The sum of the product of two and nine and the product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers is 100.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression can be written as,
[tex]\dfrac{(2 \times 9)+(2 \times 36)}{9} \times (2+3+5)[/tex]
The result of the above expression will be,
[tex]\dfrac{(2 \times 9)+(2 \times 36)}{9} \times (2+3+5)\\\\=\dfrac{18+72}{9} \times (10)\\\\[/tex]
= (90/9) × 10
= 10 × 10
= 100
Hence, the sum of the product of two and nine and the product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers is 100.
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h(x) = x² +1 k(x)=x-2
(h+k)(2) =
Will give Brainly
Answer:
(h + k) (2) = 5
Step-by-step explanation:
[tex]h(x) = x{^2} + 1 \space\ \space\ \space\ \space\ \space\ \space\ \space\ k(x) = x -2\\\\[/tex]
(h + k) (x) = h(x) + k(x)
= x² + 1 + x - 2
= x² + x -1
∴ (h + k) (2) = (2)² + 2 -1
= 5
Which system of equations is represented in the graph? On a coordinate plane, a horizontal line is at y = negative 2 and another line goes through (0, negative 3) and (6, 0). y = negative 2. x minus 2 y = 6. y = negative 2. x + 2 y = 3. x = negative 2. 2 x minus y = 3. x = negative 2. 2 x + y = negative 3.
The system of equations that is represented in the graph is:,y = -2.x-2y =6..Option B is correct.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
Two lines may be seen on the graph:
y = -2
The lines pass through (-3) and (6, 0). We use the slope-intercept form to get the second line's equation: y=mx+c
m = 0-(-3)/(6-0)
m=3/6
m=1/2
Substitute the values as;
[tex]\rm y = \frac{1}{2}x+c[/tex]
For the point x = 0 and y = -3
[tex]\rm y = \frac{1}{2}x-3[/tex]
The equation can be written as;
x - 2y = 6
The system of equations that is represented in the graph is:,y = -2.x-2y =6..
Hence, option B is correct.
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how did you find the height? thats what im confused on. A=(1/2)b x (h)
A triangle is a three-edged polygon with three vertices. The height of the triangle can be written as h = (2A)/b.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The complete question is:
Given the equation of the area of a triangle. how did you find the height of the triangle? A=(1/2)b x (h)
(Hint: Solve the equation for h)
Given the equation of the area of the triangle. Therefore, the height of the triangle can be written as,
A=(1/2)b x (h)
2A = b x h
h = (2A)/b
where h is the height of the triangle and b is the length of the base of the triangle.
Hence, the height of the triangle can be written as h = (2A)/b.
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7) Which statement about perpendicular lines is true?
A. Perpendicular lines form 90° angles.
B. Perpendicular lines share no points.
C. Perpendicular lines have the same slope.
D. Perpendicular lines are equidistant along their lengths.
Answer:
is the a. Perpendicular lines form 90° angles.
The sum of three consecutive even integers is 96
Answer:
The sum of three consecutive even integers is 96
31+32+33=96
Rationalize the denominator.
Hello and Good Morning/Afternoon!
Let's take this problem step-by-step:
What the problem asks for:
⇒ to rationalize the denominator
⇒ rationalize means that you multiply the numerator and
demonimator by the denominator
Let's put that into action:
[tex]\frac{\sqrt{a +1}-2 }{\sqrt{a+1}+2 } * \frac{\sqrt{a +1}+2 }{\sqrt{a+1}+2 }\\=\frac{a +1-4 }{a+1+4\sqrt{a+1}+4 } \\=\frac{a-3}{a+4\sqrt{a+1}+5 }[/tex]<== Answer
Hopefully that helps!
Theodore invests a total of $11,000 in two accounts paying 8% and 4% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $780.00.
________ was invested at 8% and
______ was invested at 4%.
The amount loaned at the interest rate of 8% is $2,500.
The amount loaned at the interest rate of 4% is $8,500.
What are the linear equations that represent the question?a + b = 11,000 equation 1
0.08a + 0.04b = 780 equation 2
Where:
a = amount loaned at the interest rate of 8%b = = amount loaned at the interest rate of 4%How much was loaned at 8% and 4%?In order to determine how much was loaned at 4%, take the following steps:
Multiply equation 1 by 0.08
0.08a + 0.08b = 880 equation 3
Subtract equation 2 from equation 3:
0.04b = 100
Divide both sides by 0.04:
b = $2500
Subtract 2,500 from 11,000 :
11,000 - 2,500 = $8,500
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In circle A shown below the measure of angle BAD is 148 degrees If mBC is 102 degrees, what is mCD?
The measure of arc CD from the given figure is 46 degrees
Circle theoremFrom the attached figure, the expression below is true;
arcBC + arcCD = <BAD
Given the following
<BAD = 148 degrees
arcBC = 102 degrees
Substitute
arcCD =148 - arcBC
arcCD = 148 - 102
arcCD = 46 degrees
Hence the measure of arc CD from the given figure is 46 degrees
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Write a sentence that describes the relationship between the dependent variable and the independent variable. (Hint: Ratio language can help.)
Sentence : "I did 60 brush strokes in 1 minute"
The dependent and the independent variable in the relationship y=60x are y and x respectively.
The Independent variables are variables whose value does not depend on any other variable. And it causes the change in other variables.
The dependent variable is those variables whose value is not independent and change in this variable is dependent on the change of the independent variable.
Given that you did 60 brush strokes in 1 minute. Therefore, the rate can be written as,
Rate = 60 strokes per minute
Now, the number of stokes in x minutes can be written as,
y = 60x
where y is the number of stokes,
x is the number of minutes
In the above relation, y is the dependent variable because its numerical value depends on time, while x is the independent variable.
Hence, The dependent and the independent variable in the relationship y=60x are y and x respectively.
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the university of detroit mercy is 3/4 miles from dana’s house. Marygrove college is 2/5 miles from her house. what is the difference in the two distances
A cars odometer reads 12,386 if the driver takes the car to and from work for three days and each trip is 32 miles one way what will the odometer read at the end of the third day
At the end of the third day, the new reading on the odometer will be 12,578 mi
What will the odometer reading at the end of the third day?
The initial odometer reading is 12,386 miles.
Then, the driver takes drives to and from work, such that each trip is 32 miles. Then each day he drives 2*2mi = 64 miles.
And he does this for 3 days, then the total distance driven is:
3*64mi = 192 miles.
At the end of the third day, the new reading on the odometer will be:
R = 12,386 mi + 192mi = 12,578 mi
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How many ways are there to give 12 identical cookies to three children, so that each child has at least two cookies?
Simple As you can see 12 cookies are there and 3 children are there so
1 children will have = 12 ÷ 3
= 4
like this each kid will have 4 cookies where 4>2
What number exceeds y by 4 less than x
Answer: y + x - 4
Step-by-step explanation:
We will write an expression for this "number" by looking at the details given.
exceeds y { can become } y +
4 less than x { can become } x - 4
Now we will put the parts together.
y + x - 4
The number that answers this question is:
y + x - 4
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Question 11 (5 points)
Select the expression that is equivalent to x+x+yxyxy.
O 2x+y³
Ox² + y²
O² + 3y
2x+3y
Answer:
I don't know if you have any questions or need any further information please contact me your Telugu movie review poster
Find the unit rate.
594 chairs in 9 rows
Submit
||
chairs per row
Answer:
66 chairs
Step-by-step explanation:
Total number of chairs = 594
Total number of rows = 9
Number of chairs per row
= 594/9
= 66 chairs
__________
Hope it helps ⚜
7. Three vertices of a parallelogram are (0, 0), (−4,0) and (0, 5). Find all 3 possible coordinates for
the fourth vertex to make a rectangle and 2 different parallelograms. Explain or justify your
coordinate choice of how you know the sides are parallel. Find the lengths of each side
mathematically.
a) rectangle coordinate:
b) parallelogram:
c) parallelogram#2:
The given vertices combine with the fourth vertex as follows;
a) Coordinates; (-4, 5)
Lengths of the sides; 4 and 5
b) Coordinates; (4, 5)
Lengths of the sides; 4 and √41
c) Coordinates; (-4, -5)
Lengths of the sides; 5 and √41
How can the vertex coordinates be found?The given vertices are;
(0, 0): The origin
(-4, 0): 4 units to the left of the origin along the abscissa
(0, 5): 5 units above the origin, along the ordinate
a) The point that forms a rectangle is above the point (-4, 0) and to the left of the point (0, 5), which gives;
The coordinates of the point that forms a rectangle is the point (-4, 5)
The lengths of the sides are;
0 - (-4) = 4
5 - 0 = 5
b) The first parallelogram is formed by moving an equal distance of the point (-4, 0) from the origin from the point (0, 5), which gives;
The first parallelogram is formed by the point (4, 5)The lengths of the sides are;
4 - 0 = 4√((5 - 0)^2 + (4 - 0)^2) = √41c) The second parallelogram is formed by the moving an equal distance of the point (0, 5) from the origin from the point (-4, 0), which gives;
The second parallelogram is formed by the point (-4, -5)The lengths of the sides are;
(5 - (-5)) = 5 and √41Learn more about parallelograms here:
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Pls help! Geometry
A)what is the area of square?
B)area of the circle?
C)area of shaded?
(a) The side length of the square is 8 m, so its area is 64 square m.
(b) The radius of the circle is 4 m, so its area is [tex](\pi)(4^{2})=16\pi[/tex] square m.
(c) Subtracting areas, we get the area of the shaded region is [tex]64-16\pi[/tex] square m.
Find the equation of the line.
Through (-11, -1); perpendicular to y=15.
Answer:
x = - 11
Step-by-step explanation:
y = 15 is a horizontal line parallel to the x- axis
a perpendicular line must therefore be a vertical line parallel to the y- axis with equation
x = c
where c is the value of the x- coordinates the line passes through.
the line passes through (- 11, - 1 ) with x- coordinate of - 11 , then
x = - 11 ← equation of perpendicular line
Answer:
x = -11
Step-by-step explanation:
The line y = 15 is a horizontal line to the x-axis passing which passes through x = 0, y = 15
The line perpendicular to y = 15 passing through (-11, -1) is a vertical line where x = -11 for all values of y including -1
So the equation is x = -11
See attached graph
What are the factors of 32Round the following items to the nearest £1:
Item
Cost
Cost rounded to nearest £1
Notebook
£2.15
£
Pencil Case
£3.80
£
Colouring Pencil
£1.49
£
?
The factors of 32 as required in the task content are; 2, 4, 8, 16, 32.
What are the factors of 32?The factors of the number 32 as required in the task content are numbers whose multiples amount to 32 and are as listed above.
The item prices as given in the task content rounded to the nearest £1 are;
Notebook
£2.15 = £2
Pencil Case
£3.80 = £4
Colouring Pencil
£1.49 = £1
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At the beginning of a population study, a city had 370,000 people. Each year since, the population has grown by 6. Let be the number of years since start of the study. Let y be the city's population . Write an exponential function showing the relationship between y and
The exponential function that gives the relationship between y and t is:
[tex]y = 370000(1.06)^t[/tex].
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, the parameters are given as follows:
A(0) = 370000, r = 0.06.
Hence the equation is:
[tex]y = A(0)(1 + r)^t[/tex]
[tex]y = 370000(1 + 0.06)^t[/tex]
[tex]y = 370000(1 .06)^t[/tex]
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A right prism has a rhombus as a base. the height of the prism is 6 inches and the volume is 144 cubic inches. which could be the lengths of the diagonals of the rhombus?
If the height of prism is 6 inches and the volume is 144 cubic inches then the lengths of the diagonals of the rhombus will be 6 by 8 inches.
Given right prism has a rhombus as a base. Height of prism is 6 inches and the volume of prism is 144 cubic inches.
A right prism is a prism in which the edges and faces are perpendicular to the base faces.
Volume is the amount of substance a container can hold in its capacity.
Volume of right prism=area of base* height
=[tex]1/2 * d_{1}* d_{2} *6[/tex]
144=(144*2)/6 * [tex]d_{1} d_{2}[/tex]
(144*2)/6=[tex]d_{1} *d_{2}[/tex]
By options we get that the lengths of diagonals could be 6 inches by 8 inches.
Hence the length of diagonals be 6 inches and 8 inches.
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Answer: Hence the length of diagonals be 6 inches and 8 inches.
Step-by-step explanation:
(edg) got it right on test
A college's football team will play 16 games next fall. Each game can result in one of 2 outcomes: a win or a loss. Find the total possible number of
outcomes for the season record.
Using the Fundamental Counting Theorem, there are 65,536 outcomes possible for the season record.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, the parameters are given as follows:
[tex]n_1 = n_2 = \cdots = n_{16} = 2[/tex]
Then the number of ways is:
[tex]N = 2^{16} = 65,536[/tex].
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Which of the set of ordered pairs contains the line 1/3x+y=15
Answer:
{(-3, 16),(0, 15),(3, 14)}
Step-by-step explanation:
just plug in the points for x and y and solve to see if 15 is the answer you get for all of them which would give you B as your answer
numbers like 0 and 1 and 3 (because it would cancel 1/3x) are good numbers to do quick math with
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find a number between 1 5/8 and 1.62501
Answer:
[tex]1 \frac{125001}{200000}[/tex] or 1.625005
Step-by-step explanation:
To find a number between two numbers, if you're allowed to pick any number you want between those two numbers, one natural choice is the midpoint... the point that is exactly halfway between the two numbers.
Finding a midpoint
To find the midpoint of two numbers, divide their sum by 2:
[tex]\text{midpoint}=\dfrac{\text{first number}+\text{second number}}{2}[/tex]
It is convenient to have both numbers in decimal form or both numbers in fraction form for adding and dividing by 2.
Fraction form:
To convert 1.62501 to a fraction, we note that the last decimal digit is in the hundred-thousandths place, so we'll need a fraction with 100,000 in the denominator.
[tex]1.62501=1\frac{62501}{100000}[/tex]
Using our midpoint formula:
[tex]\text{midpoint} = \dfrac{ 1 \frac{5}{8} + 1 \frac{62501}{100000} } {2}[/tex]
find a common denominator...
[tex]\text{midpoint} = \dfrac{ 1 +(\frac{5}{8})*\frac{12500}{12500} + 1 +\frac{62501}{100000} } {2}[/tex]
[tex]\text{midpoint} = \dfrac{ 1 + \frac{62500}{100000} + 1 +\frac{62501}{100000} } {2}[/tex]
combining like terms...
[tex]\text{midpoint} = \dfrac{ 2 +\frac{125001}{100000} } {2}[/tex]
rewriting the division as multiplication of a reciprocal....
[tex]\text{midpoint} = \left(2 +\frac{125001}{100000} \right) *\dfrac{1}{2}[/tex]
distributing...
[tex]\text{midpoint} = \left(2 *\dfrac{1}{2} +\frac{125001}{100000} *\dfrac{1}{2}\right)[/tex]
[tex]\text{midpoint} = 1 +\frac{125001}{200000}[/tex]
[tex]\text{midpoint} = 1 \frac{125001}{200000}[/tex]
So, [tex]1 \frac{125001}{200000}[/tex] is the midpoint of the two numbers, and is a number that is between them.
Decimal form:
To convert [tex]1 \frac{5}{8}[/tex] to a decimal, we divide 5 by 8. 5 divided by 8 is 0.625.
So, [tex]1 \frac{5}{8}=1.625[/tex]
To find a midpoint of 1.625 and 1.62501, we use our midpoint formula:
Using our midpoint formula:
[tex]\text{midpoint} = \dfrac{ 1.625 + 1.62501} {2}[/tex]
[tex]\text{midpoint} = \dfrac{ 3.25001} {2}[/tex]
[tex]\text{midpoint} =1.625005[/tex]
So, 1.625005 is midpoint of the two numbers, and is a number that is between them.
Extension with decimals:
Knowing the decimal form of the two numbers, 1.625 and 1.62501, we can include trailing zeros at the end of these numbers (since it is to the right of the decimal point), so that 1.625 is equivalent to 1.625000, and 1.62501 is equivalent to 1.625010.
Note that the last two digits are in the millionths place, and that changing the digit in the millionths place for the first number (while leaving all other digits as they are) will also be a number between the two numbers (all 9 of the numbers with a star written below):
1.625000
1.625001*
1.625002*
1.625003*
1.625004*
1.625005*
1.625006*
1.625007*
1.625008*
1.625009*
1.625010
Describe how the graph of a line with a slop m=1/2 differ from the graph of a line with slop m=2?
The line with slope = 2 will be closer to the y-axis than the line with slope = 1/2
How to interpret the slopes?The slopes are given as:
Slope = 2
Slope = 1/2
The greater the absolute value of the slope of a linear equation.
The closer the function is to the y-axis
This means that the line with slope = 2 will be closer to the y-axis than the line with slope = 1/2
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108 centimeters equal how many meters?
Answer:
1.08 meters
Step-by-step explanation:
Divide by 100 to find this out. 108/100 = 1.08
You can remember this by knowing that the "centi-" prefix means 100 (technically, 100ths). Just like you probably already know 100 cents in a dollar (USD) or 100 years in a century. Even the "cent" in percent means per hundred. There are 100 centimeters in a meter. A centimeter is about as wide as your little finger. A meter is close to a yard.
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{0.108 meters}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{108 centimeters}[/tex]
Find: [tex]\textsf{Covert to meters}[/tex]
Solution: In order to convert centimeters to meters we need to divide the amount of centimeters by 100 since there are 100 centimeters in one meter. After doing 108/100 we get 1.08 meters.
Margo borrows $1900, agreeing to pay it back with 3% annual interest after 13 months. How much interest will she pay?
Answer:
61.75
Step-by-step explanation:
1900x0.03x1.08333333=61.75
117 IS 7.3 PERCENT OF WHAT NUMBER?
Which problem solving strategy would be best to solve this problem?Austin, Texas is two hours ahead of San Diego, California. If the time in Austin is 1:00 P.M., what time is it in San Diego?A.guess, check and reviseB.use a formulaC.work backwardsD.write an equation
Answer:
D. Write an equation
Step-by-step explanation:
x = The time of Sand Diego
t = Current designated time
n = The difference in time
So the equation is x = t+/-n.
You can determine if it would be + or - based of the word problem.
For this word problem the equation is x = 1:00pm - 2hrs
Hope this helps.
Which expression is equivalent to-2x+5?
The equivalent expression of -2x + 5 is 5 - 2x
How to determine the equivalent equation?The expression is given as:
-2x + 5
The symmetry rule of expression states that:
a + b = b + 1
So, we have:
-2x + 5 = 5 - 2x
Hence, the equivalent expression of -2x + 5 is 5 - 2x
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