The inequality that represent age of marcus is:
[tex]24\geq 6+m\geq 9[/tex]
The possible values for age of Marcus is:
m = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Solution:
Given that,
The sum of ages of Kevin and Marcus was at least 9 years but was at most 24 years
Kevin is 6 years old
Let "m" be the age of Marcus
Thus we frame a inequality as:
[tex]24\geq \text{ sum of ages } \geq 9[/tex]
at least 9 years means that "greater than or equal to 9"
at most 24 years means "less than or equal to" 24
From given,
Sum of ages = kevin age + marcus age
Sum of ages = 6 + m
Thus the inequality is:
[tex]24\geq 6+m\geq 9[/tex]
Solve the inequality
[tex]\mathrm{If}\:a\ge \:u\ge \:b\:\mathrm{then}\:a\ge \:u\quad \mathrm{and}\quad \:u\ge \:b\\\\24\ge \:6+m\quad \mathrm{and}\quad \:6+m\ge \:9\\\\Solve\ them\ separately[/tex]
[tex]24\ge \:6+m\\\\\mathrm{Switch\:sides}\\\\6+m\le \:24\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6+m-6\le \:24-6\\\\\mathrm{Simplify}\\\\m\le \:18[/tex]
Now solve another inequality
[tex]6+m\ge \:9\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6+m-6\ge \:9-6\\\\\mathrm{Simplify}\\\\m\ge \:3\\\\\mathrm{Combine\:the\:intervals}\\\\m\le \:18\quad \mathrm{and}\quad \:m\ge \:3\\\\\mathrm{Merge\:Overlapping\:Intervals}\\\\3\le \:m\le \:18[/tex]
[tex]24\ge \:6+m\ge \:9\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:3\le \:m\le \:18\:\\ \:\mathrm{Interval\:Notation:}&\:\left[3,\:18\right]\end{bmatrix}[/tex]
Thus possible values for age of Marcus is:
m = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Angel walked 1.34 miles from home to school. He then walked 2.12 miles from school to the park. Finally, he walked 1.94 miles from the park back home. Which trip was the furthest distance? Which trip was the shortest distance?
Answer:
The furthest distance was 2.12 miles from school to the park.
The shortest distance was 1.34 miles from home to school.
The furthest distance was from school to the park, and the shortest distance was from home to school.
Explanation:In order to determine which trip was the furthest distance and which trip was the shortest distance, we need to compare the distances of each trip. Angel walked 1.34 miles from home to school, 2.12 miles from school to the park, and 1.94 miles from the park back home.
Comparing the distances, we can see that the trip from school to the park (2.12 miles) was the furthest distance, while the trip from home to school (1.34 miles) was the shortest distance.
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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.
Solve for n: -4 (3n+3) = 5 (-2-6n) -2
Answer:
Step-by-step explanation:
-12n - 12 = -10 - 30n - 2
-12n - 12 = -12 - 30n
-12n = -30n
-12n +30n = 0
18n = 0
n = 0
Answer:
-12n- 20 = -10 - 30n - 2
-12n - 20 = -12 - 30n
18n - 20 = -12
18n = 18
n = 1
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
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:
X-5/5+10 simplify this algebraic expression
Answer: X - 5 ÷ 15
Step-by-step explanation: The first step to algebra is to collect like terms. Since X is an a variable, we cannot solve X - 5. But we can solve 5 + 10, since those are both numbers. 5 + 10 is 15. So therefore, your simplified expression would be X -5 ÷ 15.
Hope this helps! Please correct me if I'm wrong! :D
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:
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)
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
lim x-1 x2 - 1/ sin(x-2)
Answer:
[tex]\lim_{x \to 1}\frac{x^2-1}{sin(x-2)}=0[/tex]
Explanation:
Assuming the correct expression is to find the following limit:
[tex]\lim_{x \to 1}\frac{x^2-1}{sin(x-2)}[/tex]
Use the property the limit of the quotient is the quotient of the limits:
[tex]\lim_{x \to 1}\frac{x^2-1}{sin(x-2)}=\frac{\lim_{x \to 1}x^2-1}{\lim_{x \to 1}sin(x-2)}[/tex]
Evaluate the numerator:
[tex]\frac{\lim_{x \to 1}x^2-1}{\lim_{x \to 1}sin(x-2)}=\frac{1^2-1}{\lim_{x \to1}sin(x-2)}=\frac{0}{\lim_{x \to 1}sin(x-2}[/tex]
Evaluate the denominator:
Since [tex]\lim_{x \to1}sin(x-2)\neq 0[/tex][tex]\frac{0}{\lim_{x \to1}sin(x-2)}=0[/tex]
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%.
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]
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 scientist studied a population of 300 lizards. It was revealed that 25/300 lizards had red spots on their back. Based on the results of her study, how many lizards in the population did NOT have spots on their backs
Answer:
[tex]\frac{11}{12}[/tex]
Step-by-step explanation:
300 - 25 = 275
275/300 = 11/12 simplified
Answer:
11/12
Step-by-step explanation:
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]
Mrs. Morales wrote a test with 19 questions covering spelling and vocabulary. Spelling questions (x) are worth 5 points and vocabulary questions (y) are worth 10 points. The maximum number of points possible on the test is 100.
Part 1 out of 4
Write an equation in slope-intercept form to represent the number of questions on the test.
The equation is .
Answer:
# of questions : y = -x + 19
Step-by-step explanation:
if ur only wanting the equation for the number of questions on the test, then it would be : x + y = 19......y = -x + 19 in slope intercept form.
and if u were wanting the number of points, then it would be :
5x + 10y = 100.....10y = -5x + 100.....y = -1/2x + 10. in slope intercept form
To express the number of questions on Mrs. Morales' test in slope-intercept form, first write the total point equation 5x + 10y = 100, then simplify and solve for y to get the slope-intercept form y = -0.5x + 10.
Explanation:To write an equation representing the number of questions on Mrs. Morales' test, we must consider the total points possible and the value of each question type. The spelling questions (x) are 5 points each, and the vocabulary questions (y) are 10 points each. The total points for the test are 100, which leads us to the equation 5x + 10y = 100.
However, to put this into slope-intercept form, we solve for y. Dividing the entire equation by 10 gives us 0.5x + y = 10. Then, isolating y yields y = -0.5x + 10, which is now in slope-intercept form where the slope (m) is -0.5 and the y-intercept (b) is 10.
The slope-intercept form provides a way to see how many vocabulary questions (y) can be on the test for a given number of spelling questions (x).
One number is 5 more than the other. Their sum is 33. Find the numbers.
Final answer:
The two numbers are 14 and 19, where one number is 5 more than the other and their sum is 33.
Explanation:
To find the two numbers where one number is 5 more than the other and their sum is 33, we can set up a system of equations. Let's call the first number x, which means the second number would be x + 5 since it's 5 more than the first. Their sum is given as 33, so we can create the following equation:
x + (x + 5) = 33
Now we simplify the equation:
2x + 5 = 33
To solve for x, we subtract 5 from both sides:
2x = 33 - 5
2x = 28
Finally, we divide both sides by 2 to find the value of x:
x = 28 / 2
x = 14
Now that we have the first number, we can easily find the second number by adding 5:
The second number is x + 5 = 14 + 5 = 19.
The two numbers are 14 and 19.
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
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.
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°.
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
which of the following is not a common procedure leading to foodborne illness:
a. undercooked foods
b. poor personal hygiene
c. overcooked foods
d. food held at improper temp
C overcooked foods will not
The statement which is not a common procedure leading to foodborne illness is overcooked foods, the correct option is C.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Four options related to foodborne illness
Now,
Out of the four options you gave only one is not a common procedure leading to foodborne illness:
a. undercooked foods b. poor personal hygiene c. overcooked foods d. food held at improper temperature
Overcooked foods may lose some of their nutritional value or taste but they are unlikely to cause foodborne illness unless they are burned or charred which can produce harmful chemicals such as acrylamide or polycyclic aromatic hydrocarbons (PAHs). However this is not a common procedure leading to foodborne illness compared to the other options.
Therefore, by unitary method the answer will be overcooked foods.
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Which numbers are the means of the proportion shown below?
2/3 = 20/30
Answer:
The means are 3 and 20.
Step-by-step explanation:
A proportion is simply a statement that two ratios are equal. In problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. To find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.
Consider given proportion
Here, 2 and 30 are the extremes and 3 and 20 are the means.
Answer:the answer is below
Step-by-step explanation: 3 and 20
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.
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
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
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]
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
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