Answer:
Let's solve for x.
5y=3x+b
Step 1: Flip the equation.
b+3x=5y
Step 2: Add -b to both sides.
b+3x+−b=5y+−b
3x=−b+5y
Step 3: Divide both sides by 3.
Answer:
x=
−1
3
b+
5
3
y
Step-by-step explanation:
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What are the 3 different forms of a quadratic function and what do the variables in each represent?
Answer:
general, factored, and vertex form.
general: y=ax^2+b^2+c
Factored: y=(x+a)(x+b)
Vertex: y=a(x-h)^2+k
Step-by-step explanation:
Clara is taking a medicine for a common cold. The table below shows the amount of medicine f(t), in mg, that was present in Clara's body after time t:
t (hours) 1 2 3 4 5
f(t) (mg) 236.5 223.73 211.65 200.22 189.41
Heidi was administered 300 mg of the same medicine. The amount of medicine in her body f(t) after time t is shown by the equation below:
f(t) = 300(0.946)t
Which statement best describes the rate at which Clara's and Heidi's bodies eliminated the medicine?
Clara's body eliminated the antibiotic faster than Heidi's body.
Clara's body eliminated the antibiotic at the same rate as Heidi's body.
Clara's body eliminated the antibiotic at half of the rate at which Heidi's body eliminated the antibiotic.
Clara's body eliminated the antibiotic at one-fourth of the rate at which Heidi's body eliminated the antibiotic.
Answer:
Clara's body eliminated the antibiotic at the same rate as Heidi's body.
Answer:
Option. B is the answer.
Step-by-step explanation:
Clara is taking a medicine for a common cold. Table that shows the amount f(t) that was present in Clara's body after time t is
t (hours) 1 2 3 4 5
f(t) (mg) 236.5 223.73 211.65 200.22 189.41
Now we will find the explicit formula of geometric sequence.
f(1) = 236.5
and f(2) = 223.73
Therefore, common ratio of the sequence = [tex]\frac{f(2)}{f(1)}=\frac{223.73}{236.5}[/tex]=0.946
So the equation will be f(t) = [tex]236.5(0.946)^{t}[/tex]------(1)
At the same time Heidi was administered 300 mg of same medicine of the same sample.
Amount of medicine in her body f(t) after time t is shown by the equation
f(t) = [tex]300(0.946)^{t}[/tex]----(2)
By comparing these equations 1 and 2, we find common ratio is same as (0.946), which reflects the rate of elimination of the antibiotic was same for both Clara and Heidi.
Option B is correct.
What is the solution to the system of equations below? y = -2x - 6 and 2y = -4x - 12
no solution
infinitely many solutions
(–3, 0)
(3, –12)
Answer: Infinitely Many Solutions
Step-by-step explanation:
Substitute y into the second equation:
2(-2x-6)=-4x-12
Then you get -4x-12=-4x=-12. Since this is 0=0 it would make it infinitely many solutions.
There are infinitely many solutions to the given system. The equations in the system are y = -2x - 6 and 2y = -4x - 12.
What are the solutions to a system?For a system of linear equations, there are three types of solutions. They are,
Unique solutionNo solutionInfinitely many solutionsInfinitely many solutions are there for a system if they both are equal on both sides while solving. (their graphs intersect at all the points)
Finding the solutions for the given system:Given the system of equations as
y = -2x - 6
2y = -4x - 12
Using substitution method, substituting first equation into the second equation,
2( -2x -6) = -4x - 12
⇒ -4x -12 = -4x - 12
Thus, both sides are equal, and the given system has infinitely many solutions.
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Select the coordinates of two points that are on the line x = 5
(5,0) and (0,5)
15, 0) and (5,-2)
5,0) and (0, 2)
0, 5) and (0, 2)
Answer:
(5,0) and (5,-2)
Step-by-step explanation:
we know that
If two points are on the line x=5, then the x-coordinates of the points must be equal to 5
therefore
The coordinates of two points that are on the line x=5 are
(5,0) and (5,-2)
Mr. Turner earned $40,000 last year. This year he estimates that he will earn 12% more money. How much does he estimate that he will earn.
Answer:
$44,800
Step-by-step explanation:
Original salary : $40,000
12% of original salary = 12% x 40,000 = 0.12 x 40,000 = $4,800
New salary = $40,000 + $4,800 = $44,800
Apollo Spas services 105 hot tubs. If each hot tub needs 165 mL of muriatic acid, how many liters of acid are needed for all of the hot tubs?
Apollo Spas would require approximately 17.325 liters of muriatic acid to service all 105 hot tubs.
Explanation:The student is looking to find out the total amount of muriatic acid, noted in liters, required to service all hot tubs. The problem states Apollo Spas needs to service 105 hot tubs, with each one requiring 165 mL of acid.
Firstly, we need to multiply the number of hot tubs by the amount of acid each one needs: 105 hot tubs * 165 mL/hot tub = 17325 mL.
However, the student needs the amount in liters, not milliliters. To convert mL to L, we need to divide the total mL by 1000 because there are 1000 mL in a liter. Therefore, 17325 mL / 1000 = 17.325 L.
So, Apollo Spas will need 17.325 liters of muriatic acid to service all 105 hot tubs.
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1
Solve for x.
(x - 4)(x - 4) = 0
A.
-16
B.
-4
C.
4
D.
16
Reset Next
Answer:
x = {4, 4}
Step-by-step explanation:
(x - 4)(x - 4) = 0 has two real, equal roots: x = 4 and x = 4. Notice that subbing 4 for x in this equation results in a TRUE equation.
The value of x in (x - 4)(x - 4) = 0 is x = (4, 4) repeated roots.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given (x - 4)(x - 4) = 0.
∴ Either (x - 4) = 0 or (x - 4) = 0.
x - 4 = 0 ⇒ x = 4 or x - 4 = 0 ⇒ x = 4.
So, x = (4, 4).
This is a case when a quadratic equation has real repeated roots.
The vertex of this graph of this quadratic equation just touches the x-axis.
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Please help with this question
Answer:
Many possible answers, including
Major Arc: JKM
Minor Arc: JM
Step-by-step explanation:
The answers you selected in this photo are correct. But let's see why.
A major arc is an arc that is bigger than a minor arc.
They are defined using a starting point and an ending point. In this case, you have many reference points (J, K, L and M), and none is identified in the question. However, the answers shown indicate they're using point J as starting point and M as ending point.
If you look at the positions of J and M on the diagram, you see you can take two routes to join them... the shortest route is the minor arc (going counter-clockwise direction from J to M). While the other route, going clockwise passes through the points K and L is much longer.... and forms the major arc.
That major arc could be identified as JKM, JLM or JKLM, since it starts at J, ends in M, but passes through points K and L, in that order.
what is the ratio of 200 to 350
Answer:
Simply Put:
Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 200 and 350 is 50
Divide both terms by the GCF, 50:
200 ÷ 50 = 4
350 ÷ 50 = 7
The ratio 200 : 350 can be reduced to lowest terms by dividing both terms by the GCF = 50 :
200 : 350 = 4 : 7
Therefore:
200 : 350 = 4 : 7
Step-by-step explanation:
convert 2000 Swiss francs to Dutch guilders
The conversion from 2000 Swiss francs to Dutch guilders requires a historical exchange rate which is not provided. The Dutch guilder is obsolete since 2002, and precise conversions cannot be made without the rate from the time period when both currencies were in use.
To convert 2000 Swiss francs to Dutch guilders, you would need to know the specific exchange rate between the Swiss franc and the Dutch guilder at the time of the conversion. Unfortunately, as of today, the Dutch guilder is no longer in use, as the Netherlands adopted the euro as its currency in 2002. However, if you were to convert currencies similar to how holders of dollars are willing to exchange $2,500 for euros or vice versa, you would need the specific exchange rate from Swiss francs (CHF) to Dutch guilders (NLG) during the time when both currencies were in use.
Without historical exchange rate data, it is impossible to provide an exact number of Dutch guilders you would receive for 2000 Swiss francs. If you have a specific date in mind, you could find the historical exchange rate for that date and then calculate the conversion using this formula:
Amount in Swiss francs * Exchange rate (CHF to NLG) = Amount in Dutch guilders
Remember, when performing historical currency conversions, it's essential to use the correct exchange rate from the time period in question.
Write a proportion to find how many points x a student needs to score on a test worth 50 points to get a test score of 40%.
Answer:
20 pts
Step-by-step explanation:
50 points corresponds to a 100% grade. How many points (x) correspond to a 40% grade?
x 40%
------------ = ---------
50 pts 100%
Then 100x = 2000, and so x = 20.
A score of 20 points would correspond with a test score of 40%.
Answer:
A score of 20 points would correspond with a test score of 40%.
Step-by-step explanation:
x 40% How many points (x) correspond to a 40% grade?
------------ = ---------
50 pts 100% 50 points corresponds to a 100% grade.
100x = 2000 divide both sides by 100
x = 20
Ali has a 64 gram bar of chocolate. on day 1 he eats half of his chocolate. on day 2 he eats half of what is left. he does the same each day.
a. when will he have only 1 gram left?
b. how much would a bar of chocolate need to weigh to last All 14 days?
Answer:
A: Day 6
B: 8196 grams (He will become obese for sure)
Step-by-step explanation:
Part A:
As you can infer from the problem, Ali halves his bar everyday, regardless of how the bar is.
Day 1= 32 grams left
Day 2= 16 grams left
Day 3= 8 grams left
Dat 4= 4 grams left
Day 5= 2 grams left
Day 6=1 gram left
He will have one gram left on Day 6
Part B:
This part is basically vice versa. Instead on halving, we need to be doubling. I will do Part a in reverse until Day 14 comes
Day 1= 1
Day 2= 2
Day 3= 4
Day 4= 8
Day 5= 16
Day 6= 32
Day 7 = 64
Day 8= 128
Day 9= 256
Day 10= 512
Day 11= 1024
Day 12= 2048
Day 13= 4096
Day 14= 8192
He will need 8192 grams of chocolate!!!
The number of days when he has only 1 gram left will be 6. And the chocolate needs to weigh to last All 14 days will be 1/256 grams.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
Ali has a 64 grams bar of chocolate.
On day 1 he eats half of his chocolate.
And on day 2 he eats half of what is left.
He does the same each day.
Then the value of a is 64 grams and b is 1/2.
y = 64 · (1/2)ⁿ
Where n is the number of days.
The number of days when he has only 1 gram left will be
1 = 64 · (1/2)ⁿ
1/64 = (1/2)ⁿ
(1/2)⁶ = (1/2)ⁿ
n = 6
The number of days when he has only 1 gram left will be 6.
The chocolate needs to weigh to last All 14 days will be
y = 64 · (1/2)¹⁴
y = 64 · (1/16384)
y = 1/256 grams
The chocolate needs to weigh to last All 14 days will be 1/256 grams.
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The length of one of the legs in a right triangle is 3 inches . If the hypotenuse is 10 inches long what the length of the other leg
Answer:
9.5 inches
Step-by-step explanation:
We are given that in a right angled triangle, one leg is 3 inches long while the hypotenuse is 10 inches long. We are to find the length of the other leg.
For this, we will use the Pythagoras Theorem.
Assuming x to be the length of the other leg.
[tex] 1 0 ^ 2 = 3 ^ 2 + x ^ 2 [/tex]
[tex]100=9+x^2[/tex]
[tex]x^2=91[/tex]
[tex]\sqrt{x^2} =\sqrt{91}[/tex]
x = 9.5
Answer:
9.53 inches
Step-by-step explanation:
In a right angles triangle, the sum of the squares of the two legs (a and b) equals the square of the the hypotenuse.
a²+b²=c²
Substituting for the values provided in the question we get the following:
3²+b²=10²
b²=10²-3²
b²=91
b=9.53 inches.
FIRST GETS BRAINLIEST
Use roots or exponents to solve the each equation. Write fractions in the simplest form
Answer:
8, 36, 81, 11, 7, 1000
Step-by-step explanation:
A
Lets start with number one.
x^2 = 64.
That means that x times x equals 64.
To find x's value, simply find the square root of 64, which is 8.
So x = 8.
For the second one, the square root of x is 6.
That means that 6 x 6 = x
6 x 6 = 36.
So, x = 36.
B
For the third one, the square root of x is 9.
That means that 9 x 9 = x
9 x 9 = 81
So, x = 81.
For the fourth one, x^2 = 121
That means x times x = 121
To find x's value, simply find the square root of 121, which is 11
So, x = 11.
C
For the fifth one, x^3 = 343.
That means that x times x times x = 343
To find x's value, simply find the square root of 343, which is 7.
So, x = 7.
For the sixth and last one, the cube root of x is 10.
That means 10 x 10 x 10 = x.
10 x 10 x 10 = 1,000
So, x = 1,000
I hope this helps! :)
What is the value of x in the equation 1.5(х + 4) — 3 = 4.5(х – 2)?
A 3
B 4
C 5
D 9
Answer:
B.4
Step-by-step explanation:
1.5(x+4) - 3 = 4.5( x-2)-----------------------open brackets on both sides
1.5 x +6 -3= 4.5x- 9.................................collect like terms
3+9 = 4.5 x- 1.5x
12=3x..................................divide by 3 both sides to get x
12/3=x
x=4
ANSWER
x=4
EXPLANATION
The given equation is
[tex]1.5(x + 4) - 3= 4.5(x - 2)[/tex]
Multiply through by 10
[tex]15(x + 4) - 30= 45(x - 2)[/tex]
We expand to get:
[tex]15x + 60 - 30= 45x - 90[/tex]
Group similar terms to get;
[tex]15x - 45x = - 90 - 60+ 30[/tex]
[tex] - 30x = - 120[/tex]
[tex] x= 4[/tex]
Solve by factoring
[tex]4m {}^{2} - 31m - 45 = 0[/tex]
A.-5/4,9
B.9,-5
C.31,-41
D.45,4
Answer:
A. -5/4, 9
Step-by-step explanation:
The solution is in the picture
Answer:
A
Step-by-step explanation:
Given
4m² - 31m - 45 = 0
Consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term
product = 4 × - 45 = - 180 and sum = - 31
The factors are - 36 and + 5
Use these factors to split the m- term
4m² - 36m + 5m - 45 = 0 ( factor the first/second and third/fourth terms )
4m(m - 9) + 5(m - 9) = 0 ← factor out (m - 9) from each term
(m - 9)(4m + 5) = 0
Equate each factor to zero and solve for m
m - 9 = 0 ⇒ m = 9
4m + 5 = 0 ⇒ 4m = - 5 ⇒ m = - [tex]\frac{5}{4}[/tex]
HELPPPPPPPPPPPPPPPPPPP
Answer:
C
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x)
= - 4x² - 6x - 1 + (- x² - 5x + 3) ← remove parenthesis
= - 4x² - 6x - 1 - x² - 5x + 3 ← collect like terms
= - 5x² - 11x + 2 → C
In the system of equations, which variable would it be easiest to solve for?
2x+4y=26
3x+y=9
The easiest to solve for is x in the first equation.
The easiest to solve for is y in the first equation.
The easiest to solve for is x in the second equation.
The easiest to solve for is y in the second equation.
Answer:
Step-by-step explanation:
The easiest to solve for is y in the second equation. Just subtract 3x from both sides, obtaining y = -3x + 9.
The value of x = 1 and y = 6. The easiest to solve for is y in the second equation.
How to estimate the value of the system of equations?
Let the equations be
2x + 4y = 26 ......(1)
3x + y = 9 ........(2)
From (2), we get
3x + y = 9
y = -3x + 9 .......(3)
then substitute the value of y in (1), then we get
2x + 4y = 26
2x + 4(-3x + 9) = 26
Simplifying the above equation, we get
2x - 12x + 36 = 26
-10x + 36 = 26
-10x = 26 - 36
-10x = -10
Then the value of x = 1
Substitute the value of x in (3), then we get
y = -3x + 9
Simplifying the equation, we get
y = -3(1) + 9
y = -3 + 9
y = 6
The value of x = 1 and y = 6.
Therefore, the correct answer is option (d) The easiest to solve for is y in the second equation.
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simplify (6x2 - 3 + 5x3) - (4x3 - 2x2 - 16
Answer:
x^3 +8x^2 +13
Step-by-step explanation:
(6x^2 - 3 + 5x^3) - (4x^3 - 2x^2 - 16)
Distribute the minus sign
6x^2 - 3 + 5x^3 -4x^3 + 2x^2 + 16
Combine like terms
x^3 +8x^2 +13
Answer:
Simplify (6x2 − 3 + 5x3) − (4x3 − 2x2 − 16).
its (C) -------> x^3 + 8x2 + 13
Step-by-step explanation:
what is the simplified form of 7 radical x^5 x 7 radical x^5
Answer:
the product of [tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex] is [tex]49\,x^5[/tex]
Step-by-step explanation:
We need to find the simplifies form of
[tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex]
We need to find product of above terms
We can write as
[tex](7*7)(\sqrt{x^5}*\sqrt{x^5})\\(7^2)((\sqrt{x^5})^2)\\49\,x^5[/tex]
So, the product of [tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex] is [tex]49\,x^5[/tex]
What is the perimeter of a rectangle if the length is 5 and the width is x?
Answer:
The perimeter of the rectangle is 10 + 2x.
Step-by-step explanation:
The formula for the perimeter of a rectangle is 2(l + w) where l = length and w = width because you add up the length of all the sides.
So we can plug in our givens into the formula and simplify:
2(5 + x)
So the perimeter is: 10 + 2x
Notice that we cannot simplify the expression further because there is an unknown (the length).
Answer:
2x + 10
Step-by-step explanation:
A rectangle has opposite sides equal
2(5 + x)
2x + 10
Write an equation of a line with the given slope and y-intercept. m = –5, b = –7 y = –5x + 7 y = –7x – 5 y = –5x – 7 y = 5x – 7
Answer:
y = - 5x - 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
here m = - 5 and b = - 7, hence
y = - 5x - 7 ← equation of line
Since b equals the y-intercept, we automatically know that the answer will be in slope-intercept form which is y = mx + b where m equals slope and b equals the y-intercept.
Given.
m = –5, b = –7
Slope intercept formula.
y = mx + b
Plug in m = -5 and b = -7.
y = -5x - 7 ← Choice C
What is the solution to x – 10 > – 12?
Answer:
x>-18
Step-by-step explanation:
A system of equations has no solution. If y=8x +7 is one of the equations,which could be the other equation
Answer:
Step-by-step explanation:
Two lines that are parallel have the same slope but different y intercepts.
So you could have any equation that satisfies y = 8x + b. The only value that b cannot have is 7. All other values including 0 are fine.
So here are a couple of examples.
y = 8x b = 0
y = 8x + 92
y = 8x + 1/2
y = 8x + pi
y = 8x - 13
7 = 8x - pi
A bag contains 3 red marbles 4 white marbles and 5 blue marbles if one marble is drawn from the bag what is the probability that the marble will be blue
Follow below steps;
The probability of drawing a blue marble from the bag:
Calculate the total number of marbles in the bag: 3 red + 4 white + 5 blue = 12 marbles.
Calculate the probability of drawing a blue marble: Number of blue marbles / Total number of marbles = 5 / 12 = 5/12.
Which description from the list below accuratley describe the relationship between ABC and DEF check all that apply.
Answer:
B. Similar
D. Same Shape
Step-by-step explanation:
In the given triangles:
∠A ≅ ∠D = 22°
∠B ≅ ∠E = 120°
∠C ≅ ∠F = 38°
Hence using the AAA axiom of geometry
Triangle ABC and DEF are similar.
More over due to the similarity of angles the triangles also have same shape.
One more thing, that can be observed is that
DE = 2* AB
EF = 2*BC
DF = 2*AC
The sides of triangle ABC are scaled with a factor of 2 which makes it similar to DEF ..
Hence,
Option B and Option D are correct ..
Answer with explanation:
Given two triangles ΔABC and ΔDEF
⇒Ratio of Sides
[tex]\rightarrow \frac{AB}{DE}(\frac{5}{10})=\frac{BC}{EF}(\frac{3}{6})=\frac{AC}{DF}(\frac{7}{14})=\frac{1}{2}[/tex]
⇒Comparison of Angles
→∠A=∠D=22°
→∠B=∠E=120°
→∠C=∠F=36°
⇒As length of corresponding sides are Proportional ,as well as corresponding Angles of two triangles are same.So Two Triangles are similar either by SSS Similarity or AA Similarity or S AS Similarity.
→If Triangles are similar then they are congruent also.
→The description which accurately describe the relationship between ΔABC and ΔDEF is:
→ Option B: Similar
Factor the expression below x^2-12x+36
Answer:
(x-6)^2
Step-by-step explanation:
x^2-12x+36
What two numbers multiply to 36 and add to -12
-6 * -6 = 36
-6 + -6 = -12
(x-6) (x-6)
(x-6)^2
Find the circumference of a circle with a radius of 6. Leave your answer in terms of 3 6 12 36
Answer:
C≈37.7 or 36
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
2x3.14x6=36
Step-by-step explanation:
If `f(x) = 2x^2 - 4x - 3` and `g(x) = (x - 4)(x + 4)`, find `f(x) - g(x).`
Answer:
[tex]\large\boxed{f(x)-g(x)=x^2-4x+13}[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2-4x-3\\\\g(x)=(x-4)(x+4)=x^2-4^2=x^2-16\qquad\text{used}\ a^2-b^2=(a-b)(a+b)\\\\f(x)-g(x)=(2x^2-4x-3)-(x^2-16)\\\\=2x^2-4x-3-x^2-(-16)\\\\=2x^2-4x-3-x^2+16\qquad\text{combine like terms}\\\\=(2x^2-x^2)-4x+(-3+16)\\\\=x^2-4x+13[/tex]
12x+15y=34
-6x+5y=3
Answer:
x = 5/6 , y = 8/5
Step-by-step explanation:
Solve the following system:
{12 x + 15 y = 34 | (equation 1)
{5 y - 6 x = 3 | (equation 2)
Add 1/2 × (equation 1) to equation 2:
{12 x + 15 y = 34 | (equation 1)
{0 x+(25 y)/2 = 20 | (equation 2)
Multiply equation 2 by 2/5:
{12 x + 15 y = 34 | (equation 1)
{0 x+5 y = 8 | (equation 2)
Divide equation 2 by 5:
{12 x + 15 y = 34 | (equation 1)
{0 x+y = 8/5 | (equation 2)
Subtract 15 × (equation 2) from equation 1:
{12 x+0 y = 10 | (equation 1)
{0 x+y = 8/5 | (equation 2)
Divide equation 1 by 12:
{x+0 y = 5/6 | (equation 1)
{0 x+y = 8/5 | (equation 2)
Collect results:
Answer: {x = 5/6 , y = 8/5