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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how many different three-letter strings can be formed from the letters a, b, c, d, e (repeats allowed) if the string must contain either all vowels or all consonants?
8 strings can be formed with all vowels from a, b, c, d, e and 27 strings can be formed with all consonants from a, b, c, d and e.
What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]
Given, the letters that can be used to create the required three letter word in question: a, b, c, d, e.
Total number of letters that can be used = 5
Total number of vowels in the available letters to be used = 2 ('a' and 'e')
Total number of consonants in the available letters to be used = 3 ('b', 'c' and 'd')
Case 1: A three letter word having all vowels where letters can be repeated
Here, since two letters are to put in three empty positions, the total number of ways to form this word = 2³ = 2 × 2 × 2 = 8
Case 2: A three letter word having all consonants where letters can be repeated
Here, since three letters are to put in three empty positions, the total number of ways to form this word = 3³ = 3 × 3 × 3 = 27
Thus, 8 strings can be formed with all vowels from a, b, c, d, e and 27 strings can be formed with all consonants from a, b, c, d and e.
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g(x)= x^2-5 9x-17 (x+1)(x-5) g(7)=
The solution for g(7) in the piecewise function g(x) = (x + 1)(x - 5) is 16
How to determine the solution for the function?From the question, we have the equation that can be used in our computation to be a piecewise function
This piecewise function is represented as g(x)
Also from the question, we have the following function that we are to compute
g(7)
This means that the value of x is 7, and we calculate g(x) when x = 7
To do this, we make use of an equation in the piecewise function, where the domain occupies x = 7
This domain is x c (2, oo)
And the function is
g(x) = (x + 1)(x - 5)
Substitute the known values in the above equation, so, we have the following representation
g(7) = (x + 1)(x - 5)
So, we have the following equation
g(7) = (7 + 1)(7 - 5)
There is no constant to add or subtract to both sides of the equation
Also, there is no factor to multiply or divide from both sides of the equation
So, we have the following representation
g(7) = (7 + 1)(7 - 5)
Solving further, we have
g(7) = 16
Hence, the solution is 16
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Lat week, Lia old 20 hand-engraved watch band, earning a total profit of $105. 0. She plan to make 50 engraved watch band to ell at the community art fair. If he ell all 50 watch band, how much profit can Lia expect to earn?
$
If Lisa sells 50 watch bands, she gets a profit of $262.50.
A unitary method is defined.
Mathematicians use the unitary method to solve problems by first determining the value of a single unit, or 1, (by dividing), and then determining the necessary value by multiplying the value of the single unit.
We must first ascertain the cost of one watch band.
To determine this, we simply divide $105 by 20, which equals $5.25.
We can divide $5.25 by 50 because she sells all 50 watchbands.
50 multiplied by $5.25 equals $262.50.
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-7 + 5x = 5x + 9 help me pls
Answer:
solve for x 7 (5x+9)=- (x-9) 7(5x + 9) = −(x − 9) 7 ( 5 x + 9) = - ( x - 9) Simplify 7(5x+9) 7 ( 5 x + 9). Tap for more steps... 35x+63 = −(x−9) 35 x + 63 = - ( x - 9) Simplify −(x−9) - ( x - 9).
Step-by-step explanation:
Rewrite 0+0+7(5x+9)= -(x----9)
Apply the distributive property. 7 (5x) + 7.9= - (x-9)
Write each trigonometrie ratio as a fraction and as a decimal rounded to the nearest hundredth.
Answer: length C to A is .001 and c to b is 0.03 and b to a is 0.04
Step-by-step explanation:
I don’t know the answer to this can you please help me
Answer:
The answer is 24 I think
Step-by-step explanation:
just multipy the numbers
e-8/find-the-slope-from-two-points
On two poinICS ZAC
he line that passes through (10, 7) and (3, 1).
wer and write it as a proper fraction, improper fraction, or r
The slop m is ( 2-3).The slope formula, or the ratio of the change in the y values to the change in the x values, is m is equal to subtraction of y2 and y1 and divide by subtraction of x2 and x1 The initial point's coordinates are x1 and y1, respectively.
How to find slop?The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1). The initial point's coordinates are x1 and y1, respectively.
(10, 7) and (3, 1).
m=(y2-y1)/(x2-x1).
3-1 / 7-10= 2/-3
The slop m is ( 2-3)
When determining the slope of a straight line without its equation, there are three steps. The first point's coordinates are x1 and y1. Step one is to locate the line's first two points. Step 2: Decide which will be (x1, y1) and which will be (x2, y2). Step 3: Determine the slope using the slope equation.
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What is the equation of the line that passes through the point (6,-5) and has a slope of -{1}{3}?
Answer:
y = - [tex]\frac{1}{3}[/tex] x - 3
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 )
here m = - [tex]\frac{1}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (6, - 5 ) into the partial equation
- 5 = - 2 + c ⇒ c = - 5 + 2 = - 3
y = - [tex]\frac{1}{3}[/tex] x - 3 ← equation of line
Pls help/ The y-intercept of f(x)=(1.6)x is ______________________ the y-intercept of the function in the graph:
The y-intercept of f(x) = (1.6)x is (a) less than the y-intercept of the function in the graph
How to complete the blank?The equation of the function is given as
f(x) = (1.6)x
To determine the y-intercept, we set x = 0
So, we have
f(0) = 1.6 * 0
Evaluate
f(0) = 0
For the graph, we have
When x = 0, the function has a value of 1
This means that
y-intercept is 1
0 is less than 1
Hence, the y-intercept of f(x) = (1.6)x is (a) less
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Please Help! What is the ratio of a:b?
a+3b/5 = a-2b/2
The ratio of a : b in the given expression is 16:3 .
In the question ,
it is given that
the algebraic expression is (a+3b)/5 = (a-2b)/2
we have to find the ratio of a:b ,
in order to find the ratio,
we cross multiplying ,
On cross multiplying , we get
2 * (a+3b) = 5 * (a-2b)
2a + 6b = 5a - 10b
5a - 2a = 10b + 6b
3a = 16b
dividing both sides by b ,
a/b = 16/3
a:b = 16:3
Therefore , The ratio of a : b in the given expression is 16:3 .
The given question is incomplete , the complete question is
What is the ratio of a:b in the expression (a+3b)/5 = (a-2b)/2 ?
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3n=1/9 Find the value of n.
PLEASE HELP
Answer: n=1/27=0.037
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3*n-(1/9)=0
Simplify 1/9
3n - 1/9 = 0
Rewrite the whole as a fraction using 9 as the denominator :
3n 3n • 9
3n = —— = ——————
1 9
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3n • 9 - (1) 27n - 1
———————————— = ———————
9 9
End of step 2
27n - 1
——————— = 0
9
Start of step 3
When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
27n-1
————— • 9 = 0 • 9
9
Now, on the left hand side, the 9 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
27n-1 = 0
Solving a Single Variable Equation:
3.2 Solve: 27n-1 = 0
Add 1 to both sides of the equation :
27n = 1
Divide both sides of the equation by 27:
n = 1/27 = 0.037
Use the following diagram for questions 1-3.
1. Find x.
2. Find y
3. Find z
Answer:
x= 40° y= 66° z=106° ....
The value of angles are x = 40° , y = 66°, z = 106°
Since there are two parallel lines and two intersecting lines forming a triangle we will use the properties of lines and triangles to find out the value of x,y,z. First of all y = 66° because of the vertical angle theorem, which means that adjacent angles formed by the intersection of two lines are supplementary or equal to 180° degrees. The third angle of the triangle formed is 74°. Using the sum of all angles of the triangle is equal to 180° we can find the third angle of triangle x which is equal to 40°. Now z can be found using the property sum of two opposite interior angles which will come out to be 106°. Hence by this, we can find all the angles.
I hope this answer helps.
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2. Identify the proportional relationship.
7x-2=y y + 1 = 3x y = 5x y=2x +4
help me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
the flight path of a rocket or a thrown object is a parabola as described by the function.
h(t) = -16t² + 40t + 7
the negative sign of the prime coefficient (-16) tells us that the parabola opens downwards, and that the vertex as the extreme point of the parabola is a maximum.
we get the extreme point of a curve by finding the zero solution of the first derivative of the function.
and the extreme value itself by using that value in the original equation and calculate the result.
h'(t) = -32t + 40
0 = -32t + 40
32t = 40
t = 40/32 = 5/4 = 1.25 seconds
h(5/4) = -16×(5/4)² + 40×5/4 + 7 =
= -16×25/16 + 10×5 + 7 =
= -25 + 50 + 7 = 32 ft
the rocket will reach its maximum height of 32 ft after 1.25 seconds.
Describe the sampling distribution of p. Assume the size of the population is 30,000. n 700, p 0.388 Describe the shape of the sampling distribution of p. Choose the correct answer below. O A. The shape of the sampling distribution of p is not normal because n s0.05N and np(1-p)210. O B. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1-p) <10. C. The shape of the sampling distribution of pis not normal because n s05N and np(1-p)<10 O D. The shape of the samplingdistrbution of p is approximately normal because n s0.05N and np(1 -p)210 Determine the mean of the sampling distribution of p. Round to three decimal places as needed.) Determine the standard deviation of the sampling distribution of p. Round to three decimal places as needed.)
The correct option regarding the sampling distribution of p, considering the Central Limit Theorem, is given as follows:
D. The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.
The mean of the sampling distribution of p is of:
0.388.
The standard deviation of the sampling distribution of p is of:
0.0184.
What is defined by the Central Limit Theorem?The Central Limit Theorem defines the distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n, in which:
The mean is [tex]\mu = p[/tex].The standard deviation is [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]The shape is approximately normal.As long as these two conditions are respected:
[tex]n \leq 0.05N[/tex][tex]np(1 - p) > 10[/tex]The values of the parameters in this context are given as follows:
N = 30000, n = 700, p = 0.388.
Hence the conditions are:
n/N = 700/30000 = 0.0233 < 0.05.np(1 - p) = 700 x 0.388 x 0.612 = 166 > 10.Then the shape is approximately normal and option D is correct.
The mean of the distribution is of:
[tex]\mu = p = 0.388[/tex]
The standard error of the distribution is of:
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.388(0.612)}{700}} = 0.0184[/tex]
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the rabbit population in a certain area is 200%of last years population. There are 700 rabbits this year how many were there last year
Answer:
the answer is 350
Step-by-step explanation:
if it increased by 200% that means it doubled
so when x is doubled we get 700
so: 2x=700
x=700/2
x=350
if the interest for 5 years on Rs 3000 is Rs 525, find the interest on Rs 2200 for 6 years at the same rate of interest.
Using the formula of simple interest, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.
In the given question,
The given principal amount = Rs 3000
The given time = 5 years
Interest amount = 525
Now finding the rate of interest.
As we know that the formula of simple interest.
I = P*R*T/100
525 = 3000*R*5/100
Multiply by 100 on both side we get
52500 = 15000*R
Divide by 15000 on both side
R = 52500/15000
R = 3.5
In the question we have to find the interest on Rs 2200 for 6 years at the same rate of interest.
To find the interest put the value in I = P*R*T/100
As given P=2200, R=3.5%, T=6 years
I = P*R*T/100
I = 2200*3.5*6/100
I = 462
Hence, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.
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nikolai and teresa are trying to decide which restaurant they should take their friend thomas to for his birthday. nikolai wants to take thomas to a vietnamese restaurant (which serves generous portions of inexpensive but delicious food), and teresa wants to take thomas to a french restaurant (which serves expensive and beautifully presented food). to resolve the issue, they decide to flip a coin. if nikolai wins the coin toss they will take thomas to the vietnamese restaurant and the next time a friend of theirs has a birthday they will take her or him to the french restaurant teresa likes. if teresa wins the coin toss, they will go to the french restaurant first and the vietnamese restaurant later. the conflict style they used is best described as:
The conflict style they used is Collaboration.
Given, that Nikolai wants to take Thomas to a Vietnamese Restaurant (which serves generous portions of inexpensive but delicious food), and Teresa wants to take Thomas to a French restaurant (which serves expensive and beautifully presented food)
To resolve the issue, they decide to flip a coin.
If Nikolai wins the coin toss they will take Thomas to the Vietnamese restaurant and the next time a friend of theirs has a birthday they will take her or him to the French restaurant Teresa likes and If Teresa wins the coin toss, they will go to the French restaurant first and the Vietnamese restaurant later.
Here, we can see that this is a win-win situation as both can go to their favorite restaurant.
So, the conflict style they used is Collaboration. As, Collaboration generates solutions that satisfy both the parties’ needs.
Hence, the conflict style they used is Collaboration.
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Which statement is true?
O
The letter has rotation symmetry only.
0
The letter has both reflection and rotation symmetry.
The letter has neither reflection nor rotation symmetry,
The letter has reflection symmetry only.
The letter has reflection symmetry only. When one half of an object or form reflects the other half, this is known as reflection symmetry. The line where you cut is referred to as the line of symmetry, generating the two equal portions, and the two halves are reflections of one another.
What is reflection symmetry?Mirror symmetry, line symmetry, reflection symmetry, and mirror-image symmetry are all terms used in mathematics to describe symmetry with respect to a reflection. To put it another way, a figure with reflectional symmetry is unaffected by reflection. There is a symmetry line or axis in 2D and a symmetry plane in 3D.
A sort of symmetry that pertains to reflections is called reflection symmetry. Line symmetry and mirror symmetry are other names for reflection symmetry. If a figure has at least one line dividing it into two halves, one half is said to be the mirror image of the other half.
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Consider the line y=-3/4x-9.
Find the equation of the line that is perpendicular to this line and passes through the point (-4, 2).
Find the equation of the line that is parallel to this line and passes through the point (-4, 2).
Equation of perpendicular line:
Equation of parallel line:
Answer:
Equation of Perpendicular Line: 4x-3y=22
Equation of parallel line:3x+4y+4=
What is the end behavior for the liner function?
Lines do not end, so there can not be an end behavior.
What is straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The equation of the right sideline is y+8 = [tex]\frac{4+8}{2-0}[/tex] (x-0)
y+8 = 6(x -0)
y =6x - 8
Now the endpoint of the line is given so it will not extend indefinitely.
Hence the Lines do not end so there can not be an end behavior.
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pls help with this question
Answer:99
Step-by-step explanation:
1/2 x18x11
99
Jonshelle is developing a new bread recipe. The relationship between cups of water, w, and cups of flour, f, is a=2/5b. What is the scale factor of flour to
water?
Answer: the i8 49
Step-by-step explanation:98493
Y-4=2/3(×+2) look like on line graph
The graph of the linear equation:
y - 4 = (2/3)*(x + 2)
Can be seen on the image at the end.
How to graph the linear equation?
Here we have the following linear equation:
y - 4 = (2/3)*(x + 2)
Isolating y, we get:
y = (2/3)*(x + 2) + 4
To graph the line, we just need to evaluate it in two different values of x so we get two points, once we get the points, we can graph them on a coordinate axis and then connect them with a line.
If we use x = 1 we get:
y = (2/3)*(1 + 2) + 4
y = (2/3)*3 + 4
y = 2 + 4 = 6
y = 6
Then we have the point (1, 6)
if x = 4 then:
y = (2/3)*(4 + 2) + 4
y = (2/3)*6 + 4
y = 4 + 4 = 8
So we have the point (4, 8)
Then the graph of the linear equation is the one you can see below:
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the augusta national golf club in augusta, georgia is an 18-hole course that consists of par-3 holes, par-4 holes, and par-5 holes. a golfer who shoots par has a total of 72 strokes for the entire course. there are two more par-4 holes than twice the number of par-5 holes, and the number of par-3 holes is equal to the number of par-5 holes. find the numbers of par-3, par-4, and par-5 holes on the course.
No. of par-3 holes be represented by = 5
No. of par-4 holes be represented by = 8
No. of par-5 holes are represented by = 5
Total number of courses in the club= 18 (given in the question)
Total shot taken by golfer=72 (given in the question)
Let par-3 holes be represented by t
Let par-4 holes be represented by f
Let par-5 holes be represented by v
forming equations:
f+2=2v
t=v
f + v + t = 18
f+2=2v
f=2v-2 -(i)
t=v -(ii)
f + t + v=18
putting values from (i) and (ii)
(2v-2) + v + v=18
2v-2+2v=18
4v=18+2
4v=20
v=20/4
v=5
Number of par-5 holes=5
from (i)
f=2v-2
putting value
f=2(5)-2
f=10-2
f=8
Number of par-4 holes=8
from (i)
t=v-
putting value
t=5
t=5
Number of par-3 holes=5
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Toss one dime.
The probability of getting heads
is 1. Predict how many times
you would get heads if you
flipped the dime 200 times.
[?] times
We can get heads for 200 times if we flipped the dime for 200 times.
What do you mean by Probability?
Probability is a mathematical measurement to measure the possibility of happening a particular incident or event mathematically.
Also, from the definition of probability, Probability is the ratio of the Number of Favorable event points to the number of total event points with respect to a particular event or incident.
[tex]Probability=\frac{Number of Favorable event Points}{Number of Total event Points}[/tex]
According to the given problem,
The probability of getting heads is 1.
Total number of flip of dime is 200
so, we can get heads from 200 flips [tex]=200*1=200 Times[/tex]
Hence, we get 200 heads from 200 flips of dime.
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The legs of an isosceles triangle are 0.3 foot less than twice the base. The perimeter of the triangle is 4.9 feet.
What is the length of one of the triangle’s legs?
A. 1.1 feet
B. 1.4 feet
C. 1.9 feet
D. 2.2 feet
The length of the given isosceles triangle legs is 1.9 feet.
What is a Linear equation?A linear equation is a equation that has degree as one.
To find the solution of n unknown quantities n number of equations with n number of variables are required.
Given that,
The perimeter of an isosceles triangle is 4.9 feet.
And, legs of the triangle are 0.3 foot less than twice the base.
Suppose the base of the triangle be x.
Then, its legs are 2x - 0.3.
As per the question the expression for the perimeter of the triangle is,
2x - 0.3 + 2x - 0.3 + x = 4.9
=> 5x - 0.6 = 4.9
=> 5x = 5.5
=> x = 1.1
Thus, the legs can be found by substituting x = 1.1 in 2x - 0.3 as below,
2 × 1.1 - 0.3
= 1.9
Hence, the length of one of the triangle’s legs is 1.9 feet.
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Help please
74°
94°
100°
106°
Answer:
106
Step-by-step explanation:
180-74=106
You can find x by looking at the corresponding angle under it and we know a straight line is 180 degrees and the other side of the x is 74 degrees then we just subtract to find the x angle
Hopes this helps please mark brainliest
A rectangle has width 2x + 0.6 and width x -0.4. The perimeter of the rectangle is
51.4 cm. What are the length and width of the rectangle?
Answer:notsure
Step-by-step explanation:
4. The drama club is printing t-shirts for its members. The printing company chargesa certain amount for each shirt plus a setup fee of $40. There are 21 students in the drama club.
a. If there are 21 students in the club and the t-shirt order costs a total of $187, how much does each t-shirt cost? Show your reasoning.
Answer:
$7
Step-by-step explanation:
You want the cost of a shirt when the cost of 21 shirts plus a $40 setup fee is $187.
CostThe total cost of the order is the sum of the setup fee and the extended cost of the shirts.
cost = (setup fee) + (number of shirts) × (cost per shirt)
187 = 40 + 21 × (cost per shirt)
Subtracting 40 gives ...
147 = 21(cost per shirt)
Dividing by 21, we have ...
7 = cost per shirt
Each T-shirt costs $7.