Dividing the segments and finding the lengths, it is found that the distance between the two cities is of 130 miles.
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We want to find the distance between cities a and d.Due to the cities along the highway, the distance is given by:[tex]ad = ab + bc + cd[/tex]
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The distance from city a to city b is 5 times the distance from city b to city c, and thus:[tex]ab = 5bc[/tex]
In terms of x, [tex]bc = x, ab = 5x[/tex]
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The distance from city b to city c is 2 times the distance from city c to city d, and thus:[tex]bc = 2cd[/tex]
In terms of x, [tex]cd = \frac{x}{2}[/tex]
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The distance between city d and city c is 10 miles, thus:[tex]\frac{x}{2} = 10[/tex]
[tex]x = 20[/tex]
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The other distances are:[tex]bc = x = 20[/tex]
[tex]ab = 5x = 5(20) = 100[/tex]
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The distance between cities a and d is:[tex]ad = ab + bc + cd = 100 + 20 + 10 = 130[/tex]
The distance between the two cities is of 130 miles.
A similar problem is given at https://brainly.com/question/24352869
write 3.777777777 as a mixed number
inductive reason what is next number in sequence 400, 200, 300, 150, 250
Answer:
125
Step-by-step explanation:
400÷2 = 200
300÷2 = 150
so,
250÷2 = 125
Solve for x: x^2+4b=0
Answer:
[tex] {x}^{2} + 4b = 0 \\ {x}^{2} = - 4b \\ x = \sqrt{ - 4b} \\ x = 2 \sqrt{b} i \\ thank \: you[/tex]
Hunter assumed he would only get 64
problems correct on his test, but he
actually got 78 correct. What was his
percent error?
Can someone please help me please?
[tex] \large \mathfrak{Answer : }[/tex]
The equation of the red parabola is :
[tex]f(x) = 1 - {x}^{2} [/tex]therefore , correct option in A
40 points please help
Answer:
[tex]\huge\boxed{-2}[/tex]
Step-by-step explanation:
Use any two points from the line.
Let them be:
(x1,y1) = (0,-2)
(x2,y2) = (-1,0)
Now,
[tex]\displaystyle Slope = \frac{y_2-y_1}{x_2-x_1} \\\\Slope = \frac{0-(-2)}{-1-0} \\\\Slope = \frac{2}{-1} \\\\Slope = -2\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Please help fast Subtract 5/8 - 1/6
Answer:
0.4583
Hope it helps you!!
Determine the domain and range of the polynomial function
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Answer:
(b) domain: all reals; range: y ≤ 6
Step-by-step explanation:
The domain of any polynomial function is always "all real numbers." There are no values of the variable for which a polynomial is undefined.
The range of a polynomial will depend on its degree and the sign of the leading coefficient. Here, the degree is even, so the range has a limit. The leading coefficient is negative, so that limit is a maximum.
Only one answer choice has these characteristics:
domain: all real numbers; range: y ≤ 6
__
The graph confirms this choice of range.
15. Create Write a real-world problem that can be solved by modeling integer
operations on the number line.
Answer:
The temperature was 80 degrees and it dropped 10 degrees. What is the temperature now?
80 - 10 = 70 degrees
Step-by-step explanation:
Solve for x. 2x^2-4x=0
A.
0, -4
B.
0, -2
C.
0, 2
D.
2, 4
A hotel has a total of 7 floors if there are 35 standard rooms on each floor how many standard rooms are there
Answer:
245
Step-by-step explanation:
multiple the amount of rooms on each floor (35) by the amount of floors (7)
35x7=245 rooms
A king Palm can grow about 21 feet a year . Estimate the height of the kind palm , yard ,after 15 years
Answer:
10.5 yards after 15 years
Step-by-step explanation:
2.1 feet times 15 years, which equals to 31.5 feet, convert 31.5 feet into yards, so divide it by 0.3, and that equals to approximately 10.5 yards
Please help me and thank you!! Show the steps also please I got 198x
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Answer:
264x³-66x
Step-by-step explanation:
The order of operations requires this be evaluated as ...
11x(96x÷4x -6) . . . . given
11x(24x·x -6) . . . . . . division inside parentheses
11x(24x² -6) . . . . . . multiplication inside parentheses
264x³ -66x . . . . . multiply by outside factor (use the distributive property)
_____
Additional comment
The appearance of the expression in parentheses may induce you to evaluate it as (96x)÷(4x) = 24. The order of operations requires that you do the division before the multiplication, left to right, so this must be evaluated as ...
((96x)÷4)x = 24x²
You need to be very careful with division and with exponents to make sure to follow the Order of Operations exactly. If you have an appropriate calculator, it will do that automatically. For example, if you tell your calculator ...
(for x=2) 11×2×(96×2÷4×2-6)
it should give you the result 1980, not 396.
Answer:
= 198x
Step-by-step explanation:
11x × { 96x ÷ 4x -6}
11x × { 24x -6}
264x - 66x
= 198x
You got the correct answer
Evaluate u + xy, if u = 18, x = 10, and y = 8
Answer:
[tex]u + xy \\ 18 + 10 \times 8 \\ 10 + 80 \\ 90[/tex]
Answer:
Solution,
here,
u=18
x =10
y= 8
=u+xy
=18+(10×8)
=18+80
=98
A contractor removed 357 cubi c ya rds of earth from a building site. If the contractor’s trucks can haul 17 cubic yards per load, how many truckloads of earth were moved?
Answer:
21 loads
Step-by-step explanation:
357/17=21
Match the expression to its value.
104
1
= 0.01
102
104
102
10,000
10-4. 102
1
= 0.000001
109
10-4
1
= 0.0001
10-
Answer:
Ans; 10⁴ —> 10, 000
Ans; 10-⁴ / 10² —> 1/ 10⁶ = 0. 000 001
Ans; 10-⁴ × 10² —> 1/ 10² = 0.01
Ans; 10-⁴ —> 1/ 10⁴ = 0. 000 1
I hope I helped you^_^
Answer:
A=a
B=d
C=c
D=b
Step-by-step explanation:
Help will give Brainly points
Paul bought a student discount card for the bus. The card allows him to buy daily bus passes for $1.30. After one month, Paul bought 12 passes and spent a total of $22.60.
How much did he spend on the student discount card?
Answer:
$10.24
Step-by-step explanation:
12(1.30)=12.36
22.60-12.36=10.24
450 m
110
equals which of the following values to the correct number of significant figures?
The equivalent expression of the given value is 4.1 m/s in two significant figures
Your question is incomplete, i believe the following is the intended question.
[tex]\frac{450 \ m}{ 110 \ s}[/tex] equals which of the following values to the correct number of significant figures ?
The express the given value in the correct significant figures we will simplify it as follows:
450 m has 2 significant figures ( 4 and 5)
110 s has 2 significant figures (1 and 1)
Thus, the resultant ratio of the two numbers will be expressed in two significant figures.
[tex]\frac{450 \ m}{110 \ s} = 4.0909 \ m/s\\\\in \ two \ significant \ figures = 4.1 \ m/s[/tex]
Therefore, the equivalent expression of the given value is 4.1 m/s
Learn more here: https://brainly.com/question/23396760
Find A in degrees C= 120° b= 5 c= 11
Answer:
36.8
Step-by-step explanation:
I think A=36.8
Hope it will help you (:
Evaluate the expression.
6(3 + 5)
26.
4
HELP
Answer =1267.2
Step-by-step explanation:
6(3+5)26.4
6×8×26.4
48×26.4
1267.2 is the answer
A triangle with a perimeter of 30 inches has sides of x+3, 2x+5, and x. find the value of x
Answer:
x = 5.5 inches.
Step-by-step explanation:
The perimeter is the sum of the 3 sides, so:-
x + x + 3 + 2x + 5 = 30
4x + 8 = 30
4x = 22
x = 5.5.
Every time Sariyah babysits, she saves $12 of her earnings. Every time Aaron
babysits, he saves $9 of his earnings. After babysitting a number of times, Sariyah
and Aaron have saved the exact same amount of
earnings. What is the least possible
amount of savings they could each have?
Answer:
The least possible amount of saving they could each have is 36$
Step-by-step explanation:
12+12+12 = 36
9+9+9+9=36
Find the nth term for the following sequences, 100,96,90,82,72.(an^2+bn+c)
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Answer:
t(n) = -n^2 -n +102
Step-by-step explanation:
We can use the first 3 terms to find a, b, c.
a(1)^2 +b(1) +c = 100
a(2)^2 +b(2) +c = 96
a(3)^2 +b(3) +c = 90
Subtract the first equation from the other two:
3a +b = -4 . . . . . . [eq4]
8a +2b = -10 . . . . [eq5]
[eq5] can be reduced to
4a +b = -5 . . . . . . [eq6]
Subtracting [eq4] from [eq6] gives ...
(4a +b) -(3a +b) = (-5) -(-4)
a = -1 . . . . . . . . simplify
Filling that into [eq4], we get
3(-1) +b = -4
b = -1 . . . . . . . add 3
Putting the values for 'a' and 'b' into the first equation gives ...
-1 +-1 +c = 100
c = 102
Then the n-th term t(n) of the sequence is ...
t(n) = -n^2 -n +102
_____
Additional comment
As you might guess, there is a generic solution for quadratic sequences. In terms of the first term (a1), first first difference (d1), and second difference (d2), the coefficients can be written as ...
a = d2/2b = d1 -3ac = a1 -d1 +d2This sequence has first differences of -4, -6, -8, -10, and second differences of -2. Putting the sequence values into the above formulas, we find ...
a = -2/2 = -1b = -4 -3(-1) = -1c = 100 -(-4) +(-2) = 102 . . . . . as aboveFind the distance between the pair of points A(7,8) B(-8,4)
Answer:
Formula:
[tex]length = \sqrt{ {(x _{1} -x_{2} )}^{2} + {(y_{1} -y_{2}) }^{2} } [/tex]
substitute:
[tex]l = \sqrt{ { \{7 - ( - 8) \}}^{2} + {(8 - 4)}^{2} } \\ \\ l = \sqrt{225 + 16} \\ l = \sqrt{241} \\ { \boxed{ \boxed{length = 15.5 \: units}}}[/tex]
PLEASE HELP!!! How does the multiplicity of a zero affect the graph of the polynomial function?
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Answer:
2, 4, 61crossStep-by-step explanation:
Consider a zero at x=1.
If it has multiplicity 1, the corresponding factor is (x -1). Now consider the sign of that factor for x = 1.1. The value is (1.1 -1) = 0.1, a positive number.
When the value of x is 0.9, the factor is (0.9 -1) = -0.1, a negative number.
This tells you that values to the left of a zero make the factor(s) associated with that zero be negative. For x-values to the right of the zero, the factor(s) will be positive.
If the multiplicity is even, the product of those factors is positive on either side of the zero. (A negative number to an even power is a positive number.) That is, the graph will not change sign from one side of an even-multiplicity factor to the other. At an odd-multiplicity factor, the graph changes sign.
__
For the problem at hand, the only even-multiplicity factor is (x -1), so the graph will not change sign at x=1. It will touch the axis (be tangent to the x-axis), but will not cross. The other zeros have odd multiplicity (1 or 3), so the graph will change sign there.
It is worthwhile to note that the higher the multiplicity, the "flatter" the graph is at the zero. You can see this in the attachment by comparing the shape of the graph at x=6 with the shape at x=2 (also an upward zero crossing).
_____
Additional comment
You may wonder why the curve is below the x-axis at x=1 when the product of the factors in that neighborhood is always positive. The reason is that there are an odd number of zeros to the right of x=1, so the product of those factors is negative.
If $1000 is invested for 2 years with a 3% yearly interest rate. What is the amount of simple interest
Answer:
Total: 1060 Gain: 60
Step-by-step explanation:
1000 (Current Amount) x 0.03 (3% as a decimal) x 2 (year amount) = 60 + 1000 (Original Amount Invested) = 1060
How do I write 680,705 in expanded form.
Answer:
600,000+80,000+700+5
PLEASE HELP- brainliest and points will be given
Answer: Choice B
[tex]\frac{1}{\sqrt{65}}<-4, 7>[/tex]
===============================================================
Explanation:
Consider a right triangle with legs a = 4 and b = 7. Through the pythagorean theorem, the hypotenuse is
c = sqrt(a^2+b^2) = sqrt(4^2+7^2) = sqrt(65)
This represents the length of the vector <-4,7>
Dividing each component by the length will normalize the vector. This is the same as multiplying by [tex]\frac{1}{\sqrt{65}}[/tex] which is what choice B shows. The phrasing "normalize the vector" means "make the vector to be of length 1". A common application of normalizing vectors will come up in computer graphics.
The original vector and the vector mentioned in choice B point in the same direction. The only thing that has changed is the length from sqrt(65) to 1.
435 divided by 15 equals what?
