If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1, then the x=8 and AC=15 units.
Given,
That A is between B and C.
AB= x+2
BC= 4x-7
AC= 2x-1
Then,
BC = AB+AC
4x-7= x+2+2x-1
4x-7= 3x+1
4x-3x=1+7
x=8
Then the length of the line AC is
AC= 2x-1
AC= 2×8-1 =15 units
Hence, If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1, then the x= 8 and AC= 15 units
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A cafeteria is 6 squared ft wide and 7 squared ft long apply the laws of exponents to write two equivalent expressions for the area of the cafeteria
The two equivalent expressions for the area of the cafeteria are:
a. x = 6² + 7² feet
b. 36 + 49 = x feet.
Given the length of the cafeteria is 7² ft and
the width of the cafeteria is 6² ft.
Area = length × width
let the area be 'x'.
x = 6² × 7²
According to the law of exponents.
x = 36 × 49
x = 1764 ft
hence we get the area as 1764 ft of the cafeteria.
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How many negative real zeros are possible for a polynomial function f, given that f(−x) has 9 variations in sign? (Select all that apply.)
*1
*2
*3
*4
*5
*6
*7
*8
*9
The possible number of negative real zeros in the polynomial function is 9
What are the zeros of a polynomial function?The zeros of a polynomial function are the x-intercepts of the function i.e. the points where the graph of the polynomial function cross the x-axis
How to determine the number of negative real zeros?The given parameters are
The polynomial function, f(x)
f(−x) has 9 variations in sign
The number of variation in sign represents the possible number of negative real zeros
Recall that
The x-intercept (or the zeros) of the function is the point or points where the graph of the function crosses the x-axis i.e. the point where the function equals 0
This means that
Number of negative real zeros = variation in sign
So, we have
number of negative real zeros = 9
Hence, the possible number of negative real zeros in the polynomial function is 9
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3 feet
15 feet
21 feet
31.5 feet
C
12 ft
9 ft
3
hich are the dimensions of a
A
B
5. W
ri
What is the value of a in this function’s equation?
A.
-1
B.
1
C.
-2
D.
2
Answer:
Because the graph has the parabol shape, so the equation of it has the function:
y = ax² + bx + c
Because the parabol has a peak at point (0; 9)
=> 9 = a.0² + b.0 + c
=> c = 9
=> The parabol has a function:
y = ax² + bx + 9
Because the parabol goes through point (3; 0)
=> 0 = a.3² + b.3 + 9
=> 9a + 3b = - 9 (1)
Because the parabol goes through point (-3; 0)
=> 0 = a.(- 3)² + b.(- 3) + 9
=> 9a - 3b = - 9 (2)
Plus (1) and (2):
=> 18.a = - 18
=> a = - 1
Substitute the result on (1)
=> b = 0
=> The function of the parabol: y = - x² + 9
=> a = - 1
=> Choose A. - 1
Abigail redecorates her house. A scale drawing of her house can be seen below. if each 6 cm on the scale drawing equals 12 ft, what are the actual dimensions of Abigail's house?
The actual dimensions of Abigail's house are 20ft, 14ft, 18ft, 16ft, 18ft.
For 6 cm in drawing his house is 12 ft on scale which is twice the drawing
This means the scale factor is 2
Therefore,
10cm = 2 × 10 = 20ft
7cm = 2 × 7 = 14ft
9cm = 2 × 9 = 18ft
8cm = 2 × 8 = 16ft
9cm = 2 × 9 = 18ft
What is scale factor?The scale factor is the quantity that is multiplied by an object's scale to produce a separate object that has the same appearance but is a different size—either scaled up or scaled down.
To increase an object by a scale factor, measure all of its sides and multiply the result by the scale factor.
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How many unique trapezoids can be drawn with base angles that each measure 60° and sides that measure 4 cm, 4 cm, 8 cm, and 12 cm?
The number of unique trapezoids that can be drawn with base angles and side measures is 1
How to determine the number of unique trapezoids?The given parameters are
Base angle = 60 degrees
Side lengths = 4 cm, 4 cm, 8 cm, and 12 cm
From the question, we understand that the given angle is the base angle
Since the base angles are equal, then the trapezoids is an isosceles trapezoid
This also means that the nonparallel sides are equal i.e. 4cm each
While the parallel sides are not i.e. 8cm and 12 cm
Hence, the number of unique trapezoids that can be drawn with base angles and side measures is 1
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Which are the first five terms of a geometric sequence in which the second term is 6 and the fourth
term is 54?
3, 6, 27, 54, 108
3, 6, 54, 486, 4,374
-18, 6, 30, 54, 78
2, 6, 18, 54, 162
The first five terms of a geometric sequence in which the second term is 6 and fourth term is 54 are 2, 6, 18, 54, 162. Thus, the correct option is option D.
A Geometric progression may be defined as a series of terms in which the ratio between each succeeding term and the preceding term of the series is constant.
It is given that the second term of the series is 6 and the fourth term is 54.
The first five terms of geometric sequence are given by a, ar, ar², ar³ and ar⁴.
Thus, ar = 6 ......(1)
ar³ = 54 ......(2)
Divide equation (2) by (1)
ar³/ar = 54/6
r² = 9
=> r = 3
Putting value of r in equation (1)
ar = 6
=> a×3 = 6
=>a = 2
Now, substituting the values of a and r the terms of Geometric progression are given by:
a = 2, ar = 6, ar² = 18, ar³ = 54 and ar⁴ = 162.
Thus, the first five terms of Geometric sequence are given by 2, 6, 18, 54, 162.
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Mitchell spent 12 hours at the doctor's office and a total of 1 hours driving
to and from the appointment. Which expression shows the total number of
hours Mitchell spent away from home for his visit to the doctor?
Answer:
12+1=x x=13
Step-by-step explanation:
12 is the hours at the doctor's office.1 is the hour driving. and x is the total time
What is the slope of the line represented by this equation?
-3X+ 8y = 12
The slope of the equation - 3 x+ 8 y = 12 is 0.375.
We are given an equation of the line:
- 3 x+ 8 y = 12
We need to find the slope of the equation.
x intercept:
- 3 x = 12
x = -4
Point 1 = ( - 4 , 0 )
y intercept:
8 y = 12
y = 1.5
Point 2 = ( 0 , 1.5 )
Slope = (y₂ - y₁) / (x₂ - x₁)
Substituting the values, we get that:
m = ( 1.5 - 0 ) / ( 0 - [-4])
m = 1.5 / 4
m = 0.375
Therefore, we get that, the slope of the equation - 3 x+ 8 y = 12 is 0.375.
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alana drew a scale drawing of an apartment. the broom closet, which is 6 feet wide in real life, is 3 inches wide in the drawing. what is the scale of the drawing?
The scale factor of Alana's drawing is 3: 72.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
The scale factor is done due to the unpractical measurement of any figure.
Dimension in real = 6 feet
Since,
1 feet = 12 inches
6 feet = 72 inches
Dimension in drawing = 3 inches.
Scale factor = Dimension in drawing / Dimension in real
Scale factor = 3/72
Hence "The scale factor of Alana's drawing is 3: 72".
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Important Please Help!!!!!!
If mary wants to bake muffins .she she has 3kg of flour. if a tray of 6 muffins 200g of of flour how many trays will she bake
Mary will bake 15 trays.
Firstly converting the amount of flour into grams that Mary has.
As per the known facts 1 kilogram = 1000 grams.
So, amount of flour in grams = 3 × 1000
Performing multiplication to calculate amount of flour
Amount of flour in grams = 3000 grams.
Now, 200 grams flour is required by number of trays = 1
So, 3000 grams flour will be required by number of trays = (1÷200)×3000
Performing multiplication and division to find the number of trays that can be baked
Number of trays = 15
Hence, Mary can bake 15 trays of muffins with 3 kilograms of flour.
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simplify the expression the square root of 3/15x
A handyman company serves customers from two cities 60 miles apart, Jonesville and Bellevue. The company would like to position a new of
between the two cities using weighted averages based on the typical number of calls received from each city. If Jonesville has a weight of 3 a
Bellevue has a weight of 5, how far from Bellevue should the office be located?
miles
Using the weighted mean, it is found that the office should be located 13.85 miles from Bellevue.
What is the weighted mean?The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
For this problem, the observations are given as follows:
Bellevue, at position 0, with a weight of 5.Jonesville, at position 60, with a weight of 3.These observations are the positions of the cities, considering that they are 60 miles apart, and their weights as given in the problem.
The weighted mean between these positions is found as follows:
M = (0 x 5 + 60 x 3)/(5 + 8) = 13.85.
The meaning of the weighted mean is that:
The office should be located 13.85 miles from Bellevue.
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A horses mane grows 1. 5 inches in 1 month. Lauras hair grows 0. 25 inch in 1 week
determine in the situation represents a proportional relationship
1:5:1 or 3:2 is the proportional relationship.
What is the proportional relationship?In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant. Two sequences are inversely proportional if corresponding elements have a constant product, also called the coefficient of proportionality.
Given Data
If considering that a month has 4 weeks approx, then Laura's hair grows( 0.25 inches×4)= 1 inch in a month.
Whereas the horse's mane grows 1.5 inches in a month.
Thus the proportional relation or ratio between growth of Horse's mane and Laura's hair for the same amount of time period is 1.5:1 or 3:2
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A lab technician is dividing a cell that has a diameter of 4.32×10−4 millimeters. Each of the new cells has a diameter measuring exactly one half of the diameter of the original cell. Which is the diameter of a new cell?
Answer:
I'm assuming that the number is supposed to be 4.32x10‾⁴, so if the new cell has half the diameter, then it's diameter would be 2.16x10‾⁴
Who knows what a black widow spider can do
Bristol's credit card has a 30.99% APR, a minimum monthly payment of 3.5%, and a current statement balance of $4,186.19. She spends $750.00 in purchases and makes the current minimum monthly payment of $146.52. What will be Bristol's next minimum monthly payment?
a)$123.69
b)$145.50
c)$167.64
d)$171.97
Bristol's next minimum monthly payment is $171.97
How was the minimum monthly payment of $146.52 computed?
The minimum monthly payment of $146.52 was computed from the current statement balance as 3.5% of $4,186.19
minimum monthly payment=$4,186.19*3.5%
minimum monthly payment=$146.52
The balance at the beginning next month is current statement balance minus the minimum monthly payment plus purchases of $750.00 and the interest for the month
beginning balance next month before interest=($4,186.19-$146.52)+ $750.00
beginning balance next month before interest=$4,789.67
beginning balance next month after interest=$4,789.67*(1+30.99%/12)
beginning balance next month after interest=$4,913.36
Bristol's next minimum monthly payment=3.5%*$4,913.36
Bristol's next minimum monthly payment=$ 171.97
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6. Seeta thinks a number and subtracts 7/3 from it. She multiplies the result by 6. The result now obtained is 2 less than twice the same number she thought of. What is the number?
Greetings from Brasil...
The number thought will be X, so
6.(X - 7/3) = 2 - 2X
X = 2Can u help me with this math plsss I will mark brainliest
Answer:
there.....................
Answer:
I4, C20, H6, O13, M3, V10, P23, G8, K19, H21, P16
Which is equivalent to √3+√12?
A. √15
B. 3√6
C. 2√3
D. 3√3
E. 5√3
Answer:
d is the correct answer to your question
Answer:
3√3
Step-by-step explanation:
√3 +√12
we can write 12 as 3 X 4
√3 + √(3+4)
√3 + √3 √4
√4 = 2
√3 + 2√3
= 3√3
Which of the following is the number form of thirty-eight and one hundred seven thousandths?
A.38.170
B.38.017
C.38.107
D.38.071
Number Form
C.) 38.107
___________________________________________________
The solution is simple. "Thirty-eight" is just 38, remaining on the left side of the decimal. Meanwhile, "one hundred seven thousandths" is 107, however on the right side of the decimal. Now you know this, put the two parts together and you have your number form; 38.107, aka. Option C.
___________________________________________________
Hope this helps! If so, lmk! Thanks and good luck!
Analia wants to know which school has the higher SAT average relative to resources invested per student
A SAT average divided by number of sports medals won
B SAT average divided by number of students
C SAT average divided Budget per student
D SAT average divided by teachers per student
M(5, 7) is the midpoint of PS The coordinates of S are (6, 9). What are the coordinates of p2
The required coordinate of point p is (4,6) of line segment PS.
Given that
M(5, 7) is the midpoint of PS The coordinates of S are (6, 9).
To determine the coordinates of p.
Here,
Let the coordinate of P be (h, k)
Now, the coordinates of the midpoint is given by,
x = [x₁ + x₂] / 2 ; y = [y₁ + y₂] / 2
now, putting x = 5, x₁ = 6, x₂ = h; y = 7, y₁ = 9 y₂ = k
5 = 6 + h / 2 ; 7 = 9 + k / 2
10 - 6 = h ; 14 - 9 = k
h = 4 ; k = 5
Thus, the required coordinate of point p is (4,6).
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Find the solution to the equation: 42-(3c+4)=2(c+4)+c
Answer:
5
Step-by-step explanation:
42-(3c+4)=2(c+4)+c
42-3c-4=2c+8+c
42-4-3c=3c+8
38-3c=3c+8
38-3c-3c=8
38-6c=8
6c=38-8
6c=30
c=30/6
c=5
How many times larger is (1.092 × 101) than (7 × 10−1)?
0.156
15.6
6.41
6.908
Step-by-step explanation:
1.092*101 is the same as 1.092*100 ( or 109.2)+1.092, which equals 110.292.
7*10 is 70-1 is 69. from here, we can just estimate it since 69*2 is 138. Once you do it, you can find that it is roughly 1.59.
I hope this helped. I didn't know what you meant by the numbers under it.
Answer:
the answer is 15.6
Step-by-step explanation:
The sum of three lengths of a fence ranges from 45 to 60 inches. Two side lengths are 9 and 18 inches. If the length of the third side is x inches, write
and solve a compound inequality to show the possible lengths of the third side.
09≤x≤18
O 18 ≤x≤ 33
036 ≤x≤ 42
045 ≤x≤ 60
If the sum of three lengths of a fence ranges from 45 to 60 inches and two side lengths are 9 and 18 inches, If the length of the third side is x inches, then the compound inequality to show the possible length of the third side is 18≤x≤33
Given,
The range of sum of three lengths = 45 to 60 inches
Length of other two side = 9 and 18 inches
Length of third side = x
Sum of three lengths = 9+18+x
= 27+x
The range of sum of three lengths is 45 to 60
then,
45≤27+x≤60
Subtract 27 from each part
18≤x≤33
Hence, if the sum of three lengths of a fence ranges from 45 to 60 inches and two side lengths are 9 and 18 inches, If the length of the third side is x inches, then the compound inequality to show the possible length of the third side is 18≤x≤33
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Answer:
B
Step-by-step explanation:
This is because 18 is less than or equal to x which is less than or equal to 33. Your welcome
Usa ecuaciones simultáneas para resolver lo siguiente:
2x + 5y = 5
4x = 3y = 3
X =
Y =
The value of x will be equal to 0 and y will be equal to 1.
It is given that there are two equations.
We have to solve both equations to get the value of x and y.
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.
As per the question ;
The two equations are
2x + 5y = 5 --- -- - - - ------ ---- --- --- ---- Equation 1
4x + 3y = 3 --- ----- ------ ----- ----- ----- -- Equation 2
Let's solve these equations to get value of x and y ;
So ;
Multiplying equation 1 , by 2 we get ;
4x + 10y = 10 --- ----- ------ ----- ----- ----- -- Equation 3
Subtract it with equation 2 ;
i.e., Equation 3 - Equation 2
(4x + 10y) - (4x + 3y) = 10 - 3
7y = 7
y = 1
And value of x will be ;
2x + 5 × 1 = 5
2x = 5 - 5
2x = 0
or
x = 0
Thus , the value of x will be equal to 0 and y will be equal to 1.
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Work out the value of each expressions.
a) 5(x³ - x) + 5x² /3 - 12x when x=3
b) 3y+16+ (y/2) -20/y when y=4
a) Simplification of the algebraic expression 5(x³ - x) + 5x²/3 - 12x when x = 3 is; 99
b) Simplification of the algebraic expression 3y + 16 + (y/2) - (20/y) is; 25
How to solve Algebraic Fractions?
a) We are given the algebraic expression;
5(x³ - x) + 5x²/3 - 12x
We want to simplify this when x = 3. Thus, we plug in 3 for x to get;
5(3³ - 3) + 5(3²)/3 - 12(3)
= 5(27 - 3) + (5 * 3) - 36
= 120 + 15 - 36
= 99
b) We are given the algebraic expression;
3y + 16 + (y/2) - (20/y)
We want to simplify this when y = 4. Thus, we plug in 4 for y to get;
3(4) + 16 + (4/2) - (20/4)
= 12 + 16 + 2 - 5
= 25
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I need Help please with aleks
Answer:i do hope this helps 1 should be f(x)=0 0=sqrt-2+2
2 should be f(x)=343.0029154 343.0029154=sqrt7^6+2
3 should be f(x)=6 6=sqrt34+2
4 should be f(x)=10 10=sqrt98+2
and im sorry if im wrong