The required difference between polynomial 2x^2+7x+6-(3x^2-x) is,
-x^2+8x+6.
To simplify 2x^2+7x+6-(3x^2-x)
Polynomial is defined as the sum of more than one variable in terms of their power.
Here,
[tex]=2x^2+7x+6-(3x^2-x)\\=2x^2-3x^2+7x+x+6\\=-x^2+8x+6[/tex]
Thus, the required difference between polynomial 2x^2+7x+6-(3x^2-x) is, -x^2+8x+6.
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you start at 11 ,10 and you move 7units left and 5 units down
Answer:
(4 , 5)
Step-by-step explanation:
Note the point: (x , y) = (11 , 10)
Note that if you are moving left or right, you are changing the x variable.
Note that if you are moving up or down, you are changing the y variable.
In this case, you are starting at (11 , 10)
You move 7 units left (subtract 7 from x):
(11 - 7 , 10) = (4, 10)
You then move 5 units down (subtract 5 from y):
(4 , 10 - 5) = (4 , 5)
(4 , 5) is your answer.
~
Identify the percent, amount, and base in this problem: 25% of what number is 40?
Final answer:
In this problem, we are given the percentage (25%) and the amount (40), and we need to find the base. To find the base, we can set up an equation and solve for x. The base in this problem is 160.
Explanation:
In this problem, we are given the percentage (25%) and the amount (40), and we need to find the base. The base represents the whole quantity or number that the percentage is taken from.
Let x be the base. We can set up the equation: 25% of x is equal to 40, or 0.25x = 40.
To find the base, we divide both sides of the equation by 0.25: x = 40 / 0.25.
Simplifying, we get x = 160. Therefore, the base is 160.
To summarize, the percent is 25%, the amount is 40, and the base is 160.
A doormat is 3 feet by 2 feet.
What is the area of the doormat?
2 1/2 ft
2
NI
3 ft
(6j^2-2j+5)+(3j^2+4j-6)
Answer:whats the heck is this
Step-by-step explanation:473658857
how do make a rational to a fraction
Answer:
Step-by-step explanation:To convert part-to-part ratios to fractions:
Use the total number as the denominator: 6 + 8 = 14.
Use each of the ratio terms as the numerator in a fraction: ...
Reduce each fraction to lowest terms: ...
The part-to-part ratio 6 : 8 converts into the fractions:
To convert a rational expression to a fraction, create a common denominator, multiply by the inverse when dividing fractions, and simplify by canceling out common factors after prime factorization.
Converting a rational expression to a fraction involves creating a common denominator for the terms involved. When dividing fractions, the process is to change the division to multiplication by the inverse of the second fraction and then multiplying the numerators and denominators as above. A conversion factor in a measurement context is simply a fraction equal to one, with the original unit in the denominator to cancel it out and the new unit in the numerator.
When simplifying fractions it's useful to remember that multiplying or dividing both numerator and denominator by the same number does not change the value of the fraction; this is often referred to as multiplying by a fraction that equals one (1/2, 2/2, 3/3, etc.). Simplifying a fraction may involve finding these 'fractions equal to one' to cancel out the same factors in both the numerator and denominator.
Select the correct locations in the table.
The table shows the federal government's budgeted revenue and expenditures from 2001 through 2010. Identify the years in which there was a
budget deficit
Year
Revenue
Expenditure
2001
$8 trillion
$6 trillion
2002
$5 trillion
$7 trillion
2003
$8 trillion
$10 trillion
2004
$9 trillion
$7 trillion
2005
$15 trillion
$18 trillion
2006
$8 trillion
$10 trillion
2007
$6 trillion
$4 trillion
2008
$2 trillion
$4 trillion
2009
$7 trillion
$4 trillion
2010
$5 trillion
$9 trillion
Reset
Next
Answer:
From the table shown the years in which there was a budget deficit are
2002,2003,2005,2006,2008,2010
Step-by-step explanation:
Budget deficit is said to be when expenditure exceed or is greater than the budgeted revenue.
For 2002:
Revenue = $5 trillion and expenditure = $7 trillion
To check for budget deficit = Revenue - expenditure ( $5 trillion - $7 trillion)
= -$2 trillion ( there was a budget deficit of $2 trillion)
For 2003:
Revenue = $8 trillion and expenditure = $10 trillion
to check for budget deficit = Revenue - expenditure ($8 trillion - $10 trillion)
= -$2 trillion (there was a budget deficit of $2 trillion)
For 2005:
Revenue = $15 trillion and expenditure = $18 trillion
to check for budget deficit = Revenue - expenditure ($15 trillion - $18 trillion)
= -$3 trillion (there was a budget deficit of $2 trillion)
For 2006:
Revenue = $8 trillion and expenditure = $10 trillion
to check for budget deficit = Revenue - expenditure ( $8 trillion - $10 trillion)
= -$2 trillion (there was a budget deficit of $2 trillion)
For 2008:
Revenue = $2 trillion and expenditure = $4 trillion
to check for budget deficit = Revenue - expenditure ( $2 trillion - $4 trillion)
= - $2 trillion ( there was a budget deficit of $2 trillion)
For 2010:
Revenue = $5 trillion and expenditure = $9 trillion
to check for budget deficit = Revenue - expenditure ( $5 trillion - $9 trillion)
= -$4 trillion (there was a budget deficit of $4 trillion)
From the table shown the years in which there was a budget deficit are
2002,2003,2005,2006,2008,2010
Budget deficit is said to be when expenditure exceed or is greater than the budgeted revenue.
For 2002:
Revenue = $5 trillion and expenditure = $7 trillion
To check for budget deficit = Revenue - expenditure ( $5 trillion - $7 trillion)
= -$2 trillion ( there was a budget deficit of $2 trillion)
For 2003:
Revenue = $8 trillion and expenditure = $10 trillion
to check for budget deficit = Revenue - expenditure ($8 trillion - $10 trillion)
= -$2 trillion (there was a budget deficit of $2 trillion)
For 2005:
Revenue = $15 trillion and expenditure = $18 trillion
to check for budget deficit = Revenue - expenditure ($15 trillion - $18 trillion)
= -$3 trillion (there was a budget deficit of $2 trillion)
For 2006:
Revenue = $8 trillion and expenditure = $10 trillion
to check for budget deficit = Revenue - expenditure ( $8 trillion - $10 trillion)
= -$2 trillion (there was a budget deficit of $2 trillion)
For 2008:
Revenue = $2 trillion and expenditure = $4 trillion
to check for budget deficit = Revenue - expenditure ( $2 trillion - $4 trillion)
= - $2 trillion ( there was a budget deficit of $2 trillion)
For 2010:
Revenue = $5 trillion and expenditure = $9 trillion
to check for budget deficit = Revenue - expenditure ( $5 trillion - $9 trillion)
= -$4 trillion (there was a budget deficit of $4 trillion)
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Factor the expression shown below completely.
18x^2-60x+50
A.
B.
C.
D.
Answer:D. 2(3x-5)^2
Step-by-step explanation:
18x^2-60x+50=2(9x^2-30x+25)
Answer:
D. 2(3x - 5)²
Step-by-step explanation:
18x² - 60x + 50
The expression can be factorize as follows;
18x² - 60x + 50
divide through by 2
2(9x² - 30x + 25)
The bracket equation can be factorized further
Find the square value that can be multiplied to get 9x² and 25
The values are 3x and 5
2( (3x- 5)(3x - 5) )
2(3x - 5)²
There are 364 first-grade students in Park Elementary School. If there are 26 more girls than boys, how many girls are there?
There are 169 boys and 195 girls in the first-grade class at Park Elementary School.
Explanation:Let's assume the number of boys in the first-grade class is x. Since there are 26 more girls than boys, the number of girls would be x + 26. The total number of students in the class is 364, so we can calculate the equation:
x + (x + 26) = 364
Simplifying the equation, we get:
2x + 26 = 364
Subtracting 26 from both sides:
2x = 338
Dividing both sides by 2:
x = 169
So there are 169 boys and 169 + 26 = 195 girls.
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When writing an inequality how would you right x not equal to 25
Answer:
≠
Step-by-step explanation:
it would be unequal to
how do you know if two polygons are similar?
Please help me with my aleks!!
Answer:
PS = 37
Step-by-step explanation:
The opposite sides of a rectangle are congruent, thus
perimeter = 2(3x + 1) + 2(4x - 3) = 136 ← distribute and simplify left side
6x + 2 + 8x - 6 = 136
14x - 4 = 136 ( add 4 to both sides )
14x = 140 ( divide both sides by 14 )
x = 10
Hence
PS = 4x - 3 = (4 × 10) - 3 = 40 - 3 = 37
5+1.5(2d-1)=0.5
How do you solve this?
Answer:
5 + 3d - 1.5 = 0.5
3d + 3.5 = 0.5
3d = -3
d = -1
Answer:
Step-by-step explanation
5+1.5(2d)1.5(-1)=0.5
5+3d-0.5=0.5
5+3d=1
3d=-4
D=1.33
x^3-64 in factored form
Answer: (x−4)(x2+4x+16)
Step-by-step explanation:
x^3 − 64 ←is a difference of cubes
. xa^3 −b^3 = ( a − b ) (a^2 + ab + b^2)
here a = x and b =4 → (4)^3 = 64
⇒ x^3 − 64 = (x − 4) (x^2 + 4x + 16 )
Answer:
[tex][{x}^{2} + 4x + 16][x - 4][/tex]
Step-by-step explanation:
Take the cube root of this expression using the Difference of Cubes [(a + b)(a² - 2ab + b²)]:
[tex]x - 4 = \sqrt[3]{{x}^{3} - 64}[/tex]
Now, since the divisor\factor is in the form of [tex]x - c[/tex], use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
4| 1 0 0 −64
↓ 4 16 64
__________
1 4 16 0 → [tex]{x}^{2} + 4x + 16[/tex]
You start by placing the c in the top left corner, then list all the coefficients of your dividend [x³ - 64]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², the 4x follows right behind it, and bringing up the rear, 16, giving you the other factor of [tex]{x}^{2} + 4x + 16[/tex]. Attach this to the first factor you started out your work on:
[tex][x - 4][{x}^{2} + 4x + 16][/tex]
I am joyous to assist you anytime.
L=4/3(C-30) solve for C literal equation
Answer:
C = [tex]\frac{3L+120}{4}[/tex]
Step-by-step explanation:
Given
L = [tex]\frac{4}{3}[/tex](C - 30)
Multiply through by 3 to clear the fraction
3L = 4(C - 30) ← distribute
3L = 4C - 120 ( add 120 to both sides )
3L + 120 = 4C ( divide both sides by 4 )
[tex]\frac{3L+120}{4}[/tex] = C
“Seven less than a number squared”
Answer:
7-x^2
Step-by-step explanation:
The required expression will be x² - 7
Expressions are functions separated by an operation sign.
For the given statement:
Let the unknown number be xThe square of the number will be x²7 less than number means we are to subtract 7 from the result x² as shown
F(x) = x² - 7
Hence the required expression will be x² - 7
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Describe a way to calculate 304-81 mentally by using reasoning other that the common subtraction algorithm. Then write a coherent sequence of equations that correspond to your reasoning
Answer:
See explanation
Step-by-step explanation:
To subtract mentally 81 from 304, complete following steps:
Step 1: Write number 304 as
[tex]304=300+4\\ \\304=200+100+3+1\\ \\304=200+20+80+3+1[/tex]
Step 2: Write number 81 as
[tex]81=80+1[/tex]
Step 3: Now subtract 80 and 1 from number 304:
[tex]304-81=(200+20+80+1+3)-(80+1)\\ \\304-81=200+20+3\\ \\304-81=223[/tex]
Final answer:
To mentally subtract 304-81, round 81 to 100, subtract from 304 to get 204, then add back the difference (19) for a result of 223.
Explanation:
To calculate 304-81 mentally, we can round 81 up to 100 to make the numbers easier to work with. We know that 304 - 100 = 204.
Since we've subtracted too much by rounding up, we need to add back the difference between 81 and 100, which is 19.
So the full calculation would be 304 - 81 = 304 - 100 + 19 = 204 + 19 = 223.
The coherent sequence of equations aligning with this reasoning would be:
304 - 100 = 204 (rounding 81 up to 100 and subtracting)100 - 81 = 19 (finding the difference between the rounded number and the original number)204 + 19 = 223 (adding the difference back)complete the square and put this function in vertex form: f(x)=x^2+20x+97
Answer:
Step-by-step explanation:
f(x)=(x²+20x+100) -3 because : 97 = 100 - 3
f(x) = (x+10)² -3 ....vertex form
4* 5+ (14 + 8) - 369
Answer:
-327
Step-by-step explanation:
20+22-369=-327
What is the velocity of a vehicle after it moves 10 meters in 2 seconds?
Answer:
v = +5 m/s
Step-by-step explanation:
v = d/t
d = 10
t = 2
v = 10/2
v = +5 m/s
Type the integer that makes the following division sentence true.
÷(−2)=−3
The integer that makes the division sentence x / (-2) = -3 true is 6.
Here's how we can solve for x:
Multiply both sides of the equation by -2 to isolate x:
x = -3 * (-2)
Simplify the right side:
x = 6
Therefore, dividing any number by -2 and then multiplying by -2 again should result in the original number. In this case, dividing 6 by -2 and then multiplying by -2 again gives us 6:
(6 / -2) * -2 = -3 * -2 = 6
Remember, when dividing by negative numbers, the result is flipped compared to dividing by positive numbers. This is why we need to multiply by -2 again to get back to the original number.
The integer that satisfies the division sentence x ÷ (−2) = −3 is 6, following the rule that multiplying two negative numbers yields a positive result.
Explanation:To find the integer that makes the division sentence true, we look at the equation given: x ÷ (−2) = −3. To solve for x, we multiply both sides by −2, because division by a number is the inverse operation of multiplying by that number. So, we have x = −3 * (−2).
According to the rules of multiplication, when two negative numbers are multiplied together, the answer has a positive sign. Therefore, we get x = 6 as our solution. Since we know that dividing a positive number by a negative number yields a negative result, our calculated integer 6 is a valid answer because 6 ÷ (−2) indeed equals −3.
Following the rules of operations with negatives, such as in the examples 5 − (+3) that becomes 5 − 3 = 2, and 2 − (−6) that turns into 2 + 6 = 8, we can consistently apply the rule for division which mirrors the multiplication rules for signs to solve for our missing integer.
the difference between 33 1/3% and 33%
Answer:
_
1/3, or 0.3 is there difference
Find the distance between (-7, 10) and (-3, 6). Round your answer to the nearest tenth, if necessary.
Answer:
5.7
Step-by-step explanation:
What is the total cost of a $39.50 family dinner after you add a 20% tip
Answer:
$7.90 tip the total is $47.40
Step-by-step explanation:
Final answer:
To find the total cost of a $39.50 family dinner after adding a 20% tip, first calculate the amount of the tip by multiplying the cost of the dinner by the tip percentage. Then, add the tip to the cost of the dinner to get the total amount.
Explanation:
To find the total cost of a $39.50 family dinner after adding a 20% tip, you first need to calculate the amount of the tip. Tip is calculated by multiplying the cost of the dinner by the tip percentage. In this case, the tip would be 20% of $39.50, which is
$39.50 × 0.20 = $7.90
Next, you add the tip to the cost of the dinner to get the total amount:
$39.50 + $7.90 = $47.40
So, the total cost of the family dinner after adding a 20% tip is $47.40.
The area of a rectangle is 42 square inches the rectangle is 7 inches long how wide is the rectangle
Answer: 6 inches
Step-by-step explanation:
formula for area of a rectangle is length times width
LW=A
substitute
7(W)=42
divide 7 on both sides
42/7 = 6
Answer: 6
Problem Set#2:
In the cafeteria, 100 milk cartons were put on for breakfast. At the end of breakfast, 27 remained.
a. What is the ratio of the number of milk cartons taken to he total number of milk cartons?
b. What is the ratio of the number of milk cartons remaining to the number of milk cartons taken?
*Answer A-B
Answer:
a. the ratio is 73:100
b. the ratio is 27:73
solve for x : 3/5(x + 2)= x-4
Answer:
x = 13
Step-by-step explanation:
Given
[tex]\frac{3}{5}[/tex](x + 2) = x - 4
Multiply through by 5 to clear the fraction
3(x + 2) = 5x - 20 ← distribute left side
3x + 6 = 5x - 20 ( subtract 5x from both sides )
- 2x + 6 = - 20 ( subtract 6 from both sides )
- 2x = - 26 ( divide both sides by - 2 )
x = 13
list the next 3 terms in the following sequence 1,2,4,8,16,32
Answer:
the next 3 terms are 64, 128, and 256
(PLEASE HELP ME IM STRUGGLING) (picture is shown) Here is an illustration of a four way stop. those roads are two lines and they intersect at a.....???
The roads are two lines and they intersect at 90° .
What is intersection of line?Intersecting lines cross each other at some arbitrary angle .
What are perpendicular lines?Two geometric objects are perpendicular if they intersect at a right angle. A line is said to be perpendicular to another line if the two lines intersect at a right angle.
According to the question
Roads have 2 lanes and have crossing lane .
Now,
Those roads are two lines and they intersect at a right angle by making 90° at there point of intersection .
So,
They are perpendicular lines .
Hence, the roads are two lines and they intersect at 90° .
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Select the correct answer.
If the function 5x + y=1 has the domain (-2, 1, 6), then what is the corresponding range?
A. {-9,6,31}
B. {9, -6, -31)
C. {-11, 4, 29}
D. (11,-4,-29)
Answer:
answer is D
Step-by-step explanation:
5(-2) + y = 1 5(1) + y = 1 5(6) + y = 1
-10 + y = 1 5 + y = 1 30 + y = 1
y - 10 = 1 y + 5 = 1 y + 30 = 1
y = 11 y = -4 y= -29
The corresponding range function 5x + y=1 which has the domain (-2, 1, 6) will be option (D) {11,-4,-29}
Corresponding rangeA function is a correspondence or rule that assigns to each element in one set, called the domain D, exactly one element from a second set, called the range R.
How to solve this problem?The Steps are as follow:
GivenFunction = 5x + y = 1
domain = (-2 , 1, 6)
Corresponding range = ?
According to subject x ∈ {-2,1,6}So we will put the value of x as -2 ,1, 6 in function to find corresponding range which will be as follow:let x = -2
∴ 5x + y =1
∴ 5(-2) + y =1
∴ -10 + y =1
∴ y = 11
x = 1
∴ 5x + y = 1
∴ 5(1) + y = 1
∴ 5 + y = 1
∴ y = -4
x = 6
∴ 5x + y =1
∴ 5(6) + y = 1
∴ 30 + y =1
∴ y = -29
So the corresponding range function 5x + y=1 which has the domain (-2, 1, 6) will be option (D) {11,-4,-29}
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If, for a certain function, f(x)= 51, calculate the following values.
a.
f(x)-8
b.
1/2f(x)
c.
1/2f(x)-8
Answer: (a) 43 (b) 25.5 (c) 17.5
Step-by-step explanation:
f(x) = 51
Replace f(x) with 51
a) f(x) - 8 = 51 - 8 = 43
[tex]b)\quad \dfrac{1}{2}f(x)\qquad =\dfrac{1}{2}\cdot 51\qquad =\dfrac{51}{2}\qquad =25.5[/tex]
[tex]c)\quad \dfrac{1}{2}f(x)-8\qquad =25.5-8\qquad =17.5[/tex]