount of money that she has = [tex](\frac{x}{2} + 5)[/tex] dollars.
Now, given that [tex](\frac{x}{2} + 5) = 9[/tex]
⇒ [tex]\frac{x}{2} = 4[/tex]
⇒ x = $8
Therefore, her weekly allowance is $8. (Answer)
Which of the following numbers is rational?
Select all that apply.
7.6
22/7
1.01
n
Answer: 7.6, 22/7, 1.01
Step-by-step explanation: