Answer:
y = 0.265x - 494.7
Step-by-step explanation:
Let median age be represent by 'a' and time be represent by 't'
In 1980, median age is given 30
which means that
a₁ = 30
t₁ = 1980
In 2000, the median age is given 35.3
which means that.
a₂ = 35.3
t₂ = 2000
The slope 'm' of the linear equation can be found by:
m = (a₂ - a₁) /(t₂ - t₁)
m = (35.3 - 30)/(2000-1980)
m = 0.265
General form of linear equation is given by:
y = mx + c
y = 0.265x +c
Substitute point (1980,30) in the equation.
30 = 0.265(1980) + c
c = -494.7
Hence the the linear equation can be written as:
y = mx + c
y = 0.265x - 494.7
A company makes concrete bricks shaped like rectangular prisms. Each brick is 10 inches long, 6 inches wide, and 4 inches tall. If they used 13,200in3 of concrete, how many bricks did they make?
Answer:
The company used 55 concrete bricks.Step-by-step explanation:
We should first find the volume of one of the rectangular bricks.
10×6×4=240in³.
Now, let's divide 13,200in³ by 240in³.
13,200÷240=55
Hence, the company used 55 concrete bricks.Hope this helps! (It's probably too complicated, I'm very sorry ;-;)
What's the equation of the parabola that has its vertex at (8,–14) and a point (5,13) that lies on the curve?
Question 13 options:
A)
y = (x + 8)2 – 14
B)
y = (x – 8)2 – 14
C)
y = 3(x + 8)2 – 14
D)
y = 3(x – 8)2 – 14
Answer:
The expression with the described characteristics is: [tex]y = 3*(x - 8)^2 - 14[/tex]. Therefore the correct answer is letter D.
Step-by-step explanation:
I believe there is a typo in the vertex's coordinate, I think it should be (8,14). I came to this conclusion by observing the possible answers, if the given vertex is correct then there are no correct answers among them. I made my best effort to explain the question in a way that can be generalized for different vertex's coordinates.
The equations are given in their vertex form. This form has the following structure:
[tex]y = a*(x - h)^2 - k[/tex]
Where (h,k) are the vertex's coordinates, in our case (8, 14). This knowledge makes easier to determine a equation with the correct vertex as shown below:
[tex]y = a*(x - 8)^2 - 14[/tex]
Where the value of "a" must be determined by applying the given point.
[tex]13 = a*(5 - 8)^2 - 14\\13 = a*(3)^2 - 14\\a*9 = 27\\a = \frac{27}{9}\\a = 3[/tex]
The expression with the described characteristics is: [tex]y = 3*(x - 8)^2 - 14[/tex]. Therefore the correct answer is letter D.
Find the remainder when f(x) = x3 − 14x2 + 7x − 10 is divided by x − 3. 184 164 −88 −122
Answer:
122
Step-by-step explanation:
For this case we must build a quotient that, when multiplied by the divisor, eliminates the terms of the divide until it reaches the remainder.
It must be fulfilled that:
Dividend = Quotient * Divisor + Remainder
we have that the remainder is 122.
have a good day
Answer:
The answer would be D) -122
On a piece of paper, graph y - 3 > 2x + 2. Then determine which answer choice matches the graph you drew. A. Graph A B. Graph B C. Graph C D. Graph D
Answer: Graph C
Step-by-step explanation:
The correct graph is C.
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Given : On a piece of paper, graph y - 3 > 2x + 2.
To find : determine which answer choice matches the graph you drew,
y - 3 > 2x + 2
y > 2x + 5
x = 0
y > 5
x = - 3
y > - 1
at x = 0, y = 5
0 < 5
origin does not lie in the shaded region,
as y > 2x + 5
line y = 2 x+ 5 is not part of solution (dotted line)
Hence Graph C is correct
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Which of the following is an equivalent form of the compound inequality -44 > -2x - 82-8?
0-2x - 8 >-44 and -2x - 82-8
O-2x > -44 and -8-8
0-2x - 8<-44 and -2x -85-8
0-2x -8<-44 and -2x - 82-8
I NEED HELP ASAP
Answer:
(d) -2x -8 < -44 and -2x -8 ≥ -8
Step-by-step explanation:
A compound inequality is a mathematical sentence that combines two simple inequalities. A solution will satisfy both inequalities. That is, it represents an "and" (intersection) condition for the solution sets.
Equivalent pairAn inequality of the form ...
a > b ≥ c
can be written as a pair of inequalities by considering what is on either side of each of the relation symbols:
left symbol: a > bright symbol: b ≥ cApplicationGiven: -44 > -2x -8 ≥ -8
We can decompose the given inequality into the system ...
-44 > -2x -8 . . . . . . . . left symbol-2x -8 ≥ -8 . . . . . . . . . right symbolWhen we compare these to the offered answer choices, we see that we need to rewrite the first inequality so the constant is on the right:
-2x -8 < -44
Then the equivalent form of the given inequality is ...
-2x -8 < -44 and -2x -8 ≥ -8
__
Additional comment
The transitive property of inequality means that ...
a > b ≥ c
implies that a > c.
You will notice that our given inequality, written in this way, becomes ...
-44 > -8 . . . . . . not true
This means the inequality has no solution. (The solution set is the empty set.)
Expression
3x2
5a²b4
2x2 + 3x - 8
Type of Polynomial
Coefficient
Constant
Answer with explanation:
An algebraic expression having one term is known as a monomial.An algebraic expression having two terms is known as binomial.An algebraic expression having three terms is known as trinomial.Numerical coefficient - Number written before variable in each term.Constant - term with no variable ( only number).Let's check the given expressions :
[tex]3x^2[/tex]
Type - Monomial ( having one term)
Coefficient of [tex]x^2[/tex]= 3
Constant =0
[tex]5a^2b^4[/tex]
Type - Monomial ( having one term)
Coefficient of [tex]a^2b^4[/tex]= 5
Constant =0
[tex]2x^2 + 3x - 8[/tex]
Type - trinomial ( having 3 terms)
Coefficient of [tex]x^2[/tex] = 2
Coefficient of [tex]x=3[/tex]
Constant = -8
Given the function f(x) = | -2x + 4 |. Complete the table.
-the table is in the picture provided help me complete it please (algebra 1)
Answer:
See below.
Step-by-step explanation:
To complete the table, start by copying the given function.
f(x) = |-2x + 4|
Now let's start with the first line of the table: x = 6.
You are finding the value of function f when x = 6.
Replace x with 6 and evaluate the expression.
f(6) = |-2(6) + 4|
f(6) = |-12 + 4|
f(6) = |-8|
f(6) = 8
Second line of table:
x = -1
f(x) = |-2x + 4|
f(-1) = |-2(-1) + 4|
f(-1) = |2 + 4|
f(-1) = |6|
f(-1) = 6
For the third and fourth lines, you are given a y value, or the value of function f, and you are looking for x. Now you use the given value to set the function equal to, and you solve for x.
Line 3: f(x) = 4
f(x) = |-2x + 4|
|-2x + 4| = 4
-2x + 4 = 4 or -2x + 4 = -4
-2x = 0 or -2x = -8
x = 0 or x = 4
Line 4: f(x) = 14
f(x) = |-2x + 4|
|-2x + 4| = 14
-2x + 4 = 14 or -2x + 4 = -14
-2x = 10 or -2x = -18
x = -5 or x = 9
The table looks like this:
x f(x)
6 8
-1 6
0,4 4
-5, 9 14
[tex] \end{center} [/tex]
For the given function f(x) = | -2x + 4 |, the data is shown in the table below.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that the function is, f(x) = | -2x + 4
Let's begin with the table's first line: x = 6, When x equals 6, you are determining the value of function f. Evaluate the equation after substituting 6 for x.
f(6) = |-2(6) + 4|
f(6) = |-12 + 4|
f(6) = |-8|
f(6) = 8
For the Second line of the table,
x = -1
f(x) = |-2x + 4|
f(-1) = |-2(-1) + 4|
f(-1) = |2 + 4|
f(-1) = |6|
f(-1) = 6
The third line of the table,
f(x) = 4
f(x) = |-2x + 4|
|-2x + 4| = 4
-2x + 4 = 4 or -2x + 4 = -4
-2x = 0 or -2x = -8
x = 0 or x = 4
Line 4: f(x) = 14
f(x) = |-2x + 4|
|-2x + 4| = 14
-2x + 4 = 14 or -2x + 4 = -14
-2x = 10 or -2x = -18
x = -5 or x = 9
Thus, for the given function f(x) = | -2x + 4 |, the data is shown in the table below.
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Paul developed a roll of film containing 36 pictures. If he made 2 prints each of half of the pictures and 1 print of each of the rest, how many prints did he make in all?
Answer:
54
Step-by-step explanation:
Total pictures in the roll = 36
half of the roll = 1/2 of the total pictures in the roll = 1/2 * 36 = 18
Given Paul made 2 prints of each of the half pictures
no. of prints made of half of the pictures = 18*2 = 36
No. of prints left after the half of the roll is printed for two prints= 36-18 = 18
No. of prints made of rest of the pictures 1
Therefore , no of prints made of rest half of pictures = 18*1 = 18
Total prints made = 36 + 18 = 54.
Thus, Paul made 54 prints in all.
What is the completely simplified equivalent of 2 over 5+i? the 'i' is 1! thx for the help!
Answer:
1/3 ≅ .33333
Step-by-step explanation:
If 'i' is 1, then 5+i is 6. 2 over 6 is 1 over 3. (2/6 = 1/3) 1 over 3 is also .3333... forever repeating.
Hope this helps!
Which phrase best describes mortgage collateral?
A.money used as a down payment for the loan
B.assets obtained after securing the loan
C.the purchased property that secures the loan
D.closing costs covered by the buyer
Answer:
C. the purchased property that secures the loan
Step-by-step explanation:
Mortgage collateral describe the use of a property e.g house to secure a loan. This collateral is always requested when a large amount of money is involved. The house could be sold if the borrower renege (fail to meet up with) on the due date as regards the agreement after collecting the loan.
Therefore, a mortgage collateral could be referred to as the purchased property that has been used to secure a loan by a borrower.
Therefore the purchased property that secures the loan is the correct answer.
What is Collateral ?Collateral refers to an asset that a borrower offers as a guarantee for a loan, such as a mortgage.
When you obtain the loan, the lender puts a lien on the collateral. The lien stipulates that the lender can seize the collateral if you don’t repay the loan under the terms of the contract.
Once you repay the loan, the lender removes the lien and no longer has a claim to the collateral.
In the case of a mortgage, the collateral is the real property.
When determining whether to approve your loan, the lender will ensure that the property ,the collateral ,is actually worth what you propose to pay for it with the loan.
If it isn’t, the lender can deny the mortgage because the asset isn’t worth the risk.
Therefore the purchased property that secures the loan is the correct answer.
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3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
a) 8
b) 9
c) 10
d) 11
e) 12
In my view option D but it can be wrong
How many numbers less than 1000 are there that use only the digits of 2088?
Answer:
17 numbers with any number of digits
12 numbers using as many digits as possible
Step-by-step explanation:
It depends on how many digits you are required to use. If you're not required to use more than one digit, then the possible numbers are ...
0, 2, 8, 20, 28, 80, 82, 88,
208, 280, 288, 802, 808, 820, 828, 880, 882
for a total of 17 numbers.
__
If you must use the maximum possible number of digits, then the 1-digit numbers and the 2-digit numbers containing 0 must be taken off the list, leaving ...
028, 082, 088, (and all the above 3-digit numbers)
for a total of 12 numbers.
When I square my number, I get the same answer as when I multiply my number by 10 and then add 144. My number is positive. What is it?
Answer:
your number is 18
Step-by-step explanation:
x^2 = (x × 10 ) + 144
x^2 = 10x + 144
x^2 - 10x - 144 = 0
using quadratic method
your answer should be
(x- 18) ( x+8 )
PLLZZZZZZZ HELP I WILLL GIVE BRAINLIEST TO THE FIRST ONE TO ANSWER
Answer:
positive
Step-by-step explanation:
Find the missing side lengths. Answers are in simplest radical form with the denominator rationalized.
Answer: D
Step-by-step explanation:
y=4√2
This triangle is isosceles. Thus, two of the legs are congruent by A.S. Thm
D is the only choice with y = 4√2.
If a rabbit can move 1 5/19 miles every hour, then how many hours would it take a rabbit to go 72 miles?
Answer:
57 hours
Step-by-step explanation:
72 ÷ (1 + (5 ÷ 19))-57
Seamstress Jane has purchased 50 yards of red fabric and 110 yards of gold fabric to make red and gold curtains. What is the largest number of curtains she can make if she wants all the curtains to be exactly the same length, and to have no fabric left over? How many yards of each kind of fabric would be used for each curtain?
Answer:
Given:
Number of yards of red fabric purchased by Jane = 50
Number of yards of gold fabric purchased by Jane = 110
We need to find the largest number of curtains she can make if she wants all the curtains to be exactly the same length.
For this we will find H.C.F. of 50 and 110.
Factors of 50 = 1, 2, 5, 10, 25, 50.
Factors of 110 = 1, 2, 5, 10, 11, 22, 55, 110.
So, Highest common factor of 50 and 110 is 10.
So, there are 10 largest number of curtains she can make if she wants all the curtains to be exactly the same length.
Number of yards of red fabric is given by:
50/10=5
Number of yards of gold fabric is given by
110/10=11
Hence, there are 5 red fabrics and 11 gold fabrics that would be used for each curtain.
If two similar cones have volumes of 320 cm³ and 1,080 cm³, find the scale factor.
A. 1/3
B. 2/3
C. 3/4
D. 7/8
Answer:
B. 2/3
Step-by-step explanation:
Ms. White measured the number of the ounces of juice left behind by 3 students after breakfast. She plotted the data on the line plot shown below
Answer: The answer is 7 3/4 :)) <3 have a good day.
The amount of juice left by the three students is (31/4) ounces.
What is dot plot?A dot plot, also called a dot chart, is a type of simple histogram-like chart used in statistics for relatively small data sets where values fall into a number of discrete bins.
Given is that Ms. White measured the number of the ounces of juice left behind by 3 students after breakfast.
The total juice left by 3 students is equivalent to -
{x] = 2 x {2[tex]\frac{1}{4}[/tex]} + 3[tex]\frac{1}{4}[/tex]
{x} = 2 x 9/4 + 13/4
{x} = 18/4 + 13/4
{x} = 31/4
Therefore, the amount of juice left by the three students is (31/4) ounces.
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In a newspaper, it was reported that yearly robberies in Springfield were down 2% to 245 in 2014 from 2013. How many robberies were there in Springfield in 2013?
Answer:
250
Step-by-step explanation:
245 / 0.98 = 250
am I correct? if not what's the right answer?
Answer:
2x+y -3 =0
Step-by-step explanation:
0 = Ax + By + C is the general form of a line
2x+4y +2 = 3y +5
Subtract 3y from each side
2x+4y-3y +2 =3y+5-2y
2x+y +2 = 5
Subtract 5 from each side
2x+y +2-5 = 5-5
2x+y -3 =0
Someone please help me it’s 20 points please help!!!
Answer:
[tex]g(1)=1[/tex]
Step-by-step explanation:
Use just the definition for the appropriate section of the Domain that includes x=1,
that is the third definition:
[tex]g(x)=x^3-x^2+1\\g(1)=(1)^3-(1)^2+1\\g(1)=1[/tex]
Find the area of the shaded polygons:
Answer:
6.5 square units
Step-by-step explanation:
There are MANY ways to do this problem, most of them involving breaking it into 3 or four shapes. But this one is easier if you do most of it by taking out the squares and half squares.
Squares - 3
Half squares - 4 (totals 2 squares)
Triangle - 1 - 1/2bh = 1/2x1x3 = 1.5
TOTAL = 3+2+1.5=6.5
Answer:
6 sq. un
Step-by-step explanation:
Select the expression that is equivalent to 3(2x + 5) − 4x. A. 2x + 15 B. x + 8 C. x + 15 D. 2x + 5
Answer:
A. 2x + 15
Step-by-step explanation:
3(2x + 5) - 4x =
= 6x + 15 - 4x
= 2x + 15
Answer: A. 2x + 15
Answer:
2x +15
Step-by-step explanation:
3(2x + 5) − 4x
Distribute
6x + 15 -4x
Combine like terms
2x +15
How do i solve for y and x?
Answer:
You use the facts about a 30, 60, 90 triangle.
Step-by-step explanation:
The angles in a triangle add up to 180.
90+30+x=180
120+x=180
x=60
This is a 30-60-90 right triangle.
The side opposite the 30 degree angle is a.
The side opposite the 90 degree angle (hypotenuse) is 2a.
The side opposite the 60 degree angle is a[tex]\sqrt{3}[/tex]
We know the side opposite the 90 degree angle.
2a = 12[tex]\sqrt{3}[/tex]
Divide by 2.
a=6[tex]\sqrt{3}[/tex]
a is the side opposite the 30 degree angle (y)
Because we know a, we can find a[tex]\sqrt{3}[/tex].
6[tex]\sqrt{3 } (\sqrt{3})[/tex]
The square roots cancel, leaving 3.
6 times 3 is 18.
Therefore, the side opposite the 60 degree angle (x) is 18.
Which of the lines in the picture are lines of symmetry of the given figure? Please explain!
Answer:
n,r,t
Step-by-step explanation:
The line of symmetry can be defined as the axis or imaginary line that passes through the center of the shape or object and divides it into identical halves. As you can see above the lines n,r,t are the only lines that give identical halves of the figure
What is 131x682 can anyone tell me the step of doing it I don’t know how to
Answer:
91232
Step-by-step explanation:
Which of the following is a numerical expression that involves addition? x + 8 7 – x 2 + 5 6x
Answer:
x+8
Step-by-step explanation:
This is because in this answer, there are two terms with an addition sign in between them.
WIL GIVE BRAINLIEST IF ANSWER FAST! Evaluate the expression 7x2y, when x = 4 and y = 2. 112 224 542 718
Answer:
224
Step-by-step explanation:
Substitute x = 4 and y = 2 into the expression and evaluate
7x²y = 7 × 4² × 2 = 7 × 16 × 2 = 7 × 32 = 224.
Hope this helped you!
Find the volume of a pyramid with a square base, where the side length of the base is
12.8 in and the height of the pyramid is 20.4 in. Round your answer to the nearest.
tenth of a cubic inch.
Answer:
Volume = 1114.1 [tex]in^3[/tex]
Step-by-step explanation:
Recall that the formula for the volume of a pyramid is given by:
[tex]Volume=\frac{1}{3} \,B\,*\,H[/tex]
where B is the area of the pyramid's base (in our case a square of side 12,8 in), and H the pyramid's height (in our case 20.4 in).
Then the square base of the pyramid has an area given by: [tex](12.8\,\,in)^2=163.84\,\,in^2[/tex]
Finally,we can now write the volume of the pyramid as:
[tex]Volume=\frac{1}{3} \,B\,*\,H\\Volume=\frac{1}{3} \,(163.84)\,*\,20.4\,\,in^3\\Volume=1114.112\,\,in^3[/tex]
Rounding the answer to a tenth of a cubic inch, we get:
Volume = 1114.1 [tex]in^3[/tex]