Answer:
x = 3
y = -2
Step-by-step explanation:
x + 2y + 1 = 0
2x - 3y - 12 = 0
Multiply first equation by -2.
-2x + -4y + -2 = 0
2x - 3y - 12 = 0
Add equations.
0x + -7y - 14 = 0
Solve for y.
-7y = 14
y =-2
Put y as -2 in the first equation and solve for x.
x+2(-2)+1=0
x + -4 + 1 = 0
x = 0 + 4 - 1
x = 3
Answer:
[tex]\boxed{x = 3, y = -2}[/tex]
Step-by-step explanation:
[tex]x+2y +1 = 0[/tex]
=> [tex]x+2y = -1[/tex] -------------------(1)
[tex]2x-3y-12 = 0[/tex]
=> [tex]2x-3y = 12[/tex] -------------------(2)
Multiplying (1) by 2
=> [tex]2(x+2y) = 2(-1)[/tex]
=> [tex]2x+4y = -2[/tex] ------------------(3)
Subtracting (3) from (2)
=> [tex]2x-3y+2x-4y = 12+2[/tex]
=> -3y-4y = 14
=> -7y = 14
Dividing both sides by -7
=> y = -2
Now, Put y = -2 in Eq (1)
=> x+2(-2)+1 = 0
=> x -4+1 = 0
=> x - 3= 0
Adding 1 to both sides
=> x = 3
If $6a^2 + 5a + 4 = 3,$ then what is the smallest possible value of $2a + 1$?
Answer: 0
Step-by-step explanation:
The given equation: [tex]6a^2+5a+4=3[/tex]
Subtract 3 from both the sides, we get
[tex]6a^2+5a+1=0[/tex]
Now , we can split 5a as 2a+3a and [tex]2a\times 3a = 6a^2[/tex]
So, [tex]6a^2+5a+1=0\Rightarrow\ 6a^2+2a+3a+1=0[/tex]
[tex]\Rightarrow\ 2a(3a+1)+(3a+1)=0\\\\\Rightarrow\ (3a+1)(2a+1)=0\\\\\Rightarrow\ (3a+1)=0\text{ or }(2a+1)=0\\\\\Rightarrow\ a=-\dfrac{1}{3}\text{ or }a=-\dfrac{1}{2}[/tex]
At [tex]a=-\dfrac{1}{3}[/tex]
[tex]2a+1=2(-\dfrac{1}{3})+1=-\dfrac{2}{3}+1=\dfrac{-2+3}{3}=\dfrac{1}3{}[/tex]
At [tex]a=-\dfrac{1}{2}[/tex]
[tex]2a+1=2(-\dfrac{1}{2})+1=-1+1=0[/tex]
Since, [tex]0< \dfrac{1}{3}[/tex]
Hence, the possible value of 2a+1 is 0.
Need help, please!! Don't anwser if you don't know it!!!!!!
Answer:
C
Step-by-step explanation:
On the horizontal axis, as the discount (%) increases by 1(%), on the vertical axis; the sales increase (%) increases by 3(%).
When the discount is 10%, the sales increase is 32%.
When the discount is 20%, the sales increase is 62%.
20 - 10 = 10
10 × 3 = 30
32 + 30 = 62 (correct)
Un estanque tiene 13/2 litros de leche y se le agregan 87/10. ¿Cuánta leche quedó en el estanque? ¿Sí en el estanque caben 65/4 litros, cuántos litros más se pueden agregar?
If f(x) = 2x2 - 5 and g(x) = x2 - 4x - 8, find (f - g)(x).
O A. (f- g)(x) = x2 - 4x - 3
O B. (f- g)(x) = x2 + 4x + 3
O C. (f- g)(x) = 3x2 - 4x - 13
O D. (f - g)(x) = -x2 - 13
The value of (f - g)(x) is x² + 4x + 3 if f(x) = 2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
f(x) = 2x² - 5
g(x) = x² - 4x - 8
(f - g)(x) = f(x) - g(x)
= (2x² - 5) - (x² - 4x - 8)
= 2x² - 5 - x² + 4x + 8
= x² + 4x + 3
(f - g)(x) = x² + 4x + 3
Thus, the value of (f - g)(x) is x² + 4x + 3 if f(x) = 2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.
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Determine the settlement set of the following trigonometric equations! cos (x - 1/3π) = cos 1/2π, 0 ≤ x ≤ 2π
cos (x - π/3) = cos (π/2)
Then we need x - π/3 = π/2
Solving the equation:
x - π/3 = π/2
x = π/2 + π/3
x = 5π/6
Every day, Jason runs for 34 minutes and lifts weights for 49 minutes. How many minutes will Jason spend working out in 8 days?
Answer:
664 minutes
Step-by-step explanation:
34 + 49 = 83
83 minutes a day
83 x 8 = 664
Answer:223
Step-by-step explanation:
Represent the expression
(4 x 1,000) + (3 x 100) + (6 x
1/100) + (7x1/1000)
as a decimal number.
Work Shown:
4*1000 = 4000 = 4 thousand
3*100 = 300 = 3 hundred
6 * (1/100) = 0.06 = 6 hundredths
7 * (1/1000) = 0.007 = 7 thousandths
add up the results
4000 + 300 + 0.06 + 0.007 = 4300.067
The expression (4 x 1,000) + (3 x 100) + (6 x 1 / 100) + (7 x 1 / 1000) in simplified as the decimal number 4,300.067.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ (4 x 1,000) + (3 x 100) + (6 x 1 / 100) + (7 x 1 / 1000)
Simplify the expression, then we have
⇒ 4,000 + 300 + 0.06 + 0.007
⇒ 4,300.067
The expression (4 x 1,000) + (3 x 100) + (6 x 1 / 100) + (7 x 1 / 1000) in simplified as the decimal number 4,300.067.
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The cost of a cell phone bill (C) increases when the number of text messages (T) increases. Write the correct equation for this scenario, and solve for the cost when the number of texts is 4.
Answer:
[tex]c = \frac{2}{5} t[/tex], if the number of texts is 4, then the cost is $1.60.
Step-by-step explanation:
If 2 texts costs $5, then each text costs $[tex]\frac{2}{5}[/tex].
So, we can setup the equation to [tex]c = \frac{2}{5} t[/tex].
If the number of texts is 4, we can substitute that into our equation.
[tex]c = \frac{2}{5} \cdot 4[/tex]
[tex]c = \frac{8}{5}[/tex]
[tex]c = 1.60[/tex]
Hope this helped!
Find m∠MON pls______
Answer:
57°
Step-by-step explanation:
∠LOM and ∠MON are complementary angles, so they add up to 90.
This means that:
3x-15 + 5x-23 = 90 =>
8x - 38 = 90 =>
x = 128/8 = 16
So m∠MON = 5*16 - 23 = 57°
Answer:
Step-by-step explanation:
(3x-15)=90
find x
x=35
input it into the equation
42+23 =m<mon
x=45 degrees
The co ordinates of the point where lines ax = by and ay=6x intersects are
Answer: (0, 0)
Step-by-step explanation:
ax = by ay = 6x
[tex]\dfrac{ax}{b}=y\qquad \quad y=\dfrac{6x}{a}[/tex]
Use substitution:
[tex]\dfrac{ax}{b}=\dfrac{6x}{a}\\\\\\\text{Cross Multiply:}\\a^2x=6bx\\\\\\\text{Solve for x:}\\a^2x-6bx=0\\x(a^2-6b)=0\\x=\dfrac{0}{a^2-6b}\\\large\boxed{x=0}[/tex]
Substitute x = 0 to solve for y:
[tex]\dfrac{ax}{b}=y \\\\\dfrac{a(0)}{b}=y\\\\\large\boxed{0=y}[/tex]
Please i need help pic included
Answer:
They using an Algebra calculator on your chromebook :)
Answer:
Slope: -3
y-intercept: 5
x | y
0 | 5
5/3 | 0
GEOMETRY
1.) find the value of z and show work
a) Explain the difference in how an inscribed angle and central angle are draw
b) Explain the difference in how their measures compare to the subtended arc.
Answer:
z = 8.5
Step-by-step explanation:
Let O be the center of the circle, and A, B, C are three points on the circle.
Draw OA and OC are shown in the figure. To make the central angle.
In the figure the measure of arc AC is 118 degrees. measure of central angle and subtrahend arc is same. So, central angle is
[tex]\angle AOC=118^{\circ}[/tex]
Subtended angle on arc AC is
[tex]\angle ABC=(6z+8)^{\circ}[/tex]
According to central angle theorem of circle, central angle is twice of angle subtended by the arc.
[tex]\angle AOC=2\times \angle ABC[/tex]
[tex]118^{\circ}=2\times (6z+8)^{\circ}[/tex]
[tex]118=12z+16[/tex]
[tex]118-16=12z[/tex]
[tex]102=12z[/tex]
[tex]\dfrac{102}{12}=z[/tex]
[tex]8.5=z[/tex]
Therefore, the value of z is 8.5.
Help me with this please I have no idea what to do. It says solve for a if the line through the two given points has the given slope a, 3) and (-3, - 1), m = -2
Answer:
a=-5
Step-by-step explanation:
When you do this every time the slope will go down 2 and over 1 which is rise over run or slope. You can see the y coordinates go down 4 points and every time is should go down 2 so you will know that it would have gone down 2 times so a+2 should equal -3 so if we subtract 2 from both sides we would get a=-5 and that is our answer.
Answer:
a = - 5
Step-by-step explanation:
Calculate the slope m using the slope formula and equate to - 2
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (a, 3)
m = [tex]\frac{3+1}{a+3}[/tex] = [tex]\frac{4}{a+3}[/tex] = - 2 ( multiply both sides by a + 3 )
- 2(a + 3) = 4 ( divide both sides by - 2 )
a + 3 = - 2 ( subtract 3 from both sides )
a = - 5
A teacher is grading exit tickets on the train. It takes
him 42.5 seconds to grade each exit ticket, and he will
arrive at his destination in 5 minutes. The teacher knows
he will need to save 30 seconds to pack up his materials.
What is the maximum number of exit tickets that he can
grade?
A) 8
B) 7
C) 6
D) 5
Answer:
6 papers
Step-by-step explanation:
5 minutes = 5 * 60 = 300 seconds
He needs to save 30 seconds
300 - 30 = 270 seconds
270 seconds / 42.5 seconds per paper
6.352941176 papers
Rounding down since he want to completely grade the paper
6 papers
What is the margin of error for 95% confidence for a sample of size 250 where p = 0.45?
A. 0.0541
B. 0.0775
C. 0.0706
D. 0.0617
Answer:
0.0617
Step-by-step explanation:
so the formula is 1.96[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
P is the proportion (.45) and n is the sample size (250). Inserting these into the problem, we get 1.96[tex]\sqrt{\frac{.45(1-.45)}{250} }[/tex]. Solving this out, you should solve the inside of the square root to get .00099. Take the square root of this, and multiply by 1.96 to get your answer!
This method applies to any problems with the same basic format. Good luck!
which of the following is the range of the function based on the input-output table?
Answer:
Range { 1000,1100,1200,1300,1400,1500,1600}
Step-by-step explanation:
The range of the function is the output, so it would be the values of the pay per month
Range { 1000,1100,1200,1300,1400,1500,1600}
Answer:c
Step-by-step explanation:
Usando uma régua informe as medidas de um dos seus cômodos ( banheiro) abaixo:
COMPRIMENTO: 2,30 METROS LARGURA: 1,46 METROS
Determine a área desse cômodo
Temos ai um retangulo. Para usa area, basta multiplicar a medidas - que no caso sao 2,3m e 1,46m
Area Comodo = 2,3 x 1,46
Area Comodo = 3,358m²Which set of ordered pairs represents a function?
{(-3,4), (-7,2), (-7,-4),(-9, -5)}
{(-2,4), (0,5),(-9,9),(-9,7)}
{(-4,-6), (-7, -5),(-4,-7), (1,1)}
{(5,-2), (-8,-6),(4, -2), (-6,3)}
Answer:
The correct answer is D.
Step-by-step explanation:
A function is when an input value has only one output value.
It cannot be A, because -7 produces both 2 and -4.
It cannot be B, because -9 produces both 9 and 7.
It cannot be C, because -4 produces both -6 and -7.
Therefore, it has to be D.
What is an equivalent equation for 3 x = 12 minus 4 y when solved for x? X = 4 minus four-thirds y x = 4 + four-thirds y x = negative 4 + four-thirds y x = negative 4 minus four-thirds y
Answer:
[tex]x = 4 - \frac{4}{3}y[/tex]
Step-by-step explanation:
If we have the equation [tex]3x = 12-4y[/tex], we can simplify this equation down.
Divide both sides by 3:
[tex]x = 4 - \frac{4}{3}y[/tex] .
Hope this helped!
Answer:
X = 4 minus four-thirds y
Step-by-step explanation:
Well to solve for x we single it out.
3x = 12 - 4y
Divide 3 by everything,
x = 4 - 4/3y
Thus,
X = 4 minus four-thirds y.
I do hope this helps :)
Theo made sails for a Model boat he cut along the diagonal of a rectangular piece of cloth to make two sales as shown below what was the area of the square feet of one to
Answer:
You need to give more information.
Step-by-step explanation:
URGENT!!! Please help me with this question!!!!!! I will not accept nonsense answers!
Answer:
B
Step-by-step explanation:
The inscribed angle's arc measures 36°, and central angle's arc measures 72°.
Answer:
the answer is B
Step-by-step explanation:
If f(x) and g(x) are quadratic functions but (f + g)(x) produces the graph below, which statement must be tru
Answer:
The leading coefficients of f(x) and g(x) are Opposites.Option A is the correct option.
Step-by-step explanation:
As the graph of ( f + g ) ( x ) is a line. So, ( f + g ) ( x ) is linear which means x² of f ( x ) and x² of g ( x ) get cancelled on adding . They must be equal and opposite in sign.
So, Option A is correct.
Hope this helps..
Best regards!!
Which option is it??????
Answer:
both the equation and it's inverse are functions
a student answered 44 questions correctly on a test with 55 questions. what percent of the test was answered correctly?
(plz tell me how to figure it out)
Answer:
80%
Step-by-step explanation:
The basic idea of this problem is to convert [tex]\frac{44}{55}[/tex] into a percentage. [tex]\frac{44}{55}[/tex] can be simplified to [tex]\frac{4}{5}[/tex] which is also 80%.
Answer:
Step-by-step explanation:
44 out of 55
divide :44/55=0.8
to convert it to decimal you multiply by 100 and put percentage next to it
0.8*100=80
%80
How to do this question plz
Answer: x=10
Step-by-step explanation:
We can use the pythagorean theorem here: a^2 + b^2 = c^2, where c is the hypotenuse.
The values for c and one of the legs are already given, so we can plug them into the equation to find the length of the other leg x:
(square root of 200)^2 + x^2 = (square root of 300)^2
200 + x^2 = 300
x^2 = 100
x = 10
Answer:
Step-by-step explanation
square root 300 square - square root 200 square = x square
300 - 200 = x square
100 = x square
square root 100 = x
10= x
Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
Answer:
1/3
Step-by-step explanation:
So there are 12 natural numbers in total: (113 - 102) + 1
Then there are the prime numbers: 103, 107, 109, and 113
so there are 4/12 prime numbers or 1/3
Answer:
1/3
Step-by-step explanation:
We can list all the numbers from 102 to 113:
To check if each number is prime, we simply have to check divisibility by 2, 3, 5, and 7 — if any of these numbers are not divisible by those, it will have no factors lower than its square root, and will therefore be prime.
102 - composite, multiple of 2
103 - prime
104 - composite, multiple of 2
105 - composite, multiple of 5
106 - composite, multiple of 2
107 - prime
108 - composite, multiple of 2
109 - prime
110 - composite, multiple of 2
111 - composite, multiple of 3
112 - composite, multiple of
113 - prime
4/12 or 1/3 of the numbers in this list are prime.
The speed at which a ball bits the ground is proportional to the
height to which the ball rebounds. If the ball hits the ground at
a speed of 20 miles per hour and rebounds to a height of 10 feet,
then how fast must it be traveling (in miles per hour) to rebound
to a height of 15 feet?
Answer:
30 mph
Step-by-step explanation:
let s represent speed and h represent rebound.
Given that s is proportional to h then the equation relating them is
s = kh ← k is the constant of proportion
To find k use the condition s = 20, h = 10, then
20 = 10k ( divide both sides by 10 )
2 = k
s = 2h ← equation of proportionality
When h = 15 , then
s = 2 × 15 = 30 mph
Fill out the following table. Do you see a pattern? Do you think this will always be true? Why or why not?
*Trolling answers will be flagged & reported, thank you.*
Answer:
Please see table completed attached
Yes, there are several patterns, since these two trigonometric functions are periodic with same periodicity, and also satisfy the Pythagorean identity for the same angle.
Step-by-step explanation:
Notice that we are asked about a table of trigonometric functions for the so called "special angles" which render values associated with half of the square root of a counting number between 0 and 4:
[tex]\frac{\sqrt{0} }{2}=0 \\\frac{\sqrt{1} }{2}=\frac{1}{2} \\\frac{\sqrt{2} }{2}\\ \frac{\sqrt{3} }{2}\\ \frac{\sqrt{4} }{2}=\frac{2}{2} =1[/tex]
These two trigonometric functions also satisfy the Pythagorean identity for any angle [tex]\theta[/tex] in the unit circle, so the equality to one will always be true:
[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]
They are also periodic functions of period [tex]2\,\pi[/tex], so their resulting values will be repeated with that periodicity.
Use technology to find the line of best fit for the following data. (−17,8), (−14,7), (−11,6), (−12,4), (−10,1), (−7,3), (−3,2), (−3,0), (−2,−4), (0,−2), (2,−3), (6,−5), (4,−6) When the equation of the line is in the form y=mx+b, what is the value of b?
Answer: Intercept (b) = - 2.2567
Step-by-step explanation:
(−17,8), (−14,7), (−11,6), (−12,4), (−10,1), (−7,3), (−3,2), (−3,0), (−2,−4), (0,−2), (2,−3), (6,−5), (4,−6)
Using the online regression calculator :
ŷ = -0.60205X - 2.2567
y is the predictor variable
X - the independent variable
0.60205 = slope or gradient
- 2.2567 = intercept (b) where the line best fit cross the y-axis.
The linear regression line is made using the least-squares method. The value of b is -2.2567.
How does linear regression work?Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least-squares method.
Given the points of the data(−17,8), (−14,7), (−11,6), (−12,4), (−10,1), (−7,3), (−3,2), (−3,0), (−2,−4), (0,−2), (2,−3), (6,−5), (4,−6).
Now, Since the question states about using the technology, therefore, if we use the online regression calculator:
ŷ = -0.60205X - 2.2567
y is the predictor variable
X - the independent variable
-0.60205 is the value of m which is the slope or gradient of the regression line, while -2.2567 is the value of the intercept of the regression line.
Hence, the value of b is -2.2567.
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Alexandria is practicing her long distance running. On day 0, she can run 2 miles without stopping. She wants to add 1/4 mile to her run each day. What is the slope for this linear relationship?
Answer:
1/4
Step-by-step explanation:
The slope of a graph is always the rate of change for every value of x, in this case, days. Since she is adding 1/4 of a mile to her run each day, this means that the slope of this linear relationship is 1/4.
She increases a full mile in 4 days, just a little note.