Answer:
6/19
Step-by-step explanation:
19 = total pens (blue pens + green pens + red pens)
6 = total number of blue pens
Maggie owes the clerk $85 dollars. Each of 5 friends will help pay the debt. How much will each friend pay? Find the solution and what it means in the context of the problem.
Clara knows she is 450 yards from the local swimming pool on the map on her phone the pool is 2/3 inch from her current location if her current locations is 4 inches from home on the same map how far is she from home
Clara is 2700 yards far from the home.
How to Calculate Yard and inches?In mathematics, yard and inches are two different units of length. we can say that yard is the one of the measurement of length. Conversion of yard in various quantities is as below:
In inches :1 yard = 36 inches
In feet :1 yard = 3 feet
In meters :1 yard = 0.914 meters
How to solve statement based questions ?For the statement based question first of all try to find out that what is given in the statement and what we have to find out. Now, try to form the statements in the mathematical notation and then solve the equations by performing certain mathematical and algebra operations according to need.
Now, for the given question :
as, Clara is 450 yards from the local swimming pool on the map on her phone and the pool is 2/3 inch from her current location.
Therefore, the pool distance is 450 / (2/3) = 675 yards
Now, distance of current location = 4 inches
Thus, Distance from the home = 675 × 4 = 2700 yards
Hence, Clara is 2700 yards far from the home.
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You walk down a hill for 45 meters. You accomplish this in 9 seconds. What is your velocity?______m/s.
Don't forget to include a negative sign if the answer is negative!
Ex: 10 m/s or -10 m/s. DO NOT USE DECIMALS.
Velocity is 5m/s.
In the given statement is :
You walk down a hill for 45 meters. You accomplish this in 9 seconds. What is your velocity? ______m/s.
Firstly, Let's know the:
What is Velocity?
Velocity refers to the rate of change in displacement with respect to time.
Furthermore, distance and displacement are the key points of the velocity.
Now, Calculate the velocity, by using formula of Velocity
Velocity = Displacement/ time
And, Velocity = 45/9 = 5m/s.
Therefore Velocity is 5m/s
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Given the following piecewise defined functions, evaluate each of the problems below.
h(x) ={7, when x<0
{x+1, when 0 ≤x ≤4
{√x-1, when x>4
1.h(0)
2.h(10)
3.h(-3)
4.h(3)
The values of the functions are h(0) = 1, h(10) = 3, h(-3) = 7 and h(3) = 4
How to evaluate each of the function values from the piecewise function?The piecewise function is given as:
h(x) = {7, when x<0
{x+1, when 0 ≤x ≤4
{√x-1, when x>4
Next, we solve the function values
1. Function h(0)
This means that x = 0
To do this, we make use of h(x) = x + 1 because x= 0 is in its domain
So, we have
h(0) = 0 + 1
h(0) = 1
2. Function h(10)
This means that x = 10
To do this, we make use of h(x) = √x - 1 because x= 10 is in its domain
So, we have
h(10) = √10 - 1
h(10) = √9
h(10) = 3
3. Function h(-3)
This means that x = -3
To do this, we make use of h(x) = 7 because x= -3 is in its domain
So, we have
h(-3) = 7
4. Function h(3)
This means that x = 3
To do this, we make use of h(x) = x + 1 because x= 3 is in its domain
So, we have
h(3) = 3 + 1
h(3) = 4
Hence, the values of the functions are h(0) = 1, h(10) = 3, h(-3) = 7 and h(3) = 4
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What is the value of the function when x = 8?
Enter your answer in the box.
Coordinate grid with a line graphed.
Answer:-4 is your answer
Step-by-step explanation: When x = 8 your y = –4 (which is the function)
Do the circles having the equations (x - 2)2 + y2 = 4 and (x + 2)2 + y2 = 4 intersect on the Cartesian plane? If so, where do they intersect?
Answer: (0,0)
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{(x-2)^2+y^2=4} \atop {(x+2)^2+y^2=4}} \right. \\Hence,\\(x-2)^2+y^2=(x+2)^2+y^2\\(x-2)^2=(x+2)^2\\x^2-2*x*2+2^2=x^2+2*x*2+2^2\\-4x=4x\\-4x+4x=4x+4x\\0=8x\\[/tex]
Divide both parts of the equation by 8:
[tex]0=x[/tex]
Hence,
[tex](0+2)^2+y^2=4\\2^2+y^2=4\\4+y^2=4\\y^2=0\\y=0\\Thus,\ (0,0)[/tex]
Answer:
The two circles intersect at one and only point A(0 , 0)
Step-by-step explanation:
Let ς₁ be the circle of equation :
ς₁ : (x - 2)² + y² = 4
and ς₂ be the circle of equation :
ς₂ : (x + 2)² + y² = 4
Consider the point M (x , y) ∈ ς₁∩ς₂
M ∈ ς₁ ⇔ (x - 2)² + y² = 4
M ∈ ς₂ ⇔ (x + 2)² + y² = 4
M (x , y) ∈ ς₁∩ς₂ ⇒ (x - 2)² + y² = (x + 2)² + y²
⇒ (x - 2)² = (x + 2)²
⇒ x² - 4x + 4 = x²+ 4x + 4
⇒ - 4x = 4x
⇒ 8x = 0
⇒ x = 0
Substitute x by 0 in the first equation:
(0 - 2)² + y² = 4
⇔ 4 + y² = 4
⇔ y² = 0
⇔ y = 0
Conclusion:
The two circles intersect at one and only point A(0 , 0).
Evaluate the expression shown below and write your answer as a fraction in
simplest form.
3/4 - 3/10
Chang wants to plant grass in his backyard. His backyard is in the shape of a rectangle. Its length is 32 feet and its width is 21 feet. Suppose each pack of seed covers 12 square feet. How many packs of seed will he need to cover the backyard?
Answer:
56 packs of seeds
Step-by-step explanation:
To find the area of Chang's backyard, we can use the formula for an area of a rectangle.
Area = length·width or A = lw
32·21 = 672 sq ft.
To find how many packets of seed he will need to cover the backyard, we can take the area of Chang's yard and divide it by how many square feet each pack of seed covers.
672/12 = 56
Chang will need 56 packs of seeds to cover the backyard.
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (×,y) be the unknown endpoint. Apply the midpoint formula, and solve the
two equations for x and y.)
midpoint (=4,5), endpoint (0, - 4)
Answer:
See below
Step-by-step explanation:
For x : from end point to midpoint 0====> 4 is 4 units ...add 4 more to get x = 8 for other endpoint
For y 5====> -4 is - 9 add -9 more to midpoint to get y = -13
doug entered a canoe race. He rowed 3 1/3 miles in 1/3 hour. What is his average speed in miles per hour?
Answer:
10 MPH
Step-by-step explanation:
Doug entered a canoe race. He rowed 3 1/3 miles in 1/3 hour. What is his average speed in miles per hour?
If Doug rowed 3 1/3 miles in 1/3 hour the equation is:
3 1/3x = 1/3
multiply both sides by 3:
3(3 1/3x) = 3(1/3)
10x = 1 hour
Doug rowed 10 MPH
Answer:
10 mile per hour
Step-by-step explanation:
3 1/3 mile = 3.3333333333333333333333333333333 mile
1/3 hour = 0.3333333333333333333333333333333333 hour
divide 3.33333333333333333333333 by 0.3333333333333333333333333
= 3.333333333333333333333333333333333 * 1/.33333333333333333333
= 3.3333333333333333333333333 * 3
= 9.99999999999999999999999
= 10
Rewrite x^4y^2 − 2x^3y^3 using a common factor.
x^2y(xy − 2xy^2)
x^2y^2(x^2 − 2xy)
2xy^2(x^2 − x^2y)
2xy(x^3y − x^2y)
Answer:
x^2y^2(x^2 − 2xy) ..............
The rewritten polynomial of x⁴y² - 2x³y³ is x²y²(x²-2xy).
What is the greatest common factor?The greatest number that can divide the numbers in equal parts.
It is called as greatest common factor.
We have a polynomial,
x⁴y² - 2x³y³.
Factor out the common terms,
x⁴y² - 2x³y³,
= x²y²(x²-2xy)
Therefore, x²y²(x²-2xy) is the required expression.
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Lesson 1.10: Daniel works at least 30 hours a week. He works as a math tutor
and as a teacher. The number of hours Daniel works as a tutor (y) is at most
twice the number he works as a teacher (x).
• Write the set of inequalities that represents the constraints of the situation
and state a point (x, y) that is the feasible region.
The set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)
How to write the set of inequalities that represents the constraints of the situation and state a point (x, y) that is the feasible region.The given parameters are:
Number of hours = at least 30 hours a week
This means that
x + y ≥ 30
Also, we have:
The number of hours Daniel works as a tutor (y) is at most twice the number he works as a teacher (x).
This means that
y ≤ 2x
Substitute y ≤ 2x in x + y ≥ 30
x + 2x ≥ 30
This gives
3x ≥ 30
Divide
x ≥ 10
Substitute x ≥ 10 in y ≤ 2x
y ≤ 2 x 10
Evaluate
y ≤ 20
Hence, the set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)
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at 111111:55\text{ p.m.}55 p.m.55, start text, space, p, point, m, point, end text, thomas ties a weight to the minute hand of a clock. the clockwise torque applied by the weight (i.e. the force it applies on the clock's hand to move clockwise) varies in a periodic way that can be modeled by a trigonometric function. the torque peaks 151515 minutes after each whole hour, when the minute hand is pointing directly to the right, at 3\text{ nm}3 nm3, start text, space, n, m, end text (newton metre, the si unit for torque). the minimum torque of -3\text{ nm}−3 nmminus, 3, start text, space, n, m, end text occurs 151515 minutes before each whole hour, when the minute hand is pointing directly to the left. find the formula of the trigonometric function that models the torque \tauτtau applied by the weight ttt minutes after thomas attached the weight. define the function using radians.
The trigonometric function's formula, which simulates the torque (tau) that the weight applied t minutes after Thomas attached it is
[tex]3 Sin (\frac{2\frac{22}{7} }{60} (t-51))[/tex]
The angular speed of the minutes hand is
[tex]w = \frac{2 (\frac{22}{7}) }{60}[/tex] rad/min
Following the application of weight, the torque as a function of time t is,
[tex]t= t_{0} sin (w (t-5) min)\\ = (3 Nm) sin ((\frac{2 (\frac{22}{7} }{60} ) rad/min (t-5) min)[/tex]
[tex]= (3 Nm) sin ( \frac{2 (\frac{22}{7} }{60} (t-5) rad ) \\= 3 sin (\frac{2 \frac{22}{7} }{60} (t-5)[/tex]
What is torque ?Torque, which is also known as the moment of a force, is the propensity of a force to rotate the body to which it is applied. Force (F) x Distance (r) = Torque is how torque is calculated. The distance (r) between the pivot point and the force's action point. A vector quantity is a torque. As a vector quantity, torque always has a direction that is perpendicular to the plane that contains the vectors of force and displacement.
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What is 9.4 divide. By 4 equal
Answer:2.35
Step-by-step explanation:
The value of the expression is 2.35.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
9.4 ÷ 4
= 9.4/4
= 94/(10 x 4)
= 94/40
= 2.35
Thus,
The value of the expression is 2.35.
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why does the inequality sign have to be flipped when dividing by a negative number?
The inequality sign have to be flipped when dividing by a negative number.
What is inequality?
The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
The given statement is the inequality sign have to be flipped when dividing by a negative number.
According to given question we have
A number that is larger when positive becomes "more negative," and thus smaller when negative, and vice versa.
Dividing by a negative number is the same as dividing by a positive number and then multiplying by −1. Dividing an inequality by a positive number retains the same inequality. But, multiplying by −1 is the same as switching the signs of the numbers on both sides of the inequality, which reverses the inequality:
a<b⟺−a>−b.
Ex:
when dividing both sides by a negative number, we reverse the inequality sign.
Take −3x<9
To solve for x, we divide both sides by −3 and get
x>−3.
Therefore, the inequality sign have to be flipped when dividing by a negative number.
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4(-15).
Which problem would give the same result? Select two options.
15 + 15 + 15 + 15
4 + 4 + 4 + 4
(–1)(15 + 15 + 15 + 15)
(–15) + (–15) + (–15) + (–15)
Answer:
the last two because it needs to be negative
Answer:
The last 2 options
Step-by-step explanation:
4(-15) = -60.
(–1)(15 + 15 + 15 + 15) = -60.
(–15) + (–15) + (–15) + (–15) = -60.
a magician designed an unfair coin so that the probability of getting a head on a flip is $60\%$. if he flips the coin three times, what is the probability that he flips more heads than tails? express your answer as a common fraction.
Probability of getting a head is 60%
More heads than tails means these possibilities are
2 Heads - 1 Tail
3 Heads - 0 Tails
Probability of 2 Heads and 1 Tail = C (3,2) (.60) ^2 (.40)
=3 * (.36) (.40)
=3 * .144
=3 (144/1000)
=3 (18/125)
=54/125
Probability of 3 Heads = (.60) ^3
= .6 (.36)
= .216 = 216 / 1000
= 27 / 125
Hence, total probability = 54 / 125 + 27 / 125
= 81 / 125
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What will be the location of the x value of R' after using the translation rule (x + 4, y - 7), if the pre-image R is located at ( 24, -13)
The location of the x value of R' after using the translation rule is 28
What will be the location of the y value of R' after using the translation rule?The translation rule is given as:
(x + 4, y - 7)
The pre-image of R is located at (24, -13)
Rewrite as
R = (24, -13)
When the translation rule is applied, we have:
R' = (24 + 4, -13 - 7)
Evaluate
R' = (28, -20)
Remove the y coordinate
R'x = 28
Hence, the location of the x value of R' after using the translation rule is 28
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corporation uses trucks to transport bottles from the warehouse to different retail outlets. gasoline costs are per mile driven. insurance costs are per year. calculate the total costs and the cost per mile for gasoline and insurance if the truck is driven (a) miles per year or (b) miles per year. (round the cost per mile to the nearest cent, $x.xx.)
The total cost = $5000 (Option A) and $9400 (Option B)
Cost per mile = $0.33 (option A) and $0.25 (Option B)
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given:
Cost of gasoline for each mile driven = $0.20Cost of insurance for each year = $2000To find: Total costs and cost per mile, when the truck is driven (A) 15000 miles per year (B) 37000 miles per year.
Finding:
(A) By unitary method,
When the truck is driven 1 mile, cost of gasoline = $0.20
When the truck is driven 15000 miles, cost of gasoline = $ 0.20(15000) = $3000 in an year
Cost of insurance in an year = $2000
Thus, total cost = $ 3000 + $2000 = $5000
Now, for per mile cost:
Cost of gasoline = $0.20
Cost of insurance = $0.13
Thus, Cost per mile = $0.20 + $0.13 = $0.33
(B) Again, by unitary method,
When the truck is driven 1 mile, cost of gasoline = $0.20
When the truck is driven 37000 miles, cost of gasoline = $ 0.20(37000) = $7400 in an year
Cost of insurance in an year = $2000
Thus, total cost = $ 7400 + $2000 = $9400
Now, for per mile cost:
Cost of gasoline = $0.20
Cost of insurance = $0.5
Thus, Cost per mile = $0.20 + $0.5 = $0.25
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what is the value of 64 ⅔ ?
Answer:16
explanation:
=64⅔
=(4)3×⅔(there is 3 and 3 will be cancel)
=(4)²(4²=4×4)
=16 Ans
The figure shows three quadrilaterals on a coordinate grid: A coordinate plane is shown. Figure Q is a quadrilateral with sides measuring 5 and 2. Figure S is a quadrilateral with sides measuring 5 and 2. Figure W is a quadrilateral with sides measuring 10 and 4. Which of the following statements is true about the three quadrilaterals? (4 points) a Q and W are similar but not congruent. b W and S are similar and congruent. c W and Q are similar and congruent. d Q and S are similar but not congruent.
Using the concepts of similarity and congruence, the correct statement is given by:
a. Q and W are similar but not congruent.
What are similar figures and what are congruent figures?Similar figures are figures that have the same angles and the same format, for example, all quadrilaterals are similar.Congruent figures are similar and also have equal side lengths.For this problem, we have that:
All the figures are quadrilaterals, hence all the figures are similar.Figures Q and S have the same side lengths, while Figure W has different side lengths. Hence Q and S are congruent, while Q and W and W and S are not.Hence the correct statement is given as follows:
a. Q and W are similar but not congruent.
From the two bullet points, we justify we the other statements are not correct.
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The equation 7(v-5)=-21 is solved in several steps below. For each step, choose the reason that best justifies it.
The solution to the equation is, v = 2.
See the steps explained below.
How to Solve an Equation?Given an equation, 7(v - 5) = -21, the following steps would be taken as shown below:
7(v - 5) = -21 ---> Given
7v - 35 = -21 ----> distribution property
7v - 35 + 35 = -21 + 35 -----> addition property of equality
7v = 14
Divide both sides by 7
7v/7 = 14/7 -----> division property of equality
v = 2
Thus, the solution to the equation as solved above is: v = 2.
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HELP ASAP
Find the coordinates of B
Answer:
the answer is B
Step-by-step explanation:
a baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. the baker wants the volume of the delivery box to be 540 cubic inches. if the width of the delivery box is 3 inches longer than the length and the height is 4 inches longer than the length, what must the length of the delivery box be?
The length of the rectangular solid delivery box is 6 inches.
Volume of a rectangular solid, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units
It is given that, the volume of the delivery box is 540 cubic inches, the width of the delivery box is 3 inches longer than the length and the height is 4 inch longer than the length.
Width of the rectangular solid delivery box = (length + 3) inches
Height of the rectangular solid delivery box = (length + 4) inches
Now,
let us assume that the length of the rectangular solid delivery box is X.
So, Width = (X+3) inches and Height = (X+4) inches.
Volume of rectangular solid delivery box = Length × Width × Height
=> Length × Width × Height = 540 cubic inches.
After putting all the values in the above equation,
=> X × (X+3) × (X+4) = 540
=> X=6 inches
Therefore, the length of the rectangular solid delivery box is 6 inches.
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Mikey spent 20.25 on coffe tagt coat 4.50 per pound how many pounds did mikey buy
Answer:
4.5 lb of coffee
Step-by-step explanation:
4.5/20.25
Can someone please help mee (20 points
brainliest!!!)
Answers:
16.50 for the first box
10 for the second box
======================================
Explanation:
Part (a)
Plug in x = 20 and solve for p.
0.2x+4p = 70
0.2*20+4p = 70
4 + 4p = 70
4p = 70-4
4p = 66
p = 66/4
p = 16.50
They should charge $16.50 per gallon if the demand is 20 million gallons.
------------------------
Part (b)
Let's say the price is initially $10 per gallon. The starting price could be anything you want.
Plug p = 10 into the equation and solve for x.
0.2x+4p = 70
0.2x+4*10 = 70
0.2x + 40 = 70
0.2x = 70-40
0.2x = 30
x = 30/(0.2)
x = 150
The demand is 150 million gallons if the price were $10 per gallon.
Now let's increase the price by $0.50 to get to p = 10.50
Let's solve for x based on this larger value of p.
0.2x+4p = 70
0.2x+4*10.50 = 70
0.2x+42 = 70
0.2x = 70-42
0.2x = 28
x = 28/(0.2)
x = 140
The demand is now 140 million gallons if the price were $10.50 per gallon.
The demand has gone down by 10 million gallons (since 150-140 = 10).
Find the distance between each pair of points. Round to one decimal place. A(-4, 6) and B(3, -7), and E(-6, -5) and F(2, 0).
AB=(
EF=
To one decimal place, round. points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).
The distance between AB is [tex]\sqrt{185}[/tex]=13.601 and EF is [tex]\sqrt{89}[/tex]=9.433.
Given that,
To one decimal place, round.
A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).
We have to find the distance between two points that are AB and EF.
1. The distance between 2 points A and B.
A(-4, 6) and B(3, -7).
Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
Here, x₁=-1,x₂=3 and y₁=6,y₂=-7
After substituting we get,
[tex]\sqrt{{(3 -(-1)} )^{2} +(-7 -6 )^{2} }\\[/tex]
[tex]\sqrt{{(3 +1} )^{2} +(-7 -6 )^{2} }\\[/tex]
[tex]\sqrt{{(4} )^{2} +(-13 )^{2} }\\[/tex]
[tex]\sqrt{16 +163}\\[/tex]
[tex]\sqrt{185}[/tex]
13.601
Therefore, the distance between AB is [tex]\sqrt{185}[/tex]=13.601.
2.The distance between 2 points E and F.
E(-6, -5) and F (2, 0).
Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
Here, x₁=-6,x₂=2 and y₁=-5,y₂=0
After substituting we get,
[tex]\sqrt{{(2 -(-6)} )^{2} +(0 -(-5) )^{2} }\\[/tex]
[tex]\sqrt{{(2 +6} )^{2} +(0 +5 )^{2} }\\[/tex]
[tex]\sqrt{{(8} )^{2} +(5 )^{2} }\\[/tex]
[tex]\sqrt{64 +25}\\[/tex]
[tex]\sqrt{89}[/tex]
9.433
Therefore, the distance between EF is [tex]\sqrt{89}[/tex]=9.433.
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Your friend says that the line with the equation 2x + 3y = 7 has a slope of 2. explain to them the error in their thinking.
Answer:
The error of their thinking is that they did not convert the equation to slope intercept form, so they assumed that the 2x was the slope. They got the standard form mixed up with slope intercept.
I hope this helps you!
HELP ASAP DU TODAY...... WILL GIVE BRAINILIS.
Short Answer
Note: Your teacher will grade your responses to questions 6–7 to ensure that you receive proper credit for your answers.
1. Explain why (4, 1) is not a solution to the equation y = 3x +
2. Pizza costs $1.50 per slice. Use a table and an equation to represent the relationship between the number of slices of pizza bought and the total cost.
Answer: y = 3x+1
Step-by-step explanation: If (4,1) is a solution of y = 3x+1, that means if we plugin the respective values of (4,1), we should have an EQUALITY:
1 = 3(4) + 1
1 = 13 , which is wrong, then the point (4,1) is NOT a solution of y = 3x+1.
Can someone please help mee (20 points + brainliest!!!)
Answer:
A) x = 225 - 7.5p
B) x = 180 millions of gallons
Step-by-step explanation:
A) Make "x" the subject:
[tex]\sf \rightarrow 0.4x + 3p = 90[/tex]
[tex]\sf \rightarrow 0.4x = 90-3p[/tex]
[tex]\sf \rightarrow x = \dfrac{90-3p}{ 0.4}[/tex]
[tex]\sf \rightarrow x = 225-7.5p[/tex]
B) Demand when the price per gallon is $6:
substitute p = 6
[tex]\sf \rightarrow x = 225-7.5(6)[/tex]
[tex]\sf \rightarrow x = 225-45[/tex]
[tex]\sf \rightarrow x =180[/tex]