Jose can spend no more than 24$ to buy oranges and apples. He will pay 3$ per pound for oranges and $4 per pound for apples. Draw a graph that represents the number of pounds of oranges as the number of pounds of apples Jose can buy.
Hint First, write an inequality. Then, find the x and y intercepts to draw your line. Consider whether you need a solid or dotted line. Do not forget to shade.
Answers
let
x----------------- > number of pounds of apples Jose can buy----> 4$ per pound
y-----------------> number of pounds of oranges Jose can buy----> 3$ per pound
we have that
4x+3y<=24----------------- > this is the inequality required
with x>=0 and y>=0
using a graph tool
see the attached figure
the x-intercept is the point (6,0) maximum number of pounds of apples
the y-intercept is the point (0,8) maximum number of pounds of oranges
The solution is the triangular figure shown in the drawing
Related Questions
Suppose that m∠A = m∠D. Which other fact would guarantee that the triangles are SIMILAR? A) AB DE = CB FE B) m∠C = m∠F C) m∠A + m∠B + m∠C = 180° D) 180° - m∠D = m∠E + m∠F
Answers
The ratio of corresponding sides are similar, that it:
AB/DE=CB/FE=CA/FD
also the corresponding angles should be equal.
hence the answer is:
A] AB/DE=CB/FE and m∠C=m∠F
During dance practice, Sasha drank 21⁄2 pints of water, and on the way home she drank 1⁄2 cup of water. How much water did she drink in total?
Answers
Sasha drank a total of 51⁄2 cups of water by converting the pints to cups and then adding the half cup she drank on the way home.
To calculate the total amount of water Sasha drank, we need to add the volume of water she drank during practice and the volume she drank on the way home. However, we first need to convert the measurements so that they are in the same unit.
There are 2 cups in a pint, so 21⁄2 pints of water is equivalent to 5 cups of water (since 2 pints = 4 cups and 1/2 pint = 1 cup). Adding the additional 1/2 cup she drank on the way home gives us:
5 cups (from 21⁄2 pints)+ 1/2 cup (drank on the way home)
5 + 1/2 = 51⁄2 cups in total
Therefore, Sasha drank a total of 51⁄2 cups of water.
a rectangular prism has a volume of 144 cm3. the base is a square with a length of 4 cm. what is the height of the prism
Answers
Answer:
9 cm
Step-by-step explanation:
The volume is given by the formula ...
V = LWH
Filling in the given numbers, you have ...
144 cm^3 = (4 cm)(4 cm)H
H = (144 cm^3)/(16 cm^2) = 9 cm
The height of the prism is 9 cm.
Determine the distance between point (x1, y1) and point (x2, y2), and assign the result to pointsdistance. the calculation is: distance=(x2−x1)2+(y2−y1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√distance=(x2−x1)2+(y2−y1)2 you may declare additional variables. ex: for points (1.0, 2.0) and (1.0, 5.0), pointsdistance is 3.0.
Answers
d: √ [(x2 - x1) ^ 2 + (y2 - y1) ^ 2]
Example,
for points (1.0, 2.0) and (1.0, 5.0):
d: √ [(1 - 1) ^ 2 + (5 - 2) ^ 2]
d: 3.0
Answer:
the distance between point (x1, y1) and point (x2, y2) is:
d: √ [(x2 - x1) ^ 2 + (y2 - y1) ^ 2]
The volume of a cylinder varies jointly with the square of the radius and the height. If the volume of a cylinder is 50.265 cubic inches when the radius is 2 inches and the height is 4 inches, what is the volume when the radius is 3 inches and the height is 7 inches?
Answers
Answer with Step-by-step explanation:
The volume of cylinder is given by
V=πr²h
Where r is the radius and h is the height
The volume of a cylinder is 50.265 cubic inches when the radius is 2 inches and the height is 4 inches.
50.265=π×2²×4
⇒ π=50.265/16
Now when r=3 inches and h=7 inches
V=π×3²×7
[tex]V=\dfrac{50.265}{16}\times 9\times 7\\ \\V=199.336[/tex]
Hence, volume of the cylinder when the radius is 3 inches and the height is 7 inches is:
199.336 cubic inches
Which pair of expressions is equivalent using the Associative Property of Multiplication? (3 points) 5(3a ⋅ 4) = 15a ⋅ 20 5(3a ⋅ 4) = (3a ⋅ 4) ⋅ 5 5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4 5(3a ⋅ 4) = 5 ⋅ 3a ⋅ 4 6
Answers
Answer:
5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4
Step-by-step explanation:
The Associative Property is applied to two types of operations: addition and multiplication. This property indicates that, when there are three or more terms in these operations, the result does not depend on the way in which the terms are grouped.
In this sense, the associative property for the sum is mathematically given by:
[tex](x+y)+z=x+(y+z)[/tex]
and for the multiplication by:
[tex](xy)z=x(yz)[/tex]
Now, let:
[tex]x=5\\y=3a\\z=4[/tex]
Using the Associative Property of Multiplication:
[tex](xy)z=x(yz)\\\\Replacing\hspace{3}the\hspace{3}values\\\\(5\cdot 3a)\cdot4=5(3a\cdot 4)[/tex]
Therefore the equivalent expressions are:
5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4
Answer: C
Step-by-step explanation: Sorry If I am wrong, ty!!
-☈⊙⌘☿
So I was doing my math homework and I got stuck on this one... Can anyone please help
Answers
That would be (n+5)(n+5)(n+5), which is equal to n3 +125. Hope it helps! :)
Latifah makes $12 per hour. She works 18 hours per week. She calculates that in 4 weeks, she will earn $864. If her hourly rate and weekly hours are rounded to the nearest ten, which amount represents an estimate of the amount she will make over 4 weeks? Is her original calculation reasonable?
Answers
she makes $216 per week. If her hourly rate and weekly hours are rounded to the nearest tenth then it would make her weekly pay $200. Her hourly pay is now $10 and her weekly hours are 20. Now multiply the 20 (weekly hours) by 4 (which would be 4 weeks) 20x4= 80. So 80 hours in 4 weeks. Now her hourly pay is $12 rounded to the nearest tenth = $10 per hour. SOOO the $10 multiplied with the 80= $800 in 4 weeks.
Answer and step-by-step explanation:
Rounding her hourly rate to the nearest ten, we get $10.
Rounding her number of hours to the nearest ten, we get 20.
This gives us an estimate of 10(20)(4) = $800
Her original calculation is reasonable; it is higher because the actual hourly rate is larger than the estimate, so her amount of pay should be higher than the estimate.
John is walking home with his younger brother, Don. Their home is on opposite corner of a rectangle lot with dimensions of 500 feet by 800 feet. John decides to walk along two sides of the lot, While don takes the diagonal path home. About how much farther does john walk than don?
Answers
Diagonal = sqrt ( 500^2 + 800^2) = 943.4 feet.
Distance along 2 sides of rectangle = 500 + 800 = 1300 feet
So John walks 1300 - 943.4 = 356.6 feet more than Don.
The distance that John walk more than Don is 356.60 ft.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.
Given that John is walking home with his younger brother and their home is on opposite corner of a rectangle lot with dimensions of 500 feet by 800 feet.
Since John is walking on the sides, the lenght covered by John will be the sum of the sides.
Sum of the sides of the rectangle = 500 ft + 800 ft
Sum of the sides of the rectangle = 1300 ft
Further, Don is walkin on the diagonal, the lenght covered by Don will be the diagonal of the rectangle.
(Diagonal)² = (500 ft)² + (800 ft)²
(Diagonal)² = 250000 ft² + 640000 ft²
Diagonal² = 890000 ft²
Diagonal = 943.39811 ft
The distance that John walk more than Don is:
Distance = 1300 ft - 943.39811 ft = 356.60 ft
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Which expression is equivalent to(4+6i)^2
Answers
Use the FOIL method
4(4) = 16
4(6i) = 24i
6i(4) = 24i
6i(6i) = 36i², or -36 (note, i² = -1)
24i + 24i = 48i
16 + 48i - 36 = 48i - 20
48i - 20 is your answer
hope this helps
the answer is -20+48i
Find the angles of a rhombus in which a diagonal length is equal to the length of a side.
Answers
We can draw the figure as shown in attachment.
Then you can see an equilateral triangle ABD.
So here angle A, B and D all will be 60 degrees.
So one of the angles of rhombus becomes 60°.
Rhombus is a parallelogram.Hence the adjacent angle becomes 120°.
Finally,angles of rhombus are 60 ,120,60,120.
The diagram represents the floor of a museum. The figure is made up of a rectangle and a triangle.
What is the area of the floor?
Enter your answer in the box.
______ ft2 I'll but the link for the pic
Answers
The figure is formed of a rectangle and a triangle
The rectangle has dimensions:length=38ft and width=20ft
The triangle has dimensions:base=33ft and height=9ft
Area of rectangle=length*width of rectangle
Area of triangle=[tex] \frac{1}{2} [/tex]*base*height
Area of figure= area of rectangle + area of triangle
Area=length*width+[tex] \frac{1}{2} [/tex]*base*height
Area=38*20 + [tex] \frac{1}{2} [/tex]*33*9
Area=760+[tex] \frac{1}{2} [/tex]*297
So we have, Area=760+[tex] \frac{297}{2} [/tex]
Or, Area=760+148.5
Area=908.5
Area of the floor=908.5[tex] ft^{2} [/tex]
Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <1, -2>, v = <-4, 8>
A) Orthogonal
B) Neither
C) Parallel
Answers
u dot v = 1*(-4) + (-2)*8
u dot v = -4 - 16
u dot v = -20
The nonzero dot product tells us that u and v are not orthogonal
u = k*v
<1,-2> = k*<-4,8>
<1,-2> = <-4k, 8k>
1 = -4k implies that k = -0.25
-2 = 8k implies that k = -0.25
The fact we get the same k value each time tells us the two vectors are parallel (they point in the same direction on the compass). One vector is a scaled version of the other.
Answer: C) Parallel
Explain why 1/12+1/12+1/12 is the same as 1/4
Answers
Explanation of why 1/12+1/12+1/12 equals 1/4 through adding fractions with common denominators.
Adding fractions:
Convert all fractions to have a common denominator.
Add the numerators together.
Keep the denominator the same.
Therefore, 1/12 + 1/12 + 1/12 = 3/12 = 1/4.
Solve for Y please!!!
Answers
Using this information, we can make and solve an equation:
8y - 4 = 60° (we know that it is equal to 60°, since it is an equilateral triangle)8y = 64° (we added both sides by 4 to get the y's alone on one side)y = 8° (we divide both sides by 8 to find out what just y is)-------------------------------------------------------------------------------------------------------------Answer:
So y is equal to 8°
Write an equation in slope- intercept form of the line through points S(-7,-6) and T(10,8)
Answers
The slope-intercept form of the line passing through points S(-7,-6) and T(10,8) is calculated by first determining the slope or 'rise over run' which is 14/17. Subsequently, the slope and point T(10,8) are used to find the y-intercept which is -8/17. Hence, the equation of the line is y = 14/17x - 8/17.
Explanation:To create an equation in the slope-intercept form we first need to find the slope or rise over run given our two points S(-7,-6) and T(10,8). The formula to find the slope (m) = (y2 - y1) / (x2 - x1). By substituting the values into the formula we get (8-(-6)) / (10-(-7)) = 14/17, which is our slope (m).
Next, we use the slope (m) and one point, let's take T(10,8), in the equation y = mx + b to find the y-intercept (b). Substituting the known values into the equation gives us 8 = 14/17*10 + b. Solving for b gives us b = -8/17.
Therefore, the slope-intercept form of the line passing through the given points S(-7,-6) and T(10,8) is y = 14/17x - 8/17.
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To write the equation of a line in slope-intercept form, find the slope and y-intercept. For the points S(-7,-6) and T(10,8), the equation is y = (14/17)x + 70/17.
Explanation:To write the equation of a line in slope-intercept form, we need to find the slope (m) and the y-intercept (b). The slope can be found using the formula:
m = (y2 - y1) / (x2 - x1)
After finding the slope, we can substitute it along with one of the given points into the slope-intercept form equation: y = mx + b, where y and x are the coordinates of any point on the line. Solving the equation will give us the value of the y-intercept.
So, for the given points S(-7,-6) and T(10,8),
Find the slope: m = (8 - (-6)) / (10 - (-7)) = 14/17Substitute the slope and one point into the slope-intercept form equation: Solve for b: -6 = -98/17 + b, b = -6 + 98/17, b = 70/17Therefore, the equation in slope-intercept form is: y = (14/17)x + 70/17 Learn more about Equation of a line here:https://brainly.com/question/21511618
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A retired couple invested $6000 in bonds at a simple interest rate of 5.1%. At the end of one year, how much interest did they receive on their investment? Please show your work.
Answers
[tex] \frac{5.1}{100} \times 6000 \\ = 0.051 \times 6000 \\ = 306 \\ 306 + 6000 = 6306[/tex]
they have received $306
The retired couple received $306 in simple interest on their investment of $6000 at a rate of 5.1% for one year.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find the simple interest earned by the retired couple on their investment of $6000 at a rate of 5.1% for one year
we can use the formula: I = P × r × t
where I is the simple interest,
P is the principal (the amount invested),
r is the interest rate (as a decimal), and
t is the time period (in years).
Plugging in the given values, we get:
I = 6000 × 0.051 × 1
I = 306
Therefore, the retired couple received $306 in simple interest on their investment of $6000 at a rate of 5.1% for one year.
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A rectangular park is 5/6 miles wide and 1 5/7 miles long. What is the area of the park?
Please hepl me can't find answer from others!!!!
Answers
5 x 12
6 x 7
60/42
or
10/7
or
1 3/7
Solve the equation on the interval (0,2pi )
2 Sin Θ cos Θ = -1
Answers
To solve the trigonometric equation 2sin(θ)cos(θ) = -1 on the interval (0,2π), use the double angle identity and find the solutions to be θ = π/4 and θ = 3π/4.
Solve the trigonometric equation:
2sin(θ)cos(θ) = -1
Use the double angle identity: sin(2θ) = 2sin(θ)cos(θ)
Substitute and solve to get sin(2θ) = -1
Find the solutions within the given interval (0,2π) which are θ = π/4 and θ = 3π/4.
Three golfers, Vijay, Ernie, and Phil , during five years had a total of 221 top-10 finishes. Ernie had 13 more top-10 finishes than Phil. Vijay had 16 more top-10 finishes than Phil. Determine the number of top-10 finishes for each golfer.
Answers
x: number of top-10 finishes for Vijay.
y: number of top-10 finishes for Ernie.
z: number of top-10 finishes for Phil.
We write the following system of equations:
x + y + z = 221
y = 13 + z
x = 16 + z
Solving the system we have:
Step 1:
x + y + z = 221
(13 + z) + (16 + z) + z = 221
3z + 29 = 221
z = (221-29) / (3)
z = 64
Step 2:
y = 13 + z
y = 13 + 64
y = 77
Step 3:
x = 16 + z
x = 16 + 64
x = 80
Answer:
the number of top-10 finishes for each golfer is:
Vijay: 80
Ernie: 77
Phil 64
Lacie is filling a bucket with water. Which is the best unit for Lacie to use to describe the amount of water in a full bucket? A. millimeters B. milliliters C. liters D. meters
Answers
What is the period of y = 3cot(4x - 3pi)
Answers
The period is π/2.
The period of y = 3cot(4x - 3pi) is π/2 units.
The period of the function y = 3cot(4x - 3π) is calculated as the reciprocal of the absolute value of the parameter in front of x.
To find the period, identify the coefficient of x, which is 4 in this case. The period is then given by 2π/|4| = π/2.
Therefore, the period of the given function y = 3cot(4x - 3π) is π/2 units.
Sam bought 9 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 38 cards left. How many cards did Sam start with?
Answers
He bought 9 new cards:
x + 9
His dog ate half (Which means he also had half left)
0.5(x+9)
There are 38 cards left:
0.5(x+9) = 38
0.5x + 4.5 = 38
0.5x = 38 - 4.5
0.5x = 33.5
x = 33.5 ÷ 0.5
x = 67
So Sam had 67 cards to start off with.
Note: You may want to write 0.5 as half (1/2) .. it is just clumsy to type that, so I kept it as decimal.
what is the probability of obtaining six tails in a row when flipping a coin?
Answers
now, what is the probability of getting Tails AND Tails AND Tails AND Tails AND Tails AND Tails?
well, keep in mind that AND means "times" or the product, so, since the probability of getting tails once is 1/2, the probability of getting tails 6 times in a row is
[tex]\bf \cfrac{1}{2}\cdot \cfrac{1}{2}\cdot \cfrac{1}{2}\cdot \cfrac{1}{2}\cdot \cfrac{1}{2}\cdot \cfrac{1}{2}\implies \cfrac{1}{64}\implies 0.015625\implies 1.5625\%[/tex]
by definition, empirical is equal to
Answers
number of successful trials/ total number of trials
Step-by-step explanation:
Is this the right Answer?
Answers
Figure 1 moves to figure 2 after the translation rule (x,y) ---> (x+1, y+2)
Figure 2 moves to figure 3 after the rotation 90 degrees clockwise around the origin
Figure 3 moves to figure 4 after the translation rule (x,y) ---> (x+2, y-3)
Figure 4 is in quadrant IV. The size does not change
-----------------------------------------------
Answer: Choice B) Quadrant IV; no
What does the graph of f(x)=-(x-3)^2+11 look like
Answers
Answer:
opens downward with a vertex of (3,11)
Step-by-step explanation:
just took the test
Write2/3and3/4 as a pair of fractions with a common denominator
Answers
[tex] \dfrac{2}{3} \times \dfrac{4}{4} = \dfrac{2 \times 4}{3 \times 4} = \dfrac{8}{12} [/tex]
[tex] \dfrac{3}{4} \times \dfrac{3}{3} = \dfrac{3 \times 3}{4 \times 3} = \dfrac{9}{12} [/tex]
Answer: 8/12 and 9/12, respectively.
what is the missing reason in the proof?
Answers
Answer:
Perpendicular bisector theorem
Step-by-step explanation:
Perpendicular bisector theorem: if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints.
So, if segment ST is the perpendicular bisector of segment RV, then, by perpendicular bisector theorem, any point in segment ST (like S) is equidistant from points R and V, in consequence, segments RS and SV are equal.
The volume of a cones is 6 pie, if a cylinder has the same diameter and height as the cone what is it's volume?
Answers
now, notice, the volume of the cylinder is really about the same as the volume of a cone, just 3 times larger, assuming "h"eight and "r"adius for both is the same amount.
now, if we know the cone with that "h" and "r" has a volume of 6π, the cylinder is.... well, you already know.