Answer:
[tex] \sf \large \: x=7 or x=−3[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
|x+8|=|2x+1|
Solve Absolute Value.
|x+8|=|2x+1|
We know eitherx+8=2x+1orx+8=−(2x+1)
x+8=2x+1(Possibility 1)
x+8−2x=2x+1−2x(Subtract 2x from both sides)
−x+8=1
−x+8−8=1−8(Subtract 8 from both sides)
−x=−7
−x/−1 = −7/−1
(Divide both sides by -1)
x=7
x+8=−(2x+1)(Possibility 2)
x+8=−2x−1(Simplify both sides of the equation)
x+8+2x=−2x−1+2x(Add 2x to both sides)
3x+8=−1
3x+8−8=−1−8(Subtract 8 from both sides)
3x=−9
3x/3 = −9/3
(Divide both sides by 3)
x=−3
Check answers. (Plug them in to make sure they work.)
x=7(Works in original equation)
x=−3(Works in original equation)
Answer:
7
Step-by-step explanation:
x+8=2x+1
Subtract x on both sides. Subtract 1 on both sides
x=7
What is an equation of the line that passes through the point (-4,5) and is perpendicular to the line 4x+y=7?
Answer:
y = [tex]\frac{1}{4}[/tex] x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4x + y = 7 ( subtract 4x from both sides )
y = - 4x + 7 ← in slope- intercept form
with slope m = - 4
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex] , then
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute )- 4, 5 ) into the partial equation
5 = - 1 + c ⇒ c = 5 + 1 = 6
y = [tex]\frac{1}{4}[/tex] x + 6 ← equation of perpendicular line
The length of a white blood cell is approximately 1.4\cdot 10^{-5}1.4⋅10
−5
meter.
The length of a small virus cell is approximately 2.0\cdot 10^{-7}2.0⋅10
−7
meter.
How many times as long as the small virus cell is the white blood cell?
[tex]0.7\times10^{-2}[/tex] times as long as the small virus cell is the white blood cell.
Given that, the length of a white blood cell is [tex]1.4\times10^{-5}[/tex] meter and the length of a small virus cell is [tex]2.0\times10^{-7}[/tex] meter.
We need to find how many times as long as the small virus cell is the white blood cell.
What is scientific notation?To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.
If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive.If the given number is smaller than 1, then the decimal point has to move to the right, so the power of 10 will be negative.Now, [tex]\frac{1.4\times10^{-5}}{2.0\times10^{-7}}[/tex]
=[tex]0.7\times10^{-2}[/tex]
Therefore, [tex]0.7\times10^{-2}[/tex] times as long as the small virus cell is the white blood cell.
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Question 1
A computer is set to shut down if the temperature exceeds 40°C. Give an equivalent statement using degrees Fahrenheit
Question 2
A certain brand of makeup is guaranteed not to run if the temperature is less than 35°C. Give an equivalent statement using degrees Fahrenheit
Answer:
1. 104F
2. 95F
Step-by-step explanation:
Formula for Celsius to Fahrenheit is
[tex](C*1.8) + 32 = F[/tex]
Question one:
40 times 1.8 = 72
72+32 = 104 Fahrenheit
Question two:
35 times 1.8 = 63
63+32 = 95 Fahrenheit
(2.0 x 10^4)(3.0 x 10^3) = ?
Answer:
6 x 10^7
Step-by-step explanation:
(2x3)(10^4 x 10^3)
6 x 10^4+3
6 x 10^7
Help me solve rational or irrational problems (15 points)
Answer:
Hello yeily, I think and believe they are all rational..
Step-by-step explanation:
Hope it helps <=/
The length and breadth of a land are x m and y m respectively . If perimeter of the land is 420 m, then
a. Write the equation which represent perimeter of land
b. If length of the land is 120 m, then find the breadth
Answer:
90 m
Step-by-step explanation:
a. Perimeter = 2( length + breadth) 2(x + y)
Answer: Perimeter: 2(x + y) = 420
or 2x + 2y = 420
Using the values given
b.
2x + 2y = 420 (perimeter p= 420)
2(120) + 2y = 420 (length x = 120)
240 + 2y = 420
2y = 420 - 240 = 180 (subtract 240 on both sides)
y = 190/2 = 90 m
Tanner is going to play at an arcade. There is a $4.50 admission fee, and each game costs $0.75 to play. If Tanner only brought $20.00 to spend, what is the maximum number of games that he can afford to play?
Answer:
[tex]12 > x[/tex]
Step-by-step explanation:
[tex]20 > .75x + 4[/tex]
Is the equation you need to set up.
Then you want to subtract four from both sides ehich ends up giving you
[tex]16 > .75x[/tex]
Then divide 16 by 4 (this gives you a fourth) you get four
Then multiple 4 by 3 to get .75 of 16 which is 12
Hope this helps!
If yoy have any other questions feel free to ask!
Answer:
Tanner can play 20 games in the arcade and will have 50 cents left over.
Step-by-step explanation:
20 = 4.50 + 0.75x
Subtract 4.5 from both sides.
15.5 = 0.75x
Plug in numbers for x until it is equal more that 15.5
x = 20
0.75(20) = 15
0.75(21) = 15.75 < too much
. How many minutes will she need to finish labeling all books if she takes no breaks and labels 10 books per minute?
Answer:
(a) 75 minutes
(b) 50 minutes
Mrs Lee is 40 years old and her son is twice her daughter's age. Mrs Lee will be thrice her son's age when her daughter is 12-year old. How old will Mrs Lee be when her 2 children's combined age is 5/11 of her age?
The age of Mrs. Lee when her 2 children's combined age is [tex]\frac{5}{11}[/tex] of her age will be [tex]44[/tex] yrs. old
As per the question statement, Mrs. Lee, who is 40, has a son who is twice as old as her daughter. Mrs. Lee will be thrice her son's age when her daughter is 12-year old. We are asked that how old Mrs Lee be when her two children's combined ages are 5/11 of her own age.
This question is a classic example of forming and solving linear equations.
When Mrs. Lee was 40, her son was twice her daughter's age.
Let d = her daughter's age when Mrs. Lee was 40.
Then her son was 2d yrs. old when Mrs. Lee was 40.
When her daughter is 12, Mrs. Lee will be three times her son's age.
This means [tex](12 - d)[/tex] years have passed since Mrs. Lee was 40.
So, if her daughter was 12 at this time, that means her son was [tex]2d + (12 - d)[/tex]
And, Mrs. Lee's age at this time was [tex]40 + (12 - d)[/tex]
Mrs Lee was thrice her son's age at this time:
[tex]40 + (12 - d) = 3(2d + 12 - d))[/tex]
[tex]40+12-d=6d+36-3d\\4d=16\\d=4[/tex]
So, Mrs. Lee's age when her daughter was 12 is [tex]40 + 12 - 4 = 48[/tex] yrs. old
Her daughter was 8 yrs. old 4 years earlier.
Thus, Mrs Lee's age when her daughter was 20 was [tex]48 - 4= 44[/tex] years old.
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a. if the data are normally distributed with standard deviation $390, find the percentage of vacationers who spent less than $1,200 per 12-day vacation. round to the nearest hundredth of a percent.
The percentage of vacationers who spent less than $1,200 per 12-day vacation is 7.78%.
What is normal distribution?The normal distribution, also recognized as that of the Gaussian distribution, would be a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far away from the mean. The normal distribution is represented graphically as a "bell curve."
Now, according to the question;
The formula for finding the z-score is;
z = (x - μ)/σ
where,
x is the score
μ is the mean
σ is the standard deviation.
Summer vacation costs $1,755 for the average local family.
The distribution is normal, with a standard deviation of $390.
We need to figure out what percentage of families took vacations less than $1200.
The mean is $1,755
∴ μ = $1,755
∵ The standard deviation is $390
∴ σ = 390
∵ The vacation cost is under $1200
∴ x = $1200
Substitute the values in the formula of z score.
z-score = (1200 - 1,755)/390 = -1.42
Use the negative normal distribution table of z
P(z < 1,200) = 0.07782
P(x < 1,200) = P(z < 1,200)
P(x < 1,200) = 0.07782
P(x < 1,200) = 7.78%
Therefore, the percentage of vacationers who spent less than $1,200 per 12-day vacation is 7.78%.
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The complete question is -
International travel is usually more expensive than domestic travel. A recent survey found that the average per-person cost of a 12-day international vacation is $1,755. This includes transportation, food, lodging, and entertainment.
a. if the data are normally distributed with standard deviation $390, find the percentage of vacationers who spent less than $1,200 per 12-day vacation. round to the nearest hundredth of a percent.
a large dump truck can move 1,500 tons/h of gravel from one point to another on a work site. what is this rate in lb/s? note that
This rate in lb/s is 833.33 lb/s if a large dump truck can move 1,500 tons/h of gravel from one point to another on a work site.
What do you mean by ton/h and lb/s?The term "ton-hour" refers to a cooling service that provides 12,000 BTU of cooling, measured as a function of the amount of chilled water that flows through the Energy Transfer Station, the temperature difference between the chilled water at the Delivery Point, and the Return Point and the total BTU gain that occurs.
The imperial and US customary systems of measurement both utilize the unit of mass known as the pound (symbol: lb). The precise weight of the international avoirdupois pound, or today's standard pound, is 0.45359237 kilos. 16 avoirdupois ounces make up an avoirdupois pound.
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let be the largest integer whose square has exactly digits when written in base . what is , expressed in base ?
The largest integer whose square has exactly digits when written in base is 28 in base 9 .
An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z .
Largest base 9 three digit number = 888
And it can be represented as 728 in base 10, largest square is 26^2 26 that is 28 in base 9.
Therefore the largest integer whose square has exactly digits when written in base is 28 in base 9 .
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20867
how many numbers are in the first $20$ rows of pascal's triangle (from the $0$th row to the $19$th row)?
Numbers in the first 20 rows of pascal's triangle are 210
Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra.
We have been given that:
Numbers of rows = 20
Pascal's triangle formula
1 + 2 + 3 + ….+ 19 + 20 = n (n + 1) / 2
n=20
(20)×(21)/ 2 = 210
Pascal's triangle patterns is its symmetry. Observe that in any row, if we read the consecutive numbers from the left, we will obtain the same as if we read them from the right.
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Alexis and her sister bought school supplies.
Alexis bought 5 spiral notebooks and 6 book
covers for $27. Her sister bought 4 spiral
notebooks and 2 book covers for $16. Find
the cost for each spiral notebook and each
book cover.
The cost of each spiral notebook is $3 and the cost of each book cover is $2
Given that Alexis and her sister bought school supplies. Alexis bought 5 spiral notebooks and 6 book covers for $27. Her sister bought 4 spiral notebooks and 2 book covers for $16 and asked to find out the cost of each spiral notebook and each book cover.
Let's assume spiral notebooks as "x" and book covers as "y".
As a result, two linear equations in two variables will be formed.
⇒5x+6y=$27; Let's assume this equation as A
⇒4x+2y=$16; Let's assume this equation as B
Multiply equation B with 3
⇒12x+6y=$48; Let's assume this equation as C
Equation c- Equation A
⇒$48-$27=7x
⇒7x=$21
⇒x==$3
The cost of the spiral notebook is $3
From equation A
⇒5($3)+6y=$27
⇒$15+6y=$27
⇒6y=$12
⇒y=$2
The cost of the book cover is $2
Therefore,The cost of each spiral notebook is $3 and the cost of each book cover is $2
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Solve seven and three eighths times negative one and two thirds.
295 over 24
one and three fourths
negative seven and one fourth
negative 295 over 24
The evaluation of the expression gives -295/24. The correct option is the fourth option- negative 295 over 24 (-295/24)
Evaluating an ExpressionFrom the question, we are to evaluate the given expression
The given expression is,
7 3/8 × -1 2/3
To solve the expression, we will covert the fractions from mixed to improper fractions
7 3/8 × -1 2/3
59/8 × - 5/3
Multiplying, we get
-295/24
Hence, the evaluation of the expression gives -295/24. The correct option is the fourth option- negative 295 over 24 (-295/24)
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A jeweler has 5 rings, each weighing 12 g, made of an alloy of 5% silver and 95% gold. She decides to melt down the rings and add enough silver to reduce the gold content to 75%. How much silver should she add?.
The amount of silver that should be added is 48% . A jeweler is said to have 5 rings that weigh 12 g apiece and are composed of an alloy of 20% silver and 80% gold.
What are linear equations?
An equation between two variables that, when plotted on a graph, produces a straight line.
The material will weigh 12 × 5 = 60 grams after melting all 5 rings.
The alloy's 20% silver and 80% gold content have been disclosed to us. Let's further say that the melted material receives an additional x grams of silver, resulting in a composition of 64% gold and 36% silver.
Thus, we can construct the following equation:
Amount of gold before = Amount of gold after mixing
So the equation we get
80% of 60 grams =64% of (X + 60) gram
0.80 × 60 = 0.64 (x + 60)
48 = 0.64x + 38.4
0.64x = 9.6
x = 9.6/0.64
x = 15
So
Amount of silver that needed to be added
= 0.64(15 + 60)
= 0.64(75)
= 48%
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I know someone is gonna solve this in 5 minutes but I don't get it.
Answer: See diagram below
Scale factor = 3
============================================================
Explanation:
The given L shape has a perimeter of 3+1+2+1+1+2 = 10 units. I added up the exterior sides of this shape.
We want the perimeter to be 30 units, so we scale it by a factor of 3. Since 30/10 = 3.
This means we'll triple each side
The vertical side on the left originally 3 units long is now 3*3 = 9 units. The bottom side that is 2 units long is now 2*3 = 6 units. And so on.
See the diagram below.
Notice in the red figure the sides add to 9+3+6+3+3+6 = 30 to help confirm our answer.
Convertir o.83333 = 0.83 a fracción común
Answer:
83/100
Step-by-step explanation:
You move 2 times to the right your answer will be 83/100
PLEASE HELP I WILL GIVE OUT BRAINLIST ONLY FOR THE RIGHT ANSWERS
The measure of angle 2 and angle3 are 133 ad 47 degrees respectively
Vertical angles and angle on a straight lineFrom the given diagram, the measure of angle 1 and 2 are congruent. (vertical angles)
Given he following parameters
m<1 = 133 degrees
Since m<1 = m<2, hence m<2 = 133 degrees
Also;
m<2 + m<3 = 180
133 + m<3 = 180
m<3 = 180 - 133
m<3 = 47 degrees
Hence the measure of angle 2 and angle3 are 133 ad 47 degrees respectively
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2x - 3y = 16
5x - 3y = 13
solve the systems of equations
The solution to the system of equation is (-1, -6)
System of equationGiven the system of equations
2x - 3y = 16
5x - 3y = 13
Subtract to have:
2x-5x = 16 - 13
-3x = 3
x = -3/3
x = -1
Substitute x = -1 into 1 to have:
2(-1) - 3y = 16
-2 - 3y = 16
-3y = 16 + 2
-3y = 18
y = -6
Hence the solution to the system of equation is (-1, -6)
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ms adams shares out 50 between niamh and jack in the the ratio 3:7
Answer:niamh gets 15 and jack gets 35
Step-by-step explanation:
think of the raito 3:7 as 3x:7x. then we can do: 3x + 7x = 50, which means 10x = 50. then we can find x by dividing 50 by 10, so x is 5. then we can find 3x, whihc is 3x5 = 15. then find 7x, so 7x5 = 35. so niamh gets 15 and jack gets 35
Convert the mixed number to an improper fraction 3 1/3
Answer: 10/3
Step-by-step explanation:
multiply the denominator, "3", by the mixed number "3", then add the numerator "1". So 3*3+1=10/3 (the denominator stays the same)
Answer: [tex]\frac{10}3}[/tex]
calculate the length in m of a right triangle's hypotenuse when the other two sides measure 2 m and 4m respectively.
The length of hypotenuse is 4.5 meters.
The length of hypotenuse can be calculated using Pythagoras theorem. Writing the Pythagoras theorem below -
Hypotenuse² = Base² + Perpendicular²
The given other two sides will be base and perpendicular. So, keeping the values in mentioned equation of Pythagoras theorem to find the value of Hypotenuse.
Hypotenuse² = 2² + 4²
Taking square of the numbers to find the value of Hypotenuse
Hypotenuse² = 4 + 16
Performing addition to find the value of Hypotenuse
Hypotenuse² = 20
Hypotenuse = [tex]\sqrt{20}[/tex]
Taking square root to find the value of Hypotenuse
Hypotenuse = 4.5 meters
Hence, the length in meters of a right triangle's hypotenuse is 4.5 meters
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10 POINTS!!!!!!!!!!! PLEASE HELP QUICKLY!!!!!! SCREENSHOT ATTACHED
Answer:
18
Step-by-step explanation:
∠BCD=2x (alternate interior angles)
∠BCD+∠CDE=180° (same side interior angles)
Thus, 10x=180, meaning x=18.
What is the area of parallelogram ABCD with vertices A (2, 3), B (7, 3), C (8, -5), and D (3, -5)?
The area of the parallelogram ABCD with the vertices is 40 square units
What is the area of parallelogram ABCD with vertices?The vertices are given as
(2, 3), B (7, 3), C (8, -5), and D (3, -5)
From the graph, we have the following dimensions
Base = 5 units i.e. distance AB
Height = 8 units i.e. the distance between the parallel sides
The area of the parallelogram is then calculated as
Area = Base * Height
So, we have
Area = 5 * 8
Evaluate
Area = 40
Hence, the area of the parallelogram ABCD with the vertices is 40 square units
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(1’^0)^1 d) (1v0’)^(0v1) Logic statements
We need to know about logic statements to solve this problem. The solution of the logic statements are 0 and 1 respectively.
Logical operators are used to form logical statements, logical operators compute result based on boolean values true and false or binary 1 and 0. The common logical operators are AND and OR. AND is represented by ^ symbol and OR is represented by v symbol, ' means negation of the value, which means that true becomes false and vice versa. For AND operator, it works like multiplication, 0 and 1 yield 0, 1 and 1 yields 1 and 0 and 0 yields 0. For OR operator it works like addition, 0 and 1 yields 1, 1 and 1 yields 1 and 0 and 0 yields 0. For the logical statements given in the question we need to first compute the logical statement inside the bracket and then compare the inner result with the outer value.
(1'^0)^1 =(0^0)^1=0^1=0
(1v0')^(0v1)=(1v1)^(0v1)=1^1=1
Therefore we found the values of the logical statements to be 0 and 1 respectively.
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the top of the john hancock building is a rectangle whose length is 60 ft more than the width. the perimeter is 520 feet. find the width and the length of the rectangle.
The length and width of rectangle is 160 feet and 100 feet.
The perimeter of the rectangle is calculated by the formula -
Perimeter = 2 × (length + width)
As per the given information, length = (60 + width)
Keep the values in formula to find the breadth of rectangle.
520 = 2 × (60 + width + width)
520 = 2 × (60 + 2 × width)
(60 + 2 × width) = [tex]\frac{520}{2}[/tex]
(60 + 2 × width) = 260
2 × width = 260 - 60
2 × width = 200
Width = [tex]\frac{200}{2}[/tex]
Width = 100 feet
Keep the value in formula to find the length of perimeter
520 = 2 × (length + width)
Length + 100 = [tex]\frac{520}{2}[/tex]
Length = 260 - 100
Length = 160 feet
Hence, the length and width of rectangle is 160 feet and 100 feet.
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a machine shop has eight screw machines but only three spaces available in the production area for the machine. in how many different ways can the eight machines be arranged in the three spaces available?
The eight machines can be arranged in the three available spaces in 336 ways.
Here we have 8 screw machines with 3 spaces. To find the different way, permutation will help.
Different ways = 8 P 3
= 8! / (8! -3!)
= 8! / 5!
= 8 x 7 x 6 x 5! / 5!
= 6x7x8 = 336.
Therefore, in 336 different ways the eight machines be arranged in the three spaces available.
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The width rectangle is three less than twice its length. If the area of the rectangle is 193 cm² what is the length of the diagonal?
Answer:
Step-by-step explanation:
Givens
Let the Length = L
Let the width = w
w = 2*L - 3
Area = L * w
Area = 193
Solution
Area = 193
193 = L*(2L - 3)
193 = 2L^2 - 3L Subtract 193 from both sides.
2L^2 - 3L - 193 = 0
You have to use the quadratic formula get the answer. Without going through all all that, I will tell you that the only value you can use for L is 10.6
L = 10.6
w = 2* 10.6 - 3 = 18.4
But you want the diagonal. Use the Pythagorean Theorem to get it.
Diagonal^2 = L^2 + w^2
Diangonal^2 = 10.6^2 + 18.4^2
Diagonal^2 = 450.92 Take the square root of both sides
√diagonal^2 = √450.92
Answer
The diagonal is 21,23
Please help and disregard the work I’ve done because I feel it’s wrong
GIVEN THE FOLLOWING:
Mario's car rate consumption. R = 24.5mile/gallon
Distance covered each day, D = 32.3 miles
Cost of gas $2.89/gallon
REQUIRED: (a) To calculate how much he spends on gas each week.
We proceed as follow:
Mario uses 1 gallon of gas for every 24.5 miles.
For 32.3 miles, he will use [tex]\frac{32.3}{24.5} ~gallons~ of gas=\frac{325}{245} ~gallons[/tex]
Now, a gallon of gas costs $2.89
[tex]\frac{325}{245}~gallons~will~cost =?[/tex]
[tex]\frac{325}{245} ~*2.89=3.81[/tex]
$3.81 is how much he spends each workday.
There are 5 working days in a week.
Therefore, for a week, he spends:
[tex]3.81~*~5~=19.05[/tex]
therefore, for each work week, he spends $19.05 on gas.
(B) To calculate how many miles he can drive with $15.00 worth of gas
We proceed thus:
A gallon of gas costs $2.89.
$15.00 will amount to:
$15.00/$2.89 = 5.19 gallons
Recall that Mario uses 1 gallon of gas for every 24.5 miles.
Therefore, 5.19 gallons will be used for:
[tex]5.19~*24.5=127.155 ~miles[/tex]
≈ 127 miles
Therefore, with gas worth $15.00, Mario will cover a distance of 127 miles
Answered by:AshTheNeko