Answer:
D. 3x - 3Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=5x-2,\ g(x)=2x+1\\\\\text{Substitute:}\\\\(f-g)(x)=(5x-2)-(2x+1)\\\\=5x-2-2x-1\qquad\text{combine like terms}\\\\=(5x-2x)+(-2-1)\\\\=3x-3[/tex]
Graph y = √x + 2 and y = 3x on the same set of coordinate axes. Use the graphs to find the exact solutions to the equation √x + 2 = 3x. Then, find the solutions using an algebraic method.
Answer:
x = 1
Step-by-step explanation:
The graph is shown below. The solution is x = 1.
___
√x +2 = 3x . . . . given
√x = 3x -2 . . . . . subtract 2
x = 9x^2 -12x +4 . . . . square both sides
9x^2 -13x +4 = 0 . . . . subtract x to put in standard form
(x -1)(9x -4) = 0 . . . . . factor the quadratic
x = 1 . . . or . . . x = 4/9 . . . . values of x that make the factors zero
The "solution" x = 4/9 is extraneous, in that it does not satisfy the equation. It would correspond to the intersection of the line with the negative branch of the square root function. That is, it does satisfy -√x +2 = 3x.
The solution is x=1.
Which of the following is a monomial?
Answer:
[tex]20x^{11}[/tex]
Step-by-step explanation:
An expression in algebra that contains one term is called a monomial.
These include numbers, whole numbers and variables that are multiplied together.
Any number, a whole number without variables can also be monomial, like 32, 5236 etc.
So, here the monomial is [tex]20x^{11}[/tex].
Option (A) represents a monomial which has only one term option (A) 20x¹¹ is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
As we know in the monomial there will be only one term.
Option (C) and Option (D) contains two terms so they are not monomial.
Option (B) contain fractional term.
Thus, option (A) represents a monomial which has only one term option (A) 20x¹¹ is correct.
Learn more about Polynomial here:
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PLEASE HELP, ATTACHED IS THE PROBLEM
hypotenuse = 8
unknown leg = b
known leg = 4
Pythagorean theorem:
[tex]c=\sqrt{{a}^{2}+{b}^{2}}[/tex]
The answer is
[tex]8=\sqrt{{b}^{2}+{4}^{2}} [/tex]
Which shows how to find the value of this expression when X=-2 and Y = 5?
(3x3y=272
31-216
(-2)4
21954
Answer:
Option 1 is correct
Step-by-step explanation:
Given expression is:
[tex](3x^3y^{-2})^2\\[/tex]
Putting the values
[tex]= [3 (-2)^3 (5)^{-2}]^2\\We\ have\ to\ make\ the\ powers\ positive\\= [{\frac{3(-2)^3}{5^{2}} }]^2\\= \frac{[{3(-2)^3}]^2}{(5^2)^2} \\Applying\ outer\ power\\= \frac{3^2(-2)^6}{5^4} \\[/tex]
Hence option one is correct ..
Nine less than the product of 2 and number is equal to 7
Answer:
x = 8
Step-by-step explanation:
Step 1: Write an equation
2x - 9 = 7
Step 2: Use the Addition Property of Equality
2x = 16
Step 3: Use the Division Property of Equality
x = 8
Answer:
number = 8
Step-by-step explanation:
Let "number" = x. Set the equation.
"product of 2 and number" = 2(x)
"nine less" = -9
"equal to 7" = "= 7"
2x - 9 = 7
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 9 to both sides.
2x - 9 (+9) = 7 (+9)
2x = 7 (+9)
2x = 16
Divide 2 from both sides.
(2x)/2 = (16)/2
x = 16/2
x = 8
8 is your answer.
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Find the factored form of
-7y - y2 = 0
Answer:
-y(7+y) =0
Step-by-step explanation:
-7y - y^2 = 0
Factor out a -y
-y(7+y) =0
Using the zero product property
-y =0 and 7+y =0
y=0 7-7+y = 0-7
y=0 y = -7
Find the distance between the points given. (0, 6) and (5, 12) √145 √61 √11
Answer:
√61
Step-by-step explanation:
Distance between 2 points (x1, y1) and (x2,y2) is given by
Distance = √ [ (x2-x1)² + (y2-y1)² ]
in our case, x1 = 0, y1 = 6, x2 = 5, y2 = 12
Distance
= √ [ (5-0)² + (12-6)² ]
= √ [ (5)² + (6)² ]
= √ 61
Answer:
√61
Step-by-step explanation:
The distance between two points is given by
d = sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt( (5-0)^2 + (12-6)^2)
=sqrt( 5^2 + 6^2)
= sqrt(25+36)
= sqrt(61)
Which quadratic inequality does the graph below represent?
NEED TO KNOW BEFORE 14 MINUTES PLZ!!!!
If you look at the graph, the line crosses the y axis at (0,3).
That means you can eliminate the inequality that shows the y intercept as -3 (which is the 3rd option)
Also the inequality has to have y ≤ .... so that the correct part of the graph is shaded. This elimates all of the inequalities that has y ≥ ... ( which is the 2nd and 4th option)
This leaves you with only the first inequality left:
y ≤ 2x² - 8x + 3
-----------------------------------------------------------------------
Answer
y ≤ 2x² - 8x + 3
Help me please algebra 2 PLEASSEEEEE!!!
Answer:
29.74 degrees.
Step-by-step explanation:
Tan(theta) = opposite / adjcent.
opposite = 8
adjacent = 14
Tan(theta) = 8/14
Tan(theta) = 0.5714
theta = tan^-1(0.5714)
theta = 29.74 degrees
PLEASE HELP AS FAST AS POSSIBLE PLEASE
Find the product of (-8y2 + 3) and (-4y - 3).
A) 32y3 + 24y2 - 12y - 9
B) -32y3 - 24y2 + 12y - 9
C) 12y3 - 12y - 9
D) -8y2 - 4y - 9
Answer:
A) 32y³ + 24y² - 12y - 9
Step-by-step explanation:
(-8y² + 3)(-4y - 3) = (-8y² x -4y) + (-8y² x -3) + (3 x -4y) + (3 x -3)
= 32y³ + 24y² - 12y - 9
The product of [tex]-8y^2+3[/tex] and [tex]-4y-3[/tex] is:
[tex]32y^3+24y^2-12y-9[/tex]
Step-by-step explanation:We are asked to find the product of the two expressions which are given by:
[tex]-8y^2+3[/tex] and [tex]-4y-3[/tex]
i.e.
we are asked to find the product of a quadratic and a linear polynomial.
We are asked to find the result of:
[tex](-8y^2+3)\cdot (-4y-3)[/tex]
Hence, on using the distributive property we have:
[tex]-8y^2(-4y-3)+3(-4y-3)\\\\=-8y^2\times -4y-8y^2\times (-3)+3\times (-4y)+3\times (-3)\\\\i.e.\\\\=32y^3+24y^2-12y-9[/tex]
The correct answer is: Option: A
What is the image of (1, -6) for a 180° counterclockwise rotation about the origin?
a( -1,-6)
b( -1,6)
c(6,1)
d( -6,-1)
Answer: option b
Step-by-step explanation:
It is important to know that, by definition, the rule for 180 degrees counterclockwise rotation is:
[tex](x,y)[/tex]→[tex](-x,-y)[/tex]
Therefore, given the point (1, -6) we can find the image obtained for for a 180° counterclockwise rotation about the origin by applying the rule mentioned before.
Then, the image is:
[tex](1,-6)[/tex]→[tex](-(1),-(-6))=(-1,6)[/tex]
Answer:
The correct answer option is b. ( -1, 6).
Step-by-step explanation:
We are given a point which is rotated 180 degrees counterclockwise about the origin (0, 0). We are to find the coordinates of the image of this point after the rotation.
The rule for rotating a point 180 degrees counterclockwise is:
(x, y) ---> (-x, -y)
So for the given point, the coordinates of the image will be:
(1, -6) ---> (-1, -(-6)) ---> (-1, 6)
A group of adults and students went on a class trip to Washington, DC. The number of male students was 1 more than 7 times the number of adults. The number of female students was half the number of male students. If the total number of people who went on the trip is 82, find the numbers of male students and female students. The number of male students is . The number of female students is .
Answer:
see below
m = males = 50
e = females = 25
a = adults = 7
Step-by-step explanation:
Givens
Let the adults = a
let the males students = m
lef the female students = e
Equations
a + m + e = 82
m = 7*a + 1
e = 1/2 * (7a + 1)
Solution
a + 7a + 1 + 1/2(7a + 1) = 82 Remove the brackets on the left.
a + 7a + 1 + 3.5*a + 1/2 = 82 Combine the like terms on the left.
11.5a + 1.5 = 82 Subtract 1.5 from both sides.
11.5a + 1.5 - 1.5 = 82 - 1.5 Combine
11.5a = 80.5 Divide by 11.5
a = 80.5/11.5
a = 7
The number of adults = 7
===============================
m = 7a + 1
m = 7*7 + 1
m = 50
===============================
e = 1/2 m
e = 1/2 * 50
e = 25
What is the absolute value of….
1. |-5|?
2. |13|?
3. |25|?
4.|-7|?
Answer:
1. 5
2. 13
3. 25
4. 7
Step-by-step explanation:
|-5|=5
|13|=13
|25|=25
|7|=7
The exponential curve of best fit is given as y = 4(7)*. Find the value of y when x= 3.
Answer:
1372
Step-by-step explanation:
y=4(7)^3
You multiply 7x7x7 which gives you 343
Now you plug that in.
y=4(343)
Multiply it and you get
y=1372
Write an equation in standard form for the circle?
Answer:
(x - 3)² + (y - 5)² = 64Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
Look at the picture.
We have
center at (3, 5) → h = 3 anf k = 5
radius r = 8
Substitute:
[tex](x-3)^2+(y-5)^2=8^2\\\\(x-3)^2+(y-5)^2=64[/tex]
What’s the answer?????????????
Answer:
1) binomial
2) monomial
Step-by-step explanation:
mono-think one
bi-think two
tri-think thee
poly-1 or more
So 1 goes with binomial
and 2 goes with monomial
See if you can figure out 3 and 4
I can check them.
Study the products shown. Is there a pattern? (x + 3)2 = x2 + 6x + 9 (x + 4)2 = x2 + 8x + 16 (x + 5)2 = x2 + 10x + 25 (x + 6)2 = x2 + 12x + 36
Answer:
Yes,a similar formula is used to find all the products
Step-by-step explanation:
The formula applied in this case is;
(a+b)²= (a+b) (a+b)= a(a+b)+b(a+b) = a²+ab+ab+b²= a²+2ab+b²
In the first one;
[tex](x+3)^2= (x+3) (x+3) = x(x+3)+3(x+3) = x^2 +3x+3x+9 = x^2 +6x +9[/tex]
In the second one;
[tex](x+4)^2 = (x+4) (x+4) = x(x+4)+ 4(x+4) = x^2 +4x+4x+16 = x^2 +8x+16[/tex]
⇒This is the same for the third and fourth product.
Answer:
3rd option is right
Step-by-step explanation:
What is the square root of a^3 and b^4 expressed in simplified form?
Answer:
(a)(b²)√a
Step-by-step explanation:
√(a³b⁴)
Root both variables. Note that pairs of the same variables can be brought out of the root.
√(a³) = √(a * a * a) = a√a
√(b⁴) = √(b * b * b * b) = b²
(a)(b²)√a is your answer.
7,125,000,000. What is this to the nearest billion?
Answer:
7 billion
Step-by-step explanation:
Rounding decreqases when number is under 5 and if its above (Ex, 7,685,000,000) it is rounded to 8 billion. But here, it is under 5 so it is 7 billion.
Answer:
7,000,000,000
Step-by-step explanation:
Note the Billions place value. 7 is in the billions place value. To find out if you round up or down, look at the place value directly to the right of the one you are trying to find, in this case, being the hundred million place value. The value inside the hundred million place value is a 1.
Note that the number has to be 5 or greater to round up, or else you round down. Because 1 < 5, you round down.
7,125,000,000 rounded to the nearest billion is 7,000,000,000.
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some one please help me with these questions please answer any that you know are correct i cant risk any wrong answers
1. Add. (−5x ^4 +6x^2−43)+(6x^4−x^2+12x+12)
express the answer in standard form.
enter your answer in the box
2. ADD (x^3-2x^2+4)+(2x^3 + x^2−2)
Express the answer in standard form.
Enter your answer in the box.
3.ADD (1+7x^3-x^2) + (x^3+2+2x^2)
express the answer in standard form .
enter your answer in the box
Answer: 1) x⁴ + 5x² + 12x - 31
2) 3x³ - x² + 2
3) 8x³ + x² + 3
Step-by-step explanation:
1) Line up like terms and add the coefficients of each term
-5x⁴ + 6x² - 43
+ 6x⁴ - 1x² + 12x + 12
x⁴ + 5x² + 12x - 31
2) Line up like terms and add the coefficients of each term
1x³ - 2x² + 4
+ 2x³ + 1x² - 2
3x³ - x² + 2
3) Line up like terms and add the coefficients of each term
7x³ - 1x² + 1
+ 1x³ + 2x² + 2
8x³ + x² + 3
Which country was an ally of the United States durning World War II
Answer:
United Kingdom , France, Soviet Union , and China
Step-by-step explanation:
United Kingdom , France, Soviet Union , and China was an ally of the United States durning World War II.
indicate the equation of the line through (2,-4) and having slope off 3/5.
By using the concept of slope of a Straight line,we arrive to the conclusion that the equation of line through (2,-4) and having slope off 3/5 is y = - (1/2)x - 26/5.
The slope of this Straight line is given as=3/5
Thus,the equation of the straight line becomes y=(3/5)x [tex]+[/tex]c.
Now,if substituting the Slope of the line in the equation of this line.
y=(3/5)x [tex]+[/tex]c.
In the point(2,-4):
-4=(3/5)(2) [tex]+[/tex] c
-4=(6/5) [tex]+[/tex] c
c=-4-(6/5)
= - 26/5
Therefore, the final equation is y= - (1/2)x - 26/5
To learn more about Straight line,
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What is the area of the kite?
Answer:
= 135 m²
Step-by-step explanation:
First we divide the kite into 2 isosceles triangles
The bigger triangle has base angles = 45°
We can use these angle as follows to find the common base of the two triangles.
Cos 45=adjacent/9√2
Adj=9√2×cos 45
=9
common base =9×2=18
We can use the angle 45° above to find the height of the bigger triangle.
Tan 45°=opposite/adjacent
Opposite = adjacent×Tan 45
=9 tan 45=9
Area =1/2BH+1/2Bh where B is the common base H is the height of the big triangle, h represents the height of the smaller triangle.
A=1//2× 18 × 9 +1/2× 18 × 6
= 135 m²
if 1/64=4^2s-1 * 16^2s+2 what is the value of s?
a) -1
b)0
c)1
D) no solution
Answer:
its A :(
Step-by-step explanation:
Find the slope of the line through (3, 7) and (–1, 4)
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Slope = change in y ÷ change in x
The line passes through (3,7) and (-1,4)
Slope = [tex]\frac{7 - 4}{3 - -1}[/tex] = [tex]\frac{3}{4}[/tex]
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
According to the data we have the following points:
[tex](x_ {1}, y_ {1}): (- 1,4)\\(x_ {2}, y_ {2}) :( 3,7)[/tex]
Substituting we have:
[tex]m = \frac {7-4} {3 - (- 1)} = \frac {3} {3 + 1} = \frac {3} {4}[/tex]
Thus, the slope of the line is [tex]\frac {3} {4}[/tex]
Answer:
[tex]\frac {3} {4}[/tex]
A transformation T : (x,y) (x-5,y +3) the image of A(2,-1) is
[tex]A'=(2-5,-1+3)=(-3,2)[/tex]
The table shows values for functions f(x) and g(2)
What is the solution to f(x) = g(x)?
Select each correct answer.
X= -2
X= -1
X= 0
X= 1
X= 2
Answer:
The solutions are x=0, x=1
Step-by-step explanation:
we know that
The solution of the equation f(x)=g(x)
are the values of x when the value of f(x) is equal to the value of g(x)
Observing the table
For x=0
f(0)=1 and g(0)=1
so
For x=0 ------> f(x)=g(x)
For x=1
f(1)=1/2 and g(1)=1/2
so
For x=1 ------> f(x)=g(x)
therefore
The solutions are x=0, x=1
What is 77543 rounded to the nearest hundred
[tex]77500[/tex]
Step-by-step explanation:In this case, the digit in the hundredths place is a [tex]5[/tex]. We need to take a look at the next digit to the right, which is a [tex]4[/tex].
Since it is [tex]4[/tex] or less, we can simply replace the [tex]4[/tex] and the rest of the digits to the right with [tex]0[/tex]s to round it.
If the [tex]4[/tex] was [tex]5[/tex] or more, we would round the [tex]5[/tex] up to [tex]6[/tex] and replace the remaining digits to the right with [tex]0[/tex]s.
Answer:
77500
Step-by-step explanation:
To round something to the nearest hundred, we first look to the 10s digit. It is 4. Since 4 is less than 5, then we keep the same hundreds place. So we get 77500.
I need help with finding the arc measure of this problem.
Answer:
180+69=249
I got 180 from the ABC, that is half the circle then + the 69
I know the answer I got is wrong help.
Answer:
∠2 = 18°
Step-by-step explanation:
∠WXZ = ∠1 + ∠2 ← substitute ∠1 = 3∠2
∠WXZ = 3∠2 + ∠2, that is
72 = 4∠2 ( divide both sides by 4 )
18 = ∠2, that is
∠2 = 18°