Nancy and Matilda will meet in 3 hours.
Step-by-step explanation:
Given,
Distance to cover = 60 miles
Speed of Matilda = 12 miles per hour
Speed of Nancy = 8 miles per hour
Combined speed of Nancy and Matilda = 8+12 = 20 miles per hour
Let,
x be the time taken by them
Distance = Speed * Time
[tex]60=20*x\\60=20x\\20x=60[/tex]
Dividing both sides by 20
[tex]\frac{20x}{20}=\frac{60}{20}\\x=3[/tex]
Nancy and Matilda will meet in 3 hours.
Keywords: distance, speed
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In 3 hours Nancy and Matilda meet.
Given
Nancy and Matilda are 60 miles apart, cycling towards each other on the same road.
Matilda rides 12 miles per hour and Nancy rides 8 miles per hour.
What is speed?Speed is defined as the ratio of distance and time.
The time will take to meet Nancy and Matilda is given by;
[tex]\rm \dfrac{12}{8}=\dfrac{x}{60}\\\\8 \times x=60\times 12\\\\8x=720\\\\x = \dfrac{720}{8}\\\\x=90[/tex]
Therefore.
The time taken to meet them is;
[tex]\dfrac{12}{8}+\dfrac{90}{60}\\\\1.5+1.5= 3[/tex]
Hence, in 3 hours will they meet.
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please help!!
I thought it was c but its not
Answer:
Choice D.
82.8
Step-by-step explanation:
We can use law of cosines since we are given three sides.
[tex]z^2=y^2+x^2-2yx \cos(Z)[/tex]
Since [tex]z[/tex] is opposite side of angle [tex]Z[/tex], then [tex]z=12[/tex]:
[tex]12^2=10^2+8^2-2(10)(8) \cos(Z)[/tex]
[tex]144=100+64-160 \cos(Z)[/tex]
[tex]144=164-160 \cos(Z)[/tex]
[tex]-20=-160 \cos(Z)[/tex]
[tex]\frac{-20}{-160}=\cos(Z)[/tex]
[tex]\frac{20}{160}=\cos(Z)[/tex]
[tex]\frac{1}{8}=\cos(Z)[/tex]
[tex]\cos^{-1}(\frac{1}{8})=Z[/tex]
[tex]82.819^\circ=Z[/tex]
Option D is correct.
y intercept of a number that has the points (-30,-9)and a slope of -5/6
Answer:
Y= -5/6 - 9
Step-by-step explanation:
A milk tank is in the form of cylinder whose radius is 1.5 m and length is
7m. Find the quantity of milk in litres that can be stored in the tank.
Answer
49500litres
Step-by-step explanation:
Check attachment
How many triangles can be made with the angle 70°, 70°, and 70°
Is 100 a solution of 10-0.035d > 4? Write a question that solving this problem could answer
Answer:
Therefore d = 100 is a solution of the given equation.
A question that solving this problem could answer is "what is the range of d"
d < 171.43
Step-by-step explanation:
i) the given equation is 10 - 0.035d > 4
ii) if d = 100 then 10 - (0.035[tex]\times[/tex] 100) = 10 - 3.5 = 6.5 > 4
Therefore d = 100 is a solution of the given equation.
A question that solving this problem could answer is "what is the range of d"
10 - 0.035d > 4
therefore -0.035d > 4 - 10
therefore -0.035d > -6
therefore 0.0035d < 6
therefore d < 6 / 0.035 [tex]\Rightarrow[/tex] d < 171.43
Final answer:
100 is a solution to the inequality 10 - 0.035d > 4 because, after substituting d with 100, the inequality 6.5 > 4 holds true.
Explanation:
To determine whether 100 is a solution of the inequality 10 - 0.035d > 4, we substitute d with 100 and check if the inequality holds true:
10 - 0.035(100) > 4
10 - 3.5 > 4
6.5 > 4
Since 6.5 is indeed greater than 4, we can confirm that 100 is a solution to the inequality.
A corresponding question this problem could answer might be: "If a part-time employee loses $0.035 from their savings for each day they work, after how many days will their savings be reduced to less than $4 if they initially had $10?" Solving the inequality would help find the maximum number of days the employee can work before their savings fall below $4.
Natalia Knox tosses a fair die six times. What is the probability that she will toss exactly two 5's?
Answer:
[tex]\large\boxed{\large\boxed{1/36}}[/tex]
Explanation:
1. By definition
Probability = # favorable outcomes / # possible outcomes2. Possible outcomes
The possible outcomes is the sample space. The first toss has 6 possible outcomes and the second toss has other 6 possible outcomes; thus, the sample space has 6 × 6 = 36 different outcomes.
3. Favorable outcomes
Tossing exactly two 5's is just one of the 36 possible outcomes. Thus. the number of favorable otucomes is 1.
4. Computation
Probability = 1/36It takes 23 minutes for 6people to paint 6 walls.
How many minutes does it take 9people to paint 9walls
It would take 9 people 34.5 minutes to paint 9 walls.
23 divided by 6 equals 3.83. That is how many minutes it takes one person to paint one wall. Multiply 3.83 by 9 and you get your answer, 34.5 minutes.
the length of a rectangle is 7 meters more than the width. if the perimeter is 166, what are the length and width?
Answer:
Length = 45
Width = 38
Step-by-step explanation:
2a + 2(a + 7) = 166
4a + 14 = 166
4a = 152
a = 38
a = Width
38 = Width
a + 7 = Length
(38 + 7) = Length
45 = Length
Gerald earns $150.00 per week selling magazine subscriptions. For each subscription he sells, he earns 25% on his total sales (S). If he wants to earn at least $450.00 next week, how much does he need to sell?
Answer:
At least 12
Step-by-step explanation:
25 percent of 150 is 37.50. 0.25 X 150
450/37.5 = 8
Answer:12
Step-by-step explanation:
Find 25% of 150 and then divide 450 with the answer of 25%.
A business owner pays $1,200 per month in rent and a total of $120 per hour in employee salary for each hour the store is open. On average, the store brings in $200 in net sales per hour.
Which equations can be solved to determine the break-even point if C(x) represents the cost function, R(x) represents the revenue function, and x the number of hours per month the store is open?
C(x) = 1,200+120x R(x) = 200x
C(x) = 1,200+120 R(x) = 200x
C(x) = 200x R(x) = 1,200+120x
C(x) = 200x R(x) = 1,200+120
Option A: [tex]C(x)=1,200+120 x R(x)=200 x[/tex] is the equation.
Explanation:
Let x represents the number of hours per month the store is open.
It is given that the the monthly rent(expense) = $1200
Also, the employee salary for each hour(expense) = $120x
Thus, the total expense C(x) is [tex]1200+120x[/tex]
It is also given that the income per hour(revenue) is $200x
Thus, the revenue function R(x) is [tex]200x[/tex]
The break - even point is given by
Total expense = Revenue
Thus, [tex]C(x)=1,200+120 x R(x)=200 x[/tex] is the equation.
Hence, Option A is the correct answer.
Answer:
A
Step-by-step explanation:
Which of the following expressions is equivalent to (12x^4-4x^3+7x+6)+(3x^2-4x+14)
An expression that is equivalent to [tex](12x^4-4x^3+7x+6)+(3x^2-4x+14)[/tex] include the following: D. [tex]12x^4-4x^3+3x^2+3x+20[/tex]
In Mathematics and Euclidean Geometry, the degree of a polynomial function is the highest power among each of its term.
The leading coefficient represents the coefficient of the leading term while the leading term is the term with the highest degree. Also, a constant polynomial is a polynomial that has only a constant term and no variable.
In this exercise and scenario, your are required to add the polynomial functions together.
First of all, we would rearrange the polynomial functions by collecting like terms and then add them together as follows;
[tex]12x^4-4x^3+3x^2-4x+7x+6+14\\\\12x^4-4x^3+3x^2+3x+20[/tex]
Complete Question:
Which of the following expressions is equivalent to [tex](12x^4-4x^3+7x+6)+(3x^2-4x+14)[/tex]?
A [tex]12x^4-x^3+3x+20[/tex]
B [tex]15x^6-8x^4+21x+6[/tex]
C [tex]15x^6-4x^3+3x+20[/tex]
D [tex]12x^4-4x^3+3x^2+3x+20[/tex]
Final answer:
To find the equivalent expression, add like terms from both expressions, resulting in 12x⁴ - 4x³ + 3x² + 3x + 20.
Explanation:
To find the expression equivalent to (12x⁴-4x³+7x+6)+(3x²-4x+14), we simply add the like terms from both expressions.
Firstly, observe that there are no other terms with the same degree as 12x⁴ and -4x³, so they will remain as they are.
Next, add the coefficients of the x terms and the constants: 7x + (-4x) = 3x and 6 + 14 = 20.
However, there's a 3x² term in the second expression which doesn't have a matching term in the first expression, so it also remains unchanged.
Combining all these, the equivalent expression is 12x⁴ - 4x³ + 3x² + 3x + 20.
Which expression is equivalent to 8x + 12y?
Answer:
4(2x+3y)
Step-by-step explanation:
If 2 meters of fabric costs $3.45, what should 7 meters cost?
Answer:
10.07$
Step-by-step explanation:
6 meters of fabric = 10.35
divide 3.45 by 2
1.72
add 1.72+10.35
10.07$
Answer:
Set up a proportion 2m/$3.45 = 7m/x
then cross multiply
7(3.45)=2x
then divide both sides by 2
x=12.075 which is roughly $12.08
Step-by-step explanation:
write 3 different subtraction equations that equal 14.
Answer:
17-3=14
37-23=14
20-6=14
Answer:
15-1=14
48-34=14
137-123=14
Step-by-step explanation:
To check work
14+1=15
14+34=48
14+123=137
What is the solution to the inequality?
−4x−8>−20
A) x>−3
B) x<3
C) x>3
D) x<−3
Add 8 to both sides: -4x>-12
Divide both sides by -4: x>3
Flip the sign since we divided by a negative: x<3
So the correct answer is B
Hope this helped!
Answer:
The answer is B
Step-by-step explanation:
The was done, I did the question and it is right.
Does anyone know this?
Answer:
About 51.43 degrees.
Step-by-step explanation:
In order to find the angle measures, you divide 360 by the number of sides your shape has. In this case you divide 360 by 7.
Please help me due today i beg of u plzz I’m desprate no one would help me
a) The expression for perimeter of rectangle is 4x+34.
b) The expression for area of rectangle is 24x+60.
Step-by-step explanation:
Given figure is a rectangle;
Length of rectangle = 12
Width of rectangle = (x+5)+x = 2x+5
a) Perimeter of model
Perimeter of rectangle = 2(Length + Width)
Perimeter of rectangle = [tex]2(12+2x+5)[/tex]
Perimeter of rectangle = [tex]2(2x+17)[/tex]
Perimeter of rectangle = 4x+34
The expression for perimeter of rectangle is 4x+34.
b) Total area of rectangle
Area of rectangle = Length * Width
Area of rectangle = [tex]12*(2x+5)[/tex]
Area of rectangle = 24x+60
The expression for area of rectangle is 24x+60.
Keywords: area, rectangle
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PLS HELP!!
A graphic designer created a logo on 8 1/2 by 11 inch paper. In order to be placed on a business card, the logo needs to be 1 7/10 by 2 1/5. What is the scale factor of the dilation?
Answer:
0.2 (compression)
Step-by-step explanation:
Given
Length of paper = 11 inches,
Width of paper = 8 1/2 = 17/2 inches
Length of logo = 2 1/5 = 11/5 inches
Width of logo = 1 7/10 = 17/10 inches
Scale factor based on Length
=Length of Logo ÷ Length of paper
= 11/5 ÷ 11
= 0.2 (since it is less than 1, this is a compression)
(Sanity Check: Check width scale factor = length scale factor)
Scale factor based on width
=Width of Logo ÷ Width of paper
= 16/10 ÷ 17/2
= 0.2 (this is the same as the length scale factor so this checks out ok!)
What is two plus two divided by four?
Answer:1
Step-by-step explanation:2+2=4
4/4=1
jack wants to build a square picture frame for his mother if the area of the franks is 49 square inches what is the perimeter
Answer:7
Step-by-step explanation:
7+7+7+7 is 49
Answer:
perimeter is 36
Step-by-step explanation:
49 square root is 9
since it is a square 4 side lengths x 9 = 36
Solve for a side in right triangles
Answer:
2.30
Step-by-step explanation:
The side of interest is opposite the given angle, and the hypotenuse is given. The sine relation tells you ...
sin(A) = a/c
a = c·sin(A) = 3·sin(50°)
a = BC ≈ 2.2981 ≈ 2.30
The number of boys in the classroom is three more than the number of girls if there are 19 students how many are boys and how many are girls
Answer:
11 boys 8 girls
Step-by-step explanation:
There are 19 total students.
There are 3 more boys than girls
girls + 3 = boys ( because there are three more boys)
boys + girls = 19
You can substitute g +3 for b so:
2 girls +3 = 19
19 - 3 = 16
16/2 = girls
8 = girls
Once you find g just subtract the amount of girls from 19 to get the amount of boys.
19 kids - 8 girls = 11 boys
The school marching band has a budget of up to $750 to cover 15 new uniforms and
competition fees that total $300. How much can they spend for one uniform?
a.
Write an inequality to represent this situation.
b.
Solve the inequality and describe what it means in the situation.
a. The inequality 15x+300≤750 represents the situation.
b. It means that the band can spend at most $30 on each uniform without exceeding the budget.
Step-by-step explanation:
Given,
Budget = $750
Competition fee = $300
Uniforms to make = 15
Let,
x be the amount for each uniform.
a. Write an inequality to represent this situation.
Uniforms to make * Cost per uniform + Competition ≤ Budget
15x+300 ≤ 750
The inequality 15x+300≤750 represents the situation.
b. Solve the inequality and describe what it means in the situation.
[tex]15x+300\leq 750\\15x+300-300\leq 750-300\\15x\leq 450[/tex]
Dividing both sides by 15
[tex]\frac{15x}{15}\leq \frac{450}{15}\\x\leq 30[/tex]
It means that the band can spend at most $30 on each uniform without exceeding the budget.
Keywords: inequality, division
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The inequality representing this situation is 15x + $300 <= $750. Solving for x gives x <= $30
The student is interested in determining how much the school marching band can spend on each new uniform given a specific budget constraint. To represent this situation, we need to establish an inequality.
Writing the inequality-
Let's denote the cost of one uniform as x. With 15 uniforms needed and competition fees totalling $300, the inequality that represents the budget situation is:
15x + $300 <= $750
Solving the inequality-
To solve for x, subtract $300 from both sides of the inequality:
15x <= $450
Next, divide both sides by 15:
x \<= $30
This means that they can spend at most $30 for each uniform. The inequality tells us the maximum spending cap for one uniform, ensuring the total cost for all uniforms plus competition fees does not exceed the available budget of $750.
Pleaaassseee help me help my son!!! How do I get the sequence for the next 3 numbers 2,4,8,14,...?
The next three numbers in sequence are 22, 32 and 44
Solution:
Given sequence is:
2, 4, 8, 14, ...
We have to find the next 3 numbers in sequence
Let us understand the logic used in this sequence
[tex]First\ term = 1^2 -1+2 = 1 + 1 = 2\\\\Second\ term = 2^2 -2 + 2 = 4\\\\Third\ term = 3^2 - 3 + 2 = 9 - 1 = 8\\\\Fourth\ term = 4^2 -4 + 2 = 16-2 = 14[/tex]
Thus the formula used is:
[tex]a_n = n^2 - n +2[/tex]
Where, "n" is the location of term in sequence
To find the next three terms:
[tex]Fifth\ term = 5^2 - 5 + 2 = 25 - 3 = 22\\\\Sixth\ term = 6^2 - 6 + 2 = 36 - 4 = 32\\\\Seventh\ term = 7^2 -7 + 2 = 49 - 5 = 44[/tex]
Thus the next three numbers in sequence are 22, 32 and 44
What is the value of x?
Step-by-step explanation:
[tex](8x - 8) \degree \: and \: (7x + 8)\degree \: are \: \\ vertically \: opposite \: angles. \\ vertically \: opposite \: angles \: are \: \\ congruent \\ \therefore \: (8x - 8) \degree \: = \: (7x + 8)\degree \\ \therefore \: 8x - 7x = 8 + 8 \\ \huge \pink{ \boxed{\therefore \: x = 16\degree}}[/tex]
Answer:
16
Step-by-step explanation:
As the angles are vertically opposite
7x + 8 = 8x - 8
x = 16
what is 3 1/5 minus 2 1/4
Answer:
19/20
Step-by-step explanation:
3 1/5 - 2 1/4
16/5 - 9/4
64/20 - 45/20
19/20
Answer: 19/20
Step-by-step explanation:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
3 1/5 becomes 16/5
2 1/4 becomes 9/4
LCD = 20
20+20+20+20+20+10+5+5
the answer to this equation is 120
Answer:
120
Step-by-step explanation:
Three runners run along a 1.5 mile trail one Saturday morning. The graph shows the runner’s locations starting at 9:00 a.m.
Who is at the trail start at 9:00 a.m.?
Answer:
Andy
Step-by-step explanation:
Since hes 0 away from it meaning he’s there
Answer: 1) Andy 2) Caedin 3) 9:08am 4) Berta
Step-by-step explanation: first is Andy because it says “the locations starting at 9am “and the starting point is 0 and Andy is the only one there. Second is Caedin because he decreases at first but increases later on. Third because they started at 9am and the x-axis (minutes) says 8 so it could only mean they cross paths at 9:08am, the last one is Berta because she closest
1. Kelly has a rock garden with a length of 6 feet. She constructs a scale model of the rock garden using the scale 1 inch:2 feet.
(a) What is the length of the garden in her model? Show your work, including your proportion.
(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?
Answer:
(a) 3 inches
(b) Her scale model drawing WILL fit on the piece of paper 8.5 by 7 inches
Step-by-step explanation:
Scaling
We use scales to represent realities in reduced spaces. In the case of lengths or surfaces, the scale allows us to draw the shapes in normal sheets of paper.
(a)
Kelly's rock garden has a length of 6 feet. She uses a 1 inch:2 feet scale. this means that the model length is
6 feet*1 inch/2 feet = 3 inches
(b)
The width of the model is 5 inches, keeping the same scale it means the real length is
5 inches * 2 feet / 1 inch = 10 feet
The model will have 3 inches by 5 inches, it perfectly fits on any regular piece of paper
Indicate whether each statement is true or false by checking the appropriate box in the table below.
Statement
2x is a factor of the expression (2x+y)
(2x+y) is a factor of the expression 3(2x+y).
(2x+y) is a sum of two terms.
3(2x+y) is a product of two terms
Answer:
False, False, True, False
Step-by-step explanation:
The correct statements are:
(2x+y) is a factor of the expression 3(2x+y).
(2x+y) is a sum of two terms.
a) 2x is a factor of the expression (2x+y): False.
2x is not a factor of (2x+y) because it doesn't divide evenly into it.
b) (2x+y) is a factor of the expression 3(2x+y): True.
(2x+y) is a factor of 3(2x+y) because it divides evenly into it.
c) (2x+y) is a sum of two terms: True.
(2x+y) is a sum of the two terms 2x and y.
d) 3(2x+y) is a product of two terms: False.
3(2x+y) is a product of three terms: 3, 2x, and y.
Hence the b and c are the correct statements.
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