Answer:
y=-65/9
Step-by-step explanation:
12(5+2y)=4y-(5-9y)
60+24y=4y-5+9y
60+24y=13y-5
60+24y-13y=-5
60+9y=-5
9y=-5-60
9y=-65
y=-65/9
The value of y that satisfies the equation is y = -65/11.
The equation is given as follows:
12(5+2y) = 4y - (5 - 9y)
To find the value of y that satisfies the equation, we can solve for y by simplifying the equation.
Given equation:
12(5 + 2y) = 4y - (5 - 9y)
First, let's simplify both sides of the equation:
60 + 24y = 4y - 5 + 9y
Next, let's combine like terms:
24y - 4y - 9y = -5 - 60
Simplifying further:
11y = -65
Finally, divide both sides of the equation by 11 to solve for y:
y = -65/11
Therefore, the value of y that satisfies the equation is y = -65/11.
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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:
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
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)
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).
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 .
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.
What is the value of y 79° And 37
The value of y is 64°
Solution:
The image of the question is attached below.
Given two angles of a triangle.
One angle is 79°.
Other angle is 37°.
Let the unknown angle be y.
Triangle sum property:
Sum of all the angles of a triangle = 180°
⇒ y + 79° + 37° = 180°
⇒ y + 116° = 180°
⇒ y = 180° – 116°
⇒ y = 64°
Hence the value of y is 64°.
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.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.
6) Happy Paws charges $20.00 plus $2.50 per hour to keep a dog during the day
Woof Watchers charges $9.00 plus $3.75 per hour, Write an equation and solve
it to find for how many hours the total cost of the services is equal, Use the
variable h to represent the number of hours,
Answer:
8.8 hours
Step-by-step explanation:
Given: Happy Paws charges $20.00 plus $2.50 per hour to keep a dog.
Woof Watchers charges $9.00 plus $3.75 per hour.
Lets assume the number of hours service provided be "h".
First, writing an equation for Happy paws cost for service.
Total cost of service= [tex]\$ 2.5\times h+ \$ 20[/tex]--- equation 1
Second, writing an equation for Woof watchers cost of services.
Total cost of service= [tex]\$ 3.75\times h+ \$9[/tex]--- equation 2
Now, finding number of hours services provided, when cost of service will be equal for both service provider.
∴ [tex]2.5h+ 20= 3.75h+ 9[/tex]
Solving the equation now to find number of hour.
⇒ [tex]2.5h+ 20= 3.75h+ 9[/tex]
Subtracting both side by 2.5h
⇒ [tex]20= 3.75h+ 9-2.5h[/tex]
Subtracting both side by 9
⇒ [tex]1.25h= 11[/tex]
Dividing both side by 1.25
⇒[tex]h= \frac{11}{1,25}[/tex]
∴[tex]h= 8.8\ hours[/tex]
Hence, 8.8 hours is the number of hours when cost of service will be equal for both service provider.
Stella owns 120,000 acres of land. She plans to divide 30% of the land to be farm land. How much land does she have that is NOT gonna be farm land?
Answer:
40,000
Step-by-step explanation:120,000 divided by 30% is 40,00 because 120,000 divide by 30 is 40,000
Answer:84,000 acres is NOT gonna be farm land and 36000 acres will be farm land.
Step-by-step explanation:
The parking lot at the theater has 9 rows.There are 40 parking spots in each row. How many cars can park in the parking lot ?
Answer: 360 cars can park in the parking lot.
40 parking spots x 9 rows = 360 cars
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.
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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).
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]
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
if 50% of 2:3 solution of milk and water is replaced with water, then the concentration of the solution is reduced by?
Answer:
Step-by-step explanation:
Let the quantity of milk and water be 40 and 60 respectively.
After removing 50% of solution,
Quantity of milk = 20 and quantity of water = 30
Therefore, the concentration of the solution is reduced from 40 to 20. Hence the solution is reduced by 50%.
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
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
A baseball team played 162 games. They won 44 more games than they lost. How many games did they lose?
Answer:
Step-by-step explanation:
Total game played = 162
Let the games lost be = x
Game won = x + 44
x + x + 44 = 162
2x = 162 - 44
2x = 118
x = 118/2
x = 59
The number of games lost is 59
What is x raised to the 1/2 power multiplied by x raised to the 1/5
Answer:
[tex]x^{3/5}[/tex]
Step-by-step explanation:
[tex]x^{1/2}*x^{1/5}\\[/tex]
Remember, when multipling common variables by an exponent, add the exponents
[tex]x^{\frac{1}{2} + \frac{1}{5}}\\x^{6/10} = x^{3/5}[/tex]
A rectangle is 5 times as longer than it is wide. Its width is three-sixteenths of its perimeter. Find its perimeter.
How do you write y= 1/2 x+2 in standard form?
Answer:
The equation is already in the standard form.
y
=
1
2
y
=
x
+
2
Step-by-step explanation:
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%
A parallelogram has one angle that measures 120°. What are the measures One of three angles in a parallelogram?
Answer:
60 degrees
Step-by-step explanation:
First we need to know how many degrees are in a parallelogram. We can use the formula 180(n-2) (n is the number of sides)
This works out to 180(4-2)=360 degrees.
Now we can set up the following equation as:
2(120)+2x=360 Subtract 240 from both sides to get:
2x=120 Divide by 2 to get:
x=60 degrees
Therefore we know 2 angles are each 120 degrees and the other 2 are 60 degrees.
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
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
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
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
what is 5 1/2-1 2/7 in the simplest form
Answer:
31/14
Step-by-step explanation:
5 1/2 - 1 2/7
By multiplying
5/2 - 2/7
By Elysium
(35-4)/14
31/14
Answer:
[tex]4\frac{3}{14}[/tex]
Step-by-step explanation:
[tex]5\frac{1}{2}-1\frac{2}{7}=\frac{11}{2}-\frac{9}{7}=\frac{77-18}{14}=\frac{59}{14}=4\frac{3}{14}[/tex]
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