The rectangle can be divided into 6 ways as, 1 × 56 or 56 × 1, 2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.
What is rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.
Given:
Darren has a piece of wood that is 7 in by 8 in
The area of the rectangle can be given by,
[tex]Area = Length\times width[/tex]
Area = 7 × 8
Area = 56
You can now divide the length and width as shown below,
Rectangle = 1 × 56 or 56 × 1
Rectangle = 2 × 28 or 28 × 2
Rectangle = 4 × 14 or 14 × 4
Therefore, the rectangle can be divided into 6 ways as 1 × 56 or 56 × 1, 2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.
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here is an equation that is true for all values of x:5(x+2)=5x+10. Elena saw this equation and says she can tell 20(x+2)=4(5x+10)+31 is also true for any value of x. How can she tell? Explain your reasoning.
Elena is wrong, because the two sides of equation are not equal for all values of x
Step-by-step explanation:
An equation of x is true for all values of x when the left hand side
is equal to the right hand side
To prove that an equation is true for all values of x do that
Simplify the left hand side and the right hand sideSolve the equation to find x, you will find the x in the left hand side is equal to x in the right hand side, so they canceled each other, and the numerical terms in the two sides equal each other, that means the equation is true for any values of xLets check that with given equation 5(x + 2) = 5x + 10
∵ 5(x + 2) = 5x + 10
- Simplify the left hand side
∵ 5(x) + 5(2) = 5x + 10
∴ 5x + 10 = 5x + 10
- Subtract 5x from both sides
∴ 10 = 10
∵ L.H.S = R.H.S
∴ The equation is true for all values of x
Lets do that with Elena's equation
∵ 20(x + 2) = 4(5x + 10) + 31
- Simplify the two sides of the equation
∵ 20(x) + 20(2) = 4(5x) + 4(10) + 31
∴ 20x + 40 = 20x + 40 + 31
- Add like terms in the right hand side
∴ 20x + 40 = 20x + 71
- Subtract 20x from both sides
∴ 40 = 71 ⇒ and that not true
∵ L.H.S ≠ R.H.S
∴ The equation is not true for all values of x
Elena is wrong, because the two sides of equation are not equal for all values of x
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Elena took the original equation, multiplied both sides of it by 4 and added 31 to both sides. Because she did the same thing to both sides of the equation, it is equal to the original equation and therefore is true for all values of `x`.
Claire Judice
Mixed Multistep Factoring (Equation)
Dec 01, 6:42:28 PM
Solve algebraically for all values of x:
5x5 + 6x4 + 80x3 + 96x² = 0
Answer:
Submit Answer
Answer:
The values of 'x' are -1.2, 0, 0, [tex]-4i[/tex] or [tex]4i[/tex].
Step-by-step explanation:
Given:
The equation to solve is given as:
[tex]5x^5+6x^4+80x^3+96x^2=0[/tex]
Factoring [tex]x^2[/tex] from all the terms, we get:
[tex]x^2(5x^3+6x^2+80x+96)=0[/tex]
Now, rearranging the terms, we get:
[tex]x^2(5x^3+80x+6x^2+96)=0[/tex]
Now, factoring [tex]5x[/tex] from the first two terms and 6 from the last two terms, we get:
[tex]x^2(5x(x^2+16)+6(x^2+16))=0\\x^2(x^2+16)(5x+6)=0[/tex]
Now, equating each factor to 0 and solving for 'x', we get:
[tex]x^2=0\\x=0\ and\ 0\\\\5x+6=0\\x=\frac{-6}{5}=1.2\\\\x^2+16=0\\x^2=-16\\x=\sqrt{-16}=\pm 4i[/tex]
There are 3 real values and 2 imaginary values. The value of 'x' as 0 is repeated twice.
Therefore, the values of 'x' are -1.2, 0, 0, [tex]-4i[/tex] or [tex]4i[/tex].
The steps to convert 23/4 to a decimal are shown below
Answer:
23/4 = 5.75
Step-by-step explanation:
What is a mineral?
a. an element
b. a rock formed from something that was once living
c. a naturally formed solid substance with a crystal structure
Answer:
The answer is definitely C. a naturally formed solid substance with a crystal structure
Use the information given to identify the a7 term of the geometric sequence: a2 = −5, r = 2
Answer:
[tex]a_{7}[/tex] = - 160
Step-by-step explanation:
The n th term of a geometric sequence is calculated as
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Given
a₂ = - 5, then
a₁r = - 5, that is
2a₁ = - 5 ⇒ a₁ = - 2.5, thus
[tex]a_{7}[/tex] = - 2.5 × [tex](2)^{6}[/tex] = - 2.5 × 64 = - 160
Triangles a and b are right angled. show that the two shorter sides in triangle a have the same length as the two shorter sides in triangle B
explain why the two triangles are congruent
The two shorter sides in triangle A can be demonstrated to be the same length as the two shorter sides in triangle B by showing 'a' equals 'p' and 'b' equals 'q'. The two triangles would accordingly be congruent using the Side-Side-Side (SSS) Postulate.
Explanation:Triangles A and B are right-angled triangles, which means each has one angle that measures 90 degrees. You're asking to show that the two shorter sides in triangle A have the same length as the two shorter sides in triangle B. This would mean that these sides are congruent.
Firstly, let the two shorter sides in triangle A are 'a' and 'b', and in triangle B are 'p' and 'q'. If triangle A and B are congruent, this means 'a' should equal 'p' and 'b' should equal 'q'.
Finally, the two triangles would be congruent based on the Side-Side-Side (SSS) Postulate, which states that if the three sides of one triangle are congruent to the three sides of a second triangle, then the two triangles are congruent.
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Final answer:
To show that two right angled triangles are congruent, you compare the two shorter sides. If they are equal in length, then the triangles are congruent by the Side-Angle-Side (SAS) postulate, as the right angle is also congruent.
Explanation:
To demonstrate that two right angled triangles, Triangle A and Triangle B, are congruent when the two shorter sides have the same length, first let's assume they are right angled at vertex C. If the sides AC and BC are congruent to the sides A'C' and B'C' respectively in triangles ABC and A'B'C', and since right angles are always congruent, then by the Side-Angle-Side (SAS) postulate of congruency, the two triangles are congruent.
According to the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (this is expressed as c² = a² + b²), we know that if the two legs a and b are congruent in two right triangles, then the hypotenuses will also have to be congruent.
If Triangle A and Triangle B have sides of equal lengths and right angle at C, the triangles are congruent by the SAS postulate, proving that both triangles are identical in shape and size.
Artemis took out a 30-year loan from her bank for $190,000 at an APR of
9.6%, compounded monthly. If her bank charges a prepayment fee of 6
months' interest on 80% of the balance, what prepayment fee would Artemis
be charged for paying off her loan 16 years early?
O
A. $5822.42
O
B. $7390.60
O C. $6182.58
O D. $7382.56
The prepayment fee of $6182.58 would be charged to Artemis for paying off her loan 16 years early.
Answer: Option C
Step-by-step explanation:
30 year loan at 9.6% interest yields.
Number of month = 30 (12) = 360 months
Annual percent interest of [tex]\frac{9.6 \%}{12}[/tex] = monthly percent interest of .8%
The formula for the present value of an ordinary annuity, as opposed to an annuity due, is as follows
[tex]P M T= \frac{P \times r}{1-(1+r)^{n}}[/tex]
With r and n adjusted for periodicity, where
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the interest rate (also known as the discount rate)
n = the number of periods in which payments will be made
[tex]P M T= \frac{190000 \times 0.008}{1-(1+0.008)^{-360}} = \frac{1520}{1-(1.008)^{-360}} = \frac{1520}{1-0.0567}=\frac{1520}{0.9432}[/tex]
PMT = $1611.50 per month
Her loan 16 year early. It means
[tex]\text { Worth of loan after } 14 \text { year } = 190000 \times(1.008)^{168} = 3.814 \times 190000=\$ 724641.16[/tex]
Worth of monthly payments for 14 year
[tex] = \frac{1611.50 \times\left\{(1.008)^{168}-1\right)}{0.008} = \frac{1611.50 \times(3.81-1)}{0.008} = \frac{4.534 .6}{0.008} = \$ 566825.15[/tex]
Amount still owed after 14 year = difference of the above two
=$724641.16 - $566825.18
=$157816.01
Prepayment fee = [tex](0.8 \times 157816.02) \times\left((1.008)^{6}-1\right)[/tex]
= 126252.82 (1.049-1) = 126252.82 (1.0489-1) = $6182.63
a flag pole is 30 feet tall a bug crawls 14 feet up the pole then it crawls another4 feet up the pole how much firther must the bug crawl to get to the top
Answer:
12 more feet
Step-by-step explanation:
Reason why is because if you add 14 and 4 you get 18 then you add 18 with 12 and you get 30. (hope this helps)
Given: ΔАВС, m∠ACB = 90°
CD
⊥
AB
, m∠ACD = 60°,BC = 6 cm
Find CD, Area of ΔABC
Answer:
CD = 5.196 cm
Area = 31.177 sq. cm.
Step-by-step explanation:
See the attached diagram.
Given that ∠ ACB = 90° in Δ ABC.
Now, CD ⊥ AB and ∠ CDB = ∠ CDA = 90°
Given that ∠ ACD = 60° and BC = 6 cm.
We have to find the length of CD and the area of Δ ABC.
Now, ∠ CAD = 90° - ∠ ACD = 90° - 60° = 30°
Again, ∠ CBD = 90° - ∠ CAD = 90° - 30° = 60°.
Now, from Δ BCD, [tex]\sin 60 = \frac{CD}{BC} = \frac{CD}{6}[/tex]
{Since Δ BCD is a right triangle and ∠ CDB = 90°}
⇒ [tex]CD = 6 \times \sin 60 = 5.196[/tex] cm. (Answer)
Now, from Δ ACD, [tex]\sin 30 = \frac{CD}{AC} = \frac{5.169}{AC}[/tex]
{Since Δ ACD is a right triangle and ∠ ADC = 90°}
⇒ [tex]AC = \frac{5.196}{\sin 30} = 10.392[/tex] cm
So, the area of Δ ABC = [tex]\frac{1}{2} \times BC \times AC = \frac{10.392 \times 6}{2} = 31.177[/tex] sq. cm. (Answer)
Answer:
CD=3√3
Step-by-step explanation:
Okay, how many weeks would you have to work to pay for Gary's $1200 mistake?
The number of weeks requires is 15 weeks
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
$85.00 a week just from Allowance
So, Gary have to work
=1200/85
= 15 weeks
Hence, the number of weeks requires is 15 weeks.
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The complete question is
can someone help me please?
Question : If you have a job or allowance, how much do you take home per week?
I put that I make $85.00 a week just from Allowance and my half job.
So the question is : how many weeks would you have to work to pay for Gary's $1200 mistake?
[calculate $1200 � your take home pay amount = answer in weeks]
Weeks for Laptop:
how many weeks would you have to work to pay for your little mistake with the $13 bounced check? You know, that $4300 messup? Weeks for pizza :
Help please thanks
Final answer:
Jason will have to work approximately 6.67 weeks, or about 6 weeks and 5 days, to pay off a $1200 mistake if he earns $4.50 per hour after government income reduction.
Explanation:
To calculate how many weeks a student would have to work to pay for a $1200 mistake, we will use the information provided about Jason's income and work scenario as a reference. According to the information, Jason nets $4.50 for every hour of work due to a reduction in government income. Thus, if Jason has to repay $1200, we will divide this amount by his net hourly income to find the total hours he needs to work.
$1200 ÷ $4.50 per hour = 266.67 hours
Now, to convert these hours into weeks, we assume a standard work week is 40 hours. Therefore, we divide the total hours by 40 hours per week.
266.67 hours ÷ 40 hours per week = 6.67 weeks
Jason will have to work approximately 6.67 weeks to pay off a $1200 mistake.
what is the measure of the vertex angle of an isosceles triangle i’d one of its base angles measures 42°
The measure of the vertex angle of the isosceles Δ is 96°
Step-by-step explanation:
In the isosceles triangle
Two sides are equal in lengthsThe angle between the two equal sides is called vertex angleThe other two angles are called base anglesThe base angles are equal in measure∵ The measure of one of the base angles of an isosceles Δ = 42°
- The base angles are equal in measure
∴ The measure of the other base angle = 42°
∵ The sum of the measures of the interior angles of any Δ = 180°
∴ 42 + 42 + measure of the vertex angle = 180
∴ 84 + measure of the vertex angle = 180
- Subtract 84 from both sides
∴ measure of the vertex angle = 96°
The measure of the vertex angle of the isosceles Δ is 96°
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Abc bookstore sells new books, n, for $12, used books, u, for $8, and magazines, m, for $5 each. The store earned $340 revenue last month. The store sold 5 more used books than new books, and twice as many magazines as new books. Using substitution method, how many magazines, new books, and old books did ABC bookstore sell?
Answer:
The number of new books sold = 10
The number of used books sold (u) = 15
The number of magazines sold (m) = 20
Step-by-step explanation:
Let us assume the number of new books = n
So, the number of used books sold (u) = New books sold + 5 = n + 5
Also, the number of magazines sold (m) = 2 x ( Number of new books sold)
= 2 n
⇒ u = n + 5, m = 2 n
Here, the cost of each new book n- = $12
So, the cost of n new books = n x ($12) = 12 n
the cost of each used book u = $8
So, the cost of u = (n+ 5) used books = n+5 x ($8) = 8 n + 40
the cost of each magazine m = $5
So, the cost of m = (2n ) magazines = 2n x ($5) = 10 n
Also, total earnings = $340
⇒ 12 n + 8n +40 + 10 n = 340
or, 30 n = 300
or,n = 300/30 = 10
Hence the number of new books sold = n = 10
The number of used books sold (u) = n + 5 = 15
The number of magazines sold = m = 2 n = 20
Answer:
14
Step-by-step explanation:
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Rob is saving to buy a new MP3 player for every $16 he earns babysitting he saved $5 on Saturday rob earned $80 babysitting how much money did he save
Answer:
He saved $25.
Step-by-step explanation:
If Rob saves $5 for every $16 he earns, he is saving the folowing franction of his income: [tex]\frac{5}{16} =0,3125=31,25\%[/tex]. Then if his income equals $16, he will save [tex]\$16\times{0,3125}=\$5[/tex].If his income is $80, he will save [tex]\$80\times{0,3125}=\$25[/tex]Another way to understand this problem would be to think that [tex]\$80=5\times{\$16}[/tex]. Then, receiving $80 is the same as receiving 5 times $16. If he saves $5 for every $16 he receives, he would save 5 times $5 = $25.Shauna is 10 inches shorter than Ryan. Together their heights total 140 inches. How tall is each person?
Answer:
Ryan: 75
Shauna: 65
Step-by-step explanation:
x = ryan's height
x - 10 = shauna's height
x + (x - 10) = 140
2x - 10 = 140
2x = 150
x = 75
Shauna is 65 inches tall and Ryan is 75 inches tall.
Let the height of:
Shauna be represented with s
Ryan be represented with r.
Sum of their heights : s + r = 140
The equation that represents Shauna's height : r - 10
Substitute for Shauna's height in the first equation:
r - 10 + r = 140
Solve for r
2r = 150
r = 75 inches
Substitute for r in the first equation
75 + s = 140
s = 140 - 75
s = 65 inches
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to determine the volume of an irregular piece of silver Jennifer's emergency in a graduated cylinder filled with water and observes the water level rises from 60 cubic centimeters to 80 cubic centimeters
Answer:Here are some more problems to solve.
Calculate the volume of a paperback book with the following dimensions:
Length = 12 cm
Width = 3 cm
Height = 20 cm
Calculate the volume of a steel bar with the following dimensions:
Length = 5 cm
Width = 2 cm
Height = 30 cm
Now determine the density of the steel bar if its mass is 2.34 kg. (Hint: Convert to grams first.)
A cork has a volume of 5.0 cm3 and a mass of 1.2 grams. Calculate its density.
Water has a density of 1 g/cm3. If you placed a cork and a steel paper clip in a jar of water, what do you think would happen? Use your knowledge of density to explain the outcome.
Step-by-step explanation:
If a binomial event has a probability of success of 0.8, how many successes
would you expect out of 6000 trials?
A.4800
B.3600
C.2400
D.1200
Answer:
A) Out of 6,000 trials, one can expect 4800 successes.
Step-by-step explanation:
Here, the total number of trials = 6,000
The probability of winning each trial = 0.8
Now, as we know in a BINOMIAL EVENT:
q = n x p
⇒ The number of success out of 6,000 trials
= 6,000 x (0.8) = 4800
Hence, out of 6,000 trials, one can expect 4800 successes.
Please answer this correctly
Is the answer
5:15pm
6:03am
2:15pm
7:03am
Answer:
2:15 PM
Step-by-step explanation:
When the plane arrives in Seattle, the time in eastern time period would be 5:15 PM. From eastern to pacific, the time goes back 3 hours. 5:15 - 3 hours is 2:15. Since the time is still in the afternoon, it is still PM.
Answer:
2:15pm
Step-by-step explanation:
1) Take 1:09pm and add 4 hours and 6 mins to the time
2) 1 hour and 9 minutes + 4 hours and 6 minutes = 5:15pm (in eastern time)
3) Subtract 3 hours from 5 hours and 15 minutes. This equals 2:15pm
This would be the answer because of the time zone change.
A tree shadow is 95 cm long. At the same time of the day Samantha stands next to the tree in measures her shadow to be 30 cm long. Samantha is 150 cm tall. What is the height of tree in centimeters
The height of tree is 475cm.
Step-by-step explanation:
Given,
Shadow of Samantha = 30cm
Actual height of Samantha = 150cm
Ratio of Shadow to actual height of Samantha = 30:150
Shadow of tree = 95cm
Actual height of tree = x
Ratio of shadow to actual height of tree = 95:x
Using proportion,
Ratio of Shadow to actual height of Samantha :: Ratio of shadow to actual height of tree
[tex]30:150::95:x\\[/tex]
Product of mean = Product of extreme
[tex]150*95=30*x\\14250=30x\\30x=14250\\[/tex]
Dividing both sides by 30;
[tex]\frac{30x}{30}={14250}{30}\\x=475\\[/tex]
The height of tree is 475cm.
Keywords: ratio, proportion
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To find the height of the tree, set up a proportion: 150 cm / 30 cm = x / 95 cm. Solving for x, the height of the tree is 475 cm.
Explanation:To find the height of the tree, we can set up a proportion using the lengths of the shadows. Let x represent the height of the tree. The proportion would be:
150 cm / 30 cm = x / 95 cm
Cross-multiplying and solving for x, we get:
x = (150 cm times 95 cm) / 30 cm = 475 cm
Therefore, the height of the tree is 475 cm.
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Help I’m stuck in algebra 2
Answer:
1. 81
2. 43
3. 14
4. 32
5. 216
6. 6,7760.25
Hope it's helpful ;)
help help help help
Answer:
The correct answer is Helena
Kristina used synthetic division to divide the polynomial f(x) by x−2, as shown on the table. What is the value of f(2)? −14 −11 −2 −1 A synthetic division setup with respective columns containing the following numbers column 1 containing two as a divisor, column 2 containing negative 1, blank and negative 1, column 3 containing negative 5, negative 2, negative 7, and column 4 containing three, negative 14, negative 11.There is a line above the numbers negative 1, negative 7 and negative 11.
Answer:
-11
Step-by-step explanation:
The answer to the first one sould be -11
2x^3 +5x^2−x−6
Write 5x^2 as 4x^2 + x^2......and we have.....
2x^3 + 4x^2 + x^2 - x - 6
2x^2 ( x + 2) + ( x + 2)(x - 3)
(x + 2) [ 2x^2 + x - 3]
(x + 2) (2x +3) (x - 1)
x^3−4x^2−3x+18 = 0
Using some synthetic division, we have
3 [ 1 - 4 -3 18 ]
3 -3 -18
_______________
1 -1 -6 0
The remaining polynomial is x^2 - x - 6 which factors as (x - 3) ( x + 2)
So .... the factored form is (x - 3) ( x - 3) ( x + 2) = ( x + 2) ( x - 3)^2 = 0
Answer:
-11 is correct for all future users.
Step-by-step explanation:
the probability against drawing the ace of diamonds from a standard deck of 52 cards?
89%?
93%?
98%?
96%?
Answer:
98%
Step-by-step explanation:
There is 1 ace of diamonds. So the probability of drawing any other card is 51/52 ≈ 98%.
Answer:
98 percent
Step-by-step explanation:
since drawing a ace of diamonds out of the deck is 1/52 not drawing it is a 51/52 which is about 98 percent
how much of the circle is shaded 1/3+2/7
Final answer:
To find out how much of the circle is shaded by adding 1/3 and 2/7, we determine the least common denominator, convert each fraction, and then add the numerators. The shaded area of the circle is 13/21.
Explanation:
The student asked how much of the circle is shaded if you add the fractions 1/3 and 2/7. To find this, we need to calculate the sum of these two fractions. Since 1/3 is less than 1/2 and 2/7 is also less than 1/2, their combined value must be less than 1. To add fractions, you need a common denominator. The least common multiple of 3 and 7 is 21, so we will convert each fraction to have a denominator of 21:
1/3 becomes 7/21,2/7 becomes 6/21.Now, we add the numerators while keeping the denominator the same:
7/21 + 6/21 = 13/21.
This represents the shaded area of the circle in fraction form. Therefore, 13/21 of the circle is shaded.
what is 9c+90<-27?????
========================================
Work Shown:
9c + 90 < -27
9c + 90 - 90 < -27 - 90 .... see note 1
9c < -117
9c/9 < -117/9 ... see note 2
c < -13
-----------
note 1: I'm subtracting 90 from both sides to undo the "plus 90" that is happening on the left side
note 2: I divided both sides by 9 to undo the multiplication. The expression 9c is the same as 9*c or "9 times c". The inequality sign will not flip as we are dividing both sides by a positive number.
Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 9, 10, 11, 12, ...
Answer:
[tex]T_n= 9+(n-1)[/tex]
Step-by-step explanation:
The Given sequence is 9, 10, 11, 12
We need to find the expression to describe the sequence.
Let [tex]T_n[/tex] be the [tex]n^{th}[/tex] term of the sequence.
Let n represent the position of the term.
Let a be the first term in the sequence.
and d be the common difference between the sequence
Hence the expression to find the above sequence is given below;
[tex]T_n= a+(n-1)d[/tex]
when n=1 d= 1 a = 9
[tex]T_1 = 9+(1-1)1 = 9 + 0 = 9[/tex]
when n=2 d= 1 a = 9
[tex]T_2 = 9+(2-1)1 = 9 + 1 = 10[/tex]
when n=3 d= 1 a = 9
[tex]T_3 = 9+(3-1)1 = 9 + 2 = 11[/tex]
when n=3 d= 1 a = 9
[tex]T_4 = 9+(4-1)1 = 9 + 3 = 12[/tex]
Hence the expression is [tex]T_n= 9+(n-1)[/tex]
The expression to describe the sequence 9, 10, 11, 12, ... is 8 + n, with n representing the position of the term in the sequence.
The sequence given is 9, 10, 11, 12, ..., which is an arithmetic sequence where each term increases by 1 from the previous term. To write an expression that represents the nth term of this sequence using n to represent the position of the term (with n = 1 for the first term), we need to find a formula that calculates the value of each term based on its position.
The first term of the sequence is 9 when n = 1. The second term is 9 + 1, and the third term is 9 + 2, and so on. Generalizing this, the nth term can be written as the first term value (9) plus the number of terms after the first one, which is (n - 1), since for the first term, n - 1 equals 0. Therefore, the final expression is:
9 + (n - 1)
We can simplify this expression as: 8 + n
This expression will give us the value of each term in the sequence based on its position n.
What are the roots of the polynomial equation x cubed minus 5 x + 5 = 2 x squared minus 5?
To find the roots of the polynomial equation x^3 - 5x + 5 = 2x^2 - 5, rearrange the equation to equal zero and use methods such as synthetic division or factoring to solve the cubic equation.
Explanation:To find the roots of the polynomial equation x3 - 5x + 5 = 2x2 - 5, we need to set the equation equal to zero and rearrange it:
x3 - 2x2 - 5x + 5 + 5 = 0
x3 - 2x2 - 5x + 10 = 0
Now, we can use various methods to solve this cubic equation, such as synthetic division, factoring, or using a graphing calculator. On finding the roots of the equation, we can determine the values of x.
Two whole Numbers A and B satisfy the following conditions find A and B A-B=18
Answer:
The Whole numbers that satisfies the condition A - B = 18 is
A = 25
B= 7
Step-by-step explanation:
Whole number:
Whole numbers are positive numbers, including zero, without any decimal or fractional parts.
They are numbers that represent whole things without pieces.
The set of whole numbers is represented mathematically by the set: {0, 1, 2, 3, 4, 5...}
so there are many answers to this question which satisfies A- B = 18
Few are given below
A = 19 and B = 1 ∴ 19 - 1 = 18
A = 20 and B = 2 ∴ 20 - 2 = 18
A = 18 and B =0 ∴ 18 - 0 = 18
A = 39 and B = 21 ∴ 39 - 21 = 18
A = 25 and B= 7 ∴ 25 - 7 = 18
i.e A should be always greater than B to satisfy A- B = 18 condition.
What’s the answer for 1/2x-9=-25
Answer:
-32
Step-by-step explanation:
1/2x-9=-25
1/2x= -25+9
1/2x=-16 /multiply 2
x=-32
[tex]\text{Hello there!}\\\\\text{Solve:}\\\\\frac{1}{2}x-9=-25\\\\\text{Add 9 to both sides}\\\\\frac{1}{2}x=-16\\\\\text{Divide both sides by 1/2 or 0.5}\\\\\boxed{x=-32}[/tex]
JobFind charges employers x dollars to post a job on their website. They offer a 16%
discount if 20 or more jobs are posted. If 31 jobs are posted by a specific employer,
express the discount as a percent.
Answer:
[tex](31x)\times 16\%[/tex]
Step-by-step explanation:
Given: Discount offered is 16% on 20 or more job posting.
x dollars is charged on every job posting on website.
Now, lets find the discount on 31 job posting.
∴ Total cost on 31 job posting = [tex]\textrm{charges for one job posting}\times \textrm{Total number of job posting}[/tex]
⇒ Total cost on 31 job posting= [tex]x\times 31= \$ 31x[/tex]
As we know 16% discount been offered for 20 or more job posting
∴ Discount offered on 31 job posting = [tex]31x\times 16\%[/tex]
Discount offered by JobFind to the employer is [tex](31x)\times 16\%[/tex]
Final answer:
The discount percentage for posting 31 jobs on JobFind is 16%, which remains constant as it meets the criteria of posting 20 or more jobs.
Explanation:
To express the discount as a percent for an employer posting 31 jobs on JobFind, we need to calculate the percentage reduction based on the original price. Since 31 jobs qualify for a 16% discount, the calculation is straightforward.
Given:
The original discount offered is 16% for 20 or more jobs.
The number of jobs being posted is 31, which exceeds the 20 job threshold.
Hence, the discount percentage for 31 jobs remains the same as the original discount percentage, which is: 16%.
No further calculations are necessary because the question simply asks to express the given discount, not to calculate the total discounted amount or savings.
the area of a rectangle is 90 in2^. the ratio of the length to the width is 5:2. find the length and the width
Length and width of rectangle is 15 inches and 6 inches respectively
Solution:Given that area of a rectangle is 90 square inch
Ratio of length to the width = 5: 2.
Need to determine length and width of rectangle.
As ratio of length to the width is 5 : 2
Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.
The formula for area of rectangle is given as:
[tex]\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}[/tex]
Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:
[tex]\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}[/tex]
On solving the above expression for x we get
[tex]\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}[/tex]
[tex]\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}[/tex]
Hence length and width of rectangle is 15 inches and 6 inches.