The set on which h is continuous is { (x, y) | 5x + 4y > 20 }. The function f(x, y) is a linear function and is defined for all values of x and y.
To determine the set on which h is continuous, we need to examine the domains of the functions f(x, y) and g(t), as well as the composition of these functions.
The function f(x, y) is a linear function and is defined for all values of x and y. The function g(t) is defined for all non-negative values of t (i.e., t ≥ 0), since it involves the square root of t.
The composition g(f(x, y)) is then defined for all (x, y) such that 5x + 4y - 20 ≥ 0, since f(x, y) must be non-negative for g(f(x, y)) to be defined. Simplifying this inequality, we get 5x + 4y > 20, which is the set on which g(f(x, y)) is defined.
Finally, the function h(x, y) = g(f(x, y)) is a composition of two continuous functions, and is therefore continuous on the set on which g(f(x, y)) is defined. Therefore, the set on which h is continuous is { (x, y) | 5x + 4y > 20 }.
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A teacher gave a test to a class in which 10% of the students are juniors and 90% are seniors. The average score on the test was 84. The juniors all received the same score, and the average score of the seniors was 83. What score did each of the juniors receive on the test
Each junior receives 93 score on the test. It is also the average score of the juniors.
Given Information
It is given that 10% of the strength of the class consists of juniors and 90% consists of seniors.
Let us assume the total strength of the class is 100, then,
Number of seniors = 90
Number of juniors = 10
It is also given that the average score of the class = 84
And, average score of the seniors = 83
Another given information is that all the juniors all received the same score, which is their average score. Let it be x.
Average Score of Juniors
Total marks obtained by the seniors = Number of seniors × Average score of seniors
= 90 × 83
= 7470
Total marks obtained by the juniors = Number of juniors × Average score of juniors
= 10x
Average marks on the test = Total marks / Total number of students
⇒ 84 = (7470 + 10x)/100
⇒ 84 × 100 = 7470 + 10x
⇒ 10x + 7470 = 8400
⇒ 10x = 8400-7470
⇒ 10x = 930
⇒ x = 930/10
⇒ x = 93
Thus, each junior scores 93 on the test.
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Melissa is planning a rectangular vegetable garden with a square patch for tomatoes
The expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.
A square is a quadrilateral with all four sides equal, and all four angles at 90°, whereas a rectangle is a quadrilateral with opposite pair of sides equal, and all four angles at 90°.
In the question, we are informed that Melissa is planning a rectangular vegetable garden with a square patch for tomatoes.
The side of the square is given to be x feet.
We are asked to write expressions for the length and width of the rectangular garden.
For the length of the rectangle:-
We are informed that she wants the length of the garden to exceed three times the length of the tomato patch by 2 feet.
Thus, the length of the garden can be shown as the expression 3x + 2 feet.
For the width of the rectangle:-
We are informed that she also wants the garden's width to exceed the width of the tomato patch by 5 feet.
Thus, the width of the garden can be shown as the expression x + 5 feet.
Thus, the expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.
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The provided question is incomplete. The complete question is:
"Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden's width to exceed the width of the tomato patch by 5 feet.
Let x represent the length, in feet, of the square tomato patch.
Write expressions to represent the length and width of Melissa's vegetable garden in terms of x.
Enter the correct answer in the box."
Find the center and radius of the circle with the equation: (x-0^2 + (y+1)^2 = 4
a.
center: (-5, 1)
radius: 4
c.
center: (-5, 1)
radius: 2
b.
center: (5, -1)
radius: 4
d.
center: (5, -1)
radius: 2
The center and radius of the circle is (b) center: (-5, 1) radius: 2
How to determine the center and the radius?The circle equation is given as:
(x-5)^2 + (y+1)^2 = 4
The circle equation is represented as:
(x-a)^2 + (y-b)^2 = r^2
Where:
Center = (a,b)
Radius = 4
By comparison, we have:
(a, b) = (-5, 1)
r^2 = 4
This gives
(a, b) = (-5, 1)
r = 2
Hence, the center and radius of the circle is (b) center: (-5, 1) radius: 2
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Solve 5x=125 using the one-to-one property of exponents.
A) X=In(125)
B) x = 1
C) x = 3
OD) x = 5
Answer:
C) x = 3
Step-by-step explanation:
Given equation:
[tex]5^x=125[/tex]
Rewrite 125 with base 5: 125 = 5³
[tex]\implies 5^x=5^3[/tex]
[tex]\textsf{Apply the one-to-one property of exponents}: \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]
[tex]\implies x=3[/tex]
23. Which equation translates y = | x | by 8 units to the left?
y = |x-81
y = |x + 81
y = |x|-8
y = |x | +8
Answer:
y = |x + 8|
Explanation:
Please see the table attached below.
Answer:y=|x+8|
Step-by-step explanation:
Apply the distributive property to factor out the greatest common factor. 24j-16=
Answer:
8(3j - 2).
Step-by-step explanation:
24j-16
GCF = 8
so the answer is
8(3j - 2).
find the slope of a line parallel to the line through the given points. E(5, 7), F(3, 1) •-3
•-1/3
•1/3
Answer:
3
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (1 - 7)/(3 - 5)
slope = -6/(-2)
slope = 3
Parallel lines have equal slopes.
Answer: 3
explain how the following problem could be solved. then, solve the problem. a full-grown dog is about one-eighth as heavy as a cow. together, they weigh 360 kg.
The problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.
The weight of the cow, on solving the equation, is found to be 320 kg.
The weight of the full-grown dog = (1/8)*320 kg = 40 kg.
We assume the weight of the cow to be x kg.
The weight of a full-grown dog is given to be one-eight of a cow, that is, the weight of a full-grown dog = (1/8)*x = x/8 kg.
Thus, the sum of the weights of the full-grown dog and the cow = x/8 + x kg.
But, we are given that together, they weigh 360 kg.
This can be shown as the linear equation in the one variable:
x/8 + x = 360.
Thus, the problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.
To solve the problem, we solve the equation as follows:
x/8 + x = 360,
or, (9/8)x = 360 {Simplifying},
or, x = 360*8/9 {Cross-Multiplying},
or, = 320.
Thus, the weight of the cow, on solving the equation, is found to be 320 kg.
The weight of the full-grown dog = (1/8)*320 kg = 40 kg.
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Find the equation of the line that passes through the given points. (1, 4.5) and (3, 6)
Answer:
y=0.75x+3.75
Step-by-step explanation:
The slope is
[tex] \frac{6 - 4.5}{3 - 1} = \frac{3}{4} [/tex]
Substituting into point-slope form,
y - 6 = 0.75(x - 3)
y - 6 = 0.75x - 2.25
y = 0.75x + 3.75
250-{(135+34)÷(46-33)}-15 simplify
Answer:
222
Step-by-step explanation:
Hey there!
250 - {(135 + 34) ÷ (46 - 33)} - 15
= 250 - 169/(46 - 44) - 15
= 250 - 169/13 - 15
= 250 - 13 - 15
= 237 - 15
= 222
Therefore, your answer should be:
222
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Ed records the temperature of two pots of water. The pots are the same size and material. Pot X has a temperature of 56 degrees Fahrenheit, and pot Y has a temperature of 49 degrees Fahrenheit. What conclusion can Ed make about the pots of water
Answer:
The water in pot X is hoter than that of pot Y
Answer:
A is the answer
Step-by-step explanation:
Help with these two problems and show work please !!
Answer:
1) [tex]x_1=-1-2\sqrt{2},\ x_2=-1+2\sqrt{2}[/tex]
2) [tex]x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]
Step-by-step explanation:
[tex]{\large \textsf{ Quadratic Formula: }}x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]
Given quadratic equations:
1. [tex]x^2+2x-7=0[/tex]
2. [tex]4x^2-3=x^2-5x-4[/tex]
1. x² + 2x - 7 = 0
[tex]\implies a=\textsf{1},b=\textsf{2},c=\textsf{-7}[/tex]
Step 1: Substitute the given values into the formula and simplify.
[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{2})\pm \sqrt{(\textsf{2})^2-4(\textsf{1})(\textsf{-7})}}{2(\textsf{1})}\\\implies x&=\dfrac{-2\pm \sqrt{4-4(-7)}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{4+28}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{32}}{2}\end{aligned}[/tex]
Step 2: Simplify the radicand (under the square root).
[tex]\begin{aligned}x&=\dfrac{-2\pm \sqrt{16\times2}}{2}\\x&=\dfrac{-2\pm 4\times\sqrt{2}}{2}\\x&=\dfrac{-2\pm 4\sqrt{2}}{2}\end{aligned}[/tex]
Step 3: Separate into two solutions and simplify them.
[tex]\implies x_1&=\dfrac{-2 - 4\sqrt{2}}{2},\ x_2&=\dfrac{-2 + 4\sqrt{2}}{2}[/tex]
[tex]\begin{aligned}\implies x_1&=\dfrac{-2}{2}+\dfrac{- 4\sqrt{2}}{2},\ x_2=\dfrac{-2 + 4\sqrt{2}}{2}\\\implies {x_1&=\boxed{-1-2\sqrt{2}},\ x_2=\boxed{-1+2\sqrt{2}} \end{aligned}[/tex]
----------------------------------------------------------------------------------------------------------------
2. 4x² - 3 = x² - 5x - 4
Step 1: Set the equation to zero (by moving the "x² - 5x - 4" to the left).
4x² - 3 - x² + 5x + 4 = 0 [ Combine like terms. ]
3x² + 5x + 4 = 0
[tex]\implies a=\textsf{3},b=\textsf{5},c=\textsf{1}[/tex]
Step 2: Substitute the given values into the formula and simplify.
[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{5})\pm \sqrt{(\textsf{5})^2-4(\textsf{3})(\textsf{1})}}{2(\textsf{3})}\\\implies x&=\dfrac{-5\pm \sqrt{25-12}}{6}\\\implies x&=\dfrac{-5\pm \sqrt{13}}{6}\end{aligned}[/tex]
Step 3: Separate into two solutions.
[tex]\implies x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]
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22. If 1 m,m/19 - 118°, and m/16 - 48°, calculate m/12.
0 0
103"
98
109⁰
110"
18
17
19 20
14
16
13
15
11
10
12
9
63
5
m
Answer: [tex]110^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle 20=62^{\circ}[/tex] (linear pair)
[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)
[tex]m\angle 12=110^{\circ}[/tex] (linear pair)
Find all solutions to 2w^4 - 5w^2 + 2 = 0
asap please
Answer:
w = ±[tex]\sqrt{1/2}[/tex] or w= ±[tex]\sqrt{2}[/tex]
Step-by-step explanation:
if we say some variable y = w^2, we can rewrite the equation to:
2y^2 - 5y + 2 = 0
this can be factored into (2y-1)(y-2) = 0
putting w^2 back in the place of y, that's (2w^2 - 1)(w^2 - 2) = 0
The equation is a fourth degree polynomial, so there are four roots, or four values of w that will cause the equation to equal 0.
If 0 is multiplied by anything, the result is 0, so we set 2w^2 - 1 = 0 and solve for w, which is ±√1/2, then set w^2 - 2 = 0 to get w = ±√2 as our roots
the four solutions are ±√1/2 and ±√2
(because the positive counts as one solution and the negative another solution)
Can someone help me with the first question please
Answer:
(c) 5y -17x +99 = 0
Step-by-step explanation:
The median of a triangle is the line through a vertex and the midpoint of the opposite side. The median of ΔXYZ from vertex Y will be the line through point Y and the midpoint of XZ.
MidpointThe midpoint of XZ is the average of the coordinates of X and Z.
M = (X +Z)/2
M = ((1, -2) +(8, -7))/2 = (9, -9)/2 = (4.5, -4.5)
Line through two pointsThe slope of the median can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
The slope of line YM is ...
m = (-4.5 -4)/(4.5 -7) = -8.5/-2.5 = 17/5
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
The line with slope 17/5 through point Y(7, 4) is ...
y -4 = 17/5(x -7)
Subtracting the right side, and multiplying by 5 gives ...
5(y -4) -17(x -7) = 0
5y -17x +99 = 0 . . . . equation of the median through Y
From points a and b on level ground the angles of elevation of the top of a building are 25degree and 37 degree respectively. if [ab] =57m, calculate to the nearest metre, the distances of the top of the building from a and b if they are both on the same side of the building
The distance of the top of the building from a is 163m and that from b is 115m .
Calculating the Perpendicular Distance of the Top From Ground
It is given that the angle of elevations of the building top from a and b are 25° and 37° respectively.
ab = 57m
Let the top of the building be point c and the distance between the building and the point b be x. Then, from the figure, we can deduce the following,
In Δacd, tan 25° = cd/ad
⇒ 0.4663 = cd /(x+57)
⇒ cd = 0.4663(x+57) ......................... (1)
In Δbcd, tan 37° = cd/x
⇒ 0.7536 = cd/x
⇒ x =cd / 0.7536 .......................... (2)
Solving for the Distance cd
Substitute the value of in equation (2) to equation (1) to get,
cd = 0.4663 ((cd/0.7536)+57)
cd = 0.4663(cd+42.9552)/0.7536
0.7536cd = 0.4663cd + 20.03
0.7536cd - 0.4663cd = 20.03
0.2906cd = 20.03
cd = 20.03/0.2906
Thus, the distance cd ≈ 68.93m
Finding the Distance cb and Distance ca
In Δacd, sin25° = cd/ca
⇒ 0.4226 = 68.93/ca
ca = 68.93/0.4226
ca = 163.10
∴ The distance ca ≈ 163m
Similarly, in Δbcd, sin37° = cd/cb
⇒ 0.6018 = 68.93/cb
cb = 68.93/0.6018
cb =114.54m
∴ The distance cb ≈ 115m
Therefore, the points a and b are at a distance of 163m and 115m respectively from the top of the building.
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Analyze the diagram below and complete the instructions that follow. (7x - 3) (12x -7) Solve for x.
Answer:
Step-by-step explanation:
(7x-3)(12x-7)
we are solving for x and we are multiplying.
we start with the x's 7x*12x= 84x
-3*-7=21
so now we have
84x+21=0
the 0 is a placer for answering the question
we minus 21 to both sides
84x=-21
now we divide
84/-21= -4
x=-4
Solve 3[-x + (2 x +1)]=x-1
The result of the evaluation of the equation given in the task content is; x =-2.
What is the solution of the equation?It follows from the task content that the equation given whose solution is to be determined is;
3[-x + (2 x +1)]=x-1
The equation can be solved as follows;
-3x + 6x +3 = x-1
2x = -4
x = -2
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What is the relation between the variables in the equation
a. varies inversely as y
b.xvaries directly as y
Please select the best answer from the choices provided
O
O
A
B
C
O
y
-7?
c. y varies directly as x¹
d. y varies inversely as ¹
The relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y
How to determine the relation between the variables in the equation?The complete question is added as an attachment
From the attached figure, we have the following equation
x^4/y = 7
Multiply both sides of the equation by y
x^4 = 7y
The above represents a direct variation from x^4 to y.
Where 7 represents the variation constant
Hence, the relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y
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The perimeter of a parallelogram is 180 cm. One side exceeds the other by 10 cm.
What are the lengths of adjacent sides of the parallelogram?
Answer:
One side is 40 cm and the adjacent side is 50 cm
Step-by-step explanation:
We can use a rectangle because a rectangle is a parallelogram. Draw a rectangle. Write the width as x and the length as x + 10. We find the perimeter by adding all 4 side lengths.
Two side lengths are x and two side lengths are x + 10. If we add all of this together we get 180
x +x +x+10+x+10 = 180
4x + 20 = 180 Combine the like terms. There are 4 x's and 10+10 is 20
4x = 160 Subtract 20 from both sides
x = 40 Divide both sides by 4
So, two sides are 40 and two sides are 50, this will add up to 180
Answer:
40 cm & 50 cm
Step-by-step explanation:
one side = X cm (??)
the other side =X+10 cm
Solve
2(x+x+10)=180
x+x+10=90
2x=80
x = 80/2
x=40
therefore
x+10=50cm
True or false: the mayans wrote the digits in their numerals in a vertical format
Answer:
True
Step-by-step explanation:
successor of -501 is
Answer:
-500
Step-by-step explanation:
since 501 has a negative sign,add 1 to to the number,the next number will be -500
-501 +1 = -500
successor in this case means a number that succeeds another
(03.01 MC)
Simplify
the square root of 4 divided by 3 to the third power , the square root of 4
Answer: [tex]\frac{2}{9}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{4} }{3^{3} }[/tex]
The square root of 4 can be written as 2
3 to the third power can be written as 9
So, the answer is [tex]\frac{2}{9}[/tex]
Plss help give brainiest if right!
the speed of the boat going with a current is 20 mph. when the
boat goes against the current, the speed is 16 mph. find the speed of
the boat in still water and the speed of the current.
Answer:
The speed of the boat in still water is 18 mph.
The speed of the current is 2 mph
Step-by-step explanation:
Let x constitute the charge of the boat in nonetheless water.
Let y constitute the rate of the contemporary.
When the boat is going against the modern-day, the rate is sixteen mph. Assuming it traveled against the modern at the equal time as going upstream, its general speed may be (x - y) mph. It way that
x - y = 16 (equation 1)
Going downstream, the boat averages 20 mph. Assuming it traveled with the current, its standard pace would be (x + y) mph. It way that
x + y = 20 (equation 2)
Adding each equation, it becomes
2x = 36
x = 36/2
x = 18 mph
Substituting x = 18 into equation 1, it will become
18 - y = 16
y = 18 - 16
y = 2 mph
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Hi I don't know how to do this
Using a system of equations, the weight of 5 apples, 2 oranges are 4 bananas is given as follows:
B. 1147 gm.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Weight of an apple.Variable y: Weight of an orange.Variable z: Weight of a banana.Considering the data given, the equations are:
3x + 5y = 928.4y + 6z = 1088.5x + 3z = 799.From the first equation:
3x = 928 - 5y.
x = 309.33 - 1.667y.
From the second equation:
6z = 1088 - 4y
z = 181.33 - 0.667y
Replacing in the third equation:
5x + 3z = 799
5(309.33 - 1.667y) + 3(181.33 - 0.667y) = 799
10.336y = 12961.64
y = 1291.64/10.336
y = 125 gm.
The other weights are:
x = 309.33 - 1.667y = 309.33 - 1.667 x 125 = 101 gm.z = 181.33 - 0.667y = 181.33 - 0.667 x 125 = 98gm.The weight of 5 apples, 2 oranges are 4 bananas is:
5x + 2y + 4z = 5 x 101 + 2 x 125 + 4 x 98 = 1147 gm, option B.
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Select all the correct systems of equations. Which systems of equations have infinite solutions? 2x + 5y = 31 6x - y = 13 y = 14 - 2x 6x + 3y = 42 2x + y = 14 x = 13-2y Reset 2x + y = 10 -6x = 3y + 7 y = 13-2x 4x - 3y = -19 2x + y = 17 Next -6x = 3y - 51
Answer:
The system of equations y=14-2x and 6x+3y=42.
Step-by-step explanation:
Please see attachment to see the answer as a graph.
Hope this helps!
Derrick had a 0.250 batting average at the end of his last baseball season, which means he got a hit 25% of the times he was up to bat. if derrick had 47 hits last season, how many times did he bat?
The number of times that Derrick batted last season is 188 times.
How many times did Derrick bat?
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to denote percentage is %.
A percentage of 25% here means that twenty five times out of hundred times, Derrick hit the ball. In order to convert a percentage to a decimal, divide the percentage by 100.
Number of times Derrick bat last season = Number of hits last season / percentage of his batting average
47 / 25%
47 / 0.25 = 188
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Your dad says you can have a new puppy if you build the dog house. Before building, you need to determine the dimensions. Choose the dimensions of the base, the length, and the width of the dog house. Choose dimensions that you think are reasonable for whatever type of puppy you would get. Once you plan the base and walls, you need to decide on the height of the roof (represented by the dotted line in the image below). The roof is a triangle with two sides that are the same length.
Find the height of the roof using the dimensions you chose. You are hoping to put shingles on the roof and need to know what the square footage of the roof will be. Use the dimensions to calculate the area of the roof.
Hint: Remember to find the area of the entire roof.
The area of Entire roof is 12 feet².
What is Pythagorean theorem?The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle)
Given:
As, the roof peak with a 3 and the roof overhang the sides is 4.
Now, Using Pythagorean theorem.
a² + b² = c ²
15² + 13² = c²
c² = 225+ 169
c = 19.8 (or 20)
So, the length of diagonal is 24.
Roof Dimension 36 x 24 or (
Area of Roof = 3 x 2
= 6 unit²
and, area of the entire roof = 2 x6 = 12 ft²
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Find the missing side length of the triangle.
Answer:
c = 10
Explanation:
Use Pythagoras theorem: a² + b² = c²
where 'a' and 'b' are legs and 'c' is the hypotenuse (the longest side)
Here given: a = 8 cm, b = 6 cm, c = ?
Substituting values:
8² + 6² = c²
c² = 64 + 36
c² = 100
c = √100
c = 10
Answer:
10 cm
Step-by-step explanation:
[tex]a^2=b^2+c^2[/tex]
[tex]a^2=6^2+8^2[/tex]
[tex]a^2=100[/tex]
[tex]\sqrt{a^2}=\sqrt{100[/tex]
a=10
Find the digits x and y such that number 90x0y07 is divisble by 2017
No digit with the format 90x0y07 is divisible by 2017
How do determine the digits x and y?The given parameters are:
Dividend = 90x0y07
Divisor = 2017
The dividend is a 7-digit number, and the divisor is a 4-digit number
So, the quotient must be 3 to 4 digits.
Comparing the first and last digits of 90x0y07 and 2017;
The first and last digits of the quotient must be 4 and 1, respectively
So, we have:
90x0y07 = 2017 * 4a1
Assume a = 9.
So, we have:
90x0y07 = 2017 * 491
90x0y07 = 990347
The above is 6-digit.
So, we make use of a 4-digit quotient
This gives
90x0y07 = 2017 * 4ab1
Next, we make use of trial by error.
After several attempts, we conclude that no digit with the format 90x0y07 is divisible by 2017
The closest attempt is
90x0y07 = 2017 * 4471
90x0y07 = 9018007
Where:
x = 1, y = 0 and the digit between x and y is 8, not 0
Read more about digits at:
https://brainly.com/question/1553674
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