Answer:
4.0007, 4.5, 4.7569, 4.9675, 47,005, 47.569, 47.965
Step-by-step explanation:
The roots of the polynomial are the height, length, and width of a rectangular box (right rectangular prism). A new rectangular box is formed by lengthening each edge of the original box by 2 units. The volume of the new box is ________.
The volume of the new box is 30 units³.
We can infer the roots are rational integers from the response options, thus this polynomial ought to be simple to factor. The coefficients of x must multiply by 10, hence they must be in some sequence of 5, 2, 1 or 10, 1. Since we can try each one separately, we can express the factored form as follows:
(5x-p)(2x-q)(x-r)
Due to the fact that p, q, and r must multiply to 6, they must be either 3, 2, 1 or 6, 1, 1 in some sequence. Once more, we may test each one in a different place to determine if they multiply properly.
When we multiply the x-terms and attempt (5x - 2)(2x - 1)(x - 3), the answer is 29. Try adding the x² terms together, they equal -39. Consequently, the roots are 2/5, 1/2 and 3 Now if you add 2 to each root, you get the volume is
= 12/5 × 5/2 × 5 = 30 units³
Therefore, The volume of the new box is 30 units³.
The question is incomplete. The complete question is:
"the roots of the polynomial 10x³ - 39x² + 29x - 6 are the height, length, and width of a rectangular box (right rectangular prism). a new rectangular box is formed by lengthening each edge of the original box by 2 units. what is the volume of the new box?"
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write your answer to the nearest 1/4 inch
Answer:
Step-by-step explanation:1/3
The measurement of the line segment to the nearest 1 / 4 inch is C. 5 ³ / ₄ inches.
How to measure the line segment ?To measure the line segment, you should look at the length of the line segment, while taking into account the measurements between the integrals.
There are 3 sections between each integral, with the suceeding integral being the 4 the section. Seeing as there are 4 sections therefore, it means that each section accounts for :
= 1 / 4 inches
The last integral is 5 inches and then there are 3 section after that. The measurement of the line segment then is:
= 5 + ( 3 x 1 / 4 )
= 5 + 3 / 4
= 5 ³ / ₄ inches
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The question is:
Measure the line segment
Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P′Q′R′ has vertices P′(4, 0), Q′(3, 1), and R′(−1, −2).
Plot triangles PQR and P′Q′R′ on your own coordinate grid.
Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)
(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/2
(B) Coordinates of Δ P"Q"R"
P" (-4,0)
Q"(-3,1)
R"(1,-2)
(C) Triangles PQR and P"Q"R" are not congruent.
Given
ΔPQR is transformed into ΔP'Q'R'
Coordinates of P, Q, R are
P (8,0),
Q(6,2)
R(-2,-4)
Coordinates of P'Q'R' are
P′(4, 0)
Q′(3, 1)
R′(−1, −2)
(A) By Distance formula we can find the distance between P Q and P'Q'
Distance formula = [tex]D = \sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]
Where D = Distance between two points
from distance formula we can write that
PQ = [tex]\sqrt{(6-8)^{2} +(2-0)^{2} } = \sqrt{4+4} =2 \sqrt{2}[/tex]
Similarly
P'Q'= √2
PQ /P'Q' = 2
hence the scale factor of dilation is 1/2 (Compression)
(B )The Coordinates of Reflection about y axis can be written for a point
(x,y) as (-x,y)
So the Coordinated of Δ P"Q"R" can be written as
P" (-4,0)
Q"(-3,1)
R"(1,-2)
(C) ΔPQR and ΔP"Q"R" are similar triangles but they are not congruent because their sides are not equal in size.
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Ali purshacsed a coat that costs 38$ sales tax was 4.5% of the purchase price how much did Ali pay in sales tax
The amount ali paid in tax is $1.71.
How to measure the rate of change of something as some other value changes?
Suppose that we have to measure the rate of change of y as x changes, then we have:
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where we have
[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]
Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.
(5 change per 3 unit can be rewritten as 5/3 change per 1 unit)
We are given that;
Cost of coat=$38
Rate= 4.5%
Now,
To find out how much Ali paid in sales tax, we need to multiply the purchase price by the sales tax rate:
Sales tax amount = Purchase price x Sales tax rate
Sales tax rate = 4.5% = 0.045 (in decimal form)
Purchase price = $38
Sales tax amount = $38 x 0.045 = $1.71
Therefore, by the given rate Ali paid $1.71 in sales tax.
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what is the probability of obtaining a z value less than 1.5?
The probability of obtaining a z-value less than 1.5 is 0.8531 or 85.31% using normal distribution table.
The probability of obtaining a z-value less than 1.5 can be calculated using the standard normal distribution table or by using software like Excel or statistical calculators.
The standard normal distribution is a probability distribution with a mean of zero and a standard deviation of one. It is denoted by the letter Z and is used to standardize normal random variables. The standard normal distribution table provides the probabilities for different values of Z, ranging from -3.4 to 3.4.
To find the probability of obtaining a z-value less than 1.5, we need to look up the value of 1.5 in the standard normal distribution table. The table provides the area under the standard normal curve to the left of a given Z-value.
Looking at the table, we find that the probability of obtaining a z-value less than 1.5 is 0.8531, which means that approximately 85.31% of the area under the standard normal curve is to the left of 1.5.
This means that if we have a normally distributed variable with a mean of zero and a standard deviation of one, there is a 85.31% chance that the z-value will be less than 1.5.
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What are the values of X and Y?
The ratio of the short side to the long side is 9/4 and the ratio of the hypotenuse to the long side is 5/4.
What is triangle ?
A triangle is a two-dimensional shape with three straight sides and three angles. It is one of the most basic and important shapes in geometry.
The three sides of a triangle can be of different lengths, or they can be of the same length, in which case it is called an equilateral triangle. The angles of a triangle can also vary, and they always add up to 180 degrees. Triangles can have acute angles (less than 90 degrees), right angles (exactly 90 degrees), or obtuse angles (greater than 90 degrees).
According to given information :
Ratio of short to long sides:
x/9 = 9/4
To solve for x, we can cross-multiply:
4x = 9 * 9
4x = 81
x = 81/4
So the ratio of the short side to the long side is:
x/9 = (81/4) / 9 = 81/36 = 9/4
Ratio of hypotenuse to long sides:
y/9 = 15/12
To solve for y, we can cross-multiply:
12y = 9 * 15
12y = 135
y = 135/12 = 45/4
So the ratio of the hypotenuse to the long side is:
y/9 = (45/4) / 9 = 45/36 = 5/4
Therefore, the ratio of the short side to the long side is 9/4 and the ratio of the hypotenuse to the long side is 5/4.
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Brianna surveyed a representative sample of students at her school to collect data about the numbers of Internet-compatible devices they own. Use the data in the table. Select all the valid inferences.
Internet-Compatible Devices
Number of Devices Number of Students
1 18
2 25
3 or more 7
Students are more likely to own exactly 2 devices than any other number.
More students own 3 devices than own more than 3 devices.
Less than half as many students own 3 or more devices as compared to students who own 1 device.
10 more students own 1 device than own 3 or more devices.
None of the students own exactly 5 devices.
The valid inferences are (a) and (c)
How to determine the valid inferencesFrom the data in the table, we can make the following valid inferences:
Students are more likely to own exactly 2 devices than any other number. This is because the highest number of students (25) own 2 devices, which is more than the number of students who own 1 device (18) or 3 or more devices (7).Less than half as many students own 3 or more devices as compared to students who own 1 device. This is true because the number of students who own 1 device (18) is more than twice the number of students who own 3 or more devices (7)Using the above as a guide, we have the following:
Other inferences are invalid
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115% is it growth or decay
Answer:
decay
Step-by-step explanation:
Because you are dying every second of the day and are growing only when your body is resting
Answer:
hey, good morning! the answer to this equation is growth!
Step-by-step explanation:
because if you figure out what 115% is as a decimal which is 1.15. and this decimal is above 1.
good luck!
A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34.5-foot shadow. How tall is the building (Round your answer to the nearest tenth.)
The height of the building which casts a 103-foot shadow is 95.5 foot.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34.5-foot shadow
We need to find the height of the building.
Let us consider x be the height of building.
Form a proportional equation.
x/103=32/34.5
Apply cross multiplication
34.5x=32×103
34.5x=3296
Divide both sides by 34.5
x=3296/34.5
x=95.5
Hence, 95.5 foot be the height of the building which casts a 103-foot shadow.
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What are rations equivalent to 5:3 ( can not be 10:6)
Answer: 20:12
Step-by-step explanation:
Answer:
15:9
Step-by-step explanation:
multiply both by 3,4,5,6,7,8,9,etc.
Explain why the value of 2.8 is greater than the value of 2.58.
2.58 is greater than 2.8 because 2.8 is closer to 0 on a number line.
2.58 is less than 2.8 because 2.58 is closer to 3 on a number line.
2.8 is greater than 2.58 because 2.8 is closer to 3 on a number line.
2.8 is less than 2.58 because 2.58 is closer to 0 on a number line.
The correct answer is: 2.8 is greater than 2.58.
What is decimal value?A decimal value is a number expressed in the decimal system, which is based on the number ten. It includes a decimal point that separates the whole number part from the fractional part. The digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts of a whole number, which are expressed in powers of ten (tenths, hundredths, thousandths, etc.). For example, in the decimal value 3.14, the digit 3 represents the whole number part, and the digits 1 and 4 represent the tenths and hundredths parts, respectively. Decimal values are commonly used in mathematics, science, and everyday life to represent quantities that are not whole numbers, such as measurements, percentages, and money values.
Given by the question.
because the digit in the tenths place is larger in 2.8 than in 2.58. In decimal notation, the digit immediately to the right of the decimal point represents tenths, and larger values in this place indicate a larger overall value. In this case, 2.8 has a digit of 8 in the tenths place, while 2.58 has a digit of 5 in the tenths place. Therefore, 2.8 is greater than 2.58. The location of the numbers on a number line is not relevant for comparing decimal values, unless they have the same digit in the tenths.
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7.
A
В
70°
E
85
959х950
15
85
?
C
Solve for the indicated angle or arc
Answer:
BC = 100°
Step-by-step explanation:
You want the measure of arc BC formed by two chords that intersect at 85° and intercept an opposite arc of 70°.
Angle at crossing chordsThe angle formed by crossing chords is the average of the angles they intercept. Here, that means ...
85° = (? +70°)/2 . . . . the crossing angle is 85°
170° = ? +70° . . . . . . multiply by 2
100° = ? . . . . . . . . . subtract 70°
The intercepted arc BC is 100°.
2.In a pond, the area that is covered by algae doubles each week. When the algae was
first spotted, the area it covered was about 12.5 square meters.
a. Find the area, in square meters, covered by algae 10 days after it was spotted.
Starting amount
Show your reasoning.
b. Explain why we can find the area covered by algae 1 day after it was spotted by
multiplying 12.5 by V2.
Answer:
Step-by-step explanation:
a) The area covered by algae 10 days after it was first spotted is approximately 32.64 square meters.
b) We can find the area covered by algae one day after it was first spotted by multiplying [tex]12.5^{1/7}[/tex] by 2.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
a.
To find the area covered by algae 10 days after it was first spotted, we need to convert 10 days into weeks, since the growth rate is given in terms of weekly doubling.
There are 7 days in a week,
So 10 days are approximately 1.43 weeks (10/7).
Let A be the area covered by algae in square meters after n weeks.
Then we can use the formula for exponential growth:
A = 12.5 x [tex]2^n[/tex]
Substituting n = 1.43, we get:
A = 12.5 x [tex]26^{1.43}[/tex]
A ≈ 32.64
Therefore,
The area covered by algae 10 days after it was first spotted is approximately 32.64 square meters.
b.
We know that the area covered by algae doubles each week.
One week is equivalent to 7 days, so after one week, the area covered by algae will be twice the initial area of 12.5 square meters, or 25 square meters.
We can represent this mathematically as:
A = 12.5 x [tex]2^1[/tex]
Now, let's consider what happens after two weeks, or 14 days.
The area covered by algae will double again, so it will be four times the initial area of 12.5 square meters or 50 square meters.
We can represent this mathematically as:
A = 12.5 x 2²
Using the same reasoning, we can find that after three weeks (21 days), the area covered by algae will be eight times the initial area or 100 square meters:
A = 12.5 * 2³
In general, we can see that after n weeks, the area covered by algae will be 2^n times the initial area of 12.5 square meters. This can be written as:
A = 12.5 x [tex]2^n[/tex]
If we want to find the area covered by algae after one day, we can use the fact that one day is equivalent to 1/7 of a week.
So, after one day, the area covered by algae will be:
A = 12.5 x [tex]2^{1/7}[/tex]
Simplifying this expression using the laws of exponents, we get:
A = [tex]12.5^{1/7}\times2[/tex]
Therefore,
We can find the area covered by algae one day after it was first spotted by multiplying [tex]12.5^{1/7}[/tex] by 2.
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A first-time homebuyer is comparing mortgage rates. Option A offers the homebuyer 5.25% annual simple interest. Option B offers the homebuyer the same interest rate but compounded semiannually. If the repayment period is the same length for both loans, which option will result in the least amount of interest added to the loan? Option A will have the least amount of interest because simple interest generates earnings from both principal and interest. Option A will have the least amount of interest because simple interest generates earnings from principal only. Option B will have the least amount of interest because compound interest generates earnings from principal only. Option B will have the least amount of interest because compound interest generates earnings from both principal and interest.
Answer:
If the repayment period is the same length for both loans, the interest option that will result in the least amount of interest added to the loan is B. Option A will have the least amount of interest because simple interest generates earnings from principal only.
What is the simple interest?
The simple interest is the interest system that does not compute interest on accumulated interest.
Unlike simple interest, compound interest charges interest on accumulated interest.
Thus, the simple interest system applies the interest rate on the principal only for each period to determine the amount of interest.
Step-by-step explanation:
Have a nice day
PLEASE HELP ASAP‼️‼️‼️Are the sides proportional?
Set up each ratio of sides and determine if they are equal
ratios. Show all of your work.
3.61 cm
R
44°
S
11.97 cm
9.71 cm
IS
N
T
17.955 cm
14.565 cm
121°
44°
M
L
5.415 cm
The side lengths form a proportional relationship, and the ratios are;
17.955/11.97 = 14.565/9.71 = 5.415/3.61.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
First is Congruent angle measures, then Proportional side lengths.
Here, the triangles are similar, because they have the same angle measures.
17.955/11.97 = 14.565/9.71
= 5.415/3.61.
Thus, the side lengths form a proportional relationship, have a ratio of 1.5.
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Solve the Magic Square
The missing numbers for the respective rows are:
row 1: 4/5
row 2: -4/5 and -2/5
row 3: -3/5 and 6/5
How to evaluate for the missing numbersMissing number for row 1(top row):
1 - 1/5 = 4/5
Missing number for row 2 (2nd number for last column):
3/5 - 1 = -2/5
Missing number for row 2 (1st number for first column):
-2/5 - 2/5 = -4/5
Missing number for row 3 (1st number for first column):
1/5 + (-4/5) = -3/5
Missing number for row 3 (2nd number for second column):
4/5 + 2/5 = 6/5
Therefore, row 1 have the missing number; 4/5. Row 2 missing numbers from left; -4/5 and -2/5. Row 3 missing number from left; -3/5 and 6/5
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Possible question:
If the sum of the first two numbers in row 1 is equal to 1 and the sum of the first two in last column to the right is equal to 3/5. Find the missing numbers.
Mr. Yu applies 12 ounce of fertilizer to every 58 square meter of his lawn.
How many ounces of fertilizer does Mr. Yu use per square meter for his lawn?
Enter your answer in the box as a fraction in simplest form.
ounces per square meter
The amount of urea per square meter in form of fraction will be 6/29 ounce/meter².
What exactly is a fraction?
In mathematics, a fraction is used to represent a piece or part of a whole. It symbolises the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, while the bottom number is known as the denominator. The denominator describes the total number of equal parts in a whole, whereas the numerator defines the number of equal parts taken.
5/10, for example, is a fraction.
In this case, 5 is the numerator and 10 is the denominator.
Now,
Given that Total area=58 square meter
Total Urea used=12 ounce
then urea used for 1 square meter=12/58
=6/29 ounce/meter².
Hence,
The amount of urea per square meter in form of fraction will be 6/29 ounce/meter².
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Prove by contradiction in a right triangle with integer sides, the two shorter sides cannot both be odd
Prove by contradiction that in a right triangle with integer sides, the two shorter sides cannot both be odd.
Assume that the two shorter sides, a and b, of a right triangle are both odd integers. Then the hypotenuse, c, must also be an integer. From the Pythagorean theorem, we know that c2 = a2 + b2. We can rewrite this as c2 = (2m + 1)2 + (2n + 1)2, where m and n are integers. We can expand the left-hand side of the equation to get c2 = 4m2 + 4n2 + 4m + 4n + 1. Since c2 is an even integer, 4m2 + 4n2 must be an even integer as well. But, since 4m + 4n + 1 is odd, the only way to make the left-hand side of the equation an even integer is if 4m2 + 4n2 is an odd integer, which is impossible.
Therefore, our initial assumption that a and b are both odd integers is false. Thus, in a right triangle with integer sides, the two shorter sides cannot both be odd.
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x^2 + 12x + 32 and g(x) = x + 4, find (f/g)(x) and express the result as a polynomial in simplest form.
The result is (x + 8).
What is a polynomial?Polynomial is an equation written with terms of the form kx^n.
where k and n are positive integers.
There are quadratic polynomials and cubic polynomials.
Example:
2x³ + 4x² + 4x + 9 is a cubic polynomial.
4x² + 7x + 8 is a quadratic polynomial.
We have,
x² + 12x + 32 and g(x) = x + 4.
Now,
(f/g)(x)
= (x² + 12x + 32) / (x + 4) _____(1)
Now,
We can factorize x² + 12x + 32.
x² + 12x + 32
= x² + (8 + 4)x + 32
= x² + 8x + 4x + 32
= x(x + 8) + 4(x + 8)
= (x + 4) (x + 8) ______(2)
From (1) and (2),
(f/g)(x)
= (x² + 12x + 32) / (x + 4)
= (x + 4) (x + 8) / (x + 4)
= x + 8
Thus,
The result is (x + 8).
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Han bought a scooter for $3,200. In 5 years, the value of the scooter will depreciate by 65%. What will the value of the scooter be after 5 years?
The required value of the scooter after 5 years will be $1,120.
What is Percentage?Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, if there are 20 students in a class and 5 of them are boys, the percentage of boys in the class can be calculated as follows:
Percentage of boys = (Number of boys / Total number of students) x 100%
According to question:After 5 years, the scooter will depreciate by 65%, which means its value will be reduced to 35% of its original value.
35% of $3,200 = 0.35 x $3,200 = $1,120
Therefore, the value of the scooter after 5 years will be $1,120.
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factor completey x^2+7x-18
Answer:
[tex]\huge\boxed{\sf (x - 9)(x + 2)}[/tex]
Step-by-step explanation:
Given expression:x² + 7x - 18
Using mid-term break formula.
Multiply the side terms. [-18 × x² = -18x²]Now, split the mid-term in such two factor, such that multiplying both gives the side terms.We can split -7x (mid term) into -9x + 2x since -9x × 2x = -18x²So,
= x² - 9x + 2x - 18
Now, take x from (x² - 9x) and 2 from (2x - 18) common
= x(x - 9) + 2(x - 9)
Take (x - 9) common
= (x - 9)(x + 2)[tex]\rule[225]{225}{2}[/tex]
1. Write these percentages as common fractions in simplest form: a)75%
You only showed one btw.
75%=3/4
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
What is a percentage?A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
If we know that percentages are fractions of 100, we know that 75% is equivalent to [tex]\frac{75}{100}[/tex].
Simplifying [tex]\frac{75}{100}[/tex]:
[tex]\frac{75}{100}[/tex] = [tex]\frac{3}{4}[/tex]Therefore, 75% as a simplified fraction is [tex]\frac{3}{4}[/tex].
hey, good morning i have a question!
2x^+4=8^x
Answer:
the solution to the equation 2x^+4=8^x is x = 1.
Step-by-step explanation:
To solve the equation 2x^+4=8^x, we can start by simplifying both sides of the equation.
First, we can rewrite 8^x as (2^3)^x, using the property that 8 is equal to 2 raised to the power of 3.
So, the equation becomes:
2x^+4 = (2^3)^x
2x^+4 = 2^(3x)
Next, we can rewrite 2x^+4 as 2^2 * 2^x, using the property that a^b * a^c = a^(b+c).
So, the equation becomes:
2^2 * 2^x = 2^(3x)
2^(x+2) = 2^(3x)
Now, we can equate the exponents on both sides of the equation:
x + 2 = 3x
2x = 2
x = 1
Therefore, the solution to the equation 2x^+4=8^x is x = 1.
Answer:
Below
Step-by-step explanation:
2 x^4 = 8^x <====not sure syntax is correct(?)
Solving GRAPHICALLY shows x = - .61181
Pls help me I am struggling thanks
The value that should go on the flyer from the environmental group can be found to be 60, 000 m ².
The reason why the building developer chose a different unit from the environmental group is to try to understate the amount of land they would be building on.
How to find the value ?The conversion factor for square kilometers and meters squared is :
1 km ² = 100, 000 m²
0. 06 km ² would then be :
= 0. 6 x 100, 000
= 60, 000 m ²
The building developer chose to use square kilometers to make it seem as though the amount of land they were using was little so as not to have people being angry with the amount of land they would use. The environmental group chose meters squared for the opposite effect to make it seem like a lot of land was to be used.
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87% of what number is 106
If y varies inversely as x, and y = 3 when
x = 8, find y when x = 6.
Answer:
Step-by-step explanation:
Y is 2 when X is 6
if the circumference of a circle is 516 cm, find the area
Answer: 266256π
Step-by-step explanation:
♡ Hope this helps ♡
Please answer that asap
The value of gravitational force between two masses is,
⇒ Gravitational force (F) = 3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Two masses are,
m₁ = 6
m₂ = 8
d = 4
Now, We know that;
Gravitational force (F) = m₁ m₂ / d²
Substitute all the values we get;
Gravitational force (F) = m₁ m₂ / d²
Gravitational force (F) = 6 × 8 / 4²
Gravitational force (F) = 48/16
Gravitational force (F) = 3
Thus, The value of gravitational force between two masses is,
⇒ Gravitational force (F) = 3
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Kara's family car holds 20 gallons of gasoline. Each day the car uses 0.7gallons of gasoline. A warning light comes on when the remaining gasoline is 1.8 gallons or less, Starting from a full tank, can Kara's family drive the car for 18 days without the warning light coming on? Explain your reasoning. Yes, they can drive for 18 days because the gas tank has more than 1.8 gallons in the tank. O No, they can not drive for 18 days because the gas tank has less than 1.8 gallons in the tank.
what is the area of 4 walls of square room??
A square room contains 256 cubic meter of air. IF THE cost of painting it's 4 walls at rs 50 per Sq. meter is Rs 6400,find the cost of carpeting its floor at Rs 99 per Sq. Meter.