Final answer:
The two consecutive integers whose sum is 373 are 186 and 187. We derived the equations n + (n + 1) = 373 and solved for n to find the first integer.
Explanation:
To find two consecutive integers whose sum is 373, let's denote the first integer as n. The next consecutive integer will be n + 1. When we add these two integers together, their sum should equal 373, which gives us the equation:
n + (n + 1) = 373
Simplifying this equation, we get:
2n + 1 = 373
To solve for n, we subtract 1 from both sides of the equation:
2n = 372
Divide both sides by 2:
n = 186
So the first integer is 186. The next consecutive integer is:
n + 1 = 186 + 1 = 187
Therefore, the two consecutive integers that sum to 373 are 186 and 187.
Divide. Do not round your answer.
52.72 - 8
Answer:
6.59
Step-by-step explanation:
52.72 ÷ 8 = 6.59
So the answer is 6.59
If h(x) = 6 - X, what is the value of (10)
Answer:
-4 = h(x)
Step-by-step explanation:
[tex]6 - 10 = -4[/tex]
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Find Sn for the given arithmetic series.
a1 = 18, d = –3, n = 14
Answer:
- 21
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], thus
[tex]S_{14}[/tex] = [tex]\frac{14}{2}[/tex][( 2 × 18) + (13 × - 3) ]
= 7 (36 - 39) = 7 × - 3 = - 21
The sum of the arithmetic series with the first term 18, common difference -3, and 14 terms is 231.
Explanation:To find the sum, Sn, of an arithmetic series where a1 is the first term, d is the common difference, and n is the number of terms, you can use the formula:
Sn = ⅓n × (a1 + an)
First, find the nth term (an) using the formula:
an = a1 + (n - 1)d
For a1 = 18, d = –3, and n = 14:
an = 18 + (14 - 1)(-3)
an = 18 - 39 = –21
Sn = ⅓(14) × (18 + (–21))
Sn = 7 × (18 - 3) × 33
Sn = 231
So, the sum of the series is 231.
evaluate the problem below -4 1/6 + 5 2/3
Answer:
3/2 (or 1 1/2)
Step-by-step explanation:
-4 1/6 + 5 2/3 (express as improper fractions)
= -25/6 + 17/3 (convert fractions common denominator i.e 6)
= -25/6 + (17/3)(2/2)
= -25/6 + (17 x 2)/6
= -25/6 + 34/6
= 9/6
= 3/2
=1 1/2
31. The bus fare in a city is $1.25. People who use the bus
have the option of purchasing a monthly discount pass for
$15.00. With the discount pass, the fare is reduced to $0.75.
Determine the number of times in a month the bus must
be used so that the total monthly cost without the discount
pass is the same as the total monthly cost with the discount pass.
The bus must be used 30 times in a month for the total monthly cost without the discount pass to be the same as the total monthly cost with the discount pass.
Explanation:The mathematical problem deals with determining the number of times one must take a bus ride for a monthly discount pass to be as cost-effective as individual fare payments. To solve it, we must set up an equation based on the cost of bus rides. Let's denote the number of bus rides as 'n'.
Without the pass, each ride is $1.25, so n rides would cost 1.25n dollars.
With the pass, each ride is $0.75 and you also need to pay $15 for the monthly pass, so n rides would cost 0.75n + 15 dollars.
To find out the break-even point, we set these two expressions for the total cost equal to each other:
1.25n = 0.75n + 15
Solving this equation gives us:
0.5n = 15, n = 15/0.5 = 30.
Therefore, the bus must be used 30 times in a month for the total monthly cost without the discount pass to be the same as the total monthly cost with the discount pass.
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Nat’s grocery bill was $150, which includes a 5% club discount. What was nats bill before the discounts
Answer:
$157.89
Step-by-step explanation:
The original price is x
you took away 5%, making the new price 95% of x, or .95x
Put it in an equation
.95x = 150
x = 150/.95
x = 30/.19
x = 3000/19
x=157 17/19
x is about $157.89
The amount Nat's paid at the club before the discount is $157.90
Given:
Total bill including discount = $150
Discount = $5
Amount before discount = x
Total bill including discount = Amount before discount - (Discount × Amount before discount)
150 = x - (5% × x)
150 = x - (0.05 × x)
150 = x - 0.05x
150 = 0.95x
divide both sides by 0.95
x = 150 / 0.95
x = 157.89473684210
Approximately,
x = $157.90
Therefore, amount Nat's paid at the club before the discount is $157.90
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5. Point M is the midpoint of segment AB. The coordinates of
point A are (-8, 3) and the coordinates of M are (-2, 1).
What are the coordinates of point B?
Answer:
(4, -1)
Step-by-step explanation:
Since it takes negative two to get from 3 to 1, you also have to deduct 2 from 1, which is -1 [y-coordinate]. Now, since it takes six to get from -8 to -2, you also have to add 6 to -2, which is 4 [x-coordinate].
So, point B is (4, -1).
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Which lines are parallel? Check all that apply.
89.5°
91.51
88.5°
89.5°
90.5°
The lines that are parallel to each other are as follows;
b║fc║eHow to know lines that are parallel from the angles?When parallel lines are cut by a transversal, angles relationship are formed.
This angle relationship includes corresponding angles, alternate angles, vertical angles and many more.
Therefore, the lines that are parallel are as follows;
b║f : If you use alternate angle theorem you will notices line b and f are parallelc║e: using alternate and corresponding angle theorem you will notice both line c and e are parallel.learn more on parallel lines here: https://brainly.com/question/10652739
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Julia recorded the number of trips each of his classmates made to fast food restaurants last week in the dit plot below which of the following would be the best measure of center
Mean absolute deviation of the following would be the best measure of center. Option A is correct.
What is a boxplot?A boxplot is a visual representation of a data set's dispersion and centers.
The interquartile range and the mean of the data set are two examples of spread measures. The mean, average, and median are examples of center measures.
A box plot is a graph that allows us to readily compare the median number of teeth in mammals and reptiles.
The scatter plot below shows how many visits to fast food establishments each of his classmates made throughout the previous week.
The best indicator of the center would be the mean absolute deviation of the following.
Hence option A is correct.
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explain how reading the digits ro the right of the decimal point and knowing the name of the least place value help yoi read a decimal number.use examples .604 and 1.604 in your explanation
Final answer:
Reading decimal numbers requires understanding the places to the right of the decimal point: tenths, hundredths, thousandths, etc. The least significant place value—which in 0.604 is the thousandth place—helps in reading, rounding, and performing operations like moving the decimal point or using scientific notation.
Explanation:
Understanding how to read decimal numbers is important in mathematics. When reading the digits to the right of the decimal point, the name of each place value position helps you determine the value of the digit. For example, in the number 0.604, the digit '6' is in the tenth place, which means it represents six tenths, the digit '0' is in the hundredth place, acting as a placeholder, and the '4' is in the thousandth place, representing four thousandths. Similarly, in 1.604, the '1' is in the ones place, the '6' is in the tenth place, the '0' is a placeholder in the hundredth place, and the '4' is in the thousandth place.
Knowing the least place value is also important when rounding or when dealing with operations that affect the decimal point. For instance, if we need to move the decimal point or deal with scientific notation, recognizing the least significant digit's place value informs us how to maintain numerical accuracy. If you understand that the least significant digit in 1.604 is the '4' in the thousandth place, you would keep the decimal up to three places if you were to round or shift the decimal in calculations.
What is the GCF of 36, 48, and 60?
Answer:
12
Step-by-step explanation:
Problem Set#3:
Choose a situation that could be described by the following ratios, and write a sentence to describe the ratio in the context of the situation you chose.
For example:
3: 2 When making pink paint the art teacher uses the ratio 3:2. For every 3 cups of white paint she uses in the mixture, she needs to use 2 cups of red paint.
a. 1 to 2
b. 29 to 30
c. 52:12
*Answer A-C
The ratios 1:2, 29:30, and 52:12 can be represented in different situations, such as recipe measurements, voting results, and quantities of colored marbles.
Explanation:a. 1 to 2: In a recipe for pancakes, the ratio 1:2 could be used to represent the ratio of flour to milk. For every 1 cup of flour, you would need 2 cups of milk.
b. 29 to 30: Suppose a group of students are voting for their favorite ice cream flavor, and there are 29 votes for chocolate and 30 votes for vanilla. The ratio of 29:30 represents the ratio of votes for chocolate to votes for vanilla.
c. 52:12: Let's say you have a bag of different colored marbles, and there are 52 red marbles and 12 blue marbles. The ratio 52:12 would then represent the ratio of red marbles to blue marbles in the bag.
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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
Answer:
[tex]y> \frac{2}{3}x+3[/tex]
Step-by-step explanation:
we have the points
(-3,1) and (0,3)
step 1
Find the slope m of the line
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{3-1}{0+3}[/tex]
[tex]m=\frac{2}{3}[/tex]
step 2
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=\frac{2}{3}[/tex]
[tex]b=3[/tex] ----> the y-intercept is the point (0,3)
substitute the values
[tex]y=\frac{2}{3}x+3[/tex]
step 3
Find the equation of the inequality
we know that
The slope is positive
Everything to the left of the line is shaded ( The inequality is of the form y > ax+b or y ≥ ax+b)
Is a dashed line (The inequality is of the form y > ax+ b or y < ax+b)
therefore
The equation of the inequality is of the form y > ax+b
The inequality is
[tex]y> \frac{2}{3}x+3[/tex]
see the attached figure to better understand the problem
lost 6balls yesterday bought 12 balls, then lost 4 balls, how many balls did i have to begin with
Answer
2
Step-by-step explanation:
as -6+12-4
Evaluate expression using the value given for the variable
7b - 2a, when a = -3 and b = 4
Answer:
34
Step-by-step explanation:
Substitute the given values for a and b into the expression
7(4) - 2(- 3) = 28 - (- 6) = 28 + 6 = 34
PLEASE HELP which number in the replacement set {1,2,3,4} makes 6x + 4 = 22 a true statement?
3 is the correct answer bebe :)
6*3=18
18+4=22
simplify 20+3xy-3+4y^2+10-2y^2
51pts! which expression represents a difference of squares?
A. 81-49y^2
B. 25k-64
C. t^2+100
D. 4x^2-16x
Answer:
A.
Step-by-step explanation:
81 - 49y^2 = (9 - 7y)(9 + 7y)
FOIL the equation.
(9 - 7y)(9 + 7y)
81 + 63y - 63y - 49y^2
81 - 49y^2
The correct answer is option A. 81 - 49y².
What are different squares?It exists easily identified by looking at the numbers, the number shows a perfect square, and the variable y exists also squared
That is 9² = 81 and 7² = 49
Also, the sign in-between them must be a negative sign, when the expression consists of the above, then it provides a different square.
81 - 49y²
9² - 7²y²
(9 - 7y)(9 +7y)
Opening back the parenthesis to verify our answer
(9 - 7y)(9 +7y)
9(9+7y) -7y(9+7y)
81 +63y -63y -49y²
81 - 49y²
Therefore, the correct answer is option A. 81 - 49y².
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look at the attached file.
please show your work on how you got the answer
Answer:
D
Step-by-step explanation:
[tex]\frac{f(x)}{g(x)}[/tex]
= [tex]\frac{2x+4}{2x^2+4x}[/tex]
Factor out 2 on the numerator and 2x on the denominator.
= [tex]\frac{2(x+2)}{2x(x+2)}[/tex]
Cancel the factor (x + 2) on the numerator/ denominator
= [tex]\frac{2}{2x}[/tex] ← cancel the 2 on numerator/ denominator
= [tex]\frac{1}{x}[/tex] : x ≠ 0
find the equation of the horizontal line that contains the point (-4,8). express the equation using either the general form of the slope intercept form of the equation of a line
Answer: [tex]y=8[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
We know that this is a horizontal line. This means that:
[tex]m=0[/tex]
Knowing that this line contains the point (-4,8) we can substitute this coordinates and [tex]m=0[/tex] into [tex]y=mx+b[/tex], and then solve for "b":
[tex]8=0(-4)+b\\\\b=8[/tex]
Therefore, the equation of this line in Slope-intercept form is:
[tex]y=(0)x+8\\\\y=8[/tex]
Final answer:
The equation of the horizontal line that contains the point (-4,8) is y = 8 and it demonstrates that for a horizontal line, the slope is 0 and the y-coordinate remains constant along the line.
Explanation:
The equation of a horizontal line that contains a given point can be determined by looking at the y-coordinate of that point. Since a horizontal line has a slope of 0, the y-coordinate of any point on the line does not change. Therefore, the equation of the horizontal line that contains the point (-4,8) is simply y = 8. This equation indicates that the y-value will always be 8, regardless of the x-value, which is characteristic of a horizontal line. In the slope-intercept form of the equation of a line, which is y = mx + b, the slope (m) is 0, and the y-intercept (b) is 8.
A bus has 40 seats . There are as many adults as children riding the bus so there are
Answer:
20 children and 20 adults
Step-by-step explanation:
20 + 20 = 40
Answer:
20 adults 20 children
Step-by-step explanation:
if theres the same amount of children and adults just do 40/2
What are the zeros of f(x) = (x − 5)(x − 4)(x − 2)?
Answer:
x=5 , x=4, x=2
i got this answer by setting the x-5=0 then solve for x. same for each x-5, x-4, x-2.
Answer:
The zeros are 2,4 and 5.
Step-by-step explanation:
Consider the provided function.
[tex]f(x) = (x-5)(x-4)(x-2)[/tex]
To find the zeros equate the function equal to 0.
[tex](x-5)(x-4)(x-2)=0[/tex]
The zeros are:
[tex](x-5)=0[/tex] or [tex](x-4)=0[/tex] or [tex](x-2)=0[/tex]
[tex]=5[/tex] or [tex]x=4[/tex] or [tex]x=2[/tex]
Hence the zeros are 2,4 and 5.
Chandresh has several fishing rods that she would like to pack in boxes. One box is shown below.
Which fishing rod will fit in the box shown?
A. 17-inch fishing rod
B. 24-inch fishing rod
C. 27-inch fishing rod
D. 32-inch fishing rod
Answer: A, 17 inch
The box is 21 inches long, anything longer and it won't fit. 17 inch is the only thing shorter than 21.
Answer:
the green means its right at the top
Step-by-step explanation:
3. Find the annual salary when the monthly salary is $4,725,
Answer:
4725 * 12 = $56,700
Step-by-step explanation:
Salary for 1 month = 4725
Salary for 12 months = 56700 (4725 times 12)
Answer:
$56,700
Step-by-step explanation:
Since there are 12 months in a year, you take the Monthly salary and multiply it by 12 to get the annual salary
What is the value of c?
A.84
B.80
C.100
D.50
If g(x) = x2 + 3, find g(4).
011
19
16
08
Answer:
11
Step-by-step explanation:
What is 14/49 in its simplest form???
Answer:2/7
Step-by-step explanation: 14 divided by 2 equals 7 and 49/7 equals 7 which means 7 is your GCF because seven going into both numbers
Answer:
2/7
Step-by-step explanation:
14÷7 / 49÷7 = 2/7
As lucia fills her fish tank, she notices that it fills 8 cubic centimeters of water in 4 minutes. How many cubic centimeters of water does it fill in 1 minute?
Answer:
2 cubic centimeters per minute
Step-by-step explanation:
8 cubic centimeters filled per 4 minutes
divide 8 by 4 = 2
2 cubic centimeters per minute
Answer: 2 cubic centimeters
Step-by-step explanation:
Given : As lucia fills her fish tank, she notices that it fills 8 cubic centimeters of water in 4 minutes.
i.e. Time taken to fills 8 cubic centimeters of water = 4 minutes
By UNITARY METHOD, we have
Amount of water it fills in 1 minute (i.e. Unit rate) = [tex]\dfrac{\text{8 cubic centimeters }}{\text{4 minutes}}[/tex]
= [tex]\dfrac{8}{4}=2[/tex] cubic centimeters
Therefore, it fills 2 cubic centimeters in 1 minute.
Hence, the correct answer is 2 cubic centimeters.
257
What names apply to this number
Answer:
Step-by-step explanation:
Whole, integer, rational, real
Seth went to sticker station.he bought 1 sheet of 100 ,4 strips of 10 , and 6 single soccer stickers, and he bought 8 strips of 10 and 3 single animal stickers. How many stickers did Seth buy?
Answer:
229
Step-by-step explanation:
100+40+6+80+3
ok why is your math so easy