In the system of equations, b is a constant. If the system has infinitely many solutions, what is the value of b?
Answers
Answer:
The value of b is 9.5
Step-by-step explanation:
If a system of equations has infinitely many solutions, that means the two equations are equal
If the system of equations ax + by = c, dx + ey = f, then
a = d ⇒ coefficients of xb = e ⇒ coefficients of yc = f ⇒ numerical termsLet us use this fact to solve the question
∵ 3x - y = 19 ⇒ (1)
∵ 1.5x - 0.5 y = b ⇒ (2)
∵ This system of equations has infinitely many solutions
∴ The coefficients of x must be equal
∴ The coefficients of y must be equal
∴ The numerical terms must be equal
→ Multiply equation (2) by 2 to make the coefficients of x and y on it
equal the coefficients of x and y in equation (1)
∵ 2(1.5x) - 2(0.5y) = 2(b)
∴ 3x - y = 2b ⇒ (3)
→ By comparing equations (1) and (3), 19 must equal 2b
∵ 2b = 19
→ Divide both sides by 2
∴ b = 9.5
∴ The value of b is 9.5
Related Questions
A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second car has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 825 miles, for total gas cumsumption of 40 gallons. How many gallons were consumed by each car
Answers
Answer:
Number of gallons consumed by first car = 15 gallons
Number of gallons consumed by second car = 25 gallons
Step-by-step explanation:
Given that:
Fuel efficiency of first car = 30 miles per gallon
Fuel efficiency of second car = 15 miles per gallon
Total distance traveled = 825 miles
Total gas consumption = 40 gallons
To find:
Number of gallons consumed by each car = ?
Solution:
Let the number of gallons consumed by first car = [tex]x[/tex] gallons
As per question statement, number of gallons consumed by second car:
[tex]40-x[/tex]
Number of miles covered by a car = Fuel efficiency [tex]\times[/tex] Number of gallons consumed
Number of miles covered by first car = 30 [tex]\times[/tex] [tex]x[/tex]
Number of miles covered by second car = 15 [tex]\times[/tex] ([tex]40-x[/tex])
Using the given statement:
[tex]30x+15(40-x)=825\\\Rightarrow 30x+600-15x=825\\\Rightarrow 15x=225\\\Rightarrow x =15\ gallons[/tex]
Therefore, Number of gallons consumed by first car = 15 gallons
Number of gallons consumed by second car = 40 - 15 = 25 gallons
-2(-g + 5)
someone please explain how to simplify then combine like terms
Answers
Answer:
2g-10
Step-by-step explanation:
-2(-g+5) take the -2 and multiply each term in the ()
-2*-g= 2g Two negatives multiplied turns it into a positive number
-2*5= -10
The answer is 2g-10
Please helppppp!!!!!!!!
Answers
Answer: I think it's B
Step-by-step explanation: You can use the answer if you want.
Simplify 81 to the negative 3 fourths power. (1 point)
Question 8 options:
1)
−27
2)
negative 1 over 27
3)
27
4)
1 over 27
Answers
Answer:
negative 1 over 27
Step-by-step explanation:
81 * negative 1 over 27 = -3
Answer:
[tex] \dfrac{1}{27} [/tex]
Step-by-step explanation:
[tex] 81^{-\frac{3}{4}} = [/tex]
[tex] = \dfrac{1}{81^{\frac{3}{4}}} [/tex]
[tex] = \dfrac{1}{(\sqrt[4]{81})^3} [/tex]
[tex] = \dfrac{1}{(3)^3} [/tex]
[tex] = \dfrac{1}{27} [/tex]
Pleaseeeee answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!
Answers
Answer:
45 miles
Step-by-step explanation:
Use the Pythagorean Theorem. Imagine a line connecting the ends of the right angle you made by driving. It would make a right triangle. You are trying to find the hypotenuse. Use the formula [tex]a^{2} +b^{2} =c^{2}[/tex]. Square 27, or multiply 27 by 27, to get 729. Add this to the square of 36, 1296. So [tex]c^{2}[/tex] = 2025. Find the square root of 2025. [tex]\sqrt{2025}[/tex] = 45. Hope this helped ^^
help please and maybe explain the answer if you have time
Answers
Answer:
I would say that it's A 1/3 because it's the slope and that's what a rate of increase is
A dog has a litter of 5 puppies. You plan to adopt 2 of the puppies. In how many ways can you choose 2 of the puppies from the litter?
Answers
Step-by-step explanation:
Number of choices = 5C2 = 5 * 4 / (1 * 2) = 10.
Calculate the value of y
Answers
Answer:
157°
Step-by-step explanation:
(4x - 5)° = (x + 16)°.. (vertical angles)
4x - 5 = x + 16
4x - x = 16 + 5
3x = 21
x = 21/3
x = 7
(x + 16)° + y ° = 180°...(Linear pair angles)
(7 + 16)° + y° = 180°
23° + y° = 180°
y° = 180° - 23°
y° = 157°
A quantity with an initial value of 120 decays exponentially at a rate of 9.5% every 7
hours. What is the value of the quantity after 3.25 days, to the nearest hundredth?
Answers
Answer:
39.46
Step-by-step explanation:
Need help solving #7 please
Answers
Answer:
False
Step-by-step explanation:
The equation says 21 is greater than or equal to 27, so it is false
5. - (m+) =
— Чт - 1=34
Answers
Answer:
The objective of this study was to examine the chronic effects on lower-body strength in resistance trained men of performing varying training volumes over 6
Step-by-step explanation:
The number of people call 911 on March 25th?
A) continuous
B) discrete
C) categorical
Answers
Answer:
I think the answer is continuous hope this helps
Step-by-step explanation:
Also got subscribe to my YT channel BlxeVxbes
A family restaurant chain wants to test the market for a new menu item: a grilled chicken sandwich with chipotle salsa. They are interested in both how to market the item and the right price to charge for it. They decide to offer the sandwich at 60 different restaurants in the chain, using two different descriptions on the menu. Half the restaurants' menus will emphasize "healthy eating" and half will emphasize "value." These two groups of restaurants will be further divided in three groups, each charging either a High, Medium, or Low price for the sandwich. After a month, they will measure what proportion of customers order the new sandwich.
Answers
Answer:
Experimental units, factors & treatments in experiment.
Step-by-step explanation:
Experimental Units are the 60 restaurants.
Factors are the : Menu description & price
Treatments in experimental design : Healthy Low Price, Healthy Medium Price, Healthy High price & Value low price, Value medium price, Value high price.
Estimate and then solve 8,784 ÷ 61 = ___. answers: 133 134 143 144 I WILL MARK U BRAINLEIST IF ITS RIGHT
Answers
Answer:
The answer is 144
Step-by-step explanation:
Answer:
Ummm...
8,784/61=
144, D ??why is b the answer ???????????????????/
Answers
Answer:
Step-by-step explanation:
its b cuz when u replace any value of x from B to the equation, the value of y satisfies the values of y in B. For instance
y = 4 * -3 + 2
= -10
the value of y is -10 which satisfies the value of y in B but when u use a value of another table suppose A it would be,
y = 4 * 7 + 2
= 30
but the value y corresponding to the value of x we used is not 30
HOPE IT HELPED
4a I do not understand the process
Answers
Answer:
9/40
Step-by-step explanation:
He needs 5/8, he already has 2/5, so still needed is 5/8-2/5.
To add or subtract fractions, the denominators must be equal.
Simplest approach is to multiply them. 8 times 5 is 40, so 40 is the new denominator we need for both fractions.
So first we convert 5/8 to 25/40.
Then we convert 2/5 to 16/40.
Now we can subtract them:
25/40 - 16/40 = 9/40.
9/40 cannot be simplified so this is the final answer.
There are some basic rules you need to know to work with fractions. If above work is too fast, comment below for deeper explanation.
All you need to do is subtract 5/8 - 2/5 and to do that, you would need a common denominator. So just,
5 2
— —
8 5
Multiply the two bottoms to get 40 and do the same thing with the top that you did with the bottom so....
5 x 5 = 25
— —
8 x 5 = 40
2 x 8 = 16
— —
5 x 8 = 40
Subtract 25 - 16 = 9 and keep the denominator the same so 9/40 is your answer.
Please help me with this
Answers
Answer:
A
Step-by-step explanation:
Is this true or false? The following graph represents a proportional relationship
A. True
B. False
Answers
Answer:
True
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
What is the 5th term of an arithmetic sequence of 20 terms with first and last terms of 2 and 59, respectively
Answers
Answer:
14
Step-by-step explanation:
aₙ = a₁ + (n-1)*d
59 = 2 + (20-1) * d
59 = 2 + 19d
19d = 59-2 = 57
d = 3
5th term: a₅ = 2 + 4 * 3 = 14
Answer:
14
Step-by-step explanation:
what is the equation of this graph?
Answers
Answer:
C. x=4
Step-by-step explanation:
In this graph the x value never changes, it is always equal to four. In this line the slope is undefined and there is no y-intercept. For all straight vertical lines, the equation will be x equals to whatever x value it is.
help meeeeeeeeeee its limited
Answers
Answer:
2 2/4
Step-by-step explanation:
add the buttons greater then 1 and it will be 2 2/4
12. Four shovels of sand are used for every 5 shovels of gravel in making concrete.
How much gravel is needed for 64 shovels of sand?
Answers
Answer:
80
Step-by-step explanation:
64s : Xg
4s.Xg = 5g.64s
X = (5g*64s)/4sg
= 5*64/4
= 5*16
= 80
James calculated the height of a cylinder that has a volume of 324 pi cubic inches and a radius of 12 inches. His work is shown below. V = B h Step 1: 324 pi = pi 12 squared h Step 2: 324 pi = 24 pi h Step 3: StartFraction 324 pi over 24 pi EndFraction = StartFraction 24 pi over 24 pi EndFraction h Step 4: h = 13.5 pi inches What is the first error that James made when calculating the height of the cylinder? In step 1, he substituted into the volume formula incorrectly. In step 2, he calculated 12 squared incorrectly. It should be 144 rather than 24. In step 4, the Pi should have canceled, making the correct answer 13.5 cm. James calculated the height of the cylinder correctly.
Answers
Answer:
I believe the answer is B let me know if it's wrong
Answer:
(B) In step 2, he calculated 12 squared incorrectly. It should be 144 rather than 24.
What happens to the graph of f(x) when it is multiplied
by a number between - 1 and 0?
Answers
y < -6( x − 18) − 2 when y = 46?
Answers
Well since y would be 46 if this is just you trying to find x, the answer would be x < 10
which expression can be written as 5x(2+7)
Answers
Answer:
Step-by-step explanation:
5x(2+7)
10x+35x
45x
There are no choices. But above is the answer if I need to solve it.
HOPE THIS HELPS
in the expression 15- the sum of 6 and. 7 do you add or subtract first
Answers
Answer:
Add
Step-by-step explanation:
By the way this question was worded, I'm going to say add. If I were to write the expression out, I personally would write it like this:
[tex]15-(6+7)[/tex]
And parentheses always occur first.
Hope this helps!
can someone please help me out with this.
Answers
16. Keisha has a bag that contains 3 red, 2 orange, 1 yellow, and 2 purple marbles. She will
randomly choose 1 marble from the bag. What is the probability that Kelsha will choose
an orange marble?
O.
3
8
2
-bh
1
0
8
o
0
1
4
2
Answers
Answer:
1/4
Step-by-step explanation:
you add 3+2=5+2=7+1=8 which is the total amount 8. Then the question is asking What is the probability that Kelsha will choose
an orange marble then the orange marble is 2 which is 2/8. Then simplify 2/8 get to 1/4.
Find The Angle (See Image)
Answers
Answer:
do you how many there is 5 angles if thats what ur asking
Step-by-step explanation: