Complete question:
Given Q(x) = 7x − 3 and P(x) = 7x3 − 3x2 + 42x − 27, find P(x) ÷ Q(x) . (Divide using long division.)
Answer:
[tex]\frac{7x^3 \ - \ 3x^2 \ + \ 42x \ - \ 27}{7x \ - \ 3} = \ \ x^2 + 6 \ \ \frac{-9}{7x \ - \ 3}[/tex]
The quotient = x² + 6 and the remainder = - 9
Step-by-step explanation:
Given;
Q(x) = 7x − 3
P(x) = 7x³ − 3x² + 42x − 27
To divide P(x) by Q(x) using long division, we apply the following method;
x² + 6
---------------------------------
7x − 3 √ 7x³ − 3x² + 42x − 27
− (7x³ - 3x²)
-------------------------------------
42x − 27
− (42x − 18)
----------------------------------------
− 9
[tex]Therefore, \ \frac{7x^3 \ - \ 3x^2 \ + \ 42x \ - \ 27}{7x \ - \ 3} = \ \ x^2 + 6 \ \ \frac{-9}{7x \ - \ 3}[/tex]
The quotient = x² + 6 and the remainder = - 9
2. Write the slope-intercept form of the equation for each graph described. Line passing through (-5, 12) and parallel to the line whose equation is y = 2x + 5. Y =
Answer: y = 2x+22
========================================================
Explanation:
The equation y = 2x+5 is in the form y = mx+b
m = 2 = slope
b = 5 = y intercept
Parallel lines have equal slopes, but different y intercepts. So the answer will be in the form y = 2x+c, where b and c are different numbers. Since b = 5, this means c must be some other number. If c = 5, then we'd have the exact same line.
Let's plug in (x,y) = (-5,12), along with the slope m = 2, and solve for c
y = mx+c
12 = 2(-5)+c
12 = -10+c
12+10 = c
22 = c
c = 22
Since m = 2 and c = 22, we go from y = mx+c to y = 2x+22
The equation of the parallel line is y = 2x+22
The graph is below.
Someone please help me with this math problem? !!
Answer:
x = -1
Step-by-step explanation:
If you input -1 to both functions, you get 3.
The equation below has one solution. 9 x minus 10 = 3 x + 2 What is the solution to the equation? –2 –1 1 2
Answer:
x=2
Step-by-step explanation:
Graph the solution of the inequality 3/7(35x-14)<_ 21x/2+3
Answer:
You'll have a closed circle at x = 2, and shading to the left
See the diagram below
=========================================================
Explanation:
The fractions here are 3/7 and 21/2. The denominators of which are 7 and 2 respectively. The LCD is 7*2 = 14.
If we multiply both sides by 14, then this will clear out the denominators and make the fractions go away.
14*(3/7) = (14*3)/7 = 42/7 = 814*(21/2) = (14*21)/2 = 294/2 = 147So if we multiplied both sides by 14, then we have these steps
[tex]\frac{3}{7}(35x-14) \le \frac{21x}{2}+3\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}+3\right)\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}\right)+14*\left(3\right)\\\\6(35x-14) \le 147x+42\\\\[/tex]
--------------------------
Let's isolate x
[tex]6(35x-14) \le 147x+42\\\\6(35x)+6(-14) \le 147x+42\\\\210x-84 \le 147x+42\\\\210x-147x \le 42+84\\\\63x \le 126\\\\x \le 126/63\\\\x \le 2\\\\[/tex]
The graph of this will consist of a closed or filled in circle at x = 2. We shade to the left to represent numbers smaller than 2.
So either x = 2 or x < 2.
If we used an open hole at 2, then we wouldn't be including 2 (but we want to include this endpoint).
See the diagram below.
ABC is a triangle. Work out angle x
Answer:
I think it is 52 degrease
Step-by-step explanation:
Need answer :))))))))
Answer:
cost per serving can be used as a result of using your head to think
Which equation describes the summer for two vectors plotted below?
Answer:
B
Step-by-step explanation:
Please help. I am really stuck on this little problem. I need to find the domain and Range for this graph.
Answer:
This isn't the answer but if you can take a pic of this and put it in this app called "Math-way" or "Photo-math" those help me
Draw an angle and then draw the opposite ray to one of its sides to form a linear pair. Find the measure of the angle formed by the angle bisector of the original angle and the opposite ray if the original angle bisector measures 50 degrees, 90 degrees, and 150 degrees If the angle equals 50 degrees then the measurement of the required angle is
Answer:
1. 155 degree
2. 135 degree
3. 105 degree
Step-by-step explanation:
1. Let the original angle is 50 degree, the opposite angle which forms a linear pair is 180 - 50 = 130 degree.
Now the angle bisector is 25 degree from the original ray , the angle between the bisector and the opposite ray is 130 + 25 = 155 degree.
2. Let the original angle is 90 degree, the opposite angle which forms a linear pair is 180 - 90 = 90 degree.
Now the angle bisector is 45 degree from the original ray , the angle between the bisector and the opposite ray is 90 + 45 = 135 degree.
3. Let the original angle is 150 degree, the opposite angle which forms a linear pair is 180 - 150 = 30 degree.
Now the angle bisector is 75 degree from the original ray , the angle between the bisector and the opposite ray is 30 + 75 = 105 degree.
A chocolate factory uses 16 of a bag of cocoa butter in each packet of chocolate. The factory used 13 of a bag of cocoa butter today. How many packets of chocolates did the factory make?
Answer:
13/16 of a packetStep-by-step explanation:
Solve using ratios:
1 packet ⇒ 16 bagsx packets ⇒ 13 bagsFind x:
x*16 = 1*13x = 13/16Factor the expression below. A. (x − 6)(x − 6) B. 6(x2 − x + 6) C. (x − 6)(x + 6) D. (x + 6)(x + 6)
Step-by-step explanation:
X(x+6) - 6(x+6)
X+6x-6x-36
X-36
Annie invests $400 in a bank that offers 5.5% simple annual interest after 6 years her investment will increase by blank dollars
Answer:
Her investment will increase by 551.54 dollars
Step-by-step explanation:
So we know that the exponential function formula is f(x)=a(1+r)^x
So knowing that we can input values
So now we have f(x)=400(1+0.055)^6
Since it is annual we will only have the interest yearly so that changes are equation to look like this f(x)=400(1+0.055/1)^6
So next we have to add 1 and 0.055 which is 1.055
So we input that into the equation so now we have f(x)=400(1.055/1)^6
Now we have to do (1.055/1) to the power of six, so we get 1.37884280676
Now we have to 1.37884280676 times 400, which would be 551.537122705.
Assuming they want to the nearest 100th it would be 551.54
So the answer is 551.54 dollars
Hopefully, that helped. If I made any mistake or I am incorrect feel free to correct me. :)
Drag each expression to the correct category.
Apply the produc rules to determine the sign of each expression.
[tex]( - \frac{4}{9} )( \frac{7}{4} ) = \: \: negative [/tex]
[tex]( - 2 \frac{3}{4} )( - 1 \frac{1}{5} ) = \: \: positive[/tex]
[tex](3)( - 3)( - 3)( - 3)( - 3) = \: \: positive[/tex]
[tex]( - \frac{1}{6} )( - 2)( - \frac{3}{5} )( - 9) = \: \: positive[/tex]
[tex]( - \frac{4}{7} )( - \frac{3}{5} )( - 9) = \: \: negative[/tex]
[tex]( - \frac{10}{7} )( \frac{8}{3} ) = \: \: negative[/tex]
Can somebody help me with this question?
Answer:
.
Step-by-step explanation:
(06.01)Four graphs are shown below: Which graph represents a negative linear association between x and y?
Answer:
Step-by-step explanation:
A negative linear association between x and y means that as x increases, y decreases at the same rate, creating a line with a negative slope. This line will tend from upper left to lower right. 2 of those graphs tend from upper left to lower right, but only one of them is a linear representation. That is graph D.
Tzar Bomba
(Soviet)
15
Trinity
Bravo
Hiroshima
10 -
Mike
Bunker Buster
Illustration From October 2002
Issue of Popular Mechanics" (pg. 69)
Determine the following about the graph:
• Is the graph misleading?
수
.
Does the graph have missing or inaccurate titles, labels, or keys?
e
Does the vertical axis start at 0?
.
Are images used instead of bars?
.
Is the perspective or orientation misleading?
Answer:
Below
Step-by-step explanation:
1. Potentially, yes. The display of the smaller bombs in the "magnifying glass" display can be very misleading.
2. Yes - the vertical axis labels the tonnage of the nuclear blast while displaying the height of each mushroom cloud.
3. Maybe? While the first number displayed in the vertical axis is 5 (Mt), it is most likely that the 0 is unlabeled rather than non-existent.
4. Yes - images of the mushroom cloud produced by each bomb.
5. Absolutely - the larger display of the smaller bombs can create major conflict in understanding the size of each.
x/5 = 2/3 = 5/y find the ratio from x to y
Answer:B
Step-by-step explanation:because im smart
Calculate the median of the following data 18, 24, 55, 59, 34, 39, 22, 32, 57, If 55 is replaced by 33, calculate the new median
Answer:
34, and if 55 was replaced with 33, the new median would be 33.
Step-by-step explanation:
The median is the number that is in the middle of a data set, once the numbers are organized from least to greatest. If we put the numbers in order (18, 22, 24, 32, 34, 39, 55, 57, 59), the number in the middle is 34. If we do the same, but replace 55 with 33, (18, 22, 24, 32, 33, 34, 39, 57, 59), we get 33 as the median.
y4+5y2+9 factorise please help me
[tex]\displaystyle\ y^4 +5y^2+9=(y^2+3)^2-y^2=(y^2-y+3)(y^2+y+3)[/tex]
Answer:
Solution given;
[tex] y^{4}+5y²+9[/tex]
keeping [tex]y^{4} and 9 together [/tex]
[tex]y^{4}+9+5y²[/tex]
[tex](y²)²+3²+5y²[/tex].....[I]
we have
a²+b²=(a+b)²-2ab
or
a²+b²=(a-b)²+2ab
same like that
[tex](y²)²+3²=(y²+3)²-6y² or (y²-3)²+6y²[/tex]
remember that while adding or subtracting the left term 5y² either adding 6y²or subtracting 6y²
should make the term perfect square
while subtracting it makes perfect square
so
we take
(y²)²+3²=(y²+3)²-6y²
again
substituting value of
(y²)²+3² in equation 1 and it becomes
(y²+3)²-6y²+5y²
solve like terms
(y²+3)²-y²
again
we have
a²-b²=(a+b)(a-b)
by using this.
(y²+3+y)(y²+3-y)
rearrange it
(y²+y+3)(y²-y+3) is a required factorisation form.
which polygon has an interior angle sum of 1080
Answer:
octagon which has eight sides.. (1st option )
[tex]find \: the \: volume \: of \: cylinder \\ \\ radius \: = 4 \: cm \\ \\ height \: = \: 10 \: cm \: \\ \\ [/tex]
Which of the following statements must be true about a rhombus?
The consecutive sides of a rhombus are parallel.
The diagonals of a rhombus are perpendicular.
The diagonals of a rhombus are congruent.
The opposite angles of a rhombus are supplementary.
Answer:
Step-by-step explanation:
The diagonals of a rhombus are perpendicular
Answer: Choice B) The diagonals of a rhombus are perpendicular
=============================================================
Explanation:
Let's go through the answer choices to see which are true statements, and which are false.
A) This is false because consecutive sides must meet up at a vertex point, or else they won't be next to each other. Consecutive sides can never be parallel (regardless what type of quadrilateral we're dealing with, or any polygon for that matter). In other words, consecutive sides share a common point on both segments, which is why they're not parallel. Instead, it should be phrased as "opposite sides of a rhombus are parallel" which is a true statement. B) This is true. If the diagonals are perpendicular, then we could have either a kite or a rhombus. C) This is false. If the diagonals are congruent, then we have a rectangle. We could have a square (which is both a rhombus and a rectangle at the same time), but that's only for specific cases. In a more general sense, we could have a non-square rectangle that isn't a rhombus. D) This is false. A rhombus is a type of parallelogram. For any parallelogram, the opposite angles are always the same measure. The only time the angles are supplementary is when we have a rectangle; otherwise, the angles won't add to 180.Question 18 of 25
Line s is the perpendicular bisector of JK. If line s intersects JK at point L.
which of the following statements must be true?
Check all that apply.
O A. JL = KL
B. Line sis perpendicular to JK
C. Point L is the midpoint of JK
OD. Line s intersects JK at a 180° angle
O E. Line sis parallel to JK
SUBMIT
Answer:
See below.
Step-by-step explanation:
A perpendicular bisector of a segment is perpendicular to the segment and intersects the segment at its midpoint.
A. JL = KL True
B. Line s is perpendicular to JK True
C. Point L is the midpoint of JK True
D. Line s intersects JK at a 180° angle False
E. Line s is parallel to JK False
help i’m so confused
Answer:
-27/7
Step-by-step explanation:
put x into the equation
help me pls i dont get this
Answer: B. 80
Step-by-step explanation:
Solve the equation they've given you:
[tex]\frac{3}{4} S=60\\\frac{3S}{4} =60\\3S=60*4\\3S=240\\S=80[/tex]
Answer:
B. 80
Step-by-step explanation:
(3/4)S = 60
You want to isolate S. S is being multiplied by 3/4.
You need to multiply 3/4 by its reciprocal to get rid of the 3/4 on the left side.
The reciprocal of 3/4 is 4/3.
The rule with equations is that you are allowed to multiplied both sides of an equation by the same number. Multiply both sides of the equation by 4/3.
4/3 * (3/4) * S = 4/3 * 60
12/12 * S = 4/3 * 60/1
1 * S = 240/3
S = 80
Answer: B. 80
Need help, please answer this
Answer:
In this exercise we need to solve the equation
3(x-2) = 2x + 6 - 2
We operate the parentheses and the right side
3(x-2) = 2x + 4
3x - 6 = 2x + 4
We add 6 to both sides
3x -6 + 6 = 2x + 4 + 6
3x = 2x + 10
We substract 2x
3x - 2x = 2x + 10 - 2x
x = 10
x = 10
Step-by-step explanation:
I need help with this, Im never good with these
Answer:
(a) basketball
(b) hat
(c) stuffed animal
explanation:
I'm not sure if got right but from what i see;
Chances from 1-23 you get a stuffed boi
Chances from 24-54 you get a hat (why)
Chances from 55-100 you get a basketball
Winner 5 got 90, which is between 55-100
Winner 6 got 35, which is between 24-54
winner 8 got a 7, which is between 1-23
Hope I didn't read it wrong
Find the height h of the triangle.
Answer:
A, 12 times the square root of 3
Step-by-step explanation:
24 sqaured plus 12 squared=432
square root of 432=20.9
12 times the sqaure root of 3=20.9
solve for x. Round to the nearest tenth, if necessary.
Answer:
44.4
Step-by-step explanation:
Sin=opposite/hypotenuse
Sin40=x/69
x=69sin40
x=44.4 rounded from 44.352
please help urgent !!!
Answer:
The answer is "sugar= 200g, flour=600g, and butter=400g".
Step-by-step explanation:
[tex]50\ g \ sugar = 15\ biscuits\\\\3 \times 50 \ g = flour \\\\150\ g = flour\\\\2 \times 50 \ g = butter \\\\ 100 \ g = butter\\\\\frac{60}{15} = 4\\\\ 4 \ \text{times as much}\\\\4 \times 50\ g = 200\ g \ of\ sugar\\\\4 \times 150\ g = 600\ g \ of\ flour\\\\4 \times 100\ g = 400\ g \ of\ butter\\\\[/tex]
