if r and s represent the solutions of the equation below and r>s, what is the value of the difference r-s?
(3x+14)x=5
Answer:
16/3
Step-by-step explanation:
(3x + 14)x = 5
3x² + 14x = 5
3x² + 14x - 5 = 0
3x² + 15x - x - 5 = 0
3x(x + 5) - 1(x + 5) = 0
(3x - 1)(x + 5) = 0
x = 1/3 & -5
Here,
r = 1/3
s = -5
r - s
1/3 - (-5)
1/3 + 5
1 + 15/3
16/3
the value of the difference r-s is [tex]\bold{\frac{16}{3}}[/tex]
Answer:
Solution given:
(3x+14)x=5
opening bracket
3x²+14x=5
3x²+14x-5=0
Doing middle term factorisation
3x²+(15-1)x-5=0
3x²+15x-x-5=0
3x(x+5)-1(x+5)=0
(3x-1)(x+5)=0
either
x=-5
or
3x-1=0
3x=1
x=⅓
According to question value of x is r>s
so
⅓>-5
so
r=⅓
and
s=-5
Now
r-s=⅓-(-5)=[tex]\frac{1+5*3}{3}=\frac{16}{3}[/tex]
What is the simplified form of the expression? HELP ASAP
Answer:
[tex]360[/tex]
Step-by-step explanation:
[tex] \frac{5(14 - 2)^{2} }{2} = \frac{5 {(12)}^{2} }{2} = \frac{5(144)}{2} \\ \\ \frac{720}{2} = 360[/tex]
Answer:
The answer is option (d) 360.
Step-by-step explanation:
Solution :[tex]\implies{\tt{\dfrac{5(14 - 2)^{2} }{2}}}[/tex]
[tex]\implies{\tt{\dfrac{5(12)^{2} }{2}}}[/tex]
[tex]\implies{\tt{\dfrac{5(12 \times 12) }{2}}}[/tex]
[tex]\implies{\tt{\dfrac{5(144) }{2}}}[/tex]
[tex]\implies{\tt{\dfrac{5 \times 144 }{2}}}[/tex]
[tex]\implies{\tt{\dfrac{5 \times \cancel{144}}{ \cancel{2}}}}[/tex]
[tex]\implies{\tt{5 \times 72}}[/tex]
[tex]\implies{\tt{360}}[/tex]
[tex]\dag{\underline{\boxed{\sf{\red{360}}}}}[/tex]
Hence, the answer is 360.
[tex]\rule{300}{1.5}[/tex]
Learn More :✧ BODMAS :
↝ BODMAS rule is an acronym used to remember the order of operations to be followed while solving expressions in mathematics.
It stands for :-
⠀ ⇝ B - Brackets,
⠀ ⇝ O - Order of powers or roots,
⠀ ⇝ D - Division,
⠀ ⇝ M - Multiplication
⠀ ⇝ A - Addition
⠀ ⇝ S - Subtraction.
↝ It means that expressions having multiple operators need to be simplified from left to right in this order only.
✧ BODMAS RULE :
↝ First, we solve brackets, then powers or roots,then division or multiplication (whatever comes first from the left side of the expression), and then at last subtraction or addition.
⠀ ↠ Addition (+)
⠀ ↠ Subtraction (-)
⠀ ↠ Multiplication (×)
⠀ ↠ Division (÷)
⠀ ↠ Brackets ( )
[tex]\rule{300}{1.5}[/tex]
What is the product?
it tells you the answer..
The product of matries [tex]\left[\begin{array}{cc}5&-2\\-6&2\end{array}\right][/tex] and [tex]\left[\begin{array}{c}-1\\-1\end{array}\right][/tex]is option c. [tex]\left[\begin{array}{c}-3\\4\end{array}\right].[/tex] By perform matrix multiplication of 2x2 matrix with 2x1 matrix.
Given the matrices:
[tex]A = \left[\begin{array}{cc}5&-2\\-6&5\end{array}\right][/tex]
[tex]B = \left[\begin{array}{c}-1\\-1\end{array}\right][/tex]
To find the product, perform matrix multiplication.
Using the given matrices, the multiplication can be done as follows:
[tex]\left[\begin{array}{cc}5&-2\\-6&2\end{array}\right] \times \left[\begin{array}{c}-1\\-1\end{array}\right][/tex]
Multiply each element in the corresponding row of the first matrix by the corresponding column of the second matrix and summing the products.
[tex]=\left[\begin{array}{cc}(5\times-1)+(-2\times-1)\\(-6\times-1)+(2\times-1)\end{array}\right][/tex]
On multiplying the term in brackets gives:
[tex]=\left[\begin{array}{cc}-5+2\\6-2\end{array}\right][/tex]
On performing the algebraic sum gives:
[tex]=\left[\begin{array}{cc}-3\\4\end{array}\right][/tex]
Therefore, the product of the matrices is [tex]\left[\begin{array}{cc}-3\\4\end{array}\right].[/tex]
Matrix multiplication is an important operation in linear algebra and has applications in various fields, including physics, computer science, and engineering.
It allows us to perform transformations, solve systems of equations, and represent linear relationships between variables.
Learn more about matrix multiplication here:
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#SPJ6
What is the answer to 3(y - 1 + 2y)
Answer:
Collect like terms.
3((y+2y)-1)
3((y+2y)−1)
2 Simplify (y+2y)-1(y+2y)−1 to 3y-13y−1.
3(3y-1)
3(3y−1)
can someone please help me with this? pls & thank you!
Answer:
see explanation
Step-by-step explanation:
Equation for Fast Internet is
45 + 50.45x
Equation for Quick Internet is
57.95x
To find when they cost the same , equate the 2 equations
45 + 50.45x = 57.95x ← required equation
Solve the equation by subtracting 50.45x from both sides
45 = 7.5x ( divide both sides by 7.5 )
6 = x
Both services would cost the same after 6 months
The supplement of the complement of an angle is 132 degrees. What is the supplement of that angle
Based on the information given, it should be noted that the supplement will be 48°.
It should be noted that two angles are called supplementary angles when the values that are added together will be equal to 180°.
In this case, we've been informed that one of the angles is 132°. Therefore, the value of the second angle will be:
= 180° - 132°
= 48°
The second angle is 48°.
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Hi, let me help you out!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
In this problem, we're trying to find the supplement of [tex]\tt{132\textdegree}[/tex].
Supplementary angles add up to [tex]\tt{180\textdegree}[/tex].
So, let's find its supplement:
[tex]\tt{\angle x+132=180}[/tex], where x is the unknown angle.
Subtract 132 from both sides of the equal sign:
[tex]\boxed{\tt{\angle x=48\textdegree}}[/tex] [tex]\longleftarrow\tt{We\:conclude\:that\:this\:is\:the\:answer.}[/tex]
I hope it helps you! Have an awesome day!
If you need any explanation or clarification, feel free to comment and ask me, and I'll respond asap and do my best to help you out! :D
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve using substitution.
=
10x + 4y = -14
X = 1
-
Submit
Answer:
-6
Step-by-step explanation:
10x1 + 4y = -14
10+4y=-14
4y=-14-10
4y = -24
y = -24/4
y = -6
At time t= 0, a storage tank is empty and begins filling with water. For t > 0 hours, the depth of the water in the tank is increasing at a rate of W (t) feet per hour. Which of the following is the best interpretation of the statement W' (2) > 3?
a. Two hours after the tank begins filling with water, the depth of the water is increasing at a rate greater than 33 feet per hour.
b. Over the first two hours after the tank begins filling with water, the depth of the water is always increasing at a rate greater than 3 feet per hour.
c. Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.
d. Over the first two hours after the tank begins filling with water, the rate at which the depth of the water is rising is always increasing at a rate greater than 33 feet per hour per hour.
The given function is the rate of change of the water depth. therefore,
W'(t) is the second derivative.
The correct option is; d. Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.Reasons:
The volume of water in the tank is 0 at time t = 0 (the tank is empty)
The function that gives the rate at which the depth of water in the tank is
increasing at time t > 0 is W(t).
Where;
t = The time in hours
Therefore;
W'(t), the derivative of the function of the rate at which the water in the
tank is increasing in feet per hour is the rate of increase of W(t).
Which gives;
W'(2) = The rate of change of the rate at which the water level is rising (second derivative) two hours after begins to fill with water, per hour per hour.
Therefore;
W'(2) > 3 = Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.Learn more about second derivative here:
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PERIMETER PLEASE HELP
Answer:
164 round = 160
your answer now can you please help me
Step-by-step explanation:
A bottle of juice costs $1.85, and a pack of 6 bottles of lemonade costs $5.40. If Jimmy
buys 3 bottles of juice and a dozen bottles of lemonade, how much money should he
spend in all?
Answer:
Step-by-step explanation:
+
1.85
5.40
_____
6. 2 5
PLEASE PLEASE HELP ME
Answer:
Assuming that it ends at 9.5. The domain is (-8 , 9.5). However, assuming it continues further to the right, it could be (-8 , ∞)
Range is the area covered vertically. Assuming it ends at 9.5 it would be (4 , -4) However, assuming it continues further down vertically, it would/could be (4 , -∞)
Neither.
Step-by-step explanation:
Domain is the area covered horizontally. Assuming that it ends at 9.5. The domain is (-8 , 9.5). However, assuming it continues further to the right, it could be (-8 , ∞)
Range is the area covered vertically. Assuming it ends at 9.5 it would be (4 , -4) However, assuming it continues further down vertically, it would/could be (4 , -∞)
It is neither because it is on the x-axis.
Help please. I dont know how to do this :((
Answer:
You need the distance of all four sides so that is:
2 * (5y +1) + 2 * (2y -3) which equals
10y + 2 + 4y -6 and that equals
14y -4
Step-by-step explanation:
Look at the translation of the shape. Describe the translation that moves EFGH to E'F'G'H'.
3 boxes left 4 boxes up
4 boxes right 3 boxes up
4 boxes left 3 boxes up
Answer:
4 boxes left 3 boxes up.
Step-by-step explanation:
Maya ate breakfast and wanted to leave her waitress a 15% tip. Her meal cost
$7.50. How much money should Maya leave for the TIP?
Answer:
$1.13
Step-by-step explanation:
You multiply 0.15*7.5, and you get 1.125, which you add up to $1.13
initial value on this table
Answer:correct me if I’m wrong but it’s 0.
Step-by-step explanation:
85-51=34. 34
—————=. —————=17
5-3. 2
And once 17 is the slope/rate of change,you can either go back 17 each time or….do an equation : f(x)=17(x-3)+51
6√21 ×√28
please show work :D
Answer:
84√3
Step-by-step explanation:
6√21√28
6√7√3√7√4
(6√7√3√7)(2)
(6*7)(√3)(2)
(42)(√3)(2)
84√3
[tex]6\sqrt{21} \cdot \sqrt{28}\\\\=6 \left(\sqrt{21 \times 28 \right)\\\\=6\left(\sqrt{588}\right)\\\\=6\left(\sqrt{196 \times 3}\right)\\\\=6\left(14\sqrt 3\right)\\\\=84\sqrt{3}[/tex]
I need help and I can’t find any sadly. Help!!
Answer:
Step-by-step explanation:
for 1. The addition property of equality esssentially means that if you were to add/subtract the same value to both sides of the equation, the equation would remain equal. this would be associated with 3. since adding 12 to both sides would give x on one side and 16 on the other which is equal to x=16
for 2. "given" just means the problem, so it is the 1st option. it just means "given the problem..."
for 3. collectiing like terms is the addition of -5x +6x. since they are on the same side eof the equation, and are in the same measurements (of x) they can be combined to eqaul positive x, this is represented by option 2
if silas sandwich measures, 3 yards 2 feets 3 inches, How many inches in total does silas sandwich measure
========================================================
Work Shown:
1 yard = 3 feet
3 yards = 9 feet (multiply both sides by 3)
3 yards + 2 feet = 9 feet + 2 feet = 11 feet
1 foot = 12 inches
11 feet = 132 inches (multiply both sides by 11)
11 feet + 3 inches = 132 inches + 3 inches = 135 inches
Solve the system of equations.
2x-y =7
1x-y = 10
Answer:
(-3, -7)
Step-by-step explanation:
2x - y = 7 multiply by -1 ⇔ -2x + y = -7
1x - y = 10 Do not change ⇔ 1x - y = 10
-x = 3
x = -3
Use the second equation to solve on y when x = -3
-1x - y = 10
-1(-3) - y = 10
3 - y = 10
-y = 10 - 3
-y = 7
y = -7 Solution: (-3, -7)
Help?please rnnnn………
Answer:
8,176
Step-by-step explanation:
You have to first do 8 × 5110 = 40,880
Then you divide 40,880 by 5
40,800 ÷ 5 = 8,176
f(x)=4x+6 g(x)=4x-6 if g(x)=f(x)+k what is the value of k
Answer:
k=-6-6=-12
Im pretty sure that's the answer
David has a loyalty card good for a 19% discount at his local hardware store. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $32? Round to the nearest cent.
Discounts are used to reduce the original price of an item.
David will pay $25 and 92 cents for an item of $32, before tax
The discount (d) is given as:
[tex]d =19\%[/tex]
The price (p) of the item is given as:
[tex]p = \$32[/tex]
So, the amount (A) paid before tax is calculated using:
[tex]A = p \times (1 - d)[/tex]
Substitute known values
[tex]A = \$32 \times (1 - 19\%)[/tex]
Express percentage as decimal
[tex]A = \$32 \times (1 - 0.19)[/tex]
Subtract 0.19 from 1
[tex]A = \$32 \times 0.81[/tex]
Multiply 32 and 0.81
[tex]A = \$25.92[/tex]
Hence, David will pay $25 and 92 cents for an item of $32, before tax
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Consider the line y=-5x+3. Find the equation of the line that is parallel to this line and passes through the point (3,4). Find the equation of the line that is perpendicular to this line and passes through the point (3, 4).
Answer:
parallel
y= -5x + 19
perpendicular
y= (1/5)x + 17/5
Step-by-step explanation:
yeah-ya......... right?
if I was 14 in 1947 then how old am I?
Express the following numbers in usual form:
(i) 8.02×10^-5
(ii) 4.5×10^3
(iii) 7×10^-5
(iv) 1.0001×10^8
(v) 4.3×10^12
(vi) 3.61492×10^5
(i) Given number = 8.02×10^-5
⇛ 8.02/100000
⇛ (802/100)/100000
⇛ 802/10000000
⇛ 0.0000802
The usual form of 8.02×10^-5 is 0.0000802
(ii) Given number = 4.5×10³
⇛4.5×1000
⇛ (45/10)×1000
⇛ 45×100
⇛ 4500
The usual form of 4.5×10³ is 4500
(iii) Given number = 7×10^-5
⇛ 7/100000
⇛ 0.00007
The usual form of 7×10^-5 is 0.00007
(iv) Given number = 1.0001×10⁸
⇛ 1.0001×100000000
⇛ (10001/10000)×100000000
⇛ 10001×10000
⇛100010000
The usual form of 1.0001×10⁸ is 100010000
(v) Given number = 4.3×10¹²
⇛ 4.3×1000000000000
⇛ (43/10)×1000000000000
⇛ 43×100000000000
⇛ 4300000000000
The usual form of 4.3×10¹² is 4300000000000
(vi) Given number = 3.61492×10⁵
⇛ 3.61492×100000
⇛ (361492/100000)×100000
⇛ 361492
The usual form of 3.61492×10⁵ is 361492
How does a plastic fork, whale, hospital and chocolate bar relate with each other?
Answer:
They all include the letter A
Step-by-step explanation:
a letter is chosen at random from the word 'mathematics'. Fin the probability that letter T is not chosen.
Answer:
2/11 is the answer of your question
Find the value of two numbers if their sum is 147 and their difference is 51
No links
Answer:
99 and 48
Step-by-step explanation:
99+48=147
99-48=51
A youth group earns $600 for charity and decides to put it in a bank. Calculate the amount of money the group will have for each scenario.
Part A chase bank pays simple interest at 5% and the group leaves the money for 5 years
part B witney bank pays an interest rate of 4% compounded annually and the group leaves the money for 6 years
Based on the types of compounding and the interest rates, the following are true:
Part A - The group will have $750Part B - The group will have $759.19When using simple interest, the amount the group will have is:
= Amount x ( 1 + rate x number of years )
= 600 x ( 1 + 5% x 5)
= $750
When using compound interest, the group will have:
= Amount x ( 1 + rate) ^ Number of years
= 600 x ( 1 + 4%)⁶
= $759.19
In conclusion, compound interest yields more.
Find out more about compound interest at https://brainly.com/question/25263325.
A restaurant is considering reducing its meal sizes, because it noticed many of its customers cannot finish their meals. The manager decided to weigh the left-over portion of the meals before putting them in to-go containers. The line plot displays the weights of the left-over portions of the meals. If the left-over portions are divided equally among the customers, how much food would each customer take home? Weight of Left-over Meals A. B. C. D.
Answer:
1/2
Step-by-step explanation:
You need to add all the fractions up to get 1/2 is what food the costumers brought home
Answer:
1/2
Step-by-step explanation:
i got it correct!!