Which expression represents the distance between −14.6 and −5.2 on the number line?
Answers
Answer:
9.4
Step-by-step explanation:
We are given that two integers -14.6 and -5.2
We have to find distance between -14.6 and -5.2.
Difference between =-5.2-(14.6)
Difference=-5.2+14.6=9.4
Distance is the absolute value of 9.4
Therefore,
[tex]\mid 9.4\mid =9.4[/tex]
Distance between -14.6 and -5.2 is 9.4
Related Questions
please help. Wire is 12.5 cents a foot. How many feet can you buy for a dollar?
Answers
Use the formula to evaluate the series -3+6-12+24-...-a7
Formula:Sn=a1(1-r^n)/1-r
In the formula for a finite series, a1 is the first term, r is the common ratio and n is the number of terms.
Answers
-3 , +6 , -12 , +24 ,.... <---- to get the next term's value, you multiply it by -2
thus, is a geometric sequence, and -2 is the "common difference", and the first term is -3 of course.
so... what's the sum of the first 7 terms?
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=-3\\ r=-2\\ n=7 \end{cases}[/tex]
[tex]\bf S_7=\sum\limits_{i=1}^{7}\ -3\cdot (-2)^{i-1}\implies S_7=-3\left( \cfrac{1-(-2)^7}{1-(-2)} \right) \\\\\\ S_7=-3\left( \cfrac{1-(-128)}{1+2}\right)\implies S_7=-3\left( \cfrac{129}{3} \right)\implies S_7=-3(43) \\\\\\ S_7=-129[/tex]
You just won a contest! you will receive $100,000 a year for 20 years, starting today. if you can earn 12 percent on your investments, what are your winnings worth today?
Answers
C × {{1 - [1/(1 + r)t]}/r} +c
C = 100,0000
r = .12
t = 20
= 100000 * {{1 - [ 1/ (1 + .12)^19]}/ .12} + 100000
approximately 836,577.69
I am using a scientific calculator so just insert right the number and you will come up with the correct answer. The answer in this question is $836,577.69
Write 96 39/40 as a decimal
Answers
[tex] 96\frac{39}{40} = \frac{3,879}{40} = 96.975 \\ \\ Answer: 96.975[/tex]
How I got my result: Solve the mixed fraction: [tex] 96\frac{39}{40} [/tex] by multiplying the outer number ( [tex]96[/tex] ) by the denominator ([tex]40[/tex] ) then whatever [tex]96(40)[/tex] equals we add the numerator ([tex]39[/tex] ) to it, then get the answer and keep the denominator the same. Lastly, divide our new number by [tex]40[/tex] and it'll give you your result
Anyhow!
Good luck on your assignment and enjoy your day!
~[tex]MeIsKaitlyn:)[/tex]
If 7.02 is subtracted 43.8 the correct answer will be
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hope this helped!
all the types of shapes that can be created by taking cross-sections of a cube
Answers
Answer:
✅ triangle
✅ pentagon
✅ hexagon
✅ trapezoid
❌ octagon
Step-by-step explanation:
"is it possible for four consecutive even numbers to have a sum that is ten more than the sum of the smallest two numbers"
Answers
4 consecutive even numbers...x, x + 2, x + 4, x + 6
x + x + 2 + x + 4 + x + 6 = (x + x + 2) + 10
4x + 12 = 2x + 12
4x - 2x = 12 - 12
2x = 0
x = 0........no, it is not possible <==
How does the graph of y=-(2x+6)^2+3 compare to the graph of the parent function?
Answers
[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]
now, with that template in mind, let's see,
[tex]\bf y=\stackrel{parent~function}{x^2}\implies y=\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{+0})^2\stackrel{D}{+0} \\\\\\ y=\stackrel{A}{-1}(\stackrel{B}{2}x\stackrel{C}{+6})^2\stackrel{D}{+3}\quad \begin{cases} A=-1&\textit{reflection over x-axis}\\ B=2\\ C=6&\textit{horizontal shift of }\frac{C}{B}\to \frac{6}{2}\to 3\\ &\textit{to the left}\\ D=3&\textit{vertical shift upwards of 3 units} \end{cases}[/tex]
Data were collected on monthly sales revenues (in $1000s) and monthly advertising expenditures ($100s) for a sample of drug stores. the regression line relating revenues (y) to advertising expenditure (x) is estimated to be modifyingabove y with caret equals negative 48.3 plus 9.00 xy=−48.3+9.00x. what is the interpretation of the slope?
Answers
Answer:
The interpretation of the slope is that for each $1000 you spend, your revenue increases by $900.
Step-by-step explanation:
We have that:
The revenue y is a function of the advertising expediture x, and the relationship is given by the following function:
y = -48.3 + 9x.
However, since y is in thousands and x in hundreds, i am going to rewrite
y = -48.3 + 0.9x
This means that if you spend no money in advertising, you lose -48.3 thousands of dollars. However, for each $1000 you spend, your revenue increases by $900.
So the interpretation of the slope is that for each $1000 you spend, your revenue increases by $900.
x2= 121 can anyone solve it
Answers
I hope this helps :D
a quarterback made 345 pass completions during one football season. if this was 60% of his attempts,how many passes did he attempt?
Answers
divide completions by percentage
345 / 0.60 = 575 pass attempts
0.60x = 345
x = 345 / 0.60
x = 575 <== total attempts
You randomly select one card from a standard deck. event a is selecting a fivea five. determine the number of outcomes in event
a. then decide whether the event is a simple event or not.
Answers
In a standard deck of cards, there are a total number of 52 different card. From those 52 cards, 4 cards are numbered as five. Therefore the probability of selecting a card of five is:
Probability = 4 / 52 = 1 / 13
Assuming that no replacement is made, so the probability changes with each draw, since the total number of cards decreases from 52 to 51 to 50 and so on. Therefore this is not a simple event.
Use the distributive property to create an equivalent expression to 54+18x
Answers
Just take out 18 from each term to get a binomial. Multiply what you factored out, 18, by the remaining binomial.
Answer:
An equivalent expression to 54+18x, using the distributive property is 18(3+x)
Step-by-step explanation:
In the problem we have the binomial (54+18x), and we are asked to use the distributive property, this means that we can find a factor wich is distributed in both terms of the binomial.
We know that any number, or in this case any polinomial (or binomial), can be multiplied times 1 and will stay the same number, and we only need to write this 1 in a way that could resolve our problem, in particular we can say that
[tex]1=\frac{18}{18}[/tex]
then we can distribute the denominator, so we calculate:
[tex](54+18x)=1(54+18x)=\frac{18}{18}(54+18x)=18(\frac{54}{18}+\frac{18x}{18})=18(3+x)[/tex]
And the equivalent expression to (54+18x) is 18(3+x).
working together Katherine and Julianna can plant new trees on there recently divorced land in 4 days working alone it would take Giuliana to days longer than it would take Catherine to plant the trees how long would it take Katherine working alone to plant the trees
Answers
Two people = 1/4
One person = 1 / x + 2
The other person = 1 / x
Solve for x and you can find other person’s rate:
1 / x + 1 / x + 2 = 1 / 4
x = 3 + (sqrt17), 3 – (sqrt17)
x = 7.21
the other solution would be:
Let t be the time necessary by the 1st person to do the job alone
then
(t + 2) is the time required by the 2nd person alone
Let the completed job = 1
A classic work equation:
Each person will do a fraction of the job, the two fractions add up to 1
4/ t + 4 / t + 2 = 1
multiply by t(t+2), results
4(t+2) + 4t = t(t+2)
4t + 8 + 4t = t^2 + 2t
Arrange them as a quadratic equation
t^2 + 2t -8t - 8
t^2 -6t - 8 = 0
then use the quadratic equation, the answer will be 7.21.
It will take Katherine approximately 7 days working alone to plant the trees.
78 million converted in scientific notation
Answers
The correct answer is:
7.8 × 10⁷
Explanation:
To write a number in scientific notation, we want the decimal behind the first non-zero digit in the number. The first non-zero digit in 78 is 7; this means we want 7.8. In order to have the decimal point behind the 7, we need to move the decimal 7 places. This is the exponent of 10 in our scientific notation, which gives us
7.8 × 10⁷
***ANSWER ASAP****
Use synthetic division to solve (x^3-x^2-17x-15)/(x-5)
Answers
5 | 1 -1 -17 -15
. | 5 20 15
- - - - - - - - - - - - - - - -
. | 1 4 3 0
which translates to
[tex]\dfrac{x^3-x^2-17x-15}{x-5}=x^2+4x+3[/tex]
Answer: [tex]1x^2+4x+3[/tex]
Step-by-step explanation: Given expression (x^3-x^2-17x-15)/(x-5).
We need to divide it x^3-x^2-17x-15 by x-5 using synthetic division .
In order to solve by synthetic division, we would write all the coefficients of given divisor polynomial:
And we divide them by 5 using synthetic division method.
______________
5 | 1 -1 -17 -15 Getting first number down.
| 5 20 -15 Multiplying each down number by
- - - - - - - - - - - - - - - - divisor 5.
1 4 3 0 5×1=5 , 5×2=20, 5×2=15
Subtracting those products from coefficients.
Now, writing the final polynomial degree 1 less than 3, that is 2.
So, [tex]1x^2+4x+3[/tex] would be our quotient.
Write a 2 column proof
Prove x=45
Answers
Opposite angles are equal, so
2x + 6 = 96
2x = 96 - 6
2x = 90
x = 90÷2
x= 45
Answer:
Look at the below steps.
Step-by-step explanation:
We have been given two intersecting lines:
The given angles are vertically opposite angles:
[tex]2x+6=96[/tex]
On simplification we get:
[tex]2x=90[/tex]
On further simplification we get:
[tex]x=\frac{90}{2}[/tex]
[tex]x=45[/tex]
Hence proved that x=45.
Help and get 6 points!
Answers
15b. 3
15c.
[tex]2 \frac{1}{2} [/tex]
write 60 as the product of two factors
Answers
Joseph needs to find the quotient of 3216 divided by 8. In which place is the first digit of the quotient?
Answers
Raquel throws darts at a coordinate grid centered at the origin. Her goal is to create a line of darts. Her darts actually hit the coordinate grid at (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6). Which equation best approximates the line of best fit of the darts? y = 0.6x + 0.6 y = 0.1x + 0.8 y = 0.8x + 0.1 y = 0.5x + 0.6
Answers
Solution:
The points at which Raquel Darts hit the coordinate grid having center at the origin are (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6).
As we can see that not all points are collinear.
As line of best fit is the the line which passes through some points , may be not through the single point, or all the points.
Plotting all the options on coordinate grid i.e on a scatter plot and then determining , the line of best fit of the darts is
y= 0.6 x + 0.6 →→Option (A), the reason being it passes through a point (9,6).
A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.
Answers
The value of "a" is 2.
To find the value of "a," we can use the formula for the equation of a line, which is y = mx + b.
First, we need to find the slope, represented by "m," using the given points (-1, -5) and (4, 5). The slope formula is (y2 - y1) / (x2 - x1).
Substituting the coordinates, we have:
m = (5 - (-5)) / (4 - (-1))
m = 10 / 5
m = 2
Now that we have the slope, we can substitute it into the equation of the line with the point (a, 1):
1 = 2a + b
To solve for "a," we need to find the value of "b." We can substitute one of the given points into the equation and solve for "b."
Using (-1, -5):
-5 = 2(-1) + b
-5 = -2 + b
b = -3
Now we can substitute the values of "b" and "a" into the equation:
1 = 2a - 3
To isolate "a," we add 3 to both sides:
1 + 3 = 2a
4 = 2a
Dividing both sides by 2, we find:
2 = a
Therefore, the value of "a" is 2.
A car company said that its top five models had the following fuel efficiency ratings: 26.3 mpg, 28.95 mpg, 33.6 mpg, 35 mpg, 38.24 mpg. What is the average mpg rating of these five models, recorded to the appropriate degree of precision? A. 32 mpg B. 32.0 mpg C. 32.4 mpg D. 32.42 mpg
Answers
The average fuel efficiency rating, calculated by adding the mpg ratings and dividing by five, is 32.418 mpg, rounded to the nearest hundredth as 32.42 mpg. The answer is D. 32.42 mpg.
To find the average fuel efficiency rating of the top five models, we need to calculate the mean mpg rating. To do this, we add up all the mpg ratings and then divide by the number of models:
Add the fuel efficiency ratings together: 26.3 + 28.95 + 33.6 + 35 + 38.24.
The sum is 162.09 mpg.
Divide this sum by the number of cars, which is 5: 162.09 ÷ 5.
The average is 32.418 mpg.
To record the average to the appropriate degree of precision, we consider the place values of the original data provided. The given ratings include mpg values recorded to the nearest hundredth, as in 28.95 mpg and 38.24 mpg. This means the average should also be recorded to the nearest hundredth: 32.42 mpg. Therefore, the correct answer is D. 32.42 mpg.
On a blueprint, a wall that is 45 feet long is 6 inches long. How long should a girder appear on the blueprint if the girder is actually 30 feet long?
Answers
Answer:
4 inches
Step-by-step explanation:
1 foot = 12 inches
45 feet --- 6 inches
From this we can conclude that the scale of the Blueprint is:
1 foot in actual = 1/90 foot on blueprint
If the girder is actually 30 feet long, then
30 feet --- (1/90*30*12) inches
30 feet --- 4 inches
Each side of a square is increasing at a rate of 5 cm/s. At what rate is the area of the square increasing when the area of the square is 25 cm2?
Answers
da/dt=2sds/dt
we know each side increases at 5cm/s
da/dt=2s(5cm/s)
note, when a=25cm2, s=5cm
so da/dt=2(5cm)(5cm/s)=[50cm2/s]
Speed skiing takes place on a course that is 2/3 mile long. How many feet long is the course? Show work too
Answers
1 mile = 5280 feet
5280 * 2/3 =
5280 *2 = 10560
10560/3 = 3520
it is 3520 feet long
Find the circumference of a circle with a diameter of 6 cm. Leave your answer in terms ofmc149-1.jpg.
9mc149-3.jpg cm
12mc149-4.jpg cm
24mc149-5.jpg cm
6mc149-2.jpg cm
Answers
C = 6Pi
That looks like the last option, but I can't tell because the question looks funny with the mc149-2.jpg in the middle.
Answer:
D. [tex]6\pi\text{ cm}[/tex].
Step-by-step explanation:
We are asked to find the circumference of a a circle with a diameter of 6 cm.
We will use circumference of circle to solve our given problem.
[tex]C=\pi\cdot D[/tex], where,
C = Circumference of circle,
D = Diameter of circle,
Upon substituting [tex]D=6\text{ cm}[/tex] in above formula we will get,
[tex]C=\pi\cdot 6\text{ cm}[/tex]
[tex]C=6\pi\text{ cm}[/tex]
Therefore, circumference of our given circle would be [tex]6\pi\text{ cm}[/tex] and option D is the correct choice.
A contractor is building a circular swimming pool. The radius of the circle 12 feet. He needs to know the circumference in order to buy tile to put around the edge of the pool. What is the circumference if he uses =22/7 ?
Answers
Diameter is twice the radius so that would be 24 feet
C = Pi X 24
C = (22/7) X 24
C = 75.428 Feet.
7-4.9t=15+7.6t solve for t
Answers
Start with adding 4.9t to both sides to get 7=15+12.5t
Then subtract 15 from both sides to get -8=12.5t
Divide both sides by 12.5t so you will get -0.64=t.
Plug this back in to the equation to check your work.
7-4.9(-.64)=10.136
15+7.6(-.64)=10.136
Your bird feeder holds 3⁄4 quarts of birdseed. Your scoop holds 3⁄8 of a cup. How many scoops of birdseed will fill the feeder?
Answers
[tex] \frac{3}{4} [/tex] ÷ [tex] \frac{3}{8} [/tex]
Next, since you are dividing, you would flip the second fraction and change it to multiplication.
[tex] \frac{3}{4} [/tex] × [tex] \frac{8}{3} [/tex]
Now, you would cross simplify it (you can also do this at the end instead, but this way is easier).
[tex] \frac{1}{1} [/tex] × [tex] \frac{2}{1} [/tex]
The last step would be to solve it.
[tex] \frac{1}{1} [/tex] × [tex] \frac{2}{1} [/tex] = [tex] \frac{2}{1} [/tex] = 2
You would need 2 scoops of birdseed to fill the feeder.
I hope this helps!
Answer
It is 2 scoops
Step-by-step explanation:
3⁄8 x 1⁄4 = 3⁄32 quart
3⁄4 ÷ 3⁄32 = 8 scoops