Answer:
Two solutions were found :
x = 6
x = -1
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(3x2 - 15x) - 18 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
3x2 - 15x - 18 = 3 • (x2 - 5x - 6)
Trying to factor by splitting the middle term
3.2 Factoring x2 - 5x - 6
The first term is, x2 its coefficient is 1 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 1 • -6 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .
-6 + 1 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1
x2 - 6x + 1x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-6)
Add up the last 2 terms, pulling out common factors :
1 • (x-6)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-6)
Which is the desired factorization
Equation at the end of step 3 :
3 • (x + 1) • (x - 6) = 0
In Conclusion, the answer would be 0.
A cable television provider offers six
different news stations. If 25% of the
stations offered are news, how many
stations are offered by the provider?
Answer:
24 stations
Step-by-step explanation:
we know that
six stations represent 25% of the stations offered
so
using a proportion
Find out how many stations represent a percentage of 100%
[tex]\frac{6}{25\%}=\frac{x}{100\%}\\\\x=6(100)/25\\\\x=24\ stations[/tex]
What is the volume of the pyramid?
km
Answer:
V=lwh/3
Step-by-step explanation:
Can someone please help me answer this?
KNOWLEDGE CHECK: ALEKS
The value of x that satisfies the equation 41 - x = 157 is x = -116.
To solve for x in the equation 41 - x = 157, we need to isolate x on one side of the equation.
Let's go step by step:
Step 1: Start with the given equation.
41 - x = 157
Step 2: Get rid of the constant term on the left side (41) by subtracting it from both sides of the equation.
(41 - x) - 41 = 157 - 41
Simplifying the left side:
41 - 41 - x = 157 - 41
0 - x = 116
Step 3: We have -x on the left side, and we want to solve for x, so we need to get rid of the negative sign in front of x.
To do that, we can multiply both sides of the equation by -1.
When we multiply a number by -1, the sign changes.
(-1) * (-x) = (-1) * 116
Simplifying the left side:
x = -116
Step 4: Now we have found the value of x, which is x = -116.
To verify our solution, we can substitute the value of x back into the original equation and see if it holds true:
41 - (-116) = 157
Simplifying:
41 + 116 = 157
157 = 157
Since both sides of the equation are equal after simplification, our solution x = -116 is correct.
Therefore, the value of x that satisfies the equation 41 - x = 157 is x = -116.
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how do i find the area of this stop sign using subtraction?
Answer:
745.12
Step-by-step explanation:
30 x 30 = 900 which is the sign if it were a square
then you subtract the four corner pieces
900 - 4([tex]\frac{1}{2}[/tex](8.8 x 8.8))
900 - 2(77.44)
900 - 154.88
= 745.12
6. Use the image below to find the missing value.
Using the segment addition postulate, find the value of m.
AB = 4m - 15
BC = Sm - 6
AC = 15
Option C:
The value of m is 4.
Solution:
Given data:
AB = 4m – 15
BC = 5m –6
AC = 15
To find the value of m:
Using segment addition postulate,
AB + BC = AC
4m – 15 + 5m –6 = 15
Arrange the like terms together.
4m + 5m – 15 – 6 = 15
9m – 21 = 15
Add 21 on both sides of the equation,
9m = 36
Divide by 9 on both sides of the equation.
m = 4
The value of m is 4.
Option C is the correct answer.
Answer:
is 4
Step-by-step explanation:
i got it right on the test
In ΔGHI, the measure of ∠I=90°, the measure of ∠G=21°, and GH = 31 feet. Find the length of IG to the nearest tenth of a foot.
Answer:
[tex]IG=28.9\ ft[/tex]
Step-by-step explanation:
we know that
In the right triangle GHI
[tex]cos(G)=\frac{IG}{GH}[/tex] ----> by CAH )adjacent side divided by the hypotenuse)
substitute the given values
[tex]cos(21^o)=\frac{IG}{31}[/tex]
solve for IG
[tex]IG=cos(21^o)(31)=28.9\ ft[/tex]
see the attached figure to better understand the problem
Answer:
24.6
Step-by-step explanation:
Which property is demonstrated in the equation 4×7×3 = 7×4×3
A)Symmetric
B)associative
C)property of zero
D)cummutative
Answer:
B) associative
Step-by-step explanation:
The associative property of multiplication says you can choose which pair of numbers to multiply first, so when every operation is multiplication, you can move parentheses without changing the answer.
The given equation 4×7×3 = 7×4×3 demonstrates the Commutative Property. This is the property which states that the order in which numbers are multiplied or added does not affect the result.
Explanation:The equation 4×7×3 = 7×4×3 demonstrates the Commutative Property. In mathematics, the Commutative Property refers to the fact that the order in which numbers are multiplied does not change the result of the multiplication. This is why we can rearrange the factors 4, 7, and 3 in any order and still get the same product.
For instance, we can express the commutative property of multiplication as a×b = b×a. So, in your example, the equation 4×7×3 = 7×4×3, is an application of this principle as you are simply rearranging the order of numbers being multiplied.
Please remember that this rule applies only to addition and multiplication, not subtraction or division.
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I need help please and can you explain
ANSWER ASAP!!!!
The app uses 2^28 bytes.
Step-by-step explanation:
Step 1: Given total storage used by the app = 4^4 Megabytes. Also, 1 MB = 2^20 bytes. Find total storage used by app in bytes.⇒ 4^4 × 2^20 = (2²)^4 × 2^20 = 2^8 × 2^20
= 2^8+20
= 2^28 bytes (using the law of exponents a^m × a^n = a^m+n)
Answer these 2 questions and you get 15 points
Question 1: Option B: [tex]\frac{10}{14}=\frac{5}{7}[/tex]
Question 2: Option C: [tex]\frac{12}{18}=\frac{4}{6}[/tex]
Solution:
Question 1:
Given ratio is [tex]\frac{10}{14}[/tex].
To find the equivalent ratio of [tex]\frac{10}{14}[/tex].
10 and 14 have the common factor 2.
So divide both numerator and denominator by the common factor 2.
[tex]$\frac{10}{14}=\frac{10\div2}{14\div 2}[/tex]
[tex]$=\frac{5}{7}[/tex]
[tex]$\frac{10}{14}=\frac{5}{7}[/tex]
Hence option B is the correct answer.
Question 2:
Given ratio is [tex]\frac{10}{14}[/tex].
To find the equivalent ratio of [tex]\frac{12}{18}[/tex].
12 and 18 have the common factor 3.
So divide both numerator and denominator by the common factor 3.
[tex]$\frac{12}{18}=\frac{12\div3}{18\div 3}[/tex]
[tex]$=\frac{4}{6}[/tex]
[tex]$\frac{12}{18}=\frac{4}{6}[/tex]
Hence option C is the correct answer.
A trapezoid was made by joining a pentagon and a triangle. the dimensions of the trapezoid are- height: 1 feet, bases 1/2 feet and 1 1/2 feet. the dimensions of the triangle are- height: 1/2 feet, base 1/2 feet. what is the area of the pentagon
Answer
3
Step-by-step explanation:
the formulas say it
If 8x - 4 = 6x - 10, find the value of 5x
Answer:
5x=-15
Step-by-step explanation:
8x-6x=4-10
2x=-6
x=-3
5x=-15
What is the decimal equivalent of the rational number -1/8
Answer:
-0.125
Step-by-step explanation:
To find the decimal version of the fraction, divide using a calculator or long division.
-1 / 8 = -0.125
Best of Luck!
Evaluate 60 • x-60 · 15, when x=8.
Step 1 60• x-60 • 15 = 60(x - 15)
Step 2
Step 3
= 480 – 15
Step 4
465
Where is the error
Answer:
The right answer is, -420
Step-by-step explanation:
Because we use common factor:
60 (x - 15)
We multiply for each term:
60 (x) - 60 (15)
60 (8) - 60 (15)
We solve:
480 - 900 = -420
You need 2 gallons of juice for every 12 people attending the open house. How many gallons of juice would be needed for 156 people?
Answer:
26 gallons of juice
Step-by-step explanation:
156/12 = 13
13x2=26
Answer: 26 gallons
Step-by-step explanation:
2 gallons for every 12 people so you want to do 156 divided by 12 which would be 13. That shows that there are 13 times more people than there were before. You would then multiply 2 by 13 which would give you 26 gallons of juice.
Spinning Spinner 1st Simulation Colors Tally red 14 yellow 6 green 19 blue 1 2nd Simulation Colors Tally red 24 yellow 17 green 28 blue 11 3rd Simulation Colors Tally red 26 yellow 24 green 32 blue 38 Jill conducted three simulations of spinning a fair spinner (four sections of different colors--red, blue, yellow, green). The first simulation consisted of 40 spins, the second simulation consisted of 80 spins and the third simulation consisted of 120 spins. The results were recorded in the tables shown. Do the results for the green section follow the law of large numbers? Why or why not? A) no, because the probability of green is the same for each of the simulations. B) yes, because the probability of green is different for each of the simulations. C) no, because with each simulation, as the number of trials increase, the probabilities vary greatly and do not approach the theoretical probability of 1 4 . Eliminate D) yes, because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of 1 4 .
Answer: D
Step-by-step explanation: yes, because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of
1/4.
The answer is D
Step-by-step explanation:
because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of
1
4
. The law of large numbers indicates that if an event of probability p is observed repeatedly during independent repetitions, the ratio of the observed frequency of that event to the total number of repetitions approaches p as the number of repetitions becomes arbitrarily large.
7 + 7x; 7(x+1)
Are these equivalent?
TRUE or FALSE?
Answer:
I believe it would be true
(2x^3+4x^2-3)+(6x^3+4x-4)
Answer:
8x^3 + 4x^2 + 4x -7
Step-by-step explanation:
Add like terms.
Answer: everything is explained in the picture
Step-by-step explanation:
The lid of a jewelry box is in the shape of a triangular prism. The lid has a height of 10 inches. The triangular base of the lid has a base of 6 1/2 inches and a height of 3 1/2 inches. What is the volume of the lid to the nearest tenth?
The volume of the lid is approximately 113.8 cubic inches.
Explanation:The volume of the lid can be found by multiplying the area of the triangular base by the height of the lid. The area of a triangle can be found by using the formula: Area = (base x height) / 2. In this case, the base is 6 1/2 inches and the height is 3 1/2 inches. Plugging these values into the formula, we get: Area = (6.5 x 3.5) / 2 = 11.375 square inches. Now, to find the volume of the lid, we multiply the area by the height: Volume = 11.375 x 10 = 113.75 cubic inches. Rounding to the nearest tenth, the volume of the lid is 113.8 cubic inches.
The volume of the lid is 113.8 cubic inches.
To determine the volume of the lid of the jewelry box, we need to use the formula for the volume of a triangular prism, which is V = (1/2 * base * height of triangular base) * height of the prism.
First, calculate the area of the triangular base:
Base of the triangular base: 6.5 inchesHeight of the triangular base: 3.5 inchesArea = 1/2 * 6.5 inches * 3.5 inches = 11.375 square inchesNext, multiply the area of the triangular base by the height of the prism:
Height of the prism: 10 inchesVolume = 11.375 square inches * 10 inches = 113.75 cubic inchesTherefore, the volume of the lid to the nearest tenth is 113.8 cubic inches.
Use the Pythagorean Theorem to find the missing side. Round your answer to the nearest hundredth.
19 m
52 m
Answer:
55m
Step-by-step explanation:
a²+b²=c²
19 x 19 = 361
52 x 52 = 2704
2704 + 361= 3065
the square root of 3065 is 55.4 so round that to 55.
five friends split the cost of parking at an amusement park. each of them also buys a $30 ticket. Write an algebraic expression that represents the amount of money each friend spends.
Answer: A/5+30*5
Step-by-step explanation:
For every 6 children there is 1 adult so if there’s 66 children how many adults are there?
Answer:
11
Step-by-step explanation:
6 : 1
66 : X
X/66 = 1/6
X = 11
Write a division equation that has the solution x= 16
Answer:
2x ÷ 4 = 8
Step-by-step explanation:
2x ÷ 4 = 8
2x/4 = 8
2x = 32
x = 16
A 23-year-old female buys 25/50/100 liability insurance, collision insurance with a $250 deductible, and comprehensive insurance with a $100 deductible. What is her total annual premium? Use the base premium and rating factor tables used to calculate the annual car insurance premium of a person.
Answer: $1090.80
Step-by-step explanation:
Answer:
$1,090.80
Step-by-step explanation:
Bodily injury; 25/50=$220
Property; 100=$375
Collision deductibles;$250=$185
Comprehensive deductibles;$100=$129
220+375+185+129 = 909
909*1.2=1,090.8
Took the test
Jorge is setting up his tent. He is using two nylon ropes to pull the tent taut and stabilize it at each end. If the tent is 5 feet tall, and Jorge stakes the ropes into the ground 3 feet from the tent, what is the total length of nylon rope he will use, to the nearest tenth of a foot? Show all of your work. PLEASE HELP ME !!!!!!!!!!
Answer: 5.8 ft
Step-by-step explanation:
We can use the Pithagorean Theorem in this problem, in order to find the length of the rope:
[tex]h^{2}=a^{2}+b^{2}[/tex]
Where:
[tex]h[/tex] is the length of the rope (the hypotenuse of the right triangle formed by the height of the tent, the rope and the ground)
[tex]a=5 ft[/tex] is the height of the tent (one of the legs of the right triangle)
[tex]b=3 ft[/tex] is the other leg of the right triangle
Solving the equation with the given data:
[tex]h^{2}=5^{2}+3^{2}[/tex]
Finding [tex]h[/tex]:
[tex]h=\sqrt{(5 ft)^{2}+(3 ft)^{2}}[/tex]
[tex]h=\sqrt{25 ft+9 ft}[/tex]
[tex]h=5.83 ft \approx 5.8 ft[/tex] This is the total length of nylon rope
Find two numbers, if
Their sum is − 1/3 and their difference is 18
Let the two numbers be [tex]x,y[/tex].
We have
[tex]\begin{cases}x+y=-\frac{1}{3}\\x-y=18\end{cases}[/tex]
From the second equation, we derive [tex]x=18+y[/tex]
Plugging this value in the first equation, we have
[tex]18+y+y=-\dfrac{1}{3} \iff 2y=-\dfrac{1}{3}-18\iff 2y=-\dfrac{55}{3} \iff y=-\dfrac{55}{6}[/tex]
And we derive
[tex]x=18+y=18-\dfrac{55}{6}=\dfrac{53}{6}[/tex]
Answer:
The two numbers are: -9.17 and 8.83
Step-by-step explanation:
Let the two numbers represent 'x' and 'y'
Their sum is − 1/3 ==> x + y = -1/3 .................(eqn 1)
Their difference is 18 ==> x − y = 18 ....................(eqn 2)
from equation 2,
x = 18 + y
therefore, substitute for 'x' in (eqn 1) to get y
(18+y) + y = -1/3
18 + 2y = -1/3
2y = -1/3 − 18
2y = -[tex]18\frac{1}{3}[/tex]
2y = - 55/3
y = (-55/3) / 2
y = -55/3 x 1/2
y = -55/6 = -9.17
Substitute for 'y' in either equation
picking (eqn 2)
x − (-9.17) = 18
x + 9.17 = 18
x = 18 − 9.17
x = 8.83
On Saturday, local hamburger shop sold a combined total of 450 hamburgers and cheeseburgers. The number of cheeseburgers old was two times the number of hamburger sold. How many hamburgers were sold on Saturday?
Answer:
There was 150 hamburgers sold on Saturday
Step-by-step explanation:
Step 1: Make an equation
2x + x = 450
Step 2: Solve for x
2x + x = 450
3x / 3 = 450 / 3
x = 150
Answer: There was 150 hamburgers sold on Saturday
Final answer:
The local hamburger shop sold 150 hamburgers on Saturday. This was found by setting up a system of equations where H represents hamburgers and C represents cheeseburgers, and solving for H.
Explanation:
To determine how many hamburgers were sold on Saturday, we can set up a system of equations based on the information given:
Let H represent the number of hamburgers sold.
Let C represent the number of cheeseburgers sold.
We are told that the total number of hamburgers and cheeseburgers sold is 450, so:
H + C = 450
We also know that the number of cheeseburgers sold was two times the number of hamburgers sold, so:
C = 2H
Now we substitute the second equation into the first one to solve for H:
H + 2H = 450
3H = 450
H = 450 / 3
H = 150
Therefore, on Saturday, the local hamburger shop sold 150 hamburgers.
ava bought 6 packages of tulip bulbs and 12 bags of dafodill bulbs for a total of $198 grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs
Answer:
Answer:
Step-by-step explanation:
Let x represent the cost of one package of tulip bulbs.
Let y represent the cost of one bag of daffodil bulbs.
Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. This means that
6x + 12y = 198- - - - - - - - - - - - -1
Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. This means that
14x + 12y = 254- - - - - - - - - - - - 2
Subtracting equation 2 from equation 1, it becomes
- 8x = - 56
x = - 56/-8
x = 7
Substituting x = 7 into equation 1, it becomes
6 × 7 + 12y = 198
42 + 12y = 198
12y = 198 - 42
12y = 156
y = 156/12
y = 13
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Step-by-step explanation:
Answer:
Step-by-step explanation:
Let x represent the cost of one package of tulip bulbs.
Let y represent the cost of one bag of daffodil bulbs.
Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. This means that
6x + 12y = 198- - - - - - - - - - - - -1
Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. This means that
14x + 12y = 254- - - - - - - - - - - - 2
Subtracting equation 2 from equation 1, it becomes
- 8x = - 56
x = - 56/-8
x = 7
Substituting x = 7 into equation 1, it becomes
6 × 7 + 12y = 198
42 + 12y = 198
12y = 198 - 42
12y = 156
y = 156/12
y = 13
4
answers left
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Unlock all verified answers
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Ask your own homework questions
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The length of a rectangle is 2 units more than the width. The area of the rectangle is 48 units. What is the width, in units, of the rectangle?
Final answer:
To find the width of a rectangle when the length is 2 units more than the width and the area is known to be 48 units, you can use algebraic equations to determine the width. In this case, the width of the rectangle is 6 units.
Explanation:
To find the width of the rectangle:
Let x be the width of the rectangle.
Since the length is 2 units more than the width, the length is x + 2.
Given that the area is 48 units, use the formula for the area of a rectangle: width x length = area. Therefore, x(x + 2) = 48.
Solve for x by setting up the equation: x^2 + 2x - 48 = 0.
Factor the quadratic equation: (x + 8)(x - 6) = 0.
Since the width cannot be negative, the width of the rectangle is 6 units.
The width of the rectangle is 6 units.
According to the question, the length is 2 units more than the width, so we can express the length as ( w + 2 ) units.
The area of a rectangle is given by the product of its length and width. Therefore, we can set up the following equation to represent the area of the rectangle:
[tex]\[ \text{Area} = \text{length} \times \text{width} \] \[ 48 = (w + 2) \times w \][/tex]
Expanding the right side of the equation, we get:
[tex]\[ 48 = w^2 + 2w \][/tex]
To find the value of w, we need to solve the quadratic equation. Let's rearrange the equation to set it equal to zero:
[tex]\[ w^2 + 2w - 48 = 0 \][/tex]
Now, we can factor this quadratic equation:
[tex]\[ (w + 8)(w - 6) = 0 \][/tex]
Setting each factor equal to zero gives us two possible solutions for w:
[tex]\[ w + 8 = 0 \quad \text{or} \quad w - 6 = 0 \][/tex]
Solving for w, we get:
[tex]\[ w = -8 \quad \text{or} \quad w = 6 \][/tex]
Since the width of a rectangle cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is:
[tex]\[ w = 6 \text{ units} \][/tex]
The length and width of a rectangle are 4 feet and 3 feet, respectively. A similar rectangle has a length of 10 feet. What is the width of the second rectangle?