Answers
Answer:
a. (7, 27) Polly was incorrect.
b. (3, 1) Polly was correct.
Step-by-step explanation:
a.
y = 4x - 1
2x - y = -13
We can solve this by substitution. Our first equation gives us y. Plug that into our second equation for each instance of y.
2x - y = -13
2x - (4x - 1) = -13
First distribute the negative sign across the parentheses.
2x - 4x + 1 = -13
Combine like terms.
-2x + 1 = -13
-2x = -14
Divide both sides by -2.
x = 7
Now that we know x, plug its value into one of our original equations.
y = 4x - 1
y = 4(7) - 1
Solve.
y = 28 - 1
y = 27
Our solution is (7, 27).
Let's check our answer by plugging both values into one of our original equations.
2x - y = -13
2(7) - 27 = -13
Solve.
14 - 27 = -13
-13 = -13
Your solution is correct.
Polly's solution was (-2, -9), which is incorrect.
b.
3x + 6y = 15
-2x + 3y = -3
Let's solve this by elimination. To solve by elimination means to eliminate a variable from the equation.
We have 3x & -2x and 6y & 3y. Notice that 6 and 3 can be simplified easily. To eliminate y, we want to multiply each factor of the second equation by -2.
-2x + 3y = -3
-2(-2x + 3y = -3)
4x - 6y = 6
Write the equations together.
3x + 6y = 15
4x - 6y = 6
Now we can see that the y variable will cancel out.
Apply the elimination method.
3x + 6y = 15
4x - 6y = 6
________
7x = 21
Divide both sides by 7.
x = 3
Now that we know x, plug its value into one of our original equations.
3x + 6y = 15
3(3) + 6y = 15
Solve.
9 + 6y = 15
6y = 15 - 9
6y = 6
y = 1
Our solution is (3, 1).
Let's check our answer by plugging both values into one of our original equations.
-2x + 3y = -3
-2(3) + 3(1) = -3
Solve.
-6 + 3 = -3
-3 = -3
Your solution is correct.
Polly's solution was (3, 1), so she was correct.
Hope this helps!
Related Questions
The value of a piece of land in a town is increasing every year . Its value, in dollars, t years after 1970 and until 2001 can be modeled by the function 31, 000(1.001) ^ t . What is the domain of the function ?
A. All whole numbers greater than or equal to 1971 and less than or equal to 2001 .
B. All real numbers greater than or equal to 1971 and less than or equal to 2001 .
C . All non - negative real numbers less than or equal to 31.
D. All whole numbers less than or equal to 31
Answers
Answer:
D. All whole numbers less than or equal to 31
Step-by-step explanation:
The x value in this situation is the number of years after 1970 and until 2001.
This means that the domain will be the number of years after 1970 and until 2001.
Since the situation calculates the value of land in years after 1970, the domain will start at 0. Since it is until 2001, which is 31 years after 1970, the domain will go up to 31.
So, the domain will include all whole numbers less than or equal to 31.
The correct answer is D. All whole numbers less than or equal to 31
The domain of the function is a real number from 1971 to 2001. Then the correct option is B.
What is an exponent?Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
The value of a piece of land in a town is increasing every year.
Its value, in dollars, in t years after 1970 and until 2001 can be modeled by the function
[tex]\rm y = 31, 000(1.001) ^ t[/tex]
Then the domain of the function will be
All real numbers are greater than or equal to 1971 and less than or equal to 2001.
More about the exponent link is given below.
https://brainly.com/question/5497425
9>x
choose all the answer that apply
x=2
x=5
x=9
Answers
Answer:
X = 9
I could not find any of the others close to it,, sorry if I’m wrong
Step-by-step explanation:
Help Will give crown
Answers
the answer is actually 4/6 pls give branliest and thanks
Answer:
28 gallons
Step-by-step explanation:
50% full
50% + 7 gallons = 75%
50% + 25% = 75%
25% = 7 gallons
[tex]\frac{25}{100}= \frac{7}{y}[/tex]
25 × y = 100 × 7
25y = 700
25y ÷ 25 = 700 ÷ 25
y = 28
Find the perimeter of the figure.
Answers
Answer:
56 meters or 56 m
Step-by-step explanation:
We first want to find the small square at the top it has 3 sides of the same length so it must be a square
5+5+5 is = to 15.
Then to find the bottom rectangle we so 7+7+11+11+5 and we get 14+22+5 and then 36+5 to end up getting 41
Then 41+15=56
PLS ACTUALLY HELP ME , I WILL MARK BRAINLIEST
Answers
Answer: 15/8
Step-by-step explanation:
Which table is a proportional relationship?
Answers
Answer:
The blue one
4, 2
6, 3
12, 6
Step-by-step explanation:
a) The pass marks in an examination is 40%. Rajani secured 295 marks and
failed by 25 marks. Find the full marks of the examination
Answers
Answer:
320 marks = 40 percent therefore the total marks for the exam= 320+320+160=800 marks.
Step-by-step explanation:
let the full marks be " x "
Rajani has scored 295 marks , if she would had scored 25 more marks then she would had passed the examination,
So, passing marks :
=》295 + 25
=》320
passing percentage ( P% ) :
=》
[tex]40 = \dfrac{passing \: \: marks}{total \: \: marks} \times 100[/tex]
=》
[tex]40 = \dfrac{320}{x} \times 100[/tex]
=》
[tex]x = \dfrac{320 \times 100}{40} [/tex]
=》
[tex]x = 8 \times 100[/tex]
=》
[tex]x = 800[/tex]
So, passing marks = 800 marks
Explain how you will evaluate 4[ 3(62+1)] - 63
Answers
Answer:
693
Step-by-step explanation:
You can simply apply BODMAS(Bracket of Division Multiplication Addition Subtraction)
Here, the brackets come first
62+1=63
63*3=189
189*4=756
756-63=693
Answer:
720
Step-by-step explanation:
First you do the things inside the parenthesis which is 62 + 1 = 63
Which gives you this -----> 4[ 3 x 63]-36
Then do the brackets (brackets are these btw "[ ]" )
After doing the brackets you should bet this 4 x 189 - 36
Then you do the multiplication -----> 756 - 36
756 - 36 = 720
Suppose you are making a sail in the shape of a right triangle for a sailboat. The length of the longest side of the sail is 65 ft. The sail is to be 63 ft high. What is the length, in feet, of the third side of the sail?
Answers
Answer:
in right angled triangle ABC
hypotenuse [h]=65ft
base[b]=xft
height[p]=63ft
by using Pythagoras law
h²=p²+b²
65²=63²+x²
x²=65²-63²
x=√256
x=16feet
so the third side of the sail is 16ft.
Base:-
√H²-P²√65²-63²√16²16ftUptown Cable, a cable TV provider, charges each customer $120 for installation, plus $25 per month for cable programming. Uptown’s competitor, Downtown Cable, charges each customer $60 for installation, plus $35 per month for cable programming. A customer who signs up with Uptown will pay the same total amount for cable TV as a customer who signs up with Downtown if each pays for installation and cable programming for how many months?
3
3
6
6
10
10
18
18
30
Answers
Answer:
B) Six Months.
Step-by-step explanation:
We can write an equation to model each situtation.
Let m be the number of months and c be its total cost.
Uptown Cable charges $120 for the initial installation fee plus $25 per month. In other words, its total cost is:
[tex]c=120+25m[/tex]
Downtown Cable charges an initial $60 fee plus $35 per month. So:
[tex]c=60+35m[/tex]
To find after how many months will the two services remain the same, we can set the two equations equal to each other and solve for m. So:
[tex]120+25m=60+35m[/tex]
Solve for m:
[tex]60=10m\Rightarrow m=6[/tex]
The two cable companies will charge the same after six months of use.
Notes:
If the customer uses the service for less than six months, then Downtown Cable is better since its initial cost is lower.
If the customer uses the service for more than six months, then Uptown Cable is better since its rate per month is lower.
A highschool science teacher has 78 students. Of those students, 35 are in the band and 32 are on a sports team. There are 16 students who are not in the band or on a sports team. One student from the 78 students will be selected at random. Let even B represent the event of selecting a student in the band, and let event s represent the event of selecting a student on a sports team
Answers
Answer: s sports team because what i was thinking is that the band has a lot of kids so there for there gonna put that kid on the sports team or if the kid likes sports or if the kid likes band.
Step-by-step explanation:
An algebraic expression that contains three terms is called?
Monomial
Binomial
Trinomial
None of these
Answers
Answer:
Step-by-step explanation:
If the expression contains 3 terms none of which can combine with any other, the the expression is a Trinomial. An example of such a thing is f(x) = x^2 + 2x + 1.
The x cannot combine with the x^2 nor with the 1. The same can be said for the x^2 and the 1.
Answer:
Trinomial
Step-by-step explanation:
I got it Correct
Can someone plz help me find the missing side using sin or cos and rounding it to the nearest tenth
Answers
Answer:
65.73
Step-by-step explanation:
use the law of sines
a/Sin A = b /Sin B
36/sin 84 = 33/sin x
sin x = (33(sin 84))/36
x = 65.73
¿vienes y entretienes es una rima consonante o asonante?
AYUDA ES URGENTE. NO RESPONDAN CON TONTERIAS SI NO REPORTO
GRACIAS :)
Answers
Answer:
La rima asonante se caracteriza porque solo coinciden los sonidos vocálicos en la última sílaba de cada verso, mientras que la rima consonante es aquella donde coinciden tanto vocales como consonantes.
Step-by-step explanation:
es sonante
Chase is trying to pick out an outfit for the first day of school. He can choose from 4
pairs of pants, 7 t-shirts, 5 sweaters or hoodies, and 2 pairs of shoes. How many
different outfits does Chase have to choose from?
Answers
Answer: 88
Step-by-step explanation:
Answer:
4 or 7
Step-by-step explanation:
chase has a long situation
Karina deposito S/. 3000 en un banco en un banco a una tasa de interes simple del 2% mensual ¿Cuánto ganara en dos años
Answers
Answer:
En dos años ganará S/. 4440.
Step-by-step explanation:
Puedes encontrar la respuesta utilizando la fórmula para calcular el valor futuro:
VF=VP*(1+(i*n))
VP= valor presente= 3000
i= tasa de interés= 0.02
n= número de periodos de tiempo= 24 meses (2 años corresponden a 24 meses)
VF=3000*(1+(0.02*24))
VF=3000*(1+0.48)
VF=3000*1.48
VF=4440
De acuerdo a esto, la respuesta es que en dos años ganará S/. 4440.
EXTREMELY URGENT!!!!! 25 points to who gets it right
in the following diagram, the length of ab is 9 units, and the length of bd is 2 units. find x, the length representing cb. give your answer to one decimal place.
Answers
20.3 units
i’m sorry if wrong, hope this helps!!
(-18, -17)
(18,-17)
(18 , 17)
(-18 , 17)
Answers
Answer:
(-18, -17) in 3rd Quadrant
(18, -17) in 4th Quadrant
(18, 17) in 1st Quadrant
(-18, 17) in 2nd Quadrant
-TheUnknownScientist
Paula packages the syrup in one pint jars. She can fit 24 jars in each box how many boxes can she completely fill with jars of syrup from 50 maple trees
Answers
Answer:
2
Step-by-step explanation:
Paula packages syrup in one pin jars
She can fit 24 jars in each box
Therefore the number of boxes she can fill with 50 jars can be calculated as follows
24+24
= 48
Hence the jars can fix 2 boxes
Please answer correctly
Answers
URS= 20º
Hope this helps!!
Which is a solution to the equation
79 - 2 - 472
g.
96
Answers
Answer:
[tex]-395[/tex]
Step-by-step explanation:
[tex]79-2= 77-472 = -395[/tex]
Graph the function. f(x)=2x^2-5
please help ill give you brainliest
Answers
f(x)=2x^2+0x-5
Find the vertex
0/4=0=x
Input x into the equation to find y or f(x)
0+0-5=f(x)
(0,-5) = Vertex
Now find a random x coordinate to input into the equation.
Let's do 4.
32+0-5=f(x)=27
It may not look like a parabola due to it being uneven.
The graph of the function that represents a vertical parabola with vertex at ( 0 , -5) has been plotted and attached with the answer.
What is a Function ?A function is a law that links two variables , a dependent and an independent variable .
The given function is
f(x) = 2x² - 5
y = a( x-h)² +k
this is an equation of a vertical parabola
(h,k) is the vertex
here ( 0 , -5) is the vertex
The graph of the function has been plotted and attached with the answer.
To know more about Function
https://brainly.com/question/12431044
#SPJ2
Can anyone help me with this math please I will give brainlist!! I used all my points for this question!!
Answers
9514 1404 393
Answer:
15.4567.0787040.7872.0Step-by-step explanation:
Locate the digit to the right of the place you're rounding to. If that digit is 5 or more, add 1 to the digit in the place you're rounding to. Drop all digits to the right of the one you're rounding to, unless it is left of the decimal point. In that case, zero any digits between the one you rounded and the decimal point. (See problem 3 for an example of this.)
If you're rounding to the ones place (nearest whole number), and that digit ends up being 0, then put a decimal point after it to indicate it is a significant digit.
The second attachment shows the names of the number places, if you need a reminder.
Mr. Huong's 4th grade set a goal of reading 30 minutes a night. They read 5 minutes on Monday night, 10 minutes on Tuesday night, and 15 minutes on Wednesday night. If they continue this pattern, on what night will they reach their goal of reading 30 minutes? O A. Saturday OB. Friday c. Sunday O D. Thursday O E. Monday
Answers
In the triangle below, with right angle
Find the degree measure of each angle in the triangle.
Answers
Answer:
90°, 62.8° and 27.2°
Step-by-step explanation:
180 = 5x + 133
47 = 5x
9.4= x
2 * 9.4 + 44 = 62.8°
3 * 9.4 - 1 = 27.2°
2/7 done! If it’s right I will put brainliest!
Answers
Answer:
The name of the marked angle is (angle BAD)
Step-by-step explanation:
How do I find the point of intersection?
Answers
Answer:
(-1 3/5, 2 3/5)
Step-by-step explanation:
Red Line:
m = 3-(-1)/-2-2 = 4/-4 = -1
b = 1
equation: y = -x + 1
Blue Line:
m = 5-1/2-(-4) = 4/6 = 2/3
find 'b':
5 = 2(2/3) + b
15/3 = 4/3 + b
b = 11/3
equation: y = 2/3x + 11/3
Find Point of Intersection:
-x + 1 = 2/3x + 11/3
multiply each side by 3 to get:
-3x + 3 = 2x + 11
-5x = 8
x = -8/5
find 'y':
y = -(-8/5) + 1
y = 8/5 + 1 = 13/5
y = 2 3/5
Please help, I will give brainliest to whoever helps!
Answers
Answer:
H
Step-by-step explanation:
I'm legit smart bro quit playing
Answer:
C
Step-by-step explanation:
x - 1 = 0
x = 1
2x + 5 = 0
2x = - 5
x = - 5/2
Option C is the correct answer
Q1) Braden has five quarters, three dimes, and four nickels in his pocket. He pulls one coin out of his pocket. What is the probability Braden pulls out a dime.
Answers
On a map,the scale shown is 1inch:5miles.If an island is 75 square inches on the map,what is the actual area of the island?
Answers
1 inch = 5 miles
1 square inch =25 square miles
25 square miles x 75 square inches = 1,875 square miles
Answer : 1,875 square miles