Answer:
x = 17/6
Step-by-step explanation:
First of all remove parenthesis by using distribution
6x + 9 - 12x + 24 = 16
Then collect all like terms
-6x + 33 = 16
After that move the constant to the right
- 6x = 16 - 33
Calculate 16 - 33
-6x = -17
Divide both sides
x = 17/6
Hope this helps!
7.
A dental office starts the month with 2,258 latex examination gloves. At month's end,
784 gloves remain. How many gloves were used?
which equation can be represented by the number line
Answer:
B
Step-by-step explanation:
The arrow is going left four units. Since it's going left, we know that we are adding a negative number and since it's going left 4 units, we know that we are adding -4 in our equation. This narrows it down to options B and D. However, the arrow usually represents the second number being added, hence, the answer is B.
Determine whether each set {p1,p2} is a linearly independent set in P3.
1. The polynomials p1 (t) = 1 + t2 and p2(t) = 1 - t2.
2. The polynomials p1 (t) = 2t + t2 and p2(t) = 1 + t.
3. The polynomials p1(t) = 2t - 4t2 and p2(t) = 6t2 - 3t.
Answer:
1) The polynomials [tex]p_{1}(t) = 1 +t^{2}[/tex] and [tex]p_{2}(t) = 1-t^{2}[/tex] are linearly independient, 2) The polynomials [tex]p_{1}(t) = 2\cdot t +t^{2}[/tex] and [tex]p_{2}(t) = 1+t[/tex] are linearly independent, 3) The polynomials [tex]p_{1}(t) = 2\cdot t - 4\cdot t^{2}[/tex] and [tex]p_{2}(t) = 6\cdot t^{2}-3\cdot t[/tex] are linearly dependent.
Step-by-step explanation:
A set is linearly independent if and only if the sum of elements satisfy the following conditions:
[tex]\Sigma_{i=0}^{n} \alpha_{i} \cdot u_{i} = 0[/tex]
[tex]\alpha_{0} = \alpha_{1} =...=\alpha_{i} = 0[/tex]
1) The set of elements form the following sum:
[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]
[tex]\alpha_{1}\cdot (1+t^{2})+\alpha_{2}\cdot (1-t^{2}) = 0[/tex]
[tex](\alpha_{1}+\alpha_{2})\cdot (1) +(\alpha_{1}-\alpha_{2})\cdot t^{2} = 0[/tex]
From definition this system of equations must be satisfied:
[tex]\alpha_{1} + \alpha_{2} = 0[/tex] Eq. 1
[tex]\alpha_{1}-\alpha_{2} = 0[/tex] Eq. 2
From Eq. 2:
[tex]\alpha_{1} = \alpha_{2}[/tex]
In Eq. 1:
[tex]2\cdot \alpha_{1} =0[/tex]
[tex]\alpha_{1} = 0[/tex]
[tex]\alpha_{2} = 0[/tex]
The polynomials [tex]p_{1}(t) = 1 +t^{2}[/tex] and [tex]p_{2}(t) = 1-t^{2}[/tex] are linearly independient.
2) The set of elements form the following sum:
[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]
[tex]\alpha_{1}\cdot (2\cdot t+t^{2})+\alpha_{2}\cdot (1+t) = 0[/tex]
[tex]\alpha_{2}\cdot (1) +(2\cdot \alpha_{1}+\alpha_{2})\cdot t +\alpha_1 \cdot t^{2} = 0[/tex]
From definition this system of equations must be satisfied:
[tex]\alpha_{2} = 0[/tex]
[tex]2\cdot \alpha_{1}+\alpha_{2} = 0[/tex]
[tex]\alpha_{1} = 0[/tex]
The polynomials [tex]p_{1}(t) = 2\cdot t +t^{2}[/tex] and [tex]p_{2}(t) = 1+t[/tex] are linearly independent.
3) The set of elements form the following sum:
[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]
[tex]\alpha_{1}\cdot (2\cdot t-4\cdot t^{2})+\alpha_{2}\cdot (6\cdot t^{2}-3\cdot t) = 0[/tex]
[tex](2\cdot \alpha_{1}-3\cdot \alpha_{2})\cdot t + (-4\cdot \alpha_{1}+6\cdot \alpha_{2})\cdot t^{2} = 0[/tex]
From definition this system of equations must be satisfied:
[tex]2\cdot \alpha_{1}-3\cdot \alpha_{2} = 0[/tex] (Eq. 1)
[tex]-4\cdot \alpha_{1}+6\cdot \alpha_{2} =0[/tex] (Eq. 2)
It is easy to find that each coefficient is multiple of the other one, that is:
[tex]\alpha_{1} =\frac{3}{2}\cdot \alpha_{2}[/tex] (From Eq. 1)
[tex]\alpha_{1} = \frac{6}{4}\cdot \alpha_{2}[/tex] (From Eq. 2)
[tex]\alpha_{1} = \frac{3}{2}\cdot \alpha_{2}[/tex]
Which means that polynomials [tex]p_{1}(t) = 2\cdot t - 4\cdot t^{2}[/tex] and [tex]p_{2}(t) = 6\cdot t^{2}-3\cdot t[/tex] are linearly dependent.
graph h(t)=-2(t+5)^2+3, find h(-8)
Answer:
h(-8)=-15
Step-by-step explanation:
Substitute t=-8
h(-8) =-2(-8+5)^2+3
=-2(-3)^2+3
=-2(9)+3
=-18+3
=-15
h(-8) = - 15
Step-by-step explanation:h(t) = - 2(t + 5)² + 3
replace t with - 8
h(-8) = - 2(- 8 + 5)² + 3
h(-8) = - 2(-3)² + 3
h(-8) = -2×9 + 3
h(-8) = - 18 + 3
h(-8) = - 15
The perimeter of the original rectangle is 16 feet. A small rectangle has a length of 6.2 feet and width of 1.8 feet. A larger rectangle has a length of 12.4 feet and width of blank. Not drawn to scale What is the perimeter of the enlarged rectangle? Round to the nearest tenth if necessary.
Answer:
32 ft
Step-by-step explanation:
The length of the larger rectangle is double that of the smaller one. If we assume the rectangles are similar, the perimeter will be double as well:
2·(16 ft) = 32 feet . . . . perimeter of larger rectangle
__
The width of the larger one is 2·1.8 ft = 3.6 ft.
Answer:
C) 32 feet
Step-by-step explanation:
＼(ﾟｰﾟ＼)
Solve for t.
-1 (t + 8) = -1.7
Answer:
t=-6.3
Step-by-step explanation:
-1 (t + 8) = -1.7
-1*t+-1*8=-1.7
-1t-8=-1.7
+8 +8
-1t=-1.7+8
-1t=6.3
-1t/-1=6.3/-1
t=-6.3
I hope this helped you.
Please mark Brainliest.
Have a great day!!!!!!!!
Answer: -6.3
Step-by-step explanation:
distribute whats in the parenthesis and you should get -1t-8= -1.7add 8 on both sides... -8 should cancel out with the positive 8 and you should get 6.3 when solving for -1.7+8. Drop your -1t divide -1 on both sides and the answer should be -6.3let me know if you have any questions
Keith sold half of his comic books and then bought nine
more. He now has 20. How many did he begin with?
Answer:
22 comic books.
Step-by-step explanation:
(20 - 9) * 2 First subtract 9 from 20
11 * 2 Multiply 11 by 2
22 is the product
Angles that are supplementary
Answer:
Two angles are said to be supplementary when they add up to 180°.
Answer:
Angles are supplementary if the add up to 180 degrees
Step-by-step explanation:
So many different angles can be supplementary.
Examples:
Ajacent Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
And a few other angles
Hope This Helps :)
A square has the following vertices. Find the area of the square.
(-7,-5), (-4,-2), (-1,-5), (-4,-8)
(1 point)
O V18 square units
O 18 square units
O V6 square units
O 6 square units
Answer:
18 square units
Step-by-step explanation:
Since the shape is a square lets find the distance between two close point then square the distance to find the answer.
Lets take the point (-7,-5), (-4,-2)
Distance= √((y2-y1)²+(x2-x1)²)
Distance= √((-2--5)²+(-4--7)²)
Distance= √((-2+5)²+(-4+7)²)
Distance= √((3)²+(3)²)
Distance= √(9+9)
Distance= √18 units
Area= distance ²
area= √18²
Area= 18 square unit
Consider the following planes. x + y + z = 5, x + 3y + 3z = 5A) Find parametric equations for the line of intersection of the planes. B) Find the angle between the planes.
Answer:
Step-by-step explanation:
Consider the following planes. x + y + z = 5, x + 3y + 3z = 5
the parametric equations for the line of intersection of the planes are determined as follows:
From the first plane, the normal of the first plane is [tex]n_1 = (1,1,1)[/tex]
from the second plane, the normal of the second plane is [tex]n_2 = (1,3,3)[/tex]
[tex]n_1 \times n_2 = \begin {vmatrix} \left \begin{array}{ccc}i&j&k\\1&1&1\\1&3&3 \end{array}\right \end {vmatrix}[/tex]
= i(3-3) -j(3-1)+k(3-1)
= i(0) - j(2) + k(2)
= -2j +2k
Suppose z = 0
x+y + 0 = 5 ---(1)
x+3y + 3(0) = 5 (2)
subtracting by elimination
-2y = 0
y = 0/-2
y = 0
The intersection on point of the plane is (5,0,0)
The equation of plane is r (t) =(5, 0, 0) + t(0, -2, 2)
∴
(x(t), y (t), z(t) ) = (5, -2t, 2t)
B) Find the angle between the planes
The angle between the planes can be represented by the equation:
[tex]cos \theta = \dfrac{a_1a_2+b_1b_2 + c_1c_2}{\sqrt{a^2_1+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}[/tex]
[tex]cos \theta = \dfrac{1 \times 1+1\times 3 +1 \times 3}{\sqrt{1^2+1^2+1^2}\sqrt{1^2+3^2+3^2}}[/tex]
[tex]cos \theta = \dfrac{1+ 3 +3}{\sqrt{3}\sqrt{19}}[/tex]
[tex]cos \theta = \dfrac{7}{\sqrt{3}\sqrt{19}}[/tex]
[tex]\mathbf{\theta = cos ^{-1} (\dfrac{7}{\sqrt{57}})}[/tex]
What is the value of the expression when y = 2? StartFraction 2 minus y Over 4 plus y EndFraction plus StartFraction 3 (y plus 2) Over y EndFraction
Answer:
12
Step-by-step explanation:
Answer:
2.4
Step-by-step explanation:
I need some help with this question. "A scale drawing of a school bus has a scale of an inch to 5 feet. If the length of the school bus is in inches on the scale drawing, what is the actual length of the bus?"
Answer:
45 Feet
Step-by-step explanation:
4.5 divided by 0.5=9
9 times 5=45
Hoped this helped!
9 pencils cost 7.74 what is the equation of the cost of 6 pencils
Answer:
6 pencils cost $5.16.
Step-by-step explanation:
1. Find the cost of one pencil.
Divide: $7.74 ÷ 9 = $0.86 for one pencil
2. Multiply 0.86 by 6
$0.86 × 6 = $5.16
Answer:
2/3 multiply with 7.74
=5.16
Andre and Morgan are both headed to Florida for vacation. Andre will drive 70 miles per hour. Morgan will drive 55 miles per hour but will leave 3 hours earlier than Andre. How many hours will Morgan have been driving before Andre catches up with her?
Answer:
14hours
Step-by-step explanation:
Since Andre and Morgan are both heading to the same location i.e Florida, they will have the same distance.
Distance = Speed × Time
For Morgan:
His speed = 55mi/hr
Let his time = x
Distance covered by Morgan = 55x
For Andre
His speed = 70mi/hr
Time = x-3 (since morgan leaves 3 hours earlier than Andre)
Distance covered = 70× (x-3) = 70(x-3)miles
Since they are driving towards the same location;
55x = 70(x-3)
55x = 70x-210
55x-70x = -210
-15x = -210
x = 210/15
x = 14
Hence Morgan will have been driving 14hours before Andre catch up
Twice a number is at most 36.
Answer:
18?
Step-by-step explanation:
Need help on this one. Sort of confused.
Answer:
I'm just as confused as you lol
soIve: 12 = -4(-6x - 3)
x = -0.625
x = -0.375
x = -2
x = 0
Answer:
The answer is "x = 0"
Step-by-step explanation:
Step-by-step explanation: Hope this answer is helpful...
Make me as brainliest...
I need help with this pls ASAP
Give two points with integer coordinates that have a slope of 2/5 between them.
Answer:
yes
Given a 2D line e.g. (3,10) -> (8.3,16.5), how can I find any point on that line that has has whole-number coordinates?
I can easily iteratively walk along one of the axis in integer steps, seeing if the value on the other axis is integer, but this is slow for very very long lines.
What the hello does this mean -----> 42 × 10 = 10 – 4 × 70
Answer:
whatever 42 times 10 equals, it also equals what ten minus 4 times seventy is
Step-by-step explanation:
so both 42 × 10
and 10 – 4 × 70
EQUAL
420
(pffft 420....sorry its funny)
Answer:
Associative properties
Step-by-step explanation:
42 x 10 = 420
(10-4)=6
6 x 70 = 420
Find the volume of the shipping box using the two methods and show your work: Packing cubes Using the volume formula Explain how both methods provide the same measurement of volume for the shipping box.
Answer:
Volume is the measure of how big an object is in three dimensions, so the volume of a box measure how much room there is inside of the box. To find it, you need to make a few simple measurements of length, width, and height, and then multiply them.
Step-by-step explanation:
A report on Americans' attitudes toward teachers' pay found that 82% of the respondents to the survey upon which the report is based think that teachers don't make enough money. Which factor is most relevant when evaluating this report? A. 49% of the respondents were women. B. 78% of the respondents were married. C. 51% of the respondents were men. D. 62% of the respondents were educators.
Answer:
I think the answer is A. 49% of the respondents were women
From the site a certain ramp has a right triangular shape its height is 30 cm and it’s horizontal length is 3 m what calculation will give us the estimated length of the ramp in meters
Answer:
[tex]a^{2} +b^{2} =c^{2}[/tex]
Step-by-step explanation:
C is the horisontal and a or b can be the height, plug in the numbers and you solve for length.
Answer:
(sqr) 30^2/100^2+3^2
Step-by-step explanation:
4(6c+5) - 2(3c - 5) = 120
Answer:
[tex]c=5[/tex]
Step-by-step explanation:
[tex]4(6c+5)-2(3c-5)=120[/tex]
Use the distributive property to expand the equation:
[tex]4(6c)+4(5)-2(3c)-2(-5)=120\\\\24c+20-6c+10=120[/tex]
Combine like terms to simplify the equation:
[tex]24c-6c+20+10=120\\\\18c+30=120[/tex]
Subtract 30 from both sides:
[tex]18c+30-30=120-30\\\\18c=90[/tex]
Isolate the variable c. Divide both sides by 18:
[tex]\frac{18c}{18}=\frac{90}{18}\\\\ c=5[/tex]
So, c is equal to 5.
:Done
Which graph represents the inequality 3y-5x<-6?
Answer:
First Graph
Step-by-step explanation:
3y-5x<-6
3y<5x-6
y<5/3x-6/3
y<5/3x-2
plug in the coordinates (0,0)
0<0-2
0<-2
0 is not less than -2
therefore the graph would be shaded opposite of (0,0)
Write a number (in standard form) that has the digit 7 in the thousands place. Use the digit 7 only once.
Answer:
7123
Step-by-step explanation:
The only requirement is to have 7 in the thousands place, which I've done, and the rest of the numbers can be any number you choose!
Sofia invests her money in an account paying 7% interest compounded semiannually. What is the effective annual yield on this account? Enter your response as a percentage rounded to two decimal places and omit the percentage sign
Answer:
7.12
Step-by-step explanation:
The formula for the effective annual yield is given as:
i = ( 1 + r/m)^m - 1
Where
i = Effective Annual yield
r = interest rate = 7% = 0.07
m= compounding frequency = semi annually = 2
i = ( 1 + 0.07/2)² - 1
i = (1 + 0.035)² - 1
= 1.035² - 1
= 1.071225 - 1
= 0.071225
Converting to percentage
0.071225 × 100
= 7.1225%
Approximately to 2 decimal places = 7.12
Therefore, the annual effective yield = 7.12
Select the relationship that does represent a function.
Answer:
Picture number 3 is the answer
Step-by-step explanation:
A function is a relation in which each element in the domain is paired with exactly one element in the range not 2.
Picture number one has a range left with no domain so it's not a function
Picture number 2 is showing an element in the domain which paired 2 elements in the range so it's not a function
Picture 3 is correct because each element in the domain macthes one element in the range.
Picture 4 is wrong because it's showing elements in the domain that matches 2 elements in the range. Hope it makes sense.
The required relationship that represents a function is given by 3rd image. Option C is correct.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
The first image has a range with no domain, hence it is not a function. In 2nd image depicts an element in the domain that paired two elements in the range, indicating that it is not a function. In 3rd image, it is valid because each element in the domain corresponds to one element in the range. In picture 4, it is incorrect since it depicts domain components that match two range elements.
Thus, the required relationship that represents a function is given by 3rd image. Option C is correct.
Learn more about function here:
brainly.com/question/21145944
#SPJ2
3. Determine if the equation represents y as a function of x.
9x + 3y = 12
L1 : y = 2x , (2) find the equation of the line L2 perpendicular to L1 passing through the point P = (1, 2).
Answer:
2y+x = 5Step-by-step explanation:
Given the line L1 as y = 2x perpendicular to an unknown line L2 passing through the point P = (1, 2), we are to find the equation of line L2. to find the equation of the line L2, we will use the point-slope equation of a line expressed as y-y₀ = m(x-x₀)
m is the slope of the unknown line
(x₀, y₀) is the given point.
First is to get the slope of the known line:
comparing the line L1: y = 2x with the standard equation of the line y = mx+c, it can be seen that m = 2
Then we will calculate the slope of the required line.
Since L1 is perpendicular to L2, the product of their slope will be -1 i.e
mm₁ = -1 where m₁ is the slope of the required line L2.
Given m =2
m₁ = -1/m
m₁ = -1/2
Finally we will calculate the equation of line L2 by substituting the slope of line L2 and the point in the point slope equation above;
y-y₀ = m(x-x₀)
Given (x₀, y₀) = (1,2) and m₁ = -1/2
y-2 = -1/2(x-1)
open the parenthesis
y-2 = -x/2+1/2
multiply through by 2:
2y-4 = -x+1
2y+x = 1+4
2y+x = 5
Hence the equation of the line L2 is 2y+x = 5