Answer:
x + 2y = 5
Step-by-step explanation:
y = mx + b the m is the slope or gradient.
y=2x+3 The slope is 2.
When lines are perpendicular, the slopes are opposite inverses of each other. So, the perpendicular slope to 2 is -1/2. I would write the answer in the point slope of the line and then change the equation to the stand form
y -2 = -1/2(x -1) Distribute the -1/2
y - 2 = -1/2x + 1/2 Add 1/2 x to both sides
1/2x + y -2 = 1/2 Add 2 to both sides
1/2x +y = 5/2 Multiply by 2 to clear the decimal
x + 2y = 5
an elevator can carry 15 adults or 20 children at one time. During the course of a day, the elevator carries a full passenger load 52 times. if all the passengers were children, how many more people would the elevator carry then if all the passengers were adults
Answer:
Step-by-step explanation:
20(kids per ride) x 52(number of rides) = 1040. 15(adults per ride) x 52(number of rides) = 780. 1040-780= 260 more kids than adults.
Which number sentence is true? OA. 2 3/4 >2.68 2² OB. 7.895 x 10² > 5.43 x 10³ OC. √63>811 OD. 1-151> 13.21
All the expressions like (a), (b) and (c) are true sentences in the form of inequality.
What is inequality expression?
The inequality expression in a sentence consist of two algebraic expression with the inequality symbols. And the solution of an inequality is a number which when substituted for the variable to makes the inequality as a true statement.
According to the question, the given inequality expressions in the form of the sentence is as follows:
(a) 2(3/4) > 2.68;
(b) 7.895 x 10² > 5.43 x 10³;
(c) √63 > 8.11;
(d) |-1.5| > |3.2|
In this, all the expressions like (a), (b) and (c) are true sentences in the form of inequality.
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a = 5.2 cm and B = 67°.
Work out the area of the triangle. Round
your answer to 1 DP.
The area of the triangle for the given parameter is 12.4 squared cm.
How to calculate the area of the triangle?
In mathematics, the area of the triangle is classified into three forms isosceles, scalene and equilateral. Depending upon the sides of the triangle, it is classified. That means, when the two sides are equal then the triangle is isosceles triangle.
According to the question, the given parameters for the calculation of the area of the triangle is as written below:
Side of the triangle(a) = 5.2 cm. Angle of a triangle(B) = 67°.
Using standard formula for the area of the triangle, we get:
Area of the triangle = (1/2)(5.2)(5.2)sin(67°) = 12.4384 = 12.4 squared cm.
Hence, the area of the triangle for the given parameter is 12.4 squared cm.
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(2^3×2^4) simplify and expression 7th grade.
The simplified expression of (2^3×2^4) is 2^7
How to evaluate the expression?The expression is given as
(2^3×2^4)
The base of the above expression are the same
i.e. Base = 2
This means that we can apply the law of indices
When the law of indices is applied, we have the following equation:
(2^3×2^4) = 2^(3 + 4)
Evaluate the sum in the above equation
So, we have
(2^3×2^4) = 2^7
Hence, the simplified expression of the expression given as (2^3×2^4) is 2^7
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alex has a circular rug the radius of the rug is 5 1/4 feet which is closest to the area of the rug use 22/7
The area when Alex has a circular rug the radius of the rug is 5 1/4 feet is 86.625 feet².
How to calculate the area?It should be noted that the area of a circle is given the formula:
Area of a circle = πr²
where π = 22/7
r = radius = 5 1/4
Therefore, the area will be:
Area = πr²
Area = 22/7 × (5 1/4)²
Area = 22/7 × 25 1/16
Area = 86.625 feet²
The area is 86.625 feet².
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-1 1/3 - 1/6 subtract using number line
The addition of the two negative numbers has a result of -3/2, and is illustrated on the number line given at the end of the answer.
How to add two negative numbers?To add two negative numbers, we keep the negative signal and then we add the quantities, that are represented by the numbers without the signal.
For this problem, the numbers are given as follows:
-4/3, which is the mixed number -1 and 1/3, given by -1 - 1/3 = -3/3 - 1/3 = -4/3.The fraction -1/6.Hence the addition of the negative numbers is given as follows:
-4/3 - 1/6 = -8/6 - 1/6 = -9/6 = -3/2.
The result is of -3/2.
As for the number line, we have two negative numbers, hence each increment is to the left of the number line. The sum of the two increments, starting at zero, of 1/6 and of 4/3, combine to 3/2, as given by the image at the end of the answer.
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If a construction crew paved 9680
yards of road, how many miles of road
did they pave? (1760 yards = 1 mile)
Answer: m = 5.5
Step-by-step explanation:
9680 / 1760 = m
m = 5.5
Suppose sin a + cos b = -0.2 while sin b + cos a = 1.6. What is the value of sin(a+b)?
The value of the trignometric expression sin(a+b) is 0.3.
Given the trignometric equations sin a + cos b = -0.2 and sin b + cos a = 1.6
So, squaring both equations and adding them
we have
[tex](sin a + cos b)^2 = -0.2^2\\(sin a + cos b)^2 = 0.04\\sin^2a+cos^2b + 2 sina cos b= 0.04\\(sin b + cos a)^2 = 1.6^2\\sin^2b+cos^2a + 2 sinb cos a= 2.56\\\\[/tex]
adding both equations
[tex]sin^2a+cos^2b + 2 sina cos b + sin^2b+cos^2a + 2 sinb cos a= 0.04+2.56\\[/tex]
1+1+2( sina cos b + cos a sin b)= 2.6
2( sina cos b + cos a sin b) = 0.6
( sina cos b + cos a sin b) = 0.3
We know that sin(a+b)= ( sina cos b + cos a sin b)
So,
sin(a+b)=0.3
Therefore, the value of sin(a+b) = 0.3
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a researcher is interested in the travel time of utrecht university students to college. a group of 50 students is interviewed. their mean travel time in 16.7 minutes. for this study the mean of 16.7 minutes is an example of a:
For this study, the mean of 16.7 minutes is an example of a (B) Statistic.
What do we mean by Statistic?As opposed to methods for gathering statistical data, mathematical statistics is the application of probability theory, a subfield of mathematics, to statistics. Mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory are some of the specific mathematical methods used in this. Due to the abstract concepts and ideas that you will encounter later in your study, statistics stands out as the more challenging area of math. When you actually try to understand what's happening in a statistics equation or problem, you'll discover that the concepts are very challenging.So, the appropriate choice is an option (B).
In this case, a researcher is interested in how long it takes Utrecht University students to get to class. For this study, a sample of 50 students was gathered, and the sample mean for travel time was found to be 16.7 minutes.Since the sample means is a sample statistic, option (B) is the right choice.Therefore, for this study, the mean of 16.7 minutes is an example of a (B) Statistic.
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The correct question is given below:
A researcher is interested in the travel time of Utrecht University students to college. A group of 50 students is interviewed. Their mean travel time in 16.7 minutes. For this study, the mean of 16.7 minutes is an example of a(n)
A. Parameter
B. Statistic
C. Population
D. Sample.
there are 10 boys and 15 girls. The teacher chooses a student by random. Eric says that the probability for a boy to be chosen is 0.5. Jenny says he is wrong. Who is correct. Give reasons
In a case whereby there are 10 boys and 15 girls and the teacher chooses a student by random, then the probability that a boy will be chosen is 2/5 which means Jenny is right.
How can the probability be calculated?Since there are there are 10 boys and 15 girls, then the total number of the population will be (10+15)=25
Then the probability of that a boy will be chosen if one of them is been chosen at random will then be =10/25 = 2/5
Therefore, Jenny is very correct because the probability of that a boy will be chosen if one of them is been chosen at random will then be 2/5.
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2-b/3= -5/2 if you guys can help me thank you very much.
Answer:
b = 13.5
Step-by-step explanation:
2-b/3 = -5.2Multiply both sides of the equation by 6, the least common multiple of 3,212 - 2b = -15Subtract 12 from both sides-2b = -15 - 12Subtract 12 from -15 to get -27-2b = -27Divide both sides by -2b = -27/-2You can simplify -27/-2 by dropping off the negative sings making it b = 27/2Divide 27/2 to get 13.5 Or you can just simplify 27/2 to 13 1/2There are different ways you can solve this equation. Let me know if you'd like to know a different way.
Have a Good Rest of Your Day.
50 POINTS__ Solve for z and graph the solution.
–7 ≥ z–10 ≥ –14
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.
Answer:
Step-by-step explanation:
please look at the pic
By using internal angles of the triangles and the definition of supplementary angles, the measure of the angle MNP is equal to 54°.
How to determine a missing angle in a geometric systemHerein we find a geometric system formed by two common semirrays with a common vertex at point N and a line segment MP such that triangle MPN is a right triangle. By Euclidean geometry we know that the sum of the measures in the internal angles equals 180°:
m ∠ NMP + m ∠ MNP + m ∠ MPN = 180° (1)
And the two angles at point P are supplementary angles:
24 · x + m ∠ MPN = 180° (2)
Then, by (1):
90° + 9 · x + m ∠ MPN = 180°
m ∠ MPN = 90° - 9 · x
By (1) in (2):
24 · x + 90° - 9 · x = 180°
15 · x = 90°
x = 6
Then, the measure of the angle MPN is equal to:
m ∠ MNP = 9 · x
m ∠ MNP = 9 · 6
m ∠ MNP = 54°
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Pls help me and show steps too, I’m so lost. I’m giving a lot of points
Answer:
x=16
Step-by-step explanation:
I apologize I have not done geo in a while so I am not sure what the theorem is, but there is a theorem that states that when a transversal intersects with two parallel lines, two angles that are facing the same direction are the same angle. (the two white angles that i have marked are equal)
next, two lines that intersect each other will have the same angle measurements on opposite sides (the green marked angles are equal)
so that means 3x - 8 = x + 24
and when you simplify that, you get 2x = 32 ---> x = 16
Exercises
Write an algebraic expression for each verbal expression.
Four times a number?
The mathematical expression is as follows.
1) 4(v +3)
2) 15v -7
What is algebraic expression?An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x 2 2xy + c.
Given Data
Suppose the number is v
1) To obtain: four times the product of v and 3.
Accordingly, we must first add v and 3, and then multiply the result by 4.
The mathematical expression is as follows.
= 4(v+3)
2) Assume that v is the given integer.
What we're aiming for is: 7 less than 15 times v.
This calls for multiplying the v by 15 and then taking 7 out of the result.
The expression in algebra would be as follows:
= 15v - 7
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G(x)=-x^2/4+7
Over which interval does have a negative average rate of change?
Answer: [tex](-\infty, 0][/tex]
Step-by-step explanation:
This is a parabola that opens down (because of the negative leading coefficient).
So, the average rate of change (i.e., the slope of the secant) is negative when the function is decreasing.
The function is decreasing to the left of the vertex, which is at (0, 7).
So, the function has a negative average rate of change for [tex](-\infty, 0][/tex].
Note that although there is a stationary point at x = 0, and that the graph isn't decreasing at this point, the average rate of change is still negative when considering a point to the left.-0.6 as a fraction in simplest form
By dividing and multiplyinh the decimal by 10, we will see that:
-0.6 = -6/10
How to write the decimal as a fraction?Here we have the following decimal: -0.6
And we want to write it as a fraction.
To do so, we just need to multiply it and divide it by 10 as many times as digits we have after the decimal point. In this case we have only one digit after the decimal point, so we multiply and divide by 10 only once.
-0.6 = -0.6*(10/10) = (-0.6*10)/10 = -6/10
That is the fraction form of the given decimal.
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A cash discount of 8% is allowed on an item which costs £45. How much money is saved if a customer decides to pay in cash?
If a costumer decides to pay in cash then saved £3.6.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
A cash discount of 8% is allowed on an item which costs £45.
Now, The amount of Saved money calculated as;
Since, A cash discount of 8% is allowed on an item which costs £45.
Hence,
Saved money = 8% of £45
= 8 x 45 / 100
= 3.6
Thus, Saved money = 3.6
Therefore, If a costumer decides to pay in cash then saved £3.6.
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is Figure C a scaled copy of Figure D (Thank you!)
Answer:
Step-by-step explanation:
Figure D is a dialation of Figure C.
Each of the sides of Figure D is proportionate to Figure C
The scale factor is 1.5
3:2 = 4.5:3 = 3:2=3:2
A 5oz jar of jam costs $2.50. How much is the unit price per ounce?
The unit price per ounce of the jar of jam is $0.50
How to determine the unit price per ounce for the jam?From the question, the given parameters are
Volume = 5 oz
Cost of jam = $2.50
The unit rate of the jam is calculated as
Unit rate = Cost of jam/Volume
Substitute the known values in the above equation
So, we have the following equation
Unit rate = 2.50/5
Evaluate the quotient
So, we have the following equation
Unit rate = 0.5
Hence, the unit price per ounce is $0.50
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if c=4 work out the value of
c/2 + 6
Using arithmetic operations, If the value of c = 4 then the value of (c/2) + 6 is 7
The given expression is (c/2) + 6
The value of c = 2
To find the value of (c/2) + 6 we have to do the suitable arithmetic operation after substituting the value c in the expression
Substitute the value of c in the given expression (c/2) + 6
(c/2) + 6 = (2/2) + 6
Divide 2 by 2 first
(2/2) + 6 = 1+6
Add one and six
1+6 = 7
Hence, by using the arithmetic operation, if the value of c = 4 then the value of (c/2) + 6 is 7
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-12/x = 24/8 what does x equal
Simply 24/8 to 3.
-12/x = 3
Since x is the number being divided, we take the divisor and divide it by the quotient.
x = -12/3 = -4.
you make 12 equal payments. you pay a total of $1224. How much is each payment
What is the total number of Goals Scored in all 10 games combined? *
Number of goals
0
1
2
3
Your answer
Frequency
3
4
2
1
Based on the information given, the total number of Goals Scored in all 10 games combined is 11 goals.
How to illustrate the information?It should be noted that in Mathematics, frequency simply has to do with the number of occurence that an event has based on the data or the information that's illustrated.
Based on the information given, it should be noted that the number of goals as well as the frequency are given. This will be illustrated we:
Total number of goals will be:
= (0 × 3) + (1 × 4) + (2 × 2) + (3 × 1)
= 0 + 4 + 4 + 3
= 11 goals
Therefore, 11 goals are scored.
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what is 1+1x3/2+10x3450/2+300-500 I don't know what is it
Answer:
17052 1/2
You're Welcome
TASK E5.1
1 The length, width and height of the cuboid are
measured to the nearest cm.
volume = length x width x height
What is the lowest possible value
of the volume of the cuboid?
Main Book Page 139
7 cm-
4cm
9cm
The length, width and height of the cuboid are measured to the nearest cm, volume = length x width x height, the lowest possible value of the volume of the cuboid is [tex]cm^{3}[/tex].
What is volume?Volume is measurement of three-dimensional space that is occupied. Numerous imperial units or the SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have symbiotic relationship. The volume of a container is typically thought of as its capacity, not as amount of space it takes up. In other words, volume is the amount of fluid (liquid or gas) that the container may hold.
Volume was initially measured using naturally occurring vessels of a comparable shape and then with standardized containers. Arithmetic formulas can be used to quickly calculate volume of several straightforward three-dimensional shapes. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine volumes of more complex shapes. No object in the dimensions of zero, one, or two has volume; in the dimensions of four and above, the hypervolume is a concept similar to the standard volume.
Volume = 7cm*4cm*9cm = 252[tex]cm^{3}[/tex]
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-2x + 3y = -6 and -3x - 2y = 11
Step-by-step explanation:
-2x + 3y = -6
-3x - 2y = 11
-5x + y = 5
y = 5 + 5
y = 10
-2x + 3(10) = -6
-2x + 30 = -6
-2x = -6 - 30
-2x = -36
x = -18
i have no idea
Identify which graph can be used to solve each equation. Enter the letter of the correct graph next to the
equation.
Pleaseee help me
Please help me, I am very confused, I have no idea what to do.
Solve for x: (1 point) negative 9 over 8, multiplied by x minus 7 equals negative 25
Answer:
Step-by-step explanation: