Answer:
Question 1
Given expression:
[tex]-2x^3 (4x^3+5x^6)[/tex]
Apply the distributive law [tex]a(b+c)=ab+ac[/tex]:
[tex]\implies -2x^3 \cdot4x^3+-2x^3 \cdot 5x^6[/tex]
Multiply the numbers:
[tex]\implies -8x^3 x^3-10x^3 x^6[/tex]
Apply exponent rule [tex]a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies -8x^6-10x^9[/tex]
In standard form we write it in order from the greatest degree:
[tex]\implies -10x^9-8x^6[/tex]
Therefore, as the polynomial is degree 9, it is a nonic polynomial.
End behaviors
As the leading coefficient is negative and the leading degree is odd:
[tex]f(x) \rightarrow + \infty \textsf{, as } x \rightarrow - \infty[/tex]
[tex]f(x) \rightarrow - \infty \textsf{, as } x \rightarrow + \infty[/tex]
----------------------------------------------------------------------------------------------
Question 2
Factor the given function to find the zeros
Given function:
[tex]f(x) =x^3+15x^2 +63x+49[/tex]
[tex]f(-1) =(-1)^3+15(-1)^2 +63(-1)+49=0[/tex]
Therefore [tex](x+1)[/tex] is a factor of the function
[tex]\implies x^3+15x^2 +63x+49=(x+1)(x^2+bx+49)[/tex]
[tex]=x^3+(b+1)x^2+(b+49)x+49[/tex]
Comparing coefficients ⇒ b = 14
[tex]\implies x^3+15x^2 +63x+49=(x+1)(x^2+14x+49)[/tex]
Factoring [tex](x^2+14x+49)[/tex]:
[tex]\implies (x^2+14x+49)=(x+7)(x+7)=(x+7)^2[/tex]
Therefore,
[tex]f(x)=(x+1)(x+7)^2[/tex]
To find the zeros, equate to the function zero:
[tex](x+1)(x+7)^2=0[/tex]
Therefore,
[tex]x+1=0 \implies x=-1 \textsf{ with multiplicity 1}[/tex]
[tex]x+7=0 \implies x=-7\textsf{ with multiplicity 2}[/tex]
Jack and his children went into a restaurant where they sell hamburgers for $6 each
and tacos for $2 each. Jack has $30 to spend and must buy at least 8 hamburgers and
tacos altogether. If x represents the number of hamburgers purchased and y
represents the number of tacos purchased, write and solve a system of inequalities
graphically and determine one possible solution.
Answer:
i think the solution is 128
Step-by-step explanation:
There are 2 squares, 2 triangles, 2 hexagons, and 2 circles in a teacher’s bag of shapes. If a student randomly selects 1 shape from the bag, what is the probability that the student selects a circle?
a 0.75
b 0.5
c 0.25
d 0.2 pls hurry
grade 5 classify the quadrilateral
Answer:
Step-by-step explanation:
A quadrilateral is a four-sided shape. Two sides of a shape are parallel if lines placed along them never cross. In a quadrilateral, parallel sides must be opposite sides. This means they do not share a vertex.
Answer:
A simple example could be a square or a rectangle. They both have four sides and they have parallel lines.
Step-by-step explanation:
PLEASE MARK AS BRAINLIEST!!!
Solve for g.
g/6 - -53 = 57
Step-by-step explanation:
g/6 - -53 = 57
g/6 + 53 = 57
g/6 = 4
g = 4×6 = 24
please help no links!
I'm not sure you're not giving enough information but I'd probably go with B
THE FASTEST AND CORRECT ANSWER GETS BRAINLIEST!!! ANSWER TO GET BRAINLIEST!!!!!!!!!
i think answer is 16 minutes
Because 5÷3=1.6
Remove the point so it will be 16 min.
Im not sure if my answer is correct
Select all the correct conversions.
4 cups = 16 fl oz
9 qt =214 gal
6 gal = 24 qt
8 cups = 2 pt
4 fl oz =12 cup
Answer:
4 fl oz =12 cup
9 qt =214 gal and 6 gal = 24 qt
Step-by-step explanation:
*If you don’t know the answer please don’t comment*
1. Based on the information in the two-way table, what is the probability that a person selected at random is a left-handed male?
(Two-way table at the bottom)
A.) 4%
B.) 6%
C.) 52%
D.) 38%
2. Based on the information in the two-way table, what is the probability that a person selected at random is a right-handed?
A.) 56%
B.) 44%
C.) 10%
D.) 90%
Answer:
1.A
2.D
Step-by-step explanation:
Brainliest pls hardstuck ambitious
8. Mrs. Reed bought 6 carnations that were
$0.39 each. How much money did she
spend?
Answer:
2.34
Step-by-step explanation:
:)
2.34
Multiply 0.39 by 6!
If the diagonal of a rectangle measures 60 inches and one side measures 48 inches, what is the length of the other side of the rectangle?
Answer:
36
Step-by-step explanation:
Using pythag, 60^2 - 48^2 = 3600 - 2304, which is 1296, whose square root if 36. This is also a 3-4-5 triangle.
Answer:
36
Step-by-step explanation:
60 power 2 minus 48 power 2 under square root = 36
What is the y-intercept (b) of the line with the equation y=3x+4
Answer:
your y-intercept is the line at which that line crosses or bisects the y-axis.
.°. y=4
PLEASE HELP!
8th grade math
Find the Surface Area of the cone.
→
(Round the answer to nearest tenth.)
( use π = 3.14 )
Thanks!
~
Answer:
[tex]\sf \huge{\boxed{\sf area = 653.1 cm^2}}[/tex]
Explanation:
[tex]\sf \boxed{\sf area \ of \ cone=\pi r^2 +\pi rl }[/tex]
Given:
radius: 8 mslant height: 18 musing this formula:
[tex]\hookrightarrow \sf \pi r^2 + \pi rl[/tex]
[tex]\hookrightarrow \sf (3.14)(8)^2 +(3.14)(8)(18)[/tex]
[tex]\hookrightarrow \sf 653.1 cm^2[/tex]
Please help, and if you do, please answer all three questions. 30 points!! Everything is listed below!!
Answer:
the answer is 45%.
Step-by-step explanation:
if you add 5% divided by 3 = 15%.
So if you add all of those plus the 30% you will be getting 45%.
can i please have the answer
volume of cuboid : 400 cm²
A cuboid has its base length similar.volume of a cuboid : side * side * height
[tex]\hookrightarrow \sf 4 * 10 * 10[/tex]
[tex]\hookrightarrow \sf 400 \ cm^2[/tex]
Solution:
We know that:
[tex]\tex\text{Volume of square based cuboid:} \ \text{Length} \times \text{Length} \times \text{Height}[/tex]
[tex]\text{Length = 10 cm}[/tex]
[tex]\text{Height = 4 cm}[/tex]
Finding the volume of the square based cuboid:
[tex]\tex\text{Volume of square based cuboid:} \ \text{Length} \times \text{Length} \times \text{Height}[/tex]
[tex]\tex\text{Volume of square based cuboid:} \ 10 \times 10 \times 4[/tex]
[tex]\text{Volume of square based cuboid:} \ 100 \times 4[/tex]
[tex]\boxed{\bold{\text{Volume of square based cuboid:} \ 400 \ \text{cm}^{3}}}[/tex]
Help please it’s due tommorow and I don’t know how to do it
Answer:
Where is the question?
Step-by-step explanation:
Where is the question?
Answer:
theres nothing here, you forgot to attach something or this is a prank
Step-by-step explanation:
22.40 tourists are coming from Switzerland to visit Mt Everest. They planned to stay at Everest base camp for 4 days. For this purpose they ordered some squared base pyramid tent in Nepal. A tent can holds people and each person have o fitx3ft space on the ground withi 48 cu. of air to breadth. Find the total cost of all tents at the rate of Rs.560 per feet square
The cost of 32.57ft^2 is Rs. 18,239.2 which is the cost of renting one tent.
Data;
Height = 48cu = 48 cubic feet = 3.63 feetedge length = 3ftarea = ?Area of a Square PyramidThe formula of a square pyramid is given as
[tex]A = l^2 + 2l\sqrt{\frac{l^2}{4} + h^2} \\[/tex]
Let's substitute the values and solve for the area of the square pyramid.
[tex]A = l^2 + 2l\sqrt{\frac{l^2}{4} + h^2} \\\\A = 3^2 + 2*3\sqrt{\frac{3^2}{4} + 3.63^2} \\A = 9 + 6{\sqrt{15.43} } \\A = 32.57ft^2[/tex]
Since the cost of 1 square foot = Rs. 560
32.57 ft^2 = x
[tex]1sq = 560\\32.57 = x\\x = 32.57 * 560\\x = 18,239.2[/tex]
The cost of 32.57ft^2 is Rs. 18,239.2 which is the cost of renting one tent.
Learn more on area of square pyramid here;
https://brainly.com/question/22744289
PLS HELP
_______exists when a figure can be reflected such that a pre-image and the image are the same
(will give brainliest)
Answer:
Hello! symmetry
Step-by-step explanation:
Symmetry is a mirror image of an image.
Cut a hexagon in half for example
_AnnieTheDreamGirl, 3.9.22
there are 40 rows of seats in a class.Each row has 120 chairs.How many students can sit in the class?
Answer:
4800 students
Step-by-step explanation:
120x40=4800students
4800 can sit in the class
Based on the experiment, what is the probability of landing on heads? Ty flipped a coin and counted how many times it landed on heads and how many times it landed on tails. The frequencies are shown in the following table. Result Number of Times Flipped Heads 26 Tails 30 Based on the experiment, what is the probability of landing on heads? Enter your answer as a fraction, like this: 42/53ur answer as a fraction, like this: 42/53
Answer:
the possibility of it landing on heads is 50/50
there is a 50% chance of it landing on heads and there is a 50% chance of it landing on tails
Step-by-step explanation:
however, there is also more of a possibility of it landing on tails because of the fact that Ty flipped the coin and it landed on tails more than heads
so I'd say abt 85/100 are the possibilities of it landing on heads
What are some differences of a credit and debit card?
Answer:
A credit card you have to pay back the money you spend to the credit card company.
While with a debit card it takes money straight out of your bank account.
(10x -20) (6x + 8)°
what is the value of x
Answer:
X=12
Step-by-step explanation:
Add the two equations together and equate them to 180 due to the geometrical reason that angles on a straight line add up to 180.
10X-20+6X+8=180 (collect like terms)
10X+6X=180-8+20
16X=192 (Divide both sides by 16)
X=12
Hope that helps :)
How many linear equations make up a system of linear equations?
Abby is decorating the bulletin board outside her classroom. She needs 1/4 of a sheet for each Easter egg and 4 full sheets for the title. if she has 18 sheets how many Easter eggs can she make
Answer:
3.5 easter eggs, or if you round, 3 total eggs
Step-by-step explanation:
18-4=14
14/4=3.5
She can make 3.5 easter eggs, or if you round, 3 total eggs
Azakai writes the expression "one third of the product of 9 and a number." a. Write an Algebraic expression that is equivalent to Azakai's expression. b. Write a second algebraic expression that is different from, but equivalent to your first expression.
Let the number be x
[tex] \rightarrow \: 9x = \frac{1}{3} \\ [/tex]
a second algebraic expression that is different from, but equivalent to the first eexpression
[tex]\rightarrow \: x = \frac{1}{27} \\ [/tex]
Answer:
=> let the unknown number be x
so ,
=> 9x = 1/3 ..i)
=> x = 1/27 ...ii) { it's different but equivalent }
Guys please help me
Answer:
around 20
Step-by-step explanation:
PQ is almost perpendicular to NR ,so first get PR by Pythagorean Theorem, sqt21^2+14^2= 25.23
then plug in NPR this triangle, again by Pythagorean, get approximately 20.989
Bertie Beetle walks so that he is the always exactly the same distance from Crumb A and Crumb B
The intersection of the circle with the arc drawn would be at points C and D.
How is an arc of a circle formed?In Geometry, an arc is a trajectory that is formed when the distance from a given point has a fixed numerical value.
How to show the path that Bertie walked?The steps that are to be taken to determine points C and D include:
Crumb A should be taken as the center of the circle and the radius of the arc would be 1.3 cm.Crumb B should be taken as the center of the circle and the radius of the arc would be 3.5 cm.The intersection of the circle with the arc drawn would be at points C and D.Read more on arc length here: https://brainly.com/question/20594692
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Complete Question:
Bertie Beetle walks so that he is always exactly 1.3 cm from Crumb A. Adam Ant walks so that he is always exactly 3.5 cm from Crumb B. There are only two points at which they can meet - mark the points with crosses.
Rectangle ABCD has vertices A(2, 3),
B(1, 4), C(0, 3), and D(3, 5). Find the
vertices of rectangle A'B'C'D' after a
translation of one units right(+1) and 2 units down(-2)
Answer:
Step-by-step explanation:
−3 (x+4) −2 ≥ 2x+6
Solve for X.
Answer:
[tex]x \leqslant - 4[/tex]
Step-by-step explanation:
[tex] - 3(x + 4) - 2 \geqslant 2x + 6[/tex]
[tex] - 3x - 12 \geqslant 2x + 6[/tex]
[tex] - 3x14 \geqslant 2x + 6[/tex]
[tex] - 3x - 2x \geqslant 6 + 14[/tex]
[tex] - 5x \geqslant 20[/tex]
[tex] \frac{ - 5x}{ - 5} \leqslant \frac{20}{ - 5} [/tex]
[tex]x \leqslant - 4[/tex]
WHEN DIVIDING OR MULTIPLYING BY A NEGATIVE NUMBER, YOU MUST CHANGE THE SIGNS:
[tex] \leqslant \\ \geqslant \\ > \\ < [/tex]
Vera orders some prints of photos that she uploaded to her computer. She orders 3 of the 5 x 7 prints for $0. 89 each, 12 of the 4 x 6 prints for $0. 15 each and 1 of the 8 x 10 prints for $2. 99. She also orders a photo album for $8. 69. Vera pays taxes that are 7% of the total purchase price. Her shipping charges are based on the following table: Amount of Purchase Standard Shipping Express Shipping up to $20 free $3. 50 $50 up to $100 $6. 35 $8. 20 $100 up to $200 $7. 80 $11. 60 $200 and over $10. 50 $16. 45 Vera selects standard shipping and the company bills her credit card $20. 78 for the total of the online purchase. Determine if Vera has been billed correctly for her purchase. A. Vera has been billed correctly. B. Vera has not been charged enough for her purchase. C. Vera has been over charged by $1. 13 for her purchase. D. Vera has been over charged by $3. 50 for her purchase.
For the total purchase, vera has been overcharged by $3. 50 for her purchase.
What will be the total purchasing price of the vera?We have information that
3 orders at 0.89$
[tex]=3\times 0.89=2.67[/tex]$
12 orders for 0.15$
[tex]=12\times0.15=1.8[/tex]$
for 1 order 2.99$
[tex]=1\times 2.99=2.99[/tex]$
and also 8.69$ for a photo album
so total amount = 2.67+1.8+2.99+8.69= 16.15$
Now 7% of the tax =[tex]16.15\times1.07=17.2805[/tex]
Thus the difference of the amount =20.78-17.2805=3.5$
Thus the total purchase, vera has been overcharged by $3. 50 for her purchase.
To know more about logical questions follow
https://brainly.com/question/1403435
Answer:
D. Vera has been over charged by $3.50 for her purchase.
Step-by-step explanation:
I just did the assignment!