Mrs. Bankhead is planning a party for her son's 10th birthday. The table represents the
quote she received form Party City.
Number of
Balloons
2
4
6
8
Total Cost of
Balloons
6
12
18
24
7
1 point
The slope is:
2
ООО
6
The formula for slope is (y2 - y1)/ (x2 - x1)
Let's use (2,6) and (4,12)
12 - 6 = 6
4 - 2 = 2
6/2 = 3
The slope is 3.
please help!!
Write a matrix representing the system of equations
Answer:
[tex](4, -1, 3)[/tex]
Step-by-step explanation:
We have the system of equations:
[tex]\left\{ \begin{array}{ll} x+2y+z =5 \\ 2x-y+2z=15\\3x+y-z=8 \end{array} \right.[/tex]
We can convert this to a matrix. In order to convert a triple system of equations to matrix, we can use the following format:
[tex]\begin{bmatrix}x_1& y_1& z_1&c_1\\x_2 & y_2 & z_2&c_2\\x_3&y_2&z_3&c_3 \end{bmatrix}[/tex]
Importantly, make sure the coefficients of each variable align vertically, and that each equation aligns horizontally.
In order to solve this matrix and the system, we will have to convert this to the reduced row-echelon form, namely:
[tex]\begin{bmatrix}1 & 0& 0&x\\0 & 1 & 0&y\\0&0&1&z \end{bmatrix}[/tex]
Where the (x, y, z) is our solution set.
Reducing:
With our system, we will have the following matrix:
[tex]\begin{bmatrix}1 & 2& 1&5\\2 & -1 & 2&15\\3&1&-1&8 \end{bmatrix}[/tex]
What we should begin by doing is too see how we can change each row to the reduced-form.
Notice that R₁ and R₂ are rather similar. In fact, we can cancel out the 1s in R₂. To do so, we can add R₂ to -2(R₁). This gives us:
[tex]\begin{bmatrix}1 & 2& 1&5\\2+(-2) & -1+(-4) & 2+(-2)&15+(-10) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\0 & -5 & 0&5 \\3&1&-1&8 \end{bmatrix}[/tex]
Now, we can multiply R₂ by -1/5. This yields:
[tex]\begin{bmatrix}1 & 2& 1&5\\ -\frac{1}{5}(0) & -\frac{1}{5}(-5) & -\frac{1}{5}(0)& -\frac{1}{5}(5) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3&1&-1&8 \end{bmatrix}[/tex]
From here, we can eliminate the 3 in R₃ by adding it to -3(R₁). This yields:
[tex]\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3+(-3)&1+(-6)&-1+(-3)&8+(-15) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&-5&-4&-7 \end{bmatrix}[/tex]
We can eliminate the -5 in R₃ by adding 5(R₂). This yields:
[tex]\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0+(0)&-5+(5)&-4+(0)&-7+(-5) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&-4&-12 \end{bmatrix}[/tex]
We can now reduce R₃ by multiply it by -1/4:
[tex]\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\ -\frac{1}{4}(0)&-\frac{1}{4}(0)&-\frac{1}{4}(-4)&-\frac{1}{4}(-12) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}[/tex]
Finally, we just have to reduce R₁. Let's eliminate the 2 first. We can do that by adding -2(R₂). So:
[tex]\begin{bmatrix}1+(0) & 2+(-2)& 1+(0)&5+(-(-2))\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 1&7\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}[/tex]
And finally, we can eliminate the second 1 by adding -(R₃):
[tex]\begin{bmatrix}1 +(0)& 0+(0)& 1+(-1)&7+(-3)\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 0&4\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}[/tex]
Therefore, our solution set is [tex](4, -1, 3)[/tex]
And we're done!
Solve each inequality and graph it's solution set on a number line.
1. 0<2x-10<20
2. x+7<7 OR 5+2x>8
Pls Help 40 Points
Hey there!
1) 0<2x−10<20
0+10<2x−10+10<20+10(Add 10 to all parts)
10<2x<30
10/2 <2x/2 < 30/2 (Divide all parts by 2)
5<x<15
Answer:
5<x<15
Graph in first image
2) x+7<7
Step 1: Subtract 7 from both sides.
x+7−7<7−7
x<0
OR
5+2x>8
Step 1: Simplify both sides of the inequality.
2x+5>8
Step 2: Subtract 5 from both sides.
2x+5−5>8−5
2x>3
Step 3: Divide both sides by 2.
2x/2 > 3/2
x > 3/2
Emmett deposited $90 in an account earning 5% interest compounded annually.
To the nearest cent, how much will he have in 2 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
The value of the account after two years given the amount deposited and the rate of interest would be $99.23.
What is compound interest?Compound interest is when both the amount deposited and the interest already accrued increase in value when interest is paid.
What is the value of the account?The formula that can be used to determine value of the account is:
B=p(1+r)^t
where:
B = balancep = principal r = the interest ratet = time$90(1.05)^2 = $99.23
To learn more about compound interest, please check: https://brainly.com/question/26367706
(9x + 4) (2x2 – 17x - 9) = 0
-
Step-by-step explanation:
So leave (9x+4) and factor (2x2-17x-9) .
Factors into (2x+1)(x-9).
Now set (9x+4)=0 and find x. x= -4/9
set (2x+1)=0 x = -1/2
set x-9=0 so x=9. you have 3 solutions which are -4/9, -1/2, and 9.
What is 5^8 plus 9375?
Answer:
400000
Step-by-step explanation:
5^8 = 390625
390625 + 9375 = 400000
Answer:
400,000
Step-by-step explanation:
We solve for 5^8 first,
this means that 5 is being multiplied by itself 8 times.
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 390,625
Now we add this to 9,375:
390,625 + 9,375 = 400,000
what is 1/3-(-5/3)=
Answer:
1/3 - (-5/3) = 2
Step-by-step explanation:
1/3 - (-5/3)
Subtracting a negative is the same as adding a positive.
1/3 + 5/3 = 6/3, or 2
7b+2 b = 2
3(2c-10)
1+2.1y-0.9y+4
Answer:
If you were to solve for, 7b+ 2b = 2 then;
7b+ 2b = 2
Combine like terms first:
(7b + 2b)
9b = 2
Then divide by 9 from both sides to solve for b:
/9 /9
b = 2/9 or 0.222..
If you were to solve for, 3(2c - 10) then;
3(2c - 10)
Use the distributive property, and multiply 3 to both 2c and 10:
3(2c) - 3(10)
6c - 30
If you were to solve for, 1 + 2.1y - 0.9y + 4 then;
1 + 2.1y - 0.9y + 4
Combine like terms:
(1 + 4) (2.1y - 0.9y)
5 + 1.2
You pick a card at random. 2 3 4
What is P(4 or factor of 90)?
Write your answer as a fraction or whole number.
Sacas una carta al azar. 2 3 4
¿Cuánto es P(4 o factor de 90)?
Escribe tu respuesta como una fracción o como un número entero.
Answer:
P (4 or factor of 90) = 1
Step-by-step explanation:
Given :-
Three cards numbered 2, 3, 4
To Find :-
P (4 or factor of 90)
Solving :-
4 is required and we know that 2 and 3 are both factors of 90.
Therefore, P (4 or factor of 90) = 1
Solution :-
P (4 or factor of 90) = 1
Answer:
1
Step-by-step explanation:
P(2) = 1/3
P(3) = 1/3
P(4) = 1/3
2 and 3 are factors of 90
⇒ P(factor of 90) = P(2) or P(3) = 1/3 + 1/3 = 2/3
Therefore,
P(4 or factor of 90) = P(4) or P(factor of 90) = 1/3 + 2/3 = 1
A square is cut into two identical rectangles. Find the perimeter of each rectangle if the perimeter of the square is 48 cm.
thankyou ~
Solution:
perimeter of rectangle = 2 ( Length + Width )
a square has all sides of similar length. thus [ length = width ]Find length/width:
2 (length + length) = 48
2(length) = 24
length = 12 cm
width = 12 cm
⇒ The dimensions of square: 12 x 12
If the square cut into half, the dimensions of either length or width will half.
Therefore, the perimeter of rectangle:
→ 2 (length + width)
→ 2 ( 12 + 6 )
→ 2 ( 18 )
→ 36 cm
plss say hi and follow my yt paycake&kelp!
Answer:
hi
Step-by-step explanation:
Answer:
ok
Step-by-step explanation:
Choose the best graph that represents the following systems of linear inequality.
Answer:
C
Step-by-step explanation:
using the power of elemination,looking at the first equation,we singled out the top 2, now looking at the 2nd equation, we see the y intercept is 2 meaning it has to be graph c
Which of the following is a solution of y - x < -3?
(6, 2)
(2, 6)
(2, -1)
Answer:
(6,2)
Step-by-step explanation:
Answer:
(2,6)
Step-by-step explanation:
x=2
y=6
x-y<-3
2-6<-3
-4<-3
-3 is greater than -4
Hope it helps u
Please mark it as the brainliest answer...
Josephine wants to divide the shed into two compartments. One compartment will have a volume of 100ft^3. What is the volume of the second compartment ?
Allie is single, has an adjusted gross income of $25,005 and one exemption of $12400. How much is his tax according to the table? Hint: find taxable income first. $1246 $1263 $1318 $1324
Allie's tax amount is the amount deducted from his taxable income
Allie's tax amount is $1427
How to determine the tax?The given parameters are:
Adjusted gross income = $25,005
Exemption = $12400
Start by calculating the taxable income using
Taxable income = Adjusted gross income - Exemption
So, we have:
Taxable income = $25,005 - $12400
Evaluate the differences
Taxable income = $12605
The question is incomplete.
So, I will use the table of the single taxable income tax bracket and rates, 2016
Using the table, the tax amount on an income of $12605 is:
Tax = $927.50 + 15% * (Amount - $9275)
So, we have:
Tax = $927.50 + 15% * ($12605 - $9275)
Evaluate
Tax = $1427
Hence, Allie's tax amount is $1427
Read more about taxable income at:
https://brainly.com/question/25783927
Answer:
The real answer is $1318
Step-by-step explanation:
I hope this helps
select the digit in the thousands place for 689,234
Answer: the thousands place is where the nine is
Step-by-step explanation: Hope this helps!
Answer:
The remaining number in thousands units is 9
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Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
Approximately how many sentences should your Summary contain?
Answer:
5-6 I think
Step-by-step explanation:
correct answer only!!!
Question/answer choices below as pictures
Answer:
Last graph: [tex]\langle-7,-9\rangle[/tex]
Step-by-step explanation:
Here, [tex]u=\langle-2,-7\rangle[/tex] and [tex]v=\langle5,2\rangle[/tex]. Thus, [tex]u-v=\langle(-2)-5,(-7)-2\rangle=\langle-7,-9\rangle[/tex], making the last graph the correct answer.
What is 15% off 1200
Answer:
1020
Step-by-step explanation:
pls rate brainliest!
Answer:
1020
Step-by-step explanation:
First we need to find out what 15 is so we can divide 1200 by 100 to get 12 so 1% = 12 so 15 x 12 = 180
1200-180=1020
In a construction project, you are required to create a perimeter wall for a rectangular garden that measures 600 feet long and 100 feet wide. You need to leave space for two gates on each of the longer sides of the garden. Each gate is 50 feet long. What is the total length of the wall?
Answer:
1,300 feet
Step-by-step explanation:
600 - 50 = 550
550 + 550 + 100 + 100 = 1,300
Stephen, Paul & Bridget share some money in the ratio 3 : 4 : 2.
In total, Stephen and Bridget receive £50.
How much does Paul get?
Answer:
£40.
Step-by-step explanation:
In terms of ratio units, Stephen and Bridget together get 3+2 = 5, while Paul receives 4. That is, Paul gets 4/5 of their combined total, or ...
4/5 · £50 = £40
Paul gets £40.
Given parameters:
Ratio of their money = 3 : 4 : 2
Total amount received by Stephen and Bridget = 50
Unknown :
How much did Paul get = ?
Solution:
The amount Paul got is a fraction of the total.
We need to find the total amount first;
Amount Stephen and Bridget got = [tex]\frac{ratio of stephen and bridget}{total ratio} x total amount[/tex]
let the total amount = y;
50 = [tex]\frac{3+2}{9}[/tex] x y
[tex]\frac{5y}{9}[/tex] = 50
5y = 450
y = 90
Now, the amount Paul got;
= [tex]\frac{4}{9} x 90[/tex]
= 40
The amount Paul got is £40
Examine the lines that are cut by transversals to determine the measure of angle 1.
What is the measure of angle 1?
m <1: _____
Why?
Answer: 48 degrees
Step-by-step explanation:
Alternate interior angles theorem
Answer:
m <1=
✔ 48°
Why?
✔ It corresponds to the 48-degree angle.
Step-by-step explanation:
PLEASE HELP!!!!!!!The product of 2v3 and 3v12 in simplified form is?
Answer:
install socratic it will give you all answer no kiding
1 + 2 x 4x+1
4x^2 + 5x+1 x x^2-4
Answer: 1 + 2 x 4x+1=10
Step-by-step explanation: 4x^2 + 5x+1 x x^2-4= also= 10
Please help and explain why it is the answer please!
9514 1404 393
Answer:
d) m∠a = m∠f
Step-by-step explanation:
Where a transversal crosses parallel lines, certain relationships between the angles are established. Effectively, the two same-side interior angles are supplementary, as they would be in a parallelogram. Here, those are angles B and F, or angles A and E.
The vertical- and linear-angle relationships give rise to all of the other ways this is expressed. For example, angles A and B are a linear pair, so supplementary. Since B and F are supplementary, and B and A are supplementary, F = A. Using more formal language, ...
m∠a = m∠f
write an algebraic expression for each phrase
a number n divided by 4.
will give brainlliest
The table below shows four problems using decimals. Problem Number Problem 1 One ounce of pretzels has 2.93 g of protein. How many grams of protein are in a 6-ounce package of pretzels? 2 Paul rides his bike at an average rate of 13.8 miles per hour. If he rode for 3.2 hours, how far did he ride? 3 Sonya made an 8-slice whole wheat pizza with cheese and veggies. If the whole pizza had 1567.9 calories, how many calories are in one slice? 4 One slice of multigrain bread has 12.4 carbs. Jules uses 6 slices to make sandwiches for his friends. How many carbs did he use? Which problem would be solved using division, and what is the solution to the problem? will give brainlliest
Answer:
its A
Step-by-step explanation:
Answer:
It is c
Step-by-step explanation:
-35 POINTS- A bag contains 30 cards numbered 1 to 30. You are going to select one card, replace the card, and then draw a second card. What is the probability you will draw a 4 and then a number less than 10? Simplify your answer.
Answer:
36
Step-by-step explanation:
you simplify 26 simplify it again and the simplify answer is 36
Answer:
1 / 100. is the answer. got it correct.
Step-by-step explanation:
3. What figures are formed when a diagonal is drawn in a quadrilateral
a. triangles
b. squares
c. parallelograms
4.which is TRUE about the sides of parallelogram?
a. 1 pair of sides are parallel and equal
b. 2 pairs of sides are parallel and equal
c. 4 sides are equal
5.if two diagonal are drawn in a rhombus or in a square, which of the following will be formed
a. 2 triangles of the same size
b. 2 pairs of triangles of the same size
c. 4 triangles of the same size
6. which of the following describes the sides of a square or of a rhombus
a. no sides are equal
b. two sides are equal
c. all sides are equal
Answer:
3. What figures are formed when a diagonal is drawn in a quadrilateral
a. triangles
4. which is TRUE about the sides of a parallelogram?
b. 2 pairs of sides are parallel and equal
5. if two diagonal are drawn in a rhombus or in a square, which of the following will be formed
a. 2 triangles of the same size
6. which of the following describes the sides of a square or of a rhombus
c. all sides are equal
Hope it helps!!!Brainliest pls!!!. On Mary’s MP3 player for everly 3 pop songs Maria had she also had 4 country songs. If she has 15 pop songs on her MP3 player, how many country songs does she have? ________________
Answer:
20
Step-by-step explanation:
every three pop add 4 country you will get 4 8 12 16 20 making 20 your answer