Answers
Answer: C
Step-by-step explanation:
The HL Theorem states that if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
In this case, 16 is the hypotenuse (the longest side of a right triangle) and 13 is the leg.
Related Questions
You have 140 tomatoes and 13 onions left over from your garden. You want to use these
to make jars of tomato sauce and jars of salsa to sell at a farm stand. A jar of tomato
sauce requires 10 tomatoes and 1 onion, and a jar of salsa requires 5 tomatoes and 1
onion. You will make a profit of $2 on every jar of tomato sauce and a profit of $1.50 on
every jar of salsa sold. The owner of the farm wants at least three times as many jars of
tomato sauce as jars of salsa. How many jars of each should you make to maximize
profit?
3. A company produces two types of tables, T1 and T2. It takes 2 hours to produce the parts
of one unit of T1, 1 hour to assemble and 2 hours to polish. It takes 4 hours to produce
the parts of one unit of T2, 2.5 hour to assemble and 1.5 hours to polish. Per month, 7000
hours are available for producing the parts, 4000 hours for assembling the parts and 5500
hours for polishing the tables. The profit per unit of T1 is $90 and per unit of T2 is $110.
How many of each type of tables should be produced in order to maximize the total
monthly profit?
Answers
1. To maximize the profit :
28 jars of salsa and
0 jars of tomato sauce should be made.
which make maximum profit of $42.
2. In order to maximize the total monthly profit
2300 units of T₁ type table and and
600 units of T₂ type table should be made
which provide maximum profit of $273000.
What is an Inequality?In Algebra, inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa. If the relationship between two algebraic expressions is defined using the inequality symbols, then it is called literal inequalities.
1. Let x be the numbers of jars of tomato sauce
Let y be the number of jars of salsa sauce
Profit P(x, y)=2x+1.5y
x≥0
y≥0
10x+5y≤140
x + y ≤13
The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.
A at (0,13)
B at (0,28)
C at (14,0)
D at (15,0)
E at (15, -2)
Evaluate profit P(x, y) at each vertex
A at (0,13):P(0,13)=$19.5
B at (0,28):P(0,28)=$42
C at (14,0):P(14,0)=$28
D at (15,0):P(15,0)=$30
E at (15, -2):P(15,-2)=30-3=$27
The maximum profit of $42 is at vertex B.
Which means production of 28 jars of salsa and 0 jars of tomato sauce provides maximum profit of $42.
2. Let x be the number of tables of type T₁
and y the number of tables of type T₂
Profit P(x, y)=90x+110y
x≥0
y≥0
2x+4y≤7000
x+2.5y≤4000
2x+1,5y≤5500
The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.
A at (0,0)
B at (0,1600)
C at (1500,1000)
D at (2300,600)
E at (2750,0)
Evaluate profit P(x, y) at each vertex
A at (0,0):P(0,0)=0
B at (0.1600):P(0,1600)=90(0)+110(1600)=176000
C at (1500,1000):P(1500,1000)=90(2500)+110(1000)=245000
D at (2300,600):P(2300,600)=90(2300)+110(600)=273000
E at (2750,0):P(2750,0)=90(2750)+110(0)=247500
The maximum profit of $273000 is at vertex D.
which means production of 2300 tables of type T₁ and 600 tables of type T₂ makes maximum profit.
1. Hence, maximum profit is made by making
28 jars of salsa and
0 jars of tomato sauce getting
$42 of profit.
2. Hence the company needs to produce
2300 tables of type T₁ and
600 tables of type T₂,
in order to maximize its monthly profit which is equal to $273000.
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-2y - 10 = x -10x
- y = −14
Answers
Answer:
Step-by-step explanation:
-2y-10=x-10x
-2(-14) - 10= x - 10x
28 - 10 = x - 10x
18= x-10x
18= -9x
/-9 /-9
-2=x
Each side when you plug in (-2) for x and (-14) for y you get 18.
If, when you plug in the number, you get different numbers for each side, then that means there's a mistake and the answer is wrong.
Hope this helps!
What is the name of the point where the two axes cross?
Answers
As per the concept of graph, the name of the point where the two axes cross is origin.
Graph in math is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Here we have to identify the name of the point where the two axes cross.
As we all know that the horizontal axis in the coordinate plane is called the x-axis and the vertical axis is called the y-axis.
Here we have also know that the point at which the two axes intersect is called the origin.
Where the origin is at 0 on the x-axis and 0 on the y-axis.
And these intersecting x- and y-axes divide the coordinate plane into four sections
Finally all these four sections are called quadrants.
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Philip is having a party and wants to spend less than $572. He has already spent $500. The only item left on his list is sodas, which cost $8 per case. How many cases of soda, x, can Philip purchase and stay under his budget? Select the number line that includes the largest number of cases of soda that Philip can purchase and still stay under his budget.
Answers
Answer:
x = 8
Step-by-step explanation:
572 - 500 = 72
72 / 8 = 9.
But in order to spend less than 572, he has to buy 8 cases. If he buys 9 cases he will be exactly 572.
Answer:
9 or fewer cases
Step-by-step explanation:
Solving a two step equation:
First, determine how much he has left to spend
572 - 500 = 72
He has 72 dollars left to spend on soda
Each case is 8 dollars.
Divide how much he has to spend by the cost of each case
72/8 = 9
He can buy up to 9 cases and stay under budget.
help please (photo attached)
Answers
Answer:
slope = -1
Step-by-step explanation:
any 2 points:
(2,2) (0,4)
to find the slope we use the formula:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
slope is:
2/-2 = -1
Answer:
The slope is =
2/-2 = -1
Step-by-step explanation:
Also i hope you have a wonderful day !
If 2x − 1 ≤ f(x) ≤ x2 − 2x + 3 for x ≥ 0, find lim x→2 f(x).
Answers
The limit as x approaches 2 or lim x→2 is 4.
When calculating a limit, the goal is to find the value of the function as x approaches the given value. In this case, the given value is 2. As x approaches 2, the values of the function will approach 4, which is the upper bound of the given inequality. This means that the limit as x approaches 2 is 4.
To prove this, we can look at the inequality and find the values of the function at x = 1 and x = 3. For x = 1, the function value is -1, which is less than 4. For x = 3, the function value is 7, which is greater than 4. This means that the function values are increasing as x gets closer to 2, so the limit as x approaches 2 is 4.
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The figure shows two circles, with centers A and B, externally tangent at point C. The common tangents to the two circles meet at point P and AP = 30. If the radius of the circle with center A is 10, what is the length of BP?
Answers
The length of the line segment BP = 15 using the trigonometric ratio of sine for the angle P.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the right triangles formed by points at P, A and the tangent to the bigger circle with its radius as base;
radius r = 10 and hypotenuse AP = 30
sinP = 10/30 {opposite/hypotenuse}
sinP = 1/3
Also for the smaller circle, with right triangle formed by points at P, B and the tangent to the smaller circle with its radius as base;
radius r and hypotenuse BP = 20 - r
sinP = r/(20 - r)
1/3 = r/(20 - r)
3r = 20 - r {cross multiply}
3r + r = 20 {collect like terms}
4r = 20
r = 20/4 {divide through by 4}
r = 5
BP = 20 - 5
BP = 15
Therefore, length of the line segment BP is derived using the trigonometric ratio of sine as 15.
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An amusement park has a two merry-go-rounds. The first merry-go-round has a circular platform with a diameter of 13 meters. The second merry-go-round has a circular platform with a diameter of 19 meters. What is the difference between the areas of the larger and smaller merry-go-round’s platform?
Answers
Answer:
150.72
Step-by-step explanation:
Area of circle formula is r²π
Do find radius you do d/2, diameter/2. 13/2= 6.5
6.5 * 6.5 = 42.25
π is also known as 3.14
42.25 * 3.14 = 132.665
That is the area of the smaller one.
For the larger one, 19/2 = 9.5
9.5 * 9.5 = 90.25
90.25 * 3.14= 283.385
Now you subtract both of them and the difference is 150.72.
Hope this helps !!
-Ketifa
Answer
150.72 m2
Step-by-step explanation:
Find the radius of the larger
merry-go-round.
19^2 = 9.5
Substitute 9.5 for r in the formula for the
area of a circle.
A-n • 9.52
= 71 -90.25
- 283.385
Find the radius of the smaller
merry-go-round.
13-^-2-6.5
Substitute 6.5 for r in the formula for the
area of a circle.
A~n • 6.52
= n - 42.25
-132.665
Subtract the area of the smaller merry go-round from the area of the larger
merry-go-round.
283.385 - 132.665 = 150.72
As a 11 1/3 inch candle burns down, its height decreases 1/6 inch each hour. How many hours does it take for the candle to burn completely?
SHOW YOUR WORK
Answers
The number of hours after which the candle is burned completely is
68 hours.
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,
Candle height = 11(1/3) inches
Each hour the height decreases by 1/6 inch.
Now,
The equation to find the number of hours x after which the candle is burnout is 11(1/3) - (1/6)x = 0
Solve for x.
11(1/3) - (1/6)x = 0
11(1/3) = (1/6)x
34/3 = (1/6)x
x = (34 x 6) / 3
x = 34 x 2
x = 68
Thus,
After 68 hours the candle is completely burnt.
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9. In Figura 3, triunghiul MNP este dreptunghic,
M
(N = 90°, NAIMP și A E MP.
a) Care este proiecția punctului N pe ipotenuză?
b) Care este proiecția punctului N pe cateta care trece prin
vârful P?
c) Precizează proiecţiile catetelor pe ipotenuză.
.
Answers
Answer:
Its b
Step-by-step explanation:
describe the relationship between the two quantities in the graph.
Answers
given that x=2,find the value of y and z for the simultaneous equation x+y-z=1
Answers
Answer:
y=z-1, z=y=1.
Step-by-step explanation:
As x=2
So,
x+y-z=1
2+y-z=1
y-z=-1
y=z-1, z=y+1
The answer i’m on a timer
Answers
Answer:
D. Down 5, Left 2
Step-by-step explanation:
-5 on the outside means it will go down 5.
+2 directly grouped with the variable means it will do the opposite, so it goes left 2.
You have two numbers. If you double the first number and add it to the second number, the sum is 10. An equation to represent this situation could be: 2x + y = 10 1) Plot at least five points on this coordinate plane that make the statement and your equation true. What do you notice about the points you have plotted? 2) Using a different color, plot 3 point in the same coordinate plane that do not make the equation true.
Answers
Answer:
(a) See attachment 1
All points lie on the same line
(b) See attachment 2
Step-by-step explanation:
Given
[tex]2x + y = 10[/tex]
Solving (a): Plot 5 points that make the equation, true
First, we calculate the points
Make y the subject
[tex]y = 10 - 2x[/tex]
[tex]x = 0 \to y = 10 - 2* 0 = 10[/tex]
[tex]x = 1 \to y = 10 - 2* 1 = 8[/tex]
[tex]x = 2 \to y = 10 - 2* 2 = 6[/tex]
[tex]x = 3 \to y = 10 - 2* 3 = 4[/tex]
[tex]x = 4 \to y = 10 - 2* 4 = 2[/tex]
So, we will plot the following points
[tex](0,10)\ (1,8)\ (2,6)\ (3,4)\ (4,2)[/tex]
See attachment 1
Notice that all points lie on the same line
Solving (b):
Point (5,7) does not make the equation true, and that is why it lies outside the line
See attachment 2
Find the value of x (and y, if applicable)
Answers
Answer:
13√(2) = x
Step-by-step explanation:
The given is an isosceles triangle so the two side lenghts are same (13 units)
in right triangles the square lenght of the hypotenus is equal to sum of two side's square lenght
13^2 + 13^2 = x^2
169 + 169 = x^2
338 = x^2
13√(2) = x
A side of the triangle below has been extended to form an exterior angle of 62°. Find the value of xx.
Answers
Answer:
Photo?
Step-by-step explanation:
If there is a photo linked I dont see it
Also: Dont click the stpid link below its malware
Maria finished with 160 percent of her original amount. If she finished with 7200, what was Maria's original amount
Answers
On solving the provided question, we can say that the equation will be 1.8x=7200 => x=4000
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here,
the equation will be
1.8x=7200
x=7200/1.8
x=4000
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Place from least to greatest:
0.66, 0.654, 0.7, 0.64
Answers
Least to greatest: 0.64, 0.654, 0.66, 0.7
Answer:
1. 0.64
2. 0.654
3. 0.66
4. 0.7
Caleb and Isaiah are siblings they share a 14 segment chewy worm according to age how old could they be. Caleb gets eight pieces Isaiah gets six.
Answers
Answer:
1/6
Step-by-step explanation:
plz help 20 points math
Answers
Answer: -4/-6
Step-by-step explanation:
Me pueden ayudar? :)
Answers
.Answer:
Step-by-step explanation:
Which expression is equivalent to -12(3x-3/4)
-36x-8
-36x+8
-36x-9
-36x+9
Answers
Answer:
-36x+9
Step-by-step explanation:
Answer:
-36x + 9. i hope this help :)))
What are multiplying EXPONENTRAL terms with the same base which best explains how to simplify the expression
Answers
Answer:
Adding the exponents
Step-by-step explanation:
Multiplying exponential terms with the same base
To multiply exponents with same base , we use exponential property
[tex]a^m \cdot a^m=a^{m+n}[/tex]
When we multiply exponents with same base then we add the exponents
So, adding the exponents best explains to simplify the expression that has same base with exponents .
What is the volume of the rectangular prism?
Answers
^answer:^
~10 cubic feet~
^step by step explanation:^
first, calculate the volume of the front “panel” of the shape. (5 cubic centimeters because 5 times 3 is 15 and 15 times 1/3 is 5. 5 times 2 is 10.
simpelest form of the ratio 2 weeks to 30 days
Answers
Answer:
7:15 ,2 weeks=14 days and 30 days divide by 2 = 7 and 15 put them to a ratio and you'll get 7:15.
By choosing an appropriate line, use the
diagram to estimate the solutions to these
simultaneous equations:
2
y = -x +1.5
y = 1.5x2.5
Answers
So on solving the provided question, here we can say that by is a simultaneous equations the value of x = - 3/5 and y = 9/10
What is the simultaneous equation formula?Multiple algebraic equations that have the same unknowna as the give in the variables and the same answer are referred to as simultaneous equations. This suggests that there is a single solution to the simultaneous equations. Examples of simultaneous equations include: 2x - 4y = 4, 5x + 8y = 3, and others. This implies that the simultaneous equations have a single solution. The simultaneous equations 2x - 4y = 4, 5x + 8y = 3, and others are examples.
y = -x + 1.5
y = 1.5x + 2.5
x = -3/5
y = 9/10
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8) A rectangle is 9 feet long and has a perimeter of 32 feet. What is the width of the
rectangle? Show your work.
Answers
Answer:
288
Step-by-step explanation:
32 x 9=288
30% of n = 84
please help I'll put as brainlisest
Answers
Write 30% as 30100Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
30100 of 84 = 30100 × 84Therefore, the answer is 25.2
If you are using a calculator, simply enter 30÷100×84 which will give you 25.2 as the answer.
Evaluate the expression of x = 6 3x+5
Answers
Answer: the explanation ain't in a file smh its 23
Step-by-step explanation: 3x6+5=23[][][][]brainliest?
Pablo poured about 10 ? of medicine onto a spoon.
A) millimeters
B)liters
Answers
Answer:
A
Step-by-step explanation:
10 liters won't fit on a spoon