Answer and Step-by-step explanation:
Samantha's recipe has:
3 parts cranapple juice
2 parts lemonade
In total, this recipe has:
t = 3 + 2
t = 5
ratio = [tex]\frac{2}{5}[/tex]
Caden's recipe has
4 parts cranapple juice
3 parts lemonade
In total:
t = 4 + 3
t = 7
ratio = [tex]\frac{3}{7}[/tex]
The punch with stronger lemon taste will be the one whose recipe have a bigger proportion of lemon.
For Samantha's recipe, the proportion is 2 ÷ 5 = 0.4
For Caden's, 3 ÷ 7 = 0.43
Caden's punch will have a slightly stronger taste of lemon, because its proportion is slightly higher than Samantha's.
k(x) = (x + 1)2 – 25
What would this be rewritten in factored form?
Answer:
[tex]k(x)=(x-4)(x+6)[/tex]
Step-by-step explanation:
[tex]k(x)=(x+1)^2-25\\\\[/tex]
to factorize it you have to remember the difference of squares that says
[tex]a^2-b^2=(a-b)(a+b)[/tex]
so we have
[tex](x+1)^2\\\\(x+1)^2=a^2\\\\25\longrightarrow 5^2\\\\5^2=b^2\\\\[/tex]
and we apply the formula
[tex](x+1)^2-25=[(x+1)-5][(x+1)+5]\\\\=(x+1-5)(x+1+5)\\\\=(x-4)(x+6)[/tex]
so there you have it
[tex]k(x)=(x-4)(x+6)[/tex]
What is the equation of the line that passes through the points (−2,4) and (0,3)?
Answer:
y=-1/2x+3
Step-by-step explanation:
What is the lcm of 12 & 9 pls help im in class and i dont have a clue
Answer:
36 is the lcm of this question
can some one plz help me with a queston i posted
Answer:
ok what is it
Step-by-step explanation:
Tell whether the ratios form proportions
4:20 and 6:30
9/18,3/8
9514 1404 393
Answer:
yesnoStep-by-step explanation:
1) Each of the ratios can be reduced to 1 : 5, Since both can be reduced to the same ratio, the do form a proportion.
4 : 20 = 1 : 5
6 : 30 = 1 : 5
__
2) The first ratio can be reduced to 1/2. The second ratio is not 1/2 and cannot be reduced. Since they are different ratios, they do not form a proportion.
9/18 = 1/2
3/8 = 3/8
Tell whether the equation has one, zero, infinitely many solutions.
3 ( y-2) = 3y - 6
infinitely many solutions
Step-by-step explanation:Hi there !
3(y - 2) = 3y - 6
3y - 6 = 3y - 6 | + 6
3y = 3y
true ∀ y ∈ R
Good luck !
Round the factors and estimate the products.
a.
656 x 106 -
น
b. 3,108 x 7,942 -
C.
425 x 9,311 -
what is this i wanna drop out
Answer:
a. 70,000
b. 24,000,000
c. 3,600,000
Step-by-step explanation:
You round all the numbers and multiply the rounded numbers.
So...
a. 656 = 700
106 = 100
7000*100= 70,000
b. 3108 = 3000
7942 = 8000
3000*8000= 24,000,000
c. 425 = 400
9311 = 9000
400*9000= 3,600,000
Can you solve Please ASAP!
Answer:
x = 7/12
Step-by-step explanation:
Write the expression in exponential form with the base of 2
[tex]2x^{3x-3}[/tex] = [tex]32^{3x-2}[/tex]
[tex]2^{3x-3}[/tex] = [tex]2^{15x-10}[/tex]
Since the bases are the same, set the exponents equal
x - 3 = 15 - 10
Move variable to the left-hand side and change its sign
3x - 15x - 3 = -10
Move constant the the right-hand side and change its sign
3x - 15x = -10 + 3
Collect like terms
-12x = -10 + 3
Calculate the sum
-12x = -7
Divide both sides o the equation by -12
x = 7/12
Solution
7/12
Alternate form
x = 0.583
we want to factor the following expression 3x^2-16y^5 which pattern can be used to factor the expression U and V are either constant integers or single variable expressions
Answer: we cant use any patterns
Step-by-step explanation:
Solve for x and y.
(please help asap)
Answer:
x = 4
y = 1
Step-by-step explanation:
At first, let us find the third angle in the triangle which has a right angle and an acute angle of measure 52°
∵ The sum of the interior angles of a triangle is 180°
∴ 52° + 90° + (6x + 14y)° = 180°
→ Add the like terms
∴ 142° + (6x + 14y) = 180°
→ Subtract 142° from both sides
∴ (6x + 14y)° = 38° ⇒ (1)
→ By using the two triangles
∵ The two triangles are congruent
∴ (15x - 8y) = 52° ⇒ (2)
Now we have a system of equations to solve it
→ Multiply equation (1) by 5 and equation (2) by -2 to make the
coefficients of x equal in values and different in signs
∵ 5(6x + 14y) = 5(38)
∴ 30x + 70y = 190 ⇒ (3)
∵ -2(15x - 8y) = -2(52)
∴ -30x + 16y = -104 ⇒ (4)
→ Add equations (3) and (4) to eliminate x
∵ 86y = 86
→ Divide both sides by 86 to find y
∴ y = 1
→ Substitute the value of y in equation (1) to find x
∵ 6x + 14(1) = 38
∴ 6x + 14 = 38
→ Subtract 14 from both sides
∴ 6x = 24
→ Divide both sides by 6
∴ x = 4
Three years ago, Jolene bought $500 worth of stock in a software company. Since then the value of her purchase has been increasing at an average rate of 12 1 2 % per year. How much is the stock worth now? (Round each money calculation you make to the nearest cent.)
Answer:
The stock is worth $702.5.
Step-by-step explanation:
Giving the following information:
Present Value= $500
Number of periods (n)= 3 years
Growth rate (i)= 12%
To calculate the value of the stock today, we need to use the following formula:
FV= PV*(1+i)^n
FV= 500*(1.12^3)
FV= $702.5
The stock is worth $702.5.
An art museum had 275,760 visitors last year. The museum was open every day of the year except for 5 holidays. How many visitors did the museum have each day, on average?
Answer:766 people on average because 275,760 divided 360 because 365=1 year 365-5=360 and 275760/360=766
Step-by-step explanation:
Which of the following is not a way to represent the solution of the inequality 3(2x − 1) greater than or equal to 4(2x − 3) − 3? (1 point)
x less than or equal to 6
6 greater than or equal to x
A number line with a closed circle on 6 and shading to the left
A number line with a closed circle on 6 and shading to the right
Answer:
A number line with a closed circle on 6 and shaded to the right.
Step-by-step explanation:
Answer:a number line with a closed circle on 6 and shading to the right
Step-by-step explanation:I think I’m right! Good luck
A can run 3 miles in 30 minutes. How long will it take
the runner to run 2.5 miles? Use the diagram to explain.
Answer:
It will take her about 25 minutes.
Step-by-step explanation:
30 divided by 3 is ten.
It takes ten minutes to run each miles.
I don't have a diagram, but try drawing a graph with the information.
PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEEEe
Answer:
-140 = x
Step-by-step explanation:
Answer:
-140 =x
Step-by-step explanation:
-5(x) = -4x - 11
please help i don’t understand i need to evaluate the function
Answer:
x=11
Step-by-step explanation:
-5x=-4x-11
-5x+4x=-11
-x=-11
x=11
what is the average rate of change for the line graphed in the figure above
Answer:
5/8
Step-by-step explanation:
I used the slope formula of y2-y1/x2-x1
Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and range of the function.
f(x)= -(x - 9)2 - 23
Answer:
thank u
Step-by-step explanation:
|5x+9|=4x solve for all values of x
Which division problem does the number line below best illustrate?
A number line going from 0 to 2 in increments of 0.2.
2 divided by one-fifth = 10
1 divided by one-fifth = 10
2 divided by one-tenth = 5
1 divided by one-tenth = 5
Answer:
A
Step-by-step explanation:
Hope this helps!!!!!!!!!!!!!!!!!!:)
Answer:
is it C OR A
Step-by-step explanation:
The function r(x) = –0.000345(x – 50)2 + 2.1 can be used to model the curve of a road designed to allow for water to run off in rainstorms depending on the distance from the shoulder of the road, x, in feet. A European firm studying these curves is going to convert feet to meters using the function m(x) = 0.3048x. Which composition can be used to model the curve of the road in terms of meters?
Answer:
- 0.000105156(x - 50)² + 0.64008
Step-by-step explanation:
Given the curve function model : -0.000345(x - 50)² + 2.1 ; Which is measured in feets :
To convert the curve model in feets to metres +, using the function :
m(x) = 0.3048x
Multiply m(x) by r(x)
Hence,
m(r(x)) = 0.3048(-0.000345(x - 50)² + 2.1)
m(x) = - 0.000105156(x - 50)² + 0.64008 ; measured in meters
Frank also has an eraser. It has a mass of 3g, and a volume of 1cm3. What is its density?
Which of the following is the solution to 17 - 2x=-11?
1.)14
2.)-14
3.)-3
4.)3
Choose the correct written expression for: 25 – (3 x 4).
Answer:
13
Step-by-step explanation:
Answer:
25 minus the product of 3 and 4.
Step-by-step explanation:
PEMDAS
and... I just took the test and it was correct answer.
Write the equation of the line in slope-intercept form containing the point (2,4) and with a slope of
3/2.
Answer:
y=3/2x+1
Step-by-step explanation:
y=mx+b is the slope-intercept form
y=3/2x+b
we are looking for b now
plug in the points you provided
2=x, 4=y
4=3/2(2)+b
4=3+b
b=1 which is the intercept
Simplify.
xb2aaayx3yyb3xxabby4x2
Answer:
is that even a real equation?
What is X? −2(x−6)= x+5
Answer:
x=-1
Step-by-step explanation:
-2(x-6)=x+5
-2x-(-12)=x+5
-2x+12=x+15
-2x -----^
x+2x=3x
+15 turns into minus 15
12-15= -3
-3=3x
-1=x
Answer: 7/3 or 2.333333333
Step-by-step explanation:
Distribute -2 to x and -6
-2x + 12 = x + 5
Subtract x from both sides
-3x + 12 = 5
Subtract 12 from both sides
-3x = -7
Divide -3 from both sides
X= 7/3 or 2.333333333
3/4 + 5/6 divided by 2/3
Answer:
2
Step-by-step explanation:
Answer:
Hello
Step-by-step explanation:
The awnser to your question is 2
Amy can run the 150 meter dash in 50 seconds. John can run 1200 meters in 400 seconds. How fast does Amy run. How fast does john run?
Answer:
Amy and John both run 3 meters in 1 second
Step-by-step explanation:
Amy: 150/50=3 meters in 1 second
John: 1200/400=3 meters in 1 second
A fishing boat with two people on it runs out of gas while out in a bay. The people set off an emergency flare from a height of 2 meters above the water. The flare has an initial vertical velocity og 30 meters per second. How long does it take the flare to reach its maximum height? What is that height?
Answer:
Step-by-step explanation:
time taken to reach the max height is expressed according to the projectile equation;
tmax = u/g
Given u = 30m/s
g is the acceleration due to gravity = 9.81
t = 30/9.81
t = 3.0secs
hence it will take the flare 3.06secs to reach its maximum height.
Max height = u²/2g
Max height = 30²/2(9.81)
Max height = 900/19.62
Max height = 45.87m
If the people set off an emergency flare from a height of 2 meters above the water, the total height will be 45.87 + 2 = 47.87m