Answer:
its (5x+8)(25x^2-40x+64
Step-by-step explanation:cuz
If f(x)= 5x-12, what is f(2)
Answer:
-2
Step-by-step explanation:
f(x)= 5x-12
f(2)= 5(2)-12 = 10 - 12 = -2
Answer: -2
Step-by-step explanation: f(x)= 5x-12
f(2)= 5(2)-12 = 10 - 12 = -2
thats how i do it
Will someone help me plz
Answer:
Associative property of addition
Step-by-step explanation:
The order of the addition doesn't matter. That is what the brackets show.
Answer:
Associative Property of AdditionStep-by-step explanation:
[tex]\bold{Commutative\ Property\ of\ Addition:}\ a+b=b+a\\\\\bold{Inverse\ Property\ of\ Addition:}\ a+(-a)=0\\\\\bold{Commutative\ Property\ of\ Multiplication:}\ a\cdot b=b\cdot a\\\\\bold{Associative\ Property\ of\ Addition:}\ a+(b+c)=(a+b)+c\\\\\text{We have}\ 7+(4+4)=(7+4)+4\\\\\text{It's Associative Property of Addition.}[/tex]
Jada created the two-way table below to describe the performance of her basketball team this season.
Which statements are supported by the data in the table? Check all that apply.
The team is twice as likely to win a home game as they are an away game.
The team wins 3/5 of their home games.
The team wins 1/2 of their games.
The team played a total of 27 games.
The team won a total of 6 games.
The team lost more home games than away games.
...........................WIN..........LOSS
HOME GAMES ... 6 ..........10
AWAY GAMES .....3.............8
Answer:
The correct option is 1, 4 and 6.
Step-by-step explanation:
The given two-way table is
WIN LOSS TOTAL
HOME GAMES 6 10 16
AWAY GAMES 3 8 11
TOTAL 9 18 27
Total number of home games won by team is 6 and total number of away games won by team is 3. It means the team is twice as likely to win a home game as they are an away game.
The correct option is 1.
Total number of home games = 16.
Home game won by team is
[tex]\frac{6}{16}=\frac{3}{8}[/tex]
Option 2 is incorrect.
Total games = 27
Total games won by the team = 9
Total part of games won by team is
[tex]\frac{9}{27}=\frac{1}{3}[/tex]
Option 3 is incorrect.
The team played a total of 27 games.
Option 4 is correct.
The team won a total of 9 games.
Option 5 is incorrect.
Total home games loose by team = 10
Total away games loose by team = 8
The team lost more home games than away games.
Option 6 is correct.
Therefore the correct option is 1, 4 and 6.
Answer:
4 and 6
Step-by-step explanation:
took quiz
For the following geometric sequence, find the explicit formula.
{1, -3, 9, ...}
Answer:
the explicit formula for given geometric sequence {1,-3,9,..} is [tex]a_{n}= (-3)^{n-1}[/tex]
Step-by-step explanation:
We are given the series
1,-3,9,...
the common ratio is:
-3/1 = -3
9/-3 = -3
So, the common ratio in the series is -3
a₁ = 1
The formula used for geometric series is:
[tex]a_{n}= a_{1}(r)^{n-1}[/tex]
Putting values of a₁ and r
[tex]a_{n}= 1(-3)^{n-1}[/tex]
[tex]a_{n}= (-3)^{n-1}[/tex]
So, the explicit formula for given geometric sequence {1,-3,9,..} is [tex]a_{n}= (-3)^{n-1}[/tex]
which graph shows the solution set for 2x+3>-9.
Answer:
x > -6
The solution above is graphed correctly in the last option choice.
Step-by-step explanation:
We have been given the equation 2x + 3> -9
In order to graph the solution, we must find the value of x
2x + 3 > -9
Subtract three from both sides
-9 - 3 = -12
2x > -12
Divide both sides by 2
x > -6
To determine how to graph the solution, look at the inequality symbol. If the symbol is "greater than" then you would graph the line going left. If it was "less than" than you would graph the line going right.
In our problem, we have the "greater than" symbol which means we will be graphing our line going to the right, and since we start our line from -6 we know the last option is the correct answer.
What type of number is 25,747. whole number, integer, rational or irrational
Answer:
25747 is all you mentioned except irrational
Step-by-step explanation:
Whole numbers are counting numbers or also 0. If you can count to it and you can but no one wants to in this cases because that's a big number, then it is a whole number for sure. So 25747 is a whole number which means it is also an integer and also a rational number. It is definitely not irrational.
25,747 is a positive whole number and thus is classified as an integer. It is also a rational number, but it is not an irrational number. Therefore, 25,747 is both a whole number and a rational number.
The number 25,747 is an example of a positive whole number and can also be classified as an integer. In mathematics, an integer is defined as any whole number without a fractional or decimal component, which can be positive, negative, or zero. Since 25,747 is a whole number greater than zero, it is specifically a positive integer.
A rational number is a number that can be expressed as the ratio of two integers, such as fractions or any number that has a finite or repeating decimal expansion. Clearly, 25,747 qualifies as a rational number since it can be written as 25,747/1.
An irrational number, on the other hand, cannot be expressed as a simple fraction - examples include π (pi) and √2 (the square root of 2), both of which have non-repeating, non-terminating decimal expansions. Therefore, 25,747 is not irrational.
Whole numberIntegerRational numberIn conclusion, 25,747 is a positive whole number, which means it is an integer and a rational number, but not an irrational number.
:
Malik received a $300 gift card from his grandparents and is using it only to pay for his karate lessons, which cost $30 per month.
Determine what amount, in dollars, remains on the card after 8 months.
Answer:
60$ will be left
Step-by-step explanation: 30x8 = 240. subtract 300-240 and you get 60
Answer:
60
Step-by-step explanation:
30*8=240
300-240=60
Which of the following will give you the incorrect slope? (1 point)
the quantity y subscript two minus y subscript one over the quantity x subscript two minus x subscript one.
the quantity y subscript two minus y subscript one over the quantity x subscript one minus x subscript two.
the quantity y subscript one minus y subscript two over the quantity x subscript one minus x subscript two.
rise over run
Answer:
2nd one
Step-by-step explanation:
No mixing order so the second one.
You can do either
(y2-y1)/(x2-x1) or (y1-y2)/(x1-x2) which will give you rise/run in either situation
Answer:
2nd one
Step-by-step explanation:
got it right on the test and got 100%
hope this helps :)
Plzzz helppp me!!! And thank
Answer:
A. The slope is 4.
B. The y-intercept is 8.
C. The equation is y = 4x + 8
Step-by-step explanation:
We know that there is a flat $8 cost in addition to $4 per ride. We can express this by using:
y = 8 + 4x.
y is the total cost
x is the number of rides
The question wants the equation in slope-intercept form.
Slope-intercept form of a line: y = mx + b
m = slope
b = y-intercept
y = 8 + 4x ➵ y = 4x + 8
Now that we have the slope-intercept form of the line, we can answer the problems.
A. The slope is 4.
B. The y-intercept is 8.
C. The equation is y = 4x + 8
Solve for x in the equation y^2 + 2x + 1 = 17.
Answer:
x = −1 ± √17
Hope this helps and have a nice day! :)
Answer:
B
Step-by-step explanation:
So your equation is actually x^2+2x+1=17
Left hand side is already set for rewriting it as a perfect square
So you have actually that (x+1)^2=17
Now you just take square root of both sides
x+1=(pm) sqrt(17) (pm) means plus or minus
x=-1 (pm) sqrt(17) I subtracted 1 on both sides
B
A beach resort is offering two weekend specials. One includes a two night stay with 3 meals and costs $195. The other includes a three night stay with 5 meals and costs $300. How much is the cost of a one night stay?
Answer: $75 per night and $15 per meal
Step-by-step explanation:
a 1 night cost $15
What's the equation defining?
Mathematics written statement indicating the equality of 2 expressions. this consists of the sequence of symbols that are split in the left or right sides joined by the equal sign. e.g, 2 + 4 + 5 = 11 is an equation.
Do equations always contain terms?
When equality holds, the total weight on the each side is the same. Equations often contain terms other than a unknowns. These other terms, which are assumed to known, is usually known as constants, coefficients and parameters
Step-by-step explanation:
offer 1 : (1) 2*night+3*meal=195
(2) night=(195-3*meal)/2
offer 2: (3) 3*night+5*meal=300
if we replace eq (2) in eq (3)
3*(195-3*meal)/2+5*meal=300
292.5+0.5meal=300
meal=$15
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Which of the following are solutions to the equation 3x2 + 7x + 4 = 0
Select all that apply
O x=-1
O x=-4/3
x=3/4
x=1
For this case we have the following quadratic equation:
[tex]3x ^ 2 + 7x + 4 = 0[/tex]
Where:
[tex]a = 3\\b = 7\\c = 4[/tex]
According to the quadratic formula we have:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Substituting:
[tex]x = \frac {-7 \pm \sqrt {7 ^ 2-4 (3) (4)}} {2 (3)}\\x = \frac {-7 \pm \sqrt {49-48}} {6}\\x = \frac {-7 \pm \sqrt {1}} {6}\\x = \frac {-7 \pm1} {6}[/tex]
We have two roots:
[tex]x_ {1} = \frac {-7 + 1} {6} = \frac {-6} {6} = - 1\\x_ {2} = \frac {-7-1} {6} = \frac {-8} {6} = - \frac {4} {3}[/tex]
Answer:
[tex]x_ {1} = - 1\\x_ {2} = - \frac {4} {3}[/tex]
Answer:
x = -4/3 x=-1
Step-by-step explanation:
3x^2 + 7x + 4 = 0
Factor the equation
(3x+4) (x+1) = 0
Using the zero product property
3x+4 =0 x+1 =0
3x+4-4=0-4 x+1-1=0-1
3x=-4 x=-1
3x/3 = -4/3
x = -4/3 x=-1
Which best explains if quadrilateral WXYZ can be a parallelogram? WXYZ is a parallelogram because diagonal XZ is bisected. WXYZ is not necessarily a parallelogram because it is unknown if CZ = CY. WXYZ is a parallelogram because ZC + CX = ZX. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
Answer:
D. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
Step-by-step explanation:
edge2021
The statement which best explains that the quadrilateral WXYZ can be a parallelogram is D. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal.
In order to find this, we have to know the properties of the diagonals of a parallelogram.
Here given a parallelogram WXYZ.
The diagonals of a parallelogram bisect each other.
That is, if WXYZ is a parallelogram,
WC = CY and ZC = CX
But it is unknown that these are equal.
Hence the correct option is D.
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The point slope form of the equation of the line that passes through (-5-1) and (10.-7) is
standard form of the equation for this line?
Answer:
The standard form of the equation for this line can be:
l: 2x + 5y = -15.
Step-by-step explanation:
Start by finding the slope of this line.
For a line that goes through the two points [tex](x_0, y_0)[/tex] and [tex](x_1, y_1)[/tex],
[tex]\displaystyle \text{Slope} = \frac{y_{1} - y_{0}}{x_{1} - x_{0}}[/tex].
For this line,
[tex]\displaystyle \text{Slope} = \frac{(-1) - (-7)}{(-5) - 10} = -\frac{2}{5}[/tex].
Find the slope-point form of this line's equation using
[tex]\displaystyle \text{Slope} = -\frac{2}{5}[/tex], andThe point [tex](-5, -1)[/tex] (using the point [tex](10, -7)[/tex] should also work.)The slope-point form of the equation of a line
with slope [tex]m[/tex] andpoint [tex](x_{0}, y_{0})[/tex]should be [tex]l:\; y - y_{0} = m(x - x_0)[/tex].
For this line,
[tex]\displaystyle m = -\frac{2}{5}[/tex], and[tex]x_0 = -5[/tex], and[tex]y_0 = -1[/tex].The equation in slope-point form will be
[tex]\displaystyle l:\; y - (-1) = -\frac{2}{5}(x - (-5))[/tex].
The standard form of the equation of a line in a cartesian plane is
[tex]l: \; ax + by = c[/tex]
where
[tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are integers. [tex]a \ge 0[/tex].
Multiply both sides of the slope-point form equation of this line by [tex]5[/tex]:
[tex]l:\; 5 y + 5 = -2x -10[/tex].
Add [tex](2x-5)[/tex] to both sides of the equation:
[tex]l: \; 2x + 5y = -15[/tex].
Therefore, the equation of this line in standard form is [tex]l: \; 2x + 5y = -15[/tex].
justin ran 800 meters in track meet today. How many yards did he run? Round your asnwer to the nearest tenth.
874.890 i think, sorry if im wrong
The ratio of two numbers is 5 to 4. The sum of the numbers is 99. What number is the greater of the two numbers?
Answer:
The greatest number of the two is 5
Step-by-step explanation:
Ratios = 5 : 4
Total ratio = 5 + 4 = 9
Sum = 99
To determine the greatest number, solve
5/9 × 99
495/9 = 55
and the second no.
4/9 × 99
396/9 = 44
So the numbers are 55 : 44
The greatest number is 5. ( which is 55)
The greater of the two numbers is 55.
What is a Ratio?It is a small part of the whole collection.It is used to segregate the collections in different unequal or equal parts.
Given:
Ratio of the two numbers is 5:4.
Let, the common factor between two numbers be x.
∴ The two numbers are 5x and 4x.
According to the given condition:
⇒ 5x + 4x = 99
⇒ 9x = 99
⇒ x = 11
The two numbers are:
5x = 5 × 11
5x = 55
4x = 4 × 11
4x = 44
Therefore, 55 is the greater of the two numbers.
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100 Points last one i promise! helpp!
Answer:
$40.35
Step-by-step explanation:
First, solve for the sales price. Change the percentage into a decimal:
60% = 60/100 = 0.60
Next, multiply 0.60 with the original price, 97:
97 x 0.60 = 58.2
Subtract 58.2 from the original price:
97 - 58.2 = 38.8
Now, change the tax percentage into a decimal.
4% = 4/100 = 0.04
Multiply 0.04 with the sales price:
38.8 x 0.04 = 1.552
Add the sales price (rounded to nearest hundredth) to the sales price:
1.55 + 38.8 = 40.35
$40.35 is your answer.
~
Answer:
40.35
Step-by-step explanation:
First find the discount
97 * 60%
97 *.6 = 58.2
Subtract the discount to find the new price
97-58.20 =38.80
Next find the tax
38.80 * 4%
38.80 * .04
1.55
We add the tax to the sales price
38.8+1.55
40.35
Help plz. Ignore the orange color around the choices.
Hello There!
Your answers would be #1 and #3
If Earl jogged 5 yards forward and then jogs 9 yards back, we are subtracting 9 from 5 and we get a difference of -4. This is because he jogged backward from his position after 5 yards.
If Clarissa had $49 in her checking account, we subtract $53 because she bought a pair of shoes so we get a difference of also -4
Answer:
the first one was the answer
Jimmy is selling used books at a yard sale. A customer buys 9 books at a cost of $0.75 each and pays with a $20.00 bill. Jimmy must determine c, the amount of change in dollars he should give the customer. Which equation represents c?
20-0.75C=9
20-0.75-9c
0.75(9)+c+20
0.75+9+20
Answer:
it is C
Step-by-step explanation:
on edge
What is the base of expression 9^12
Answer:
the answer is 9
Step-by-step explanation:
A bag contains 10 green , 10 orange, 10 pink , and 10 purple chips each numbered 1 through 10. a chip is chosen at random.
What is the probability that the chip is purple, given that the card is a 4?
Answer: [tex]\bold{a.\quad \dfrac{1}{4}}[/tex]
Step-by-step explanation:
Since it is already given that the number is a 4 and each of the four colors only has one 4, then the probability for green is:
[tex]P=\dfrac{\text{number of green 4's}}{\text{total number of 4's}}=\dfrac{1}{4}[/tex]
If you wanted to find the probability that it is a four and it is green then you would calculate the probability as:
[tex]P=\dfrac{\text{number of 4's}}{\text{total number of numbers}}\times \dfrac{\text{number of greens}}{\text{total number of colors}}\\\\\\.\ =\dfrac{4}{40}\times\dfrac{1}{4}\\\\\\.\ =\dfrac{1}{40}[/tex]
[tex]2x^{2} + 9x - 18 = 0[/tex]
Answer:
x = - 6, x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Assuming you require the solution to the equation
Given
2x² + 9x - 18 = 0
To factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 18 = - 36 and sum = + 9
The factors are + 12 and - 3
Use these factors to split the x- term
2x² + 12x - 3x - 18 = 0 ( factor the first/second and third/fourth terms )
2x(x + 6) - 3(x + 6) = 0 ← factor out (x + 6) from each term
(x + 6)(2x - 3) = 0
Equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
What are the zeros of the function shown in the graph?
The graph starts at the bottom left, continues up through the x axis at negative three to a maximum around y equals three, goes back down through the x axis at negative one to a minimum around y equals negative one, and goes back up through the x axis at one.
A. −1, 1, 2
B. −2, −1, 1
C. −3, −1, 1
D. −1, 1, 3
Answer:
The zeroes of the function are -3 , -1 , 1 ⇒ 3rd answer
Step-by-step explanation:
* Lets explain the meaning of the zeroes of the function
- The zeroes of the function are the values of x when f(x) = 0
- That means the coordinates of the intersection points between the
curve and the x-axis
- Ex: If the graph of f(x) intersects the x-axis at points (p , 0) , (q , 0) ,
(r , 0) then the zeroes of f(x) are p , q , r
* Lets solve the problem
- The graph starts at the bottom left
- It continues up through the x-axis at negative three
- That means it intersects the x-axis at point (-3 , 0)
∴ The first zero of the function is -3
- It goes to a maximum around y equals three
- It goes back down through the x-axis at negative one
- That means it intersects the x-axis again at point (-1 , 0)
∴ The second zero of the function is -1
- It goes to a minimum around y equals negative one
- It goes back up through the x-axis at one
- That means it intersects the x-axis again at point (1 , 0)
∴ The third zero of the function is 1
∴ The function has three zeroes -3 , -1 , 1
* The zeroes of the function are -3 , -1 , 1
Connie has to solve the following problem
5 boxes of cereal costs $12.50. How much will 18 boxes cost
Choose EVERY proportion Connie could use to solve this problem
Answer:
$45
Step-by-step explanation:
$12.50÷5=$2.50
$2.50×18=$45
or
12.50/5=n/18
Answer: Cost of 18 boxes is $45.
Step-by-step explanation:
Since we know that
Cost of 5 boxes of cereal = $12.50
We will use "Unitary method":
Cost of 1 box of cereal is given by
[tex]\dfrac{12.50}{5}\\\\=\$2.5[/tex]
So, Cost of 18 boxes would be
[tex]\$2.5\times 18\\\\=\$45[/tex]
Hence, cost of 18 boxes is $45.
17x - 6 + 3x - 5 = x + 11 + 4x
Answer:
x = 22/15
Step-by-step explanation:
17x - 6 + 3x - 5 = x + 11 + 4x
Combine like terms on each side.
20x - 11 = 5x + 11
Add 11 to both sides. Subtract 5x from both sides.
15x = 22
Divide both sides by 15.
x = 22/15
Answer: 20x-11=5x+11
Step-by-step explanation:
In the diagram, C and D are located such that AB is divided into three equal parts. What are the coordinates of C and D?
Step-by-step Answer:
Topic: Points of division
There are scary looking formulas that can be used, but it is much easier to calculate by reasoning.
Given : A(-3,6), B(6,-3)
Solution:
The idea is to subdivide the DIFFERENCE in coordinates into thirds, and add onto that of A. We choose A as the starting point, but method works equally well if we chose B.
Difference in coordinates (delta) between A & B is then
delta(Bx-Ax, By-Ay)
=(6-(-3), -3-6)
=delta(9, -9)
One third of difference (for point C)
=delta/3 = (3,-3)
So coordinates of point C
= A(-3,6)+(3,-3)
= C(0,3)
Two thirds of difference (for point D)
= (2/3)delta = (6, -6)
Coordinates for point D
= A(-3,6)+(6,-6)
= D(3,0)
If you prefer to use formulas, it would be
New coordinates = (Xa+(Xb-Xa)*k, Ya+(Yb-Ya)*k)
where
Xa,Xb = x-coordinates of points A & B respectively.
Ya,Yb = y-coordinates of points A & B respectively.
k=ratio (usually less than 1)
Here
k for point C = 1/3
k for point D = 2/3
Coordinate of C is: (0,3)
and Coordinate of D is: (3,0)
Step-by-step explanation:We know that if a point C(x,y) divides the given line segment A(a,b)B(c,d) into ratio of m:n
then the coordinates of points C are:
[tex]x=\dfrac{m\times c+n\times a}{m+n},\ y=\dfrac{m\times d+n\times b}{m+n}[/tex]
Point C cuts the line segment AB in the ratio 1:2.Here A(a,b)=A(-3,6)
and B(c,d)=B(6,-3)
This means that the coordinate of Point C are:
[tex]x=\dfrac{1\times 6+2\times (-3)}{1+2},\ y=\dfrac{1\times (-3)+2\times 6}{1+2}\\\\i.e.\\\\x=\dfrac{6-6}{3},\ y=\dfrac{-3+12}{3}\\\\i.e.\\\\x=0,\ y=\dfrac{9}{3}\\\\i.e.\\\\x=0,\ y=3[/tex]
Hence, the coordinates of Point C are: (0,3)
Similarly Point D cuts the line AB in the ratio 2:1Hence, the coordinates of point D is calculated by:
[tex]x=\dfrac{2\times (6)+1\times (-3)}{1+2},\ y=\dfrac{2\times (-3)+1\times 6}{1+2}\\\\i.e.\\\\x=\dfrac{12-3}{3},\ and\ y=\dfrac{-6+6}{3}\\\\i.e.\\\\x=\dfrac{9}{3},\ y=\dfrac{0}{3}\\\\i.e.\\\\x=3,\ y=0[/tex]
Hence, the coordinate of Point D is: (3,0)
Which of the following is a correct equation for the line passing through the
point (-3,2) and having slope m = 2/3?
Check all that apply.
A. V-2 ={(x+3)
c. "=3x+4
D. 21 – 3y = - 12
Answer:
[tex]2x-3y=-12[/tex]
Step-by-step explanation:
We can use the point-slope formula given by:
[tex]y-y_1=m(x-x_1)[/tex]
The given line passes through the
point (-3,2) and having slope [tex]m=\frac{2}{3}[/tex].
We substitute the given point and slope to get:
[tex]y-2=\frac{2}{3}(x--3)[/tex]
[tex]y-2=\frac{2}{3}(x+3)[/tex]
we clear the fraction to get;
[tex]3y-6=2(x+3)[/tex]
[tex]3y-6=2x+6[/tex]
[tex]3y-2x=6+6[/tex]
[tex]3y-2x=12[/tex]
Or in standard form:
[tex]2x-3y=-12[/tex]
The correct equation for a line passing through the point (-3,2) with a slope of 2/3 is y = 2/3x + 4, which corresponds to option C in the provided choices.
To find a correct equation for a line passing through a specific point with a given slope, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point through which the line passes.
In this problem, we have the point (-3, 2) and a slope of 2/3. Substituting these values into the point-slope form gives us:
y - 2 = 2/3(x + 3).
After multiplying both sides by 3 to eliminate the fraction, the equation becomes:
3(y - 2) = 2(x + 3).
Expanding and simplifying this equation further, we end up with:
3y - 6 = 2x + 6,
or
y = 2/3x + 4, which matches option C.
Therefore, the correct equation for the line passing through the point (-3, 2) with a slope of 2/3 is y = 2/3x + 4.
Solve the system y-10=3x, 2y = 6x + 20
Answer:
they are the same line! hence there are infinite number of solutions
Step-by-step explanation:
y-10=3x (rearrange)
we get: y = 3x + 10 ----------- eq. (1)
2y=6x+20 (divide both sides by 2)
we get: y = 3x + 10 ----------- eq. (2)
We can see that (1) = (2).
i.e they are the same line! hence there are infinite number of solutions.
Identify the similar triangles and find x. Then find the measures of the indicated sides.
Answer:
The similar triangles are Δ KMJ and Δ NML
The value of x is 3
KM = 6 and NM = 3
Step-by-step explanation:
* Lets revise the cases of similarity
1) AAA similarity : two triangles are similar if all three angles in the first
triangle equal the corresponding angle in the second triangle
- Example : In ΔABC and ΔDEF, m∠A = m∠D, m∠B = m∠E and
m∠C= m∠F then ΔABC ≈ ΔDEF by AAA
2) AA similarity : If two angles of one triangle are equal to the
corresponding angles of the other triangle, then the two triangles
are similar.
- Example : In ΔPQR and ΔDEF, m∠P = m∠D, m∠R = m∠F then
ΔPQR ≈ ΔDEF by AA
3) SSS similarity : If the corresponding sides of two triangles are
proportional, then the two triangles are similar.
- Example : In ΔXYZ and ΔLMN, if
then the two triangles are similar by SSS
4) SAS similarity : In two triangles, if two sets of corresponding sides
are proportional and the included angles are equal then the two
triangles are similar.
- Example : In triangle ABC and DEF, if m∠A = m∠D and
then the two triangles are similar by SAS
* Now lets solve the problem
- ∠KMJ is a aright angle and M is on JL
∴ m∠JML = 180° ⇒ straight angle
∵ m∠JMK + m∠LMN = m∠JML
∴ 90° + m∠NML = 180° ⇒ subtract 90° from both sides
∴ m∠NML = 90°
- In Δ KMJ and ΔNML
∵ m∠KMJ = m∠NML ⇒ proved
∵ m∠KJM = m∠NLM ⇒ given
- By using the second case above (AA similarity)
∴ Δ KMJ ≈ Δ NML
* The similar triangles are Δ KMJ and Δ NML
- From similarity
∴ Their sides are proportion
∴ [tex]\frac{KM}{NM}=\frac{MJ}{ML}=\frac{KJ}{NL}[/tex]
∵ KJ = 10 and NL = 5
∵ KM = 3 + x and NM = x
- Substitute these values in the proportion relation
∵ [tex]\frac{KM}{NM}=\frac{KJ}{NL}[/tex]
∴ [tex]\frac{3+x}{x}=\frac{10}{5}[/tex]
- By using cross multiplication
∴ 5(3 + x) = 10(x) ⇒ simplify
∴ 5(3) + 5(x) = 10x
∴ 15 + 5x = 10x ⇒ subtract 5x from both sides
∴ 15 = 5x ⇒ divide both sides by 5
∴ 3 = x
* The value of x is 3
∵ KM = 3 + x
∵ x = 3
∴ KM = 3 + 3 = 6
∵ NM = x
∴ NM = 3
* KM = 6 and NM = 3
- Check the ratio
∵ KM/NM = 6/3 = 2
∵ KJ/NL = 10/5 = 2
∴ The sides are proportion
Answer:
Triangle JMK is similar to triangle LMN.
[tex]x = 3[/tex].
[tex]\rm \overline{KM}= 6[/tex].
[tex]\rm \overline{NM} = 3[/tex].
Step-by-step explanation:
The angle [tex]\rm N\hat{M}L[/tex] is a right angle for it is complementary with another right angle, [tex]\rm K\hat{M}J[/tex].
The diagram also indicates that angle [tex]\rm \hat{J}[/tex] is equal to angle [tex]\rm \hat{L}[/tex]. As a result, [tex]\rm \triangle JMK \sim \triangle LMN[/tex] for two of their angles are equal.
Consequently,
[tex]\displaystyle \rm \frac{(\overline{MN})}{(\overline{MK})} = \frac{(\overline{LN})}{(\overline{JK})}[/tex].
Let [tex]x[/tex] be the length of segment [tex]\rm MN[/tex].
[tex]\displaystyle \frac{x}{3+x} = \frac{5}{10}[/tex].
Cross multiply. In other words, multiply both sides by [tex]10(3 + x)[/tex].
[tex]10x = 5(3 + x)[/tex].
[tex]x = 3[/tex].
[tex]\rm \overline{KM} = 3 + \mathnormal{x} = 6[/tex].
[tex]\rm \overline{MN} = \mathnormal{x} = 3[/tex].
Kate is making pizza. She puts 8 ounces of cheese on each pizza. If she has 4 24-ounce packages of cheese, how many pizzas can she make?
A.3 pizzas
B.6 pizzas
C.9 pizzas
D.12 pizzas
24 ounce can / 8 ounces = 3 pizzas per can.
3 pizzas per can x 4 cans = 12 total pizzas.
The answer is D.
Answer: D.) 12 pizza