Angie makes a spicy salsa by adding red pepper flakes to a chunky tomato mix in proportional amounts. For example, she mixes 1/2 teaspoon of red pepper flakes to 2 cups of tomato mix.
Represent the relationship between red pepper flakes, in teaspoons, to tomato mix, in cups, in two different ways (table, graph, or equation)explain the variables
Answer:
[tex]y = \frac{1}{4}x[/tex]
x y
4 1
8 2
12 3
16 4
Step-by-step explanation:
Angie makes a spicy salsa by adding red pepper flakes to a chunky tomato mix in proportional amounts. For example, she mixes [tex]\frac{1}{2}[/tex] teaspoon of red pepper flakes to 2 cups of tomato mix.
So, the amount of tomato mix in cups is the independent variable represented by x and the amount of red pepper flakes in teaspoon is the dependent variable represented by y and the relation between them is given by y = kx, as the relation is proportional.
Now, putting x = 2 and y = [tex]\frac{1}{2}[/tex], we get
[tex]\frac{1}{2} = 2k[/tex]
⇒ k = [tex]\frac{1}{4}[/tex]
Therefore, the equation is [tex]y = \frac{1}{4}x[/tex] (Answer)
Now, in table the relation will be given by
x y
4 1
8 2
12 3
16 4 (Answer)
The relationship between red pepper flakes and tomato mix can be represented by a table showing different quantities matching the ratio, and by an equation, p = (1/4) * t, which expresses the amount of red pepper flakes (p) needed for any given amount of tomato mix (t).
To represent the relationship between red pepper flakes and tomato mix which Angie uses to make her spicy salsa, we will use a table and an equation.
Table Representation:
Red Pepper Flakes (teaspoons)Tomato Mix (cups)1/22141 1/2628
In the table, the amount of red pepper flakes increases proportionally with the amount of tomato mix. This proportional relationship can also be represented numerically.
Equation Representation:
Let's define p as the amount of red pepper flakes in teaspoons and t as the amount of tomato mix in cups. The ratio given is 1/2 teaspoon of red pepper flakes to 2 cups of tomato mix, which simplifies to 1/4 teaspoon per cup. Thus, the equation is:
p = (1/4) * t
This equation states that for every cup of tomato mix, you use 1/4 teaspoon of red pepper flakes. Therefore, if Angie has t cups of tomato mix, she will need p = (1/4) * t teaspoons of red pepper flakes.
T=42-0.7t how fast did the temperature drop?
The given equation describes a linear relationship between temperature and time. The slope, -0.7, indicates that the temperature is dropping at a rate of 0.7 degrees per unit of time.
Explanation:The equation given, T=42-0.7t, is in the form of a linear equation, y=mx+b, where T is the temperature in degrees Celsius, t is the time, 42 represents an initial temperature, and -0.7 is the slope representing the rate of temperature change over time.
In this equation, the slope, -0.7, tells us that the temperature is decreasing or dropping at a rate of 0.7 degrees per unit of time. This could be per minute, per hour, etc., depending on the context given.
Note that because the '-0.7' is negative, we know that the temperature is decreasing, or dropping, rather than increasing. If it were positive, it would mean the temperature is rising. Thus, when you're asked how fast the temperature is dropping, the answer based on this equation is that it's dropping at a rate of 0.7 degrees per unit of time.
Learn more about Rate of Temperature Change here:https://brainly.com/question/11482539
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The temperature drops at a rate of 0.7 degrees per time unit, as indicated by the coefficient of t in the equation T = 42 - 0.7t.
The equation given, T = 42 - 0.7t, suggests a relationship between temperature (T) and time (t), where the temperature drops over time due to some cooling process, such as a cold front arriving. To determine how fast the temperature is dropping, we look at the coefficient of t in the equation, which is -0.7. This means that for every unit of time that passes, the temperature drops by 0.7 units. Thus, the rate of temperature drop is 0.7 degrees per time unit, assuming the temperature is measured in degrees and time in matching time units (likely minutes or seconds).
Which quadratic function is represented by the graph?
Of(x) = 0.5(x + 3)(x - 1)
f(x) = 0.5(x - 3)(x + 1)
f(x) = 2(x + 3)(x - 1)
f(x) = 2(x - 3)(x + 1)
The correct quadratic function represented by the graph is [tex]\(f(x) = 0.5(x + 1)^2 - 2\)[/tex], and doesn't match with any of the options provided.
To find the quadratic function represented by the given graph, we first identify the vertex and then use it to determine the coefficient [tex]\(a\)[/tex] in the quadratic function.
1. Vertex Calculation:
- The x-coordinate of the vertex, [tex]\(h\)[/tex], is the average of the x-intercepts: [tex]\(h = \frac{1 + (-3)}{2} = -1\).[/tex]
- Since the focus lies 2 units below the vertex, [tex]\(k = -2\).[/tex]
2. Vertex Form of the Quadratic Function:
The vertex form is [tex]\(f(x) = a(x - h)^2 + k\)[/tex], where [tex]\((h, k)\)[/tex] is the vertex.
Substituting [tex]\(h = -1\) and \(k = -2\)[/tex], we get [tex]\(f(x) = a(x + 1)^2 - 2\).[/tex]
3. Determine [tex]\(a\):[/tex]
Using the x-intercept (1, 0):
[tex]\[0 = a(1 + 1)^2 - 2\][/tex]
[tex]\[0 = 4a - 2\][/tex]
[tex]\[4a = 2\][/tex]
[tex]\[a = \frac{1}{2}\][/tex]
4. Quadratic Function:
Substitute [tex]\(a = \frac{1}{2}\)[/tex] into the vertex form:
[tex]\[f(x) = \frac{1}{2}(x + 1)^2 - 2\][/tex]
Therefore, the correct quadratic function represented by the graph is [tex]\(f(x) = 0.5(x + 1)^2 - 2\).[/tex]
The question probable maybe:
Which quadratic function is represented by the graph?
f(x) = 0.5(x + 3)(x - 1)
f(x) = 0.5(x - 3)(x + 1)
f(x) = 2(x + 3)(x - 1)
f(x) = 2(x - 3)(x + 1)
(Given in the attachment)
Altogether Central High School's bands have 40 trumpets and 35 tubas. Carlee says the ratio of trumpets to tubas is 40:35. Danny disagrees and says the ratio is 8:7.
Actually, they are both correct. Explain why these are equivalent ratios.
Answer:
Explanation is given below.
Step-by-step explanation:
Given:
Number of Trumpets = 40
Number of tubas = 35
Carlee says, the ratio of trumpets to tubas = 40 : 35
Danny says, the ratio of trumpets to tubas = 8 : 7
To explain why the two ratios are equivalent.
Solution:
Equivalent ratios are all ratios which are equal to each other in their reduced to simplest form.
The ratio of trumpets to tubas can be given as = [tex]\frac{40}{35}[/tex]
To reduce the ratio to its simplest form, we divide both numbers by their G.C.F.
The G.C.F. for 40 and 35 is 5.
So, we divide numerator and denominator by 5.
⇒ [tex]\frac{40\div5}{35\div 5}[/tex]
⇒ [tex]\frac{8}{7}[/tex]
Thus, the simplest ratio of trumpets to tubas can be given as = 8:7
This is why both Danny and Carlee are correct with the ratios of trumpets to tubas.
Carlee gave the direct ratio, while Danny gave the simplest ratio.
Select all that apply.
What did scribes in medieval Europe do?
became nomadic preachers
copied books and other religious material
kept records and wrote about current events
preserved learning and libraries
developed a way to treat eyestrain
Final answer:
Scribes in medieval Europe had several important roles:
including copying books and religious material, keeping records and writing about current events,preserving learning and libraries.Explanation:
Scribes in medieval Europe had several important roles:
They copied books and other religious material: Scribes were responsible for hand-copying books, particularly ones related to Christian theology, such as the Bible. They also copied classical Greek or Roman writings that would have otherwise been lost. These hand-copied books, known as illuminated manuscripts, were often beautifully illustrated.They kept records and wrote about current events: Scribes also played a crucial role in keeping records and documenting current events. They wrote about important historical and political events, as well as religious and civil information.They preserved learning and libraries: Monasteries, where many scribes worked, became major centers of learning in medieval Europe. Scribes helped preserve knowledge from the ancient world by copying and preserving books. They also contributed to the development of libraries.Jaidyn has read 135of the 180 pgs in the book. What is the percentage of the the book he has read
Answer:
40%
Step-by-step explanation:
180 - 135 = 45
so, 40%
Answer:
25%
Step-by-step explanation:
135/180= .75
because of 100% - 75% = 25%
The graph for the equation y=-2x+1 is shown below. If another equation is graphed so that the system has no solution, which equation could that be
Answer:
B. y = -1/2 (4x + 2)
Step-by-step explanation:
your welcome :) and sorry that I'm a bit late
Find the 20th term of the arithmetic sequence 15, 9, 3, -3, ...
The 20th term is -106
15,9,3,-3,-9,-15,-21,-28,-35,-41,-46 (10) -6 x 10 = -60
-60 + -46
-106
You're just subtracting by 6.
Answer:
-99
Step-by-step explanation:
you subtract by 6 every number.....
-3-6=-9
-9-6=-15
so on and so on until you get to the 20th term.....
Proportions 18/4=x/10
Answer:
x=45
Step-by-step explanation:
18/4 = x/10
[tex]\frac{18}{4}[/tex] = [tex]\frac{x}{10}[/tex]
use cross-multiplication
10*18=180
180/4=45
x=45
To the nearest minute, how long will it take to mow the lawn if 3000yd^2 can be mowed per hour? show your work.
Answer:
[tex]In\ 1\ minute\ lawn\ can\ be\ mowed=50\ yd^2[/tex]
Step-by-step explanation:
[tex]Given,\\\\In\ 1\ hour\ lawn\ can\ be\ mowed= 3000\ yd^2\\\\we\ know\ that\\\\1\ Hour=60\ minutes\\\\In\ 60\ minutes\ lawn\ can\ be\ mowed=3000\ yd^2\\\\In\ 1\ minute\ lawn\ can\ be\ mowed=\frac{3000}{60}\ yd^2\\\\In\ 1\ minute\ lawn\ can\ be\ moved=50\ yd^2[/tex]
Kendra is three times her daughter's age plus seven years Kendra is 49 years old write an equation to find her daughter's age
Answer: [tex]49 = 3x + 7[/tex]
Step-by-step explanation:
Let the daughter's age be x and Kendra's age be y , then from the first statement;
[tex]y = 3x + 7[/tex]
Since Kendra's age is 49 , substitute it into the equation , we have
[tex]49 = 3x + 7[/tex]
subtract t from both sides
[tex]49 - 7 = 3x[/tex]
[tex]42 = 3x[/tex]
divide through by 3
[tex]x = 14[/tex]
Therefore : the daughter's age is 14
Answer:
3x+7=49
Step-by-step explanation:
which inequality is equivalent to -m>_15
Answer:
m<=-15
Step-by-step explanation:
You invested into a content management company that specializes in peer to peer networks four years ago with a stock value
of $56.30 a share. Today, a single share of the company is worth $32.21. Given this information, determine the decay factor
for the four year period and round your answer to the hundredth place.
a 57.0
C. 570
b. 0.57
d. 1.57
Answer:
0.57
Step-by-step explanation:
56.30 divided by 1.57=32.21
If 2y + 6 = 1 −3y, then y = −−−−−−
Answer:
y = -1
Step-by-step explanation:
Add 3y to both sides:
2y + 3y + 6 = 1 - 3y + 3y
Simplify:
5y + 6 = 1
Subtract 6 from both sides to isolate the y value:
5y + 6 - 6 = 1 - 6
Simplify:
5y = -5
Divide by 5 on both sides to solve:
5y/5 = -5/5
Simplify:
y = -1
f(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, ∞) and g(x) = 2x2 + 8x + 6, compare f(x) and g(x). Select the statement that is not correct?
A) Both functions have the same vertex.
B) Both functions have the same domain.
C) Both functions have the same x-intercepts.
D) Both functions are decreasing on the interval (−∞, −2).
Answer:
B) Both functions have the same domain.
C) Both functions have the same x-intercepts.
D) Both functions are decreasing on the interval (−∞, −2).
Step-by-step explanation:
step 1
Find the vertex of f(x)
we know that
The x-coordinate of the vertex is the midpoint of the roots
we have
x=-1 and x=-3
so
the midpoint is
(-1-3)/2=-2
The y-coordinate of the vertex is -4 (because the range is [−4, ∞))
therefore
The vertex of f(x) is the point (-2,-4)
Is a vertical parabola open upward
The vertex is a minimum
The domain is all real numbers
step 2
we have
[tex]g(x)=2x^2+8x+6[/tex]
Find the vertex
Factor the leading coefficient
[tex]g(x)=2(x^2+4x)+6[/tex]
Complete the square
[tex]g(x)=2(x^2+4x+4)+6-8[/tex]
[tex]g(x)=2(x^2+4x+4)-2[/tex]
Rewrite as perfect squares
[tex]g(x)=2(x+2)^2-2[/tex]
Is a vertical parabola open upward
The vertex is the point (-2,-2)
The domain is all real numbers
The range is the interval [−2, ∞)
Find the x-intercepts
For g(x)=0
[tex]0=2(x+2)^2-2[/tex]
[tex]2(x+2)^2=2[/tex]
[tex](x+2)^2=1\\x+2=\pm1\\x=-2\pm1[/tex]
so
The roots or x-intercepts are
x=-1 and x=-3
Verify each statement
A) Both functions have the same vertex
The statement is false
The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)
B) Both functions have the same domain.
The statement is true
The domain is all real numbers
C) Both functions have the same x-intercepts
The statement is true (see the explanation)
D) Both functions are decreasing on the interval (−∞, −2)
The statement is true
Because the x-coordinate of the vertex is the same in both functions, and both functions open upward
Answer:
The answer is A
Step-by-step explanation:
a food truck sells salad for $6.50 each and drinks for $2.00 each. The food truck's revenue from selling a total of 209 salads ans drinks in one day was $836.50. How many salads were sold that day?
Answer:
93
Step-by-step explanation:
s= salads d= drinks
$6.5s + $2d = $836.5
s + d =209
s = 209-d
6.5 (209-d) + 2d = 836.5
1358.5 - 6.5d + 2d = 836.5
-4.5d = -522
d = 116
s = 209 - 116 = 93
PLS HELP ASAP
Determine if the side lengths 9, 9, and 17 form a triangle. If it is a triangle, classify it by its sides.
It's not a triangle.
scalene triangle
isosceles triangle
equilateral triangle
Answer:
To find that a triangle can be made from these measurements you should know that the sum of two of its sides should be greater than the third side.
lets see if this rule applies...
9+9 = 18 ( greater that 17 ; its third side)
17 + 9 = 26 (greater than 9 ; its third side)
therefore, a triangle can be formed
as two of its sides are equal , it is an isosceles triangle
Answer:
isosceles triangle
Step-by-step explanation:
two of its sides are equal
Five percent is the same as 1:20?
No, The answer is 120% and 0.5% = 0.05
Hope this helped!
BTW can I have brainliest
Please Help !
TRYING TO MAKE HONOR ROLL
Which point represents the solution to the system of equations below ?
Answer:
I think its c. but i could be wrong
Ben works in a sandwich shop. On average, he makes 3 sandwiches every 10 minutes. If Ben works 6 hours how many sandwiches will he make?
Answer: 108
Step-by-step explanation:
18 sandwiches are mad every hour then multiply it by 6 .
The interior angles formed by the sides of a hexagon have measures that sum to 720°. What is the measure of angle F? Enter your answer in the box. m∠F= ° An irregular hexagon labeled ABCDEF with angle A parenthesis x minus sixty parenthesis degrees, angle B parenthesis X minus forty parenthesis degrees, angle C one hundred thirty degrees, D one hundred twenty degrees, E one hundred ten degrees, F parenthesis x minus twenty parenthesis degrees
Answer: [tex]m\angle F=140\°[/tex]
Step-by-step explanation:
The missing figure is attached.You know that the sum of the interior angles of an hexagon is 720 degrees.
Based on that and given the figure attached, you can set up the following equation:
[tex](x-60)+(x-40)+130+120+110+(x-20)=720[/tex]
The next step is to solve for "x" in order to find its value. This is:
[tex]x-60+x-40+130+120+110+x-20=720\\\\3x=720-240\\\\3x=480\\\\x=\frac{480}{3}\\\\x=160[/tex]
Now you must substitute the valUe of "x" calculated above, into [tex]m\angle F=(x-20)\°[/tex]:
[tex]m\angle F=(160-20)\°[/tex]
Finally, evaluating, you get that the measure of the angle F is:
[tex]m\angle F=140\°[/tex]
Answer:
114 is the real correct answer
Step-by-step explanation:
May God Bless
sixteen and two-tenth subtracted from two times a number
Step-by-step explanation:
Let the required number = x
To find, the required number = ?
According to question,
∴ 2x - 16 - 2 × 10 = 0
⇒ 2x - 16 - 20 = 0
⇒ 2x - 36 = 0
⇒ 2x = 36
⇒ x = 18
∴ The required number = 18
Thus, the required number is 18.
Answer: x=18
Explanation:
In a class room of 30 students, 18 are female and 12 are male. If you randomly select one person, what is the probability you will select a female
start time 1:20 pm end time 2:00pm elapsed time
Answer:
40 minutes
Step-by-step explanation:
Elapsed time = end time - start time
Elapsed time = 2:00 - 1: 20
Elapsed time = 40 minutes
GIVING BRAINLIEST Consider these proportions: 3:7.5 4:10 5:12.5 6:15 Which of the following proportions belongs to the above set? A 1:2.5 B 2:4.5 C 7:12.5 D 8:20 a. A and B c. C and D b. B and C d. D and A
Answer:
3:7.5 = 1:2.5 = 2:5
4:10 = 2:5
5:12.5 = 10:25 = 2:5
6:15 = 2:5
A and D belong to this set:
A: 1:2.5 = 2:5
D: 8:20 = 2:5
The expression 3(x-9) is equivalent to
O 3(x)+9.
O 3(x)+3(9).
3(%) – 9.
O 3(x) - 3(9)
Answer:
D)
Step-by-step explanation:
3(x-9)=3x-27
3x^+7x-6 factor completely
The factor for given equation [tex]3x^2+7x-6[/tex] is (3x-2) and (x+3).
Step-by-step explanation:
To find the factors of the equation,
1) Multiply the coefficient of the [tex]x^2[/tex] and the constant value.
⇒3×(-6)= -18.
2) Now find two numbers that can result is in -18 while multiplying and 7 (middle term or coefficient of x) while adding.
⇒9 × (-2) = -18.
9+(-2)= 7.
Now spit the equation as[tex]3x^2+9x-2x-6[/tex].
=[tex](3x^2+9x)-(2x-6)[/tex].
=3x(x+3) - 2(x+3).
=(x+3)(3x-2). (by taking out the common term x+3)
∴ The factor for given equation [tex]3x^2+7x-6[/tex] is (3x-2) and (x+3).
Subtract.
6x^2 -5x + 3
- (3x² + 8x-4)
O A. 3x² – 3x+7
O B. 3x² + 134-1
O c. 3x² + 3x - 1
OD. 3x2 - 13x+7
Answer:
6x² - 5x + 3 - (3x² + 8x - 4) = 3x² - 13x + 7
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/Coefficients
Expanding/FactoringStep-by-step explanation:
Step 1: Define
Identify given.
6x² - 5x + 3 - (3x² + 8x - 4)
Step 2: Simplify
[Distributive Property] Distribute negative:∴ we have subtracted the two trionomials!
---
Topic: Algebra I
Answer:
3x²-13×+7
Step-by-step explanation:
hope this helps -olive
Find two consecutive even integers such that the sun of the larger and twice the smaller is 62.
Answer:
20 and 22.
Step-by-step explanation:
Let the consecutive integers be a and b
Then b = a + 2
a is the smaller integer.
[tex]\begin{array}{rcl}2a + b & = & 62\\2a + a + 2& = & 62\\3a + 2 & = & 62\\3a & = & 60\\a & = & \dfrac{60}{3}\\\\& = & \mathbf{20}\\\end{array}[/tex]
a = 20
b = 20 + 2 = 22
The two integers, in ascending order, are 20 and 22.
Check:
2(20) + 22 = 62
40 + 22 = 62
62 = 62
OK.
If 8 = −3r +7r, then r =_____
Answer:
r = 2
Step-by-step explanation:
Given
8 = - 3r + 7r ← combine terms
8 = 4r ( divide both sides by 4 )
2 = r
Answer:
r=2
Step-by-step explanation:
8 = −3r +7r
Step 1: Combine like-terms (-3r + 7r = 4r)
8=4r
Step 2: Divide both sides by 4 to isolate the variable
(8 divided by 4 = 2)
(4r divided by 4 = r)
2=r