The length of the rectangle is 7 centimeter and the width of the rectangle is 4 centimeter
A rectangle has length 3 cm greater than it’s width
Consider the width of the rectangle = x
The length of the the rectangle = x + 3
The area of the rectangle = 28 square centimeter
The area of the rectangle = The length of the the rectangle × The width of the rectangle
Substitute the values in the equation
x(x+3) = 28
Apply the distributive property
[tex]x^2[/tex] + 3x = 28
[tex]x^2[/tex] + 3x -28 = 0
Split the middle term and solve the equation
[tex]x^2[/tex] -4x + 7x -28 = 0
Take common term outside
x(x-4) + 7(x-4) =0
Take common term outside
(x+7) (x-4) = 0
x = -7, 4
The length cannot be negative value
x = 4 centimeter
Then the length of the rectangle = x + 3
= 4 +3
= 7 centimeter
Hence, the length of the rectangle is 7 centimeter and the width of the rectangle is 4 centimeter
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(x³-15)+(x-1) Divide using synthetic division
The quotient is x²+x+1 - 14/(x-1) after divide x³-15 by x-1.
What is synthetic division?
In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.
The divisor is x - 1.The dividend is (x³-15).
Step 1:Take the constant term of the divisor with the opposite sign and write it to the left.
Write the coefficients of the dividend to the right (missed terms are written with zero coefficients).
Step 2:Write down the first coefficient without changes:
Step 3:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Step 4:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum
Step 5:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum.
We have completed the table and have obtained the following resulting coefficients: 1,1,1,−14.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
The quotient is x²+x+1 and the remainder is -14.Therefore (x³-15)÷(x-1) = x²+x+1 - 14/(x-1)
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What is the value of the following numerical expression?
-23 +-15+|-17| + -35
A. -56
B.-26
C. 1-261
D. 56
The value of expression -23 +-15+|-17| + -35 is -56
In this question, we have been given a numerical expression.
-23 +-15+|-17| + -35
We need to find the value of given numerical expression.
Consider given numerical expression,
-23 +-15+|-17| + -35
= -23 + (-15) + |-17| + (-35)
= -23 - 15 + |-17| - 35
We know that for any real number a, |±a| = a
So, |-17| = 17
= -38 + 17 - 35
= -56
Therefore, the value of expression -23 +-15+|-17| + -35 is -56
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"14 more than twice a number" translate expression
Answer: 14=2x
Step-by-step explanation:
the answer is 14=2x7=14
a=4 b=2, find value of a) 3ab
b) a+5b
Answer:a. 24
b. 14
Step-by-step explanation:
a. 3ab=
3*a*b=
3*4*2=
12*2=24
b. a+5b=
a+5*b=
4+5*2=
4+10=14
Answer: a) 24
b) 14
Step-by-step explanation:
step1: We have to substitute the numbers.
step2: Then finish the answer.
a) 3ab = 3 x 4 x 2 = 24
b) a+5b = 4 + 5 x 2 = 4 + 10 = 14
Epsilon3 is an exoplanet with a mass of 9.43x10^27g. It has a radius of 7.6x10^8cm. What is the density of the planet? What is it made of?
The density of the planet is 4.81 g/cm^3, and with this in mind, we assume that the planet is made of titanium or yttrium.
How to get the density of the planet?Density is defined as the quotient between mass and volume.
Here we know that the mass is:
9.43*10²⁷g
And the radius is 7.6x10^8cm, remember that the volume of a sphere of radius R is:
V = 3.14*(3/4)*R³
Then in this case the volume is:
V = 3.14*(3/4)*(9.43*10⁸ cm)³ = 1.96*10²⁷ cm³
Then the density is:
D = (9.43*10²⁷g)/(1.96*10²⁷ cm³) = 4.81 g/cm^3
For this density, we can assume that the planet is made of Titanium or Yttrium (or a combination of a lot of elements like most planets)
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an instructor gives a course grade of b to students who have total score on exams and homeworks between 800 and 900, where the maximum possible is 1000. if the total scores have approximately a normal distribution with mean 830 and standard deviation 50, about what proportion of the students receive a b?
Let x denote the score. Assuming x follows normal distribution with
mean m = 70 and SD = 5 ,
we first calculate P( x < or = 80)
The SNV is z = (x — m) /SD
When x = 80, Z = ( 80 — 70)/5 = 2
So, P( x < or= 80)
= P( z < or= 2)= Area under the standard normal curve on LHS of z = 2=0.5000 + 0.4772=0. 9772, which is the relative frequency of x < or = 80Given that total number of students is
N = 1000. Let f be the number of students who have scored < or equal to 80,Then f/N = relative frequency = 0.9772Hence f = 0.9772 X N = 0.9772 X 1000 = 977learn more about binomial distrubution click here:
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At school, 40% of the sixth grade students said that hip hop was their favorite kind of music. If 100 sixth grade students prefer hip hop music how many sixth graders are at the school
If 100 sixth grade students prefer hip hop music, the number of sixth graders at the school is 250.
How many sixth graders are at the school?Percentage is a measure of frequency that is used to express a number as as a fraction of 100. In order to change a value to percentage, multiply the number by 100. The sign that represents percentage is %.
In order to determine the number of sixth graders, divide the number of sixth graders that prefer hip hop music by the percentage.
Number of sixth graders = number that prefer hip hop / percentage
100 / 40%
100 / 0.4 = 250
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Dan and Sydney are getting high-speed Internet access at the same time. Dan's provider charges $60 for installation and $42.95 per month. Sydney's provider has free installation and charges $52.75 per month. After how many months will Dan and Sydney have paid the same amount for high-speed Internet service?
Pls someone answer this, it’s due in a couple mins
The number of months till Dan and Sydney would have paid the same amount for the high-speed Internet service is 6.12 months
How to find the number of months?Assuming the number of months is denoted as x, the total cost equation for Dan's provider would be:
= Installation cost + internet charge per month x number of months
= 60 + 42.95x
The total cost equation for Sydney's provider is:
= Installation cost + internet charge per month x number of months
= 0 + 52.75x
= 52.75x
To find the number of months till Dan and Sydney pay the same amount, equate the equations:
60 + 42.95x = 52.75x
52.75x - 42.95x = 60
9.8x = 60
x = 60 / 9.8
x = 6.12 months
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state how the 2 triangles are congruent?? SSS and SAS HELP ASAPPP??
The two triangles are congruent by SAS criterion.
What is SAS criterion?According to this standard, two triangles are said to be congruent if their two sides are equal to the sides of another triangle and their respective angles are also equal. The "Side-Angle-Side" triangle congruence theorem is referred to as the SAS Criterion.According to the Side-Angle-Side theorem of congruency, two sides and the angle they produce are congruent if they are equivalent to two sides and the included angle of another triangle.Verification:
Let's carry out an exercise to demonstrate SAS's validity. AB=PQ, BC=QR, and ∠B=∠Q are given. To demonstrate: ΔABC≅ΔPQRPlacing the triangle ABC over the triangle PQR will cause B to fall on Q and the AB side to coincide with the PQ side.Point A falls on point P because AB=PQ.The side BC will fall along the side QR since ∠B=∠Q.Point C is in line with point R since BC=QR. As a result, BC and QR coincide, while AC and PR coincide.ΔABC will therefore match ΔPQR. Consequently, ΔABC ≅ ΔPQR. This exemplifies the SAS congruence criterion.To learn more about SAS criterion, refer to https://brainly.com/question/22472034
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Which of the following expressions is equivalent to 2y (3y^2 + 4y^4)
The expression that is equivalent to the given expression is 6y³ + 8y⁵
Evaluating an expression and determining an equivalent expressionFrom the question, we are to determine the expression that is equivalent to the given expression
The given expression is
2y (3y^2 + 4y^4)
This can be properly written as
2y (3y² + 4y⁴)
Now, to determine the expression that is equivalent to this expression, we will expand the expression by applying the distributive property.
2y(3y² + 4y⁴)
2y(3y²) + 2y(4y⁴)
Multiplying
6y³ + 8y⁵
Hence,
The expression is 6y³ + 8y⁵
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please help will give brainliest
Step-by-step explanation:
2x - 27 + 3x + 27 = 180
5x = 180
x = 36
You have 84,000 grams of a radioactive kind of tellurium. How much will be left after 75
minutes if its half-life is 25 minutes?
grams
Answer:
10,500 g
Step-by-step explanation:
Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 25 minutes. After 75 minutes, then, the amount of radioactive atoms is halved three times. Therefore:
1st half-life: [tex]84000\text{ g}\div{2}=42000\text{ g}[/tex]
2nd half-life: [tex]42000\text{ g}\div{2}=21000\text{ g}[/tex]
3rd half-life: [tex]21000\text{ g}\div{2}=10500\text{ g}[/tex]
How many solutions can be found for the linear equation?
3(x + 4) = 3x + 4
Responses
A infinitely many solutionsinfinitely many solutions
B no solutionno solution
C two solutionstwo solutions
D one solution
Answer:
B No solution
Step-by-step explanation:
3(x+ 4) = 3x + 4 Distribute the 3
3(x) + 3( 12) = 3x + 4
3x + 12 = 3x + 4 There is not number that I can multiply by 3 and then add to 12 on one side and add to 4 on the other side of the equal sign to make a true statement, so the answer is no solution.
3x + 12 = 3x +4 Subtract 3x from both sides
12≠4. A false statement means no solution.
When the equation is simplified and the coefficient of the variable (the number before the letter) is the same on both sides of the equation and the constraints (the numbers without letters) are different, this will result in no solution.
Samuel orders four DVDs from an online music store. Each DVD costs $9.97. He has a 25% discount code, and sales tax is 7.75%. Round sales tax amounts to the nearest cent. What is the total cost of his order?
The total cost of his order of DVDs will be $32.23.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Samuel orders four DVDs from an internet-based music store. Every DVD costs $9.97. He has a 25% markdown code, and the deal charge is 7.75%.
The cost of DVDs after discount will be given as,
⇒ 4 x $9.97 x (1 - 0.25)
⇒ $29.91
The cost of DVDs after tax will be given as,
⇒ $29.91 x (1 + 0.0775)
⇒ $32.23
The total cost of his order of DVDs will be $32.23.
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Rachel used 12 centimeters of tape to wrap 3 presents. How many presents did Rachel wrap if she used 20 centimeters of tape?
The number of wrapped present with 20 centimeters of tape is given as 5 presents.
How to solve for the wrapped presentsIn this question, we have the following values
12 centimeters of tape was used to wrap 3 presents
hence we would have
12 = 3 presents - - - - 1
Then we are to know the presents that would be wrapped with the use of 20 centimeters of tape.
we would have
20 = ? presents - - - 2
We have to bring the equations together
12 = 3 presents
20 = ? presents
? is the presents that is to be wrapped with 20 centimeters of tape. It is our unknown.
We would have to cross multiply
12 x ? = 3 x 20
12? = 60
We would have to divide through by 12 in order to get the unknown
? = 60 / 12
? = 5
Hence the number of presents that she wrapped is given as 5
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A person invested $440 in an account growing at a rate allowing the money to double every 8 years. How long, to the nearest tenth of a year would it take for the value of the account to reach $2,860?
The time that It would take for the value of the account to reach $2,860 is; 21.6 years
How to solve compound interest problems?We are told that a person invested $440 in an account growing at a rate allowing the money to double every 8 years. Thus, the account balance can be modeled by the equation;
A = 440(2)^(t/8)
where;
A is final amount
t is in years
We want to find t when A = 2860. Thus;
2860 = 440(2^(t/8))
divide both sides by 440 to get;
6.5 = 2^(t/8)
log(6.5) = (t/8)log(2)
t = 8 * log(6.5)/log(2)
t ≈ 21.604
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In a company, 85% of the workers are women. If 675 people work for the company who aren't women, how many workers are there in all?
Answer:
so there are 3825 worker in total
Step-by-step explanation:
675=15%
women=85%
how much workers are 5%=675/3 =225
225=5%
how many workers is 85%= 85/5=17
85%=225x17=3825
its easy but i dont want to do it because im to lazy
The equation of the given line written in the slope-intercept form is: y = 21x + 10.25.
What is a slope?
The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.
Note that the general slope equation is:
y = mx + b
Where
m is the slope of the line and
b is the y-intercept.
In this specific instance, m is the change in the price of the ticket
b is the additional fee value that needs to be included for each ticket
Hence, the cost of the ticket (y) is given as:
y = (change rate of x) + added fee to every order
Where rate of change = 21; and
The fee added to each order is 10.25
Given the above, the general equation becomes:
y = 21x + 10.25
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the price of a car was increased by 4% to £22 what was the price before
13.80
Step-by-step explanation:
22 - 4% is your answer
Can anyone write the equation of the graph?
The equation of the graph represented by the figure is f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we have the following graph that can be used in our computation:
The graph is an absolute value graph
As a general rule, an absolute value is expressed as
y = |x - h| + k
In this case, the vertex is
Vertex = (h, k)
As a general rule, the vertex of a function is the minimum point on the graph
On the given graph, the minimum point is (3, 5)
This means that
(h, k) = (3, 5)
Substitute the values (h, k) = (3, 5) in the equation y = |x - h| + k
So, we have the following representation
y = |x - 3| + 5
Rewrite the equation as a function
f(x) = |x - 3| + 5
Hence, the equation is f(x) = |x - 3| + 5
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48+3u=9u
Solve for u
Answer:
u=8
Step-by-step explanation:
48+3u=9u
-3u both sides
48=6u
divide by 6 on both sides
8=u
Graph the line with the equation y=− 6/1x +1
Answer:
The answer is (1, 6)
Step-by-step explanation:
observation refers to the . a. mean of all variable values associated with one particular entity b. estimated continuous outcome variable c. set of recorded values of variables associated with a single entity d. goal of predicting a categorical outcome based on a set of variables
The correct option is c. that is observation is set of recorded values of variables associated with a single entity.
What is observation?
An observation is a case of the data being collected.
For example, if we were collecting data on students in the class, the observations would be each individual student in the class. It could be the student's height, weight, marks scored, etc.
A variable is an attribute or characteristic of the observation we record in our data.
Also an observation in statistics is a value of something of interest measured or counted during a study or experiment: a person’s height, a bank account value at a certain point in time, or number of animals.
Therefore from the given option c is correct.
Observation is set of recorded values of variables associated with a single entity.
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Use the diagram and the given angle measure to find the other three measures
The other three measures are:
∠1 = 159°∠2 = 21°∠4 = 21°What is Angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.This, I assume, refers to two lines that cross and create four angles.
The sum of the additional angles 2 and 3 is 180°.Angles 2 and 3 equal 180°.159⁰ + angle 2 = 180⁰angle 2 = 180⁰ - 159⁰angle 2 = 21⁰The same applies to angles 2 and 4 since angles 1 and 3 are vertical angles.
Since vertical angles are congruent in measure, it is simple to determine their measurements.
Hence, the three measures are:
∠1 = 159°∠2 = 21°∠4 = 21°To learn more about Angles click on the link
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Find the inverse of A =
Answer:
(-4,-1) and (3,1), respectively.
Step-by-step explanation:
I am not quite sure if the question is necessarily asking for this, but the x and y values are switched to get the points of the inverse. (-1,-4) --> (-4,-1) and (1,3) --> (3,1). I hope that makes sense!
8x - 4 = 12x + 6 + x
Answer:
X = −2
Step-by-step explanation:
Combine 12x and x to get 13x. Subtract 13x from both sides. Combine 8x and −13x to get −5x. Add 4 to both sides. Add 6 and 4 to get 10. Divide both sides by −5. Divide 10 by −5 to get −2.
Answer: x= -2
Step-by-step explanation:
8x-4=12x+6+x
8x-12x-x=6+4
-4x-x=10
-5x=10
x= -2
what 29,000 divided by 50,000
Answer:
.58
Step-by-step explanation:
What is the equation of the line in slope-intercept form?
the line perpendicular to Y = 4/9x - 6 through (5, -6)
The required equation will be y = -1/3x + 21/4 in slope-intercept form.
What is the equation of a line?The general equation of a line is y = mx + c
where m is the slope of the line and c is the intercept.
First, we need to determine the slope of the given line.
y = 4/9x - 6
Here the slope of the given line is 4/9.
The required line is perpendicular to a given line
So the required line's slope will be m₂ = -1 / (4/9) = -9/4
The line passes through the point (5, -6) which is given in the question,
Now we can use the point-slope form of a line to create the equation of the new line:
(y + 6) = (-9/4) (x - 5)
y = (-9/4)x + 45/4 - 6
y = -1/3x + 21/4
Hence, the required equation will be y = -1/3x + 21/4 in slope-intercept form.
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Find the equation of the linear function represented by the table below in slope-
intercept form.
The equation of the linear function is represented by the table given in the slope-intercept form is y = x -1.
What is an equation of a line?
A line's equation is a single representation of all of the line's points. The general form of a line equation is ax + by + c = 0, and each point on the line satisfies this equation. The slope of the line and a point on the line are the two necessary components to create the equation of a line.
The equation of a line, in the slope-intercept formula:
y = mx + b
In which,
m is the slope, that is, how much y changes when x changes by 1.
b is the y-intercept, that is, the value of y when x = 0.
Given two points (x,y), the slope is the change in y divided by the change in x.
We have points (-1, -2) and (1, -4).
[tex]m = \frac{(-2 - (-4))}{1 - (-1)}[/tex]
m = 1;
Then,
y = 1x + b
Point (-1,-2) means that when x = -1 and y = -2, we use this to find b.
y = 1x + b
-2 = 1(-1) + b
b = -2 + 1
b = -1
Thus,
y = x -1.
Hence, the equation of the linear function is represented by the table given in the slope-intercept form is y = x -1.
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find the domain and range of the function !! NEED NOW
Answer:
Domain = { -2 , 0 , 2 , 4 }
Range = { 3 }
Step-by-step explanation:
Domain is the x-values that the Function have and Range is the y-values that the Function have corresponding to these x-values
Since the x-values for the Function attached are -2 , 0 , 2 , 4
and the y-values for the Function is 3
Then the Domain = { -2 , 0 , 2 , 4 }
and the Range = { 3 }
Glad to Help
