Answer:
Length of longest piece is 82 ft
Step-by-step explanation:
Let the measure of the second piece be x
First piece be y
second piece is 6 ft less than 3 times the first
x = 3y - 6
y = (x + 6)/3
3rd piece = 2 + 2/3 * x
= 2 + 2x/3
Adding all equals 168
we only add in terms of x
so we have;
x + (x + 6)/3 + 2 + 2x/3 = 168
Multiply through by 3
3x + x + 6 + 6 + 2x = 504
6x + 12 = 504
6x = 492
x = 492/6
x = 82 ft
So the other pieces are
(x + 6)/3 = 82+6/3 = 88/3 ft
And lastly
2 + 2x/3
= 2 + 164/3 ft
what is the percent increase im 13 to 14, round to the nearest percent
please hurry
Answer:
20 percent
Step-by-step explanation:
What is the answer for 3(x+5)=5x+7
Answer:
4 = x
Step-by-step explanation:
First, distribute the 3 to the x and 5.
3x + 15 = 5x + 7
Now, subtract 3x from both sides and 7 from both sides.
8 = 2x
Now, divide by 2 on both sides.
4 = x
#teamtrees #WAP (Water And Plant)
6x⁴+5x³-10x+4 how to factorize this polynomial
Yes, this is polynomial, and your answer will be:
(2x − 1) (3x − 2) (x^2 + 2x + 2)
Edit:
Factor 6x^4 + 5x^3 − 10x + 4 using the rational roots test.
(2x − 1) (3x^3 + 4x^2 + 2x − 4)
Factor 3x^3 + 4x^2 + 2x − 4 using the rational roots test.
(2x − 1) (3x − 2) (x2 + 2x + 2)
The factorized form of the given polynomial is (2x − 1)(3x − 2)(x² + 2x + 2).
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The polynomial is given in the question, as follows:
6x⁴ + 5x³ − 10x + 4
We have to factor using the rational roots test,
⇒ (2x − 1)(3x³ + 4x² + 2x − 4)
Similarly, factor 3x³ + 4x² + 2x − 4 operates the rational roots test.
⇒ (2x − 1)(3x − 2)(x² + 2x + 2)
Thus, the factorized form is (2x − 1)(3x − 2)(x² + 2x + 2).
Learn more about the polynomial here:
brainly.com/question/11536910
#SPJ2
what is the 7th term of the geometric sequence below? 7,-14,28,-56
Answer:
The 7th term of given sequence is: 448
Step-by-step explanation:
Given sequence is:
7,-14,28,-56
Here
a1 = 7
a2 = -14
a3 = 28
First of all we have to find the common ratio. The common ration is the ratio between two consecutive terms of a geometric sequence and is same for all consecutive terms of a geometric sequence.
So,
[tex]r = \frac{a_2}{a_1} = \frac{-14}{7} = -2\\r = \frac{a_3}{a_2} = \frac{28}{-14} = -2\\[/tex]
The common ratio is -2.
The general formula for geometric sequence is given as:
[tex]a_n = a_1r^{(n-1)}[/tex]
Putting values
[tex]a_n = 7.(-2)^{n-1}[/tex]
For 7th term, putting n=7
[tex]a_7 = 7*(-2)^{7-1}\\= 7 * (-2)^6\\= 7 *64\\= 448[/tex]
Hence,
The 7th term of given sequence is: 448
Answer:
A
Step-by-step explanation:
Name how the triangles are congruent in this image
A contractor bought 6.4 ftof sheet metal. She has used 3.7 ft2 so far and has $43.20 worth of
sheet metal remaining. The equation 6.4x - 3.7x = 43.2 represents how much sheet metal is
remaining and the cost of the remaining amount. How much does sheet metal cost per square
foot?
Sheet metal costs $
per square foot.
-need help ASAP- please and thank you
Answer:
$16
Step-by-step explanation:
To find the cost per square foot we have to solve the given equation for x:
6.4x - 3.7x = 43.2
2.7x = 43.2
Divide both sides of the equation by 2.7 to isolate the x:
2.7x/2.7 = 43.2/2.7
x = 16
The sheet metal costs $16 per square foot.
Hope this helps :)
help plz idk okhehehehehe
can somone help me pls ?
[tex]\huge\mathtt{Hello!}[/tex]
[tex](6x - 23) = (4x + 9)[/tex]
[tex]6x -4x = 9 + 23[/tex]
[tex]2x = 32[/tex]
[tex]x = 16[/tex]
It is because the sides are equal, so the angles opposite to them also are equal.
Have a nice day!
Rosa purchaded a sofa that was on sale for 20% off. The sofa cost $ 1850. How much does the Sofa cost?
Answer:
Step-by-step explanation:
370
Arthur is playing a television game show. He starts with 0
points. Arthur answers questions with the following point
values: 30, -20, 10, -20, 60, -100
What is the point value of a question Arthur can answer so
that he has 0 points again
A. -60
B. -40
C. 40
D. 60
Answer: -40
Step-by-step explanation:
1. 30 -20 = 10
2. 10 + 10 = 20
3. 20 - 20 = 0
4. 0 + 60 = 60
5. 60 - 100 = -40
a drink recipe calls for lemon juice and apple juice. the equation below represents the proportional relationship between the cups of lemon juice (L) and apple juice (a) in the recipe.
Answer: ima newbie
Step-by-step explanation:
Always include the steps and/or background required to get to the final answer. Let’s help other people understand and solve future problems on their own. Show all the calculation if it is a numerical question.
lupita and kevin walk to school.lupita walks 3/5 mi.kevin walks 0.65 mi.who walks a greater distance to school?how much greater?
Answer:
0.05
Step-by-step explana
Find the 15th term in the arithmetic sequence 7, 10, 13, 16, 19,... Question 4 options: 49 42 35 52
Answer:
49
Step-by-step explanation:
first you find the difference between the first two numbers so we do 10-7=3, then plug in 3 for the next 2 numbers 10+3=13, so we know our rule is +3 so now we do 3*14=42 then we do 7+42=49
621000 in scientific notation
Answer:
the correct answer is 6.21×10^5
Answer:
6.21 x 10^5
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
estimate the solution to the system of equations
omg, I just said the answer was B.
Johnny took a math test with 25 questions He answered 22 questions correctly in order to get an a he had to get 90% of them right. On the same exam Johnny's friend Jessie answered 4 times more questions correct than incorrect. Who got a higher percentage on the test. Johnny or Jessie?
Answer:
Jessie
Step-by-step explanation:
Jessie answered 4 more times correct that Johnny so she will get a better grade.
Jeremiah uses
1/3
cups of veggies for every
1/5
cup of dip when making a snack mix. Enter the number of cups of veggies Jeremiah uses for 1 cup of dip.
1 and 2/3 cups of veggies
Which answer shows 8.45x 104 written in standard form?
.0000845
8,450
Ο Ο Ο Ο
84,500
Ο 8,450,000
in un rombo l'area e' di 234,95c2 , mentre l'altezza misura 12,7cm
Answer:
la diagonale più lunga dovrebbe essere 37cm.
Step-by-step explanation:
Se cerchi la diagonale più lunga la formula dovrebbe essere questa:
A=p*(q/2)
234,95 = 12,7*(x/2)
234,95/12,7 = x/2
18,5 = x/2
18,5*2 = x
37 = x
Write the given trinomial if possible as a square of a binomial or as an expression opposite to a square of a binomial: 15ab-9a^2-6 1/4b^2
Answer:
[tex] - \bigg(3a - \frac{5}{2} b) \bigg)^{2} [/tex]
Step-by-step explanation:
[tex]15ab-9a^2-6 \frac{1}{4} b^2 \\ \\ = 15ab-(3a)^2-\frac{6 \times 4 + 1}{4} b^2 \\ \\ = 15ab-(3a)^2-\frac{24+ 1}{4} b^2 \\ \\ = 15ab-(3a)^2-\frac{25}{4} b^2 \\ \\ = 15ab- (3a)^2- \bigg(\frac{5}{2} b \bigg)^2 \\ \\ = - \{ - 15ab + (3a)^2 + \bigg(\frac{5}{2} b \bigg)^2 \} \\ \\ = - \{ (3a)^2 + \bigg(\frac{5}{2} b \bigg)^2 - 15ab \} \\ \\ = - \bigg(3a - \frac{5}{2} b \bigg)^{2} [/tex]
82 added to a number is the same as 36
Answer:
-46
Step-by-step explanation:
Find the Lcm of 9,12 and 24
Answer:
144
Step-by-step explanation:
Avni designs a game in which a player either wins or loses 4 points during each turn. Which equation represents all numbers of points, p, a player may have after his or her first turn of the game? A. p = 4 B. p = –4 C. |p| = 4 D. |p| = –4
Answer:
C |p| = 4
Step-by-step explanation:
If a player wins 4points during each turn, then, the total points will be +4points
If the player looses 4points, total points lost will be -4points
The total number of point p the player can have will be represented as;
|p| = 4 (since is both positive and negative 4 )
Note that the nodulus of a variable will return both positive and negative value of that variable
rationalise the denominator and simplify
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Step-by-step explanation:
[tex] \bf \underline{Given-} \\ [/tex]
[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ [/tex]
[tex] \bf \underline{What\: to\: do-} \\ [/tex]
To rationalise the denominator
[tex] \bf \underline{Solution-} \\ [/tex]
[tex]\textsf{We have,}[/tex]
[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ [/tex]
[tex]\textsf{The denominator is 5+2√3. Multiplying the numerator and denominator by 7-4√3,}\\[/tex]
[tex]\textsf{we get,}\\[/tex]
[tex] ⟹\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \\ [/tex]
[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 + 4 \sqrt{3} )(7 - 4 \sqrt{3}) } \\ \\ [/tex]
[tex]\textsf{⬤ Applying Algebraic Identity
(a+b)(a-b) = a² - b² to the denominator}\\[/tex]
[tex]\textsf{We get,}\\[/tex]
[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 {)}^{2} - (4 \sqrt{3} {)}^{2} } \\ \\ [/tex]
[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 8 \sqrt{3 \times 3} }{49 - 48} \\ \\ [/tex]
[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 24 }{1} \\ \\ [/tex]
[tex]⟹(35 - 24) - 6 \sqrt{3} \\ \\ [/tex]
[tex]⟹11 - 6 \sqrt{3} \: \: \: \tt \red{ Ans}. \\ \\ [/tex]
[tex] \bf \underline{Hence \:the \:denominator\: is\: rationalised.}\\[/tex]
An industrial factory makes / yards of chain every minute. The cost of each yard of chain is $2.00. What is the total cost for all chain produced in 10 minutes?
Answer:
Cost = $86.67
Step-by-step explanation:
Given
Yards = 4⅓ (missing part of the question)
Cost per yard = $2.00
Required
Determine cost of chains produced in 10 minutes
If 4⅓ yards is made in a minute, then
4⅓ * 10 yards are made in 10 minutes
Total = 4⅓ * 10
Total = 13/3 * 10
Total = 130/3 yards
Cost of a yard of chain is $2.00.
Cost of 130/3 yards would be:
Cost = $2.00 * 130/3
Cost = $260.00/3
Cost = $86.67 (approximated)
Hence, the required cost is approximately $86.67
Does anyone know ?!!!
Answer:
72 square units
Step-by-step explanation:
area of a paralellogram = bh
Base = 6
Height = 12
6 x 12 = 72 square units
Is ABC a right angle? Why or why not?
Answer:
3.Yes, because triangle ABC has a 90 degree angle.
4.No, because triangle XYZ doesn’t have a 90 degree angle.
Determine the remaining sides and angles of the triangle ABC
what is the measure of angle B
what is the length of side a
what is the length of side b
Answer:
The measure of angle B is 41.5°
The length of side a is 30.6 feet ⇒ to the nearest tenth
The length of side b is 32.9 feet ⇒ to the nearest tenth
Step-by-step explanation:
The sum of the measures of the interior angles in a triangle is 180°In the given Δ ABC
∵ m∠A = 38.1°
∵ m∠C = 100.4°
→ By using the fact above
∵ m∠A + m∠B + m∠C = 180°
∴ 38.1 + m∠B + 100.4 = 180
→ Add the like terms in the left side
∴ 138.5 + m∠B = 180
→ Subtract 138.5 from both sides
∴ m∠B = 41.5°
∴ The measure of angle B is 41.5°
∵ a is the opposite side of ∠A
∵ b is the opposite side of ∠B
∵ c is the opposite side of ∠C
→ By using the sine rule
∴ [tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
∵ c = 48.4 ft, m∠A = 38.1°, m∠B = 41.5°, and m∠C = 100.4
→ Substitute them in the sine rule above
∴ [tex]\frac{a}{sin38.1}[/tex] = [tex]\frac{b}{sin41.5}[/tex] = [tex]\frac{48.4}{sin100.4}[/tex]
→ By using cross multiplication between the 1st and the 3rd fractions
∴ a × sin 100.4 = 48.8 × sin 38.1
→ Divide both sides by sin 100.4
∴ a = 30.61429861
∴ The length of side a is 30.6 feet ⇒ to the nearest tenth
→ By using cross multiplication between the 2nd and the 3rd fractions
∴ b × sin 100.4 = 48.8 × sin 41.5
→ Divide both sides by sin 100.4
∴ b = 32.87596206
∴ The length of side b is 32.9 feet ⇒ to the nearest tenth
Evaluate the expression.
1.2 exponent 2
answer choices =
1.44
14.4
1.728
1.5
Answer:
1.44
Step-by-step explanation:
Answer:
the answer is 1.44
Step-by-step explanation:
Because the exponent of a number says how many times to use the number in a multiplication. In 1.2 exponent 2 the "2" says to use 1.2 twice in a multiplication, so 1.2'2 = 1.2 × 1.2 = 1.44 In words: 1.2'2 could be called "1.2 to the power 2" or "1.2 to the second power.
Your welcome
The original price of a desk was $80. And its price was marked
down to $70 during the holiday. What was the percentage of
discount for the desk during the holiday?
Answer:
Required Answer:-Amount of discount =80-70=10$
percentage:-
[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac{10}{80}}\times 100 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {10}{4}}5 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {50}{4}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 12.5\% [/tex]
Answer: the answer is 12.5
Step-by-step explanation: