The ages will be:
Henry's weight = 38kg
David =35kg
Peter = 50 kg
How to calculate the weight?Let Henry's weight be represented by x
David is 3kg lighter. This will be x-3.
Peter is 15kg heavier. This will be:
= x-3 + 15 = x +12
This will be:
x + x-3 + x + 12 = 123
3x + 9 = 123
3x = 123 - 9
3x =114
Divide
x = 114/3 = 38
Therefore, Henry's weight = 38kg
David =x - 3 = 38 - 3 = 35kg
Peter =35 + 15 50 kg
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the sum of 4 times a number and 9 is equal to 6
use the variable y for the unknown number
Answer:
-3/4
Step-by-step explanation:
4y + 9 = 6
4y = 6-9 = -3
y = -3/4
The first step in determining the solution to the system of equations, y=x²-4x-3 and y= 2x+5, algebraically is to
set the two equations equal
as-x²-4x-3=2x+5. What is the next step?
Set y = 0 in y=-x2²-4x-3.
O Factor each side of the equation.
Use substitution to create a one-variable equation.
O Combine like terms onto one side of the equation
Answer: The first step in determining the solution to the system of equations algebraically is [-4,-2].
Step-by-step explanation:
Determining the solution to the system of equations,
so, y=-x²-4x-3 and y= 2x+5, algebraically is to set the two equations are equal to:
-x²-4x-3 =2x+5
Then the solve in this equation
To put all terms into the lest side of the equation and group the terms:
solve it: -x²-4x-3-2x-5=0
-x²+(-4x-2x)+(-3-5)=0
-x²-6x-8=0
now you can multiply this equation by -1
x²+6x+8=0
and solve it using Quadratic equation
x(1,2)=[-b±√[tex]b^{2}[/tex]-4ac]/2a
replace with a=1,b=6,c=8 values
x(1,2)=[-6±√[tex]6^{2}[/tex]-4.8.1]/2.1
x(1,2) =[-6±√4]/2
x(1,2) =[-6±2]/2
x(1,2) =[-4,-2]
The first step in determining the solution to the system of equations algebraically is [-4,-2].
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HELP
The coordinates of point T are (0,4). The midpoint of ST is (1,−3). Find the coordinates of point S.
The coordinates of S are (-1 , 11)
In the given statement is :
The coordinates of point T are (0,4). The midpoint of ST is (1,−3).
To find the coordinates of point S.
Now, According to the question:
Let the coordinate of point S are (x, y).
T (0, 4) is the mid point of ST
=> [tex]\frac{x+1}{2}=0 , \frac{y+(-3)}{2}=4[/tex]
=> x+1 =0 , y -3 = 8
=> x = -1 , y = 11
So, the coordinates of S are (-1 , 11)
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745.5×101 i really need help
Answer: 75295.5
Step-by-step explanation:
Answer: 75255.1
Step-by-step explanation: 745.1×101
Multiply 745.1 and 101 to get 75255.1.
FACTOR
[tex]\frac{101.7541}{2.5}[/tex]=75255[tex]\frac{1}{10}[/tex]=75255.1
Suppose the price of a sweater is $10. Jaylen's marginal benefit for purchasing each additional sweater is given in the table below. He
gets the most benefit from the first sweater and less benefit from each additional sweater. If Jaylen is behaving rationally, how many
sweaters will he purchase?
1st sweater
2nd sweater
3rd sweater
4th sweater
5th sweater
6th sweater
50
35
30
23
12
8
The number of sweaters that Jaylen will purchase, based on his marginal benefit, is 5 sweaters.
What is marginal utility?Marginal utility or benefit is the added satisfaction that a consumer derives from the consumption of an additional unit of a product or service.
Using the concept of marginal utility, we can determine the number of units consumers will be willing to purchase.
The law of marginal utility states that a consumer will continue to purchase more of an item until their marginal benefit or utility is fewer than the cost of the item.
For instance, Jaylen will buy sweaters until his marginal benefit is lower than the price of a sweater ($10).
Jaylen is likely to buy 5 sweaters since his marginal benefit, though progressively reducing, still exceeds the price of the sweaters.
Data:Price per sweater = $10
Marginal Benefits
1st sweater 50
2nd sweater 35
3rd sweater 30
4th sweater 23
5th sweater 12
6th sweater 8
Thus, based on marginal utility, Jaylen will purchase 5 sweaters.
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The probability that Roger wins a tennis tournament (event A) is 0.45, and the probability that Stephan wins the tournament (event 8) is
0.40. The probability of Roger winning the tournament, given that Stephan wins, is O. The probability of Stephan winning the tournament.
given that Roger wins, is 0. Given this information, which statement is true?
O A
Events A and Bare not independent because P(AB) # PA)
The true statement is that C. Events A and B are not independent because P(A|B) ≠ P(A).
How to illustrate the information?The probability that Roger wins a tennis tournament (event A) is 0.45 i.e. P(A)=0.45
The probability that Stephan wins the tournament (event B) is 0.40 i.e. P(B)=0.40
It should be noted that if A and are independent events, then P(B|A) = P(B). This isn't possible in this situation.
Therefore, the true statement is that events A and B are not independent because P(A|B) ≠ P(A).
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The probability that Roger wins a tennis tournament (event A) is 0.45, and the probability that Stephan wins the tournament (event B) is 0.40. The probability of Roger winning the tournament, given that Stephan wins, is 0. The probability of Stephan winning the tournament, given that Roger wins, is 0. Given this information, which statement is true?
1.Events A and B are independent because P(A|B) = P(A).
2.Events A and B are independent because P(A|B) ≠ P(A).
3. Events A and B are not independent because P(A|B) ≠ P(A).
4. Events A and B are not independent because P(A|B) = P(A).
GIVING BRAINIEST IF CORRECT!!!!
Express in simplest radical form.
Your answer is in the screenshot!
The empire state building in new york city is about 1,450 feet high (including the antenna at the top) and 400 feet wide. Andre wants to make a scale drawing of the front view of the empire state building on an 8 1/2 inch by 11 inch piece of paper. select a scale that you think is the most appropriate for the scale drawing.
A. 1 inch to 1 foot
B. 1 inch to 100 feet
C. 1 inch to 1 mile
D. 1 centimeter to 1 meter
E. 1 centimeter to 50 meters
F. 1 centimeter to 1 kilometer
The scale factor that is most appropriate for the scale drawing is 1 centimeter to 50 meters. (Correct choice: E)
What scale factor is the most appropriate to make an scale drawing of the Emipre State Building?
Scale factor are useful resources to make representations of huge and diminute representations of entire systems based on the application of length ratios defined below:
d / d' = r (1)
Where:
r - Length ratio, in feet per inchd - Real length, in feetd' - Scale length, in inchesNow we find the minimum reduction scale to fit the building in the paper.
Width
r' = 400 ft / 8.5 in
r' = 47.058 ft / in
Height
r' = 1,450 ft / 11 in
r' = 131.819 ft / in
The minimum reduction scale to fit the building in the paper is 131.819 ft / in (approx. 15.818 m / cm, that is 1 centimeter to 15.818 meters), that is, 1 centimeter to 131.819 feet. Then, the scale factor that is most appropriate for the scale drawing is 1 centimeter to 50 meters.
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17. Higher Order Thinking The average rate
that human hair grows is 1.27 centimeters
per month. Elena let her hair grow for
3 months. Then she got 1.9 centimeters of
her hair cut off. If Elena's hair grows at the
average rate, how much longer is Elena's
hair now than 3 months ago? Explain how
to solve the problem. Then solve.
Elena's hair has grown in length overall net by. 1.81cm
It is given to us that the average rate at which human hair grows is 1.27 centimeters per month.
Elena allowed her hair to grow for three months, so that's a given. Then she had her hair chopped short by 1.9 cm.
Elena's hair naturally grows at a typical rate.
First, we'll figure out how much Elena's hair has grown in three months, and then from that figure, we'll deduct the length that has been trimmed.
Elena's hair grew 3.x*1.27=3.81 cm in three months.
The amount of hair that was removed was 1.9 cm.
Elena's hair has grown in length by 3.81 cm over the course of three months, minus the length that has been chopped, for a total net growth of 1.91 cm.
Growth in 3 months less the length that was removed is 3.81 – 1.9 = 1.91 cm
Hence, the total net growth of Elena's hair is 1.81cm
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A baseball team has home games on Friday and Sunday. The two
games together earn $3546.00 for the team. Friday's game
generates $374.00 less than Sunday's game. How much money
was taken in at each game?
The money earned on friday is $1586 and on sunday is $1960.
What is meant by linear equation in one variable?A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable.
Let us assume the money generated by Friday game is 'F'.
Let us assume the money generated by Sunday game 'S'.
The two games together earn $3546.00 for the team.
Equation will become;
F + S = 3546.00 ........(equation 1)
Friday's game generates $374.00 less than Sunday's game. Thus,
F = S - 374.00
Since, F = S - 456.50 use the substitution method and put this value in equation 1.
(S - 374.00) + S = 3546.00
Simplifying the equation;
2S = 3546.00 + 374.00
2S = 3920
S = 1960.
Put this value in equation 1 and find F.
F + S = 3546.00
F + 1960 = 3546.00
F = 1586.
Thus, the money generated on friday is $1586 and on sunday is $1960.
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Given: f(x)
=
x - 2
x+8
Answer:
f×=×-2×+8=10×f=20xf=30×f
Order the following rational and irrational numbers from least to greatest.
square root of 20, -2 3/5, 10/3,3.9, 3 7/5
The order of the number from the least to the greatest is -2 3/5, 10/3,3.9, 3 7/5, 20.
What are the order of the numbers?A rational number is a number that can be expressed as the fraction of two numbers in which the decimal is not zero. A rational number can be positive or negative. An example of a rational number is 3, -1.2.
An irrational number is a number that cannot be expressed as the fraction of two numbers. An example of a irrational number is 1/3, 22/7.
In order to order a number, all the numbers should have the same form. Thus, all the numbers would be converted to decimals where possible.
-2 3/5 = -2.6
10 /3 = 3.33
3 7/5 = 4.5
In order to order the numbers, note that the farther a negative number is from zero the smaller the number is and the farther a positive number is to zero, the greater the number is.
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The ratio of stars to circles is 3 to 2. If
there are 28 circles, then how many stars are there?
Answer:
42
Step-by-step explanation:
3 to 2 can be represented as 3/2. Remember the numerator represents stars while the denominator represents circles. Set up a proportion the criss multiply. This ratio would be 3/2 = x/28. First multiply 28 x 3 and set it equal to 2x. This gives you 84=2x. Divide 2 by each side and you will get 42 stars.
Bre'Aujanaye operates a flower shop in Paris. All employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and
special events. Why type of organization does Bre'Aujanaye have?
The type of market in which all employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and special events is Oligopoly.
What is Oligopoly?An oligopoly is a market characterized by a small number of firms who realize they are interdependent in their pricing and output policies. The number of firms is small enough to give each firm some market power.
Given situation:
All employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and special events.
As, we know that A market structure known as an oligopoly occurs when a few large sellers or manufacturers control a sizable portion of a market or an entire sector.
Oligopolies are frequently the outcome of corporate collaboration as a way to increase profits.
Some examples of oligopolies include the car industry, petrol retail, pharmaceutical industry, coffee shop retail, and airlines.
So, as discussed in the given case employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and special events to make some profit.
Hence, type of market is Oligopoly.
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MOWING Cordell is mowing his front lawn. His mailbox is on the edge of the lawn. Cordell starts mowing near the mailbox and moves away from the mailbox, towards his house. He continues to move back and forth between the edge of the lawn and the house. Select a reasonable graph that shows the distance Cordell is from the mailbox as he mows. Let the horizontal axis show the time and the vertical axis show the distance from the mailbox.
The graph of the distance that Cordell moves between the home and the mailbox and time period will be a repeating graph.
Let us assume that the distance between the lawn and the mailbox of Cordell is L.
He starts moving from his home towards the mailbox. After reaching the mailbox, he returns back to the home. Let say the time when he first returns back to his home is T₁.
The graph will show that the value of distance will first increase till L and after that he will come back to his home and the distance will decrease and become zero and the time period will be T₁. This show that he had return back to his home.
Similarly, the time well he again starts from his home and reaches till the mailbox and then again reaches to his home again is T₂. The graph is again plotted in the same manner as it was done in the first case.
It is because the distance L between mailbox and his home is same.
So, we can conclude that the graph will be a repeating graph. The shape of graph will be Saw-tooth like shape.
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Nick buys a bag of cookies that contains 9 chocolate chip cookies, 6 peanut butter cookies, 7 sugar cookies and 7 oatmeal cookies. What is the probability that Nick randomly selects a sugar cookie from the bag, eats it, then randomly selects a chocolate chip cookie? Express you answer as a reduced fraction.
Answer: 2/29
Step-by-step explanation: because he has 29 cookies in total therefor if he just randomly picks a cookie from the bag this would be 2/29 as he randomly chose 2 cookies out of 29 total cookie. we have no idea what he could have chose and all the cookies are mixed in a bag.
================================================
Explanation:
There are 7 sugar cookies
This is out of 9+6+7+7 = 29 total cookies
The probability of getting a sugar cookie is 7/29
After that cookie is selected, the total drops to 29-1 = 28 cookies. The probability of getting a chocolate chip on the second selection is 9/28
Multiply the fractions mentioned to get the final answer
(7/29)*(9/28) = (7*9)/(29*28) = (7*9)/(29*7*4) = 9/(29*4) = 9/116
Taylor and Alex are looking for a daycare for their child. They want to make sure the daycare is midway between their jobs. Taylor works at the Rogers Middle School located at (4, -5), and Alex works at St. Philip's located at (2, 5). Where should the daycare be located?
The location of the coordinate of the daycare is (3, -1.5)
Midpoint of coordinatesThe formula for calculating the midpoint of coordinate is expressed as;
M(x, y) = {(x₁+x₂/2, y₁+y₂/2)}
Given the coordinate points (4, -5) and (2, 5), on substituting, we will have:
M(x, y) = {(4+2/2, -5+2/2)}
M(x, y) = (6/2, -3/2)
M(x, y) = (3, -1.5)
Hence the location of the coordinate of the daycare is (3, -1.5)
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On an inch ruler AC is 3 1/2 AB is 1 7/8 then find BC
Answer: can you give me some more information??
Step-by-step explanation:
A survey of 279 SPC students was taken at registration. Of those surveyed: 51 students had signed up for a Language Arts course 36 students had signed up for a Humanities course 18 students had signed up for both a Math and Language Arts course 8 students had signed up for both a Math and Humanities course 9 students had signed up for both a Language Arts and Humanities course 4 students had signed up for all three courses students did not sign up for any of these classes How many students signed up for only Math (of these three)?
Treating the amounts as Venn sets, we have that 161 students signed up for only Math, considering that 40 did not sign for any.
What are the Venn sets?For this problem, we consider the following sets:
Set A: Students that have signed up for Arts.Set B: Students that have signed up for Humanities.Set C: Students that have signed up for Math.4 students had signed up for all three courses students, hence:
(A ∩ B ∩ C) = 4.
8 students had signed up for both a Math and Humanities, hence:
(B ∩ C) + (A ∩ B ∩ C) = 8
(B ∩ C) = 8.
18 students had signed up for both a Math and Language Arts, hence:
(A ∩ C) + (A ∩ B ∩ C) = 18
(A ∩ C) = 14.
9 students had signed up for both a Language Arts and Humanities, hence:
(A ∩ B) + (A ∩ B ∩ C) = 9
(A ∩ B) = 5.
36 students had signed up for a Humanities course, hence:
B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 36
B + 5 + 8 + 4 = 36
B = 19.
51 students had signed up for a Language Arts course, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 36
A + 5 + 14 + 4 = 51
A = 28.
Considering that there are 279 students, and supposing 40 did not sign for any course, we have that:
A + B + C + (A ∩ B) + (B ∩ C) + (A ∩ C) + (A ∩ B ∩ C) + 40 = 279.
28 + 19 + C + 5 + 8 + 14 + 4 + 40 = 279
118 + C = 279
C = 161
161 students signed up for only Math, considering that 40 did not sign for any.
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The measure of one angle is four times the measure of its supplement. Find the measure of each angle.
The measure of the angle is 36° and its supplement is 144°.
The supplement of an angle is calculated by subtracting the value of the angle from 180°.
A linear pair of angles are supplement of one another.When two straight lines intersect at a point then any 2 adjacent angle of the four angles formed are supplementary angles. In a cyclic quadrilateral ( quadrilateral whose 4 sides touch the same circleat different points ) opposite angles are supplementary.Given that the supplement of the angle is 4 times the angle.
Let us consider the value of the angle be x°.
Therefore the value of the supplement is 4x°
Now the sum of the two supplementary angles is 180°.
∴x° + 4x° = 180°
or, 5x° = 180 °
or, x° = 36°
Therefore the larger angle = 4x° = 4 × 36° = 144° .
Hence the angles are 36° and 144° .
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11) What two numbers will √5 be between on a number line?
a) 2.01 and 2.24
62.0 and 3.25
2.1 and 2.156
d) 1.9 and 2.0
Answer:a
Step-by-step explanation:
it is 2.2360679775 which is in between 2.01 and 2.24
Answer: a. between 2.01 and 2.24
Step-by-step explanation:
√4=2
√9=3
9-4=5
5-4=1
1/5=0.2
√5=
√(4+1)=
√4+0.2=
2+0.2=2.2 ==> between 2.01 and 2.24: a
Which statement correctly describes the graph of G(x) = -3f(x)?
A. The graph of g is the graph of f horizontally stretched by a scale factor of 3 and reflected over the x-axis
B. The graph of g is the graph of f horizontally stretched by a scale factor of 3 and replicated over the y-axis
C. The graph of g is the graph of f vertically stretched by a scale factor of 3 and reflected over the x-axis
D. The graph of g is the graph of f vertically stretched by a scale factor of 3 and reflected over the y-axis
Answer:
C is the correct choice.
Step-by-step explanation:
Here are the rules for vertical stretches and reflection
Given a function f(x), a new function [tex]g(x)= a \cdot f(x),[/tex] where a is a constant, is a vertical stretch or vertical compression of the function f(x).
Since the question use a multiplicative of -3, and -3 < 0 we get the correct choice as C: The graph of g is the graph of f vertically stretched by a scale factor of 3 and reflected over the x-axis
twicw the sum of a number and 7 is more than 6 or at most -3
Answer:
2(x+7) more than(>) 6
Step-by-step explanation:
Answer:D
Step-by-step explanation:
Thank me later
Determine the number of solutions of this equation.
2(x-1)=3(x-4)
Infinitely many solutions
One solution
No solutions
Answer:
One solution.
Step-by-step explanation:
2(x-1)=3(x-4)
2x - 2 = 3x - 12
-2 + 12 = 3x - 2x
10 = x.
np bisects MNQ, measurement MNQ, measurement MNP = (6X-12)° and measurement PNQ = (4x+8)°. find measurement MNQ
The Required answer is ∠MNQ is (10x - 4)°
Two unique points on a line define the boundaries of a line segment. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Given NP bisects MNQ as shown in the given figure
A line segment that bisects two lines divides them into two equal parts.
Given ∠MNP =( 6x - 12)°
Given ∠PNQ = (4x + 8)°
We have to determine ∠MNQ as
∠MNQ = ∠MNP + ∠PNQ
= 6x - 12 + 4x + 8
= 10x - 4
Therefore, the answer for the given question is ∠MNQ is (10x - 4)°
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An image shows two right triangles A B C and D E F. Triangle A B C: Side A B is 3. Side B C is 5. Side C A is 4. Triangle D E F: Side D E is 6. Side E F is 10. Side F D is 8. Which statement about the two triangles is correct? ~ because You cannot tell if the triangles are similar because the angles are not given. is not similar to , because , while . is congruent to
If the ratio of the sides of the triangles ΔABC and ΔDEF are equal then the triangles are similar triangles. Then the correct option is B.
What is the triangle?
Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
A picture shows triangle ABC and triangle DEF.
Triangle ABC: Side AB is 3, Side BC is 5, and Side CA is 4.
Triangle DEF: Side DE is 6, Side EF is 10, and Side FD is 8.
The ratio of the sides of the triangles ΔABC and ΔDEF will be given below.
AB/DE=BC/EF=CA/FD
3/6=5/10=4/8=1/2
If the ratio of the sides of the triangles ΔABC and ΔDEF are equal then the triangles are similar triangles.
The diagram is shown below.
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Two right triangles—A B C and D E F. The triangles ΔABC and ΔDEF are comparable triangles if the ratio of their sides is the same.
Given that,
Two right triangles—A B C and D E F. Triangle A B C has a side of 3, a side of 5, and a side of 4.
Triangle D E F: sides D and E , side E and F and side F and each 6, 10, and 8.
Because the angles are not provided, making it impossible to determine whether the triangles are identical is not comparable to.
We have to find which of the two triangles' respective claims is true.
Describe the triangle.
The polygonal shape known as a triangle has three sides and three angles. The sum of the triangle's angles is 180 degrees.
Triangle ABC and triangle DEF are depicted in an image.
Triangle ABC has sides AB at 3, BC at 5, and CA at 4.
Triangle DEF has sides.
Sides DE at 6; EF at 10; and FD at 8.
The triangles ΔABC and ΔDEF side ratio will be provided below.
AB/DE=BC/EF=CA/FD
3/6=5/10=4/8=1/2
Therefore, The triangles ΔABC and ΔDEF are comparable triangles if the ratio of their sides is the same.
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Which rational number is positive
9n - 50 = 4, what does n equal?
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{9n - 50 = 4}[/tex]
[tex]\large\text{Add 50 to both sides:}[/tex]
[tex]\mathsf{9n - 50 + 50= 4 + 50}[/tex]
[tex]\large\text{Simplify it:}[/tex]
[tex]\mathsf{9n = 4 + 50}[/tex]
[tex]\mathsf{9n = 54}[/tex]
[tex]\large\text{Divide 9 to both sides:}[/tex]
[tex]\mathsf{\dfrac{9n}{9} = \dfrac{54}{9}}[/tex]
[tex]\large\text{Simplify it:}[/tex]
[tex]\mathsf{n = \dfrac{54}{9}}[/tex]
[tex]\mathsf{n = 6}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{n = 6}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
(01.01 LC)
What is the simplified form of
a
b
C
d
45√x
√√4x
√√x.√√x-√√x-√√x?
Answer:
Step-by-step explanation:
I don’t understand this question
Answer:
f(-4) = - 64
f(3) = - 15
f(-a) = - 3a² - 4a
-f(a) = 3a² - 4a
f(a + h) = - 3a² - 6ah - 3h² + 4a + 4h
Pay careful attention that you do not miss the negative signs in some of these terms
Step-by-step explanation:
The function is f(x) = -3x² + 4x
To evaluate the function at any value of x, simply substitute for x in the function expression
f(-4)