Answers
The dimensions of the rectangle are: length= 18 in and width =1 in.
QuadrilateralsThere are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The area of a rectangle can be found for the formula : l*w, where b = length and w =width. The question gives that the area is 18 in².
For this question, the length exceeds its width by 17 inches - l=w+17. Thus, from the value of area given, you can find the values of the length and width of the rectangle.
A=l*w
18=(w+17)*w
18=w²+17w
w²+17w-18=0
Next step will be solve the previous equation ( W²+17W-18=0)
[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]
Therefore,
[tex]w_1=\frac{-17+19}{2\cdot \:1}=1\\ \\ \\ w_2=\frac{-17-19}{2\cdot \:1}=-18[/tex]
For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.
As, the area (l*w) is 18 in², you have.
18=l*w
18=l*1
l=18 in
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Related Questions
100 points, please help:)
Given the graph below, state the parabola's vertex and the equation of the axis of symmetry.
1.(2, –3); x = 2
2.(2, –3); x = –3
3.(2, –3); y = 2
4.(2, –3); y = –3
5. none of the above
Answers
Answer:
1. (2, –3); x = 2---------------------------------
According to the graph, the vertex is at (2, - 3).
The axis of symmetry passes through the vertex, so its x-coordinate determines the vertical line:
x = 2The matching answer choice is 1.
Answer:
1. (2, –3); x = 2
Step-by-step explanation:
The vertex of a parabola is its turning point. This is:
the minimum point of a parabola that opens upwards, or the maximum point of a parabola that opens downwards.From inspection of the given graph, the vertex of the parabola is (2, -3).
The axis of symmetry is the vertical line that passes through the vertex and divides the parabola into two equal (symmetrical) halves.
The axis of symmetry is the x-value of the vertex.
Therefore, the axis of symmetry of the graphed parabola is x = 2.
A bag contains 6 red marbles, 3 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that all three marbles drawn will be red?
Answers
Step-by-step explanation:
First, you want to find out how many total marbles there are. We know there are 6 red, 3 blue, and 5 green. So, 6+3+5=14 total marbles. Since there are 3 blue marbles, the probability of selecting a blue marble is 3/14. This is because you are selecting from a bag of 14 total marbles, 3 of which are the color you want.
To answer this, we can use the equation P (A) = n(A)/n(S). In this equation, P (A) is the probability of the event, n (A) is the number of successful outcomes, and n (S) is the total number of possible outcomes.
For this particular problem, n (A) is 6; since there are 6 red marbles. To calculate n (S), we need to know the total number of marbles, which is 6 + 3 + 5 = 14. So, n (S) = 14.
Plugging these values into our equation gives us P (A) = 6/14, which simplifies to 3/7. To express this as a percentage, we multiply 3/7 by 100 to get 42.9%. To express this to the nearest thousandth, we can round this value to 43%.
Therefore, the probability that all three marbles drawn will be red is 43%, to the nearest thousandth.
It's important to remember that probabilities always need to add up to 100%. In this example, if the probability of drawing three red marbles is 43%, then the probabilities of drawing three blue marbles and three green marbles combined must be 57%.
at 6:00 am and the wind is blowing 32 mph with the increase of 2mph. it is currently 9:00am .how fast is the wind blowing
Answers
The total cost y of an amusement park membership and the number of months x can be represented with the equation y = 15x + 20. Find
and interpret the rate of change and initial value. The rate of change is so the cost per month is $ . The initial value is .so the initial membership fee is $
Answers
The rate of change in the equation y = 15x + 20 is 15. This means that for every increase of 1 unit in x (1 month), the total cost y will increase by 15. So the cost per month is 15 dollars.
The initial value in the equation y = 15x + 20 is 20. This means that when x = 0 (i.e. no months have passed), the total cost y is equal to 20 dollars. So the initial membership fee is 20 dollars.
Answer:
Through from posted good new dts day utilities january home tub just further january kg has last jan free k be page with questions 2:5
5) You invest in 200 shares of Lerner Windows stock and receive a semiannual dividend of
$0.78 a share. At that rate, what will be your annual income from the investment?
Answers
Answer:
your annual income from the investment would be $312.
Step-by-step explanation:
If you invest in 200 shares of Lerner Windows stock and receive a semiannual dividend of $0.78 a share, your annual income from the investment would be:
$0.78 x 200 shares = $156 in semiannual dividends
To find the annual income, you would multiply the semiannual dividends by 2:
$156 x 2 = $312
So, your annual income from the investment would be $312.
Assume an exponential function has a starting value of 16 and a decay rate of 44%. Write an equation to model the situation.
Answers
16 x 0.56^x
where 16 is the sfadtin value
0.56 is how much the amount is decreasing by each time
x= number of hours/days etc
Before jude broke his right arm, he was able to type 19 words per minute on his phone. After he broke his arm, he had to use his left hand for a while, and he could only type 12 words per minute. What is the difference between the number of words he could type in 5 minutes before and after he broke his arm
Answers
30 words in 5 minutes following the arm break.
What is unitary method?This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.
We typically utilize this technique for math calculations.
This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc
According to our question-
45 words in five minutes before to breaking his arm
9*5=45 6*5=30
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Maths sucks and this got my brain scramble
Answers
Answer:
Step-by-step explanation:
this is how I do it in Vietnam, if you don't understand, ask me
Answer:
x = 70°-----------------------------
According to the picture we have:
∠BAK ≅ ∠CBD as corresponding angles,∠BDC ≅ ∠PDK as vertical angles.Find the measure of angle PDK, using sum of angles of ΔPDK:
m∠PDK + 60° + 70° = 180° -m∠PDK = 180° - 130° m∠PDK = 50°Find x, using sum of angles of ΔBDC:
x + 60° + 50° = 180°x = 180° - 110°x = 70°2. Which of the following would be in the solution set to the system of inequalities given below?
Answers
(-4,0) would be a solution of the given system of inequality. Option A is the correct option.
What is the solution to the system of inequalities?
A linear inequality's solution is the ordered pair that is a solution to all inequalities in the system, and the graph of the linear inequality is the graph of all system solutions. In the same coordinate plane, graph one line at a time and shade the half-plane that satisfies the inequality.
Given the system of inequality is
y<-3x-6
4x-2y<-8
If (a,b) is the solution to the system of inequalities, then x=a, and y=b will satifies given system of inequalities.
Given points are (-4,0) and (0,2)
Putting x = -4 and y=0 in the given system of inequalities:
0<-3(-4)-6
→0<12-6
→0<6 (true)
4(-4)-2×0<-8
→-16<-8 (true)
Thus (-4,0) is a solution of the inequalities.
Putting x = 0 and y=2 in the given system of inequalities:
2<-3(0)-6
→2<-6 (false)
4(0)-2×2<-8
→-4<-8 (false)
Thus (0,2) is not a solution of the inequalities.
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What is the range of this absolute value function?
A. -6 ≤ y < ∞
B. -∞ < y ≤ -6
C. 5 ≤ y < ∞
D. -∞ < y < ∞
Answers
The range of this absolute value function is 5 ≤ y < ∞, the correct option is C
What is domain and range of a function?Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
We start by determining the vertex of the absolute value function
Given;
A graph of the function
Now,
From the graph we can observe that the starting of function in y axis is from 5 and ending is at infinite
Therefore the range will be 5 ≤ y < ∞.
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A grocery store is selling 4 bananas for $3.20. What is the unit price of bananas?
Answers
Answer:
To find the unit price of bananas, we need to divide the total price by the number of bananas.
Unit price = Total price / Number of bananas
In this case, the total price is $3.20 and the number of bananas is 4.
Unit price = $3.20 / 4
Unit price = $0.80
So the unit price of bananas in this grocery store is $0.80 per banana.
change the subject of each formula to the letter shown in brackets
Answers
The given formula had been changed according to the instruction.
What is a math formula?A fact or a rule expressed using mathematical symbols is the formula. An equal sign is typically used to connect two or more quantities. When you are aware of the value of one quantity, you can use the formula to determine the value of the other.
What is an example of a formula?Equations, equalities, identities, inequalities, and asymptotic expressions are a few examples of formulas. In the theory of logic, the word "formula" is also frequently used to refer to a sentential formula, also known as a propositional formula, or a formula in propositional calculus.
Here,
Given :
t = (v-u)/a
T=1001/PR
h = ((A/πr) - 3r)/2
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party city is selling a helium tank for inflating balloons for $38. Mark has two coupons that he could use. one coupon is for $5 off, and the other coupon is for 10% off. Which coupon should he use to get the better deal?
Answers
He should use $5 off coupon to get the better deal. This will make the price of helium tank $33 which is less than $10% off i.e $34.2.
What is a coupon?"Coupon" is a term used when bonds were printed on paper. The bondholder would receive a certificate serving as a representation of the bond. On the side of the document would be tear-off coupons that the bondholder could present to the company that issued the bond to receive the coupon payment.
The coupon rates are set by the governments or corporations that issue the bonds, and they can differ significantly depending on the term of the bond and/or the stability of the issuing entity. In order to compensate for the holder's longer wait for the final payment, a 30-year-term bond, for example, might have a higher rate than a note with a 1-year term.
Price when $5 off = 38 - 5
= $33
Price when 10% off = 38 - (38 × 5/100)
= $34.2
Thus, He should use $5 off coupon to get the better deal.
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What is the root of quadratic equation class 10?
Answers
The roots of a quadratic equation are the values of x for which the equation holds true. aα^2+bα+c=0 if and only if α is a root of the quadratic equation.
A quadratic equation has the conventional form ax^2+bx+c=0, where a, b, and c are real values and a0.
The coefficient of x^2 is "a." The quadratic coefficient is what it is termed. The coefficient of x is "b." The linear coefficient is its name. The constant term is "c."
The roots of a quadratic equation are the values of x for which the equation holds true. aα^2+bα+c=0 if and only if α is a root of the quadratic equation.
A quadratic equation may have two real roots that are different from one another, two equal roots, or no real roots at all.
The locations where the graph of the quadratic polynomial intersects the x-axis are known as the roots of a quadratic equation graphically.
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Product
3². 3³
5¹ 52
●
8³. 84
76.72
Expanded Form
(33) (333)
●
(5) (5.5)
(888)
(7 7 7 7 7 7) (77)
●
●
(8 8 8 8)
•
●
Exponential Form
Answers
A way to multiply a number and display it several times. by creating a basis using the number and the repeats.
What is meant by expanded form?A method of displaying several times of the same number multiplied. by forming a base with the number of repeats and the number. Its upper right has a little number written on it.
A number is typically written in exponential notation as a coefficient between 1 and 10 times the exponent, which is an integral power of 10. Write a number in the form: c 10n, where c is a number between 1 and 10 (for example, 1, 2.5, 6.3, 9.8) and n is an integer, to represent it in exponential notation (e.g. 1, -3, 6, -2).
When we expand a number to show the value of each digit, we do so by dividing it into its place values.
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Is the modulus of a complex number same as the absolute value?
Answers
Yes, the modulus of a complex number is the same as the absolute value.
The modulus of a complex number, z = x + yi, is represented as |z| = √(x² + y²) and it is a scalar value that gives the distance of the complex number from the origin in the complex plane.
The absolute value of a complex number is the same as its distance from the origin in the complex plane. The absolute value of a complex number is also represented as |z| = √(x² + y²) which is the same as the modulus.
The modulus and the absolute value are often used interchangeably when referring to the magnitude of a complex number.
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A dihwaher at a retaurant wahe 9 fork. Thee fork repreent 4% of the fork owned by the retaurant. How many fork doe the retaurant own?
Answers
The restaurant owns the 225 forks if 4% of the fork owned by the restaurant.
Percentage are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.
A dishwasher at a restaurant washes 9 fork.
These fork represent 4% of the fork owned by the restaurant.
Now, Solving the question:
We can get our answer by displaying as an equality
= 9 to 4/100
= x to 100/100
You can multiply 4 by 25 to get 100 so to get the amount of forks, multiply 9 by 25
=9 × 25 = 225
Hence, The restaurant owns the 225 fork.
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Find the area of the polygon with the given vertice. N(-2,1), P(3,1), Q(3,-1), R(-2,-1)
Answers
The area of polygon is 10 units.
To find the area of the polygon with the given vertices, we can use the shoelace formula, which is a method for finding the area of a polygon when given its vertices in a certain order.
The shoelace formula is:
Area = (1/2) * |(x1y2 + x2y3 + x3y4 + ... + xn-1yn + xny1) - (y1x2 + y2x3 + y3x4 + ... + yn-1xn + ynx1)|
where (x1, y1), (x2, y2), (x3, y3), ..., (xn, yn) are the vertices of the polygon in a certain order.
For the given vertices, we have:
N(-2,1), P(3,1), Q(3,-1), R(-2,-1)
So the area of the polygon is:
Area = (1/2) * |(-21 + 3-1 + 3*-1 + -21) - (13 + 13 + -1-2 + -1*-2)|
Area = (1/2) * |(-2 - 3 - 3 + 2) - (3 + 3 + 2 + 2)|
Area = (1/2) * |-8 - 12|
Area = (1/2) * 20
Area = 10 square units
So the area of the polygon is 10 square units.
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A baement bedroom mut have a window with an opening area of at leat 5. 7 quare feet, per the International Reidential Code. A rectangular baement bedroom window opening i 0. 75 meter wide. Among the following height, in meter, which i the mallet that will qualify the window opening per the Code?
Answers
As per the unitary method, the smallest that will qualify the window opening per the Code is 7.60 meter.
Here we have given that a basement bedroom must have a window with an opening area of at least 5.7 square feet per the International Residential Code.
Here we have also given that rectangular basement bedroom window opening is 0.75 meters wide.
Let us consider that x be the smallest that will qualify the window opening per the Code.
Therefore, the resulting code is obtained by dividing the area by the width value, then we get,
=> x = 5.7/0.75
Therefore, the value of x is written as,
=> x = 7.60
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Please help!!! I will give brainliest! Please make answer legit tho.
Answers
1/10
Step-by-step explanation:
1 hour is 60 minutes, so it would be 6/60.
then simplify and you get 1/10
What is the y-intercept of the line given by the equation below y =- 10x 14?
Answers
The y-intercept of the line given by the equation y = -10x + 14 is (0, 14)
We know that the y-intercept of the line is nothing but the point at which the line intersects the y-axis.
To find the y-intercept, we substitute x = 0 in given equation of line and solve it for y.
In this question we have been given an equation of line y = -10x + 14
to find y-intercept substitute x = 0 in given equation.
y = -10x + 14
y = -10(0) + 14
y = 0 + 14
y = 14
This means, a line y = -10x + 14 intersects the y-axis at point (0, 14)
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Use the given information to complete parts I and II. In your final answer, include all calculations.
Planet Earth has an approximate diameter of 1.2742 · 10 10 millimeters. The sun has a diameter of 1.391 · 10 6 kilometers.
Part I: Given that for every one kilometer there are 1,000,000 millimeters, which unit of measurement should be used to best represent the lengths of the sun and Earth's diameters?
Part II: Approximate how many times greater the sun's diameter is than planet Earth's.
Answers
Sun's diameter is 109.16653 times more than Earth's diameter.
Units of Length:Physical quantities such as length, current, mass, volume, temperature, area, intensity, and others are represented by units of measurement. To express the size of physical quantities, we employ a variety of measuring units, including traditional ones, the metric system, and US customary units.
Units of Length are
Kilometers, Nanometre, Millimeters, Centimeters, Meters, and Decimetres
Here we have
Planet Earth has an approximate diameter of 1.2742×10¹⁰ millimeters.
The sun has a diameter of 1.391×10⁶ kilometers.
Part I:
Given that, for every kilometer, there are 1,000,000 millimeters,
Here 1000000 = 10⁶
Then the diameter of the earth = 1.2742×10¹⁰/10⁶
= 1.2742×10⁴
Here using the unit kilometer is best to represent the lengths of the sun and earth's diameter because it allows using fewer digits compare to millimeters.
Part II
Let Earth's diameter is less 'x' times than Sun's diameter
=> [ 1.2742×10⁴ ] × x = 1.391×10⁶
=> x = 1.391×10⁶/1.2742×10⁴ = 1.0916653 × 10² = 109.16653
Therefore,
Sun's diameter is 109.16653 times more than Earth's diameter.
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What is the sign of a^{72}\cdot \left(\dfrac{-3}{7}\right)a
72
⋅(
7
−3
)a, start superscript, 72, end superscript, dot, left parenthesis, start fraction, minus, 3, divided by, 7, end fraction, right parenthesis when aaa is a negative number?
Answers
Answer:
Welcome to Gboard clipboard, any text that you copy will be saved here.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Tap on a clip to paste it in the text box.
The product is positive since [tex]a^{(72)}[/tex] is positive (without a question control), the division is negative, and 'a' is negative.
What is the sign of right parenthesis when aaa is a negative number?Let's analyze the expression step by step:
[tex]a^{72}:[/tex] This term talks to a raised to the control of 72.
left(dfrac{-3}{7}right): This term talks to -3/7, a division with a negative respect.
a: This term talks to the variable "a".
To select the sign of the expression, we have to consider the person parts:
[tex]a^{72}[/tex] can be a positive number since any positive base raised to an without-a-question control comes around in a positive respect.
left(dfrac{-3}{7}right) may be a negative division.
a may be a negative number concurring with the address.
By and by, let's put it all together:
a^{72} cdot left(dfrac{-3}{7}right) cdot a
Since a^{72} is positive, left(dfrac{-3}{7}right) is negative, and "a" is negative, the extraordinary product will be positive:
Positive number[tex](a^{72})[/tex] × Negative number left(dfrac{-3}{7}right) × Negative number (a) = Positive number.
In this way, the expression will result in positive respect when "a" may be a negative number.
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A number is increased by 7, twice the result is 41.what is the number?
Answers
Answer:
After increasing it by 7, it becomes = 2x + 7. => x = 82/2 = 41. Hence, the original number = 41.
If segments DE and AB are parallel, which of the following expressions will help Eshaal determine the length of segment BC
Answers
The expression that will help Eshaal determine the length of segment BC is: BC = DE - AB
Since segments DE and AB are parallel, we can use the following expression to calculate the length of segment BC: BC = DE - AB. This expression states that the length of BC is equal to the length of DE minus the length of AB.
If segments DE and AB are parallel, we can use a simple expression to find the length of segment BC. This expression is: BC = DE - AB. This expression states that the length of BC is equal to the difference of the length of DE and the length of AB. In other words, if we know the lengths of segments DE and AB, we can calculate the length of segment BC by subtracting the length of segment AB from the length of segment DE. This expression is a useful tool for finding the length of segment BC when we know the lengths of segments DE and AB. It is a simple and efficient way to calculate the length of segment BC without having to measure it directly.
the complete question is : If segments DE and AB are parallel, which of the following expressions will help Eshaal determine the length of segment BC?If segments DE and AB are parallel, what expression can Eshaal use to determine the length of segment BC?
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help please i need answer
Answers
Answer:
your answer is 5/12
Step-by-step explanation:
becuase im right
How do you find the quotient answer?
Answers
The number we obtain when we divide one number by another is the quotient.
The quotient is indeed the answer that is obtained when the dividend is divided by the divisor in a division problem.
The quotient can be an integer or a decimal number. When a number is completely divisible by another number, the quotient is a whole number.
When a number is not completely divisible by another number, the quotient is a decimal number.
The number is divided by another number to get a different number as an output.
Dividend = Quotient × Divisor + Remainder
If the remainder is equal to 0, then;
Dividend = Quotient × Divisor
Therefore,
Quotient = Dividend ÷ Divisor
Dividend: The number which is required to be divided
Divisor: The number which divides the given dividend
Remainder: The number which is left after the division method. When a number is completely divided then the remainder is zero.
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if f(x)=x^5 and g(x)=-2x-3x^2, which is f(g(x))?
Answers
Therefore , the solution of the given problem of function comes out to be
f(g(x)) = (-2x-3x2)⁵
What exactly do composite functions do?When the result of one function is used as the input for another, this is known as a composite function. The function f g (x) fg(x) fg(x) fg(x), also known as "f of g of x" or "f g fg fg of x," is the composition of the two functions if we have a function f and another variable function g.
Here,
Given,
f(x) = x5
g(x)=-2x-3x₂
f(g(x)) = (-2x-3x2)⁵
Therefore , the solution of the given problem of function comes out to be
f(g(x)) = (-2x-3x2)⁵
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True or False: To solve an inequality means to get the variable by itself on one side of the inequality.
Answers
Answer:
True
That is the formula to solve an inequality
if his pay rate Remains the Same how much will he earn after working 7 months
Answers
Therefore ,the solution of unitary method is monthly salary for the gym employee will be $1500.
What is the unitary method's formula?Finding the variable value of a single unit and multiplying it by the number of units is the unitary method's formula for arriving at the required value.
Here,
Given:
the amount that he earns monthly would be
= Total amount / Number of months
= $4500 / 3
= $1500
Thus He earns $1500 monthly.
The money that; the gym employee earns in 5 months would be:
= 7 × $1500
= $10500.
Therefore ,the solution of unitary method is monthly salary for the gym employee will be $1500. The employee at the gym will make $10500 over the course of five months.
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