The solution to the system of equation below is (−2, −1).
2x − 3y = −1
11x − 9y = −13
When the first equation is multiplied by −3, the sum of the two equations is equivalent to 5x = −10.
Which system of equations will also have a solution of (−2, −1)?
5x = −10
11x − 9y = −13
2x + 9y = −1
11x − 9y = −13
−6x + 9y = −1
11x − 9y = −13
−6x + 3y = −1
5x = −10
Answer:
The correct option is 1.
Step-by-step explanation:
If a system of equation have solution (a,b), then the equations of system must be satisfied by the point (a,b).
It is given that the system of have solution (-2,-1), so the equations of system must be satisfied by the point (-2,-1).
The system of equation in option 1 is
[tex]5x=-10[/tex]
[tex]11x-9y=-13[/tex]
Put (-2,-1) in the above equations.
[tex]5(-2)=-10\Rightarrow -10=-10[/tex]
[tex]11(-2)-9(-1)=-13\Rightarrow -13=-13[/tex]
Since left hand side is equal to right hand side, therefore the point (-2,-1) satisfy the equations and (-2,-1) is the solution of the given system.
Similarly check the other system of equations, whether the point (-2,-1) stratify the equations or not.
In option 2,
[tex]2x+9y=-1[/tex]
[tex]2(-2)+9(-1)=-1\Rightarrow -13=-1[/tex]
Since left hand side is not equal to right hand side, therefore the point (-2,-1) is not the solution of this system of equation.
In option 3,
[tex]-6x+9y=-1[/tex]
[tex]-6(-2)+9(-1)=-1\Rightarrow 3=-1[/tex]
Since left hand side is not equal to right hand side, therefore the point (-2,-1) is not the solution of this system of equation.
In option 4,
[tex]-6x+3y=-1[/tex]
[tex]-6(-2)+3(-1)=-1\Rightarrow 9=-1[/tex]
Since left hand side is not equal to right hand side, therefore the point (-2,-1) is not the solution of this system of equation.
Only option 1 is correct.
scientific notation of 19 hundred thousandths
Final answer:
The scientific notation of 19 hundred thousandths (0.0019) is 1.9 × 10⁻³, accomplished by moving the decimal point three places to the right.
Explanation:
The scientific notation of the number 19 hundred thousandths, which is written as 0.0019 in decimal form, involves expressing it as the product of a number between 1 and 10 and a power of 10. To convert to scientific notation, we must move the decimal point three places to the right, which will change the number to 1.9. Since we moved the decimal point to the right, the exponent will be negative. Therefore, 0.0019 in scientific notation is 1.9 × 10⁻³.
i need help on this math problem
Write the relatioship between the values of the given digits
The 6s in 6,600
Triangle PQR is formed by the three squares A, B, and C:
Which statement best explains the relationship between the sides of triangle PQR?
(PQ)2 + (QR)2 = (PR)2, because 9 + 16 = 25
PQ + QR = PR, because 9 + 16 = 25
(PQ)2 + (QR)2 = (PR)2, because 52 + 32 = 42
PQ + QR = PR, because 52 + 32 = 42
Answer:
A.[tex]PR^2=PQ^2+QR^2[/tex]
Because [tex]25=9+16[/tex]
Step-by-step explanation:
We are given that
Area of square A=[tex]9[/tex] square units
Are of square B=[tex]16[/tex] square units
Area of square C=[tex]25[/tex] square units
We have to find the relationship between sides of triangle PQR.
Side of square=[tex]\sqrt{Area\;of\;square}[/tex]
Using the formula
Side of square A=[tex]\sqrt{9}[/tex]=3 units
Side of square B=[tex]\sqrt{16}=4[/tex] units
Side of square C=[tex]\sqrt{25}=5[/tex] units
Pythagoras theorem
[tex](hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2[/tex]
Using Pythagoras theorem
[tex]PR^2=PQ^2+QR^2[/tex]
[tex]5^2=3^2+4^2[/tex]
[tex]25=9+16[/tex]
Option A is true
Tickets to a concert cost 2$ for children and 5$ for adults. If 630 people attended the concert and ticket sales totaled 2,910$, how many children attended the concert
c= children
a= adults
c+a = 630
c=630-a
2c + 5a = 2910
2(630-a) +5a=2910
1260-2a+5a=2910
1260+3a=2910
3a=1650
a = 1650/3=550
550 adult tickets
630-550 = 80 children's tickets
check:
550*5 = 2750
80*2=160
2750+160=2910
is 113,724 divisible by 3,5,6,or9
I REALY NEED HELP!
In kite ABCD, m∠ACD=82°. What is m∠DCE?
1.)41°
2.)82°
3.)90°
4.)98°
Answer:
(A)41°.
Step-by-step explanation:
We know that in Kite, the diagonals are the angle bisectors, therefore
In Kite ABCD, m∠ACD=82°, thus
[tex]m{\angle}DCE=\frac{1}{2}m{\angle}ACD[/tex]
Substituting the given value, we have
⇒[tex]m{\angle}DCE=\frac{1}{2}(82^{\circ})[/tex]
⇒[tex]m{\angle}DCE=41^{\circ}[/tex]
Therefore, the measure of m∠DCE is 41°.
Hence, option A is correct.
The graph shows the height, y, in centimeters, of a plant after a certain number of weeks, x. Shania drew the line of best fit on the graph.
A graph titled Plant Height shows Number of Weeks on x axis and Height of Plant in cm on y axis. The scales on both x and y axes are shown from 0 to 5 at increments of 5. The graph shows dots at the ordered pairs 0, 1 and 0.5, 1.2 and 1, 1.4 and 1.5, 2 and 2, 2.4 and 2.5, 2.7 and 3, 3 and 3.5, 3.3 and 4, 3.5 and 4.5, 3.8 and 5, 4. A straight line joins the ordered pairs 0, 1 and 5, 4
What would most likely be the approximate height of the plant after 7 weeks?
5.2 centimeters
7.6 centimeters
8.7 centimeters
12.7 centimeters
Answer:
5.2 cm.
Step-by-step explanation:
Given :
Number of Weeks(x) Height of Plant (y)
0 1
0.5 1.2
1 1.4
1.5 2
2 2.4
2.5 2.7
3 3
3.5 3.3
4 3.5
4.5 3.8
5 4
We are given that A straight line joins the ordered pairs 0, 1 and 5, 4
So, we will find the equation of line using two point slope form:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex](x_1,y_1)=(0,1)[/tex]
[tex](x_2,y_2)=(5,4)[/tex]
Substitute the values in the formula
[tex]y-1=\frac{4-1}{5-0}(x-0)[/tex]
[tex]y-1=\frac{3}{5}(x)[/tex] ---A
Now we are supposed to find e the approximate height of the plant after 7 weeks.
Substitute x = 7 in A
[tex]y-1=\frac{3}{5}(7)[/tex]
[tex]y=\frac{3}{5}(7)+1[/tex]
[tex]y=5.2[/tex]
Hence the approximate height of the plant after 7 weeks is 5.2 cm.
Which line has the following intercepts?
x intercept = (3/7, 0)
y intercept = (0, -1.2)
A) 7x+6y = 3
B) 7x-6y = 3
C) 7x+6y = (-3)
D) 7x-6y = (-3)
Leo spent the same amount of time working on each of 5 different weight machines and then spent 2/3 of an hour on the treadmill. If he spent a total of 1 3/4 hours at the gym, which shows the correct equation and solution for x, the number of hours Leo spent at each of the weight machines?
Let's break this down. We know that there are 5 weight machines, and Leo spent an equal amount of time on all of them. Since we don't know how long he spent on each, we'll use x. Our equation so far is 5x. Then, we know that he spent 2/3 hour on the treadmill, which we will just add to the 5x. So, now our equation is 5x + 2/3. Lastly, we know that the total time Leo spent at the gym is 1 3/4 hours, which we set the last equation equal to. Our final equation is 5x + 2/3 = 1 3/4. Then, all we have to do is solve for x. What we can do to make this easier is to change all of the fractions into numbers. After changing everything, here is our equation: 5x + 40 = 105. Then, we will subtract 40 from each side and divide both sides by 5. Therefore, Leo spent 13 minutes on each weight machine.
ANSWER:
A) 5x + 2/3 = 1 3/4 ; Leo spent 13 minutes at each machine
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Final answer:
Solving for the time Leo spent on each weight machine involves setting up an equation based on the total gym time and subtracting the time spent on the treadmill, resulting in Leo spending about 13 minutes at each weight machine.
Explanation:
To solve for the amount of time Leo spent at each weight machine, we need to set up an equation based on the total time spent at the gym. First, we know that Leo spent 2/3 of an hour on the treadmill. With a total gym time of 1 3/4 hours (which is the same as 7/4 hours), we can subtract the treadmill time to find the time spent on the weight machines. Thus, the equation can be set up as follows:
5x + 2/3 = 7/4
To solve for x, the hours Leo spent at each weight machine, follow these steps:
Subtract 2/3 from both sides of the equation: 5x = 7/4 - 2/3
Find a common denominator for the fractions and subtract: 5x = 21/12 - 8/12
Simplify the right side: 5x = 13/12
Divide both sides by 5 to solve for x: x = 13/60 hours
This means Leo spent 13/60 hours, or about 13 minutes, at each of the 5 weight machines.
common ratio of fraction in geometric sequence?
5/12,-1/6,1/15,-2/75,4/375
The common ratio between each pair of terms in the given geometric sequence of fractions is -2/5.
Explanation:A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant factor called the common ratio. To find the common ratio in a geometric sequence of fractions, we divide each term by the previous term. Let's calculate the common ratios for the given sequence:
Common ratio between 5/12 and -1/6 = (-1/6) / (5/12) = -1/6 * 12/5 = -2/5Common ratio between -1/6 and 1/15 = (1/15) / (-1/6) = 1/15 * (-6/1) = -2/5Common ratio between 1/15 and -2/75 = (-2/75) / (1/15) = -2/75 * 15/1 = -2/5Common ratio between -2/75 and 4/375 = (4/375) / (-2/75) = 4/375 * (-75/2) = -2/5As we can see, the common ratio between each pair of terms in the given geometric sequence of fractions is -2/5.
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Multiply (4+I)(1-5i)
Answer:
9 - 19i
Step-by-step explanation:
I dont understamd this problem please help------!
A work crew has a new pump and an old pump. The new pump can fill a tank in 5 hours, and the old pump can fill the same tank in 7 hours. Write and solve and equation for the time it will take both pumps to fill one tank of the pumps are used together.
If a scale model of a building is 5 inches wide by 7inches long. if the scale is 1 in.:15ft,how long is the building?
If a scale model of a building is 5 inches wide by 7inches long then the real-life length of the building is 105 feet.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
If the scale of the model is 1 inch : 15 feet, this means that every inch on the model represents 15 feet in real life.
The model is 5 inches wide by 7 inches long.
Let's use the length dimension to find the real-life length of the building:
7 inches on the model represents 7 x 15 = 105 feet in real life.
Therefore, the real-life length of the building is 105 feet.
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What is 14/28 in simplest form?
A regulation soccer goal net is 24 ft wide by 8 ft high. A soccer net for children is 6 ft wide. If the manufacturer wishes to keep the children's soccer net to scale, how tall should the children's net be? What is the scale factor? (round answer to two decimal places)
To maintain the scale of a children's soccer net to that of a regulation net, the height should be 2 feet, given that the child-size net is 6 feet wide. The scale factor used is 0.25.
Explanation:The question asks us to find the scaled dimensions for a children's soccer net based on the dimensions of a regulation soccer goal net. The original dimensions are 24 ft in width and 8 ft in height. If a children's soccer net is 6 ft wide and we want to keep the same scale, we need to calculate the height of the net in proportion to the regulation net's dimensions.
Height Calculation:
The scale factor is the ratio of the width of the children's net to the width of the regulation net. To find the height of the children's net, we multiply the height of the regulation net by the scale factor:
Scale Factor = Width of Children's Net / Width of Regulation Net
Scale Factor = 6 ft / 24 ft = 0.25
Height of Children's Net = Scale Factor × Height of Regulation Net
Height of Children's Net = 0.25 × 8 ft = 2 ft
Therefore, to maintain the scale, the height of the children's soccer net should be 2 feet, and the scale factor is 0.25.
(14y) exponent of 4 simplify plz help
Evaluate the following expression.
5-3
subtract 5-3 = 2
check 2+3 =5
Tommy and Zach are starting out at the same position. Tommy runs north at 3 miles per hour and Zach starts to run east 2 hours later at the rate of 4 miles per hour. How long until Tommy and Zach are 8 miles apart?
Zach=2 hours Tommy= 3 1/2 hours
A street that is 351ft long is covered in snow. City workers are using a snowplow to clear the street. The snowplow has tires that are 3.5ft in diameter. How many times does a tire have to turn in traveling the length of the street?
Solve x3 = 1 over 8.
Answer:
The simplified form of the provided equation is 1/2.
Step-by-step explanation:
Consider the provided equation.
[tex]x^3=\frac{1}{8}[/tex]
8 can be written as 2³
1 can be written as 1³
Therefore the provided equation can be written as:
[tex]x^3=\frac{1^3}{2^3}[/tex]
[tex]x^3=(\frac{1}{2})^3[/tex]
[tex]x=\frac{1}{2}[/tex]
Hence, the simplified form of the provided equation is 1/2.
compare the values of the underlined digets 6035 and 530 the digit is 3
What are the fractions of 48
How much is 1 foot line of quarters worth
a quarter is 1.75 mm thick
1 mm = 0.0393701 inches
0.0393701/12 = 25.4 mm per inch
25.4/1.75 = 14.5 quarters per inch
14.5 x 12 = 174 quarters per foot
174 x 0.25 = 43.50
$43.50 for a foot of quarters
Alina spent no more than $45 on gas for a road trip. The first gas station she used charged $3.50 per gallon and the second gas station charged $4.00 per gallon. Which inequality relates the number of gallons of gas she bought at the first station, x, the number of gallons of gas she bought at the second station, y, and the total amount she paid? What are the possible values of y?
Answers
A)3.5x + 4y ≥ 45, y ≥ 11.25
B)3.5x + 4y ≥ 45, 0 ≤ y ≤ 10.375
C)3.5x + 4y ≤ 45, 0 ≤ y ≤ 11.25
D)3.5x + 4y ≤ 45, y ≥ 10.375
Answer:
Option C is correct.
Step-by-step explanation:
Alina spent no more than $45 on gas for a road trip.
Let gallons bought at first station be = x
Let gallons bought at the second station be = y
The first gas station she used charged $3.50 per gallon and the second gas station charged $4.00 per gallon.
Equations become: 3.50x and 4y
Total money spent on gas is no more than $45.
So, complete equation is given as:
[tex]3.50x+4y \leq 45[/tex]
To know the possible value of y let us assume she bought all the gas from second station.
[tex]4y\leq 45[/tex]
[tex]y\leq 11.25[/tex]
As the number of gallons can not negative, range is:
[tex]0\leq y\leq 11.25[/tex]
Therefore, option C is correct.
Part A: If (72)x = 1, what is the value of x? Explain your answer.
Part B: If (70)x = 1, what are the possible values of x? Explain your answer.
The solution of the equation 72x = 1 is 1/72 and 70x = 1 is 1/70.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
72x = 1
Simplify the equation, then the value of x will be
72x = 1
x = 1/72
The equation is given below.
70x = 1
Simplify the equation, then the value of x will be
70x = 1
x = 1/70
Then the solution of the equation 72x = 1 is 1/72 and 70x = 1 is 1/70.
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sharon and anthony dropped a stone from a 150-foot cliff. find the time, t, in seconds that it will take for the stone to reach the ground. let t=1/4 square root of s, where s represents the distance in feet the stone will fall.
which of the following is an example of a common topic.
A) anyone can be brave.
B) freedom takes sacrifice.
C) the box was broken.
D) bravery.
Answer:
D. Bravery
Step-by-step explanation:
Bravery is a general topic.
the radius of the circle is πcm. the base of the triangle is πcm . the area of the circle equals the area of the triangle. what is the height of the triangle