Simplify the expression and express in standard form.
[tex]\begin{gathered} (-3x^4+x^6-9x^5+2x^2-7)+(-2x^5+x-4x^2-x^4+12) \\ =-3x^4+x^6-9x^5+2x^2-7-2x^5+x-4x^2-x^4+12 \\ =x^6-11x^5-4x^4-2x^2+x+5 \end{gathered}[/tex]So answer is,
[tex]x^6-11x^5-4x^4-2x^2+x+5[/tex]The sides of an equilibrium triangle are 9.4cm,correct to the nearest milimetre. Work out the upper bound of the perimeter of this triangle.
The perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.
What are the upper and lower bounds of an approximation?The numerical value that is rounded up to represent the supplied value's next value serves as its upper bound.
The numerical number that is rounded off for the previous value or the predicted value of the provided value is the lower bound for the supplied value.
The sides of an equilateral triangle are 9.4 cm
The perimeter of an equilateral triangle = 3 × length of the side
The perimeter of an equilateral triangle = 3 × 9.4
The perimeter of an equilateral triangle = 28.2 cm
Hence, the perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.
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Translate this sentence into an equation.68 is the product of Diane's score and 4.Use the variable d to represent Diane's score.
68 = Diane's score x 4
Equation
68= 4d
___________________
Can you see the updates?
_________________
Diane's score
4d= 68
d= 17
5.What is the area of the triangle?Include the unit of measurein your answer.:::::
Answer: Area = 126 square inches
Explanation:
The formula for calculating the area of a triangle is expressed as
Area = 1/2 x base x height
From the information in the diagram,
base = 18
height = 14
Thus,
Area = 1/2 x 18 x 14
Area = 1/2 x 252 = 252/2
Area = 126 square inches
Meow meow please help me
Answer:
area of trapezium → 1/2 × Sum of parallel sides × Distance between them.
Area → 15in² {given}
B1 → 4in
B2 → 6in
15 = 1/2 × ( 4+6 ) × h
h = 15 × 2 ÷ 10
h = 3in
I hope it's helpful
Answer:
i wouldd but likee
Step-by-step explanation:
i didnt pay a single second of attention in math
Complete the following statement. Round your answer to the nearest percent
% of $700 = $1,400
Answer:
50
Step-by-step explanation:
Solution for 700 is what percent of 1400:
700:1400*100 =
(700*100):1400 =
70000:1400 = 50
Now we have: 700 is what percent of 1400 = 50
at an ice cream store with five flavors of ice cream (peppermint, hoarhound, chocolate malt, gingerbread, and squirrel), ice cream scoops are stored inside the ice cream containers. what is the smallest number of ice cream scoops that would need to be in use so that two of the scoops would have to be stored in the same flavor ice cream container? how many ice cream scoops must be in use if 3 of them have to be stored in the same flavor ice cream container?
ANSWER: 10 ICE-CREAM SCOOPS
There are 5 icecream flavors
For each we need 2 scoops so = 2*5 = 10 scoops
therefore ther must be 10 icecream scoops in use for five flavors.
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Which relation is a function?
Responses
(1, 0), (3, 0), (1, 1), (3, 1), (1, 3)
(1, 0), (3, 0), (1, 1), (3, 1), (1, 3)
(1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
(1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
(2, 7), (6, 5), (4, 4), (3, 3), (2, 1)
(2, 7), (6, 5), (4, 4), (3, 3), (2, 1)
(9, -3), (9, 3), (4, -2), (4, 2), (0, 0)
Answer:{(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
Step-by-step explanation: hope this helps
48/8 6/w
1=?
Help me please helpp
Answer:
w = 1
Step-by-step explanation:
You have to divide 48 by 8 to get 6, so you have to divide 8 by 8 to find w.
8/8 = 1
10. Which of the following is equivalent to thisexpression?72.7-4Tutor
To answer this question we need to remember that:
[tex]a^ma^n=a^{m+n}[/tex]then:
[tex]\begin{gathered} 7^2\cdot7^{-4}=7^{2-4} \\ =7^{-2} \end{gathered}[/tex]now we need to remember that:
[tex]a^{-n}=\frac{1}{a^n}[/tex]hence:
[tex]7^{-2}=\frac{1}{7^2}[/tex]Therefore:
[tex]7^{-4}\cdot7^2=\frac{1}{7^2}[/tex]and the asnwer is A.
Select the correct answer.
Which graph shows a function and its inverse?
A. The first graph
B. The second graph
C. The third graph
D. The last graph
Answer:
B
Step-by-step explanation:
It is asking which graph show (x,y) for one line and (y,x) for the other line.
For example, the blue line shows (0,2) as a point and the red line shows ( 2,0) and so on and so on.
help please ill give brainlest !!
Answer:
-31, 9, 1, 5, 37
Step-by-step explanation:
f(x) = -2(-2)^2 + 1
f(x) = 4^2 + 1
f(x) = 8+1
f(x) = 9
f(x) = -2(0)^2 +1
f(x) = 0^2 + 1
f(x) = 0 + 1
f(x) = 1
f(x) = -2(1)^2 + 1
f(x) = -2^2 + 1
f(x) = 4+1
f(x) = 5
f(x) = -2(3)^2 + 1
f(x) = -6^2 + 1
f(x) = 36+1
f(x) = 37
Please solve with an explanation
Answer:
10.8
Step-by-step explanation:
Hello!
Once, graphed, a right triangle forms, with PQ as the hypotenuse. The other two lengths are 6 and 9.
We can use the Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]
a and b are lengthsc is the hypotenuseSolve for PQ[tex]a^2 + b^2 = c^2[/tex][tex]6^2 + 9^2 = PQ^2[/tex][tex]36 + 81 = PQ^2[/tex][tex]117 = PQ^2[/tex][tex]\sqrt117 = PQ\\[/tex]10.8 = PQThe length of PQ is 10.8.
Find the distance between the ordered pairs.
(w + 2, m) and (2t, c - 3) when w = 6, m = 3, t = 4
and c = 10.
The distance between the ordered pairs is 4 units
What is distance formula?
Distance formula calculates the distance between two coordinates. it calculates the straight line distance between two points. The formula can be given as [tex]distance=\sqrt{(c-a)^{2}+(d-b)^{2} }[/tex] for the coordinates (a, b) (c, d)
We are given the ordered pair (w+2,m) and (2t,c-3)
We are given the value w = 6, m = 3, t = 4 and c = 10.
Substituting the values in the pairs
We get,
(6+2,3),(2(4),10-3)
(8,3),(8,7)
We use distance formula to find the distance
[tex]d=\sqrt{(8-8)^{2} +(7-3)^{2} }\\ d=\sqrt{4^{2} }\\ d=4[/tex]
Hence the distance between the ordered pairs is 4 units.
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Ruth is a costume designer for the local children's theater company. Yesterday, she sewed 1 female costume and 5 male costumes, which used 52 yards of fabric. Today, she sewed 5 female costumes and 2 male costumes, which used a total of 76 yards. How many yards of fabric does each type of costume require? yards of fabric, and every male costume requires Each female costume requires yards.
Given:
Yesterday:
1 female and 5 male = 52 yards
Today:
5 female and 2 male = 76 yards
Let's find the number of yards of fabric each type of costume requires.
Let F represent the number if yards for each female customer use.
Let M represent the number of yards each male customer uses.
From this situation, we have the system of equations:
1F + 5M = 52
5F + 2M = 76
Now, let's solve the system of equations simultaneously using substitution method.
Rewrite equation 1 for F:
F = 52 - 5M
Substitute 52 - 5M for F in equation 2:
[tex]\begin{gathered} 5F+2M=76 \\ \\ 5(52-5M)+2M=76 \\ \\ 5(52)+5(-5M)+2M=76 \\ \\ 260-25M+2M=76 \\ \\ 260-23M=76 \end{gathered}[/tex]Subtract 260 from both sides:
[tex]\begin{gathered} 260-260-23M=76-260 \\ \\ -23M=-184 \end{gathered}[/tex]Divide both sides by -23:
[tex]\begin{gathered} \frac{-23M}{-23}=\frac{-184}{-23} \\ \\ M=8 \end{gathered}[/tex]Substitute 8 for M in either of the equations:
F = 52 - 5M
F = 52 - 5(8)
F = 52 - 40
F = 12
Therefore, we have the solution:
F = 12, M = 8
Each male customer requires 8 yards while each female customer requires 12 yards.
ANSWER:
• Male customer = 8 yards
,• Female customer = 12 yards
What is the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3? Responses y−1=3(x+2) y plus 1 equals 3 open parenthesis x minus 2 close parenthesis y−2=3(x+1) y minus 2 equals 3 open parenthesis x plus 1 close parenthesis y+1=3(x−2) y plus 1 equals 3 open parenthesis x minus 2 close parenthesis y+2=3(x−1)
The equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5
We need to find the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3
The point slope form of a equation of a line is
y - y₁ = m(x - x₁)
y - (-2) = 3 (x - 1)
y + 2 = 3x - 3
y = 3x - 3 - 2
y = 3x - 5
Therefore the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5.
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The width of a rectangle is 5 feet, and the diagonal length of the rectangle is 12 feet. Which measurement is closest to the length of this rectangle in feet?
The measurement is closest to the length of the rectangle is √119 ft.
What is the measure of the length of the given rectangle?Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
It is expressed as;
c = √( a² + b² )
Where c is the diagonal that divides the rectangle into two equal triangle, a and b are the other legs of the triangle.
Given the data in the question;
With ( First leg ) a = 5ftDiagonal c = 12ftSecond leg b = ?Plug the values into the formula and solve for b.
12ft = √( (5ft)² + b² )
Take the square of both sides
( 12ft )² = (5ft)² + b²
144ft² = 25ft² + b²
b² = 144ft² - 25ft²
b² = 119ft²
b = √( 119ft² )
b = √119 ft
Therefore, the measure of the length is √119 ft.
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Periodic Deposit: $? at the end of each monthRate: 7.5% compounded monthlyTime: 3 yearsFinancial Goal: $35,000O A. $2,628; $31,536 from deposits and $3,464 from interestB. $776; $27,936 from deposits and $7,064 from interestO c. $933; $33,588 from deposits and $1,412 from interestOD. $870; $31,320 from deposits and $3,680 from interest
Answer:
D. $870; $31,320 from deposits and $3,680 from interest
Explanation:
In order to calculate the monthly payment, we use the formula below:
[tex]P=\frac{A\mleft(\frac{r}{n}\mright)}{\mleft[\mleft(1+\frac{r}{n}\mright)^{nt}-1\mright]}[/tex]Given:
• The Financial Goal, A= $35,000
,• Rate = 7.5% = 0.075
,• Number of compounding period = 12 (Monthly)
,• Time, t = 3 years
Substitute into the given formula:
[tex]\begin{gathered} P=\frac{35000\mleft(\frac{0.075}{12}\mright)}{\mleft[\mleft(1+\frac{0.075}{12}\mright)^{12\times3}-1\mright]} \\ P\approx\$870 \end{gathered}[/tex]The monthly payment is $870.
[tex]\begin{gathered} \text{Total deposit}=870\times36=31,320 \\ \text{Interests}=35,000-31,320=3680 \end{gathered}[/tex]Option D is correct.
What is the distance between 3 and 15?
The most appropriate choice for distance between numbers will be given by -
Distance between 3 and 15 is 12 units
What is distance between two numbers?
At first it is important to know about number line.
A pictorial representation of real numbers has been done along a horizontal straight line. That horizontal straight line is called number line. On a number line, all the integers has been placed at equal distance apart. In between integers, fractions, decimal numbers, rational numbers and irrational numbers can be marked. Number line can be used for addition or subtraction.
Distance between two numbers indicates how far one number is situated from other number on the number line.
Here,
Distance between 3 and 15 = 15 - 3
= 12 units
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What is x in this equation
2(x-7)=-4
x = 5
2x - 14 = -4
2x = -10
x = 5
Answer: 5
Step-by-step explanation: First I took away the 2 on the left which was multiplying the brackets. Then because I did this I had to do the opposite to the other side. -4÷2
Then I just filled in the gaps 5-7=-2
3y=x-6 in standard form
Answer: x-3y=6
Step-by-step explanation:
so first subtract x to get -x+3y = -6 because standford is ax+by = c
and then multiply by -1 since x has to be positive
x-3y = 6 That is your answer
What is the slope of the line that passes through the points (-2, 2) and (-4, -1)?
Write your answer in simplest form.
The slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .
How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)
Given, the line passes through the points (-2, 2) and (-4, -1)
Now, using the formula established in the literature, we get:
slope = m = (y₂ - y₁)/(x₂ - x₁) = (-1 - 2)/(-4 - (-2)) = -3/-2 = 3/2 = 1.5
Therefore, the slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .
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3. a sociologist wishes to estimate the percentage of u.s. citizens living in poverty. what sample size should be obtained if she wishes the estimate to be within 2% points (the error) with 99% confidence if she uses the year 2000 estimate of 11.8% poverty obtained from the census?
The sample size is 1727 points for given data . Sample size is defined as the number of observations used to determine estimates for a given population. Sample size was drawn from the population .
In this question we want to find the sample size and so let's, look at the formula that is given by, the value at over 2, divided by a margin of error, whole squared times p into 1 minus p.
N= ( Z ₐ / E)² p (1-p)
In this case , Z --> Z-Score
E --> error value
P --> estimated proportion or if given standard deviations
Given that, estimate error is 2% that is margin (E) = 2% = 2/100 =0.02
Now, what we have is our confidence level and our made error, so our estimate has been given us 2 percent or confidence level is 99 percent. Now, let's get our Z values, so we use alpha(a) to find out. For alpha value 1 minus 0.99 , we get 0.01. now we are going to be 0.01 divide by 2 and get 0.005 . So, the corresponding value of Z ₀.₀₀₅ is 2.576 . The only value of p is 11.8% (year 2000 estimate ) of what is required for getting an answer
= 118/1000= 0.118
Finally, we put all these values into formula of sample size , i.e.,
N= ( 2.576 / 0.02)² (0.118 )(1- 0.118) = 1726.56 1727
Our sample size is , 1727 point.
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Line m passes through points (9, 9) and (6, 1). Line n passes through points (10, 7) and (1, 15). Are line m and line n parallel or perpendicular?
Answer:
Step-by-step explanation:
Slopes of parallel lines are the same. ( [tex]m_{1}[/tex] = [tex]m_{2}[/tex] )
Slopes of two perpendicular lines are opposite reciprocals. ( [tex]m_{1}[/tex] × [tex]m_{2}[/tex] = - 1 )
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
~~~~~~~~~~~~~
(9, 9)
(6, 1)
[tex]m_{m}[/tex] = [tex]\frac{1-9}{6-9}[/tex] = [tex]\frac{8}{3}[/tex]
(10, 7)
(1, 15)
[tex]m_{n}[/tex] = [tex]\frac{15-7}{1-10}[/tex] = - [tex]\frac{8}{9}[/tex]
Lines m and n neither parallel, nor perpendicular.
Given the slope of a line is -2 and it passes through the point (4,-5), write the equationof the line in standard form.
Answer:
The equation of the line is;
[tex]y=-2x+3[/tex]Explanation:
Given that
the slope of a line is -2 and it passes through the point (4,-5).
Applying the slope-intercept form of equation;
[tex]y-y_1=m(x-x_1)[/tex]Substituting the values of the slope and coordinates;
[tex]\begin{gathered} y-(-5)=-2(x-4) \\ y+5=-2x+8 \\ y=-2x+8-5 \\ y=-2x+3 \end{gathered}[/tex]Therefore, the equation of the line is;
[tex]y=-2x+3[/tex]Answer:
2x + y = 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (4, - 5 ) into the partial equation
- 5 = - 8 + c ⇒ c = - 5 + 8 = 3
y = - 2x + 3 ← in slope- intercept form
add 2x to both sides
2x + y = 3 ← equation in standard form
the teacher wants to select 6 students from this class. the first selected student will be a media helper, the second one will be a pledge/flag helper, the third one will be a pencil sharpener, the fourth one will be attendance taker, the fifth one will be a board eraser and the sixth one will be a calendar helper. from this class of 13 students, how many different ways can this selection be done?
From this class, the teacher wishes to selected six students. 2,2,2,2,2,3 different ways are there to selected from this class of 13 students.
Given that,
From this class, the teacher wishes to selected six students. The first chosen student will assist with media, the second will assist with pledges and flags, the third will sharpen pencils, the fourth will take attendance, the fifth will wipe the board, and the sixth will assist with the calendar.
We have to find how many different ways are there to selected from this class of 13 students.
For 13 students,
We divide like 2,2,2,2,2,3.
The first 2 student will be a media helper,
The second 2 students will be a pledge/flag helper,
The third 2 students will be a pencil sharpener,
The fourth 3 students will be attendance taker,
The fifth 2 students will be a board eraser and
The sixth 2 students will be a calendar helper.
Therefore, This many ways we can selected the students.
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The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
Answer:
A) there are no outliers in this distribution.
Answer:
Step-by-step explanation:
Answer there are no outlier
PLEASE HELP I WILL GIVE BRAINLIEST TO RIGHT ANSWER!!!!
1 3/5% of what number is 0.64?
Answer:
0.64 is 1 3/5% of 40
Step-by-step explanation:
Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buya new car, and is considering opening up a retirement account. He has a disposable income of$300/month, what would you recommend he do with this money? Why?
Problem
Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buy a new car, and is considering opening up a retirement account. He has a disposable income of $300/month, what would you recommend he do with this money? Why?
Solution
For this case the best option would be put the $45000 in a bank with a compound interest
And with the earnings each month of 300$ he can put the half of this into the account and the remain to spend on other things
Venus has a mean distance from the sun of 67,240,000 miles while mars has a mean distance from the sun of 4,213,000,000 miles. how much farther is mars from the sun than venus? a. 4,145,760,000 miles b. 4,146,260,000 miles c. 4,245,760,000 miles d. 4,280,240,000 miles
The Mean distance is 4,145,760,000 miles
The correct option is (a)
Given,
The mean distance from Venus to the sun is 67,240,000 miles.
The mean distance from Mars to the sun is 4,213,000,000 miles.
Now, According to the question
Subtract the distance of Mars to the sun from Venus to the sun :
Let's Calculate the mean distance:
= 4,213,000,000 - 67,240,000
= 4,145,760,000 miles
Hence, The Mean distance is 4,145,760,000 miles.
The correct option is (a)
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I need to know what system of inequalities is graphed below
SOLUTION:
For inequalities, the solution to is usually where the two regions meet.
The graphs here are:
[tex]\begin{gathered} x-3y\leq6\text{ (thick lines)} \\ \text{Here, checks the graph testing points (3,-1) and (0,-2)} \\ 2x\text{ }+\text{ y }>2.\text{ (broken lines)} \\ \text{Here, the checks the graph testing points (}0,2)\text{ and (1,0)} \end{gathered}[/tex]Final answer:
The final answer here is Option (B)