Consider the provided phrase.
Four times the sum of five and a number
Let the number is n and the sum of five and a number can be written as:
[tex]n+5[/tex]
Thus, four times the sum of five and a number can be written as:
[tex]4(n+5)[/tex]
Hence, the required expression is [tex]4(n+5)[/tex].
What is phrase in math?
In mathematics, we may use a phrase to describe an expression. When we describe an expression in words that incorporates a variable, we are doing so by using an algebraic expression. An example of this may be the phrase "greater than" (an expression with a variable).
run the numbers. to conduct a rational analysis of an issue. You can do the math because I was the last person to depart yesterday night and the first person to arrive this morning, and since only the overweight security guy was present. on April 7, 2005, by Dave L. Flag.
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Solve for x:
-12 = 1/2(6x - 12)
Answer:
x = -2
Step-by-step explanation:
-12 = 1/2(6x - 12) Multiply everything inside the parentheses by 1/2
-12 =1/2(6x) - (1/2)(12)
-12 = 3x - 6 Add 6 to both sides of the equation
-6 = 3x Divide both sides by 3
-2 = x
Check:
Plug -2 in for x and see if statement is true
-12 = 1/2(6x - 12)
-12 = 1/2[(6)(-2) - 12] Simplify inside the brackets
-12 = 1/2(-12 -12)
-12 = 1/2 (-24)
-12 = -12
A piece of rope 20 feet long is cut from a longer piece that is at least 32 feet long. The remainder is cut into four pieces of equal length. Describe the length of each of the four pieces.
Answer:
3
Step-by-step explanation:
32 - 20 = 12
12/4 = 3
This assumes that by remainder they mean they twelve feet left over and not the twenty feet removed. This is likely what it means.
the side of a square is 9in. what is the perimeter?
Answer:
36in
Step-by-step explanation:
A square has four sides. If the length of one is 9 inches, then we multiply it by four to get 9*4 = 36in as our perimeter.
FINAL ANSWER: 36in
Solve the system of equations.
x + y = 8
y=x²- 4
The solution for the given system of equations is (3,5) and (-4,12).
Given two systems of equations i.e. x+y=8 and y=[tex]x^{2}[/tex]-4 and asked to solve them.
⇒x+y=8; let's assume this equation as A
⇒ y=[tex]x^{2}[/tex]-4; let's assume this equation as B
From equation A
⇒y=8-x
From equation B
⇒y=[tex]x^{2}[/tex]-4
Equating both the values of y
⇒8-x=[tex]x^{2}[/tex]-4
⇒[tex]x^{2}[/tex]-8-4+x=0
⇒[tex]x^{2}[/tex]-12+x=0
{solving quadratic equation}
⇒[tex]x^{2}[/tex]-12+4x-3x=0 { factorizing the quadratic equation}
⇒[tex]x^{2}[/tex]+4x-3x-12=0
⇒x(x+4)-3(x+4)=0
⇒(x-3)(x+4)=0
Therefore, the value's of x=3,-4
⇒if x=3
From equation A
⇒y=8-3=5
For x=3 ; y=5
⇒if x=-4
From equation A
⇒y=8-(-4)=12
For x=-4 ; y=12
Therefore,The solution for the given system of equations is (3,5) and (-4,12).
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whst will be the multiplicative inverse of
3/5 - 4/27 + 5/18
Answer:


Find the multiplicative inverse of the following
(i) -13 (ii) -13/19 (iii) 1/5 (iv) -5/8 × -3/7 (v) -1 × -2/5
(vi) -1
Solution:
The reciprocal of a given rational number is known as its multiplicative inverse. The product of a rational number and its multiplicative inverse is 1.
(i) The Multiplicative inverse of -13 is -1/13
∵ -13 × (-1/13) = 1
(ii) The Multiplicative inverse of -13/19 is -19/13
∵ -13/19 × (-19/13) = 1
(iii) The Multiplicative inverse of 1/5 is 5
∵ 1/5 × 5 = 1
(iv) The Multiplicative inverse of -5/8 × -3/7 is 56/15
∵ -5/8 × (-3/7) = 15/56 and 15/56 × 56/15 = 1
(v) The Multiplicative inverse of -1 × -2/5 is 5/2
∵ -1 × (-2/5) = 2/5 and 2/5 × 5/2 = 1
(vi) The Multiplicative inverse of -1 is -1
∵ -1 × (-1) = 1
A sale at a store is 15%. If the sale price after
the discount is $35.70. What was the original
price of the sweatshirt (S)?
Answer:
$42.00
Step-by-step explanation:
Let x = the original cost of the sweatshirt
x - .15x = 35.70 We don't know the original cost so we will call it x. I know that we are taking 15 off of this number to get the sale's price. 15% means per 100, so as a fraction this would be 15/100. To make this a decimal, I would divide 15 by 100 to get .15
x - .15x = 35.70 Combine the like terms
.85x = 35.70 This is say that 85% if the original price is the sale price of 35.70
Divide both sides of the equation by .85 and we get x = 42.00
Check:
42 - .15(42) = 35.70
42 - 6.30 = 35.70
What number should be added to -28 to make the sum 0? (5 points) 28 -28 27 0
Answer:
28
Step-by-step explanation:
-28 + 28 = 0
[IMC 2014 Q23] A sector of a disc is removed by
making two straight cuts from the circumference
to the centre. The perimeter of the sector has the
same length as the circumference of the original
disc.
What fraction of the area of the disc is removed?
Answer:
Well the IMC 2014 is
IMC 2014 + hMc
Olivia counted thirty blue cars, ten red cars, and forty white cars in the parking lot. What is the ratio of white cars to blue cars, according to Olivia’s count?
3 to 4
1:4
4:1
43
Answer: I say 4/3 the fraction so your answer is D
Explanation: Because its white cars to blue cars the problem is whats equivalent to the ratio 40 to 30, 4:1 is not the same as 40 to 30 neither
is 1:4 or 3 to 4 So its D. :)
A square rug lies in the middle of a rectangular room. There are 6 feet of uncovered floor on 2 sides of the rug and 2 feet of uncovered floor on the other 2 sides. Find a polynomial expression for the area of the rootn in terms of ×, the side length of the rug.
The polynomial expression for the area of the room is f(x) = x^2 + 16x + 48.
Here, we are given that the side of the length of the rug = x
Now, the square rug is placed on the rectangular room such that on 2 sides the uncovered floor is 6 meters.
This means that the length of the 2 opposite sides of the rectangle will be (x + 6 + 6) = (x + 12)
Similarly, there is 2 feet of uncovered floor on the other 2 sides, which means that the length of other two opposite sides is- (x + 2 + 2) = (x + 4)
Kindly refer to the diagram below for a better clarity of how we found out the sides.
Now, the area of a rectangle = Length × Breadth
Thus, area of the room = (x + 12) (x + 4)
= x^2 + 4x + 12x + 48
= x^2 + 16x + 48
Thus, the polynomial expression for the area of the room is f(x) = x^2 + 16x + 48
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The names of 20 students in the class will be put in a hat. The class consists of 12 freshmen, 6 sophomores, and 2 juniors. If a sophomore was chosen there, how likely is it that another sophomore will get to play today?
If a sophomore was chosen yesterday, the probability that a sophomore will be chosen again today is 3/10.
Given, number of students name put into the hat = 20
total number of freshmen in the class = 12
total number of sophomore in the class = 6
total number of juniors in the class = 2
we are asked to determine the probability that the sophomore will be selected the second day also = ?
Calculating a situation's probability allows us to determine its likelihood. Absolute certainty in forecasting is challenging in many situations. With its help, we are only able to anticipate the likelihood, or chance, that an event would occur.
from the given data,
n(s) = 20
n(A) = 6 ⇒ as the name selected in the first day is put back in the hat.
⇒ P(A) = n(A)/n(s)
P(A) = 6/20
P(A) = 3/10
hence the probability that the another day again a sophomore will be chosen is 3/10.
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Complete the final two columns in the following frequency distribution table and then find the percentiles
and percentile ranks requested:
X f cf c%
5 2
4 5
3 6
2 4
1 3
we have found out the cumulative frequency (c f) and percentiles(c %) for the given data.
We are given the frequency distribution table as:
X f
5 2
4 5
3 6
2 4
1 3
We need to find cumulative frequency (c f) and percentiles(c %)
c % = 100 × ( c f / n )
c f means the frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.
n = 20
X f c f c %
5 2 2 10 %
4 5 7 35 %
3 6 13 65 %
2 4 17 85 %
1 3 20 100 %
Therefore, we have found out the cumulative frequency (c f) and percentiles(c %) for the given data.
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Please help also I know the answers there are wrong
If possible explain how you got the answers
The values of all the required angles are; m∠5 = 42°; m∠8 = 138°; m∠10 = 138° and m∠11 = 42°
How to Identify corresponding angles?
Corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines.
Now, we are given that; m∠1 = 42°
By corresponding angles, we can say that;
m∠1 = m∠5
Thus; m∠5 = 42°
Now, we know that sum of angles on a straight line is equal to 180° i.e. they are supplementary angles.
Now, from the diagram, we can see that m∠5 and m∠8 are supplementary angles and as such;
m∠5 + m∠8 = 180°
42 + m∠8 = 180
m∠8 = 180° - 42°
m∠8 = 138°
Now, m∠9 is a corresponding angle to both m∠1 and m∠5. Thus, we can say that; m∠9 = 42°. However, m∠9 is supplementary to m∠10. Thus;
m∠10 = 180 - 42
m∠10 = 138°
Lastly, m∠10 and m∠11 are supplementary angles and as such;
m∠10 + m∠11 = 180°
138 + m∠11 = 180
m∠11 = 180° - 38°
m∠11 = 42°
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Choose all degrees of rotation that will carry the regular pentagon onto itself.
A. 72°
B. 90°
C. 108°
D. 144°
E. 216°
Answer:
A. 72°
D. 144°
E. 216°
Step-by-step explanation:
I just answered this.
in short : we rotate each vertex on a circle arc. the center of that circle being P.
so, at the end of every 1/5 of the circle arc there is a vertex of the polygon.
therefore, with every 1/5 of a full circle rotation we move the pentagon visually onto itself.
that is starting at
360/5 = 72°
and then every additional 72°
144°
216°
288°
360°
so, A, D and E are correct
Points P(-6,10), Q(0,6), and R are collinear. One of the points is the midpoint of the segment formed by the other two points. a. What are the possible coordinates of R? b. RQ=√208. Does this information affect the answer to part a? a. The possible coordinates of R are (, ) (Type an ordered pair. Use a comma to separate answers as needed.)
Answer:
a. (-12, 14), (6, 2), (-3, 8)
b. yes; R(-12, 14)
Step-by-step explanation:
Points P(-6, 10), Q(0, -6), and R lie on a line, with one of them being the midpoint of the other two. You want to know the possible locations of R, and its location if RQ=√208.
SetupPoint M is the midpoint of AB when ...
M = (A +B)/2
If M and A are given, then B is ...
2M -A = B . . . . . . above equation solved for B
a. Possible locations of RThere are three choices for the location of R.
P is the midpoint
R = 2P -Q = 2(-6, 10) -(0, 6) = (-12, 20-6)
R = (-12, 14)
Q is the midpoint
R = 2Q -P = 2(0, 6) -(-6, 10) = (6, 12 -10)
R = (6, 2)
R is the midpoint
R = (P +Q)/2 = ((-6, 10) +(0, 6))/2 = (-6, 16)/2
R = (-3, 8)
The possible coordinates of R are (-12, 14), (6, 2), (-3, 8).
b. R for RQ=√208The length of the given segment PQ is ...
d = √((x2 -x1)² +(y2 -y1)²) . . . . . distance formula
d = √((0 -(-6))² +(6 -10)²) = √(6² +(-4)²) = √(36 +16) = √52
This is half the length of RQ, so we must have P as the midpoint of RQ.
This distance information chooses one of the three points found in part (a), R(-12, 14).
Divide -3 1/7 divided 7 2/6. Explain each step you used to find the quotient.
Answer:
-3/7
Step-by-step explanation:
[tex]-3\frac{1}{7} / 7 \frac{2}{6}[/tex]
[tex]-3 \frac{1}{7} = \frac{-22}{7}[/tex]
[tex]7\frac{2}{6} = 7\frac{1}{3} = \frac{22}{3}[/tex]
[tex]\frac{\frac{-22}{7} }{\frac{22}{3} }[/tex][tex]= \frac{-22}{7} * \frac{3}{22} = \frac{-3}{7}[/tex]
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David and John own 37-1/2 acres of land. David owns 3/5 and John owns 2/5 of the land. They decide to section it off into ¾ acre lots to rent out as garden space for people who do not have garden space at their homes. The price for the entire summer for the rent of each lot is $50. Since there is no water supply to water the gardens, David and John have asked their renters if they would like a 100-gallon water tank or a 70-gallon water tank. 60% of the renters chose 100 gallons and 40% chose 70 gallons. David calculated that they would need to fill each tank 2 times and the cost of a gallon of water is $.05.
The total spent amount on water is $220
The total area is 37.5=75/2
The number of lots is 75/2/3/4=50 nos
Total rent is 50×50=2500
So 3/5 will go to david 2500×3/5=1500
2/5 will go to john 2500×2/5=1000
So 60% Renters choose 100 gallons
Total renters is 50
60% renters is 50×60%=30 nos
40% renters choose 70 gallons
40% of 50 is 20 nos
The tank fills twice
100×30+70×20=4400 to be filled
Per gallon cost is $0.05
So the total cost is 4400×0.5=$220
So they spent $220 on water
A fraction shows part of a whole. This entire may refer to a place or a group of places.A fraction can be a portion or section of any quantity out of a whole, where the whole can be number of any value.To learn more about fraction visit:
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28+92/46-17+90
can you solve this for me
thanks
Can someone help me with this please?
Answer:
1)
D) -5<x≤-2
R) 0<y≤3
2)
D) 1≤x≤5
R)2≤y≤4
Step-by-step explanation:
(Only in 7th so might be wrong)
1)
D) -5<x≤-2
R) 0<y≤3
2)
D) 1≤x≤5
R)2≤y≤4
look at the range of where the x and y is at (1-2 included = 1<x≤2)
please help me with this math homework
Answer:
Step-by-step explanation:
(2*9/5d*9)-(1*5/9d*5)
18/45d-5/45d
13/45d
Which number line shows the solution to the inequality? – 7x+3≥ – 18
The solution to the inequality is x ≥ 3
How to determine the solutionGiven the inequality;
– 7x + 3 ≥ – 18
To determine the solution , we take the following steps;
collect like terms
-7x ≥ - 18 - 3
Find the difference
- 7x ≥ - 21
Make 'x' the subject of the formula by dividing both sides by its coefficient, - 7
We have;
-7x / -7 ≥ - 21/ -7
x ≥ 3
Thus, the solution to the inequality is x ≥ 3
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The mean diameter of holes produced by a drilling machine bit is 4.05 mm and the stan dard deviation of the diameters is 0.0028 mm For twenty holes drilled using this machine, determine, correct to the nearest whole num ber, how many are likely to have diame ters of between (a) 4.048 and 4.0553 mm and (b) 4.052 and 4.056 mm, assuming the diameters are normally distributed.
The total number of holes will be (a)15 and (b) 4 when the drilling machine is used whose standard deviation is 0.0028mm.
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
The sum of all values divided by the total number of values constitutes a dataset's mean.
The mean of the holes are given as 4.05 mm([tex]\mu=4.08[/tex])
The standard deviation is given as 0.0028 mm([tex]\rho=0.0028[/tex])
Now we will use the z-score and probability distribution to calculate the frequency of the holes to have diameter between 4.048 and 4.0553.
Here [tex]Pr(4.048\leq X\leq 4.0053)[/tex] ,so we need to compute the z-values
[tex]Z_1=\frac{X_1-\mu}{\rho} \\Z_1=\frac{4.048-4.05}{0.0028} \\Z_1=-0.7143[/tex]
Similarly:
[tex]Z_2=1.8929[/tex]
Therefore from the above statements we can say that
[tex]Pr(-0.7143\leq X\leq 1.8929)[/tex]
Solving for probability distribution we get
[tex]Pr(4.048\leq X\leq 4.0053)=0.7333[/tex]
Total number of holes=0.7333 × 20= 14.666..
Therefore the number of holes is 15
Similarly
The z-value corresponding to 4.052 mm is given by 0.71
The z-value corresponding to 4.056 mm is given by:2.14
The probability of the diameter being between 4.052 mm and 4.056 mm is 0.4838 – 0.2611 =0.2227
The number likely to have a diameter between 4.052 mm and 4.056 mm = 0.2227 × 20
= 4.454
= 4, correct to nearest whole number
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Please help me if you can thanks
Using the Pythagorean Theorem, it is found that the length of AB is of 8.54 units, considering that BC = 3 and that AC = 8.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this triangle, we have that:
The length of AB is the hypotenuse.BC = 3(|-1 - (-4)| = 3) is one side.AC = 8(4 - (-4) = 8) is the other side.Hence the length of AB is given as follows:
h² = 3² + 8²
h² = 73
h = sqrt(73)
h = 8.54 units.
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6.1 Define the term inflation.
Answer:
the action of inflating something or the condition of being inflated.
"the inflation of a balloon"
ASTRONOMY
(in some theories of cosmology) a very brief exponential expansion of the universe postulated to have interrupted the standard linear expansion shortly after the Big Bang.
2.
ECONOMICS
a general increase in prices and fall in the purchasing value of money.
"policies aimed at controlling inflation"
the distance between two cities on a map measures 3.75 inches. the scale shows that 2 inches is equal to 50 miles . how many miles apart are the cities
help me please FIJDJSHEHE
Answer: 0
Step-by-step explanation:
because -2+-1 is -3. then -3+0 is just -3. lastly -3+1 = -2 and -2 + 2 = 0
X-5>10;x=2 tell where the value is a solution of the inequality help please
Answer:
No, 2 is not a solution
Step-by-step explanation:
x - 5>10 Add 5 to both sides of the equations
x > 10 The solutions are all numbers greater than 10. Two is not greater than 10.
Evaluate Log2 11 x Log6 2
The logarithmic expression is equal to:
Log₂(11)*log₆(2) = 1.34
How to evaluate the logarithmic expression?
Here we have the logarithmic expression:
Log₂(11)*log₆(2)
Now, remember that we can rewrite:
Logₐ(b) = Ln(b)/Ln(a)
Using that we can rewrite the expression:
Log₂(11)*log₆(2) = (Ln(11)/Ln(2))*(Ln(2)/Ln(6)) = Ln(11)/Ln(6)
Now using a calculator you can find these two natural logarithms:
Ln(11)/Ln(6) = 1.34
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Write a compound inequality that represents the following phrase. Graph the solutions. all real numbers that are between -3 and 7
The inequality to represent the given condition is -3<x<7 .
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] It is frequently used to compare two numbers on the number line based on their sizes. Different types of inequalities are represented by a variety of notations, including:
The notation x < y means that x is less than y.The notation c > d means that c is greater than d.The notation a ≤ b means that a is less than or equal to b. The notation p ≥ q means that p is greater than or equal to q .The given statement gives the solutions of all real numbers between 3 and 7.
Therefore if we consider a real number x then, x>-3 and x<7 .
Combining together for a compound inequality: -3<x<7.
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solve the compound inequality 2x>-10 and 9x<18
Answer:
x = 1
Step-by-step explanation:
2 x [tex]x[/tex] = 10
10 > -10
9 x [tex]x[/tex] = 9
9 < 18