Answer & Step-by-step explanation:
This is what is called an arithmetic sequence. An arithmetic sequence adds the same number every time. If we take and subtract the 3rd term from the 4th term, we get 21. However, when we subtract 17 from 26 or 26 from 44, we get 9 and 18 respectively, which is not in keeping with the sequence.
___________________________________________________I AM ALWAYS HAPPY TO HELP :)Suppose a rabbit ate 32 carrots in 4 days. If it ate 2 more carrots each day than the day before, how many carrots did it eat each day on day 1, day 2, day 3, and day 4?
What is the value of x in the equation 8x – 2y = 48, when y = 4
Answer:
Seven(7)
Step-by-step explanation:
8x-2y=48
8x-2(4)=48
8x-8=48
8x=48+8
8x=56
Divide both sides by 8
8x/8=56/8
x=7
Your school club has a bake sale to raise money. Your club offers muffins for $.50 each and bagels for $.75 each. In one hour you raise $21 by selling 34 items. How many muffins did you sell?
Answer:
18 muffins
Step-by-step explanation:
From the information given, you can write the following equations:
x+y=34 (1)
0.50x+0.75y=21 (2)
where x is the number of muffins and y is the number of bagels.
First, you can isolate x in (1):
x=34-y (3)
Then, you can replace (3) in (2):
0.50(34-y)+0.75y=21
17-0.5y+0.75y=21
0.25y=21-17
0.25y=4
y=4/0.25
y=16
Now you can replace the value of "y" in (3):
x=34-16
x=18
According to this, the answer is that you sold 18 muffins.
Marci has a scale drawing of her new bedroom. On the drawing the length of the bedroom is 2cm. In real life her bedroom is going to be 7 meters in length. What is the scale of the drawing
Answer:
Scale for drawing is 1:350
Step-by-step explanation:
scale is ratio of size of drawing and size of actual object for which the drawing is made
it is represented as
scale = size of drawing : size of actual object
given
length of model in drawing = 2cm
length of bedroom in reality = 7 meter
since there are two units we meter and cm
we convert both in same unit that is cm for simpler calculation
1 meter = 100 cm
7 meter = 7*100 cm = 700cm
length of bedroom in reality = 7 meter = 700 cm
Thus,
scale for drawing = length of drawing/ actual length of bedroom
scale for drawing = 2 cm : 700cm = 1:350
Scale for drawing is 1:350
The polynomial x^2 - 22x + 121 represents the area (in square feet) of a square courtyard. a.) write a polynomial that represents the side length of the courtyard.
b.) Write an expression for the perimeter of the courtyard.
Answer:
Step-by-step explanation:
Since the court yard is square in nature, the area of the court yard will be exprerssed as;
A = Length * Length
A(x) = L²
Given area of the court yard A(x) = x^2 - 22x + 121
x^2 - 22x + 121= L²
Factorizing the quadratic expression
(x^2 - 11x) -(11x+ 121) = L²
x(x-11)-11(x-11) = L²
(x-11)(x-11) = L²
(x-11)² = L²
Square root both sides to the length of the courtyard
√(x-11)² = √L²
L = x-11
Hence the length of the courtyard is (x-11)ft
b) The perimeter of the courtyard P = 4L
P = 4(x-11)
P = 4x - 44
Hence an expression for the perimeter of the courtyard is 4x-44 feet
6. A landscaping company is trying to create a formula to predict the amount of time, t, required to mow a yard based on the area of the yard, A, the speed of the mower, v, and the width of the mower, w. One employee suggests a formula of t = 1.15 * A/(vw) Does this formula make sense? Explain .
Answer:
The formula makes sense
Step-by-step explanation:
For illustration purposes, we will assume the yard is a rectangle ( such assumption does not in any way invalid the arguments that follows
Dimensions of the yard
L = 10 m
w = 4 m
A = 40 m²
Arguments:
1.- The required time (t) is proportional to the area (A). That means ( keeping all parameters fixed but Area ) we need more time to mow a bigger area yard. Then t ∝ A
You can see that if the yard is 40 m² you will take let´s say 0,5 day and you will need more time if the area is 100 m² ( it seems obvious )
2.- Let´s now assume the width of the mower is 1 m if you move along the length you will need to go forward and backward 4 times. Now think about a mower of 4 m ( it does not matter if that machine exists or no, is just a mental experiment) in that case you only need one pass, then the required time is inversely proportional to the width of the mower. That means a bigger width of the mower minor required time. Then t ∝ 1/w
3.-If now we keep the width of the mower but increased the speed of the machine we will reduce the working time. Time is an inversely proportional function of the speed of the machine since each required pass will take less time. Then t ∝ 1/v
We have evaluated three parameters A, w, and v ( area, the width of the mower, and speed ) and demonstrated the way each of these parameters influences the time, so far we don´t know how much each of them contributes in the total output, for that we have to measure and get conclusions, Furthermore coefficient 1,15 (in formula seems to take into account the hole combinations of the factors)
Which describes reproducibility
Question one, how do you solve this? "A, B, and C are collinear. Find AC if AB = 12 and BC = 8"
Question two, can anyone solve these two problems i attached? They use Segment Addition and Angle Addition Postulates.
Answer:
20''Step-by-step explanation:
If points A, B and C are collinear, then A, B and C lies on the same straight line. Hence AB+BC = AC
Given
AB = 12''
BC = 8''
To get length od segment AC, we will substitute the given values into the formula above as shown;
AB+BC = AC
12 + 8 =AC
AC = 12+ 8
AC = 20''
Hence the length of AC is 20''
Solve the simultaneous equation.......2x + 10y = 50 (equation 1) and 1.5x + 25y = 90 (equation 2)
Step-by-step explanation:
2x + 10y = 50 ... 1
1.5x + 25y = 90 ...2
...1 × 2.5
5x + 25y = 125 ...3
...3 - ...2
3.5x = 35
x = 10
replaced x = 10 in ...1
2(10) + 10y = 50
20 + 10y = 50
10y = 50 - 20
10y = 30
y = 3
if <1 and <2 are supplementary angles, m<1=4x° and m<2=8x° then whats the measures of 1 and 2
Answer:
angle 1 = 60 degrees
angle 2 = 120 degrees
=====================================================
Explanation:
Supplementary angles always add to 180 degrees. In other words, the two angles form a straight line.
(angle1) + (angle2) = 180
4x+8x = 180
12x = 180
12x/12 = 180/12 .... dividing both sides by 12
x = 15
Use this x value to find the two angle measures
angle1 = 4x = 4*15 = 60
angle2 = 8x = 8*15 = 120
As a check, angle1+angle2 = 60+120 = 180, which confirms our answer.
PLEASE HELP ASAP!!!!
Which statement describes the symmetry of j(x)?
j(x) is an odd function.
j(x) is an even function.
j(x) is both an even and an odd function.
j(x) is neither an even nor an odd function.
Answer:
j(x) is an odd function
Step-by-step explanation:
We are given;
j(x) = 220/x³ and j(-x) = 220/(-x)³
Now,
when x = 1;
j(x) = 220/1³ = 220/1 = 220
j(-x) = 220/(-1)³ = 220/-1 = -220
When x = 2;
j(2) = 220/2³ = 220/8
j(-2) = 220/(-2)³ = -220/8
Now, Algebraically, function j would be even if and only if j(-x) = j(x) for all x in the domain of j. While j is odd if and only if j(-x) = -j(x) for all x in the domain of j.
From the values gotten, we can see that :j(-x) = -j(x). Thus, we can say that j(x) is an odd function.
Answer:
A) j(x) is an odd function.
Step-by-step explanation:
Simplify 2x(3x-1)+4(1-3x)
Answer:
[tex]6{x}^{2} - 2x + 4 - 12x =6 {x }^{2} - 14x + 4[/tex]
The simplified expression of 2x(3x - 1) + 4(1 - 3x) is 6x² + 4 - 14x
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
2x(3x - 1) + 4(1 - 3x)
When the brackets are opened, we have
2x(3x - 1) + 4(1 - 3x) = 6x² - 2x + 4 - 12x
Evaluate the like terms
so, we have the following representation
2x(3x - 1) + 4(1 - 3x) = 6x² + 4 - 14x
Hence, the simplified expression is 6x² + 4 - 14x
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If 9^x = 3^( 1-2x), then x =
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
I used a calculator and it's correct!
Plz click the Thanks button!
<Jayla>
-(1+7x)-6(-7-x)=36 I don't understand how to do this.
edit: nevermind i multiplied wrong, the other answer is right
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 5}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - (1 + 7x) - 6( - 7 - x) = 36}[/tex]
Distribute ( - ) sign through the parentheses
Similarly, distribute -6 through the parentheses
[tex] \dashrightarrow{ \sf{ - 1 - 7x + 42 + 6x = 36}}[/tex]
Collect like terms
[tex] \dashrightarrow \sf - 7x + 6x - 1 + 42 = 36[/tex]
[tex] \dashrightarrow \: \sf \: - x - 1 + 42 = 36[/tex]
The negative and positive integers are always subtracted but possess the sign of the bigger integer
[tex] \dashrightarrow{ \sf{ - x + 41 = 36}}[/tex]
Move 41 to right hand side and change it's sign
[tex] \dashrightarrow{\sf{- x = 36 - 41}}[/tex]
[tex] \dashrightarrow \sf \: - x = - 5[/tex]
Change the signs on both sides of the equation
[tex] \dashrightarrow \: \sf{x = 5}[/tex]
Hope I helped!
Best regards! :D
can a coefficient have two variables?
Answer: Yes, a coefficient can have two variables.
GEOMETRY TRUE OR FALSE QUESTIONS
Answer:
True an angle is two intercepting line segments that share an point
False The definition of a square is it has to have four congurent angles ,sides and 2 sets of parallel lines.
Step-by-step explanation:
8X - 17 +5X - 3 = 71
Answer: x=7
Step-by-step explanation:
got it right on edg
Answer:
x = 7
Step-by-step explanation:
8x - 17 + 5x - 3 = +71
13x - 20 = +71
+ 20 = +20
13x = 91
13x/13 = 91/13
x = 7
you allow for 5% of your net pay of $2,989.12 to be budgeted for medical expenses
the answer is $149.46 c:
Which of the following shows how to Rewrite 8 - 9 using additive inverse
Answer: 1
8-9=-1
-1 additive inverse is 1
A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles. What is the actual area of the park?
Answer:
Actual area = 21600 Sq.miles
Step-by-step explanation:
We are given;
length; L = 4 inches
Width; W = 6 inches
The scale of the map; 1 inch for every 30 miles i.e. 1 : 30
Since the scale is 1:30, let's find the find the actual dimensions and then the actual area
For the Length,
Since 1 inch represents 30 miles,
Then, 4 inches = (4 × 30)/1 = 120 miles
For the width;
Since 1 inch represents 30 miles,
Then,6 inches = (6 × 30)/1 = 180 miles
Therefore, the actual dimensions are 120 miles and 180 miles
Now, formula for area of rectangle = length × width
Thus;
Actual area = 120 × 180
Actual area = 21600 Sq.miles
Rewrite in simplest rational exponent from √x × [tex]\sqrt[4]{x}[/tex]
Answer:
4x
Step-by-step explanation:
simplify the radical by breaking the radicand up into a product of known factors.
Determine whether the given description corresponds to an experiment or observational study.a. A stock analyst selects a stock from a group of twenty for investment by choosing the stock with the greatest earnings per share reported for the last quarter.b. A marketing firm does a survey to find out how many people use a product. Of the one hundred people contacted, fifteen said they use the product.c. A political pollster reports that his candidate has a 10% lead in the polls with 10% undecided.d. A doctor gives a new medication to half of his patients with the flu and a placebo to the other half of his patients with the flu.
Answer:
A: experiment
B: observational study
C: observational study
D: experiment
Step-by-step explanation:
Which inequality represents the values of x that would allow Pattie's Produce to have a daily revenue of at least $255 from selling the packages of strawberries? A. B. C. D.
Answer:
[tex]x \geq 255[/tex]
Step-by-step explanation:
The options are not visible; however the question can still be solved
Given
Least Value = $255
Required
Determine the inequality
When the phrase "at least" is used, the its direct representation is the mathematical symbol [tex]\geq[/tex]
So: At least 255 means
[tex]\geq 255[/tex]
Representing the values with variable x, the complete inequality becomes
[tex]x \geq 255[/tex]
For all integer values of x and constant k, if (x-k)(x-5)=x^2-9x+20, what is the value of K?
A) -5
B) -4
C) 4
D) 10
E) 12
============================
Work Shown:
Expand out the left hand side
(x-k)(x-5)
x(x-5)-k(x-5)
x^2-5x-kx+5k
Note that the constant term here is 5k. Yes k seems like a variable, but it's actually a constant. Once we know k, we can replace it to get a fixed number. In this case, k = 4 since 5k = 5*4 = 20 to have it match with the 20 at the end of x^2-9x+20
For the x terms, we have -5x-kx = -5x-4x = -9x which matches with the middle term of x^2-9x+20
Therefore,
(x-k)(x-5) = x^2-9x+20
updates to
(x-4)(x-5) = x^2-9x+20
The -4 and -5 multiply to 20, and they also add to -9. This helps confirm we have the right k value.
the measure of the supplement angle is 24 more than three time the measure of the original angle. find the measures of the angles.
Step-by-step explanation:
Let x° be the original angle. Then the supplement angle is (180 - x)° and (180 - x) = 3x + 24.
180 - x = 3x + 24
4x = 156
x = 39
Hence the original angle is 39° and the supplementary angle is 141°.
The angles are 39° and 141°.
What is a complementary angle ?Two angles are said to be complementary to each other when their sum is 90°
According to the given question
The measure of the supplement angle is 24 more than the measure of the original angle.
Let the original angle be x
So from the given data it's supplement angle is 3x + 24.
We know two angles are supplementary when their sum is 180°.
∴ x + 3x + 24° = 180°
4x = 156°
x = (156/4)°
x = 39°.
So, the original angle is 39° and it's supplementary angle is 141°.
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Solve the inequality -4(x + 4) > x + 7. Give your answer as an interval.
Step-by-step explanation:
hope this answer will help you
Which of the following could be the number shown on the number line?
Answer:
Your correct answer is option B.
Step-by-step explanation:
Option b is the highest number in the options. and, the dot on the number line is closest to the 5. Therefore, your correct answer is option B.
√24 can be the number shown on the number line. Hence, option A is the right choice.
What is a number line?The integers are put at equal intervals on number lines, which are horizontal straight lines. A number line can depict all of the numbers in a series. At both ends, this line continues endlessly.
How do we solve the given question?In the question, we are given a number line showing a point between 4 and 5, which is very close to 5.
We analyze all the given options for a number similar to the number marked on the number line to get the correct option.
To remember, 4 = √16, and 5 = √25
A. √24: falls between 4 and 5 (∵ √16 < √24 < √25). And also √24 is very close to 5 (√25).B. √27: does not fall between 4 and 5 (∵ √27 > √25).C. √20: falls between 4 and 5 (∵ √16 < √20 < √25). But not very close to 5.D. √26: does not fall between 4 and 5 (∵ √26 > √25).After analyzing all the given options, only A. √24 and C. √20 fall between 4 and 5, and the closest to 5 among them is √24, so that is the right choice.
∴ √24 can be the number shown on the number line. Hence, option A is the right choice.
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what is the value of the expression 4x - 1 / 2 y + x when X is 3 + y - 3
Which inequality shows a correct relationship? A 0.203 > 0.085 B 0.870 < 0.706 C 0.374 > 3.740 D 0.725
Answer:
The answer is A (0.203 > 0.085)
b) through (2,9) and parallel to y = 3x - 2
Answer:
y = 3x+3
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