The dimensions of the rectangle are 4 yd by 7/2 yd
How to determine the dimensions of the rectangle?The area is given as:
Area = 14 yd^2
Let the width be x. So, the length is:
Length = 2x - 3
The area is then calculated as:
Area = (2x - 3) * x
Expand
Area = 2x^2 - 3x
Substitute 14 for Area
2x^2 - 3x = 14
Rewrite as:
2x^2 - 3x - 14 = 0
Factorize
(2x- 7)(x+2)=0
Solve for x
x=7/2 or x=-2
Width cannot be negative.
So, we have:
x = 7/2
Substitute x = 7/2 in Length = 2x - 3
Length = 2 * 7/2 - 3
Evaluate
Length = 4
Hence, the dimensions of the rectangle are 4 yd by 7/2 yd
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If Alicia can read 3 pages in 1 minute, how long would it take her to read 33 pages?
divide total pages by pages per minute
33 / 3 = 11 minutes
A ladder is leaning against a building. the distance from the bottom of the ladder to the building is 16 ft shorter than the length of the ladder. how high up side of the building is the top of the ladder if the distance is 8 ft less
Write a linear equation given the point and slope or two points (-7,13);slope =2
The linear equation is y = 2x+ 27.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given:
points: (-7, 13) and slope =2
As, we know the equation of line
y= mx +b
as, the line passes through the point (-7, 13) and m= 2
13 = 2(-7) +b
13 + 14 = b
b= 27
Hence, the equation of line is y = 2x+ 27
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a class has 27 students.15 are boys the rest are girls. what is the ratio of girls to total students?
Which of the following is the most appropriate unit to describe the rate at which a person reads?
A. Minutes per word, because the independent quantity is the minutes
B.Minutes per word, because the independent quantity is the words
C.Words per minute, because the independent quantity is the minutes
D.Words per minute, because the independent quantity is the words
What is this equation in slope-intercept form? -3x-2y=30
porfavor me pueden decir Cuanto es 2x2
Si es 2x^2, ya esta en forma simplificada, y no hay mas que le puedes hacer.
Si es 2 por 2, la respuesta es 4.
Please help!
A circle has center O(−3, 1) and radius 10. Which of the following points is on the circle?
V(−3, −4)
X(5, −2)
Y(−6, 0)
Z(5, 7)
The equation K = mv2 represents the energy an object has based on its motion. The kinetic energy, K, is based on the mass of the object, m, and the velocity of the object, v. Lashandra is given K and v for 10 different objects. In order to make solving more efficient, she solves the equation for m : m = . After attempting to determine the mass of a few objects, Lashandra realizes there must be something wrong with her formula. What is Lashandra’s error? She should have multiplied by 2 instead of dividing by 2. She should have multiplied by instead of dividing by 2. She should have used the square root to move the squared term to the other side of the equation. She should have squared the K when moving the v2 to the other side of the equation.
Answer:
She should have multiplied by 2 instead of dividing by 2.
Step-by-step explanation:
Note: The given equation is incorrect and second equation is missing.
Consider the given equation is
[tex]k=\dfrac{1}{2}mv^2[/tex] ...(i)
The formula find by Lashandra is
[tex]m=\dfrac{k}{2v^2}[/tex]
We need to find the Lashandra’s error.
Multiply both sides by 2 in equation (i).
[tex]2k=mv^2[/tex]
Divide both sides by [tex]v^2[/tex].
[tex]\dfrac{2k}{v^2}=m[/tex]
It means, the formula find by Lashandra is incorrect. She should have multiplied by 2 instead of dividing by 2.
Answer:
a
Step-by-step explanation:
2021 edg
These are the first sentences in the short story, "The Gift of the Magi," by O. Henry: "One dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies." Model the scenario with an equation. Let q be the number of quarters, d be the number of dimes, and n be the number of nickels.
The model which represents the total amount in terms of pennies, quarters, dimes and nickel is 0.25q + 0.10d + 0.05n + 0.60
Total amount = $1 and 87 cents = $1.87Amount in pennies = 60 cents = $0.60Number of Quarters, Nickel and Dimes = q, n and d respectively 1 quarter = $0.25 ; 1 dime = $0.10 ; 1 nickel = $0.05To create a mathematical model of the total amount :
Total worth of Quarters = 0.25qTotal worth of dimes = 0.10dTotal worth of nickel = 0.05nTotal worth of pennies = $0.60Total amount = 0.25q + 0.10d + 0.05n + 0.600.25q + 0.10d + 0.05n + 0.60 = 1.87Therefore, the model which represents the total amount is 0.25q + 0.10d + 0.05n + 0.60
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I’m needin sum help.-.
y = 4x+4
give x a number that is on the X axis line to make it a little easier
so lets say x = 2
replace x in the equation with 2
y = 4(2) +4
so y = 8+4 =12
s0 put a dot where x is 4 and y is 12
do the same thing with another number then draw a straight line through both those points
The value of y when x is 3 in the equation "y = 4x + 4" is 16. This linear relationship reflects a consistent rate of change, with each unit increase in x corresponding to a 4-unit increase in y.
In the equation "y = 4x + 4," to find the value of y when x is 3, we substitute x with 3:
y = 4(3) + 4
y = 12 + 4
y = 16
Therefore, when x is 3, y is 16. This means the point on the graph is (3, 16). The equation represents a linear relationship where y depends on x with a constant rate of change of 4. For every 1-unit increase in x, y increases by 4 units due to the coefficient of x.
In summary, for the given equation "y = 4x + 4," when x is 3, y is 16. This relationship indicates a straight line with a slope of 4 and a y-intercept of 4.
The question probable may be;
Given the equation y = 4x + 4 find the value of y when x = 3.
Jaimie swims 12 the length of the swimming pool every 14 of a minute. Enter the number of lengths of the swimming pool Jaimie swims per minute.
Which is NOT a factor pair for 60?
A) (2, 30)
B) (3, 20)
C) (4, 12)
D) (6, 10)
What is the period, in seconds, of a simple pendulum of length 2 meters? Use the gravitational constant g = 9.8 m/s^2 and round your answer to two decimal places.
Answer:
The period, in seconds to two decimal places is, 2.84 sec
Step-by-step explanation:
Using formula:
[tex]T = 2 \pi \sqrt{\frac{l}{g}}[/tex] ......[1]
where
T represents the Time period in second
l represents the length of the pendulum/
As per the statement:
Use the gravitational constant g = 9.8 m/s^2 , length of the simple pendulum(l) = 2 meters and [tex]\pi = 3.14[/tex]
Substitute the given values we have;
[tex]T = 2\cdot 3.14 \cdot \sqrt{\frac{2}{9.8}}[/tex]
⇒[tex]T = 6.28 \cdot \sqrt{\frac{1}{4.9}}=6.28 \cdot \frac{1}{2.21359436212}= \frac{6.28}{2.21359436212} = 2.83701481512[/tex]
Therefore, the period, in seconds to two decimal places is, 2.84 sec
Answer:
2.84 seconds
Step-by-step explanation:
Are these answers correct? If not, what would the answers be?
Does this graph represent a function? why or why not ?
A right triangle has a leg measuring 52 m and a hypotenuse measuring 63 m. find the length of the other leg.
A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply.
Answer:a and e
Step-by-step explanation:
Got it right
One side of a triangle is x in., another side is 2x in., a third side is 2x in., and the perimeter is 36 in.
A rectangle is 4 cm longer than it is wide, and its area is 117 cm2 . find its dimensions.
The length and width of the rectangle are [tex]13[/tex] cm and [tex]9[/tex] cm respectively whose area is [tex]117 cm^2[/tex].
Let the width of the rectangle be [tex]x[/tex].
Then the length of the rectangle is [tex]x+4[/tex].
Area of a rectangle [tex]=[/tex] length [tex]\times[/tex] width
Area [tex]= 117 cm^2[/tex]
[tex](x+4) \times x = 117[/tex]
[tex]x^2+4x=117[/tex]
[tex]x^2+4x-117=0[/tex]
[tex]x^2+13x-9x-117=0[/tex]
[tex]x(x+13)-9(x+13)=0[/tex]
[tex](x+13)(x-9)=0[/tex]
[tex]x+13=0, x-9=0[/tex]
[tex]x=-13, x=9[/tex]
Since, length cannot be negative. So, [tex]x=-13[/tex] is not possible.
So, [tex]x=9[/tex].
And [tex]x+4=13[/tex]
So, length [tex]= 13[/tex] cm and width [tex]= 9[/tex] cm.
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Write each equation in slope-intercept form of the equation of a line. Underline the slope and circle the y-intercept in each equation.
a) 3x+4y–12=0
b) 2x+y=1
Answer:
Step-by-step explanation:
Slope-intercept form of the equation is y = mx + c
Where m = slope of the line
c = y- intercept
a). 3x + 4y - 12 = 0 [Standard form of the equation of a line]
4y + 3x = 12
4y = 12 - 3x
[tex]y=\frac{1}{4}(-3x+12)[/tex]
[tex]y=-\frac{3x}{4}+\frac{12}{4}[/tex]
[tex]y=-\frac{3x}{4}+3[/tex]
Here slope of the line is [tex]-\frac{3}{4}[/tex] and y-intercept is 3.
b). 2x + y = 1
y = -2x + 1
Slope of the line is -2 and y intercept is 1
I don't get this someone help me
Which of the following proportions is false?
10/25=40/100
18/48=20/50
25/45=75/135
24/30=20/25
Karl is purchasing a $205,000 home with a 30-year mortgage at 5.5%. Because he is not making a down payment, PMI in the amount of $97.50/month is required for the first 2 years of the loan. Based on this information, what is the total cost of this loan?
Answer:
The total loan payment is:is $1,024,050
Step-by-step explanation:
To know the total cost of this loan we must sum the the purchasing the mortgage loan LM and the PMI:
L=LM+PMI
The 30-year mortgage loan of $205,000 at 5.5% interest rate can be calculated as:
LM=$205,000*(1+0.055)^30
LM=$205,000*4.984 = $1,021,710
Then for the PMI over 24 months:
PMI: $97.5* 24 = $2,340
Therefore the total loan payment is:
L= $1,021,710 + $2,340 = $1,024,050
The frequency (F) and length (L) of a wave are related by the following formula: F x L = 3.0 x 10^10. Consider that the wavelength of violet light is 1.3 x 10^−8. What is the frequency of violet light?
A) 1.7 x 102
B) 2.3 x 102
C) 2.3 x 1018
D) 4.3 x 107
Answer:
B: 2.3 x 10^18
expination:
Substitute values into the formula.
F x L = 3.0 x 10*10
F x 1.3 x 10^−8 = 3.0 x 10^10
F = 3.0 x 10^10 1.3 x 10^−8 F = 2.3 x 10^18
f(x) = -1/3 x + 7 determine the input that would give an output value of 2/3
Answer:
The correct answer is (19).
Step-by-step explanation:
Which statements are true about the linear inequality y > x – 2? Check all that apply.
The slope of the line is –2.
The graph of y > x – 2 is a dashed line.
The area below the line is shaded.
One solution to the inequality is (0, 0).
The graph intercepts the y-axis at (0, –2).
The true statements about the linear inequality y > x - 2 are that the slope of the line is 1, the graph is a dashed line, the area above the line is shaded, and the graph intercepts the y-axis at (0, -2).
When analyzing the linear inequality y > x - 2, we can identify several characteristics that relate to its graph and the solutions it represents:
The slope of the line is 1, not -2. This is because the equation is in the slope-intercept form y = mx + b, where m is the slope and here m = 1.The graph of y > x - 2 is indeed a dashed line, which indicates that the line itself is not included in the set of solutions for the inequality.The area above the line is shaded because the inequality is y > x - 2, which means all the points where y is greater (above) than x-2.One solution to the inequality is not (0, 0) because when x=0 and y=0, the inequality does not hold true (0 is not greater than -2).The graph intercepts the y-axis at (0, -2), which is the point where the line crosses the y-axis. This corresponds to the b term in the equation y = mx + b.Find the discount price for a cell phone that is on sale for 15% off if the original price is $75? $60.00 $63.75 $64.25 $86.25
Mrs. smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. the top 3% of the class is to receive a special award. assuming that the distribution of words read per minute are normally distributed, what is the minimum number of words per minute a student would have to read in order to get the award?
If Mrs. smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. The minimum number of words per minute a student would have to read in order to get the award will be: 213 words per minute
Using this formula
Minimum number of words =(z score× standard deviation) + means
Where:
z score=(100%-3%=97%)
z score= 97%=1.881
Standard deviation=175
Mean=20
Let plug in the formula
Minimum number of words =(1.881×20) + 175
Minimum number of words =37.62+175
Minimum number of words =212.62
Minimum number of words =213 (Approximately)
Inconclusion if Mrs. smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. The minimum number of words per minute a student would have to read in order to get the award will be: 213 words per minute
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is -1/17 a repeating decimal
A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely). The repeating portion of a decimal expansion is conventionally denoted with a vinculum so, for example,
The minimum number of digits that repeats in such a number is known as the decimal period.
Repeating decimal notation was implemented in versions of the Wolfram Language prior to 6 as PeriodicForm[RealDigits[r]] after loading the add-on package NumberTheory`ContinuedFractions`.
All rational numbers have either finite decimal expansions (i.e., are regular numbers; e.g., ) or repeating decimals (e.g., ). However, irrational numbers, such as neither terminate nor become periodic.
Numbers such as 0.5 are sometimes regarded as repeating decimals since.