Soyala travelled for 3 hours with a speed of 25 mph and 5 hours with a speed of 15 mph
We know that Distance = Rate x Time. The distance traveled to the library is assumed to be same as the distance traveled on the way to home from the library. Let t be the time it took to travel to the library after which (8 - t) = the time it took to travel back home. We can write following two equations using the formula for distance:
d = 25t ---------> (1)
d = 15(8 - t) = 120 - 15t -----------> (2)
Since the distance d is equal for both trips, let's set the two expressions of time t equal to each other.
25t = 120 - 15t
40t = 120
t = 3 hours
Therefore, Soyala travelled for 3 hours at 25 mph and for 8 - 3 = 5 hours at 15 mph. Each rate will yield a distance traveled of 125 miles.
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the perimeter of triangle abc is 90. if ab= 5x+1, bc= 2x+13 and ac = x+4 what type of triangle is abc
As all the length of each side of given triangle are unequal so the given triangle is scalene triangle
Perimeter of Triangle:-A triangle's perimeter is defined as the total length of its boundary.
The perimeter of a triangle is the sum of all three sides.
Here given that there is a triangle name ABC and the triangle ABC has the perimeter of 90.
∴ Sum of sides of triangle ABC will equal to the perimeter of triangle ABC
∴ AB + BC + AC = 90
As we have AB = 5x + 1, BC = 2x + 13, AC = x + 4
∴ 5x + 1 + 2x + 13 + x + 4 = 90
∴ 8x + 18 = 90
∴ 8x = 90 - 18
∴ 8x = 72
∴ x = 72/8
∴ x = 9.
So we get AB = 5x + 1 = 5(9) + 1 =45 + 1 = 46.
BC = 2x + 13 = 2(9) + 13 = 18 + 13 = 31.
AC = x + 4 = 9 + 4 = 13.
As all the length of each side are unequal so the given triangle is scalene triangle as an scalene triangle is a triangle in which all three side lengths are different and all three angle measurements are different. However, the sum of all interior angles is always equal to 180 degrees. Therefore, it satisfies the angle sum property of triangles.
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Jake has 30 fish in his aquarium. Emi has 1/3 the number of fish that Jake has and 1/2 the number of fish that Tobin has.
If the three students combined all their fish in the school's new aquarium, how many fish would there be?
Using Linear equation, The total number of fishes in the aquarium is found to be 50.
What is an linear equation in one variable?Linear equation is an equation containing one unknown variable with power one and constants.
The standard form of an linear equation in one variable x is :
ax + b = 0 , where a, b are constants
x= -b/ a is solution if this equation or we can solve this equation by adding or subtracting, multiplying, dividing same number to both sides.
Given that number of fishes jake has in the aquarium = 30
And that number of fishes Emi has is 1/3 the number of fish that jake has .
Therefore, Number of fishes that Emi has = 1/3 (30) = 10
Also given that Emi has 1/2 the number of fish that Tobin has .
Let Tobin has x fishes
⇒ 1/2(x) = Number of fishes Emi has
⇒ (1/2)x = 10, this is an linear equation in x
Multiplying both sides by 2, We get:
⇒ 2× (1/2)x = 2 ×10
⇒ x = 20
∴ Tobin has 20 fishes
If the three students combined all their fish in the school's aquarium,
the Total number of fishes = 30+20+10 = 50
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Suppose James has a credit card with a balance of $4289. Each month, the credit card company charges 5% interest. James pays off all new purchases that he makes each month without paying off the old balance or its interest. He wants to know what the balance on his credit card will be one year from now. Is this situation an example of exponential growth or exponential decay?
The balance on his credit card will be the amount of $4076.56 one year from now.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
First, we must compute James' monthly charges on his balance of 4289.
Principal = 4289
Rate = 5%
Time = 1 month = 1/12 year
Simple interest = 4289×5×1/12×100 = 17.87
The monthly charge is 17.87,
So the yearly charge would be: 12 × 17.87 = $214.44
His credit card balance one year from now = Principal - Interest
⇒ 4289 - 214.44
⇒ 4076.56
In one year, his credit card amount will be 4076.56.
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Can somebody trade lease help me I’m late on my work in school
The slopes for each couple of points are summarized below:
m = 2 / 3 m = - 3 / 4 m = - 2 m = Undefined m = 4 m = 0 m = 1 m = - 2 m = Undefined m = 4 / 3 m = - 2 / 7 m = 0 x = 6 y = 6 x = 11How to understand slopes in lines
Geometrically speaking, slopes in lines indicates the grade of steepness of the line itself. The slope of the line can be determine by knowning the coordinates of two distinct points set on Cartesian plane and using the secant line formula, whose definition is shown below:
m = Δy / Δx
Where:
m - SlopeΔx - Change in independent variable.Δy - Change in dependent variable.Now we proceed to answer on each case:
Case 1
m = [3 - (- 1)] / [3 - (- 3)]
m = 4 / 6
m = 2 / 3
Case 2
m = (- 2 - 1) / [2 - (- 2)]
m = - 3 / 4
Case 3
m = [2 - (- 4)] / [- 4 - (- 1)]
m = 6 / (- 3)
m = - 2
Case 4
m = Undefined, as Δx = 0.
Case 5
m = [3 - (- 1)] / (3 - 2)
m = 4
Case 6
m = 0, as Δy = 0
Case 7
m = (6 - 9) / (1 - 4)
m = - 3 / (- 3)
m = 1
Case 8
m = [- 5 - (- 1)] / [- 2 - (- 4)]
m = - 4 / 2
m = - 2
Case 9
m = (- 9 - 3) / (5 - 5)
m = - 12 / 0
m = Undefined
Case 10
m = (9 - 1) / (8 - 2)
m = 8 / 6
m = 4 / 3
Case 11
m = [- 6 - (- 8)] / (7 - 14)
m = 2 / (- 7)
m = - 2 / 7
Case 12
m = [- 3 - (- 3)] / (8 - 4)
m = 0 / 4
m = 0
Case 13
[8 - (- 4)] / (2 - x) = - 3
12 = - 3 · (2 - x)
12 = - 6 + 3 · x
18 = 3 · x
x = 6
Case 14
(4 - y) / (3 - 10) = - 2 / 7
(4 - y) / (- 7) = - 2 / 7
4 - y = - 2
y = 6
Case 15
(4 - 1) / (x - 7) = 3 / 4
3 / (x - 7) = 3 / 4
x - 7 = 4
x = 11
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the question is in the photo! :)
Answer:
2
Step-by-step explanation:
So to get the answer we need to figure out what x is
2×2=4
so x has to be 2
What is the average rate of change of the equation g(x)=−x2+2x−4 from x = 2 to x = 5
The average rate of change of the equation g(x) =−x²+2x−4 from x = 2 to x = 5 is -15 .
The average of change of the function f(x) from x=a to x=b is given by the formula
Average rate of change = (f(b)-f(a))/(b-a)
In the question ,
it is given that
the function is g(x) =−x²+2x−4
we need to find g(2) and g(5) .
g(2) = −(2)²+2(2)−4
= -4 + 4 -4
= -4
g(5) = −(5)²+2(5)−4
= -25 +10 -4
= -15 -4
= -19
So , Average rate of change = (g(5) - g(2))/(5-2)
Substituting the values , we get
Average rate of change = (-19 - (-4))/3
= (-19+4)/3
= -15/3
= -5
Therefore , the average rate of change of the equation g(x) =−x²+2x−4 from x = 2 to x = 5 is -15 .
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45 is divisible by which of the following numbers? (1 point) 1, 5, 8 1, 2, 3 1, 2, 5 1, 3, 5, 9
Answer:
1,3,9,5
Step-by-step explanation:
Answer:
9, 5, 1, 3
Step-by-step explanation:
i forgot my vocabulary
But i still know decent engrish
Select the equation of the line that goes through point (4,−2) and is parallel to the equation 2x+5y=15.
A. -2/5x + y= -18/5
B. -5/2x + y= -12
C. 2/5x + y= -2/5
D. 5/2x + y= 8
what is the answer to this? :(5x^4)^3
Answer:
it is 25 or 35
Step-by-step explanation:
Steven earns extra money babysitting. He charges $33.75 for 5 hours and $47.25 for 7 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits a
y represent the amount he charges.
The equation is y =
Answer:
y = 6.75x
Step-by-step explanation:
$33.75 ÷ 5 = $6.75
$47.25 ÷ 7 = $6.75
So we have y = 6.75x.
Given the equation 6(8g + 2) + 45 = 153, write a scenario similar to Parts A and B that could be represented by the equation. Solve for g and explain what each number in the equation represents, including the solution.
The value for g is 2, meaning that each family bowled 2 games.
How to solve linear equations?
Given that the largest power of the variable (or pronumeral) in these equations is 1, linear equations are also known as first-degree equations. A line on the quadratic system is represented by a linear equation. This equation's general form is axe + b = 0, where a, b, and x are all integers and x is the variable. The y-axis is parallel to this form of equation's single solution, which it symbolizes.
The steps that should be followed while solving linear equations are listed below:
1) We must first determine which variable we need to isolate.
2) Next, make a distinction between variables and constants.
3) Arrange the constants on the right and the variables on the left.
4) Using established axioms, we carry out algebraic operations to determine the variable's value.
Given, the equation is 6(8g + 2) + 45 = 153
Following the steps in the available literature, we have the equation as:
6(8g + 2) + 45 = 153 ⇒ 48g + 12 + 45 = 153 ⇒ 48g = 153 - 45 - 12 = 96
⇒ g = 96/48 ⇒ g = 2
Thus, g as suggested will determine number of times each family bowled.
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Please help!
Find the value of x and y
We can conclude that the value of angle y is 70° and x is 35°.
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.So, a measure of 'x':
We can see that ∠BAC = ∠DAE (Inversely opposite angles)
∠BAC = ∠DAE = 40°We can observe that △DAE is an isosceles triangle with ∠2x and ∠y being equal.Let 2x be y for instance:
y + y + 40 = 1802y = 180 - 402y = 140y = 140/2y = 70°Now, we know that y = 70 and similarly 2x = 70.
Now, solve for 'x' as follows:
2x = 70x = 70/2x = 35°Therefore, we can conclude that the value of angle y is 70° and x is 35°.
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the brain volumes () of 50 brains vary from a low of to a high of . use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of , assuming the estimate is accurate if it is within 15
The estimated standard deviation from the range rule is 145.5 cm3.As it is 29.8 cm3 smaller than the exact standard deviation, we consider that the estimation is not accurate enough.
Generally, brain volumes which are smaller than 921.1 cm3 can be considered significantly low and bigger than 1417.5 cm3 can be considered significantly high. Hence, brain volume of 1457.5 cm3 is bigger than the expected maximum, so it can be considered significantly high.
The calculation goes like this,
According to the range rule, the standard deviation and range, or the distance between the maximum and smallest value, are roughly inversely proportional:
[tex]s=R/4[/tex]
If we have a sample of 50 brains volumes, and they range from 910 cm3 to 1492 cm3, we can estimate the standard deviation as:
[tex]s=max-min/4[/tex]
s=1492-910/4=582/4=145.5
The exact standard deviation is 175.3 cm3.The difference is 175.3-145.5=29.8 cm3, so the estimation is not accurate enough.
The range rule of thumb states that we should anticipate a maximum value that is approximately two standard deviations above the mean and a lowest value that is approximately two standard deviations below the mean. The expected ranges are as follows given our mean volume of 1169.3 cm3 and standard deviation of 124.1 cm3:
Min= M-2s=1169.3-2*124.1=921.1
Max=M+2s=1169.3+2*124.1=1417.5
The brain capacity of 1457.5 cm3 can be regarded as significantly high because it is higher than the predicted maximum.
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select graph for solution of open sentence click until correct graph appears [×]=2
Given:
[tex]|x|=-2[/tex]Let's graph the the absolute value equation.
From the equation let's solve for x.
Since |x| = -2, there is no possible value of x that can satisfy this equation. This is because an absolute value can never be a negative number.
Therefore, we can say there is no solution.
This absolute value equation can not be graphed.
ANSWER:
No solution
Answer the two questions in the photo for easy points ( will mark brainliest if correct )
[10] D
A counter-example is an example that shows the argument can have true premises and a false conclusion.
Option D shows someone who is good at math, but isn't an engineer. This is a counter-example.
[11] B
Similar to the previous question, options A, B, and D are all dogs. However, option C is not a dog and also has four legs. Therefore, it is a counter-example.
Mark has downloaded four times as many songs on his music player as Chloe. If Mark has 40 songs, how many songs does Chloe have?
Answer:
Chloe has 10 songs.
Step-by-step explanation:
40 ÷ 4 = 10
Which system of inequalities is graphed below?
System of inequalities are :
y> [tex]x^{2} -4[/tex] and y > [tex]x^{2} +3[/tex]
What is inequality ?Inequality, A mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal toThe occurrence of an unfair and/or unequal distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different people and in various settings, the word "inequality" may indicate different things.Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.To learn more about : Inequalities
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2/4 x 1/3 because i need help
Answer:
5/6
Step-by-step explanation:
Step 1: Find the GCD (greatest common denominator)
12
Step 2: multiply your factions to represent this
[tex]\frac{2x3}{4x3} = \frac{6}{12} \\[/tex] , [tex]\frac{1x4}{3x4} = \frac{4}{12}[/tex]
Step 3: add the numerators:
[tex]\frac{6}{12} + \frac{4}{12} = \frac{10}{12}[/tex]
Step 4: reduce your fraction
[tex]\frac{10}{12} = \frac{5}{6}[/tex]
Hope that helps
Fraction multiplication
2/4 x 1/3
We reduce the fraction 2/4 to its lowest expression by extracting and canceling 2.
1/2 x (1/3)
Multiply 1/2 by 1/3 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
1 x 1/2 x 3 =====> Multiply
1/6 ====> Answer
What is the slope of the line on the graph
Answer:
Slope is -2!
y= -2x
Step-by-step explanation:
Based on the 2 points given: (3, -6) (-3, 6)
A train of length 150 metres entered a straight tunnel of length s metres. It took the entire crossing of the tunnel in a time of 15 seconds. Find the length of the tunnel if the train moves with uniform velocity equals 90 km./hr
The tunnel measures 225 meters in length.
Uniform velocity: What is it?
Velocity is the measure of how quickly an object's position changes over time and in relation to a frame of reference. A body moves across space with uniform velocity when it does so with an equal displacement per unit of time.
Velocity is equal to the product of distance and time.
It measures in m/s.
In response to the query, we are provided with the-
150m is the length of the train.
s m is the tunnel's length.
90 km/hr is the train's speed.
= 90 × 5/18 m/sec
= 25m/sec
Total distance equals (train length plus tunnel length).
[tex]Speed = \frac{Distance}{Time}[/tex]
⇒ 25 = (150 + s) / 15
⇒ 25 × 15 = 150 +s
⇒ 375 = 150 + s
⇒ 375 - 150 = s
⇒ s = 225
⇒ s = 225m
Hence, the length of the tunnel is 225 m.
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GEOMETRY HELP ASAP
F (x,y) = (...,...)
1. y or -x
2. -x or y
The function which can be the reflection along y-axis will be F(-x, y).
A function may be defined as an expression in which for every input variable x there is only one output variable y. The input variable is known as independent variable and output variable is known as dependent variable. Reflection may be defined as the changes which occur on a graph for a given curve. If reflection of a point occurs along x axis, then there will be change in the y coordinate and if reflection along y axis, then there will be change in the x coordinate. We have a function F(x, y) and we need to find reflection along y axis so there will be change in the x coordinate, so new function will be F(-x, y).
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Vab if a = √8 and b = 2√√/2
Answer:
I will assume that 2√√/2 is actually 2[tex]\sqrt{2}[/tex]
Vab = 8
Step-by-step explanation:
ab
([tex]\sqrt{8}[/tex])*( 2[tex]\sqrt{2}[/tex])
2*[tex]\sqrt{16}[/tex]
2*4
Vab = 8
Please simplify these equations
Answer:
a) 81
b) 16807
c) 1010000000
d) 390630
These are all correct. I checked.
If a car is traveling at 65 miles per hour, then
how far does it travel in 2 hours?
Answer:
130 miles
Step-by-step explanation:
65×2=130 So if I am driving at a rate of 65 mph then in one hour I drive 65 miles. Since it is in 2 hours I will have driven 130 miles.
Answer:
130 miles.
Step-by-step explanation:
so it said that the car is traveling 65 miles per hour and it wants to know how far it would go in 2 hours. so if 1 hour is 65 miles if we multiply it by two then we will get
65 miles = 1 hour
130 miles = 2 hours
PLS TELL ME ASAPPPPP
Mr. Ridley has 4 boxes of pencils and 7 single pencils. In all, he has 79 pencils. How many
pencils are there in a box?
Answer:
18
Step-by-step explanation:
You want to know the number of pencils in a box when 7 more than 4 boxes totals 79 pencils.
SetupLet b represent the number of pencils in a box. Then the total number of pencils Mr. Ridley has is ...
4b +7 = 79
SolutionThis 2-step linear equation is solved in the usual way:
Step 1: isolate the variable term
4b +7 -7 = 79 -7 . . . . . . add the opposite of the left-side constant
4b = 72 . . . . . . . . . simplify
Step 2: isolate the variable
4b/4 = 72/4 . . . . . . . . . . divide by the coefficient of the variable
b = 18 . . . . . . . . . . simplify
There were 18 pencils in each of Mr. Ridley's pencil boxes.
Write an equation for a parabola that passes through the point (2,2) and has a vertex of (3,1)
The equation of the parabola will be;
y = (x - 3)² + 1
What is mean by Parabola?
A parabola is a set of points in the plane which are equidistant from the directrix and focus.
Given that;
The vertex of the parabola = (3 , 1)
A parabola passes through the point (2,2).
Now,
Since, The equation of parabola in vertex form is;
y = a (x - h)² + k
Where, (h , k) are vertex of the parabola.
So, The equation of parabola with vertex (3, 1) will be;
y = a (x - 3)² + 1
And, It passes through the point (2,2).
So we substitute the value of (2, 2) in place of (x, y) as;
2 = a (2 - 3)² + 1
2 = a + 1
a = 2 - 1
a = 1
Substitute the value of a in above equation, we get;
The equation of parabola as;
y = (x - 3)² + 1
Therefore, The equation of the parabola will be;
y = (x - 3)² + 1
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91.276-4.319
to the nearest whole number
Answer:
that's a good question
Step-by-step explanation:
Eight workers are hired to weed a field by
hand. Each is given a plot which is 9×7
meters in size. What is the total area of
the field?
Step-by-step explanation:
1.work out area of a single plot
[tex]area = 9 \times 7[/tex]
[tex]area = 63m ^{2} [/tex]
2.multiply the area by the amount of workers
[tex]total \: area = 63 \times 3[/tex]
[tex]total \: area \: = 189m ^{2} [/tex]
Point C(6,-2)is dilated from the origin by scale factor r =3/4.what are the coordinates of point c
the coordinates of point c is (9/2, -3/2)
Explanation:The original coordinate = C(6, -2)
scale factor r =3/4
New coordinate (c) = scale factor × the original coordinate
c = 3/4(6, -2)
c = (3/4×6, -2×3/4)
c = (18/4, -6/4)
c = (9/2, -3/2)
Hence, the coordinates of point c is (9/2, -3/2)