Answer:
L = 4D + 53
After 36 days of work, the road will be 197 miles long.
Step-by-step explanation:
This question requests that an equation is found to represent the relationship between the length of a road and the days that the workers spend working on the road.
We are given that the road is 53 miles long prior to the work done by the construction crew. This means that this will be added in addition to what we will find.
L represents the length of the road after D days. Since the road is lengthened by 4 miles each day, this could be represented by 4 * D, or simply 4D.
Therefore, the equation we find can be written as L = 4D + 53.
Since we need to find how many miles the road will be after 36 days of work, substitute 36 days as D and solve for L:
L = 4(36) + 53
L = 144 + 53
L = 197
Therefore, the road will be 197 miles long after 36 days of construction.
The customers at the bank would like to withdraw money from the automated teller machine. Help them enter their personal ID numbers by completing the numeric patterns. 2, 13, 24, 35,
To withdraw money from the automated teller machine the numeric pattern required to complete the personal ID numbers is 2, 13, 24, 35,46,57,68.
As given in the question,
Using automated teller machine customers at the bank withdraw money
Numeric pattern given for the personal ID numbers is
2, 13, 24, 35
First term 'a'= 2
Common difference between consecutive terms are same
'd'=13 -2
=11
It is an arithmetic progression series
nth term = a+ (n-1)d
5th term = 2 +(5-1)11
=46
6th term =2+(6 -1)11
=57
7th term= 2+ (7-1)11
= 68
Therefore, to withdraw money from the automated teller machine the numeric pattern required to complete the personal ID numbers is 2, 13, 24, 35,46,57,68.
The complete question is:
The customers at the bank would like to withdraw money from the automated teller machine. Help them enter their personal ID numbers by completing the numeric patterns. 2, 13, 24, 35, ___, ___, ____.
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Kristen goes on a cave tour with her family. They climb down to 8 meters below ground level.
Then they climb the opposite of –8 meters to return to ground level.
How many meters did they climb in all? Enter your answer in the box.
meters
The total distance climbed by Kristen and her family is 16 meters.
It is given in the question that Kirsten and family climb down to 8 meters below ground level. Then they climb the opposite of 8 meters to return to ground level.
We have to find the total distance climbed by Kristen and her family.
We know that,
Total distance climbed by Kristen and her family = Distance climbed down the cave + distance climbed up the cave to reach ground level
Hence, we can write that,
Total distance climbed by Kristen and her family = 8+8 = 16 meters.
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What are the roots of the roots of the function f(x)=x^2+2x-1
The roots of the function f(x) = [tex]x^2+2x-1[/tex] are
x = [tex]-1+\sqrt{2}[/tex]
x = [tex]-1-\sqrt{2}[/tex]
The function is given f(x)= [tex]x^2+2x-1[/tex]
The roots of given function will be at f(x) = 0
Substitute the value in the equation
[tex]x^2+2x-1[/tex] =0
Here to find the roots of the function, we have to use the quadratic formula in the given function
Roots of the function = [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
From the given function the values of
a = 1
b = 2
c = -1
Substitute the values in the quadratic formula and find the roots of the function
= [tex]\frac{-2+/-\sqrt{2^2-4(1)(-1)} }{2(1)}[/tex]
= [tex]\frac{-2+/-\sqrt{4+4} }{2}[/tex]
= [tex]\frac{-2+/-2\sqrt{2} }{2}[/tex]
The roots of the given functions are
x = [tex]-1+\sqrt{2}[/tex]
x = [tex]-1-\sqrt{2}[/tex]
Hence, the roots of the function f(x) = [tex]x^2+2x-1[/tex] are
x = [tex]-1+\sqrt{2}[/tex]
x = [tex]-1-\sqrt{2}[/tex]
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Find the value of x.
(3x + 3) (5x + 1)
Please help me:)
Answer:
x=22
Step-by-step explanation:
Since a straight line is equal to 180 degrees,
(3x+3)+(5x+1) = 180
(3x+3)+(5x+1)-180=0
8x+4-180=0
8x-176=0
8x=176
x=176/8
x=22
Which also means that the first angle is (3(22)+3)=69 degrees
the second angle is (5(22)+1) = 111 degrees
111 + 69 = 180
What is the special angle pair relationship between the two
Answer: Alternate exterior angles
Step-by-step explanation:
please help me quickly
Answer:
80 degrees
Step-by-step explanation:
Find the X and Y values.
The answer should be written as a coordinate point (x,y)
(reward 70 points)
Answer:
(x,y)=(10,11)
Step-by-step explanation:
Drew actually has almost finished the equation. So I'm starting with the left part
[tex]2.5x+ 6= 31[/tex]
Cancel out 6 from both sides and divide both sides 2.5 which leaves us with
[tex]x=\boxed{10}[/tex]
Plug in the value of x into the second equation and simplify
y=-2.10+ 31
[tex]y=\boxed{ 11}[/tex]
I need help pleaseeee
Answer: 60 inches in 5 feet
Step-by-step explanation:
5X12=60
A rectangular sandbox has a width represented by the polynomial (x-1) and a length represented by (6x-5). What is the total area of the sandbox?
The total area of the sandbox is given by 6x^2-11x+5
Width of the sandbox = (x-1)
Length of the sandbox = (6x-5)
Rectangle area in geometry refers to the area that a rectangle occupies on a two-dimensional plane. A quadrilateral, a form of a two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another.
The formula for the area of a rectangle:
Area of rectangle = Length*Width
Substituting the value in the formula we get:
Area of rectangle = (x-1)*(6x-5)
= 6x^2-5x-6x+5
= 6x^2-11x+5
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Find two integers whose sum is -7 and whose product is 12.
Answer: -3 and -4
Step-by-step explanation:
The sum of -3 + -4 = -7
The product of -3 x -4 = 12 (a negative times a negative equals a positive)
PLEASE HELP ASAP
State whether the point is on the x-axis or the y-axis. If the point is not on an axis, state which quadrant it is in.
(10,–7)
Choose the correct answer from the drop-down menu.
Point (10,–7) is
in:
On the x axis
On the y axis
Quadrant l
Quadrant ll
Quadrant lll
Quadrant lV
The given coordinate pair, (10, -7) is not on the x–axis or the y–axis, but it is in Quadrant IV
What is a coordinate pair?
A coordinate pair specifies a point on the coordinate plane.
The coordinates of points on the x–axis have a y–coordinate of 0
Therefore, the coordinates of a point that is on the x–axis can be expressed as (x, 0)
Points that are on the y–axis have a x–coordinate of 0, which gives the coordinates of the points located on the y–axis as (0, y)
The coordinates of the given point is (10, -7), therefore, the point is neither on the x or y–axis, but in one of the four quadrants.
The coordinate of points in the first quadrant can be represented generally as (x, y)
Points in the second quadrant have the general form of (-x, y)
The points in the third quadrant can be expressed generally in the form (-x, -y)
The coordinates of points on the fourth quadrant are of the form, (x, -y)
The given point is (10, -7), therefore it is in the fourth quadrant or Quadrant IV
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What is the area, in coordinate units, of the triangle in the figure below
The area of the triangle in the image is 10 square units, thus, option C is the correct one.
What is the area of the triangle?
For a triangle of height H and a base B, the area is given by:
A = H*B/2.
In the image we can see that the base of the triangle goes from (0, 0) to (5, 0), then the length of the base is 5 units.
While the height goes from (0, 0) to (0, 4), so the height is 4 units.
Then the area will be:
A = (4 units)*(5 units)/2 = (20 square units)/2 = 10 square units.
The area is 10 square units.
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Function g is a transformation of function f.
-6 -5
4
g(x) =
لا
-2 -1
-1
f(x)
-2
-3
What is the equation of function g?
-5
-6
2
For f(x) = 2x + 3 and g(x) = -x^2 + 1, The composite function defined by (f o g)(x) is equal to (f o g)(x) = - 2 x^2 + 5
As per the question statement, We are given f(x) = 2x + 3 and g(x)=x^2+1
and we are supposed to find the composite function defined by (f o g)(x)
(f o g)(x) = f(g(x))
(f o g)(x) = 2 (g(x)) + 3
(f o g)(x) = 2( -x^2 + 1 ) + 3
(f o g)(x) = - 2 x^2 + 5
Hence, For f(x) = 2x + 3 and g(x) = -x^2 + 1, The composite function defined by (f o g)(x) is equal to (f o g)(x) = - 2 x^2 + 5
Composite Function: A function that is composed of further functions, each of which serves as the input to the next.To learn more about composite functions, click on the link given below:
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The lowest point in Denmark is 7
meters below sea level. The highest point is 173 meters above sea level. What is the range of elevations in
Denmark?
The range of elevations is 166 meters.
What is range?
Find the biggest observed value of a variable (the maximum) and subtract the smallest observed value to determine the range (the minimum). The data points between the distribution's two extremes are not taken into account by the range; just these two values are.
So as mentioned above, given to us are the lowest and highest values
So as the lowest value is 7 meters and the highest value is 173 .
Thus range is equal to 173-7
which is equal to 166.
Thus range is 166 meters.
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How can this expression be written another way?
105 + 35m
Factor using the distributive property and the greatest common factor to write an equivalent expression.
Enter your answer by filling in the boxes.
An equivalent expression to given expression is 35(3 + m)
In this question, we have been given an expression 105 + 35m
We need to write an equivalent expression of given expression.
To find an equivalent expression we factorize given expression using the distributive property and the greatest common factor.
A common number for 35 and 105 is 35.
105 = 35 × 3
So, we can write given expression as,
105 + 35m
= (35 × 3) + 35m
= 35(3 + m)
Therefore, an equivalent expression to given expression is 35(3 + m)
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Which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year? f(n 1) = f(n) 5 f(n 1) = 5f(n) f(n 1) = 1.05f(n) f(n 1) = 0.05f(n)
Answer: y = f (n 1)
Step-by-step explanation:
If we count interest rate = 5%
then if he earned 'y' amount in 1st year then in 2nd year he must earned
= y + 5% of y
== 1.05 y
here, y = f(n 1)
x =7, -2, 0, 7
y= 10,0,10,3
Is this a function?
Answer: No, this is not a function.
Functions exist when there are a unique set of x-values and each can match with a y-value. There cannot be a repeating x-value because this creates a discontinuity in the graph. You can have as many repeating y-values as you’d like as long as they each have a unique x-value and are not duplicate plot points.
Since x = 7 repeats in the domain of x-values, this cannot be a function.
Someone explain this to me please
Answer:
0.31
Step-by-step explanation:
√13.7/3.05^2 + 2.6
= 3.7/ 9.3 + 2.6
= 3.7/ 11.9
= 0.31
There are 24 total customers seated at 4 tables in a restaurant Each table has the same number of customers. At that rate, what is the maximum number of costumers who could sit at 6 tables
Answer:
36
Step-by-step explanation:
24 customers dividend into 4 tables
so 24/4 = 6
then 6 customers can sit in 1 table
in case of 6 tables 6×6 =36
36 customers would sit in 6 tables
Vicky makes 8 purses and 9 key rings to sell for charity.
The price of a purse will be twice as much as the price of a key ring.
Vicky wants to get a total of exactly £40 when she sells all the purses and all the key rings.
Work out the price Vicky needs to charge for each purse and for each key ring
Price of key ring = £1.6
Price of purse = £3.2
What is unitary method?The unitary approach is a strategy for problem-solving that involves first identifying the value of a single unit, then multiplying that value to figure out the required value.
Given Data
Vicky makes 8 purses and 9 key rings to sell for charity.
Vicky wants to get a total of exactly £40
Suppose the price of key ring be v
and the price of purses be 2v
£40 = £8(2v) + £9(v)
40 = 16v + 9v
40 = 25v
v = [tex]\frac{40}{25}[/tex]
v = 1.6
Price of key ring = £1.6
Price of purse = £3.2
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HELP QUICK!
A coordinate plane is shown below. Circle the letter of each true statement.
A. The y-coordinate for point A is 3.
B. Point D has the same x-coordinate as
point E.
C. The x-coordinate for point F is 7.
D. The ordered pair for point G is (8, 6).
E. Point H names the ordered pair (10, 9).
F. Point B is 8 units away from the origin.
G. Point C is 1 unit left and 2 units up from
point D.
In the coordinate plane shown we can say that the y-coordinate of point A is 3.
Let us now take the statement one by one and try to find out if they are true or false.
A. True. The y-coordinate for A is 3
B. False. Point D has x-coordinate of 5 and E has 6
C. True The x-coordinate for F is 7
D. True The ordered pair for point G is (8,6)
E. False. Point H names the ordered pair (9,10).
F. false point B is √34 units away from origin
G. True.
The coordinate plane is a two-dimensional surface created by combining two number lines. A single horizontal number line makes up the x-axis. The name of the vertical number line, which is the other number line, is the y-axis. The intersection of the two axes is the origin. The graphing of points, lines, and other objects can be done using the coordinate plane.
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Complete the following table of ordered pairs that are solutions of the equation
a. The complete table for the ordered pairs that are solutions to y = x³ - 4 is
x y
-1 -5
0 -4
1 -3
2 4
b. The graph of the equation is shown below
Determining Ordered pairsFrom the question, we are to complete the given table of ordered pairs that are solutions to the given equation.
The given equation is
y = x³ - 4
Now, we will determine the values of y for the given values of x
When x = -1
y = x³ - 4
y = (-1)³ - 4
y = -1 - 4
y = -5
(-1, -5)
When x = 0
y = x³ - 4
y = (0)³ - 4
y = 0 - 4
y = -4
(0, -4)
When x = 1
y = x³ - 4
y = (1)³ - 4
y = 1 - 4
y = -3
(1, -3)
When x = 2
y = x³ - 4
y = (2)³ - 4
y = 8 - 4
y = 4
(2, 4)
Thus,
The table is
x y
-1 -5
0 -4
1 -3
2 4
The graph is shown below
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Write the equation of line perpendicular to y = 4 that passes through (5, 2)
one may note that y = 4 is a horizontal line, and a line perpendicular to a horizontal line will be a vertical one, Check the picture below.
Please help me with this maths question thanks!
Answer:
x = 2
Step-by-step explanation:
x + 3 + 1/2 x + 3 +x + 1 = 12 Combine like terms
21/2 x + 7 = 12 Subtract 7 from both sides of the equation
2 1/2 x = 5
Another name for 2 1/2 is [tex]\frac{5}{2}[/tex] ([tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex])
[tex]\frac{5}{2}[/tex] x = 5 Multiply both sides of the equation by [tex]\frac{2}{5}[/tex]
[tex](\frac{2}{5})[/tex][tex](\frac{5}{2})[/tex]x = [tex]\frac{2}{5}[/tex][tex](\frac{5}{1})[/tex]
x = 2
Marisol's annual salary as an engineer is $75,000. After receiving a
promotion, her new annual salary is $80,000. What percent increase in her
salary resulted from her promotion?
The percent increase in her salary resulted from her promotion is 6.67%.
The annual salary of Marisol as an engineer = $75000.
After, the promotion salary of Marisol as an engineer = $80000.
We have to find the increment in her salary after promotion in percentage.
Before finding the increment in percentage we find the total increment in dollar in her salary after promotion.
Total increment in dollar = Salary after Promotion − Salary before Promotion
Total increment in dollar = $80,000 − $75,000
Total increment in dollar = $5000
As we know that we can find the percentage by multiplying the required number by 100 because percentage is the ratio with 100.
So, the increment in salary after promotion in percentage.
% increment = (Total increment/Salary before) * 100
% increment [tex]= (\frac{5000}{75000})*100[/tex]
% increment = 0.0667 * 100
% increment = 6.67%
Now we see that percent increase in her salary resulted from her promotion is 6.67%.
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Find the distance from a point (4, 6) to the line y = 2x - 5.
Answer:
1.34 units.
Step-by-step explanation:
The line y = 2x - 5 has a slope of 2 so the line passing through the given point will be perpendicular to y= 2x - 5 and will have a slope of -1/2.
Let this line be y = -1/2x + c.
Its passes through (4, 6) so:
6 = -1/2*4 + c
6 = -2 + c
c = 6 + 2 = 8
So, equation of this line is y = -1/2x + 8.
Now we find the point where the 2 lines intersect:
y = 2x - 5
y = -1/2x + 8
2x - 5 = -1/2x + 8
2x + 1/2 x = 5 + 8
(5/2)x = 13
x = 26/5
= 5.2.
and y = 2(5.2) - 5
= 5.4.
So, the point of intersection is (5.2, 5.4)
and the distance between the point (4,6) and the line y = 2x - 5
= √((6 - 5.4)^2 + (4-5.2)^2)
= √(0.36 + 1.44)
= √1.8
= 1.34
There is a formula you can use directly to solve this.
f(x) = 2x² + 3x - 6
g(x) = -4x + 10
Find: g(f(x))
Kevin is making potato casserole for a dinner party. He needs 2½ pounds of potatoes per guest. How many pounds of potatoes will he need for 6 guests? O 15 pounds 6.5 pounds O 25 pounds O 12.5 pounds - Previous
Answer:
15 pounds
Step-by-step explanation:
Kevin is making potato casserole for a dinner party. He needs 2½ pounds of potatoes per guest. How many pounds of potatoes will he need for 6 guests?
15 pounds
6.5 pounds
25 pounds
12.5 pounds
2.5lb × 6 guest = 15 pounds
Answer: 15 pounds of potatoes.
Step-by-step explanation:
Kevin will perform basic multiplication to find how many potatoes he needs for all of the guests. Since each person requires 2 1/2 pound of potatoes and there are a total of 6 guests, multiplying these two values will find the pounds of potatoes that are needed for all of the guests.
2 1/2 * 6 = 15 pounds of potatoes
Therefore, Kevin needs 15 pounds of potatoes to make potato casserole for everyone at the dinner party.
Solve the given right triangle for its missing angle and side measures.
An Image of a Right triangle FED With E being the right angle and FE being the base with 12units. The acute angle is F at 35degree.
Note: Figure not drawn to scale
A.
m∠D = 35°, DE ≈ 8.40 units, DF ≈ 13.65 units
B.
m∠D = 35°, DE ≈ 8.40 units, DF ≈ 14.65 units
C.
m∠D = 55°, DE ≈ 4.40 units, DF ≈ 13.65 units
D.
m∠D = 55°, DE ≈ 8.40 units, DF ≈ 14.65 units
Answer:
D
Step-by-step explanation:
the sum of the 3 angles in Δ DEF = 180° , that is
∠ D + 90° + 35° = 180°
∠ D + 125° = 180° ( subtract 125° from both sides )
∠ D = 55°
------------------------
using the tangent and cosine ratios in the right triangle
tan35° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{DE}{EF}[/tex] = [tex]\frac{DE}{12}[/tex] ( multiply both sides by 12 )
12 × tan35° = DE , then
DE ≈ 8.40 ( to 2 dec. places )
--------------------------
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{EF}{DF}[/tex] = [tex]\frac{12}{DF}[/tex] ( multiply both sides by DF )
DF × cos35° = 12 ( divide both sides by cos35° )
DF = [tex]\frac{12}{cos35}[/tex] ≈ 14.65 ( to 2 dec. places )
Kadeem and Quinn both drive 25 miles. Kadeem drives at a constant speed of 50 miles an hour. Quinn drives at a constant speed of 75 miles per hour. Who takes longer to drive 25 miles? How much longer?
Answer:
Kareem takes longer to drive the 25 miles. Kadeen takes 10 minutes longer than Quinn.
Step-by-step explanation:
The formula for time is distance over speed (distance/speed)
Kadeem
distance/speed = 25/50 = 1/2 hour = 30 minutes
Quinn
distance/speed = 25/75 = 1/3 hour = 20 minutes