Two pairs of separate sides are parallel in a quadrilateral with a single arrow once per pair of opposite sides.
What three types of quadrilaterals are there?A quadrilateral has four straight sides and is a two-dimensional form. Parallelograms, isosceles triangles, rectangles, kites, rectangles, and rhombuses are a few examples of quadrilaterals.
Option (c) illustrates a trapezoid in which one set of opposing sides has arrows indicating how they are parallel to one another. Alternative (d) has both couples of opposing sides indicated with arrows, indicating that all side are parallel, while options (a) and (b) don't even have any linear opposite sides.
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Please help bro I need help solving this polynomial and terms
The expression represents a degree five polynomial with four terms. The constant term is -6, the leading term is (1/2)x⁵, and the leading coefficient is 1/2.
What is a polynomialA polynomial expression is an algebraic expression made up of variables and coefficients, combined using only the operations of addition, subtraction, and multiplication. The variables are raised to a power, which is a non-negative integer, and the coefficients are real numbers. A polynomial can have any number of terms, but it always has a degree, which is the highest power of the variables in the expression.
For the polynomial expression, (1/2)x⁵ - 6 - x⁴ - 5x⁴
There are 4 terms which are: (1/2)x⁵, - 6, - x⁴, and - 5x⁴.
The constant term is -6
The leading term is (1/2)x⁵
The coefficient of the leading term is 1/2.
In conclusion, the expression represents a degree five polynomial with four terms. The constant term is -6, the leading term is (1/2)x⁵, and the leading coefficient is 1/2.
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Answer:
quadrinomial, 4, -6, 1/2x^5, 1/2
Step-by-step explanation:
quadrinomials are polynomials with 4 terms
constant is the number with no variable
leading term is the term at the beginning
leading coefficient is the number at the beginning
A bicycle wheel has a radius of 225 mm and has 25 equally spaced spokes. What is the approximate arc length, rounded to the nearest hundredth, between each spoke? Use 3.14 for π. Show your work.
The approximate arc length is 56.52mm.
What is an arc length?
The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc section by simulating it with connected line segments. There are a finite number of segments in the rectification of a rectifiable curve.
Here, we have
Given: A bicycle wheel has a radius of 225 mm and has 25 equally spaced spokes.
To solve this question, we have to use the formula of the length of an arc which is given as
L = θ/360 * 2πr
To find the angle between each spoke, let's divide 360 by 25
θ = 360/25
θ = 14.4
Now that we have the value of the angle, let's substitute it and solve for the length of the arc.
L = 14.4/360 * 2(22/7)(225)
L = 56.52mm
Hence, the approximate arc length is 56.52mm.
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Solve the equations for x
Answer:
Step-by-step explanation:
5=cx-ax=x(c-a)
x(c-a)/5=1
(c-a)/5=1/x
x=5/(c-a)
↑
A hot-air balloon, headed due east at an average speed of 15 miles per hour at a constant altitude of 95 feet, passes over an intersection (see
the figure). Find an expression for its distance d (measured in feet) from the intersection t seconds later.
The expression for its distance d (measured in feet) from the intersection t seconds later is d = x + 79200 t (feet)
Finding expression for distanceSince the balloon is moving due east, we only need to consider its horizontal motion, ignoring its vertical motion at a constant altitude of 95 feet.
Let's call the initial distance of the balloon from the intersection x. The distance of the balloon from the intersection t seconds later can be found using the formula for distance traveled at a constant speed:
d = x + vt
where v is the speed of the balloon (15 miles per hour) and t is the time elapsed (in hours). To convert the speed from miles per hour to feet per second, we can multiply by the conversion factor of 5280 feet per mile:
d = x + (15 miles/hour) * (5280 feet/mile) * (t hours)
d = x + (15 * 5280) t feet
d = x + 79200 t feet
So the expression for the distance of the balloon from the intersection t seconds later is:
d = x + 79200 t (feet)
Note: In this expression, x represents the initial distance of the balloon from the intersection, which is unknown.
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Suppose that Jenny, a college admissions officer for the Department of Mathematics at Smalltown University, is reading applications submitted by prospective students. The president of Smalltown University is weary about admitting too many domestic students and not enough international students. However, the applications are blinded so Jenny cannot see if an applicant is a domestic student or international student. Jenny is instructed by the president to admit exactly 20 applicants to the Department of Mathematics in a given year. Suppose that 38 domestic students and 42 international students applied to the Department of Mathematics at Smalltown University this year, and suppose that there is no difference in the qualifications of domestic and international students applying to Smalltown University.
Let represent the number of domestic applicants that Jenny selects this year. Calculate the mean, , and standard deviation, , of .
Please give the exact value for the mean and round your standard deviation to the nearest three decimal places.
The mean number of domestic applicants that Jenny selects is exactly 9.5, and the standard deviation is approximately 1.932
What is the standard deviation?Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
This is a problem involving a hypergeometric distribution since we have a fixed population (all applicants), two groups within the population (domestic and international students), and a fixed number of samples (20 students to be admitted).
Let X be the number of domestic applicants that Jenny selects this year. Then X follows a hypergeometric distribution with parameters N = 80 (total number of applicants), K = 38 (number of domestic applicants), and n = 20 (number of students to be admitted).
The mean of X is given by μ = nK/N, and the standard deviation of X is given by,
σ = √(nK(N-K)/(N²(N-1))).
Substituting the given values, we get:
μ = (20 x 38)/80 = 9.5
σ = √(203842/(80² x 79)) ≈ 1.932
Therefore, the mean number of domestic applicants that Jenny selects is exactly 9.5, and the standard deviation is approximately 1.932.
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(c) 10:35 f the foll ing ratio
The ratio 10:35 can be simplified to 2:7.
What is a Ratio?
A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
The ratio 10:35 can be simplified to 2:7.
To simplify a ratio, you can divide both values by the greatest common factor. In this case, the greatest common factor of 10 and 35 is 5, so 10 divided by 5 is 2, and 35 divided by 5 is 7.
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Simply the following ratio 10:35
why is it important to understand the concept of interest
It is important to understand the concept of interest beacause it is a part of our life and it hels us to understand the economic situation of ourselves.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
We have.
There are two types of interest commonly studied.
1)
Simple interest
2)
Compound interest
Now,
Simple interest is the interest calculated only on the principal year after year.
Whereas compound interest is the interest calculated on the principal as well as the interest after the first year.
Example:
Principal = $100
Rate = 10%
Time = 2 years
Simple interest after two years.
= 2 x (10% of 100)
= 2 x (1/10 x 100)
= 2 x 10
= $20
Compound interest after two years.
Ist year:
= (10% of 100)
= (1/10 x 100)
= $10
2nd year:
= 10% of (100 + 10)
= 1/10 x 110
= $11
So,
= 10 + 11
= $21
Thus,
The concept of interest is given above.
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In right triangle ABC, m∠A=90 ∘ , cos B=x+0.26, and sin C=3x+0.14. Solve for x.
In right triangle ABC, the value of x is equal to 0.06.
What is a right angle?In Mathematics, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.
Since the angle formed by side A is a right triangle, we have the following complementary angles;
C + B = 90
sin(C) = cos(B)
x + 0.26 = 3x + 0.14
3x - x = 0.26 - 0.14
2x = 0.12
x = 0.12/2
x = 0.06
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how can I solve binary operations?
Some way to solve binary operations are listed below
How can binary operations be solvedBy definition, binary operations involve performing arithmetic operations on two operands in a specific way.
An example of a binary expression is a + b
Where a and b are the operands & + is the operator
Some common binary operations and how to solve them are highlited below
Addition (+): To add two binary numbers, start from the right-most bit and work your way left. In binary: 1 + 1 = 10Subtraction (-): To subtract one binary number from another, use the same borrowing method as in decimal subtraction.Other operations are
Multiplication (*), Division (/) and Modulus
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Which precedents did the u. S. Constitution establish for other governments? select all that apply.
darius spend 35% of his time doing math homework. Alex spends 2/5 of his time doing math homework. Who spend more home work time on math. explain
Answer:
Alex spends more time 2/5 of 100 is 40%
1. Takis Machine Shop paid a base rate for the state's workers' compensation insurance of $9.40 per $100 paid in wages. Takis has a monthly payroll of $53,896.84. After reevaluating the frequency and severity of accidents at machine shops, the state increased the base rate to $10.40 per $100 paid in wages. Assuming the monthly payroll stays the same, how much more will Takis pay each year for state workers' compensation insurance in dollars. Round to the nearest hundredth of a percent.
2. The Madison County tax assessor determined the market value of a home to be $590,000. The rate of assessment in Madison County is 40% of market value. The tax rate is 42.73 mills. Calculate the real estate tax in dollars. Round to the nearest hundredth of a percent.
3. Vanesa Vasquez contributes $2,500 per year to her Roth IRA, an ordinary annuity, starting at age 35. If she earns 7.4% annual interest compounded annually, what is the fair market value of her Roth IRA at age 65? How much interest will she have earned in dollars? Round to the nearest hundredth of a percent.
4. Marty and Roslyn Seymour purchase a GNMA Mortgage issue bond selling at a premium of 103.7% of its $10,000 face value. The bonds are selling at a premium because they have an annual yield of 8.75%. Find the interest rate as a percent? Round to the nearest hundredth of a percent.
5. Ricardo Ramirez took out a single-payment loan for $2,500 at 7.8% ordinary interest to pay his federal income tax bill. If the maturity value of the loan was $2,548.75, in how many days would Ricardo have to pay back the loan?
Answer: do you need me to answer all or anthor example.
Step-by-step explanation:
I will answer
Would sorting the tiles with positive coefficients and tiles with negative coefficients together help to simplify an expression that involves all tiles? Explain.
Yes, it is possible to make an expression including all tiles simpler by grouping together the tiles with negative coefficients and the tiles with negative coefficients.
Negative coefficients: What are they?Simply put, negative coefficients are coefficients with negative values. A negative coefficient can be anything like -8 in the term -8z or -11 in the term -11xy. The result of multiplying the variables by the integer is negative.
What happens to a negative exponent's coefficient?A negative exponent signifies a very small number: The decimal in the coefficient is shifted eleven positions to the left as a result. A decimal number must also be moved in order to be expressed in scientific notation.
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Quadratic Expressions:Question 1
Which is a factor of x²+ 7x + 10?
Select one:
a x-5
bx-1
cx+5
dx+1
Answer:
Option C. (x + 5)
Step-by-step explanation:
This quadratic equation can either be solved using the quadratic formula or be factorised using The Double Bubble Method.
Double Bubble Method:
After listing the different pairs of factors 10, the pair (that would add together to give 7) are 2 and 5. These two factors will be used to rewrite +7x:
[tex]x^{2} + 2x + 5x + 10[/tex]
Factorization by grouping (i.e factorising each separate group sharing a common factor) will then be applied:
[tex]= x(x + 2) + 5(x + 2)[/tex]
The common factor, which is the (x + 2) expression, will be extracted:
[tex]= (x + 2)(x + 5)[/tex]
∴ [tex]x^{2} + 7x + 10[/tex] can be factorised to [tex](x + 2)(x + 5)[/tex]
It is observed that a factor of the given quadratic equation is x + 5
∴Option C
Find the value of y to the nearest tenth.
6.4
6.0
7.5
8.0
Let's consider what the question asks for:
--> the length of 'y'
To solve:
--> we need to use trigonometry
--> let's determine which function to use based on the image given
below
--> (look at image attached)
Let's use angle with measure of 53:
--> the side with length of 'y' is adjacent to it
[tex]cos(53)=\dfrac{y}{10} \\\\y=10*cos(53)=6.02[/tex]
Thus the length of that particular side is about:
--> 6.0
Answer: 6.0
∛.um what’s 4 plus 3
The solution of the radical expression ∛(4+3) will be 1.91.
What is a radical expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
The radical sign, which may be read as either the nth root of x or x radical n, expresses the root of a number. The vinculum, or horizontal line that encircles the number, and the radicand, or number beneath it, are both technical terms.
Given that the expression is ∛(4+3). The solution of the medical expression will be,
E = ∛ ( 4 + 3)
E = ∛(7)
The value of the cube root of the number 7 will be,
E = 1.91
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Six years from today you need $10,000. You plan to deposit $1,500 annually, with the first payment to be made a year from today, in an account that pays a 5% effective annual rate. Your last deposit, which
will occur at the end of Year 6, will be for less than $1,500 if less is needed to reach $10,000. How large will your last payment be? Do not round intermediate calculations. Round your answer to the nearest
cent.
Answer:
Step-by-step explanation:
We can use the formula for the future value of an annuity to find the amount you'll have in the account at the end of Year 6. An annuity is a series of equal payments made at equal intervals of time, and the future value of an annuity is the amount you'll have in the future if you invest those payments and earn a given rate of interest.
The formula for the future value of an annuity is:
FV = PMT * (((1 + r)^n - 1) / r)
where:
FV = future value of the annuity
PMT = annual payment amount
r = annual interest rate as a decimal
n = number of payments
In this case:
PMT = $1,500
r = 0.05
n = 6
Plugging in the values:
FV = $1,500 * (((1 + 0.05)^6 - 1) / 0.05)
FV = $1,500 * (1.328867 - 1) / 0.05
FV = $1,500 * 0.328867 / 0.05
FV = $1,500 * 6.577340
FV = $9,865.61
So, the amount in the account at the end of Year 6 will be $9,865.61. To find the last payment, we subtract this amount from the desired future value of $10,000:
$10,000 - $9,865.61 = $134.39
Therefore, your last payment will be $134.39.
. One number is five more than the other. Their sum is 33. Find the numbers.
Answer:
14 and 19
Step-by-step explanation:
14+5=19
14+19=33
40 books are increased in the ratio 5:4 the new number of books are?
Answer:
50
Step-by-step explanation:
4x10=40.
5x10=50
Answer:
Step-by-step explanation:
To increase a quantity in a given ratio, we can follow these steps:
Step 1: Find the total increase in the quantity.
Suppose the original number of books is "b". The total increase in the number of books is 40, so:
b + 40 = b
Step 2: Divide the total increase into two parts in the given ratio.
In this case, the ratio is 5:4, so we can divide the increase of 40 into two parts in the ratio 5:4. Let's call the first part "x". Then, the second part is 40 - x.
The first part (5x) is 5 times the second part (4x), so:
5x = 4(40 - x)
Step 3: Solve for x.
Expanding the right side:
5x = 160 - 4x
Adding 4x to both sides:
9x = 160
Dividing both sides by 9:
x = 40/9
Step 4: Find the new number of books.
The first part of the increase (x) is 40/9, and the second part (40 - x) is 40 - 40/9 = 40 * 9/9 - 40/9 = 40 * 8/9. The new number of books is the original number plus the two parts of the increase:
b + 40/9 + 40 * 8/9 = b + 40
So, the new number of books is b + 40.
What is the area of this parallelogram?
A:60cm
B:66
C:72
D:132
The area of the given parallelogram is 12 cm².
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
The formula to calculate the area of a parallelogram can thus be given as,
Area of parallelogram = b × h square units
where b is the length of the base and h is the height
According to the given parallelogram ABCD, we have
Length of the base b = 5 + 9 = 14 cm
The height h = 8 cm
Area of parallelogram = b × h
Area of parallelogram = 14 × 8
Area of parallelogram = 112 cm²
Thus, the area of the given parallelogram is 12 cm².
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The question seems incomplete, the missing figure has been attached below.
Algebra 2, Exponental Funtction.
The numeric value of the exponential function at x = 19.5 is given as follows:
f(19.5) = 178.41.
How to model an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which:
a is the initial value, the value of y when x = 0.b is the rate of change.Considering that f(4.5) = 25 and f(14) = 85, the two equations are given as follows:
ab^(4.5) = 25.ab^(14) = 85.Hence:
a = 25b^(-4.5).
Then the value of b is obtained as follows:
25b^(-4.5)b^(14) = 85.
b^(9.5) = 85/25
b = (85/25)^(1/9.5)
b = 1.14.
Then the value of a is obtained as follows:
a = 25 x (1.14)^(-4.5)
a = 13.86.
Then the function is defined as follows:
y = 13.86(1.14)^x.
At x = 19.5, the numeric value is given as follows:
y = 13.86(1.14)^19.5
y = 178.41.
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What is the surface area of the cylinder?
100 ft²
800 ft²
10 ft
10 ft
Can I possibly get help with #1?
The question is attached as an image:
The graph of the function is added as an attachment
How to graph the function in (1)From the question, we have the following parameters that can be used in our computation:
h(x) = (1/3)ˣ - 4
The above function is an exponential function shifted down from the origin by 4 units
An exponential function of this form is represented as
h(x) = a(b)ˣ + c
Where
Initial value = a
Rate = b
Shift = c
Using the above as a guide, we have the following:
a = 1
b = 1/3
c = -4
Next, we plot the graph
See attachment for the graph of the function
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1 < (c - 1)^2 ≤ 36
What is the greatest integer solution to the inequality above?
Answer:
The greatest integer solution to the inequality 1 < (c - 1)^2 ≤ 36 is c = 6.
Step-by-step explanation:
rectangular fountain has a length of L meters and a width of 3 meters less than its length. How much
es it cost to border the outside of the fountain using 1-meter tiles that cost $4 each. HINT: draw a picture.
The expression that represents the cost to the border will be 16L - 8.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides.
Perimeter of the rectangle = 2(L + W) units
A rectangular fountain has a length of L meters and a width of 3 meters less than its length. Then the equations are given as,
W = L - 3
The perimeter of the rectangle is given as,
P = 2(L + L - 3)
P = 2(2L - 3)
P = 4L - 6
The amount of money that is required for bordering the fountain is given as,
⇒ 4 × [4L - 6] + 4 × 4
⇒ 16L - 24 + 16
⇒ 16L - 8
The expression that represents the cost to the border will be 16L - 8.
And the diagram is given below.
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Solve for x, will give brainliest
Answer:
2
Step-by-step explanation:
Line MN ≅ Line LK
Since Line MN ≅ Line LK, that means the diagonals must be congruent ∴ MK ≅ NL.
Now that we know MK ≅ NL, we can set them equal to each other.
MK = [tex]16[/tex]
NL = [tex]7x + 2[/tex]
[tex]16=7x+2\\14=7x\\2=x[/tex]
Therefore, 2 is your final answer.
1. The Winston Tree Farm and Nursery has a base rate for the state's workers compensation insurance of $5.93 per $100.00 paid in wages. The monthly payroll for the nursery is $3,560. What is the monthly premium for workers compensation insurance in dollars? Round to the nearest hundredth of a percent.
2. Takis Machine Shop paid a base rate for the state's workers' compensation insurance of $9.40 per $100 paid in wages. Takis has a monthly payroll of $53,896.84. After reevaluating the frequency and severity of accidents at machine shops, the state increased the base rate to $10.40 per $100 paid in wages. Assuming the monthly payroll stays the same, how much more will Takis pay each year for state workers' compensation insurance in dollars. Round to the nearest hundredth of a percent.
3. The Madison County tax assessor determined the market value of a home to be $590,000. The rate of assessment in Madison County is 40% of market value. The tax rate is 42.73 mills. Calculate the real estate tax in dollars. Round to the nearest hundredth of a percent.
4. Vanesa Vasquez contributes $2,500 per year to her Roth IRA, an ordinary annuity, starting at age 35. If she earns 7.4% annual interest compounded annually, what is the fair market value of her Roth IRA at age 65? How much interest will she have earned in dollars? Round to the nearest hundredth of a percent.
5. Marty and Roslyn Seymour purchase a GNMA Mortgage issue bond selling at a premium of 103.7% of its $10,000 face value. The bonds are selling at a premium because they have an annual yield of 8.75%. Find the interest rate as a percent? Round to the nearest hundredth of a percent.
6. Ricardo Ramirez took out a single-payment loan for $2,500 at 7.8% ordinary interest to pay his federal income tax bill. If the maturity value of the loan was $2,548.75, in how many days would Ricardo have to pay back the loan?
Answer:
1. The monthly premium for workers' compensation insurance for the Winston Tree Farm and Nursery can be calculated as follows:
Monthly payroll: $3,560 Base rate: $5.93 per $100 Rate per $1,000: $5.93 * 10 = $59.30 Premium: $3,560 / 1,000 * $59.30 = $209.51
So, the monthly premium for workers' compensation insurance is $209.51.
2. The amount that Takis Machine Shop will pay each year for workers' compensation insurance can be calculated as follows:
Old base rate: $9.40 per $100 New base rate: $10.40 per $100 Monthly payroll: $53,896.84 Old rate per $1,000: $9.40 * 10 = $94.00 New rate per $1,000: $10.40 * 10 = $104.00 Old premium: $53,896.84 / 1,000 * $94.00 = $5,045.65 New premium: $53,896.84 / 1,000 * $104.00 = $5,610.71 Increase in premium: $5,610.71 - $5,045.65 = $565.06
So, Takis Machine Shop will pay an additional $565.06 each year for workers' compensation insurance.
3.The real estate tax for the home in Madison County can be calculated as follows:
Market value: $590,000 Rate of assessment: 40% of market value = $590,000 * 0.4 = $236,000 Tax rate: 42.73 mills = 0.04273 Tax: $236,000 * 0.04273 = $10,130.68
So, the real estate tax for the home in Madison County is $10,130.68.
4. The fair market value of Vanesa Vasquez's Roth IRA at age 65 can be calculated as follows:
Contribution: $2,500 Years of contribution: 65 - 35 = 30 Annual interest rate: 7.4% Future value: $2,500 * (1 + 0.074)^30 = $29,706.74
So, the fair market value of her Roth IRA at age 65 is $29,706.74.
The amount of interest earned can be calculated as follows:
Future value: $29,706.74 Present value: $2,500 Interest earned: $29,706.74 - $2,500 = $27,206.74
So, Vanesa Vasquez will have earned $27,206.74 in interest.
5. The interest rate as a percent for the GNMA Mortgage issue bond can be calculated as follows:
Face value: $10,000 Selling price: $10,000 * 103.7% = $10,370.00 Yield: 8.75% Price: $10,370.00 Interest: $10,370.00 - $10,000 = $370.00 Interest rate: ($370 / $10,000) * (12 / 1) = 0.09375 = 9.375%
So, the interest rate for the GNMA Mortgage issue bond is 9.375%, rounded to the nearest hundredth of a percent.
6. Let's call the number of days that Ricardo has to pay back the loan "d".
The interest on the loan can be calculated using the formula:
I = P * r * t
where I is the interest, P is the principal (the amount borrowed, $2,500), r is the annual interest rate as a decimal (7.8% as a decimal is 0.078), and t is the time in years (d divided by 365).
So we have:
I = $2,500 * 0.078 * (d / 365)
We also know that the maturity value of the loan is the sum of the principal and the interest:
$2,548.75 = $2,500 + I
So we can substitute for I:
$2,548.75 = $2,500 + $2,500 * 0.078 * (d / 365)
Expanding the right-hand side:
$2,548.75 = $2,500 + $194.00 * (d / 365)
And solving for d:
d = 365 * ($2,548.75 - $2,500) / $194.00
d = 365 * ($48.75) / $194.00
d = 365 * 0.25191780821917808
d = 91.37 days
So Ricardo would have to pay back the loan in 91.37 days.
Step-by-step explanation:
if car traveling 40 mph takes 30 feet to stop, how many seconds will it take to stop? 
Answer:
To find the time it takes a car traveling at 40 mph to stop after covering a distance of 30 feet, we need to use the formula for distance, speed, and time, which is:
distance = speed * time
Rearranging the formula, we get:
time = distance / speed
Since the speed is in miles per hour (mph), we need to convert it to feet per second (fps). One mph is equivalent to 1.47 fps, so 40 mph is equivalent to 40 * 1.47 = 58.8 fps.
Now we can plug in the values for distance and speed into the formula:
time = 30 feet / 58.8 fps
time = 0.5104 seconds
Rounding to the nearest second, we get:
time = 0.51 seconds
So, it would take the car approximately 0.51 seconds to stop after traveling 40 mph.
Step-by-step explanation:
A cargo ship contains a total of 16,770
containers that are evenly placed in 65
rows. How many containers are in each row?
ANSWER AND I'LL MARK U BRAINLIEST PLS.
Answer:258 containers
Step-by-step explanation:
Simply,
16770/65=258.
Hope this helps :]
Use the rational zeros theorem to list all possible rational zeros of the following.
Answer:
[tex]\sf \dfrac{p}{q}=\dfrac{\pm1}{\pm1},\dfrac{\pm1}{\pm3},\dfrac{\pm7}{\pm1},\dfrac{\pm7}{\pm3}=\pm 1, \dfrac{\pm1}{\pm3},\pm 7, \dfrac{\pm7}{\pm3}[/tex]
Step-by-step explanation:
Given polynomial:
[tex]f(x)=-3x^3-5x^2+x-7[/tex]
Rational Root TheoremIf P(x) is a polynomial with integer coefficients and if p/q is a root of P(x), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).
Possible p-values
Factors of the constant term: ±1, ±7
Possible q-values
Factors of the leading coefficient: ±1, ±3
Therefore, all the possible values of p/q:
[tex]\sf \dfrac{p}{q}=\dfrac{\pm1}{\pm1},\dfrac{\pm1}{\pm3},\dfrac{\pm7}{\pm1},\dfrac{\pm7}{\pm3}=\pm 1, \dfrac{\pm1}{\pm3},\pm 7, \dfrac{\pm7}{\pm3}[/tex]
Substitute each possible rational root into the function:
[tex]x=-1 \implies f(-1)=-3(-1)^3-5(-1)^2+(-1)-7=-10[/tex]
[tex]x=1 \implies f(1)=-3(1)^3-5(1)^2+(1)-7=-14[/tex]
[tex]x=-7 \implies f(-7)=-3(-7)^3-5(-7)^2+(-7)-7=770[/tex]
[tex]x=7 \implies f(7)=-3(7)^3-5(7)^2+(7)-7=-1274[/tex]
[tex]x=-\dfrac{1}{3} \implies f\left(-\dfrac{1}{3}\right)=-3\left(-\dfrac{1}{3}\right)^3-5\left(-\dfrac{1}{3}\right)^2+\left(-\dfrac{1}{3}\right)-7=-\dfrac{70}{9}[/tex]
[tex]x=\dfrac{1}{3} \implies f\left(\dfrac{1}{3}\right)=-3\left(\dfrac{1}{3}\right)^3-5\left(\dfrac{1}{3}\right)^2+\left(\dfrac{1}{3}\right)-7=-\dfrac{22}{3}[/tex]
[tex]x=-\dfrac{7}{3} \implies f\left(-\dfrac{7}{3}\right)=-3\left(-\dfrac{7}{3}\right)^3-5\left(-\dfrac{7}{3}\right)^2+\left(-\dfrac{7}{3}\right)-7=\dfrac{14}{9}[/tex]
[tex]x=\dfrac{7}{3} \implies f\left(\dfrac{7}{3}\right)=-3\left(\dfrac{7}{3}\right)^3-5\left(\dfrac{7}{3}\right)^2+\left(\dfrac{7}{3}\right)-7=-70[/tex]
As f(p/q) ≠ 0, none of the possible rational roots are actual roots of the given polynomial.
