Answer:
13 ⅓.
Step-by-step explanation:
The area of a rectangle is given by
Area = Length × Breadth
Length = 2 7/9 = 25/9 and breadth = 4 4/5 = 24/5
.: Area = 25/9 × 24/5 = 600/45 (15 can go to both the numerator and denominator)
We have 40/3 but to convert it to a mixed fraction we get 13 ⅓ as your area.
The degree of the polynomial function f(x) is 3.
The roots of the equation f(x) = 0 are -1, 0, and 4.
Which graph could be the graph of f(x)?
The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.
What is Polynomial function?
A mathematical expression of algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.
Given that;
The degree of the polynomial function f(x) is 3.
And, The roots of the equation f(x) = 0 are -1, 0, and 4.
Now, The polynomial function are calculated as;
f (x) = 0
(x + 1) (x - 0) (x - 4) = 0
x (x + 1) (x - 4) = 0
x (x² - 4x + x - 4) = 0
x (x² - 3x - 4) = 0
x³ - 3x² - 4x = 0
Thus, The polynomial function is;
x³ - 3x² - 4x = 0
Therefore, The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.
Learn more about the polynomial function visit:
https://brainly.com/question/7693326
#SPJ1
8=3+2i and z9 = 4+3i.
Answer:
8 - 3 = 5
5 divided by 2 = 2.5
i = 2.5
3 x 2.5 = 7.5
4 + 7.5 = 11.5
11.5 divided by 9 = 1.277
z = 1.277
Hope this helps!
AlphaFay
what is the standard algorithm for 72 / 3
Long division gives the answer of 24 when 72 is divided by 3.
What is long division calculator?Long division in mathematics is a strategy for breaking down complicated division problems into a series of simpler steps. It is the approach that division-based issues are typically solved using. The dividend, the quotient, the remainder, and the divisor can all be seen in the following long division.
So as we know:
Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:
3 ⟌ 7 2
Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:
2
3 ⟌ 7 2
Write the result (3 x 2 = 6) underneath the dividend after multiplying the divisor by the outcome from the previous step.
2
3 ⟌ 7 2
6
Write the solution below after subtracting the result from the previous step from the dividend's first digit (7 - 6 = 1).
Reduce the dividend's second digit (2) as follows:
2
3 ⟌ 7 2
- 6
1 2
The bottom number (12) is multiplied by the divisor (3) four times (s). Put 4 thus on top
Subtract the result of the previous step (3 x 4) from the divisor to get the solution (12), which you should write at the bottom:
2 4
3 ⟌ 7 2
- 6
1 2
1 2
Take the number above it and deduct the outcome from the preceding calculation. Write the response at the bottom after calculating (12 - 12 = 0).
The top number is the solution, and the remaining value is the bottom one.
Therefore, the result of 72 divided by 3 using long division is 24.
To know more about long division method , click here:
https://brainly.com/question/28784606
#SPJ13
Mrs. Parkow gives her class clues
about a 5-digit mystery number,
• The 3 is in a place that is 100 times
greater than the place of the 4,
The 2 is in a place that is 10 times
less than the place of the 3.
The 8 is in a place that is 10 times
less than the place of the 4.
The 7 is in a place that is 100 times
greater than the 2
•
•
What is Mrs. Parkow's
5-digit mystery number?
Mrs. Parkow's 5-digit mystery number is 73248.
What are Numbers up to 5-Digits?Ten thousand is the starting point for five-digit numbers, which go up to ninety-nine million, nine hundred and ninety-nine. Integers are present in the places of ones, tens, hundreds, thousands, and ten thousands in these numbers. Any positive number may be placed at these places, with the exception of 0 at the ten thousands place.
A general 5-digit number can be written as:
a×10000 + b×1000 + c×100 + d×10 + e where a, b, c, and d are single-digit numbers.
a is the ten thousands digit
b is the thousands digit
c is the hundreds digit
d is the tens digit
e is the units digit.
Let 8 be at one's place that is e
Now, it is given that 8 is in a place that is 10 times less than the place of the 4.
This implies 4 is at the ten's place that is d.
Next, it is given that 3 is in a place that is 100 times greater than the place of the 4.
That is 100×10 = 1000 place
So, 3 is at the place of b.
The 2 is in a place that is 10 times less than the place of the 3. So, 2 is at the place of c.
The 7 is in a place that is 100 times greater than the 2. That is 100×100 = 10,000 place.
Thus, 7 is at the place of a.
Thus, we obtain
a= 7
b= 3
c= 2
d= 4
e= 8
Therefore, the 5-digit mystery number is 73248.
To learn more about mystery numbers, visit:
https://brainly.com/question/24465179
#SPJ9
The probability that a new machine will not need any repairs within t years from now is modeled by an exponential function of t. This probability is multiplied by 0.2 whenever the time period t is extended by 3 years as shown by the function belowf(t) = (0.2)^t/3 If the probability that the machine does not need repairs right now is 1, what is the probability that the machine will not need repairs within 12 years from now, according to the model? 0.8 0.05 0.008 0.0016
viven
t = time
function
[tex]f(t)=0.2^{t/3}[/tex]what is the probability that the machine will not need repairs within 12
rocedure
[tex]\begin{gathered} f(12)=0.2^{12/3} \\ f(12)=0.0016 \end{gathered}[/tex]
The probability would be 0.0016
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.
A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 90% confidence interval for the mean score, μ, of all students taking the test?
The 90% confidence interval for the mean score, μ, of all students taking the test is; CI = (28.36, 30.64)
What is the Confidence Interval?
The formula for confidence interval is;
CI = x' ± z(s/√n)
where;
CI = Confidence Interval
x' is sample mean
z is critical value at confidence level
s is standard deviation
n is sample size
We are given;
n = 59
x' = 29.5
s = 5.2
z at CL 0f 90% = 1.645
Thus;
CI = 29.5 ± 1.645(5.2/√59)
CI = 29.5 ± 1.136
CI = (28.36, 30.64)
Read more about Confidence Interval at; https://brainly.com/question/17097944
#SPJ1
Simplify the quantity 8 minus one third times the square root of 9 end quantity squared plus the quantity 1 minus 5 end quantity squared.
The statement quantity 8 minus one third times the square root of 9 end quantity squared plus the quantity 1 minus 5 end quantity squared is simplified to 65
What are fractions?Fractions are defined as parts of a whole element, set or number.
There are various types of fractions, which includes;
Complex fractionsProper fractionsSimple fractionsMixed fractionsImproper fractionsBased on the information provided, we have;
8 minus one third times the square root of 9 = 8 - 1/3(√9)1 minus 5 end quantity squared = (1 - 5)²Now, substitute the values
(8 - 1/3(√9))² + (1 - 5)²
Find the square root
(8 - 1/3(3))²+ (-4)²
Find the square
(8 - 1)² + 16
7² + 16
49 + 16
Add the values
65
Hence, the value of the expression is 65
Learn more about square root here:
https://brainly.com/question/428672
#SPJ1
Find all angles, osO<360, that satisfy the equation below, to thenearest 10th of a degree.cos(0) =-1/6
The cosine of the angle given is negative.
Cosine is negative in the second and third quadrant
[tex]\begin{gathered} 0\leq x\leq360 \\ \cos (\theta)=-\frac{1}{6} \\ \theta=\cos ^{-1}(\frac{1}{6}) \\ \theta=80.41^0 \\ \theta=80.4^0\text{ (to the nearest tenth)} \\ \end{gathered}[/tex]In the second quadrant,
[tex]\begin{gathered} 180-\theta \\ 180-80.4=99.6 \\ \theta=99.6^0 \end{gathered}[/tex]In the third quadrant,
[tex]\begin{gathered} 180+\theta \\ 180+80.4=260.4 \\ \theta=260.4^0 \end{gathered}[/tex]Therefore, the values that satisfy the equation are 99.6 and 260.4 degrees.
Convert 32.5% to a decimal number. If needed round to the nearest thousandth.
In order to convert a percent to a decimal number we need to move the decimal point two units to the left
[tex]32.5\text{\%}=0.325[/tex]Drag and drop the number to match the division problem to its quotient.
Answer:
The correct number is -27.
Step-by-step explanation:
-81 ÷ 3 = -27
Consider the following expression 2(x+3). Which of the following represents the correct use of the distributive property? A. 2x+3 B. 2x+6 C. X + 6 D. X^2 + 6x + 9
Algebra 2, 50 points, include steps please
(6-4i)(1+5i)-(3-i)
The simplified representation of the complex number expression is
23 + 37i
a + bi, where a and b are real numbers, can be used to represent any complex number.
A complex number is a component of a number system that includes an element with the symbol I, sometimes known as the imaginary unit, and that extends the real numbers by satisfying the equation i² = -1. i was described as an imaginary number by René Descartes since no real number can fulfil the aforementioned equation. The complex number a + bi is known as having real and imaginary parts, respectively, A and b. The group of complex numbers is denoted by the letter C.The complex number expression is (6-4i)(1+5i)-(3-i)
now let us simplify,
or, (6-4i)(1+5i)-(3-i)
or, 6 + 30i - 4i -20i² -3 + i
or, 6 + 36i + 20 - 3 + i (we know that i² = -1)
or, 23 + 37i
Therefore the simplified complex expression is 23 + 37i
To learn more about complex numbers visit:
https://brainly.com/question/20566728
#SPJ1
Write the equation of the line in slope-intercept form.
The line is parallel to y + x = 3 and passes through the point (-12, 0).
Please help i will give big points
Answer:
The line is parallel to y + x =3
=> y = -x+3
the slope = -1
passes (-12, 0)
the equation would be :
y-0 = -1(x+12)
y = -x -12 Y=-x+12
Turn into mx+b form.
Y=-x+3
Plug in (-12,0)
0=-12+b
b=12
y=-x+12
It is negative X, because the slope has to be the same since it is paralle
Step-by-step explanation:
a triangle has two sides of 10 and 6 with an area of 12 units. what is the missing length.
A triangle that has two sides of 10 and 6 with an area of 12 units will have the third side length of 4.
What is the area of a triangle?The triangle can be described as the the figure that has threes sides which can be equal or varies base on the type of the triangle it is, and the area of the triangle is given, we can use the formula for the are of triangle which i s (1/2 * b * h )
Then the Area of a triangle = (1/2 * b * h)
we were given the two sides already with the area , then we can input the values as :
12 =( 1/2 * 6 * x)
where x is the third sides that is needed
x = 4
Read more about triangle here:
https://brainly.com/question/17335144
#SPJ1
Round to the place value of the underlined digit 698,072 the underlined digit is 6
We get 700,000 after rounding off to the place value of the underlined digit in the number 698,072.
According to the question,
We have the following number with 6 as the underlined digit:
698,072
When rounding off the number, please note that the digits to the right of the underlined digit would be zero. However, we need to be careful where we need to scale up the underlined number or it would remain the same.
For this, we need to check the number to the right of the underlined digit. If the number right next to the underlined digit is greater than 5 then the underlined digit has to be scaled up. And if it is less than 5 then the underlined digit remains the same.
So, after rounding off we will get:
700,000
Hence, the number after rounding off to 6 in 698,072 is 700,000.
To know more about place value here
https://brainly.com/question/27734142
#SPJ1
29-(11-2³)+6²÷4 simplify each Expression
The simplified form of the expression 29 - ( 11 - 2³ ) + 6² ÷ 4 is 35
What is the simplified form of the given expression?Given the expression in the question;
29 - ( 11 - 2³ ) + 6² ÷ 4
To simply, replace 2 raised to the power of 3 with 8 and 6 raised to the power of 2 by 36
29 - ( 11 - 2³ ) + 6² ÷ 4
29 - ( 11 - 8 ) + 36 ÷ 4
Now, remove the parenthesis by performing the operation inside the parenthesis.
29 - ( 11 - 8 ) + 36 ÷ 4
29 - 3 + 36 ÷ 4
Now, divide 36 by 4
29 - 3 + 36 ÷ 4
29 - 3 + 9
Next, add -3 and 9
29 + 6
Add 29 and 6
35
Therefore, 35 is the simplified form of the expression.
Learn more about FOIL and PEMDAS here: https://brainly.com/question/36185
#SPJ1
The volleyball team bought 12 new volleyballs. The price for each volleyball was $26. How much did the team spend? Select the choice that shows all of the partial products of 12 × 26.
A.
12, 70, 4, 400
B.
12, 90, 14, 200
C.
12, 62, 4, 260
D.
12, 60, 40, 200
========================================================
Explanation:
Imagine a rectangle that is 12 by 26. Multiplying the length and width will get us the area.
We can break the 12 into 10+2
Also, break the 26 into 20+6
Check out the diagram below. We have 4 smaller rectangles. Finding the product of those sub-areas will then get us the partial products needed.
In the bottom right corner we have a 2 by 6 rectangle, so it has area 2*6 = 12 square units. This is one of the four partial products. The other partial products are found the same way.
Once you determine the four partial products, we then add them up
12+60+40+200 = 12+100+200 = 12+300 = 312
Therefore, 12*26 = 312 which we can use a calculator to confirm.
Solve for y in terms of u, v, w, and x.
vw = -yux
VW
y =
Answer:
y= vw/ux
Step-by-step explanation:
hope this help
The data valo showed a mouse driven on a single day by random sample of 13 student calculate the 38th and the 60th percent all of the data
To get the percentile
Step 1: Write the formula
[tex]\begin{gathered} P_i=(\frac{i(n+1)}{100})^{th} \\ \\ \text{where n = 13} \end{gathered}[/tex]For the 38th percentile
[tex]P_{38}=(\frac{38(13+1)}{100})^{th}[/tex][tex]P_{38}=5.32^{th}\text{ number}[/tex]This means that the 38th percentile is between the 5th and 6th number
[tex]\begin{gathered} P_{38}=5^{th}\text{ observation}+0.32\lbrack6^{th}-5^{th}\rbrack \\ P_{38}=41+0.32(43-41)=41.64 \\ P_{38}=41.64 \end{gathered}[/tex]P38 = 41.64This means that approximately 38% of the data lie below 43, when the data are ranked
For the 60th percentile,
[tex]P_{60}=(\frac{60(13+1)}{100})^{th}[/tex][tex]P_{60}=8.4^{th\text{ }}n\nu mber[/tex]6089
[tex]P_{}=8^{th}\text{ observation}+0.4\lbrack9^{th}-8^{th}\rbrack[/tex][tex]\begin{gathered} P_{60}=56+0.4(58-56) \\ P_{60}=56.8 \end{gathered}[/tex]60
From a window 100 ft above the ground in building A, the top and bottom of building B are sighted so that the angels are 70 degrees and 30 degrees respectively. Find the height of building B?
Let's begin solving the problem by illustrating the problem using a diagram:
Let the height of building B be x
Re-drawing the triangles to show the unknown side:
Using trigonometric ratios and sine rule
Hence:
[tex]\begin{gathered} \frac{\sin110}{\frac{100}{\cos30}}\text{ = }\frac{\sin 40}{x} \\ \text{Cross}-\text{Multipy} \\ \text{x }\times\text{ sin110 }=\text{ sin40 }\times115.47 \\ \text{Divide both sides by sin110} \\ \text{x = }\frac{\sin 40\text{ }\times\text{ 115.47}}{\sin \text{ 110}} \\ x\text{ = 78.986} \\ x\text{ }\approx\text{ 79 ft} \end{gathered}[/tex]The height of the building B is 79 ft
Please help will give crown! Here is the question 2(-2)-4=12 solve it and tell me where it goes on a graph if you want, I'll give 400 points, if i can!
The solution to the given equation (2(-2) - 4 = 12) is -20 and its graphical solution is shown in the image attached below.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
Next, we would solve the given equation as follows:
2(-2) - 4 = 12
Let us introduce a variable x into the equation as follows:
x = 2(-2) - 4 - 12
x = -4 - 4 - 12
x = -20
Read more on number line here: brainly.com/question/16614696
#SPJ1
What is the answer to the question
From the right triangle, and using the definitions of the tangent and the cosine functions, we have:
[tex]\begin{gathered} \tan B=\frac{AC}{BC}=\frac{b}{a}\Rightarrow b=a\cdot\tan B...(1) \\ \\ \cos B=\frac{BC}{AB}=\frac{a}{c}\Rightarrow c=\frac{a}{\cos B}...(2) \end{gathered}[/tex]From the problem, we identify:
[tex]\begin{gathered} B=55.7\degree \\ a=266\text{ km} \end{gathered}[/tex]Finally, using these values, we can find b and c.
Using (1):
[tex]\begin{gathered} b=266\cdot\tan55.7\degree \\ \\ \therefore b=389.941\text{ km} \end{gathered}[/tex]Using (2):
[tex]\begin{gathered} c=\frac{266}{\cos55.7\degree} \\ \\ \therefore c=472.028\text{ km} \end{gathered}[/tex]What is the correct answer
The measure of angle B in triangle ABC is 158°.
What is meant by the triangle?A triangle is a 2-dimensional closed shape with three sides, three angles, and three vertices. A triangle would be a category of polygon.
The sum of a triangle's three interior angles is always 180.The sum of any two triangle sides is always bigger than this same length of a third side.A triangle's area is equal to half the product of it's own base and height.For the given angles of the triangle ABC.
∠BAC = 78° , ∠CAD = 46° and ∠ADB = 110°.
Now,
∠BAC = ∠BAD + ∠DAC
Put the values;
78° = ∠BAD + 46°
∠BAD = 78° - 46°
∠BAD = 32°
Now, in a triangle; the sum of all three angles is 180°.
In triangle ADB
∠ABD + ∠BAD + ∠BDA = 180°
Put the values;
∠ABD + 32° + 110° = 180°
∠ABD = 180° - 142°
∠ABD = 158°
Thus, the measure of angle B is 158°.
To know more about the triangle, here
https://brainly.com/question/17335144
#SPJ13
Triangle A has a height of 8 inches and a base of 2 inches. Triangle B has a height of 16 inches, what is the base?
The base of Triangle B is 1 inches.
Given,
Triangle A has a height of 8 inches
and base of Triangle is 2 inches
Let's Find the Area of Triangle A
We know that the formula of Area of Triangle
Area of Triangle = [tex]\frac{1}{2}[/tex] × b × h
where, b is the base and h is the height of triangle.
Plug the values of base and height in above formula.
Area of Triangle A = [tex]\frac{1}{2}[/tex] × 2 × 8
Hence, Area of Triangle A is 8 sq. inches
In this question, Some part is missing that is:
Triangle A is similar to Triangle B
Now, For Triangle B is given:
Triangle B has a height of 16 inches
and, to find the base of the triangle.
We know, Area of Triangle A is 8 sq. inches.
Area of Triangle B = [tex]\frac{1}{2}[/tex] × b × h
8 = [tex]\frac{1}{2}[/tex] × b × 16
8 = 8b
b = 1 inches
Hence, The base of Triangle B is 1 inches.
Learn more about Area of Triangle at:
https://brainly.com/question/19305981
#SPJ1
The telephone company offers two billing plans for local calls. Plan 1 charges $29 per month for unlimited calls and plan 2 charges $17 per month plus $0.03 per call. Use and inequality to find the number of monthly calls for which plan is more economically than plan 2
Calls greater than 400 would be more economical in plan 1 than plan 2 and the inequality is 29 < 17 + 0.03x
How to determine the more economical plan?The given parameters are:
Plan 1
Charges per month = $29Plan 2
Charges per month = $17Monthly rate = $0.03Let the number of months be x.
So, we have the following equation
Plan 1: 29
Plan 2: 17 + 0.03x
For plan 1 to be more economical plan than plan 2, then we have the following inequality
Plan 1 < Plan 2
This is represented as
29 < 17 + 0.03x
Subtract 0.03x from both sides of the inequality
So, we have
0.03x > 12
Divide both sides by 0.03
x > 400
How to interpret the result in (a)?
In (a), we have
x > 400
This means that the number of calls for the plan 1 to be more economical than plan 2, then the number of calls must be greater than 400
Read more about inequality at
https://brainly.com/question/25275758
#SPJ1
To find the height of a very tall pine tree, you place a mirror
on the ground and stand where you can see the top of the
pine tree. How tall is the tree?
6 ft
2 ft 24 ft
ти
How tall is the tree
If to find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. The height of the tree is 72 feet.
Height of a treeGiven data;
6 ft
2 ft 24 ft
Hence,
Angle of incidence = Angle of reflection
Hence,
m ∠ ACD = m ∠ ECD
Two triangle will only be the same if their corresponding angles are congruent
So,
Sine m ∠ ACD = m ∠ ECD
m Δ ABC = Δ EDC
The corresponding of similar triangles are proportional
Hence,
BC / DC = AB / ED
= 2 / 24 = 6 / ED
2ED = 24 × 6
2ED = 144
Divide both side by 2
ED = 144 / 2
ED = 72 feet
Therefore we can conclude that the tree height is measure at 72 feet.
Learn more about height here:https://brainly.com/question/73194
#SPJ1
What does congruent mean? Select all that apply. PLEASE HELP!
A None of the above
B Same Shape
C Corresponding angles are the same measure
D Corresponding sides are the same length
help me please!!!!!!11!
Answer:
[tex]y=x^2-4x-2[/tex]
Step-by-step explanation:
Standard Form of Quadratic:
[tex]y=ax^2+bx+c[/tex]
Vertex Form of Quadratic:
[tex]y=a(x-h)^2+k[/tex]
h = vertex x
k = vertex y
Think of h and k as the ordered pair (h,k).
Match this ordered pair to the vertex ordered pair.
(h,k) = (2, -6)
Plug in (h,k) into vertex form:
[tex]y = a(x-2)^2-6[/tex]
Use other point to solve for a.
[tex]3 = a(5-2)^2-6[/tex]
[tex]3=a(3)^2-6[/tex]
[tex]3=9a-6[/tex]
[tex]9=9a[/tex]
[tex]a=1[/tex]
Plug a back into vertex form and expand the expression into standard form:
[tex]y=(x-2)^2-6[/tex]
[tex]y=(x-2)(x-2)-6[/tex]
Use F.O.I.L. method to expand (x-2)(x-2).
F(first): [tex]x*x=x^2[/tex]
O(outer): [tex]x*-2=-2x[/tex]
I(inner): [tex]-2*x =-2x[/tex]
L(last): [tex]-2*-2=4[/tex]
[tex]y=x^2-2x-2x+4-6[/tex]
Combine like terms:
[tex]y=x^2-4x-2[/tex]
A linear function is transformed from y = 3/4x + 1/2 to y = 3/4x + 5/2. What is the corresponding vertical change?A)The graph is shifted up 2 units,B)The graph is shifted down 2 units. C)The graph is shifted up 4 unitsD)The graph is shifted up 5/2 units
A. The graph is shifted up 2 units
What is the distance between points A(2,9) and B(-2,6)? Round to the nearest whole number.
The distance between the point is 5.
The formula to find the distance between two points (x1, y1) and (x2, y2)
distance = [tex]\sqrt{(x2-x1)^{2} + (\\ y2-y1)^{2} }[/tex]
Substituting points A(2,9) and B(-2,6), we get
distance = [tex]\sqrt{(-2-2)^{2} + ( 6-9)^{2} }[/tex]
=[tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]
= [tex]\sqrt{16 + 9}[/tex]
=[tex]\sqrt{25}[/tex]
= 5
Therefore the distance between the two points is 5.
To know more about the distance between the two points refer to the link given below:
https://brainly.com/question/7243416
#SPJ1