Answer:
find slope m
m=y2-y1/x2-x1
m=-9-(-7)/-5-(-10)
m=-9+7/-5+10
m=-2/5
y=-2/5 x+b ( find b at point (-10,-7)
-7=-2/5(-10)+b
-7=20/5+b
b=-7-4
b=-11
y=-2/5 x -11 slope intercept form
y-(-7)=-2/5(x-(-10)
y+7=-2/5(x+10) point slope form
what is 4 1/2 * 2 1/7 as a mixed number in simplest form?
Answer:
9 9/14
Step-by-step explanation:
[tex]4\frac{1}{2}\times\:2\frac{1}{7}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{1}{2}=\frac{9}{2}\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{1}{7}=\frac{15}{7}\\\frac{9}{2}\times\frac{15}{7}\\\\\mathrm{Multiply\:fractions}:\\\quad \frac{a}{b}\times\frac{c}{d}=\frac{a\:\times\:c}{b\:\times\:d}\\\\=\frac{9\times\:15}{2\times\:7}\\\\=\frac{135}{14}\\\\[/tex]
[tex]\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\quad \frac{135}{14}\\=9\frac{9}{14}[/tex]
Rationalize the denominator of $\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$, and $D$ are integers, $D$ is positive, and $B$ is not divisible by the square of any prime. Find the minimum possible value of $A+B+C+D$.
Rationalizing the denominator involves exploiting the well-known difference of squares formula,
[tex]a^2-b^2=(a-b)(a+b)[/tex]
We have
[tex](\sqrt{16}-\sqrt2)(\sqrt{16}+\sqrt2)=(\sqrt{16})^2-(\sqrt2)^2=16-2=14[/tex]
so that
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{32}(\sqrt{16}+\sqrt2)}{14}[/tex]
Rewrite 16 and 32 as powers of 2, then simplify:
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{2^5}(\sqrt{2^4}+\sqrt2)}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{2^2\sqrt2(2^2+\sqrt2)}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{4\sqrt2(4+\sqrt2)}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+4(\sqrt2)^2}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+8}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{8\sqrt2+4}7[/tex]
So we have A = 8, B = 2, C = 4, and D = 7, and thus A + B + C + D = 21.
The rationalized form of the given surd is [tex]\frac{8\sqrt{2}+4}{7}[/tex], and the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21
Rationalizing SurdsFrom the question, we are to rationalize the denominator of the given surd.
We are to write the answer in the form
[tex]\frac{A\sqrt{B}+C}{D}[/tex]
and find the minimum possible value of A + B + C + D
The given surd is
[tex]\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}[/tex]
To rationalize the surd, we will multiply the numerator and denominator by the conjugate of the denominator
The conjugate of the denominator is [tex]\sqrt{16}+\sqrt{2}[/tex]
Therefore,
[tex]\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}} \times \frac{\sqrt{16}+\sqrt{2}}{\sqrt{16}+\sqrt{2}}[/tex]
[tex]= \frac{\sqrt{32}(\sqrt{16}+\sqrt{2})}{(\sqrt{16}-\sqrt{2})(\sqrt{16}+\sqrt{2})}[/tex]
[tex]= \frac{\sqrt{512}+\sqrt{64})}{(\sqrt{16})^{2} -(\sqrt{2})^{2} }[/tex]
[tex]= \frac{16\sqrt{2}+8}{16-2}[/tex]
[tex]= \frac{16\sqrt{2}+8}{14}[/tex]
[tex]= \frac{2(8\sqrt{2}+4)}{2(7)}[/tex]
By comparing with, [tex]\frac{A\sqrt{B}+C}{D}[/tex]
A = 8, B = 2, C = 4, and D = 7
Then, the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21
Hence, the rationalized form of the given surd is [tex]\frac{8\sqrt{2}+4}{7}[/tex], and the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21
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Give an example of a function with both a removable and a non-removable discontinuity.
Answer:
(x+5) (x=3)
(X+5) (x+1)
Step-by-step explanation:
A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator. It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x. In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.
Is two to the fourth power equal to 2×4
Answer:
No
Step-by-step explanation:
2 to the fourth power is equal to 16.
On the other hand, 2 times 4 is equal to 8.
So, they are not equivalent because 16 [tex]\neq[/tex] 8
4² is the same as the question 4 x 4 which is 16
Apply each transformation described to Figure A. If you get stuck, try using tracing paper. A figure A with a point P, a line l and a point P prime on a triangular grid. A translation which takes LaTeX: PP to LaTeX: P'P ′ A counterclockwise rotation of A, using center LaTeX: PP, of 60 degrees A reflection of A across line LaTeX: \ellℓ HTML EditorKeyboard Shortcuts
Answer:
p
Step-by-step explanation:
Laura is the fund-raising manager for a local charity. She is ordering caps for an upcoming charity walk. The company that makes the caps charges $6 per cap plus a $25 shipping fee. Laura has a budget of $1,000. What is the greatest number of caps she can buy? A.162 A. 162 B.163 B. 163 C.166 C. 166 D.167 D. 167
Answer:
Option B, 163 caps.
Step-by-step explanation:
The price of caps are = $6 per cap.
Shipping charge = $25
The total budget of the Laura = $1000
Since the $25 is shipping charge so subtract it from the budget = 1000 – 25 = $975
Here $975 will be used to buy the caps at the price of $6 per cap.
Thus, the number of caps = budget after subtracting the shipping fee / per cap price
Total caps = $975 / 6
Total caps = 162.5 or 163 caps.
find the inverse of the function f(x)=6x^2+3
Answer:
The answer is
[tex]{f}^{ - 1} (x) = \sqrt{ \frac{x - 3}{6} } [/tex]Step-by-step explanation:
f(x) = 6x² + 3
To find the inverse of the function above equate it to y
That's
f(x) = y
So we have
y = 6x² + 3
Next interchange the variables that's x becomes y and y becomes x.
x = 6y² + 3
Next make y the subject
Subtract 3 from both sides
That's
6y² + 3 - 3 = x - 3
6y² = x - 3
Divide both sides by 6
That's
[tex] {y}^{2} = \frac{x - 3}{6} [/tex]Next find the square root of both sides
[tex]y = \sqrt{ \frac{x - 3}{6} } [/tex]We have the final answer as
[tex] {f}^{ - 1} (x) = \sqrt{ \frac{x - 3}{6} } [/tex]Hope this helps you
Max spent $15 on bowling. This included a $5 charge for shoe rental and a $2.50 charge per game. If g represents the number of games, which equation can be solved to find the number of games that Max bowled?
Answer:
Step-by-step explanation:
$2.50g + $5 = $15
$2.50g = 10
g = 4 games
The equation that is used to find the number of games that Max bowled is [tex]5+2.50x=15.[/tex]
Charge for shoe rental [tex]=[/tex] $[tex]5[/tex].
Charge per game [tex]=[/tex] $[tex]2.50[/tex].
Let [tex]g[/tex] represents the number of games.
The total charge is the sum of shoe rental charge and charge per game times the number of games.
Total money spent [tex]=[/tex] $[tex]15[/tex].
[tex]5+2.50x=15[/tex]
This is the equation that is used to find the number of games that Max bowled.
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How would you combine like terms with exponents? Do you add the exponents?
Answer: When combining like terms, add or subtract the coefficients. Keep the exponents as they are.
Step-by-step explanation:
You can combine 2x^2 + 3x^2 to get 5x^2. If x =3, 3^2=9 So 2(3)^2 is 18 and 3(3)^2 is 27. 18+27=45 And 5(3)^2= 45. Same result!
You can not combine 2x^2 and 2x^3. If the value of x is 3, 2(3)^2 this term works out to =18 and 2(3)^3 =54
If you add the exponents x^5 becomes 2(3)^5 or 2×243=486. Vastly different values! Don't add exponents unless you are multiplying terms.
Yes, when combining like terms with exponents, you add the exponents only if the terms have the same base.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
When combining like terms with exponents, you add the exponents only if the terms have the same base.
For example,
3x² + 9x²
= (3 + 9)x²
= 12x²
And,
2² x 2³
= [tex]2^{2 + 3}[/tex]
= [tex]2^5[/tex]
Thus,
Yes, we add the exponents.
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Please help me!! I can't do this...
Answer:
focus and belive on your self
Step-by-step explanation:
14, the difference of 4 times a and b
How can you prove that a conjecture if false?
Answer:
To show that a conjecture is false, you have to find only one example in which the conjecture is not true. So an example could be a drawing, a statement, or a number.
What is "the sum of twice a number and six is the same as three subtracted from the number itself"?
Answer:
x=-1
Step-by-step explanation:
2x+6=3-x
Step 1: Simplify both sides of the equation.
2x+6=3−x
2x+6=3+(−x)
2x+6=−x+3
Step 2: Add x to both sides.
2x+6+x=−x+3+x
3x+6=3
Step 3: Subtract 6 from both sides.
3x+6−6=3−6
3x=−3
Step 4: Divide both sides by 3.
3x/3=−3/3
x=−1
Answer:
x=−1
The chart shows the cost of tuition at a certain state university. Model the data in the chart with a linear function, using the points (1,9941) and (3,11242). Predict the cost of college tuition in 2007-2008.
What is the linear model for the data?
Y=?
Answer:
The cost in 2007 - 2008 = $15,795.5
The linear model for the data is y = $650.5·x + $9290.5
Step-by-step explanation:
The given data can be presented as follows;
College year, x, Estimated tuition, y
1997-1998, 0, $9412
1998-1999, 1, $9941
1999-2000, 2, $10561
2000-2001, 3, $11242
2001-2002, 4, $11965
2002-2003, 5,
2003-2004, 6,
2004-2005, 7,
2005-2006, 8,
2006-2007, 9,
2007-2008, 10,
With points (1, 9941) and (3, 11242), we have the slope given by the equation;
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Which gives;
[tex]m = \dfrac{11242 - 9941}{3 - 1}= 650.5[/tex]
Therefore;
y - 11242 = 650.5 × (x - 3)
y= 650.5·x - 650.5 ×3 + 11242
y = 650.5·x + 9290.5
Therefore from the above table at 2007 - 2008, the value of x should be 10, we therefore have;
y = 650.5×10 + 9290.5 = $15,795.5
The cost (estimated tuition) in 2007 - 2008 = $15,795.5
The linear model for the data is y = 650.5·x + 9290.5.
The linear model for the data is y = 650.5x + 9290.5 and The cost of college tuition in 2007-2008 is $15795.5
Linear equationA linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the cost of tuition of battery after x years.
From the table using the points (1, 9941) and (3, 11242):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\ \\ y-9941=\frac{11242-9941}{3-1}(x-1)\\ \\ y=650.5x+9290.5[/tex]
The linear model for the data is y = 650.5x + 9290.5
At 2007-2008 (x = 10:
y = 650.5(10) + 9290.5 = 15795.5
The cost of college tuition in 2007-2008 is $15795.5
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Factor 25 - 4x^2
25 – 4x^2 = 0
Answer: (5 + 2x)(5 - 2x)
Step-by-step explanation:
It seems a bit backwards from the way these are usually set up, but still it is the difference of two perfect squares.
Do the ratios 20/10 and 1/2 form a proportion?
Answer:
Yes . Divide by 10 for 10/20 to get 1/2.
10/10= 1
20/10= 2
10/20= 1/2
if k is the midpoint of LM and k (-4,-6) and m(-7,-3). find l (endpoint)
Answer:
(-1,-9) PLEASE MARK BRAINLIEST!!!!!
Step-by-step explanation:
k(-4,-6) , m(-7,-3)
-7+4=-3
-3+6=3
-4+3=-1
-6-3=-9
(-1,-9)
The coordinate of L is (-1,-9) if the k is the midpoint of LM and k (-4,-6) and M (-7,-3).
What is an ordered double?It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
if k is the midpoint of LM and k (-4,-6) and m(-7,-3).
It is required to find the coordinate of L:
Using the mid-point theorem:
Let the coordinate of L is (x, y)
(x - 7)/2 = -4
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.
x - 7 = -8
x = -8 + 7
x = -1
(y - 3)/2 = -6
y - 3 = -12
y = -12 + 3
y = -9
The coordinate of L is (-1,-9)
Thus, the coordinate of L is (-1,-9) if the k is the midpoint of LM and k (-4,-6) and M (-7,-3).
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If segment AB is 4 units, segment AD is 23 units, and segment CD is 12 units, what is the length of segment BC?
23
A
9 units
B.
6 units
C
7 units
D
8 units
Answer:
C . 7 unitsStep-by-step explanation:
The question is lacking appropriate diagram. Find the diagram to the question attached.
From the diagram, it can be seen that AD = AB+BC+CD
Given the following
AD = 23units
AB = 4units
CD = 12units
To get C=BC, we will substitute the given segments into the expression above as shown;
23 = 4+BC+12
23 = BC + 4 + 12
23 = BC+16
Subtract 16 from both sides
23-16 = BC+16-16
7 = BC
Hence the length of segment BC is 7units.
b. What is the radius of a ball that uses one-half of the amount of rubber coating used to cover the 16-inch ball? Write your answer in simplest form.
The radius is
inches.
Question 2
A playground ball with a 16-inch diameter has a rubber coating on its surface.
a. Does a ball with a diameter that is $\frac{1}{4}$
times the diameter of the given ball need $\frac{1}{4}$
times the amount of rubber coating? Explain.
Answer:
The radius, r₂, of the ball that uses one-half the amount of rubber coating used to cover the 16-inch ball is approximately 4.66 inches
Step-by-step explanation:
The dimension of the ball with known radius = 16-inch
The surface area of the ball with 16-inch radius = 4×π×r² = π·D² = π×16² = 804.24772 in.²
Given that the ball uses one-half the rubber material coating used to cover the 16-inch ball, we have the surface area of the ball = 804.24772 in.²/2 = 402.12386 in.²
The radius, r₂ of the new ball is found as follows;
402.12386 in.² = 4×π×r₂²
r₂² = 402.12386 in.² /(4×π) ≈ 32
r₂ = √32 = 4·√2 ≈ 4.66 inches
The radius, r₂, of the ball that uses one-half the amount of rubber coating used to cover the 16-inch ball ≈ 4.66 inches.
On Saturday, a local hamburger shop sold a combined total of 404 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Saturday
Answer:134.7
Step-by-step explanation:
Does 21, 10, and 9 be the measures of the sides of a triangle
Answer:
no
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
9+10 > 21
19 >21
This is not true so it cannot make a triangle
3-12=
please help i do not understand this
Unfortunately, I do not go to Harvard Business School so I am unable to solve this complex equation.
Answer: -9
Step-by-step explanation: you want to take away 12 from 3, which will leave you in the negatives
find the value. 2⅔×2¹/7
Answer: 40/7, if you need, the mixed fraction is 5 5/7
Step-by-step explanation:
First of all, convert all the mixed fraction into improper fraction.
2 2/3=8/3
2 1/7=15/7
Then do the multiplication.
8/3 × 15/7=120/21=40/7 (You can directly simplify it to 40/7 since you can use 15 divided by 3 to get 5 left in the numerator)
Hope this helps!! :)
Please let me know if you have any question
Answer:
5.71
Step-by-step explanation:
two two by three × two one by seven
=8/3×15/7
=8×5/7 as 15 and three will divide and 15 will change to 5
=40/7
=5.71
Find the difference. 15 5/12 - 11 1/8
Answer:
4 7/24
Step-by-step explanation:
Answer:
103/24 or 4.29 or 4 7/24
Step-by-step explanation:
15 5/12 - 11 1/8
185/12 - 89/8
370/24 - 267/24 = 103/24
or
15 10/24 - 11 3/24 = 4 7/24
Plz help ASAP!!!! WILL MARK YOU BRAINLIST IF YOUR ANSWER IS CORRECT!! Question # 7 last question
Answer:
the last one
Step-by-step explanation:
i took the test
If you plug x = 3 into choice A, then you dont have any division by zero errors or square roots of negative values.
Choice B in contrast has x-9 = 3-9 = -6 under the square root, so this leads to an imaginary/complex result. Choice D is similar.
Choice C will have zero in the denominator after plugging in x = 3 since x^2-9 = 3^2-9 = 9-9 = 0.
perimeter help please quick !
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4.4}}}}}[/tex]
Step-by-step explanation:
Given,
Length of the rectangle ( l ) = 3x + 5
Breadth of the rectangle ( b ) = 2x - 1
Perimeter of the rectangle ( P ) = 52
Finding the value of x
[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + b)}}[/tex]
⇒[tex] \sf{52 = 2(3x + 5 + 2x - 1)}[/tex]
⇒[tex] \sf{52 = 2(5x + 4)}[/tex]
⇒[tex] \sf{52 = 10x + 8}[/tex]
⇒[tex] \sf{10x + 8 = 52}[/tex]
⇒[tex] \sf{10x = 52 - 8}[/tex]
⇒[tex] \sf{10x = 44}[/tex]
⇒[tex] \sf{ \frac{10x}{10} = \frac{44}{10} }[/tex]
⇒[tex] \sf{x = 4.4 \: }[/tex]
Hope I helped!
Best regards!! :D
On a coordinate plane, point M is plotted (-3,-1) and point N is plotted (4,5). What is the distance between points M and N? square root of 117 square root of 85 5 square root of 17 85
Answer:
The square root of 85
Step-by-step explanation:
The formula to find out the distance between the points is shown below:
The Distance is
[tex]= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
where,
x_1 = -3
y_1 = -1
x_2 = 4
And, the y_2 = 5
Now place these values to the above formula
So, the distance is
[tex]= \sqrt{(4+3)^2 + (5+1)^2} \\\\= \sqrt{49 + 36} \\\\= \sqrt{85}[/tex]
= 9.22 units
Hence, the distance between points M and N is 9.22 units or the square root of 85
Hence, the second option is correct
Math Do Now: Maria has a coupon for 30% at Kohl's. If she purchases $200 worth
of clothes, what is her total before taxes? *
What is the simplified form of each expression? (6 + 3)^2 - 4
Answer:
77
Step-by-step explanation:
(6 + 3)² is same as (a + b)²
Since (a + b)² = a² + 2ab + b²
Therefore,
(6 + 3)² - 4
= (36 + 36 + 9) - 4
= 81 - 4
= 77
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------------
Answer: [tex]\boxed{77}[/tex]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Since PEMDAS exists, we will do parentheses "(6+3)" first to get 9.
Then we do the exponent which is:
[tex]9^{2}[/tex] = 81.
Then we subtract.
81 - 4 = 77.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
More broken down explanation:
[tex](6+3)^{2} -4[/tex]
Add 6 and 3 to get 9.
[tex]9^{2} - 4[/tex] ≈ [tex]77[/tex]
Calculate 9 to the power of 2 and get 81.
[tex]81-4[/tex] = [tex]77[/tex]
Subtract 4 from 81 to get, you guessed it, 77!HELP PLEASE
Will give brainliest
Answer:
[tex]=7x^2+8x-2[/tex]
Step-by-step explanation:
So, on Monday, Tuesday, and Wednesday, he mowed:
[tex](4x^2+3x-4),(5x-8),(3x^2+10)[/tex]
yards, respectively.
To determine how many yards he mowed in the three days, simply add the three expressions. Thus:
[tex](4x^2+3x-4)+(5x-8)+(3x^2+10)[/tex]
Combine like terms:
[tex]=(4x^2+3x^2)+(3x+5x)+(-4-8+10)[/tex]
Add or subtract:
[tex]=7x^2+8x-2[/tex]
And it cannot be simplified further :)