The rate of the slow hike is 2.2 mph and the rate of the faster hiker is 4.4 mph.
Here in this issue, we are managing linear equations which is a condition of one variable regularly composed within the form ax+b=0 , where a and b are real numbers and x is an unknown variable. Solutions to linear equations allude to a linear equation that can have zero, one, or infinitely various solutions. A linear equation with no solutions simplifies to an untrue statement such as 1=0. A linear equation with one solution rearranges to a solution of the form x=n where n may be a real number. A Linear equation with infinitely various solutions simplifies to a true statement without a variable such as 1=1.
Here we considering the rate of the slow hiker to be x, so the rate for the fast hiker will be x+2.2
Since we know that distance = speed * time
therefore, the Distance covered in 5 hours by a slow hiker is 5x , wheras for fast hiker it will be 5(x+2.2)=5x+11 km
As we are given the condition that it i they are 33 miles apart, So
=>5x + 5x+11 = 33
=>10x = 33-11
=>10x = 22
x =22/10 => 2.2
So the rate of a slow hiker is 2.2 mph and the rate of a fast hiker is x+4.4= 4.4 mph.
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The cost of one pencil is 3$, and the total cost of three pencils in 9. Which of the following is true
The correct option is A :the number of pencils and the total cost are in a proportional relationship because the cost does not increase with the number of pencils.
Given cost of one pencil is $3
Thus when we have to find the cost of three pencils we will multiply it with 3 and would be able to get the required amount that is $ 9.
Thus we can say that the number of pencil and cost has direct relationship.
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can some one help picture below
Answer:
3 1/2
Step-by-step explanation:
each dozen needs 1/2 cup of chocolate chips so 1/2 times 7 = 3 1/2
Mrs. [Name] has 56 pencils and 42 erasers. If she wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers, what is the greatest number of students she can have in her class so there are none left over? How many pencils and erasers will each student have
The pencils and erasers that each student have is 14.
How to calculate the value?From the information, the person has 56 pencils and 42 erasers and wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers.
It should be noted that this has to do with looking for the highest common factor.
The highest common factor for 56 and 42 is 14.
The students will have 14 pencils each.
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ing Equations Practice
CONCEPT: Multi-Step Equations
C Level:
What is the value of x? Show your work and explain how you found the answer.
-4x-43 = -95
Answer:
X:15
Step-by-step explanation:
only a genius can explain i can ask my colic to help
Look at this angle:
What is the vertex?
Answer:
T. The vertex is where the angle is measured. It is often associated as the vertex angle.
Step-by-step explanation:
Hope it helps! =D
Answer:
T is the vertex
Step-by-step explanation:
the point where the angle lies , is the vertex, in this case T
using the letters forming the angle , with the vertex T placed in the middle
∠ STU or ∠ UTS
Please help me. I need this done fast.
The correct equation that is balanced using the given numbers once is;
5(-1 + (-3)) = (7 * -4) + 8
How to carry out Algebra Properties?There are some properties of Algebra such as;
Commutative Property of Addition or multiplication
Associative Property of Addition or multiplication
Transitive Property
Distributive Property
Now, looking at the given numbers, one good idea is to use only a positive digit outside the bracket on the left hand side of the equation to make it easy to balance on the right hand side of the equation. Thus, for the left hand side we will try;
5(-1 + (-3))
When that is solved we will get -20
Now, to balance that on the right hand side , we will have;
(7 * -4) + 8 which also equals -20
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Towns A and B are 240 km apart.
A bus takes 80 minutes longer than a car to travel between the two towns.
The car is travelling at 15 km/h faster than the bus which is travelling at × km/h.
(a) Find the time, in hours,
taken by the bus and the car to travel between the two towns in terms of x
(b) Form an equation in × and
show that it reduces to ×2 + 15x - 2700 = 0
(c) Solve the equation and find the speed of the bus and
the time taken by the car to travel between the two towns.
The time (in hours) taken by the bus and the car to travel between the two towns in terms of x is 5 hours 20 minutes and 4 hours respectively and the equation in x formed is [tex]x^2 + 15x -2700=0[/tex]
Given that:-
Distance between towns A and B = 240 km
A bus takes 80 minutes longer than a car to travel between the two towns.
The car is travelling at 15 km/h faster than the bus which is travelling at x km/h.
Let the speed of the bus be s km/hr and,
The time taken by the car to travel from A to B be t hours.
Hence,
(15+x)*t = (t + 80/60)*x
15t + xt = xt + 4x/3
15t = 4x/3
t = 4x/45 hours.
Hence,
(15 + x)*(4x/45) = 240
x(x + 15)/45 = 60
[tex](x^2 + 15x) = 60*45[/tex]
[tex](x^2 + 15x) = 2700\\x^2 + 15x -2700=0\\x^2-45x+60x-2700 = 0[/tex]
x(x-45) +60(x - 45) = 0
(x - 45)(x + 60) = 0
x = 45,-60
As the time cannot be negative,
x = 45 km/hr
t = (4*45)/45
t = 4 hours (time taken by car)
Time taken by bus = 4 hours + 80 minutes = 5 hours 20 minutes
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The shortest side of a right angle triangle is 6cm shorter than the hypotenuse. The difference in length of the other two sides is 3cm. If the shortest side is n - 3, show that 2n squared equals 12n. Hence, n.
The value of n in the right triangle is 12 cm.
How to find the side of a right triangle?The shortest side of a right angle triangle is 6cm shorter than the hypotenuse.
The difference in length of the other two sides is 3cm.
The hypotenuse side is the longest side of a right triangle.
Hence,
hypotenuse side = n - 3 + 6
hypotenuse side = n + 3
Shortest side of the right triangle = n - 3
Other side = n
Therefore, using Pythagoras theorem,
(n + 3)² = (n - 3)² + n²
(n + 3)(n + 3) = (n - 3)(n - 3) + n²
n² + 3n + 3n + 9 = n² -3n -3n + 9 + n²
n² + 6n + 9 = 2n² - 6n + 9
Therefore,
2n² - n² + 9 - 9 = 6n + 6n
n² = 12n
n² - 12n = 0
n(n - 12) = 0
n = 0 and n = 12
Therefore,
n = 12
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Sally invests £8000 in a savings account.
The account pays 2.8% compound interest per year.
Work out the value of her investment after 4 years.
Give your answer to the nearest penny.
The value of her investment at compound interest after 4 years will be £8934.34.
What is compound interest?
Compound interest is the adding of interest to the principle sum of a loan or deposit, or interest on interest plus interest. It is the outcome of making an investment interest, or adding it to the lent assets, rather than repaying it out or requesting return from the borrower, so that interest is received on the principle sum plus previously accrued interest in the next month. In finance and economics, compound interest is the norm. Compound interest differs from simple interest in that previously accrued interest is not added to the main amount of the current month, resulting in no compounding. The simple annual interest rate is calculated by multiplying the interest amount per period by the number of periods per year.
Given,
Principal (P) = £8000
Rate of interest (r) = 2.8% compound interest p.a.
Time (n) = 4 years
Then, according to compound interest compounded annually,
Amount = P(1+r/100)ⁿ
= 8000(1+2.8/100)⁴
= 8000(102.8/100)⁴
= 8934.34
Hence, the value of her investment at compound interest after 4 years will be £8934.34.
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help pass due! i need all help i can get!
Simplify (8h³+h-11) - (3h³+5h²-3h - 7)
a) 11h³ + 5h² - 2h - 18
b) 5h³- 5h² + 4h - 4
c) 11h³ - 5h² +4h - 4
d) 5h³ + 5h² - 2h + 4
Answer: B) 5h³- 5h² + 4h - 4
Step-by-step explanation:
First, get rid of the parenthesis by distributing the negative sign to (3h³+5h²-3h - 7).
The expression is now 8h³ + h -11 - 3h³ - 5h² + 3h + 7
Now, combine like terms. Add terms with the same exponent. Let's start with the terms with the highest exponents.
8h³ + (- 3h³) = 5h³
- 5h²
h + 3h. = 4h
-11 + 7 = -4
Rewrite the new combined terms to get 5h³- 5h² + 4h - 4
Answer:
b) 5h³-5h²+4h-4
Step-by-step explanation:
Greetings !
look at the figure i have attached above
Hope it helps !!
8. Which pair of angles are alternate interior angles?
1
3
021 and 28
21 and 27
22 and 27
023 and 26
2
4
5
7
6
8
10
9
(1 point)
Answer:
∠3 and ∠6
Step-by-step explanation:
∠3 and ∠6 because they lie inside the parallel lines (the lines going left to right) and are on opposite sides of the transversal (diagonal line)
Simplify the expression, 7√2826 - 5√63x6
Assume all variables are positive.
0-³√7
0x³√7
Ox√7
0 -x√7
Hello! So...
We are given the following to simplify:
[tex]7\sqrt{28x^6} -5\sqrt{63x^6}[/tex]
_________________________________________________
To solve this, we must simply simplify.
[tex]7\sqrt{28x^6} =14\sqrt{7} x^3[/tex]
[tex]5\sqrt{63x^6}=15\sqrt{7}x^3[/tex]
[tex]=14\sqrt{7}x^3-15\sqrt{7}x^3[/tex]
Now, add the similar elements:
[tex]14\sqrt{7}x^3 -15\sqrt{7} x^3=-\sqrt{7}x^3 \\[/tex]
Now, considering we are assuming all variables are positive in this situation, we need to convert the negative into a positive solution.
[tex]=-\sqrt{7}x^3[/tex]
[tex]= x^3\sqrt{7}[/tex]
^Hence, our solution.^
______________________________________________________
Hope this helps! If so, please lmk! Thanks and good luck!
Complete all problems (there is one on
1. Let f(x)=√x and let g(x) = 2x² - 8
a. Find fo g(x) and its domain and range
b. gof(x) and its domain and range
c. What is go f (3)?
The values of the composite function are (f o g)(x) = √2x² - 8 and (f o g)(x) = 2x - 8, while their domains are x > 2 and 0 < x < oo, respectively
Lastly, the value of (g o f)(3) is -2
How to evaluate the function?Composite function 1
The functions are given as
f(x) = √x
g(x) = 2x² - 8
The composite function definition is given as
(f o g)(x)
This composite function is calculated using the following composite function formula
(f o g)(x) = f(g(x))
Substitute the known values in the above equation
(f o g)(x) = √g(x)
This gives
(f o g)(x) = √2x² - 8
For the domain, we have
2x² - 8 > 0
This gives
x > 2
Composite function 2
The functions are given as
f(x) = √x
g(x) = 2x² - 8
The composite function definition is given as
(g o f)(x)
This composite function is calculated using the following composite function formula
(g o f)(x) = g(f(x))
Substitute the known values in the above equation
(g o f)(x) = 2f(x)² - 8
This gives
(g o f)(x) = 2(√x)² - 8
Evaluate
(g o f)(x) = 2x - 8
The function is a linear function
So the domain is the set of all real values
Substitute 3 for x in (g o f)(x) = 2x - 8
(g o f)(3) = 2(3) - 8
Evaluate
(g o f)(3) = -2
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Which of the following fractions could you add together easily?
Find system of equations algebraically. d = f; 2d + 4e - 3f = 1; - 3d + 2e + 4f = 5
The solution of the system of equation is [tex]e=1 , d= 3[/tex] [tex],f=3[/tex]
How do you solve algebra?The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions. We employ integers with definite or fixed values in algebra, such as 2, 7, 0.068, etc. In addition to integers, algebra uses variables like x, y, and z.
The solution is written as below:
Given: d= f
2d + 4e - 3f = 1 --------------1
and - 3d + 2e + 4f = 5----------------------2
Put the value of f as d because it is given,
thus equation becomes; 2d+ 4e - 3d= 1 ⇒ 4e- d= 1 ----3
-3d+2e +4d= 5 ⇒ 2e+ d=5 ----4
Thus on solving 3 and 4 we get;
[tex]4e-d=1\\+2e+d=5\\[/tex]
We get 6e= 6 which implies e= 1
And putting this value of e in equation 3 we get,
4X1 -d=1
-d= 1-4 ⇒ -d= -3
thus d = 3
Thus [tex]e=1 , d= 3[/tex]
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a triangle has base 8 cm and perpendicular height 5.2cm
work out the area of the triangle
Answer: 20.8
Step-by-step explanation:
(8*5.2)/2 so 8/2=4*5.2=20.8
Answer: 20.8 [tex]cm^{2}[/tex]
Step-by-step explanation:
1. Bobbi is on a diet to lose weight. After losing 26 pounds, Bob weighs 231 pounds. What was Bobbi's weight
before his diet? Let x represent Bobbi's original weight.
Answer:
231+26=x
x=257 pounds
A(c-b)=d
Solve for c
Please and thank
[tex]a(c - b) = d \\ \frac{a(c - b}{a} = \frac{d}{a} \\ c - b = \frac{d}{a} \\ c = \frac{d}{a} + b \\ c = \frac{d}{a} + \frac{b}{1} \times \frac{a}{a} \\ c = \frac{d}{a} + \frac{ab}{a} \\ c = \frac{d + ab}{a} [/tex]
THIRD OPTION IS THE ANSWER.
HOPETHIS HELPS
On a trip to Spain, Kiana wants to exchange some of her money from US dollars to euros. She looks at the graph to determine the exchange rate
From the given graph, the exchange rate is; 1 dollar = 0.9 euros
How to interpret slope on linear graph?The formula to find the slope from two coordinate points is;
m = (y2 - y1)/(x2 - x1)
To get the slope, let us use points A and B;
A(0, 0) and B(1, 0.9)
Thus;
Slope = (0.9 - 0)/(1 - 0)
Slope = 0.9
Let us use points C and D to verify the slope.
Slope = (2.6 - 1.7)/(3 - 2)
Slope = 0.9
Thus, 0.9 euros costs 1 dollar
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Your favorite cookies use 2 1/4 cups of flour per batch. You used 7 7/8 cups. How many pitches did you make?
Answer:
3
Step-by-step explanation:
You have 3 lots of 2 1/4 to get as close to 7 7/8 without going over it. Meaning thats how many batches you can make.
Which of the following functions is graphed below?
The functions that are shown on the graph are:
Square function.Linear function.What is square function and linear function?General equation of square function is :
f(x) = x2
It's called a parabola.It is symmetric around the y-axis (like a mirror image).Domain : R (Real numbers).It has a range of Non-Negative Real Numbers: [0, +∞)General equation of linear function is :f(x) = mx + b
where 'm' and 'b' are real numbers.
It is an algebraic functionThe domain is entirely made up of real numbers. A function's range is the set of all possible output values.To learn more about type of functions refer to :
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2. If you can bake 15 cookies in 5 minutes, then how many cookies can you
bake in 32 minutes?
Why is the variable x called x?
Lucy used 3 3/4 cups of sugar for her lemonade stand. She divided the
sugar, in equal amounts, into 6 pitchers. How much sugar went into each
pitcher?
The amount of sugar that went into each pitcher was 0.375, which was taken from the 3(3/4) cups of sugar utilized for the lemonade stand.
What is the point of dividing?Division allows us to divide a large number of objects into equal-sized groups. Division is represented by the symbol ÷.
Which property is employed in division?We can use the distributive property to divide larger numbers by breaking them down into smaller factors.
It is implied that Lucy made her lemonade stand using 3 3/4 cups of sugar.
Further, she distributed the sugar into 6 pitchers in equal portions.
Therefore, we need to divide the total cups of sugar by 6 to get the value of sugar that went into each pitcher.
sugar went into each pitcher = 3(3/4) ÷ 6
= (9/4) ÷ 6
= 2.25 ÷ 6
= 0.375
Therefore, each pitcher of sugar contained 0.375 of the 3(3/4) cups of sugar utilized for the lemonade stand.
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The double number lines show the ratio of yards to miles.
How many yards are in 4 miles?
Answer:
Guess it's 7.040 yards in 4 miles
Step-by-step explanation:
8.800÷5= 1.760 in 1 yard
4×1.760=7.040
prove me wrong
Answer:
In both number lines, from 0-8,800 and 0-5 there are 5 notches from the first and last, so what you first want to do is solve for the first number line. You can do this by divideing the largest number by the number of notchest on the line:
8,800/5 = 1760
So the notch after 0 will be 1760. To finish the pattern, you want to add the number you got after dividing the total, by itself, 4 more times, as shown:
1,760 + 1,760 = 3,520
3,520 + 1,760 = 5,280
5,280 + 1,760 = 7,040
7,040 + 1,760 = 8,800
Now the number line will look like this:
0, 1760, 3520, 5280, 7040, 8800
0, 1, 2, 3, 4, 5
Compared to the second number line we find that there are 7,040 yards in 4 miles!
Step-by-step explanation:
Hope it helps! =D
Dividing Complex Numbers:
Simplify 5/-5i
By dividing the complex number 5 / -5[tex]i}[/tex] we get the answer as :
5 / -5[tex]i}[/tex] = [tex]i}[/tex]
Simplification:A complex number is a number system that extends the real numbers with a specific element denoted I known as the imaginary unit, and satisfying the equation [tex]i^{2}[/tex] = -1; each complex number can be expressed in the form a + bi, where a and b are real numbers.
Steps to simplify complex number:
On both the numerator and the denominator, multiply the given complex number by the conjugate of the denominator.Distribute the number in the numerator and denominator to remove the parentheses.Simplify i's powers.Given complex number , 5 / -5[tex]i}[/tex]
multiply the numerator and denominator with conjugate [tex]-i /-i[/tex]
= [tex]5(-i)/-5i(-i)[/tex]
by again simplifying we get ,
= [tex]-5i/-5[/tex]
-5 common from numerator and denominator is eliminated
so we get ,
5 / -5[tex]i}[/tex] = [tex]i[/tex]
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Answer the questions about the following function.
f(x) =
X+11
X-9
(a) Is the point (3,-9) on the graph of f?
Answer:
No
Step-by-step explanation:
I just graphed f(x)=x+11, f(x)=x-9, and (3,-9) in Desmos, and you can visibly see that it isn't.
Mr. Lou teaches 7 reading groups. Each reading group has 5 students. Find how many total
students Mr. Lou teaches today if 3 students are absent.
Which expression correctly represents the problem?
7x (5-3)
(7x5)-3
KC
7-(5 x 3)
D
(7-5) x 3
11
Based on the number of reading groups, and the number of absent students, the expression for the problem is (7 x 5) - 3.
How to find the expression?Every reading group taught by Mr. Lou has 5 students. There are also 7 reading groups. This means that the total number of students under Mr. Lou is:
= Number of reading groups x Number of students per group
= 7 x 5
Then out of this total number, 3 students are absent. The expression then becomes:
= Number of students - Number o absent students
= (7 x 5) - 3
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It takes you 30 minutes to rake the leaves in your yard and
it takes your brother 45 minutes. How long does it take the two of you to rake
the leaves when working together?
Answer:
18.75
Step-by-step explanation:
I'm not exactly sure.
I divided 30 by 2 and 45 by 2 and took both answers and added them together and then took the sum of that and divided it by 2.
what do you add to 4 1/7 to make 6
Answer:
Step-by-step explanation:
4 1/7 = 29/7
6 = 42/7
What you need to add to 4 1/7 is:
6 - 4 1/7
42/7 - 29/7
13/7.
In mixed fractions, it's 1 6/7.