Answer:
point 1 = (3, 6)
point 2 = (24, -15)
Step-by-step explanation:
8/x - 10/y = 1
x + y = 9
x = 9 - y
=>
8/(9-y) - 10/y = 1
8 - 10×(9-y)/y = 9 - y
-90/y + 10y/y = 1 - y
-90/y + 10 = 1 - y
-90 + 10y = y - y²
y² + 9y -90 = 0
the solution to a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case we use y instead of x.
a = 1
b = 9
c = -90
y = (-9 ± sqrt(81 - -360))/2 = (-9 ± sqrt(441))/2 =
= (-9 ± 21)/2
y1 = 12/2 = 6
y2 = -30/2 = -15
8/x - 10/6 = 1
8 - 10x/6 = x
8 - 5x/3 = x
24 - 5x = 3x
24 = 8x
x = 3
8/x - 10/-15 = 1
8/x + 2/3 = 1
8 + 2x/3 = x
24 +2x = 3x
24 = x
A parabola can be represented by the equation y2 = 12x.
Which equation represents the directrix?
O y=-3
O y=3
O X=-3
O x= 3
Answer:
It's C
X = -3
Step-by-step explanation:
Edge 2022
The equation represents the directrix is x=-3.
the correct option is (C).
what is directrix in parabola?A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola, and the line is called the directrix . The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.
given: y²=12x
y²=4*3*x
Here a=3
So, x+a=0
x+3=0
x=-3.
Hence, the directrix of parabola is: x=-3
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if there are about 5,000.00 red blood cells in every one cubic millimiter of mrs. garcias blood and there are about 4,600,00 cubic millimiter of blood in her body. How many red blood cells does mrs. gracia has in her body?
Answer:
Step-by-step explanation:
Use a double-angle or half-angle identity to find the exact value of each expression
If 180° < θ < 270°, then 90° < θ/2 < 135°, which places θ/2 in the second quadrant so that sin(θ/2) > 0 and cos(θ/2) < 0.
Recall that
cos²(θ/2) = (1 + cos(θ))/2
==> cos(θ/2) = -√[(1 + (-15/17))/2] = -1/√17
and
sin²(θ/2) = (1 - cos(θ))/2
==> sin(θ/2) = +√[(1 - (-15/17))/2] = 4/√17
Then
tan(θ/2) = sin(θ/2) / cos(θ/2)
… = (4/√17) / (-1/√17)
… = -4
2r + st^2 - u, if r = 4, s = 6, t = 3, and u = 12
Answer:
320
Step-by-step explanation:
r = 4, so 2 x 4 = 8.
s = 6 and t = 3, so 6 x 3 = 18. 18 squared is 324.
u = 12, so 8 + 324 - 12, which equals 320.
What set of reflections would carry trapezoid ABCD onto itself?
y=x, x-axis, y=x, y-axis
x-axis, y=x, x-axis, y=x
y-axis, x-axis, y-axis
x-axis,y-axis,y-axis
find the mean of the following 205,208,205,200,210,300,210,180.
Second time I’ve posted this. Please help!! :)
Answer:
-2 is an extraneous solution because it creates 0 in the denominator.
There is one acceptable solution to the equation
Step-by-step explanation:
x² + 5x + 6 = x² + 2x + 3x + 6
= x(x + 2) + 3(x + 2)
= (x + 2)(x + 3)
[tex]\frac{x}{x+2}+\frac{2}{x^{2}+5x+6}=\frac{5}{(x+3)}\\\\\frac{x}{x+2}+\frac{2}{(x+2)(x+3)}=\frac{5}{(x+3)}\\\\\frac{x*(x+3)}{(x+2)(x+3)}+\frac{2}{(x+2)(x+3)}=\frac{5*(x+2)}{(x+3)(x+2)}\\\\\frac{x^{2}+3x+2}{(x+2)(x+3)}=\frac{5x+10}{(x+3)(x+2)}\\\\[/tex]
x² + 3x + 2 = 5x + 10
x² + 3x - 5x + 2 - 10 = 0
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x(x + 2) - 4(x + 2) = 0
(x + 2)(x - 4) = 0
x +2 = 0 or x - 4 = 0
x = - 2 or x = 4
please help finding x ASAP
Angle 2 and Angle 4 are same-side interior angles, which are supplementary.
(2x + 10) + (4x + 80) = 180
6x + 90 = 180
6x = 90
x = 15
Hope this helps!
Answer:
X = 15
Step-by-step explanation:
Angle 2 = Angle 3 since they are alternate angles
Now, angle 3 and 4 should add up to 180 since they are on a straight line
∴ (2x + 10) + (4x + 80) = 180
6x + 90 = 180
6x = 180 - 90
6x = 90
x = 15
HOPE THIS HELPS
Find DC, given that line AD is the angle bisector of
Which of the following operations is true regarding relative frequency distributions? Multiple choice question. No two classes can have the same relative frequency. The relative frequency is found by dividing the class frequencies by the total number of observations. The sum of the relative frequencies must be less than 1. The sum of the relative frequencies is equal to the number of observations.
Answer:
The relative frequency is found by dividing the class frequencies by the total number of observations
Step-by-step explanation:
Relative frequency measures how often a value appears relative to the sum of the total values.
An example of how relative frequency is calculated
Here are the scores and frequency of students in a maths test
Scores (classes) Frequency Relative frequency
0 - 20 10 10 / 50 = 0.2
21 - 40 15 15 / 50 = 0.3
41 - 60 10 10 / 50 = 0.2
61 - 80 5 5 / 50 = 0.1
81 - 100 10 10 / 50 = 0.2
50 1
From the above example, it can be seen that :
two or more classes can have the same relative frequencyThe relative frequency is found by dividing the class frequencies by the total number of observations. The sum of the relative frequencies must be equal to one The sum of the frequencies and not the relative frequencies is equal to the number of observations.(05.05) Which scenario best matches the linear relationship shown in the table?
Weeks Dollars
0 10
2 20
4 30
6 40
• Shanna had $10 in her piggy bank and earned $10 each week in allowance.
• Shanna had $10 in her piggy bank and earned $5 each week in allowance.
• Shanna had $10 in her piggy bank and spent $5 each week on stickers.
• Shanna earns $10 each week.
Answer:
• Shanna had $10 in her piggy bank and earned $5 each week in allowance.
Step-by-step explanation:
Week 0 dollars = 10
This means Shanna had $10 her piggy bank before the week started
Week 2 dollars = 20
Her account has increased from 10 to 20 dollars in two weeks. This means she is earning
Amount earned per week = change in earnings / change in week
= 20 dollars - 10 dollars / Week 2 - week 1
= 10 dollars / 2 weeks
= 5 dollars per week
Amount earned per week = $5
Therefore,
• Shanna had $10 in her piggy bank and earned $5 each week in allowance
Answer:
option b
Step-by-step explanation:
cuz its the only one that makes sense
Write the expression a 15 as a product of two exponents with the same base, one of
which equals:
a^6
Answer:
[tex]a^{6} a^{9} = a^{15}[/tex]
Step-by-step explanation:
is this the question ///
Write the expression a^15 as a product of two exponents with the same base, one of which equals: a^6
if so ...
[tex]a^{6} a^{9} = a^{15}[/tex]
Can someone help me with this math homework please!
Answer:
The third table
Step-by-step explanation:
When a function decrease over a interval, the numbers between the interval and the latest interval included must be lesser than the original first interval.
In other words, the y value for -2 must be greater than the numbers between 0 and -2 in order for the interval be decreasing.
The third table show that
Consider the function ƒ(x) = –2x – 7 and the function g(x), which is graphed above. Select the correct statement from the options that follow.
a) The function g(x) has a steeper slope than ƒ(x).
b) There isn't enough information to determine which function has a steeper slope.
c) The functions ƒ(x) and g(x) have the same slope.
d) The function ƒ(x) has a steeper slope than g(x).
Answer:
d) The function ƒ(x) has a steeper slope than g(x)
Step-by-step explanation:
We are given that
[tex]f(x)=-2x-7[/tex]
The graph g(x) passing through the point (1.2,0) and (0,4).
Let
y=f(x)=-2x-7
Slope of function f(x)
[tex]m=\frac{dy}{dx}=-2[/tex]
Slope formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the formula
Slope of g(x)
[tex]m'=\frac{4-0}{0-1.2}[/tex]
[tex]m'=-3.33[/tex]
Slope of g(x)=-3.33<-2
Slope of f(x) is greater than slope of g(x).
Therefore, function f(x) has a steeper slope than g(x).
Option d) is correct.
Answer:
It's not D its A I Just took the test.
Step-by-step explanation:
Good luck!
The slope of the line is:
A. -6
B.
C. O
D. Undefined
Answer:
The slope is undefined
Step-by-step explanation:
Since x doesn't have an existing value it leaves the slope as undefined.
Which type of transformation is this?
Answer:
A reflection across the x axis
Step-by-step explanation:
Parallelogram ABCD was reflected across the x axis to create parallelogram A'B'C'D'
help pls with explanation!!!
Answer:
18c - 30d + 36
Step-by-step explanation:
To apply the distributive property, we must "distribute" (multiply) the outer term by the terms in the parentheses. In this case, the outer term is 6, and the inner terms are 3c, 5d, and 6. Then, if there's any like terms, you must combine them.
6(3c - 5d + 6)
(6 · 3c) + (6 · -5d) + (6 · 6)
18c + -30d + 36
As you can see, there's no like terms in this expression, so the equivalent expression to 6(3c - 5d + 6) is 18c + -30d + 36.
Construct 5 equivalent equations for the equation - 3 + 2x = -4.
Answer:C
Step-by-step explanation:
Which graph shows a method for finding the image of point D if the parallelogram is reflected across the dashed line?
Answer:
The third option with the right angle
Step-by-step explanation:
By creating a perpendicular line through the line of reflection (the orange dotted line) and the point "D" we can measure the distance of D from the line of reflection. Then draw "D'" using the distance of the "D" from the line of reflection.
find the slope of the line for each pair of points (2, -10) (8, -16)
Answer:
-1
Step-by-step explanation:
We can use the slope formula since we are given two points
m = (y2-y1)/(x2-x1)
= (-16- -10)/(8-2)
= (-16+10)/(8-2)
= -6/6
= -1
help plsss
If d = c-b / a-n , then wbat is the value of b?
A) c-d / a-b
B) ca-d / ca+d
C) c-ad / 1-d
D) c+ad / d-1
Let’s think about another type of scenario. What if you were told that a bracelet requires 10 beads and 10 minutes to make while a necklace requires 20 beads and takes 40 minutes to make. The craftsman has 1000 beads to work with and he has 1600 minutes in which to work. If a bracelet costs $5 and a necklace costs $7.50, what is the maximum revenue that the craftsman can take in?
Answer:
$425
Step-by-step explanation:
Let x represent the number of bracelets made and let y represent the number of necklace made.
Since the craftsman has 1000 beads to work with, hence:
10x + 20y ≤ 1000 (1)
Also, the craftsman has 1600 minutes, hence:
10x + 40y ≤ 1600 (2)
From ploting equations 1 and 2 on the geogebra online graphing, we can see that the solution to the problem is (40, 30).
Since the bracelet costs $5 and a necklace costs $7.50, hence the maximum revenue is:
Revenue = 5x + 7.5y = 5(40) + 7.5(30) = $425
Which of the following is an example of a quadratic equation?
O A. X+10 - 33
O B. y - 4x+6
OC. x2-64-0
O D. V-746
Hello!
Answer: C. x² - 64 - 0
Good luck! :)
Can someone help me with this math homework please!
Answer:
A ; B ; D
Step-by-step explanation:
(3+1)/12 = 1/3 (ok)
(-5+1)/-2 = -4/-2 = 2 (ok)
(1+1)/-3 = -2/3 (no)
(15+1)/1 = 16 (ok)
(-2 + 1)/5 = -1/5 (no)
HELPPPP MEEEEE OUTTTTT PLEASEEEE ASAPPPP!!!!
Answer:
sin X =35/37
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin X = opp side / hypotenuse
sin X =35/37
△STR≅△LMN, SR=7b+8, and LN=11b−12. Find b and SR.
Answer:
b = 5
Step-by-step explanation:
△STR ≅ △LMN
This means the corresponding sides are equal.
SR and LN are corresponding sides.
SR and LN are equal.
The value of b is 5.
The value of SR is 43
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
△STR ≅ △LMN
This means the corresponding sides are equal.
SR = 7b + 8
LN = 11b − 12
SR and LN are corresponding sides.
SR and LN are equal.
So,
7b + 8 = 11b − 12
Subtract 7b on both sides.
8 = 11b - 7b - 12
Add 12 on both sides.
8 + 12 = 4b
20 = 4b
b = 20/4
b = 5
Now,
SR:
= 7b + 8
= 7 x 5 + 8
= 35 + 8
= 43
Thus,
The value of b is 5.
The value of SR is 43
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what amount of money is to be deposited in a bank to get RS 1225 in 9/2 year with the rate of intrest 5%
Answer:
rs.6,300
Step-by-step explanation:
Simple Interest, S.I. = Rs. 1260 =
100
PR×2
=
50
PR
-(i)
Compound Interest, C.I. = Amount(A) - Principle(P)
=P(1+
100
R
)
2
- P = PR(R/10000+1/50)=Rs.1323 -(ii)
Dividing (ii) by (I),
200
R
+1 =
1260
1323
⇒Rate,R=10%p.a.
Now,
100
PRT
=1260
⇒
100
P×10×2
=1260
The amount of money that we need to deposit in the bank to get RS 1225 is RS 1100.03.
What is compound interest?Compound interest is applicable when there will be a change in principal amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount.
Suppose we need to deposit the P amount to get RS 1225
By compound interest formula,
1125 = P(1 + 0.05)^(9/2)
P = RS 1100.03
Hence "We need to deposit Rs. 1100.03 in the bank in order to receive Rs. 1225".
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How much money will be in a bank account after 7 years if $8 is deposited at a interest rate of 5% compounded annually? Round to the nearest dollar
Ps need help ASAP
If the product of roots of the equation given below is 4, then find the value of m.
Answer:
m=-2
Step-by-step explanation:
As the product of the roots of a quadratic equation is c/a in ax^2+bx+c=0
here a=2, b=+8, c=-m^3
Given c/a=4
-m^3/2=4
-m^3=8
m^3= -8
m=-2.
What is the perimeter of the triangle?
