The length and width of the rectangle are 18 in and 1 in, respectively.
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 : b*h, where b = base and h =height.
For this question, the length exceeds its width by 17 inches - L=W+17. Here, the length is the base and the width is the height. Thus, from the value of area given, you can find the values of the length and width of the rectangle.
A=b*h
18=(W+17)*W
18=W²+17W
W²+17W-18=0
Solving this quadratic equation, you have:
[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}[/tex]
[tex]w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]
w1=1 and w2= -18
For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.
As, the area (l*w) is 18 in², see.
18=l*w
18=l*1
l=18 in
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The size of a computer monitor is usually given by the length of its diagonal. A monitor's aspect ratio is the ratio of its width to its height. This monitor has a diagonal length of 27 inches and an aspect ratio of 16:9. Using ratios and the Pythagorean Theorem the approximate width is 23.5 inches and the height is inches.
The length and width of the computer monitor is 23.36 inches
and 13.14 inches.
According to the given statement
we have given that
The length of diagonal of rectangular monitor = 27 inches
The length to width ratio is 16:9
So , Let the Length of monitor = 16x
and The Width of monitor = 9x
And we have to find the length and width of the computer monitor.
So, For this purpose,
From Pythagoras theorem
(Diagonal)² = Length² + width²
Put the values in it and then
27² = (16x)² + (9x)²
729 = 256x² + 81x²
After solving we get
337x² = 729
So, x² = 2.16
∴ x = = 1.46 inches
So, The length = 16x = 23.36 inches
And The width = 9x = 13.14 inches.
Hence, The length and width of the computer monitor is 23.36 inches
and 13.14 inches.
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The distance that you run around the track in gym class is considered ______ data.
A. discrete
B. neither continuous nor discrete
C. continuous
D. both continuous and discrete
The distance that you run around the track in gym class is considered continuous data.
How to determine the type of data?The variable is given as:
Distance
The distance travelled can take any value between 0 and the length of the track.
Take for instance;
The distance travelled can be 1km and it can also be 1.67 km
This means that the distance is continuous
Hence, the statement that completes the blank is (c) continuous
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Divide 2/8 by 9/18 . Input your answer as a reduced fraction.\
Answer:
1/2
Step-by-step explanation:
There is a couple ways of thinking about this. Probably the fastest way is the rule, but the rule is not intuitive. The rule is when you divide fraction, you keep the first fraction the same and then multiple and flip the second fraction.
2/8 x 18/9 = 36/72 To reduce the fraction, could keep dividing the top and the bottom by the same number until it is no longer possible, I could use: 2, 4 3, 9, 18, or 36. If I used 36, I would only have to divide once. 36/16 is 1 and 72/36 is 2 so my answer would be 1/2.
I could have divided the top and bottom by 2 and got 18/36 and then divide by 2 again and get 9/18 and then by 9 and get 1/2. As you can, see there are a lot of option.
The second method is in the picture that I sent you, it is a little more work, but it makes sense.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{2}{8}\div\frac{9}{18} }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Simplify \ \frac{2}{8} \ to \ \frac{1}{4}. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{4}\div\frac{18}{9} }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Use \ this \ rule: a\div \frac{b}{c}=a\times \frac{c}{b}a \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{4}\times\frac{18}{9} }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Use \ this \ rule: \frac{a}{b} \times \frac{c}d{}=\frac{ac}{bd}. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1\times18}{4\times9} \ \to \ \ Multiply }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{ \frac{18}{36}= }}\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{1}{2} }} \end{gathered}$}} \end{gathered}$}[/tex]
Bob and Carol are teenagers. Bob is two years older than Carol. If the digits of Carol's age are reversed, the new number would be three times as large as Bob's age. Find Bob's age.
Bob is 2 years older than Carol and the reverse of Carol's age is 3 times Bob's age, which makes Bob's to be 17 years.
How can Bob's age be calculated?Let 1B represent Bob's age and let 1C represent Carol's age, we can write the following equations;
1B = 1C + 2Reversing Carol's age gives;
C1 = 3 × 1BThe multiples of 3 that have the form X1 have 7 as the rightmost number.
Given that 1B is a teenager, we have;
When;
1B = 171C = 17 - 2 = 15The reverse of Carol's age is therefore;
C1 = 51 = 3 × 17Therefore, from the given description, Bob's age 1B = 17 years
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Please i really need help
for both qeutions
100 points
Answer:
7. a) slope = 5
7. b) slope = 1/2
8. slope = 1
Step-by-step explanation:
slope = rise/run
rise is the vertical change, run is the horizontal change
7. a)
Pick any two points on your line. (0,0) and (1,5) are easy to work with.
The vertical change between the two points is 5
The horizontal change between those points is 1
so slope = 5/1 = 5
7. b)
Again, you can use (0,0) as one of your points. The point (2,4) is good as the second.
slope = 4/2 = 1/2
8. We don't have a graph, but we are given two points to work with, (1,4) and (5,8). Use the formula given...
m = slope = (y2-y1) / (x2-x1)
= (8 - 4) / (5 - 1)
= 4/4
= 1
I hope that helped!
Find the solution of the differential equation that satisfies the given initial condition. du dt = 2t + sec2(t) 2u , u(0) = â2
It looks like the equation is
[tex]\dfrac{du}{dt} = 2t + \dfrac12 \sec^2(t) u[/tex]
with initial value [tex]u(0) = \frac\pi2[/tex].
Rearrange the equation to
[tex]\dfrac{du}{dt} - \dfrac12 \sec^2(t) u = 2t[/tex]
Multiply both sides by the integrating factor
[tex]\displaystyle \mu = \exp\left( \int -\frac12 \sec^2(t)\,dt\right) = \exp\left(-\frac12\tan(t)\right)[/tex]
and solve for [tex]u[/tex].
[tex]\implies e^{-\frac12 \tan(t)} \dfrac{du}{dt} - \dfrac12 \sec^2(t) e^{-\frac12 \tan(t)} u = 2t e^{-\frac12 \tan(t)}[/tex]
[tex]\implies \dfrac{d}{dt}\left[e^{-\frac12 \tan(t)} u\right] = 2t e^{-\frac12 \tan(t)}[/tex]
By the fundamental theorem of calculus, integrating both sides yields
[tex]e^{-\frac12\tan(t)} u = e^{-\frac12\tan(t)} u \bigg|_{t=0} + \displaystyle \int_{\xi=0}^{\xi=t} 2\xi e^{-\frac12 \tan(\xi)} \, d\xi[/tex]
[tex]\implies e^{-\frac12\tan(t)} u = 1\times\dfrac\pi2 + \displaystyle \int_{0}^{t} 2\xi e^{-\frac12 \tan(\xi)} \, d\xi[/tex]
[tex]\implies \boxed{\displaystyle u = \frac\pi2 e^{\frac12\tan(t)} + 2e^{\frac12\tan(t)} \int_0^t \xi e^{-\frac12 \tan(\xi)} \, d\xi}[/tex]
The points (1, 5) and (0, –2) fall on a particular line. What is its equation in slope-intercept form?
Answer:
y = 7x - 2
Step-by-step explanation:
first we need the slope of the line.
the slope is expressed a the ratio (y coordinate change / x coordinate change) when we go from one point on the line to another.
so, let's say we go from (0, -2) to (1, 5), we see
x changes by +1 (from 0 to 1).
y changes by +7 (from -2 to 5)
so the slope is +7/+1 = 7
the slope-intercept form is in general
y = ax + b
a being the slope, b being the y-intercept (the y-value for x = 0).
the point (0, -2) gives us therefore the y-intercept directly : -2.
by using the already established slope and the point (0, -2) for the y-intercept the equation of our line is
y = 7x - 2
pls help me..
look at the pic below!!
Answer:
y = 3(x - 2)² - 5==================
Given equationy = 3x² - 12x + 7Convert this to vertex formy = a(x - h)² + kFollow the stepsy = 3x² - 12x + 7 =
3(x² - 4x) + 7 = Factor out 3
3(x² - 4x + 4) - 3*4 + 7 = Complete the square
3(x - 2)² - 5 Simplify
Answer:
y = 3(x -2)² -5
Step-by-step explanation:
It looks like you want to write the standard-form quadratic ...
y = 3x² -12x +7
in vertex form.
The process is similar to that of "completing the square."
StepsFactor out the leading coefficient
Do this for the variable terms only.
y = 3(x² -4x) +7
Identify the x-term coefficient
The x-term coefficient (inside parentheses) divided by 2 is the opposite of the x-coordinate of the vertex. It is the constant term in the squared binomial of the vertex form. Square this value.
x coefficient: -4
binomial constant: -4/2 = -2
square of this: (-2)² = 4
Add this inside parentheses
To keep the overall equation unchanged, you must also subtract an equal amount outside parentheses.
y = 3(x² -4x +4) +7 -3(4)
Simplify to vertex form
Write the trinomial in parentheses as a square, and simplify the y-coordinate of the vertex.
y = 3(x -2)² -5
What are the solutions of the equation6x^2-x-1=0
Answer:
1/2
1/3
Step-by-step explanation:
x=1/2
x=-1/3
Answer:
[tex]x_{1} =-\frac{1}{3} \\x_{2} =\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]6x^{2} -x-1=0[/tex]
Factoring the equation:
[tex](3x+1)(2x-1)=0[/tex]
Extract the roots:
First factor
[tex]3x+1=0\\3x=-1\\x_{1} =-\frac{1}{3}[/tex]
Second factor
[tex]2x-1=0\\2x=1\\x_{2} =\frac{1}{2}[/tex]
Hope this helps
Rewrite each multiplication or division expression using a base and an exponent
4^5 divided by 4^2=
Using the laws of indices , 4⁵ ÷ 4² can rewritten as 4³.
What is the result of the division in exponent form?
Given the expression; 4⁵ ÷ 4²
To perform the division operation, we use one of the laws of indices;
[tex]n^a/n^b = n^{a-b}[/tex]
Given that;
n = 4a = 5b = 2Now, we apply the laws of indices ;
4⁵ ÷ 4² = 4⁵⁻² = 4³
Therefore, using the laws of indices, 4⁵ ÷ 4² can rewritten as 4³.
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Question 2 (Essay Worth 10 points)
(06.03 MC)
Use the expression 5(6 + 4x) to answer the following:
Part A: Describe the two factors in this expression. (4 points)
Part B: How many terms are in each factor of this expression? (4 points)
Part C: What is the coefficient of the variable term? (2 points) HELP NOWWWW PLSSSS
Part A
The two factors are 5 and 4x+6.
5 is a constant.4x+6 is a binomial.Part B
The first factor, 5, has 1 term.
The second factor, 4x+6, has 2 terms.
Part C
The coefficient of the variable term is 4.
Which expression is not equivalent to 8+(n-4) (8-4+n) 12+n n+4 (8+n)-4
The expression which is not equivalent to (8 + (n - 4)) is (12+n) and this can be determined by using the arithmetic operations.
Given :
Expression - 8 + (n - 4)
To simplify the given expression following steps can be used:
Step 1 - Rewrite the given expression.
= (n - 4) + 8
Step 2 - Now, remove the parenthesis in the given expression.
= n - 4 + 8
Step 3 - Now, write 8 as the addition of 4 and 4.
= n - 4 + 4 + 4
Step 4 - Subtract 4 by 4.
= n + 4
Therefore, the correct answer is (12+n).
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A freezer is shaped like a rectangular prism. It has a length of 8 feet and a height of 3 feet. The volume is 54 cubic feet. Find the width of the freezer.
Answer:
2.25 ft
Step-by-step explanation:
Volume = length x height x width
54= 8 x 3 x ?
Combine: 54= 24 x ?
Find ?: 54/24=2.25
Recheck: 24 x 2.25 = 54
Jerold's weekly pay rate is $865. He receives a 25% pay raise. How can Jerold calculate |
weekly pay rate? Select all that apply.
A
divide $865 by 0.25
B
divide $865 by 1.25
C
multiply $865 by 0.25
D
multiply $865 by 1.25
E
Solve for X:
X
125
865
100
F
Solve for x:
865
25
100
Please help ASAP!! I need to turn this is right now!!!!
Paolo used the Quantitative Reasoning Process to build a budget while he is going to college. He worked hard over the summer and saved $3,314.85 to live on during the next two semesters of school. Paolo will receive a scholarship each semester for $926.65. If he plans to use up all of his savings while at school, how much money can Paolo spend each month, on average, for things like groceries, entertainment, and miscellaneous items?
Assume two semesters equals 8 months total. Also assume Paolo has no other expenses than what he has listed here.
Scholarship for each Semester: $926.65
Tuition & Books Cost per Semester: $1,800
Housing Cost for a two-semester Contract: $1,075
If he has money left, what is the average monthly amount Paolo can afford to spend each month?
If he has overspent, what is the average monthly amount Paolo would be in debt each month?
(Indicate this amount with a negative sign)
The computation shows that the average monthly amount is 61.64.
How to calculate the value?The amount that's left will be:
= 3314.85 + (2 × 926.65) - (1800 × 2) - 1075
= 3314.85 + 1853.3 - 3600 - 1075
= 493.15
The average monthly amount will be:
= 493.15/8
= $61.64
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Determine the vertical asymptotes for the reciprocal of this function f(x)=x^2 + 3x -28
Answer:
x = -7 and x = 4.
Step-by-step explanation:
f(x) = x^2 + 3x - 28
= (x + 7)(x - 4).
The reciprocal of f(x) can be written as
1 / (x + 7)(x - 4).
When the denominator is zero we have vertical asymptotes
so they are x = -7 and x = 4.
Solving equations with fractions- how do i solve this
Answer:
23/75
Step-by-step explanation:
8/15 + x = 21/25
x = 21/25 - 8/15
now we need to bring both fractions to the same denominator (bottom part), so that we can do the subtraction.
what is the least common multiple (LCM) of 25 and 15 ? that will be the common denominator.
I usually use the prime factor factorization of the involved numbers.
15 : 3, 5 (15 = 3×5, there are no smaller prime factors)
25 : 5, 5 (25 = 5×5, there are no smaller prime factors)
the LCM is the combination of the longest chains of each prime factor :
3×5×5 = 75
so, we bring both fractions to 75 denominators.
how many 1/75th are 1/25 ? as 25×3 = 75, we have 3/3 × 1/25 = 3/75 (= 1/25).
so,
21/25 = 21×3/75 = 63/75
how many 1/75th are 1/15 ? as 15×5 = 75, we have 5/5 × 1/15 = 5/75 (= 1/15).
so,
8/15 = 8×5/75 = 40/75
remember, we have to multiply the numerator and the denominator by the same value to keep the original value of the fraction unchanged.
and now our equation looks like
x = 63/75 - 40/75 = 23/75
This Stem-and-Leaf Plot represents the heights of the students on Ralph’s basketball team. One student’s height is missing from the plot. If the mean height of all the students on the team is 61 inches, what is the missing height?
A. 55 in.
B. 59 in.
C. 61 in.
D. 65 in.
The missing height is 65.
What is the missing height?
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
Missing height = (mean x total number of students) - sum of existing heights
Sum of existing heights = (54 + 55 + 56 + 61 + 63 + 64 + 70 ) = 423
Missing height = (8 x 61) - 423 = 64
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A fair coin is tossed three times and is tails each time. What is the probability that the next toss will be
heads
The probability that the next toss will be heads is 1/8.
What is probability?The likelihood of an event occurring is described by probability. We frequently have to make forecasts about the future in real life. We may or may not be aware of the outcome of an event. When this happens, we declare that there is a chance the event will take place.
Using the probability formula, one can determine the likelihood of an event by dividing the favorable number of possibilities by the total number of options. Since the favorable number of outcomes can never be greater than the entire number of outcomes, the probability of an event happening can range from 0 to 1.
Probability of getting two tails and next heads in three tosses is,
=1/2*1/2*1/2
=1/8
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Select the correct answer from each drop-down menu.
Graph of 2 polygons. Polygon 1 at A (minus 6, 6), B (minus 4, 6), C (minus 4, 4), D (minus 6, 2) in quadrant 2. Polygon 2, A prime (minus 6, minus 6), B prime (minus 6, minus 4), C prime (minus 4, minus 4), D prime (minus 2, minus 6) in quadrant 4.
Polygon ABCD goes through a sequence of rigid transformations to form polygon A′B′C′D′. The sequence of transformations involved is a reflection across the
, followed by a reflection across the line
.
The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.
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Study the road plan shown in the figure. A service station will be built on the highway, and a road will connect it with Cray. How long will the new road be? A.54.2 mi B. 312 mi C. 46.2 mi D.400 mi
The length of the road that connects the service station with Cray is 46.2 mi.
How long will the new road be?
We need to apply the principle of similar triangles to obtain the length of the road that will connect the service station with Cray as shown in the image attached.
Hence;
The distance between Alba and Blare = 130 mi
The distance between Alba and Cray = 120 mi
Road connecting the service station with Cray =x
And;
120/130 = x/50
x = 46.2 mi
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Scott counted 23 beats in 10 seconds. What is his approximate heart rate?
123 bpm
130 bpm
138 bpm
230 bpm
Anyone is here
Answer:
138
Step-by-step explanation:
There is 60 seconds in a minute, so if the heart beats 23 times in 10 seconds, it is 138 bpm.
23 * 6 = 138
¿Cuál de los siguientes números NO es un decimal periódico?
A.
11
30
B.
11
400
C.
11
600
D.
111
90
El número decimal que no es un decimal periódico es dado por:
B. [tex]\frac{11}{400}[/tex].
¿Que es un número decimal periódico?Un decimal periódico es un número decimal en el que la misma secuencia de dígitos se repite indefinidamente.
La conversión de las fracciones para decimales són:
11/30 = 0.366666 -> Periódico.11/400 -> 0.0275 -> No es periódico.11/600 -> 0.018333333 -> Periódico, en razón de lá repetición de el 3.11/90 = 0.1222222 -> Periódico.Puede-se aprender más a cerca de números decimales periódicos en https://brainly.com/question/1192529
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Identify the domain of the function shown in the graph
Using it's concept, the domain of the function shown in the graph is:
B. [tex]-6 \leq x \leq 6[/tex].
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. In a graph, the domain is the set that contains all values of x.
From this graph, the function is defined for values of x between -6 and 6, hence the domain is given by:
B. [tex]-6 \leq x \leq 6[/tex].
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X + 2/3 = 8/9 x=? /////////////////////////////////////////
The value of x is 2/9
Given equation x +2/3 = 8/9
We need to find the value of x
Simplifying the equation is
x+2/3 = 8/9
x = 8/9 -2/3
Taking L.C.M of the denominators 3 and 9
The L.C.M is 9
So we will multiply the numerator and denominator with 1 in 8/9
And we will multiply the numerator and denominator with 3 in 2/3
Hence the new equation formed = 8/9-6/9
Solving this equation we get
8-6 / 9
= 2 / 9
Hence the value of x is 2/9
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how do u solve this? what’s the answer?
The functions that have the properties are (d) I and II only
How to determine the functions?The function property is given as:
[tex]a(x) = a^{-1}(x)[/tex]
The above implies that the inverse function and the original function are equal.
From the list of options, we have:
(a) y = x
Make x the subject
x = y --- the same as the original function
(b) y = 1/x
Make x the subject
x = 1/y --- the same as the original function
Hence, the functions that have the properties are (d) I and II only
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[tex]x^{8}+x^{4}+1[/tex]
You did not provide directions. What do you want us to do with your 8th degree polynomial?
Write the following inverse proportion: y is inversely proportional to x, when y = 5 and x = 8.
The inverse proportionality expression is y =40/x
Inverse proportionIf the variable y is inversely proportional to x, this is expressed as;
y = k/x
where
k is the constant of proportionality
If y = 5 and x = 8. then;
5 = k/8
k = 5 * 8
k = 40
Determine the inverse proportionality
Recall that y = k/x
y = 40/x
Hence the inverse proportionality expression is y =40/x
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the base of an isosceles triangle is 4/3 cm . the perimeter of the triangle is 4 2/15 cm.
Answer:
[tex]\sf 1\dfrac{2}{5} \ cm[/tex]
Step-by-step explanation:
Isosceles triangle:If two sides of the triangle are equal, then the triangle is called isosceles triangle.
Let the two equal sides = x cm
Perimeter of the triangle = [tex]\sf 4\dfrac{2}{15}[/tex] cm
[tex]\sf x + x + \dfrac{4}{3}=4\dfrac{2}{15}\\\\[/tex]
[tex]\sf 2x +\dfrac{4}{3}=\dfrac{62}{15}[/tex]
[tex]\sf 2x = \dfrac{62}{15}-\dfrac{4}{3} \ [\text{\bf LCM of 15 , 3 = 15}]\\\\2x = \dfrac{62}{15}-\dfrac{4*5}{3*5}\\\\2x = \dfrac{62}{15}-\dfrac{20}{15}\\\\2x = \dfrac{42}{15} \ [\text{\bf Divide both sides by 2}]\\\\ x = \dfrac{42}{15*2}\\\\ x = \dfrac{7}{5}\\\\ x = 1\dfrac{2}{5}[/tex]
[tex]\sf \boxed{\text{Equal sides of isosceles triangle = $1\dfrac{2}{5}$ cm}}[/tex]
Which formula gives the zeros of y = sin(x)? k pi for any positive integer k k pi for any integer k StartFraction k pi Over 2 EndFraction for any positive integer k StartFraction k pi Over 2 EndFraction for any integer k
Answer:
y =sin(x)
Step-by-step explanation:
small brain
Answer:
B: k pi for any integer k
Step-by-step explanation:
I took the test