Directions; Write a system of equations for each of the descriptions below, and then solve the systems. Hint: you can graph the equations to find the solutions.
16. Three times one number is equal to two times the larger one and their difference is 1. What are the numbers?
17. Joseph has 30 coins and they are all either dimes or nickels. The total $2.15. How many dimes does he have?
18. A golfer completed 18 holes with a total of 79 strokes. On each hole he met par, which was either four or five each time. How many holes were played in four strokes?
19. There are two numbers. The difference between them equals six, and one of the numbers is three times the other number. There are two pairs of numbers that satisfy these descriptions, What are they?
20. There is a number that is three-fifths the total of the other number. When four is added to one of the numbers their sum will be equal to the other number. There are two pairs of numbers that satisfy these descriptions. What are they?
Answers
Answer: Here are the answers. I walked you through 16 in my answer.
16. 3x=2y
1 =y-x
x=2 and y=3
17. $2.15=.10d+.05n
d=30-n
There are 17 nickels and 13 dimes
18. 18=4x+5y (since that's the total amount of holes and each par is either 4 or 5 strokes each)
4x=79-5y (since there are 79 total strokes and each was either 4 or 5)
No solution
Step-by-step explanation: For each problem, you have to write down the information you know, then define variables for the unknown. For 16, for example, they tell you that one number, which I have chosen to call x, is equal to two times the larger number, which I have chosen to name y. So, you'd have an equation that equals x. It also tells you that you need three times x, and two times y, which can be rewritten as 3x and 2y. In other words, 3x=2y. That said, you can move on to the next equation. Since you know the difference is 1, in other words, y-x=1, or y=x+1 ( I isolated y by adding x to both sides), you can put that into your equation as well. From there, I used the substitution method to solve.
3x=2y
so 3x=2(x+1)
y=x+1
3x=2(x+1) --- orig equation
3x=2x+2 --- distributive property (Multiplied x+1 by 2)
x=2 ---- subtracted 2x from both sides
**Now, to find y, you can substitute x into either equation. Since I know y=x+1 where x=2, I know that y must be 3. To check this, you can graph on Desmos. The lines should intersect at (2,3).
For 18, the lines are parallel so they never intersect. There is no solution.
answer:
16. 3x = 2y, 1 = y - x → 2, 3
17. 2.15 = 0.10d + 0.05n, d = 30 - n → 13 dimes and 17 nickels
18. 18 = 4a + 5b = 79, b = 79 - 72 = 7 → 11 holes
19. 3x - x = 6, y = 3x → Pair 1: 3 and 9, Pair 2: 9 and 3
20. a = 3/5b, 2/5b = 4 → Pair 1: 6 and 10, Pair 2: 10 and 6
i hope this helps!! ♡
Related Questions
Please help as I’m confused
Try and do 2, as I’m not bothered if you guys can’t do all 3 :)
Answers
Answer:
the formula is base x height / 2
Step-by-step explanation:
try and use this formula to help you:)
PLs, help me - an international company has 18,700 employees in one country. If this represents 32.8% of the company's employees, how many employees does it have in total? Round your answer to the nearest whole number.
Answers
Answer:
33.6% of X = 26800
X = 26800 / 33.6%
= 26800 / 0.336
= 79762
Note the answer is rounded
Step-by-step explanation:
33.6% of X = 26800
X = 26800 / 33.6%
= 26800 / 0.336
= 79762
Note the answer is rounded
help please
3/11 × 4/9 =
Answers
Answer:
4/33
Step-by-step explanation:
Multiply 3x4 across which equals 12
Multiply 11x9 across which equals 99
Simplify to equal 4/33
Hope this helps!! :)
Answer:
Exact Form:
433
Decimal Form:
0.¯¯12¯¯
Step-by-step explanation:
Two numbers have a difference of 3. The sum of their squares is 89. Find the number
Answers
Answer:
The numbers are 8 and 5
Step-by-step explanation:
The square of 8 is 64 and the square of 5 is 25. 25 plus 64 equals 89.
Please help I’m confused!
Answers
Answer:
2nd option; [tex]c=9-a+b[/tex]
Step-by-step explanation:
The first thing you need to do, is rewrite the equation without the square root.So for instance [tex]\sqrt{16}=4[/tex] and [tex]16=(4)^2[/tex] therefore [tex]a-b+c=(3)^2[/tex] Then [tex]a-b+c=9[/tex] Now we take away ' [tex]a[/tex] ' on both sides and add ' [tex]b[/tex] ' on both sidesSo [tex]a-(a)-b+(b)+c=9-(a)+(b)[/tex] Which gives us [tex]0+0+c=9-a+b[/tex] which is simply [tex]c=9-a+b[/tex]Hope this helps
X^3-4x^2+3x+2=0 find all the real values of x
Answers
Step-by-step explanation:
The factor of the polynomial is (x-2)
We know that dividing a third degree polynomial by a first degree factor will yield a quadratic of the form ax²+bx+c and possibly a remainder r,except that in this case r=0 since x-2 is a factor
We therefore equate
x³-4x²+3x+2=(x-2)(ax²+bx+c)+r
x³-4x²+3x+2=ax³+bx²+cx-2ax²-2bx-2c+r
We group terms on the RHS
x³-4x²+3x+2=ax³+x²(b-2a)+x(c-2b)-2c+r
By equating the terms on both sides,
ax³=x³,a=1
Next,
b-2a=-4
b-2(1)=-4
b-2=-4
b=-4+2
b=-2
Next,
c-2b=3
c-2(-2)=3
c+4=3
c=-1
Now we piece together our quotient quadratic using a=1,b=-2,c=-1 to obtain x²-2x-1
We now find the zeros of x²-2x-1
which are 1+√2 and 1-√2
The values of x are therefore 2,1+√2, and 1-√2
Note that I used this method in lieu of the famous polynomial division approach to teach someone also ;)
Answer:
2, 1 +/- sqrt2
or 2, 2.414, -0.414 (correct to the nearest thousandth).
Step-by-step explanation:
Let x = 2: then
f(2) = 8 - 16 + 6 + 2 = 0
So x = 2 is one of the zeros.
So one factor of the function is x-2.
If we divide the function by (x - 2) we get:
x-2)X^3-4x^2+3x+2(x^2-2x-1
x^3- 2x^2
-2x^2+3x
-2x^2+4x
-x+2
-x+2
.......
So x^2-2x-1= 0
x = [-(-2 +/- sqrt(4 - 4*-1)] / 2
x = (2 +/- sqrt8) / 2
= 1 +/-sqrt8/2
= 1 +/- sqrt2
What is sieve of eratosthenes? (Only give paragraph, no steps)
Answers
Step-by-step explanation:
In Mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2. The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that is equal to that prime.This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.
−p^3 −5p−9
Select all coefficients.
Answers
Answer:
k
Step-by-step explanation:
k
Analyzing Intersections of Lines and Planes
Use the given diagram to answer the question.
Which line is the intersection of two of the planes
shown?
х
V
w
Which line intersects one of the planes shown?
B
z
Which line has points on three of the planes shown?
Done
DO
Answers
Answer:
x z y
Step-by-step explanation:
i took the assignment
Answer:
X , Z , Y
Step-by-step explanation:
eight packs of pencils and two packs of crayons cost $30.if 7 packs of crayons cost $21, what is the ratio of the rice of the pack of crayons to the price of the packs fo pencils?
Answers
8p + 2c = 30
7c = 21
c = $3
One pack of crayons costs $3.00
Plug 3 into the top equation for the value of c and evaluate for p.
8p + 6= 30
- 6= -6
8p = 24
p = $3
One pack of pencils costs $3.00
The ratio of the price of the pack of crayons to the pack of pencils is 1:1.
chris can type 490 words in 7 minutes how many word can he type per minute
Answers
Answer:
i think 70 words per minute
Step-by-step explanation:
Archaeologists are studying a shipwreck on the
ocean floor. The wreck site is roughly shaped like a
parallelogram. The archaeologists make a map of the
site in the coordinate plane. Each unit on the map
represents 1 m. According to the map, what is the
area of the wreck site?
Answers
The area of the wreck site is 85 square m if Archaeologists are studying a shipwreck on the ocean floor.
What is parallelogram?
In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
Archaeologists are studying a shipwreck on the ocean floor. The wreck site is roughly shaped like a parallelogram.
From the table:
The vertex of the P is (9, 2)
The vertex of the Q is (-8, 2)
The vertex of the R is (-7, 7)
The vertex of the S is unknown
From the distance formula we can find the distance between points P and Q:
The distance formula can be defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\rm PQ = \sqrt{(-8-(-9))^2+(2-2)^2}[/tex]
PQ = 17 units
[tex]\rm QR = \sqrt{(-7-(-8))^2+(7-2)^2}[/tex]
QR = 5.09 ≈ 5 units
The area of the wreck site = 17x5
The area of the wreck site = 85 square m
Thus, the area of the wreck site is 85 square m if Archaeologists are studying a shipwreck on the ocean floor.
Learn more about the parallelogram here:
brainly.com/question/1563728
#SPJ2
which rational number is negative?
Answers
Answer:
-1/6, 2/-7, 30/11, 13/-19 and -15/23 are negative rationals
If X = 25, what does X equal?
Answers
Answer: it should be 25!!
Step-by-step explanation:
∠1 and ∠2 are a linear pair. If the m∠2 = 33°, find the m∠1.
Answers
Answer:
157 degrees
Step-by-step explanation:
A linear pair is 180 degrees.
180-33 = 157
Answer:
m∠1 = 147°
Step-by-step explanation:
Since both angles are a linear pair, they both add up to 180°. This means that if m∠2 = 33°, then m∠1 would be 180°-33° which is 147°.
180°-33°=147°
what is the equation of the line in slop-intercept form HELPP PLZZZZZZZZZZ
Answers
Answer:
y = 3/5x + 3
Step-by-step explanation:
(y2-y1)/(x2-x1) = slope
pick 2 points (0,3) and (-5,0)
(0-3)/(-5-0) = -3/-5 = 3/5
y = 3/5x + b
3 = 3/5(0) + b, b = 3
equation y = 3/5x + 3
what is the coefficient in the expression 10x +8?
Answers
Answer: It is 10
Step-by-step explanation:
The coefficient is: 10x
Explanation:
The coefficient is the number that comes before the variable
84 + 46 + 94 - 66 + 75 + 72 - 58 + 21 =equal what??
Answers
- 1/2(6p+16)=7 solve for p
Answers
Answer:
p = -5
Step-by-step explanation:
-1/2* 6 = -3p
-1/2*16 = -8
-3p-8 = 7
7+8 = 15
-3p=15
15/-3 = -5
Step-by-step explanation:
p
2
+6p−16
=p
2
+8p−2p−16
=p(p+8)−2(p+8)
=(p+8)(p−2)
Plzzzzz help asappppppp
Answers
The alternate interior angles theorem states that, the alternate interior angles are congruent when the transversal intersects two parallel lines. Hence, it is proved. Alternate interior angles can be calculated by using properties of the parallel lines.
Consider the triangle.
The measures of the angles of the triangle are 32°, 53°, 95°. Based on the side lengths, what are the measures of each angle?
A)mAngleA = 95°, mAngleB = 53°, mAngleC = 32°
B)mAngleA = 32°, mAngleB = 53°, mAngleC = 95°
C)mAngleA = 43°, mAngleB = 32°, mAngleC = 95°
D)mAngleA = 53°, mAngleB = 95°, mAngleC = 32°
(Make sure to explain how you solved this problem and include things to remember when measuring angles like this. Thank you!)
Answers
Answer:
b
Step-by-step explanation:
edge 2020
Which is the better buy?
141-fuid-ource container of window clearer for
$7.05
6-pint container of window dieener for $3.84
Answers
Answer:
6-pint container of window clearer for $3.84 is a better buy
Step-by-step explanation:
141-fuid-ounce container of window clearer for $7.05
7.05 : 141 = 0.05
check your work: 0.05 x 141 = 7.05
so for the first offer you will be paying $0.05 per ounce of window clearer.
6-pint container of window clearer for $3.84
1 pint = 16 ounces
6 pints = 96 ounces
3.84 : 96 = 0.04
check your work: 0.04 x 96 = 3.84
for the second offer you will be paying $0.04 per ounce of window clearer. 6-pint container of window clearer for $3.84 is a better buy because you will be paying less for each ounce of window clearer.
Answer:
the 6-pint container would be cheaper...hope this helps :)
Step-by-step explanation:
DEPERATE PLZ HELP IM ON A TIMED TEST
write the slope intercept form of the line that passes through the two points given (-1,-8) (2,10)
Answers
Answer:
y = 6x - 2
Step-by-step explanation:
Let the equation of the line be y = mx + c
m = (10 - (-8))/(2 - (-1)) = 6
sub (2, 10):
10 = 6(2) + c
c = -2
therefore, the equation of the line is y = 6x - 2
This is a question on coordinate geometry/graphs. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
60 is 25% of what number
12 is 24% of what number
Answers
60 is 25% of 240 and 12 is 24% of 50
25% is a fourth of 100%. So you want to find what number 60 is a fourth of. Multiply 60 by 4.
60x4=240
24% is 4.17th of 100%. Multiply 12 by 4.17
12x4.17=50
The length of a rectangle is twice the width if the perimeter of the rectangle 60 units find the area of the rectangle
Answers
Answer:
200
Step-by-step explanation:
Length = 2w
2w + 2l = 60
substitute l out with 2w
2w + 2(2w) = 60
2w + 4w = 60
w = 10
l = 20
Area = w • l
= 10 • 20
= 200
The ordered pairs in the table below define a function.
X Y
-2 9
0 5
2 1
4 -3
Select ALL of the equations that describe a function that is less steep than the function defined in the table.
⭕️ Y= 5
⭕️ Y = -3x
⭕️ Y = -x+6
⭕️ Y= -6x+3
⭕️ Y = -1/2x-4
Answers
Answer:
The 1st, the 4th, and the 5th ones are the answer :)
Step-by-step explanation:
Brainless to right answer...
Answers
Answer:
Ha, you said "Brainless" instead of *Brainliest*
Lol, here i am, Miss Brainless has arrived!
Step-by-step explanation:
Sry, dude, i just need points...
Answer:
The answer to this equation is 4 7/10, or 4.7.
Step-by-step explanation:
Hopefully this helps you!
6 1 message Noah's dog eats 8 ounces of dog food each day. Noah bought a 28-pound bag of dog food. How many 8-ounce servings are in a 28-pound bag of dog food?
Answers
Explanation: 28 pounds = 448 ounces
448/8=56
A scientist is studying the effects of cell phone use on headache rate. She identifies 30 people who use cell phones and 30 who do not. Each of the 60 people is given a questionnaire designed to determine headache frequency. None of the 60 people who participated in the study knew they were part of a study. Which statement is true?
Answers
Answer:
C this is a double blind study.
Step-by-step explanation:
Both groups in the experiment are blind (don't know they are in an experiment). If this answer is incorrect then its A.
Answer:
observational study
Step-by-step explanation:
the experimenters are not blind to their own tests.
Marcus said the ratio of the number of hours he spent doing homework to playing basketball was 2:3. Which statement describes this ratio?
A.
Marcus does homework or plays basketball for 2:30 hours.
B.
There are 2 to 3 hours each night that Marcus does homework or plays basketball.
C.
For every 2 hours Marcus does homework, he plays basketball for 3 hours.
D.
For every 3 hours Marcus does homework, he plays basketball for 2 hours.
Answers
Answer:
C
Step-by-step explanation: