Answer:
Sonia , John and Keisha bought 3,8 and 5 books respectively.
Step-by-step explanation:
given ,
Sonia paid 2.25 to buy book in yard sale
John paid 6 to buy book in yard sale
Keisha paid 3.75 to buy book in yard sale
cost of 1 book is equal to 0.75 cent
books bought each of them will be equal to
Sonia = [tex]\dfrac{2.25}{0.75}[/tex] = 3 books
John = [tex]\dfrac{6}{0.75}[/tex] = 8 books
Keisha = [tex]\dfrac{3.75}{0.75}[/tex] = 5 books
Hence, Sonia , John and Keisha bought 3,8 and 5 books respectively.
1) Which statement about 5y = 2x is true?
A) The equation represents a direction variation whose consent of variations is 5/2.
B) The equation represents a direct variation whose consent of variations is 2/5.
C) The equation does not represent a direction variation.
D) The equation does not represent a line through the origin.
2) What is the equation of the graph of y = |x| shifted 3 units up?
A) y = |x| – 3
B) y = |x| + 3
C) y = |x + 3|
D) y = |x – 3|
3) Two parallel lines form an inconsistent system of equations that has no solution.
True
or
False
Answer all and Show or Explain your answer :)
write in graphing form please! A parabola that opens down with no stretch factor that has a vertex of (-6,5)
If EG=25 and point F is 2/5 of the way between E and G, find the value FG. The drawing is not to scale.
a. 12.5
b. 10
c. 20
d. 15
d. 7
What is 12.7, 12 3/5 and 12 3/4 form greatest to least
What is the exact value of
Tan 17pi/12
Se implicit differentiation to find an equation of the tangent line to the curve at the given point.7x2 + xy + 7y2 = 15, (1, 1) (ellipse)
A displacement vector with a magnitude of 20. meters could have perpendicular components with magnitudes of
To find the perpendicular components of a displacement vector with a magnitude of 20 meters, use trigonometry and the Pythagorean theorem.
Explanation:The question asks for the perpendicular components of a displacement vector with a magnitude of 20 meters. Perpendicular components of a vector can be determined using trigonometry. Let's assume the vector has components Ax and Ay.
Using the Pythagorean theorem, Ax^2 + Ay^2 = 20^2. Since the components are perpendicular, we can set up a right triangle and solve for the components using the sine and cosine functions. For example, if one component is Ax = 10 meters, the other component Ay can be calculated using Ay = sqrt(20^2 - 10^2) = 10*sqrt(3) meters. Similarly, if one component is Ay = 10 meters, the other component Ax can be calculated using Ax = sqrt(20^2 - 10^2) = 10*sqrt(3) meters.
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The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s. when the length is 20 cm and the width is 10cm, how fast is the area of the rectangle increasing
One number is 4 less than a second number. twice the second number is 19 less than 5 times the first. find the two numbers.
2x+y=25. 3y=2x-13 solve by elimination
Find the angular velocity of a wheel that makes 30 revolutions in 10 seconds.
1.5π rad/sec
3π rad/sec
6π rad/sec
The angular velocity of the wheel is 6π rad/sec.
What is angular velocity?Angular velocity is the speed at which the angle between two bodies changes as an item rotates or revolves around an axis.
In one revolution,
The angular velocity is 2π rad/sec.
In 30 revolutions,
The angular velocity is 2π x 30 rad/ 10sec.
The angular velocity is 60π rad/sec.
The SI unit of angular velocity is radians per second.
Hence, The wheel's angular velocity is 6 rad/sec.
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A sports club is holding a fundraiser dinner. The function graphed models the profit, y, in dollars, from selling x tickets.
Select True or False to describe each statement.
Let
x-------> the number of tickets
y------> the profit in dollars
Let
[tex]A(0,-400)\ B(40,0)[/tex]
Find the slope of the linear equation
The slope is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{0+400}{40-0}[/tex]
[tex]m=10\frac{\$}{ticket}[/tex]
the linear equation is
[tex]y=10x-400[/tex]
Statements
case A) The y-intercept represents the cost per ticket
The statement is false
The cost per ticket represent the slope of the linear equation
The y-intercept is the value of the profit for a number of tickets equal to zero
In this problem the y-intercept is the point [tex](-400,0)[/tex]
case B) The slope represents the money spent before the sale of the first ticket
The statement is False
The slope represents the cost per ticket
the money spent before the sale of the first ticket is the y-intercept
case C) The sports club must sell more than [tex]40[/tex] tickets to make a profit
The statement is True
Because
we know that
For [tex]x=40\ tickets[/tex]
the value of the function is
[tex]y=0[/tex]
in the linear equation
[tex]y=10x-400[/tex]
For [tex]x>40\ tickets[/tex]
the profit will be
[tex]y > 0[/tex] --------> see the graph
therefore
the answer is
The sports club must sell more than [tex]40[/tex] tickets to make a profit
Answer:
the first 2 are false and the last one is true.
Step-by-step explanation:
I took the test :)
PLEASE HELP!!! Will give brainliest!
Solve for x: −3 |x + 7| = −12
A right triangle has one angle that mesures 23. The adjacent leg measures 27.6 cm and the hypotenuse measures 30cm.
What is the approximate area of triangle? Round to the nearest tenth
Area of the triangle =1/2bh
A:68.7cm^2
B.161.7cm^2
c.381.3cm^2
D450.cm^2
Joe bought a length of timber for his fence. He uses 1/5 of the wood for the first garden and 3/8 for the second garden. What fraction of the wood remains for the third garden
Joe used 1/5 of the timber for the first garden and 3/8 for the second garden. After converting these fractions to have a common denominator, we found that 23/40 of the timber was used. Therefore, 17/40 of the timber remains for the third garden.
The student is asking how much of the timber remains after Joe has used some for two gardens. Joe uses 1/5 of the wood for the first garden and 3/8 for the second garden. To solve this, we first add the fractions of wood used for both gardens to find out the total used fraction:
1/5 + 3/8
To add these fractions, we first need to find a common denominator, which in this case is 40. So we convert the fractions:
8/40 + 15/40} = 23/440
Now we subtract the used fraction from the total amount of timber, which is 1:
1 - 23/40 = 40 / 40 - 23 / 40= 17 / 40
Thus, 17/40 of the wood remains for the third garden.
Thomas paid $5 for a multicolor file folders. There were 100 folders in the box .what was the cost of each folder?
What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?
Kevin picked 13 more apples than Andy. if Kevin picked 30 apples, how many did Andy pick ? Let A= the apples sandy picked
A warehouse is packing materials to ship out to a customer. A small box has the dimensions of x inches, (x+ 2) inches and (2x) inches. Where x is the length in inches of width. A large box has the dimensions of (x+5) inches, (x + 7) inches and (3x) inches.
*Recall that Volume = (Length)(Width)(Height)
Part 1: Write an expression that represents the dimensions of the small box.
Part 2: Write an expression that represents the dimensions of the large box.
Part 3: What is the difference in the volumes of the two boxes? Show or explain or work.
1. The expression that represents the dimensions of the small box is (2x³ + 4x²).
2. The expression that represents the dimensions of the large box is (3x³ + 36x² + 105x).
3. The difference in the volumes of the two boxes is (x³ + 32x² + 105x)
What is the volume of the box?1.
Small box:
x inches,
(x+ 2) inches and
(2x) inches
Volume = length × width × height
= x × (x + 2) × (2x)
= (x² + 2x) × 2x
= 2x³ + 4x²
2.
Large box:
(x+5) inches,
(x + 7) inches and
(3x) inches.
Volume = length × width × height
= (x + 5) × (x + 7) × (3x)
= 3x³ + 36x² + 105x
4.
Difference in volume = Large box - Small box
= (3x³ + 36x² + 105x) - (2x³ + 4x²)
= 3x³ + 36x² + 105x - 2x³ - 4x²
= x³ + 32x² + 105x
Therefore, x³ + 32x² + 105x is the expression which represents the volume of the box.
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It is given that a+b=6 and ab=7. Find the value of a^2 + b^2.
When matter changes state, what two things are always conserved?
In a change of state, mass and energy are the two things that are always conserved, in accordance with the law of conservation of matter and the first law of thermodynamics, respectively.
When matter changes state, the two things that are always conserved are mass and energy. This is explained by the law of conservation of matter, which states that the total mass of the products must equal the total mass of the reactants in a chemical reaction, and the law of conservation of energy, often referred to as the first law of thermodynamics.
In any given closed system, neither mass nor energy is created or destroyed, but can be transformed from one form to another. For example, when a substance burns, its matter is not lost but is instead transformed into other substances with the same total mass. Likewise, energy can be moved or transformed, but the total amount of energy remains constant. These principles apply to both living and non-living systems, keeping the total quantity of matter and energy fixed in the universe.
Consider the equation 2x-3(2x-1)=3-4x. solve the equation for x. for each step, identity the property used to write an equivalent equation.
Steven wants to buy a $500 bicycle. Steven has no money saved, but will be able to deposit $45 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $85 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike?
Billie and Toni are driving from Chicago to Phoenix. The first day they drove 420 miles. They want to drive at 65 miles per hour for the rest of their trip. a. Write an algebraic expression to represent the situation. b. If they drive 8 hours a day for the next two days, how far have they traveled by the end of the third day?
A. We are given that they already drove 420 miles and an additional of 65 miles per hour. Therefore distance covered is:
d = 420 + 65 t
where d is distance and t is time
B. If they drove 8 hours per day for 2 days, then total time is t = 16 hours, hence:
d = 420 + 65 * 16
d = 1460 miles
The exchange rate is £1 = €1.12 how many £ would I get for €336
Square tiles 9-inches on a side cover the floor of a rectangular room exactly. the border tiles are white and all other tiles are blue. the room measures 18 feet by 15 feet. how many tiles are white
The scale drawing of a flower bed has the dimensions of 3 inches by 7 inches. The dimensions of the actual flower bed are 36 inches by 84 inches.
What is the scale factor used to find the dimensions of the drawing?
The scale factor used to find the dimensions of the scale drawing is 1/12. This is found by dividing the dimensions of the drawing by the dimensions of the actual flower bed, confirming both scale factors for length and width are equal.
Explanation:The student is asking about determining the scale factor used to create a scale drawing from the actual dimensions of an object, which in this case is a flower bed. To find the scale factor, we compare the dimensions of the drawing with those of the actual object. For the given dimensions of the drawing, which are 3 inches by 7 inches, and the actual dimensions being 36 inches by 84 inches, we can find the scale factors for the length and width separately and confirm they are the same.
For the length, the scale factor is calculated as:
Scale factor for length = Length of drawing / Length of actual object
Scale factor for length = 3 inches / 36 inches = 1/12
For the width, the scale factor is calculated as:
Scale factor for width = Width of drawing / Width of actual object
Scale factor for width = 7 inches / 84 inches = 1/12
Thus, the scale factor for the scale drawing is 1/12. This means that each unit of measurement in the drawing represents 12 units in the actual flower bed.
stella writes 1/7 of a page in 1/5 of a minute. how many minutes doesn’t it take her to write a full page?
It takes Stella 1.4 minutes to write a full page, calculated by setting up a proportion based on her rate of writing [tex]\frac{1}{7}[/tex] of a page in 1/5 of a minute.
Stella writes [tex]\frac{1}{7}[/tex] of a page in [tex]\frac{1}{5}[/tex] of a minute. To calculate how many minutes it takes her to write a full page, we can set up a proportion. Since 7/7 would make a full page, we'd need Stella to write seven times as much as she does in 1/5 of a minute. So, the math to find the time for a full page looks like this:
[tex]\frac{1}{7}[/tex] page : [tex]\frac{1}{5}[/tex] minute = 7/7 page : x minutes
Now multiply both sides by (1/5) minutes to isolate x:
[tex]\frac{1}{7}[/tex] / [tex]\frac{1}{5}[/tex] = 1/x
Cross multiply to solve for x:
[tex]\frac{1}{7}[/tex] * x = [tex]\frac{1}{5}[/tex]
x = [tex]\frac{1}{5}[/tex] / [tex]\frac{1}{7}[/tex]
x = [tex]\frac{1}{5}[/tex] * (7/1)
x = 7/5 minutes
x = 1.4 minutes
Therefore, it takes Stella 1.4 minutes to write a full page.
The town Atlanta needs $14,000 for a new playground Lanzetta Elementary school raise $5358 Lantana middle school race $2834 Atlanta high school raised eig The town Atlanta needs $14,000 for a new playground Lanzetta Elementary school raise $5358 Lantana middle school race $2834 Atlanta high school raised $4132 about how much more do they need to raise choose the best estimate
To find out how much more money is needed for the Atlanta playground, add the amounts raised by each school and subtract from the total amount needed. The schools have raised $12,324, so they still need about $1676. Therefore, $1676 more is required to meet the goal.
Let's calculate how much money the schools have already raised:
Lanzetta Elementary School raised $5358Lantana Middle School raised $2834Atlanta High School raised $4132First, add these amounts together:
$5358 + $2834 + $4132 = $12,324Next, subtract the total amount raised from the total money needed:
$14,000 - $12,324 = $1676Therefore, the town of Atlanta still needs to raise about $1676 for the new playground.