Answer:
The larger number is 33
Step-by-step explanation:
Writing and solving a system of equations
Let x and y be the numbers
sum of two numbers is 38
x+y = 38
their product is 165
xy = 165
x = 38-y
Substitute this into xy =165
(38-y) * y = 165
38y - y^2 = 165
-y^2 + 38y -165 = 0
Multiply by -1
y^2 - 38y + 165 =0
Factor
( y-33) ( y-5) = 0
Using the zero product property
y -33 =0 y-5 =0
y =33 y=5
Now we can find x for each solution
x = 38-33 =5 x = 38-5 = 33
The two numbers are 33 and 5
The larger number is 33
Find the area and perimeter of the rectangle based on information given Length = 5 Width = x + 2
Given the length and the expression that represents the width of a rectangle, you need to remember that:
• The area of a rectangle can be calculated by multiplying its dimensions:
[tex]A=lw[/tex]Where "l" is the length and "w" is the width.
• The perimeter of a rectangle is:
[tex]P=2l+2w[/tex]Where "l" is the length and "w" is the width.
Then, knowing that:
[tex]\begin{gathered} l=5 \\ w=x+2 \end{gathered}[/tex]- You can set up that the area of this rectangle is:
[tex]A=5(x+2)[/tex]Simplifying, you get:
[tex]\begin{gathered} A=(5)(x)+(5)(2) \\ A=5x+10 \end{gathered}[/tex]- And the perimeter is:
[tex]\begin{gathered} P=(2)(5)+(2)(x+2) \\ P=10+2x+4 \\ P=2x+14 \end{gathered}[/tex]Hence, the answer is:
- The area is:
[tex]A=5x+10[/tex]- The perimeter is:
[tex]P=2x+14[/tex]George is 8 years old. Hisgrandpa, Liam, is 72 yearsold. How many times olderis Liam than George?
Hello there. To solve this question, we'll find how many times George's grandpa is older than his grandson.
First, this is also called the ratio of the ages between George and his grandpa.
To find this, we divide their ages in the order Grandpa : Grandson as following:
[tex]\frac{George^{\prime}s\text{ Grandpa age}}{\text{George's age}}=\text{ }\frac{72}{8}[/tex]Simplify the fraction by a factor of 8
[tex]9[/tex]This is how many times George's grandpa is older than him.
what is the answer to 2y+12=-10
Answer:
y=-11
Step-by-step explanation:
Step 1: Subtract 12 from both sides.
2y+12−12=−10−12
2y=−22
Step 2: Divide both sides by 2.
2y/2=-22/2
And would get you y=-11
How to describe congruent triangles?
Congruency is a term used to describe two objects with the same shape and size.
In this case, two triangles are congruent if they have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position.
For instance,
these triangles are congruent. They have the same sides but in different position.
Another example is
In this case the congruency is about angles. These 2 triangles have the same angles and the same sides but in different positions.
Another instance is
They are the same triangles but in different positions.
From the first question we can see that both triangles are congruent.
This imply that they are the same but in different position:
We can note that angle C is equal to angle T, therefore
[tex]\angle T=55[/tex]In the same way, angle U is equal to angle B, then we have
[tex]\angle B=59[/tex]We can find angle A by noticing that the interior angles of a triangle add up 180, that is
[tex]\begin{gathered} \angle A+\angle B+\angle C=180 \\ \angle A+59+55=180 \\ \angle A+114=180 \\ \angle A=180-114 \\ \angle A=66 \end{gathered}[/tex]Since angle V is equal to angle A, also V=66
what is the distance between (-3,-8) and (6,-8)
Answer:
9
Step-by-step explanation:
√(6 - -3)2 + (-8 - -8)2
= √(9)2 + (0)2
= √81
= 9
Hope this helps you out :)
a teacher writes a number set on the board as shown. 5,6,7,8
Which value of x in the number set makes 6(2x+12)=144
6 is the value of x in the number set makes 6(2x+12)=144
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The number set has numbers
Five comma, six comma, seven comma eight
5,6,7,8
We need to find which value of x in the number set makes 6(2x+12)=144
Now x=5
6(2x+12)=6(2(5)+12)
=6(10+12)
=6(22)
=132
So 5 is not value of x for 6(2x+12)=144
Now x=6
6(2x+12)=6(2(6)+12)
=6(12+12)
=6(24)
=144
5 is value of x for 6(2x+12)=144
Hence 6 is the value of x in the number set makes 6(2x+12)=144
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Arianna and her friend Grace are going to a carnival that has games and rides. Arianna played 6 games and went on 3 rides and spent a total of $27. Grace played 2 games and went on 9 rides and spent a total of $41. Determine the cost of each game and the cost of each ride.
Answer:
Rides cost $4
Games cost $2.50
Step-by-step explanation:
Let g = cost of games
Let r = cost of rides
6g + 3r = 27
2g + 9r = 41 Multiple this through by -3 and then add to the equation above.
-3(2g + 9r) = (41) -3
-6g - 27r = - 123
6g + 3r = 27
-24r = -96 Divide both sides by -24
r = 4 This is the cost of the rides.
Plug is 4 for r in either of the two original equations to solve for g
6g + 3r = 27
6g + 3(4) = 27
6g + 12 = 27 Subtract 12 from both sides
6g = 15 Divide both sides by 6
g = 2.5 This is the cost of the games.
what is the probability that this student does spend more than $25 a week on gas? a. 0.2445 b. 0.7555 c. 0.6740 d. 0.8403 e. 0.4532
Using conditional probability, it is found that there is a 0.83 = 83% almost 0.8403 probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.
Probability: -
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
Conditional Probability :
Using conditional probability, it is found that there is a 0.83 = 83% = P( A∩ B) / P(A)
In which
P(B|A) is the probability of event B happening, given that A happened.P(A∩B) is the probability of both A and B happening.P(A) is the probability of A happening.In this problem:
Event A: Commute to school each day.
Event B: Spends more than $25 a week.
80% indicated that they commute to school each day. of those that commute to school each day, hence , P(A) = 0.8
Of those, 83% spend more than $25 a week on gasoline, hence .
P(B|A) = 0.83
Thus, 0.83 = 83% probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.
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9000÷20=N ????? pls answer
To get the value of N let's do the division.
The value of N is 450
Yuriy and his brother Anduray are each mailing a birthday gift to a friend. Yurly's package weighs threepounds more than two times the weight of Anduray's package. The combined weight of both packages is 9pounds.Part 1: Write a system of two linear equations to represent this situation. Define each variable that you use.
Let 'x' be the number of pounds of Yurly's package and let 'y' be the number of pounds of Anduray's package. Since the combined weight of both packages is 9 pounds, then:
[tex]x+y=9[/tex]now, we have that Yurly's package weights three pounds more than two times the weight of Anduray's, we can write this as:
[tex]x=3+2y[/tex]thus, we have the following system of equations to represent this situation:
[tex]\begin{cases}x+y=9 \\ x=3+2y\end{cases}[/tex]can you help me with some math questions the option I chose was troposphere(above the surface
1.
What do you know?
the troposphere extends 8 to 20 km above the Earth's surface. The surface temperature is 15°C and decreases at a rate of 6.5°C per kilometer away.
What do you want to find out?
The temperature at any point of the troposphere
What kind of answer do you expect?
Any value below 15°C
2. Define variables,
T is for temperature, and
d is the distance away from the surface
3. What is the b -value
b = 15
which is the Earth's surface temperature or the initial temperature for our problem
4. What is the slope
the slope 'm' equals -6.5
which means that the temperature decreases 6.5°C per km
5. write the equation
[tex]\begin{gathered} y=b+mx \\ \Rightarrow T=15-6.5d \end{gathered}[/tex]the general form for this equations is y = b + mx
thus, for our problem, the equation is: T = 15 - 6.5*d
6.
a) the slope represents the rate of change of temperature with respect to distance, since m = -6.5 °C/km , this means the troposphere is getting 6.5 °C colder per km away from Earth's surface
b) the y-intercept represents the Earth's surface temperature
Graph:
7. identify 3 points
when d = 0 then T = 15, so our first point is (0,15)
when d = 1 then T = 15 - 6.5 = 8.5 , so our second point is (1,8.5)
when d = 2 then T = 15 - 13 = 2 so our third point is (2,2)
8. calculate the slope
let's use this equation and this set of points,
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ (x1,y1)=(1,8.5) \\ (x2,y2)=(2,2) \end{gathered}[/tex]let's replace and solve
[tex]m=\frac{2-8.5}{2-1}=\frac{-6.5}{1}=-6.5[/tex]We can see that it does match the slope from our model, which is -6.5
9. graph the line and the points,
10. Complete the sentence
... ends between 8 km and 20 km above Earth.
11. temperature at the farthest point
when d = 20 then,
[tex]\begin{gathered} T=15-6.5*20 \\ =15-130 \\ =-115 \end{gathered}[/tex]... the temperature is -115°C
12. Temperature range,
from... 15 °C to -115 °C
what is 4x=20[tex]4 \times = 20[/tex]what is the anwer can u help me pleaseeee
S={5}
1) Evaluating x in this question
4x=20 Divide both sides by 4
4/4x=20/4
x=5
So x is equal to 5, in this equation 4x=20
S={5}
FOR BRAIBLIEST AND 50 POINTS! I NEED THIS ASAP!
Directions: Graph these in one cartesian plane(clue: it would form a triangle)
The solution is the area between the three lines, a triangle with vertices marked (see attached).
can yall help me with this
At Lakeville South High School, 60% of students have high-speed internet access, 30% have a mobile computing device, and 20% have both. The proportion of students that have neither high-speed internet access nor a mobile computing device is:
A. 0%
B. 10%
C. 30%
D. 80%
E. 90%
Note: the answer is 30% but I can't for the life of me figure out why
That have neither high-speed internet access nor a mobile computing device is 30%.
What is Venn diagram?Venn diagrams are utilized in various fields including business, measurements, semantics, and so forth. Venn charts can be utilized to outwardly coordinate data to see the connection between sets of things, like shared characteristics and contrasts, and to portray the relations for visual correspondence.
According to question:In school, 60% of students have high-speed internet access, 30% have a mobile computing device, and 20% have both.
Venn diagram for the situation
Thus remaining 30% students hat have neither high-speed internet access nor a mobile computing device.
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how much is -5x+2=52
Find x
-5x+2=52
_______________
-5x + 2 = 52
subtracting 2
-5x + 2 -2 = 52 -2
-5x + 0 = 50
-5x = 50
Dividing by -5
-5/ -5 x = 50/ -5
1x= -10
x= -10
__________________
Answer
x= -10
What is the answer Im stressing
The value of corresponding angle x is 157°.
What are properties of parallel lines?Properties of Parallel Lines:
The pairs of corresponding angles are equal.
The pairs of vertically opposite angles are equal.
The pairs of alternate interior angles are equal.
The pairs of alternate exterior angles are equal.
Given: m║n
So, using the property of parallel lines we have the angles on the same side of transversal are supplementary. Let 23° is tranversal to α, then
23° +α = 180°
⇒α = 180°-23°
⇒α = 157°.
Now, using the property of vertically opposite angles we have
α = x = 157°
⇒ x = 157°
Therefore, the value of x is 157°.
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Is this relation a function? Justify your answer.
11
10
9
8
7
6
5
4
3
2 3 4 5 6 7 8 9 10 11
A. Yes, because every x-value corresponds with a single y-value.
OB. No, because two points with the same y-value have different x-
values.
OC. Yes, because the number of x-values is the same as the number of
y values.
OD. Yes, because every x and y-value is positive.
PLEASE HELP ME QUICK, HURRY!!!!
The relation is a function because (a) Yes, because every x-value corresponds with a single y-value.
How to determine if the relation is a function?From the question, we have the graph to represent the given parameters that can be used in our computation
We are to find out if the graph represents a function
For a graph to represent a function, the graph must pass the vertical line test
This means that a line drawn from the x-axis must touch the points at most once
In this case, the graph would pass the vertical line test because no two points have the same y coordinate
Hence, it is a function
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Find the center and radius of the circle: x² + y² - 2x + 4y = -1
We need to complete the perfect square in x and y, that is,
[tex]x^2-2x=(x-1)^2-1[/tex]and
[tex]y^2+4y=(y+2)^2-4[/tex]Then, our given equation can be rewritten as:
[tex](x-1)^2-1+(y+2)^2-4=-1[/tex]which is equal to
[tex]\begin{gathered} (x-1)^2+(y+2)^2-5=-1 \\ \end{gathered}[/tex]By moving -5 to the right hand side, we have
[tex]\begin{gathered} \mleft(x-1\mright)^2+\mleft(y+2\mright)^2=-1+5 \\ \mleft(x-1\mright)^2+\mleft(y+2\mright)^2=4 \\ \mleft(x-1\mright)^2+\mleft(y+2\mright)^2=2^2 \end{gathered}[/tex]Since the general circle equation is
[tex]\mleft(x-h\mright)^2+\mleft(y-k\mright)^2=r^2[/tex]then, the answer is:
[tex](x-1)^2+(y+2)^2=2^2[/tex]then, the center is (h,k)= (1, -2) and the radius is r=2
can you please help me
in this problem we have that
y+20=x+15 -------> by vertical angles
isolate variable y
y=x+15-20
y=x-5 ------> equation A
and
(3x+5)+(x+15)=180 ------> by form a linear pair (sipplementary angles)
solve for x
4x+20=180
4x=160
x=40
substitute the value of x in equation A
y=40-5
y=35
therefore
x=40 and y=35
Write the transformed equation of the parent function f(x)2^x where g(x) has been translated 3 units right and reflected across the x-axis.
The transformed equation of the parent function f(x) = x² will be g(x) = x²-27.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that, the transformed equation of the parent function f(x)=x² where g(x) has been translated 3 units right and reflected across the x-axis.
The function g(x) when the g(x) has been translated 3 units right is,
g(x) = x²-27
Thus, the transformed equation of the parent function f(x) = x² will be g(x) = x²-27.
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Quadrilateral XENA is a parallelogram. T is the point of intersection of the diagonals. For each situation, write an equation and solve for y.
Answer:
b
Step-by-step explanation:
just took the test yyyyyyyyyyyyyyyyyyyyyyyyy
4. What fraction of 2hrs 15 minutes is 1/4 of an hour?
The fraction of 2 hrs 15 minutes to 1/4 of an hour is 1/9.
What is fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Since,
1 hour = 60 minutes.
2 hours = 120 minutes.
2 hours 15 minutes = 120 + 15 = 135 minutes.
1/4 of an hour = 60/4 = 15 minutes.
So, the fraction is,
[tex]\frac{15}{135} = \frac{1}{9}[/tex]
Therefore, the fraction of 2 hrs 15 minutes to 1/4 of an hour is 1/9.
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In a card game, Bryce scores three times as many points as Jordan. Jordan scores four points fewer than Keturah, and Keturah scores two times as many points as Amelia. If Amelia scores 5 points, how many points did Bryce score?
Bryce made the basket equals 18 points.Amelia received a point total of 10 points.The point Jordan scored was 6 points.
How to find Bryce points ?
In a card game, Bryce scores three times as many points as Jordan. Jordan scores four points fewer than Keturah, and Keturah scores two times as many points as Amelia.
Amelia score the point :
2*5=10
Amelia received a point total of 10 points.
Jorden score the point :
10-4 =6 points
The point Jordan scored was 6 points.
Bryce score the points
3*6 = 18 points
Where
Bryce made the basket equals 18 points.
so,Bryce made the basket equals 18 points.Amelia received a point total of 10 points.The point Jordan scored was 6 points.
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A car is traveling at a steady speed. It travels 1 miles in 2 minutes. 2 4 How far will it travel in 34 minutes? In 1 hour? The car will travel miles in 34 minutes. Simplify your answer.
To answer this question, we need to find the unit rate for the steady speed. Then, we can proceed as follows:
[tex]S=\frac{d}{t}\Rightarrow S=\frac{1\frac{1}{2}}{2\frac{1}{4}}=\frac{1+\frac{1}{2}}{2+\frac{1}{4}}=\frac{\frac{2+1}{2}}{\frac{8+1}{4}}=\frac{\frac{3}{2}}{\frac{9}{4}}=\frac{3}{2}\cdot\frac{4}{9}=\frac{12}{18}=\frac{6}{9}=\frac{2}{3}[/tex]Then, we have that the unit rate, in this case, is 2/3 miles per minute.
Hence, the car will travel in 34 minutes:
[tex]d=S\cdot t=\frac{2}{3}\cdot34\Rightarrow d=\frac{68}{3}=\frac{66}{3}+\frac{2}{3}=22+\frac{2}{3}=22\frac{2}{3}[/tex]Thus, the car will travel 222/3 miles in 34 minutes.
The car will travel in one hour or 60 minutes:
[tex]d=\frac{2}{3}\cdot60=\frac{120}{3}\Rightarrow d=40[/tex]Then, the car will travel 40 miles in one hour or 60 minutes.
Solve the equation x^2-2zx+3xy-6zy=0 for x in terms of y and z
Answer:
x = 2z
x = -3y
Explanation:
Given the below quadratic equation;
[tex]x^2-2zx+3xy-6zy=0[/tex]Let's go ahead and factor the above completely as seen below;
[tex]\begin{gathered} x(x-2z)+3y(x-2z)=0 \\ (x-2z)(x+3y)=0 \end{gathered}[/tex]We'll now apply the Zero-product property which states that if the product of two numbers is equal to zero, it means that at least one of the numbers is equal to zero.
Applying the Zero-product rule, we'll have;
[tex]\begin{gathered} x-2z=0 \\ x=2z \\ Or \\ x+3y=0 \\ x=-3y \end{gathered}[/tex]Horatios haunted house
The number of Screamers when Runners are 6 is 4,
and the number of Runners when Screamers are 10 is 15.
what is ratio?It is basically the measurement of two numbers and it compares by how much one quantity is bigger than another.
When two ratios are equal, they are usually said to be in proportion.
As given in the above questions,
Screamers:Runners= 2:3
So, let the number of screamers in first case is x
Then, x:6 = 2:3
x= 4
Hence , the number of screamers is 4.
In second case, let the number of runners is y
Then, 10:y = 2:3
y= 15
Hence , the number of runners is 15.
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8. Lori bought a shirt and a hat at a half-off sale.
If she spent a total of $21 on the two items,
what was the original price of the hat?
Answer:
the hat cost 18
Step-by-step explanation:
if the shirt is 24 half the price of the shirt is 12 so 21-12= 9 which is the price of the hat discounted.
The original price of the hat is 18 because 9 x 2 = 18
Rosita mom is 42 years old she is six times as old as Rosita. The equation 6a=42 can be used to find Rosita age .A. 36 B. 7C. 48D. 8
We have the next equation
42=6a
we need to clear a
a=42/6
a=7
the answer is 7
HELP PLEASE! Solve and show work.
4x + 6 < -6
Answer:
Step-by-step explanation:
1. 4x+6<-6
2. 4x<-6-6
3. 4x<-12
4. x<-12/4
5. x<-3
6. The answer is x < -3.