Answer:
(1, 2 ) and ([tex]\frac{8}{3}[/tex], [tex]\frac{3}{4}[/tex] )
Step-by-step explanation:
3x + 4y = 11 → (1)
xy = 2 ( divide both sides by y , y ≠ 0 )
x = [tex]\frac{2}{y}[/tex] → (2)
Substitute x = [tex]\frac{2}{y}[/tex] into (1)
3([tex]\frac{2}{y}[/tex] ) + 4y = 11
[tex]\frac{6}{y}[/tex] + 4y = 11 ( multiply through by y )
6 + 4y² = 11y ( subtract 11y from both sides )
4y² - 11y + 6 = 0
Consider the factors of the product of the y² term and the constant term which sum to give the coefficient of the y- term
product = 4 × 6 = 24 and sum = - 11
The factors are - 8 and - 3
Use these factors to split the y- term
4y² - 8y - 3y + 6 = 0 ( factor first/second and third/fourth terms )
4y(y - 2) - 3(y - 2) = 0 ← factor out (y - 2) from each term
(y - 2)(4y - 3) = 0
Equate each factor to zero and solve for y
4y - 3 = 0 ⇒ 4y = 3 ⇒ y = [tex]\frac{3}{4}[/tex]
y - 2 = 0 ⇒ y = 2
Substitute these values into (2)
y = 2 : x = [tex]\frac{2}{2}[/tex] = 1 ⇒ (1, 2 )
y = [tex]\frac{3}{4}[/tex] : x = [tex]\frac{2}{\frac{3}{4} }[/tex] = 2 × [tex]\frac{4}{3}[/tex] = [tex]\frac{8}{3}[/tex] ⇒ ( [tex]\frac{8}{3}[/tex], [tex]\frac{3}{4}[/tex] )
Given that rectangle ABCD has coordinates A(0,0), B(12,0), C(12,6), and D(0,6), F is the midpoint of AB¯¯¯¯¯, and G is the midpoint of CD¯¯¯¯¯, which of the following proves that FB=GC?
1. By the Distance Formula, the coordinates of F are (6, 0) and the coordinates of G are (6, 6).
Then FB = 12, and GC = 12.
Thus FB = GC.
2. By the Distance Formula, the coordinates of F are (6, 12) and the coordinates of G are (6, 0).
Then FG = 6, and GC = 6.
Thus FG = GC.
3. By the Midpoint Formula, the coordinates of F are (6, 0) and the coordinates of G are (6, 6).
Then FB = 6, and GC = 6.
Thus FB = GC.
4. By the Midpoint Formula, the coordinates of F are (6, 6) and the coordinates of G are (6, 0).
Then FB = 6, and GC = 6.
Thus FB = GC.
The midpoint of the sides [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are the points that half way between [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] respectively.
The option that proves [tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex] is option 3
3. By the Midpoint Formula, the coordinates of F are (6, 0) and the coordinates of G are (6, 6). Then [tex]\overline{FB}[/tex] = 6, and [tex]\overline{GC}[/tex] = 6. Thus [tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex]Reasons:
The given coordinates of the vertices of rectangle ABCD are;
A(0, 0), B(12, 0), C(12, 6), and D(0, 6)
The midpoint of side [tex]\overline{AB}[/tex] = Point F
The midpoint of side [tex]\overline{CD}[/tex] = Point F
The coordinates of point F is given by the midpoint formula, as follows;
[tex]\displaystyle \mathrm{The \ midpoint \ of \ a \ line \ with \ endpoints \ (x_1, \ y_1) \ and \ (x_2, \ y_2) = \mathbf{ \left(\frac{x_1 + x_2}{2}, \ \frac{y_1 + y_2}{2} \right) }}[/tex]
Which gives;
[tex]\displaystyle \mathrm{The \ coordinate \ of \ F \ the \ midpoint \ of \ \overline{AB} = \mathbf{ \left(\frac{0 + 12}{2}, \ \frac{0 + 0}{2} \right)} =(6,\ 0)}[/tex]
The coordinates of point F = [tex]\underline{(6, \ 0)}[/tex][tex]\displaystyle \mathrm{The \ coordinate \ of \ G \ the \ midpoint \ of \ \overline{CD} = \left(\frac{12 + 0}{2}, \ \frac{6 + 6}{2} \right) =(6,\ 6)}[/tex]
The coordinates of point G = [tex]\underline{(6, \ 6)}[/tex][tex]\overline{FB}[/tex] is parallel to the x-axis, therefore;
The length of [tex]\overline{FB}[/tex] = 12 - 6 = 6Similarly, [tex]\overline{GC}[/tex] is parallel to the x-axis, therefore;
The length of [tex]\overline{GC}[/tex] = 12 - 6 = 6Which gives;
[tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex] = 6The correct option is that proves [tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex] is option 3.
By the Midpoint Formula, the coordinates of F are (6, 0) and the coordinates of G are (6, 6). Then [tex]\overline{FB}[/tex] = 6, and [tex]\overline{GC}[/tex] = 6. Thus [tex]\overline{FB}[/tex] = [tex]\overline{GC}[/tex]
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What is an equation of the line that passes through the points (2, -7)(2,−7) and (2, -2)(2,−2)
Answer:
X = 2
Step-by-step explanation:
Slope: (- 7 - -2)/(2 - 2) = -5/0 = 0
The line is vertical (undefined
[tex] \: \: \: [/tex]
help me po
1.) if mHO =150° and mPO =80° what is the m∠HEO?
2.) if mMT =140° and mMHT =220° find m∠ MAT
answer 3-4 only
need properly answer
right answer= brainlist follow and thanks
nonsense answer will be reported
Answer:
b. secantc. 45°d. 35°d. 40°Step-by-step explanation:
1. A chord is a line segment whose end points lie on a circle. The line containing that segment is called a "secant."
__
2. The angle where chords cross is the average of the intercepted arcs:
(50° +40°)/2 = 45° . . . . measure of angle CSA
__
3. The angle where secants or tangents meet is half the difference of the intercepted arcs.
(150° -80°)/2 = 35° . . . . measure of angle HEO
__
4. The angle where secants or tangents meet is half the difference of the intercepted arcs.
(220° -140°)/2 = 40° . . . . measure of angle MAT
Please note that this is the supplement of arc MT between the tangents.
Answer:
The DNA is a double-stranded molecule that has a long chain of nucleotides. The RNA is a single-stranded molecule which has a shorter chain of nucleotides. Propagation. DNA replicates on its own, it is self-replicating. RNA does not replicate on its own.
Neuron Function: Food Preservation
Fertilizer Meaning: Exocrine Glands
Food Chain Examples: Cell Biology
Step-by-step explanation:
yo kya haal hai
group of 3 people is going on a boat tour. If each boat holds 3 people, how many will boats will the group need?
Answer:
1
Step-by-step explanation:
there are 3 people and 1 boat holds three people
10.
Identify the vertex of the parabola.
A. (−1, 0)
B. (0, −1)
C. (1, 0)
D. (0, 1)
Answer:
C. (1, 0)
Step-by-step explanation:
1,0 should be the vertex for this parabola
1,0 should be the correct answer
Create a shape with an area of 0.8 m2 and a perimeter close to 400 cm
The dimension of the shape is approximately 1.45 meters by 0.55 meters
Assume the shape is a rectangle, that has the following dimensions.
Length = x
Width = y
So, the area is:
Area = xy
The perimeter is
Perimeter = 2(x + y)
Substitute known values
[tex]\mathbf{xy = 0.8m^2}[/tex]
[tex]\mathbf{2(x+y) = 400cm}[/tex]
Express cm as m
[tex]\mathbf{2(x+y) = 4m}[/tex]
Divide through by 2
[tex]\mathbf{x+y = 2m}[/tex]
Make x the subject (ignore the units)
[tex]\mathbf{x= 2 - y}[/tex]
Substitute 2-y for x in [tex]\mathbf{xy = 0.8m^2}[/tex]
[tex]\mathbf{(2-y)y = 0.8}[/tex]
Open brackets
[tex]\mathbf{2y-y^2 = 0.8}[/tex]
Rewrite as:
[tex]\mathbf{y^2 - 2y + 0.8 = 0}[/tex]
Using a calculator, we have:
[tex]\mathbf{y \approx (0.55,1.45)}[/tex]
Recall that:
[tex]\mathbf{x= 2 - y}[/tex]
So, we have:
[tex]\mathbf{x \approx (2-0.55,2-1.45)}[/tex]
[tex]\mathbf{x \approx (1.45,0.55)}[/tex]
Hence, the dimension of the shape is approximately 1.45 meters by 0.55 meters
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Decide if the following situation is a unit rate or not why or why not?
You score 12 points in one basketball game.
Answer:
Yes, because in 1 game you scored 12 points you didn't score multiple points in multiple games.
What is 0.4184 in standard form
Answer:4.184*10^-1
Step-by-step explanation: in standard form or scientific notation
Javad had a mix of yellow and red jelly beans are shown on the graph if there are 42 jelly beans in his bag how many are red?
Answer:
there is no graph though
For any line, if you draw two right triangles using the line as the hypotenuse, do the triangles have to be similar? Why or why not?
Answer:
YesStep-by-step explanation:
If the same line holds the hypotenuse of two right triangles, both of the triangles are similar.
This is because they have same ratio of corresponding sides.
Yes .
Let's check your graph
In ∆ADE and ∆ABC
AD~BC(Parallel to y axis or y axis)AE~EC(Passing through origin and same vertice A)AB~DE(Translation by 2)Hence both triangles are similar
QUESTION 9 of 10: You enter a bid. Your cost on the product you make is $112 per unit. If you bid at $138 per unit, what percent is the price
you bid over your cost? (Round to the nearest percent)
a) 19%
b) 23%
C) 81%
Submit
From the information given, the percentage increase in the price bid over the cost will be 23%.
Cost on the product = $112.
Amount bid = $138
Therefore, the Percentage increase will be:
= (138 - 112) / 112 × 100
= 26/112 × 100
= 23%
Therefore, from the calculation above, it can be seen that the percentage increase in the price bid over the cost will be 23%.
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72% of 25 students are interested in mathematics how many are not interested in mathematics by moderators.
Answer:
7 students
Step-by-step explanation:
72/100 × 25 students = 18
18 students are interested in mathematics
therefore, 25 - 18 = 7 students are not interested
I WILL GIVE BRAINLIEST TO WHOMEVER ANSWERS (TRUTHFULLY) !!NO LINKS!!
Step-by-step explanation:
SAS ================
What it says:
If two sides and the angle between them on one triangle are congruent to the corresponding two sides and the angle between them on the other, the triangles are congruent.
Required information:
Two sets of congruent sides with a congruent angle between them
ASA ================
What it says:
If one side and both connected angles on one triangle are congruent to one side and both connected angles on the other, the triangles are congruent.
Required information:
One set of congruent sides with two sets of congruent angles on the sides
AAS ==================
What it says:
If two angles and the non-included side on one triangle are congruent to two angles and the non-included side on the other, the triangles are congruent.
Required information:
Two sets of congruent angles and one set of congruent non-included sides
HL =================
What it says:
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg on the other, the triangles are congruent.
Required information:
Congruent hypotenuse and congruent leg
Which number is both a factor AND a multiple of 4? 1,2,4,8
Answer:
1,2,4,
Step-by-step explanation:
please solve y. y/4-16=-14 and also have a bless day
Answer:
y=8
Step-by-step explanation:
Multiply both sides of the equation by 4.
y−64=−56
Add 64 to both sides.
y=−56+64
Add −56 and 64 to get 8.
y = 8
and have a good day as well
Kipton puts one marshmallow on the scale and it weighs 7.2 grams. How much would 10 marshmallows weigh?
Answer:
72 grams
Step-by-step explanation:
7.2 x 10 = 72
Donna cut away 7.75 meters of rope. Before that, she had 12 meters of rope. How much rope does Donna have left?
Answer: 4.25 meters of rope
Step-by-step explanation:
Because Donna is losing 7.75 meters of rope from her original 12 meters, this problem can simply be represented as 12 - 7.75, which equals 4.25.
Hope it helps :) and let me know if you want me to elaborate.
[tex] \: \: \: \: \: \: [/tex]
plss help me po!!
what is the measure of OS if MO = 6, OE =4 and OR=3?
a. 13
b. 8
c. 7.5
d. 7
explain your answer
see the attachment
need properly answer
nonsense answer will be reported
excellent answer will get brainlist and follow
#nospam
#nolinks
[tex] \: \: \: \: \: \: \: [/tex]
Answer:
B. 8Step-by-step explanation:
Intersecting chords theorem:
OS * OR = OM * OESubstitute values and solve for OS:
OS * 3 = 6 * 43OS = 24OS = 24/3OS = 8Correct choice is B
Help pleasee giving brainliest!!
Answer:
x=21
<1=120
Step-by-step explanation:
So to find x set up an equation like this:
(5x+15)+(3x-3)=180
since the bottom and top lines are congruent they are 'interior angles on the same side of a transversal' which are always supplementary, so that's where 180 comes from.
calculate the equation and you'll get x=21 :D
next to find 1 just put 21 in place of x: 3(21)-3=60
since it's supplementary to angle 1 you take 180-60=120
angle <1=120!
Can somebody help ????
Answer:
Answer is 4, explained answer in the comments because I didn't see the answer button, but now I do.
Bob bought 2Ibs of apples for $6. Explain how to find the unit rate and give the meaning of unit rate
Answer:
Unit rate is 3
Step-by-step explanation:
The unit rate means the value of ONE unit.
In this case, it would be the value of ONE pound of apples.
I divided 6 by 2, which gave me THREE.
12÷5/2=
Tell the answer quick!!
Answer:
4.8
Step-by-step explanation:
Answer:
4.8
Step-by-step explanation:
mark braineist pls
Find the cosine of angle U
Answer:
1st option
Step-by-step explanation:
cosU = [tex]\frac{asjacent}{hypotenuse}[/tex] = [tex]\frac{UV}{UW}[/tex] = [tex]\frac{15}{17}[/tex]
Find the sum of the product of 3/5 and 5/9 and the product of 5/9 and 3/20
Answer:
1/3 + 1/12 = 5/12
Step-by-step explanation:
Take a look on the picture
There are the solutions
to get the correct answer
Hope it helps
#LetsStudy
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The sum of the product of 3/5 and 5/9 and the product of 5/9 and 3/20 is 5/12.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
The product of 3/5 and 5/9 is,
Product = 3/5 × 5/9
= (3×5)/(5×9)
= 15 / 45
= 1/3
The product of 5/9 and 3/20 is,
Product = 5/9 × 3/20
= (5×3)/(9×20)
= 15 / 180
= 1/12
Now, the sum of the two products can be done as shown below,
Sum = 1/3 + 1/12
= 4/12 + 1/12
= (4+1)/12
= 5/12
Hence, the sum of the product of 3/5 and 5/9 and the product of 5/9 and 3/20 is 5/12.
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Please help with this as well! Mind to give the explanation too? Just so I know
Answer:
i found out how to get 50
Step-by-step explanation:
14 + 18 x 2 = 50
cuanto es "y=2x + 5" ??
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(2*x+5)=0
STEP1:
Equation of a Straight Line
1.1 Solve y-2x-5 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-2x-5 = 0 and calculate its properties
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 5/1 so this line "cuts" the y axis at y= 5.00000
y-intercept = 5/1 = 5.00000
Calculate the X-Intercept :
When y = 0 the value of x is 5/-2 Our line therefore "cuts" the x axis at x=-2.50000
x-intercept = 5/-2 = -2.50000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 5.000 and for x=2.000, the value of y is 9.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 9.000 - 5.000 = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 4.000/2.000 = 2.000
Geometric figure: Straight Line
Slope = 4.000/2.000 = 2.000 x-intercept = 5/-2 = -2.50000 y-intercept = 5/1 = 5.000005. The function f(x) is shown in this graph.
The function g(x) = -3x - 1. Compare the slopes by writing "less than, "greater than," or "equal to" in the blank.
The slope of f(x) is ______ the slope of g(x).
Answer:
The slope of f(x) is greater than the slope of g(x)
Here is:
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A jar contains 35 coins made up of 20c and 50c coins only. Then total value of the coins is
$13.90.
(I) If there were x 20c coins, write an equation in x for the number of 50c coins.
(ii) Using the given information, write an equation in terms of x for the total sum of money
the jar holds.
(iii) Solve the equation to find the number of each type of coin in the jar.
There are 12 coins which are 20 cent each and 23 coins which are 50 cent each.
Let x represent the number of 20 cent ($0.2) coins
i) Since there are 35 coins in total:
Number of 50 cent coins = 35 - x
ii) The total value of the coins is $13.90. Hence:
0.2x + 0.5(35 - x) = 13.90
iii) 0.2x + 17.5 - 0.5x = 13.90
0.3x = 3.6
x = 12
Number of 50 cent coin = 35 - x = 35 - 12 = 23
Therefore there are 12 coins which are 20 cent each and 23 coins which are 50 cent each.
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The question is the img. Please answer both if u can
Problem 1
x = number of weeks
y = amount left on gift card (in dollars)
He starts with $100. Then each week he spends $4.99 which means we subtract 4.99x from the 100 mentioned. We form the expression 100 - 4.99x which is the same as -4.99x + 100
The equation y = -4.99x + 100 is in slope intercept form with m = -4.99 as our slope and b = 100 as the y intercept.
Answer: y = -4.99x + 100=======================================================
Problem 2
The y intercept is 100 because it's the starting amount. Mark the point (0,100) on the graph.
We need one more point to form a straight line. Let's say we picked something like x = 4 to plug into the equation found earlier
y = -4.99x + 100
y = -4.99*4 + 100
y = -19.96 + 100
y = 80.04
After x = 4 weeks, Mark has y = 80.04 dollars left on the card. We'll plot the point (4, 80.04). Then we connect those points with a straight line.
Check out the diagram below.The location of (4, 80.04) can be visually marked as (4,80) since it's close enough in my opinion.
(Pythagorean theorem) find the missing side length. Round to the nearest hundredth (show steps)
Answer:
9.09
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
When looking at the triangle we see that we have the hypotenuse and the opposite side.
a = opposite
b = adjacent
c = hypotenuse (always)
So if we plug those numbers into the equation we can get the missing side length
1) a² + b² = c²
2) 9.7² + b² = 13.3²
3) b² = 13.3² - 9.7²
4) b² = 176.89 - 94.09
5) b = [tex]\sqrt{176.89 - 94.09}[/tex]
6) b = 9.093954036
Now we round to nearest hundredth
To find the nearest hundredth we have to look at the thousandth place in the thousandth place we have 3 (9.093) that rounds down so,
b = 9.09