Answer:
[tex]17[/tex] and [tex]20[/tex].
Step-by-step explanation:
Let [tex]x[/tex] denote the larger one of the two positive integers ([tex]x > 0[/tex].) The smaller integer would be [tex](x - 3)[/tex]. The square of the larger integer would be [tex]x^{2}[/tex].
The sum of the smaller integer and the square of the larger integer is [tex](x^{2} + (x - 3))[/tex]. If this sum is equal to [tex]417[/tex], then:
[tex]x^{2} + x - 3 = 417[/tex].
[tex]x^{2} + x - 420 = 0[/tex].
Solve this quadratic equation for [tex]x[/tex] through factorization. Since [tex]420 = 21 \times 20[/tex]:
[tex]x^{2} + x - (21 \times 20) = 0[/tex].
[tex]x^{2} + 21\, x - 20\, x + (21)\, (-20) = 0[/tex].
[tex](x + 21)\, (x - 20) = 0[/tex].
Thus, either [tex]x = 20[/tex] or [tex]x = (-21)[/tex] by the Factor Theorem. However, since [tex]x > 0[/tex] (the two integers are both positive,) only [tex]x = 20[/tex] is a valid solution.
Hence, the larger one of the two integers would be [tex]20[/tex]. The smaller one of the two integers would be [tex](x - 3) = (20 - 3) = 17[/tex].
2. The population, P, of a village t years after it was founded in 1970, is given by
P(t) = 8000 + 600t.
a) What is the population in 1970?
8000 is the population of village in 1970.
Given that:
The linear equation of the population, P, of a village t years after it was founded in 1970, is given by
P(t) = 8000 + 600t.
To find:
What is the population in 1970 ?
So, according the question
We have,
The population of a village after t years from 1970 in a form of linear equation is,
P(t) = 8000 + 600t.
This linear equation was founded in 1970, so t years will be counted after 1970. If we need to find the population of a village in 1971, we can use t = 1971 - 1970, which is one year. But here we have to find the population of a village in 1970, so the value of time is 0.
Now, putting the value of t.
We will be get,
P(t) = 8000 + 600t.
P(0) = 8000 + 600 × 0.
P = 8000
So, the population of a village in 1970 is 8000.
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Mia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.30 plus $4.25 per mile. The total fare was $31.05, not including the tip. How many miles was the taxi ride?
The taxi ride was 7 miles
How to calculate the number of miles ?Mia took a taxi from her house to the airport
The taxi charged a pick up fee of $1.30
They also charged $4.25 per mile
The total fare was $31.05
The number of miles can be calculated as follows
31.05 - 1.30 = 4.25x
29.75= 4.25x
Divide both sides by the coefficient of x which is 4.25
29.75/4.25= 4.25x/4.25
x= 7
Hence the taxi ride was 7 miles
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I need an equation that equals 20 like pre algebra
The equation which equals to 20 can be x + y = 20.It can also be f(x) = 5x where x = 4 and many more.
What is a function ?A function behaves like an output or response to an input.The set of all inputs are known as independent variable and the set of all outputs are known as dependent variable.
According to the given question we need an equation that equals to 20.
As the type of equation is not defined we will construct a simple equation known as linear equation in two variables.
So, It can be formed by x + y = 20 this equation has an infinite no. of solutions.Some of them are (1,19), (2,18),.....(19,1).We can also go by negative number and a positive number.
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Solve for the variable. Enter only a number for your answer. (Not x= ...
9+x=-4
I
Question 3
1 p solve for the variable
Your response's numerical variable is x=-13.
What does a math variable mean?Variable, A symbol (often a letter) used in algebra to represent an unknowable numerical value in an equation. X and Y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s are examples of frequently used variables (arc length).
How would you define algebra?Mathematical expressions are used to represent situations or problems in algebra, a branch of mathematics. We use integers with fixed or definite values in algebra, such 2, 7, 0.068, etc. In algebra, we mix variables like x, y, and z with numbers.
accordance with the data provided;
the equation is 9+x=-4
x+9=-4
(x+9)+(-9)=-4+(-9)
x+9-9=-4-9
x=-13
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What is the value of the expression when y=5 and z=4? (4y+9z)
Hey there!
(4y + 9z)
= 4y + 9z
= 4(5) + 9(4)
= 20 + 36
= 56
Therefore, your answer should be: 56
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find the measurement of the angle indicated for each trapezoid.
The measurement of the angle indicated for each trapezoid is m<B equal to 70.
What is trapezoid shape?A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides. The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs.
Given :
In the trapezoid angle
m<B=11x+15
m<C=19x+15
According to the question,
The trapezoid is a quadrilateral.
The 4 angles of a quadrilateral all equal to 360 degrees.
The angles between parallel lines add up to 180degree due to adjacent angle.
So,
The equation is
m<B+m<C=180
11x+15+19x+15=180
30x+30=180
Subtract 30 from both sides we get,
30x=150
Divide by 30 on both sides we get,
x=5
∴m<B=11x+15=11*5+15
m<B=70
m<C=19x+15=19*5+15
m<C=110
Therefore, the measurement of the angle indicated for each trapezoid is m<B equal to 70.
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W.H. must make a decision about spending $100 to fix his old water heater. It is an electric unit and costs him $125 a year to provide his home with hot water. His other option is to buy a new gas water water for $350. The new heater will save 40% on yearly operating costs. If he sells his house 3 years from now, should he buy the new heater? use break-even point method to justify answer.
W.H. must spend $100 to fix his old water heater to reduce his overall cost
If he spends money to fix his old water heater.
Repair cost of his old water heater = $100
Electricity cost for three years as he sells his house 3 years from now = $125 * 3 = $375
Total cost If he spends money to fix his old water heater = $475
If he spends money to buy new water heater
Cost of purchasing new water heater= $ 350
Reduced yearly electricity bill = $125- 40%of $ 125 = $75
Electricity cost for three years as he sells his house 3 years from now = $75 * 3 = $225
Total cost If he spends money to buy new water heater = $575
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If the slope of a line and a point on the line are known, the equation of the line can be found using the slope-intercept form, y=mx+b. To do so, substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b.
Using the above technique, find the equation of the line containing the points (-2,8) and (4,-1)
The equation of the line containing the points (-2,8) and (4,-1) is:
y = -3x/2 + 5
Given data
points (-2,8) and (4,-1)
How to find the equation of the line with the points (-2,8) and (4,-1)From the equation of the straight line y = mx + c
The slope of the line m is solved by
m = ( y2 - y1 ) / ( x2 - x1 )
m = ( -1 - 8 ) / ( 4 - -2 )
m = (-9 ) / ( 6 )
m = -3/2
using the point ( 4, -1 ) we find the intercept as
y = mx + c
-1 = -3/2 * 4 + c
-1 = -3 * 2 + c
-1 = -6 + c
-1 + 6 = c
c = 5
Substituting the values of m = -3/2 and c = 5 to the equation y = mx + c gives the equation of the line. This is done as follows
y = mx + c
y = -3/2 * x + 5
y = -3x/2 + 5
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please help with this problem if you can.
The measures of angle ACB and angle ABC are 40° and 63° respectively
How to determine the valueFrom the information given, we have that angle DAB is on a straight line
But angle D is 103°
Remember that angles on a straight line sum up to 180°
Then,
103° + Angle A = 180°
Angle A = 180 - 103
Angle A = 77°
It is important to note that sum of angles in a triangle is 180°
angle ACB + angle ABC + angle CAB = 180°
Where;
angle ACB = 3x - 14angle ABC = 3x + 9angle CAB = 77°Substitute into the formula
3x - 14 + 3x + 9 + 77 = 180
collect like terms
3x + 3x = 180 - 72
6x = 108
Make 'x' the subject
x = 108/6
x = 18
But;
Angle ACB = 3x - 14 = 3(18) - 14 = 54 - 14 = 40°
Angle ABC = 3x + 9 = 3(14) + 9 = 54 + 9 = 63°
Thus, the measures of angle ACB and angle ABC are 40° and 63° respectively.
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How much pure acid should be mixed with 3 gallons of a 20% solution in order to get a 40% acid solution?
I know how to set up the problem but I just can't seem to get the right answer. I know the formula is:
x+%1(gallons)=%2(x+gallons)
Help Please!
One gallon of pure acid must be added to get a 40% acid solution.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other
Given that
3 gallons of a 40% acid solution means you have (20%)×(3) = 0.6 gallons of acid already.
Let x of gallons of pure acid be added to get a 40% acid solution.
⇒ (0.6 +x)/(3+x) = 40%
⇒ (0.6 +x)/(3+x) = 4/10
Cross multiply, we get
⇒ 10(0.6+x) = 4(3+x)
⇒ 6 + 10x = 12 + 4x
⇒ 10x - 4x = 12 - 6
⇒ 6x = 6
⇒ x = 1
Therefore, one gallon of pure acid must be added to get a 40% acid solution.
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An individual borrowed $78,000 at an APR of 6%, which will be paid off with monthly payments of $503 for 25 years.
Based on the amount that the individual is paying monthly, the total amount that will be paid over the full term of the loan is $150,900
How much will be paid in total?The amount that the individual will pay in total over the loan's full term can be found to be:
= Amount paid per month x Number of years x number of months per year
Solving gives:
= 503 x 25 x 12
= 503 x 300
= $150,900
In conclusion the total amount paid is $150,900.
The rest of the question is:
What is the total amount paid over the full term of the loan?
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A bird flies at the top speed of 20,000 meters per hour. The bird flies 30,000 meter without stopping. for how many hours did the bird fly if it flew at top speed
Answer:
1 hour and 30 minutes
Step-by-step explanation:
I think this because it said his top speed was 20,000 and he flew 30,000 if you add another 20,000 to the 20,000 he flew in 30,000 you would get 40,000 which is 2 hours so 1 hour and 30 min. Hope it Helped!
Aspen has 306306306 green beads and 210210210 silver beads. For every 5\,\text{cm}5cm5, start text, c, m, end text of a belt that Aspen sews, they use 404040 green beads and 242424 silver beads.
After how many centimeters of the belt will Aspen have equal numbers of green and silver beads left?
Answer: I have no idea
Step-by-step explanation: can anyone else pls help me???
Answer:
30 cm
Step-by-step explanation:
X₁
From a 24-cm by 24-cm piece of cardboard, square
corners are cut out so that the sides can be folded up
to make a box. Complete parts a through c below.
a) Express the volume of the box as a function of the side x, in centimeters, of a cut-out square.
Answer:
V(x) = 4x³ - 96x² + 576xStep-by-step explanation:
Cut out square on each corner has side of x.
When folded up the height of the box becomes same as the side of the cut-out square.
Sides of the base of the box are:
24 - 2x cm as it is folded on both sides.The volume of the box which is the right square prism is:
V = Bh = a²h, where B- base area, a- side of the base, h- height.Substitute the values and find the volume:
V(x) = (24 - 2x)(24 - 2x)x = 4x³ - 96x² + 576xHELP ASAP!!! PLEASE SHOW WORK
A sports equipment manufacturer makes volleyballs for indoor and outdoor play, which bring in $8 and $5 in profit, respectively. Indoor volleyballs take 20 minutes to manufacture while outdoor balls take 10 minutes to manufacture. There are up to 4800 minutes of labor available for the manufacturing process and enough supplies for up to 120 indoor volleyballs and 400 outdoor volleyballs. How many of each type of volleyball should be manufactured to maximize profit?
A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.99mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.31mm. Would this outcome warrant a refund (meaning that it would be unusual)?
The probability that a randomly selected tire will have a depth less than 0.31mm is 0.03.
How to calculate the probability?From the information, the tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.99mm and a standard deviation of 0.35mm.
The probability that a randomly selected tire will have a depth less than 0.31mm will be:
P(X < 0.31) = P[(Z < (0.31 - 0.99)/0.35]
= P(Z < -1.943)
= 0.025
= 0.03
The probability that a randomly selected tire will have a depth less than 0.31mm is 0.03.
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a coffee company wants a new flavor of Cajun coffee. how many pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound?
24 pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound.
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Given situation:
A coffee $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound
Now, Let x be the amount of coffee which is $10 per pound
So,
10x + 3(30) = 5(x+30)
10x + 30 = 5x+150
5x + 30 = 150
5x = 120
x = 24 pounds
Hence, 24 pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound.
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a^2 = 225/64
what does a equal
Answer: a=15/8
Step-by-step explanation:
a^2 = 225/64
a=[tex]\frac{\sqrt{225}}{\sqrt{64}}[/tex]
a=15/8
Answer:
1.875 or 15/8
Step-by-step explanation:
a= square root of 224/64
=sqrt(225)/sqrt(64)
=15/8
You invested $6000 between two accounts paying 2% and 8% annual interest, respectively. If the total interest earned for the year was $360, how much was invested at each rate?
Based on the amount invested into the two accounts and their interest rates, the amount invested at each rate is:
8% - $4,0002% - $2,000How to find the amount invested at each rate?Assuming the amount invested at 2% is x, then the formula for this amount would be:
0.02x + 0.08 (6,000 - x ) = 360
Solving for x gives:
0.02x + 0.08 (6,000 - x ) = 360
2x + 48,000 - 8x = 36,000
6x = 12,000
x = 12,000 / 6
x = $2,000
The amount invested at 8% is:
= 6,000 - 2,000
= $4,000
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How to write three hundred eight and sixty thousandths in decimal number
Given numbers in the form of the decimal number are:
0.3080.060What are decimal numbers?The decimal numeral system is the most widely used system for representing both integer and non-integer numbers. It is the Hindu-Arabic numeral system's extension to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. Decimal refers to the base-10 number system, which is probably the most widely used number system. There are ten single-digit numbers in the decimal number system: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number following 9 is 10. The number following 19 is 20, and so on.Decimal numbers:
Three hundred eight thousandths ⇒ 308/1000 ⇒ 0.308Sixty thousandths ⇒ 60/1000 ⇒ 0.060Therefore, given numbers in the decimal numbers form are:
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Help meee
this question
Answer:
1/6
Step-by-step explanation:
I dunno, I put this into a calculator and that's the answer it gave me.
A boy needs to grill 13 pounds of meat for a cookout . Determine the maximum cost per pound that he can afford , if he wants to spend at most $ 80 on this meat purchase ?
Answer:$6.15
Step-by-step explanation: 80 dollars divided by 13 pounds will give us a answer and we need to round down 80/13=6.15
I will mark brainliest!!
Answer choices are:
A. a 180 degrees clockwise rotation about the origin
B. a dilation with a scale factor of 6
C. a 90 degrees clockwise rotation about the origin
D. a reflection over the line x=6
Answer:
D
Step-by-step explanation:
My mom is a teacher lol
witch if the following numbers is best represented by the point N?
Answer:
C. 6.39
its right behind 6.4, therefore it's 6.39.
A parallelogram has one angle that measures 18°. What are the measures of the other three angles in the parallelogram? °, °, and °
The angels of parallelogram is 162, 18, 162 and 18.
How to find the measures of the other three angles in the parallelogram?given that A parallelogram has one angle that measures 18° means one angle is 18°
we know that
A special variety of quadrilateral called a parallelogram has two sets of opposite sides that are parallel and equal.
The sum of all the angels of parallelogram is equal to 360°
so, the other means second angle of parallelogram is 18°
Let us assume the 3rd be x.
then the 4th also be x, because the opposite sides are equal.
now sum of all angles is 360°
then x + 18 + x + 18 = 360
2x + 36 = 360
2x = 360 - 36
x = 162.
so the 3rd and 4th angles are 162°.
Hence the angels of parallelogram is 162, 18, 162 and 18.
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can anyone help me with this also, thank you sooo sooo much to whoever helps me :)
Given the piece-wise function, the output value of f(7) is 42.
What is the output value of f(7) in the given piece-wise function?A piece-wise function is simply a function built from pieces of different functions over different intervals
Given the piecewise function in the question;
x² - x, x > 5
f(x) = {2/(x-6), x ≤ 5
f(7) = ?To determine the output value of f(7), determine where 7 falls in the given domains of the pieces of the function.
7 falls in the domain of x > 5
Hence,
f(x) = x² - x
Relace all the occurrence of x with 7 and simplify
f(7) = (7)² - 7
f(7) = 49 - 7
f(7) = 42
Given the piece-wise function, the output value of f(7) is 42.
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Samuel has $80 in his savings account before he makes a deposit of $100. After 2 weeks, he withdraws $100. How did Samuel’s savings account balance change?
There is a no change in the saving account balance because Amount after withdrawing = Amount before deposit the money.
According to the statement
We have to find that the changes in the Samuel’s savings account balance.
So, For this purpose, we know that the
Deposit amount is an amount of money paid into an account.
From the given information:
Samuel has $80 in his savings account before he makes a deposit of $100. After 2 weeks, he withdraws $100.
Then
Amount before deposit the money = $80
Amount deposited = $100
Then
Total amount after deposited = $100+80
Total amount after deposited = $180
Then
Amount After withdrawing = $180 - 100
Amount after withdrawing = $80
Then
We see that the
Amount after withdrawing = Amount before deposit the money
It means there is a no change in the saving account balance.
So, There is a no change in the saving account balance because Amount after withdrawing = Amount before deposit the money.
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Graph the polygon and its image after a dilation centered at C(−2,4) with scale factor k=2/3.
T(7,1), U(4,4), V(1,13), W(−2,4)
The graph of the resulting polygon is shown in the image attached below.
How to dilate a polygon set on Cartesian plane by rigid transformation
In this problem we find a polygon generated by four vertices, whose locations are shown in the picture and whose image must be found by using rigid transformation formulas.
Rigid transformations are transformations such that the form of a geometric loci is conserved, dilations are an example of rigid transformation. The general formula of a dilation is described below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilationP(x, y) - Original pointP'(x, y) - Resulting pointk - Dilation factorIf we know that O(x, y) = (- 2, 4), k = 2 / 3, T(x, y) = (7, 1), U(x, y) = (4, 4), V(x, y) = (1, 13) and W(x, y) = (- 2, 4), then the coordinates of the polygon are now determined:
T'(x, y) = (- 2, 4) + (2 / 3) · [(7, 1) - (- 2, 4)]
T'(x, y) = (- 2, 4) + (2 / 3) · (9, - 3)
T'(x, y) = (- 2, 4) + (6, - 2)
T'(x, y) = (4, 2)
U'(x, y) = (- 2, 4) + (2 / 3) · [(4, 4) - (- 2, 4)]
U'(x, y) = (- 2, 4) + (2 / 3) · (6, 0)
U'(x, y) = (- 2, 4) + (4, 0)
U'(x, y) = (2, 4)
V'(x, y) = (- 2, 4) + (2 / 3) · [(1, 13) - (- 2, 4)]
V'(x, y) = (- 2, 4) + (2 / 3) · (3, 9)
V'(x, y) = (- 2, 4) + (2, 6)
V'(x, y) = (0, 10)
W'(x, y) = (- 2, 4) + (2 / 3) · [(- 2, 4) - (- 2, 4)]
W'(x, y) = (- 2, 4) + (2 / 3) · (0, 0)
W'(x, y) = (- 2, 4) + (0, 0)
W'(x, y) = (- 2, 4)
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What are the coordinates of G after it is translated LEFT 4 UNITS AND UP 3
UNITS?
The coordinates are (-4,3).
Glad to help.
Mark me Brainliest. :)
The shifted point G when translated to left 4 units and up 3 units has coordinate ( -8, 6).
What are the types of translation?Rotation, translation, Reflection, and Dilation are the four types of translation.
Assuming the square boxes of the paper graph are 1 sq unit means each side is 1 unit.
Now by counting we can conclude that before shifting the point has an x coordinate of - 4 units and a y coordinate of 3 units.
∴ The coordinates of the points are (-4, 3).
Now it has been shifted left 4 units and up 3 units, We know going towards left is negative on the x coordinate and going towards up is positive on the y coordinate.
So, points after the translation is (-4 -4, 3+3) = (-8,6)
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Suppose the midpoint of line RT is M=(3,0). If R has the coordinates (-1,-4), what are the coordinates of T?
The coordinates of Point T are (7,4)
The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
The [tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
where,
([tex]x_m, y_m[/tex]) = coordinates of the midpoint
([tex]x_1, y_1[/tex]) = coordinates of the first point
([tex]x_2, y_2[/tex]) = coordinates of the second point
So, given that we have a line RT and M is the midpoint of the line RT means M divides the line in two equal segments.
Let coordinates of M be ([tex]x_m, y_m[/tex]) and coordinates of point R be ([tex]x_1, y_1[/tex]) and coordinates of point T be ([tex]x_2, y_2[/tex]).
So,
[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
[tex](3, 0) = (\frac{-1+x_2}{2}, \frac{-4+y_2}{2})[/tex]
on compairing both sides
[tex]3 = \frac{-1 + x_2}{2} \\x_2 - 1 = 6 \\ x_2 = 7[/tex]
Similarly,
[tex]0 = \frac{-4 + y_2}{2} \\y_2 - 4 = 0 \\ y_2 = 4[/tex]
So, the line RT having midpoint M has coordinates of R is (-1,-4) and
T is = (7,4).
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The coordinates of Point T are (7,4)
The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
The [tex](x_m,y_m)=(\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2})\\[/tex]
where,
([tex]x_m,y_m[/tex]) = coordinates of the midpoint
([tex]x_1,y_1[/tex]) = coordinates of the first point
([tex]x_2,y_2[/tex]) = coordinates of the second point
So, given that we have a line RT and M is the midpoint of the line RT means M divides the line in two equal segments.
Let coordinates of M be ([tex]x_m,y_m[/tex]) and coordinates of point R be () and coordinates of point T be ([tex]x_2,y_2[/tex]).
[tex](x_m,y_m)=(\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2})\\[/tex]
[tex](3,0)=(\frac{(-1+x_2)}{2},\frac{(-4+y_2)}{2})\\[/tex]
So, on compairing both sides
[tex]3=\frac{(-4+y_2)}{2}[/tex]
[tex]x_2-1=6\\x_2=7[/tex]
Similarly,
[tex]0=\frac{-4+y_2}{2}\\ y_2-4=0\\\\y_2=4[/tex]
So, the line RT having midpoint M has coordinates of R is (-1,-4) and coordinates of T is = (7,4).
Learn more about the midpoint here brainly.com/question/28224145
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