Answer:
A. ¹²/₅Step-by-step explanation:
There is no solution for system of equations: [tex]a_1x+b_1y=c_1\\a_2y+b_2y=c_2[/tex]
if: [tex]a_1=a_2\quad and\quad b_1=b_2\quad and\quad \bold{c_1\ne c_2}[/tex]
so first, we we need to transform the equations to the form where the coefficients at y will be the same:
[tex]kx-3y=4\\ 4x-5y=7\\\\ (kx-3y)\cdot5=4\cdot5\\ (4x-5y)\cdot3=7\cdot3\\\\ 5kx-15y=20\\ 12x-15y=21[/tex]
Now we have b₁=b₂ and c₁≠c₂ so the system has no solution if a₁=a₂
5k = 12
÷5 ÷5
k = ¹²/₅
Preston adopted a cat from a rescue shelter. He needs to buy some cat litter, so he compares prices at different stores. He finds the best deal at Fluffy Felines Pet Shop, which sells a 20-pound jug of cat litter for $8.60. How much does the cat litter cost per pound?
Answer:
$0.43
Step-by-step explanation:
Preston adopted a cat from a rescue shelter
He needs to buy food for his new cat so he compared the price of cat litter at different stores
Preston gets the best deal at fluffy felines pet shop
They sell 20 pound jug litter for $8.60
Therefore the cost of the cat litter per pound can be calculated as follows
= 8.60/20
= 0.43
Hence the cost of the cat litter per pound is $0.43
which of the following is equivalent to sqrt-75
A. -sqrt75
B. 3isqrt5
C. 25sqrt3
D. 5isqrt3
Answer:
D.
Step-by-step explanation:
[tex] \sqrt{-75} = \sqrt{-1 \times 75} = \sqrt{-1 \times 25 \times 3} = 5i\sqrt{3} [/tex]
The square root of the given number is 5i√3. Therefore, option D is the correct answer.
What is the square root?The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.
The given number is √(-75).
Here, √(-75) can be written as √(-25×3)
= 5i√3
Therefore, option D is the correct answer.
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Jack had 3 bags of golf balls with bbb balls in each bag; then his friend gave him 6 more golf balls.
How many golf balls does Jack have now?
Write your answer as an expression.
Answer:
y=3b + 6 ................ . ..
The answer is 3b + 6 in Khan Accademy
4x - 3 ( x - 2 ) = 21
Answer:
x = 15
Step-by-step explanation:
4x - 3 ( x - 2 ) = 21
Distribute
4x -3x +6 = 21
Combine like terms
x+6 = 21
Subtract 6 from each side
x+6-6=21-6
x = 15
Tyler can swim 1/2 mile in 1/3 hour at a constant speed how fast does Tyler swim in miles per hour
Answer:
[tex]Speed = \frac{3}{2}[/tex]mph
Step-by-step explanation:
Given
Distance = [tex]\frac{1}{2}[/tex] mile
Time = [tex]\frac{1}{3}[/tex] hour
Required
Determine the speed
To do this, we simply divide distance by time
[tex]Speed= \frac{Distance}{Time}[/tex]
[tex]Speed = \frac{1}{2} / \frac{1}{3}[/tex]
[tex]Speed = \frac{1}{2} * \frac{3}{1}[/tex]
[tex]Speed = \frac{3}{2}[/tex]
Hence, the speed is [tex]\frac{3}{2}[/tex] mile per hour
Tyler's speed is 1.5 miles per hour.
The formula for speed is:
= Distance / Time
Distance = 1/2 miles
Time = 1/3 hours
Tyler's speed is therefore:
= 1/2 ÷ 1/3
= 1 / 2 x 3/1
= 3/2 miles per hour or.
= 1.5 miles per hour
Tyler's speed is therefore 1.5 miles per hour.
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Determine whether the ratios are equivalent.
18 balloons for every 6 centerpieces
27 balloons for every 9 centerpieces
Answer:
With both ratio= 3
The ratio are equivalent
Step-by-step explanation:
Ratio= number of balloons/ number of centerpieces
For
18 balloons for every 6 centerpieces
Ratio= 18/6
Ratio= 3
For
27 balloons for every 9 centerpieces
Ratio= 27/9
Ratio= 3
Value of each ratio= 3 and 3
3=3
So they are eqtand equivalent
Angle RST is a right angle. Angle RSU has a measure of 25°. Lines R S and S T connect to form a right angle. Another line extends from point S to point U. Angle R S U is 25 degrees. What is the measure of angle TSU? 25° 45° 65° 75°
Answer:
The measure of ∠TSU = 65°
Step-by-step explanation:
Since RST is a right-angled triangle and RS and ST connect to form a right angle, ∠RST = 90°. Also, since RS and ST connect to form a right angle, ∠RST = ∠RSU + ∠TSU.
We make ∠TSU subject of the formula. So,
∠TSU = ∠RST - ∠RSU
Given that angle ∠RSU = 25° and ∠RST = 90°, substituting these values into he expression for ∠TSU, we have
∠TSU = ∠RST - ∠RSU
∠TSU = 90° - 25°
∠TSU = 65°
So, ∠TSU = 65°
The measure of ∠TSU = 65°
Answer:
65
Step-by-step explanation:
you know it forms a right angle because of the marking on it
so take 90 because thats the degree of a right angle, and subtract 25 from it and you will get your other side
90-25=x
65=x
check by adding both angles
65+25=90
prove tan^2 theta - tan^2 phi = (sin^2 theta- sin^2 phi) /cos^2 theta cos^2phi
Answer:
tan^2 theta - tan^2 phi = (sin^2 theta- sin^2 phi) /(cos^2 theta cos^2phi) (identity has been verified)
Step-by-step explanation:
Verify the following identity:
tan(θ)^2 - tan(ϕ)^2 = (sin(θ)^2 - sin(ϕ)^2)/(cos(θ)^2 cos(ϕ)^2)
Hint: | Eliminate the denominator on the right hand side.
Multiply both sides by cos(θ)^2 cos(ϕ)^2:
cos(θ)^2 cos(ϕ)^2 (tan(θ)^2 - tan(ϕ)^2) = ^?sin(θ)^2 - sin(ϕ)^2
Hint: | Express the left hand side in terms of sine and cosine.
Write tangent as sine/cosine:
cos(θ)^2 cos(ϕ)^2 ((sin(θ)/cos(θ))^2 - (sin(ϕ)/cos(ϕ))^2) = ^?sin(θ)^2 - sin(ϕ)^2
Hint: | Simplify the left hand side.
cos(θ)^2 cos(ϕ)^2 ((sin(θ)/cos(θ))^2 - (sin(ϕ)/cos(ϕ))^2) = cos(θ)^2 cos(ϕ)^2 ((sin(θ)^2)/(cos(θ)^2) - (sin(ϕ)^2)/(cos(ϕ)^2)):
cos(θ)^2 cos(ϕ)^2 (sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2) = ^?sin(θ)^2 - sin(ϕ)^2
Hint: | Put the fractions in sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2 over a common denominator.
Put sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2 over the common denominator cos(θ)^2 cos(ϕ)^2: sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2 = (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2)/(cos(θ)^2 cos(ϕ)^2):
cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2)/(cos(θ)^2 cos(ϕ)^2) = ^?sin(θ)^2 - sin(ϕ)^2
Hint: | Cancel down (cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2))/(cos(θ)^2 cos(ϕ)^2).
Cancel cos(θ)^2 cos(ϕ)^2 from the numerator and denominator. (cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2))/(cos(θ)^2 cos(ϕ)^2) = (cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2))/(cos(θ)^2 cos(ϕ)^2) = cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2:
cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2
Hint: | Express cos(ϕ)^2 in terms of sine via the Pythagorean identity.
cos(ϕ)^2 = 1 - sin(ϕ)^2:
1 - sin(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2
Hint: | Express cos(θ)^2 in terms of sine via the Pythagorean identity.
cos(θ)^2 = 1 - sin(θ)^2:
sin(θ)^2 (1 - sin(ϕ)^2) - 1 - sin(θ)^2 sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2
Hint: | Expand (1 - sin(ϕ)^2) sin(θ)^2.
(1 - sin(ϕ)^2) sin(θ)^2 = sin(θ)^2 - sin(θ)^2 sin(ϕ)^2:
sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 (1 - sin(θ)^2) = ^?sin(θ)^2 - sin(ϕ)^2
Hint: | Expand -(1 - sin(θ)^2) sin(ϕ)^2.
-(1 - sin(θ)^2) sin(ϕ)^2 = sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2:
sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 + sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2
Hint: | Evaluate sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 + sin(θ)^2 sin(ϕ)^2.
sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 + sin(θ)^2 sin(ϕ)^2 = sin(θ)^2 - sin(ϕ)^2:
sin(θ)^2 - sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2
Hint: | Come to a conclusion.
The left hand side and right hand side are identical:
Answer: (identity has been verified)
Simplify 3x + 9(X+6) =
help please
Answer:
12x +54
Step-by-step explanation:
3x + 9(X+6) =
Distribute
3x+9x +54
12x +54
Answer:
[tex] 12x + 54[/tex]
Step-by-step explanation:
[tex]3x + 9(x + 6) \\ 3x + 9x + 54 \\ = 12x + 54[/tex]
Write the slope-intercept form of the equation of the line through the given point with the given
slope.
Answer:
6) y = -7x +11
8) y = -1/3x -1
10) y = 5/4x -2
Step-by-step explanation:
It is convenient to start with a point-slope form of the equation.
y = m(x -h) +k . . . . . line with slope m through point (h, k)
__
6) m = -7, (h, k) = (2, -3)
y = -7(x -2) -3 = -7x +14 -3
y = -7x +11
__
8) m = -1/3, (h, k) = (-3, 0)
y = (-1/3)(x -(-3)) +0
y = -1/3x -1
__
10) m = 5/4, (h, k) = (4, 3)
y = 5/4(x -4) +3 = 5/4x -5 +3
y = 5/4x -2
Wakaba buys some granola bars at $0.50 each and energy drinks at $2 each for a group hike. She buys twice as many granola bars as energy drinks. If she spends $27 in total, how many granola bars and energy drinks does she buy?
gronala bars:18
energy drinks:9
Step-by-step explanation:
$0.50 •18= $9
$2.00•9=$18
$9+$18=$27
(10x + бу + 5)
Over 2
Answer:
5x+3y+5/2(5 over 2)
Step-by-step explanation:
Divide 10 by 2
divide 6 by 2
divide 5 by 2 and you stay at 5/2
Answer: 5x+3y+2.5
Step-by-step explanation: 10x+6y+5/2
10/2=5
6/2=3
5/2=2.5
A student has scores of 85,83,98 and 77 on four quizzes. What must she score on the fifth quiz to have an average of at least 84?
She should score more than 77 on the fifth quiz to have an average of at least 84 .
What is average?The average is the middle value of a set of numbers. This isn't to be confused with the median, which is the middle of a set of numbers. The average is the middle value of the numbers. If you need to find the average of a set of numbers, you add them all together and divide by the amount of numbers.
Formula of average:
[tex]Average = \frac{Sum of terms }{Number of terms }[/tex]
According to the question
A student has scores on four quizzes : 85,83,98,77
she score on the fifth quiz to have an average of at least 84
Let fifth quiz score = x
By using formula of average:
[tex]Average = \frac{Sum of terms }{Number of terms }[/tex]
As average should be at least 84
[tex]84 < \frac{85+83+98+77+x }{5 }[/tex]
420 < 343+x
420 - 343 < x
77< x
Therefore,
x should be greater than 77 .
Hence, she should score more than 77 on the fifth quiz to have an average of at least 84 .
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Write the slope intercept form of the equation of the line through (-4,5) and a slope of -2
Answer:
y=-2x-3
Step-by-step explanation:
y-y1=m(x-x1)
Find the value of X. I greatly appreciate your help
Answer:
x = 14
Step-by-step explanation:
comp = add up to be 90
3x + 14 + 2x + 6 = 90
5x + 20 = 90
5x = 70
x = 14
which property of equality was used to solve this equation
[tex]9x = 88 \\ \frac{9x}{9} = \frac{88}{9} \\ x = 9 \frac{7}{9} [/tex]
A. addition property of equality
B. subtraction property of equality
C. multiplication property of equality
D. division property of equality
Answer:
division property of equality.
Step-by-step explanation:
PLEASE HELP! We can translate ()=2|−2|−5 to the right 3 units and up 5 units to create (). Write the equation for function g.
Answer:
[tex]g(x)=2\,|x-5|[/tex]
Step-by-step explanation:
Recall that a horizontal translation (shift) in 3 units to the right involves directly subtracting 3 from the variable x (horizontal axis variable) , and that moving the function up 5 units involves adding to the whole function 5 units. That is:
[tex]g(x)=2\,|x-3-2|- 5+ 5\\g(x)=2\,|x-5|+0\\g(x)=2\,|x-5|[/tex]
Inga knows that the radius of a certain cone is 4 cm and its volume is about 134 cubic centimeters. Which is the best estimate of the cone's height?
Answer:
h=8cm
Step-by-step explanation:
V= πr^2h/3
Where
V=volume of a cone
π=pi= 3.14
r= radius=4cm
h= height = ?
V= πr^2h/3
134= 3.14*4*4*h/3
134= 50.24h/3
Divide both sides by 50.24
h/3= 134 / 50.24
h/3= 2.67
Cross product
h= 2.67*3
h= 8.01
Approximately h= 8cm
The best estimate of the cone's height is 8cm
Please help me! Thanks.
Answer:
129 is yr ANSWER........
Answer:
[tex]\huge \boxed{\mathrm{129\° }}[/tex]
Step-by-step explanation:
Adjacent angles in a parallelogram add up to 180 degrees.
[tex]\mathrm{m \angle A + m \angle B=180}[/tex]
Solving for [tex]\mathrm{m \angle B}[/tex].
[tex]\mathrm{m \angle B=180-m \angle A}[/tex]
[tex]\mathrm{m \angle B}=180-51[/tex]
[tex]\mathrm{m \angle B=129}[/tex]
Jubal wrote the four equations below. He examined them, without solving them, to determine which equation has no solution. 7 x + 1 = 7 x+ 1. 3 x + 2 = 3 x minus 2. 4 x + 1 = 3 x + 8. negative 2 x minus 1 = negative 2 x minus 1. Which of Jubal’s equations has no solution?
Step-by-step explanation:
pls make me as brainliest
Answer: The equation 3x + 2 = 3x - 2 has no solutions.
Step-by-step explanation:
So far, we know that we have four equations, and we have to find one that has no solutions. We can first examine them like Jubal did:
7x + 1 = 7x+ 1
3x + 2 = 3x - 2
4x + 1 = 3x + 8
-2x + 1 = -2x + 1
Just by looking at this, we see here that two of these equations look exactly the same even on the other side of the equation sign:
7x + 1 is the same as 7x + 1 AND
-2x + 1 is the same as -2x + 1
So we know that these are identities, meaning, they have infinitely many solutions. So, they cannot have no solutions because they are the ultimate opposite of that.
Next, looking at the other problems, we see that:
4x + 1 = 3x + 8 AND
3x + 2 = 3x - 2
Let's just take a look at the second equation from this selection. We see that this equation looks almost exactly the same on both sides of the equation sign, EXCEPT that the constants are different ( I mean 2 and -2 ). IF we WERE to add/subtract two from both sides, they wouldn't cancel out but instead leave you with 4. If you had subtracted the 3xs, then you would have been left with 0. So, 0 does NOT equal 6, so therefore, this has no solutions.
And what about 4x + 1 = 3x + 8?
If you just take a look at it, it only has one solution.
Hence, 3x + 2 = 3x - 2 has no solutions.
Andi bakes and sells cupcakes. She charges $24 per
dozen cupcakes. You can have them delivered for an
extra fee of $0.20 per mile. If Andi delivers 5 dozen
cupcakes to a customer and drives 18 miles to their
house, how much did she charge the customer?
Answer:
123.60$
Step-by-step explanation:
Step 1: 24 x 5 = $120
step 2: 18 x .20 = $3.60
step 3: $120 + $3.60 = $123.60
$123.6
Step-by-step explanation:
5 dozen= 5×$24=$120
18 miles=18×$0.20=$3.6
$120+$3.6=$123.6
thus, she charged the customer $123.6
I have a rectangular prism with a height of 30cm, a length of 15cm, and a width of 10cm. What is the volume of my prism? V= Bh B= area of the base of the rectangular prism a= L x W
Answer: V = 4500 cubic units or units^3
Step-by-step explanation:
So far, we know that the givens are:
a height of 30cm, a length of 15cm, and a width of 10cm
So we have to find the volume. The formula for volume is just V = lwh which means that the volume equals the length times the width times the height.
V = (l)(w)(h)
Now, all you have to do is to substitute the given numbers into the equation:
V = (15)(10)(30)
Simplify that:
V = 4500
Put it in the terms:
V = 4500 cubic units or units^3
Hence your answer!
Suppose Q is the midpoint of PR. Use the information to find the missing value. PR = 9x-31 and QR = 43, find x?
Answer:
x=13
Step-by-step explanation:
Q is the midpoint of PR
PQ + QR = PR
PQ= QR
PQ+QR = PR
QF + QR = PR
2QR = PR
2*43 = 9x-31
86 = 9x-31
Add 31 to each side
86+31 = 9x-31+31
117 = 9x
Divide each side by 9
117/9 = 9x/9
13 =x
Answer:
x = 13
Step-by-step explanation:
since Q is the midpoint of PR and QR is 43, then
PR = QR * 2 ⇒ 43 * 2 = 86
PR = 9x - 31
⇒ 9x - 31 = 86
⇒ 9x = 86 + 31
⇒ 9x = 117
Divide both sides by 9 ⇒ [tex]\frac{9x}{9} = \frac{117}{9}[/tex]
⇒ x = 13
VW is the bisector of AY , and they intersect at E. If EY = 3.5, what is AY?
Step-by-step explanation:
this is solutions of your questions
can someone help with number 4 i don’t understand
Answer:
b BA→ and e BC→
Step-by-step explanation:
< ABC
The vertex is B
The angle is formed by rays BA→ and ray BC→
Multiplying two functions results in h(x) = 10x2 + 12x – 16, while adding the same functions results in j(x) = 7x. Which statements describe f(x) and g(x), the original functions? Select two options. Both functions must be linear. Both functions must be quadratic. Both functions must have a y-intercept of 0. The rate of change of either f(x) or g(x) must be 0. The y-intercepts of f(x) and g(x) must be opposites.
Answer:
Both functions must be linear. The y-intercepts of f(x) and g(x) must be opposites.
Step-by-step explanation:
First we need to solve.
h(x) = 10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16
It seems tricky at first but we know a couple things. When we add the factors of h(x) together we get j(x) = 7[tex]x[/tex] so we know that when we multiply 2 numbers together it should equal 10 but add up to 7.
Lets write the possible combinations of 10:
1 x 10 = 10
2 x 5 = 10
5 x 2 = 10
10 x 1 = 10
Now which combination will add or subtract to 7?
1 - 10 = 9 1 + 10 = 11
2 - 5 = -7 2 + 5 = 7 We can stop here!
2 and 5 are in our factor, so let's write it down.
(2x ) (5x ) We know there will one + and one - because the -16. If we had two + it would be positive 16, and is we had two - it would also be positive 16 because a - x - = +
Now the last number is 16. Let's find the possible combinations of 16.
1 x 16 = 16
2 x 8 = 16
4 x 4 = 16 We will stop here because we end up repeating posibilities.
Here is where we think critically. Whichever combination we choose has to be multiplied by 2 and 5 and end up equaling 12. I think 16 is too high so let's try 2 and 8.
2x * 2 = 4x 5x * 8 = 40x Now one is positive and the other is negative. Let's try each combination.
4x - 40x = -36x -4x + 40x = 36x Neither of those are 12x. So let's Try 4 and 4.
2x * 4 = 8x 5x * 4 = 20x One will be positive and the other will be negative. Let's try each combination.
8x - 20x = -12x -8x + 20x = 12x There is our combination! Remeber when you mutiply together you have to multiply the opposite factor. Here are the combinations:
(Ax + B )(Cx + D) = (Ax*Cx) + (Ax*D) + (B*Cx) + (B*D)
(Ax - B )(Cx + D) = (Ax*Cx) + (Ax*D) - (B*Cx) - (B*D)
(Ax + B )(Cx - D) = (Ax*Cx) - (Ax*D) + (B*Cx) - (B*D)
(Ax - B )(Cx - D) = (Ax*Cx) - (Ax*D) - (B*Cx) + (B*D)
So we have:
(2x + 4) (5x - 4)
Let's prove is and multiply it back out.
2x*5x - 2x*4 + 4*5x - 4*4
10[tex]x^{2}[/tex] - 8[tex]x[/tex] + 20
10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16 So we got it right!
Now let's see if they really add up to 7x.
(2x + 4) (5x - 4) which we now need to add together
2x + 4 + 5x - 4 Rearrange
2x + 5x + 4 - 4 Combine like terms
7x + 0 or 7x It works!
So our original functions are f(x) = 2x + 4 and g(x) = 5x - 4
Now to answer the question. Select 2 options.
Both functions must be linear. Yes, because an equation with only an [tex]x[/tex] will be a straight line, if we graph both functions they are both straight lines.
Both functions must be quadratic. No, because a quadratic equation is any equation that can be rearranged in standard form as [tex]ax^{2} + bx +c = 0[/tex] Neither f(x) or g(x) can be rearranged to fit that.
Both functions must have a y-intercept of 0. No, to find the y intercept we set x to 0 and solve for y.
2x + 4 = y 5x - 4 = y
2(0) + 4 = y 5(0) - 4 = y
0 + 4 = y 0 - 4 = y
y = 4 y = -4
Neither are 0.
The rate of change of either f(x) or g(x) must be 0. Let's find the rate of change for each equation.
We need an interval so we have to find one. Let's use 1 and 2 for x, but we have to solve for y to get the coordinate.
f(x[tex]_{1}[/tex]) = 2x + 4 f(x[tex]_{2}[/tex]) = 2x + 4 g(x1) = 5x - 4 g(x2) = 5x - 4
x[tex]_{1}[/tex] = 1 x[tex]_{2}[/tex] = 2 x
y[tex]_{1}[/tex] = 2(1) + 4 y[tex]_{2}[/tex] = 2(2) + 4 y
y[tex]_{1}[/tex] = 2 + 4 y[tex]_{2}[/tex] = 4 + 4 y
y[tex]_{1}[/tex] = 6 y[tex]_{2}[/tex] = 8 y
( 1 , 6 ) ( 2 , 8 ) ( 1 , 1 ) ( 2 , 6 )
Rate of change formula is:
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Now we just plug in for each function.
f(x) = 2x + 4 g(x) = 5x - 4
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = [tex]\frac{8 - 6}{2 - 1}[/tex] = [tex]\frac{2}{1}[/tex] = 2
You can see the rate of change is not 0 for either function.
The y-intercepts of f(x) and g(x) must be opposites. Yes, we solved for the y intercepts earlier.
To find the y intercept we set x to 0 and solve for y.
2x + 4 = y 5x - 4 = y
2(0) + 4 = y 5(0) - 4 = y
0 + 4 = y 0 - 4 = y
y = 4 y = - 4
4 and - 4 are opposites, so this statement is also true.
100 POINTS !!
identify the function family which g belongs:
g(x)=5x-3
a. constant
b. none
c. quadratic
d. linear
e. absolute value
Answer:
d linear
Step-by-step explanation:
It looks a bit like a linear equation
The function g(x) = 5x - 3 is a linear function as the degree of x is one.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
g(x) = 5x - 3 is not a constant it is a function in x.
g(x) = 5x - 3 is not a quadratic function as the degree of x is one.
g(x) = 5x - 3 is also not an absolute function as we can see.
Hence g(x) = 5x - 3 is a linear function as the highest power of x or the degree of x is 1 and it is a linear function in variable x.
learn more about linear functions here :
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can someone plz help?
Answer:
Division property of equality
Step-by-step explanation:
What she did was ;
[tex]\frac{-3x}{-3} =\frac{3}{-3} \\\\x =-1[/tex]
What is da answer?Brainlest to the best answer
Answer:
g(-6)=-13
Step-by-step explanation:
[tex]g(x)=3x+5\\\\x=-6\\\\g(-6)=3(-6)+5\\\\g(-6)=-18+5\\\\g(-6)=-13[/tex]
when the problem says find g(120) and they give you g(x) you just have to put instead of x put 120
so in this case instead of x we put - 6
if
[tex] \frac{ {a}^{2x} }{ {a}^{(x - y)} } =a [/tex]
then y =
Answer:
y= 1-x
Step-by-step explanation:
● (a^2x)/a^(x-y) = a
This means that:
● 2x-(x-y) = 1
● 2x - x +y = 1
● x + y = 1
Substract x from both sides
● x+y -x = 1-x
● y = 1-x