How many solutions does the system have?
x = -6y + 3
5x + 30y = 15
one solution
two solutions
infinitely many solutions
no solution
Answer:
infinitely many solutions
Step-by-step explanation:
we have: x+6y= 3
5x+30y=15
where a1/a2 = b1/b2 = c1/c2 (1/5 = 6/30 = 3/15)
Thus, the system has infinitely many solutions.
another approach:
convert to slope-intercept form
y= -1/6x + 1/2
y= -1/6x + 1/2
thus, the system has infinitely many solutions.
(explain: if two lines have a same slope (-1/6), they can be either parallel or coincided. But in this case, they also have a same y-intercept so they must be the latter case)
Which number sentence is true?
A. 2/3 < 2/8
B. 2/3 <6/8
C.3/3 < 3/8
D.1/8 > 1/3
Answer:
2/3 < 6/8
Step-by-step explanation:
Answer:
Its B
Step-by-step explanation:
which numbers for b would make √b irrational
mark as brilliant!
Answer:
All of the options when substituted for b will make the root of b irrational
Step-by-step explanation:
Mathematically, surds are roots of non-perfect squares and they are tagged as irrational numbers
For b to be irrational, all of the numbers given would fit. This is because all of these numbers are non-perfect squares meaning they do not have square root.
So what this mean is that these numbers when put under the root umbrella are irrational numbers as they are not perfect squares
What is 4,490.9 rounded to the nearest hundred?
Answer:4,500
Step-by-step explanation:
Answer:
yeah, it is 4,500
Step-by-step explanation:
:))))))
Write an ordered pair for 3 glasses
and the amount of juice needed.
( PLEASE HURRYY !!)
Geometric proofs of segments
Again..
Given: B is the midpoint of AC
C is the midpoint of BD
Prove: AD=3AB
This one hurts to look at
Answer:
The proof is shown below.
Step-by-step explanation:
Given: B is mid point of AC and C is mid-point of BD.
To prove: AD=3AB
It is given that B is mid-point of AC.
⇒ AB = BC ...(1)
Also, C is mid-point of BD.
⇒ BC = CD ...(2)
From (1) and (2),
AB = BC = CD
Now, AD = AB + BC + CD
⇒ AD = AB + AB + AB (∵ AB = BC = CD )
Hence proved.
What would the exponential growth model be for the given situation?
[tex] \frac{ \frac{8}{5} }{ \frac{2}{25} - \frac{5}{16} } [/tex]
What is the answer of this?
Answer:
[tex]\bold{\dfrac{\frac85}{\frac{2}{25}-\frac{5}{16}}=-6\frac{82}{93}\approx-6,88}[/tex]Step-by-step explanation:
[tex]\dfrac{\frac85}{\frac{2}{25}-\frac{5}{16}}=\dfrac{\frac85}{\frac{32}{400}-\frac{125}{400}}=\dfrac{\frac85}{-\frac{93}{400}}=\\\\\\=\frac85\cdot(-\frac{400}{93})=\frac81\cdot(-\frac{80}{93})=-\frac{640}{93}=-6\frac{82}{93}\approx-6,88[/tex]
what is 3 1/8 x 2 3/5
Answer:
[tex]8\frac{1}{8}[/tex]
Step-by-step explanation:
[tex]3\frac{1}{8} \times 2 \frac{3}{5}[/tex]
[tex]=\frac{25}{8} \times \frac{13}{5}[/tex]
[tex]=\frac{25\times13}{8\times5}[/tex]
[tex]=\frac{325}{40}[/tex]
[tex]=\frac{325/5}{40/5}[/tex]
[tex]=\frac{65}{8}[/tex]
[tex]=8\frac{1}{8}[/tex]
Hope this helps :)
It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone? StartFraction 5 Over 8 EndFraction plus 5 r equals 8. + 5r = 8 5 times StartFraction 5 Over 8 EndFraction equals r. + 5r = 1 5(5 times StartFraction 5 Over 8 EndFraction equals r.) = r StartFraction 5 Over 8 EndFraction equals 5 r. = 5r
Answer:
5/8+ 5r = 1
Step-by-step explanation:
When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool.
Where r = rate in parts per minutes
Hand held hose = 8 minutes
Lawn sprinkler = x
If the hose and sprinkler are used together, it takes 5 minutes to fill the pool.
Hence:
5/8+ 5r = 1
The equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone is given as:
5/8 + 5r = 1
Michael has $10 to put in a savings account . He has two options for a saving account : Option 1 will add $ 100 to his account each week . - Option 2 will double the amount in his account at the end of each week . a) Write a function in terms of x to model each option of savings . b) Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike. Determine which option (s) will enable him to reach his goal. Justify your answer.
Answer:
Option 1:
He starts with $10, and for each week, we add $100
Then his balance as a function of weeks will be:
f(w) = $10 + $100*w
option 2.
Again, we start with $10, and for each week that passes this is doubled, then the equation will be:
g(w) = $10*(2)^w
Now, we want in week w = 7 to have at least $700, then we need to replace w by 7 in both equations and see which one is better.
option 1:
f(7) = $10 + $100*7 = $710
With option 1 he will have enough
option 2:
g(7) = $10*(2)^7 = $1280
Again, he will have more than $700 in week 7, and we can clearly see that this option is better.
If you could help I would really appreciate it, but if not that’s fine. Thank you.
A child's ladder is made of 333 sections. Each section is \dfrac{3}{4} 4 3 start fraction, 3, divided by, 4, end fraction meters long. How long is the ladder when all 333 sections are extended to make one ladder? meters
Answer:
[tex]Ladder = 2\frac{1}{4}\ m[/tex]
Step-by-step explanation:
Given
[tex]Sections = 3[/tex]
[tex]Length = \frac{3}{4}m[/tex] per section
Required
Determine the length of the ladder
The length of the ladder is calculated by multiplying the number of sections by the length of each section.
So, we have:
[tex]Ladder = 3 * \frac{3}{4}\ m[/tex]
[tex]Ladder = \frac{9}{4}\ m[/tex]
[tex]Ladder = 2\frac{1}{4}\ m[/tex]
Hence, the length of the ladder is: [tex]2\frac{1}{4}\ m[/tex] or 2.25m
PLEASE HELPPPP
ITS EASY MY BRAIN JUST HURTS
500minute
Step-by-step explanation:
if anthony rides 32 miles in 160 minute then he will ride 1 mile in 5 minutes
Match each expression on the left with an equivalent expression on the right. Some answer choices on the right will not be used.
Answer
6.038 times 100 = 603.8
603.8 / 10 = 60.38
60.38 / 1,000 = 0.06038
0.6038 times 10 = 6.038
Answer:
6.038 times 100 = 603.8
603.8 / 10 = 60.38
60.38 / 1,000 = 0.06038
0.6038 times 10 = 6.038
( Did it on college board)
Step-by-step explanation:
How do I estimate 0.509375
Answer:
round it to the nearest whole number.
Step-by-step explanation:
Please help me with this question it is my first grade so I need to get it right on the answer if you’re positive you know
for each value of y , determine whether it is a solution to 3y<24.
Answer:
1) No
2) Yes
3)No
4)Yes
Step-by-step explanation:
1) 3(8) is simplified to 24
But 24 < 24 is not a true statement because they are both equal.
2) 3(5) is simplified to 15
15 < 40 is a true statement because 15 is less than 24
3) 3(11) simplifies to 33
33 < 24 is not a true statement because 33 is more than 24
4) 3(6) simplifies to 18
18 < 24 is a true statement because 18 is less than 24
Hope this helped.
What is the numeric expression that matches 8 fewer than y?
Answer:
y-8
Step-by-step explanation:
help woth this please
Hey again!
The answer to your question is 3.8
We can do 1.9 x 2 = 3.8
Hope it helps! Let me know if you need more help.
Special Right Triangles
Answer:
first option
Step-by-step explanation:
Using the sine/ cosine ratios in the right triangle and the exact values
sin30° = [tex]\frac{1}{2}[/tex] , cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{32}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 32 ( divide both sides by 2 )
x = 16
----------------------------------------------------------
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{32}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2y = 32[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
y = 16[tex]\sqrt{3}[/tex]
help me pleaseee pleaseee
Answer:
x=3
PAW = 40
Step-by-step explanation:
-11x+173-x+43=180
-12x+ 216 = 180
12x = 36
Find the value of the question mark. *
Answer: -2m - 3n
Step-by-step explanation:
a(m+n)/a(−2n−m) = 1/ax
Rewrite the equation as 1/ax = am+n/a−2n−m.
1/ax = am+n/a−2n−m
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln( 1/ax ) = ln ( am+n/a^{−2n−m})
Expand the left side.
−x ln(a) = ln (am+n/a^{−2n−m})
Expand the right side.
−x ln (a) = (m + n) ln (a) − (−2n − m) ln (a)
Simplify (m + n) ln (a) − (−2n − m) ln (a).
−x ln (a) = 2m ln (a) + 3n ln (a)
Move all the terms containing a logarithm to the left side of the equation.
−x ln (a) −2m ln (a) − 3n ln (a) = 0
Move all terms not containing x to the right side of the equation.
−x ln (a) = 2m ln (a) + 3n ln (a)
Divide each term by −1 ln (a) and simplify.
x = −2m − 3n
pls give brainliest :)
1.Solve 3.2 + y = 8.7.
c
A
8.7
В.
5.5
C.
11.9
D.
-3.2
Answer:
B
Step-by-step explanation:
I hope this helps
Answer:
B(5.5)
Step-by-step explanation:
3.2+y = 8.7
y = 8.7-3.2
y = 5.5
Althea paid $5.00 each for two bracelets and later sold each for $15.00. She paid $8.00 each for three bracelets
and sold each of them for $9.00.
a. Write an expression that represents the profit Althea made.
b. Evaluate the expression. Name the property used in each step.
Answer:
I have the same question
Step-by-step explanation:
message me if anyone helps I need it too
What are the FACTORS of this equation?
x^2 + 11x + 30 = 0
(x + 2)(x + 15)
x = -2, x = -15
x = -5, x = -6
(x + 5),(x + 6)
um i would say 25 all together
The number of trees in a rainforest decreases each month by 0.5%. The forest currently has 2.5 billion trees. Which expression represents how many trees will be left in 10 years. Group of answer choices
Answer:
[tex]y=2.5*10^9(0.005^{12 0}) \\\\[/tex]
Step-by-step explanation:
The above question is in the form of an exponential decay. The equation for an exponential decay is given by:
[tex]y=ab^x[/tex]
where y and x are variables, b < 1, a is the initial value of y (that is the value of y when x = 0).
Let y represent the number of trees left and x represent the number of months. Given that there is currently 2.5 billion trees, therefore a = 2.5 * 10⁹, b = 0.5% = 0.005. The equations becomes:
[tex]y=2.5*10^9(0.005^x)\\\\After\ ten\ years(x=10*12\ months=120\ months):\\\\y=2.5*10^9(0.005^{12 0}) \\\\[/tex]
Factor the following polynomial fully.
10x^2 + 16x – 8
A. 2(5x – 4)(x + 1)
B. (2x + 4)(5x – 2)
C.(10x – 8)(x + 1)
D.2(x + 2)(5x – 2)
Raphael and his friends made cookies for the bake sale. Raphael made 60 cookies and his friends made 350 cookies. What percent of the total cookies did Raphael make? Round your answer to the nearest whole percent.
Answer: 16%
Step-by-step explanation:
The total amount of cookies is 410.
410 represents 100%
410/100=65/x
X represents the unknown percentage
Cross multiply: 410x=6500
Divide: x=15.85
Round up: 16%
Identifying the Graph of an Inequality
Which is the graph of 4x + 2y < 3?
y
4
TY
NA
2
2
2
21
x
41
2
4
-4-2
2.
4
-4
2.
4
2
4
-2
-2
x
Answer:
The point-slope form of the equation of a line is ...
y -h = m(x -k)
for a line with slope m through point (h, k).
Comparing this to the given equation, you see that ...
h = -2, m = 1, k = -4
The line has a slope of 1 and goes through the point (-4, -2). This information is useful for graphing.
__
You can also rearrange the equation to slope-intercept form by subtracting 2 from both sides.
y = x +2
This has a slope of 1 and crosses the y-axis at y=2. It graphs the same as the above.
The graph of 4x + 2y < 3 is the region below the line 4x + 2y = 3.
The graph is given below.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
The graph of 4x + 2y < 3 is the region in the coordinate plane that satisfies the inequality.
To graph this inequality, we can start by graphing the line 4x + 2y = 3.
This line has a slope of -2 (because it can be written in the form
y = (-2x/1) + (3/2)), and a y-intercept of (0, 3/2).
We can plot this point on the y-axis and use the slope to find other points on the line.
For example, if we move one unit to the right from the y-intercept, we will move down two units (since the slope is -2), giving us the point (1, 1/2). Similarly, if we move one unit to the left from the y-intercept, we will move up two units, giving us the point (-1, 5/2).
We can connect these points to graph the line.
Therefore,
The graph of 4x + 2y < 3 is the region below the line 4x + 2y = 3.
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ7