Answer:
See Below.
Step-by-step explanation:
We want to prove that:
[tex]x^3-13x-12\text{ is divisible by } x^2-x-12[/tex]
We can factor the divisor:
[tex]x^2-x-12=(x-4)(x+3)[/tex]
According to the Factor Theorem, if we have a polynomial P(x) divided by a binomial in the form of (x - a) and if P(a) = 0, then the binomial is a factor of P(x).
Our two binomial factors our (x - 4) and (x + 3). Thus, a = 4 and a = -3.
Evaluate the polynomial for both of these factors:
[tex]P(4)=(4)^3-13(4)-12=0[/tex]
And:
[tex]P(-3)=(-3)^3-13(-3)-12=0[/tex]
Since both yielded zero, the original polynomial is divisible by both (x - 4) and (x + 3) or x² - x - 12. Hence:
[tex]x^3-13x-12\text{ is indeed divisible by } x^2-x-12[/tex]
If a zero is
, then the graph of its function only touches the x–axis at that zero.
Answer:
Step-by-step explanation:
Yes. The zeroes of a graph are the values of x where the graph touches (or crosses) the x-axis.
Find the value x ……….
Answer: 6 because it more than thd base and less than the other triangles leg
Step-by-step explanation:
Answer:
[tex]4\sqrt{5}[/tex]
Step-by-step explanation:
[tex]x^2 = y^2 + 25[/tex]
[tex]\frac{y}{11} = \frac{5}{y}[/tex]
[tex]y^2 = 55[/tex]
[tex]x^2 = 80\\x = \sqrt{80} \\x= 4\sqrt{5}[/tex]
1) Se o 5o e o 9-o termos de uma PA são, respectivamente, 40 e 68, então a razão r da progressão é: a) r = 6 b) r = 7 c) r = 9 d) r = 11 e) r = 12 2) Inserindo-se 6 números entre 72 e 107, de modo que a sequência (72, a2, a3, a4, a5, a6, a7 ,107) seja uma progressão aritmética, tem-se a3 igual a: a) 78 b) 79 c) 80 d) 81 e) 82
Answer:
1) b) r = 7
2) e) 82
Step-by-step explanation:
Progressão aritmética:
Em uma progressão aritmética, a diferença entre termos consecutivos é sempre a mesma, chamada de razão.
O n-ésimo termo de uma PA é dado por, tomando o primeiro termo como referência:
[tex]a_n = a_1 + (n-1)r[/tex]
Tomando o m-ésimo termo como referência, tem-se que:
[tex]a_n = a_m + (n-m)r[/tex]
1) Se o 5o e o 9-o termos de uma PA são, respectivamente, 40 e 68, então a razão r da progressão é:
[tex]a_5 = 40, a_9 = 68[/tex]. Então:
[tex]a_n = a_m + (n-m)r[/tex]
[tex]68 = 40 + 4r[/tex]
[tex]4r = 28[/tex]
[tex]r = \frac{28}{4} = 7[/tex]
Então a resposta correta é dada pela alternativa b.
2) Inserindo-se 6 números entre 72 e 107, de modo que a sequência (72, a2, a3, a4, a5, a6, a7 ,107) seja uma progressão aritmética, tem-se a3 igual a:
O primeiro termo é [tex]a_1 = 72[/tex] e o oitavo termo é [tex]a_8 = 107[/tex]. Com isso, é possível encontrar a razão.
[tex]a_n = a_1 + (n-1)r[/tex]
[tex]107 = 72 + 7r[/tex]
[tex]7r = 35[/tex]
[tex]r = \frac{35}{7} = 5[/tex]
Então, o terceiro termo é:
[tex]a_3 = a_1 + 2r = 72 + 2(5) = 82[/tex]
Logo, a resposta correta é dada pela alternativa e.
Line CD passes through points C(3, 5) and D(6, 0). What is the equation of the line CD in standard form?
Answer:
the answer is 5x - 3y = 30!!
What is the rate of change of the function shown on the graph? Round to the nearest tenth.
Identify the value of y.
Answer:
y = 3
Step-by-step explanation:
A stationer buys a gel pen Rs 20 and sells it at 20% profit.For what price should he buy it so that he can make 25% profit by selling for the same selling price.
Answer:
Current selling price = Rs 20 × 120 %
= Rs 24
Cost price should be [100 ÷ 125 ] × 24
= Rs 19.20
A group of 2 adults and 4 children spent $38 on tickets to a museum. A group of 3 adults and 3 children spent $40.50 on tickets to the museum. Based on this information, how much is an adult ticket, and how much is a child ticket?
Answer:
adult $8.00
child $5.50
Step-by-step explanation:
Let the price of 1 adult ticket = x.
Let the price of 1 child ticket = y.
2x + 4y = 38
3x + 3y = 40.5
Multiply the first equation by 3. Multiply the second equation by -2. Then add them.
6x + 12y = 114
(+) -6x - 6y = -81
-----------------------------
6y = 33
y = 33/6
y = 5.5
2x + 4y = 38
2x + 4(5.5) = 38
2x + 22 = 38
2x = 16
x = 8
Answer:
adult $8.00
child $5.50
Answer:
An adult ticket is $8.00 and a child's ticket is $5.50.
Step-by-step explanation:
We form a system of 2 equations and solve them.
Let a be the price of adult ticket and c the price of a child's.
2a + 4c = 38 (A)
3a + 3c = 40.5 (B)
Multiply equation A by 3 and equation B by -2:
6a + 12c = 114
-6a - 6c = -81 Adding these 2 equations:
0 + 6c = 33
c = 33/6 = 5.5.
Now we substitute for c in equation A:
2a + 4(5.5) = 38
2a = 38 - 22
2a = 16
a = 6.
Let's now check these results by substitution in equation B:
3a + 3c = 40.5
3(8) + 3(5.5) = 24.0 + 16.5 = 40.5
- so it checks out.
Find Point P is the incenter of DEF . point p of concurrency of the angle bisectors . find PT
PT is 8 because since P is the incenter it's equidistant from all sides.
plzz help steps if possible if not its ok j=i just need to pass this class
Answer:
[tex]\text{(B) }\cos 40^{\circ}=\frac{x}{60}[/tex]
Step-by-step explanation:
In any triangle, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse (longest side) of the triangle. (a/h)
The angle marked 40 degrees has an adjacent side of [tex]x[/tex] and the hypotenuse of the triangle is 60.
Therefore, we have the equation:
[tex]\boxed{\cos 40^{\circ}=\frac{x}{60}}[/tex]
7. Complete the square to write
c(x)= x2 – 16x + 84 in vertex form.
Answer:
(x-8)²+20 vertex=(8,20)
Step-by-step explanation:
(x-8)² = -20
Graphing Form: y = 1(x-8)²+20
Show and explain all of the steps used in order to simplify the following rational expression 3x^(2)-3x / 3x^(3)-6x^(2)+3x to 1 / x-1.
Answer:
3x^2 + x^4 - x^3 + 3 - 6x
Step-by-step explanation:
Find Least Common Multiplier of 3x^(2)-3x / 3x^(3)-6x^(2)+3x to 1 / x-1
3x^2 - 3 . x/3 x^3 - 6x^2 + 3x
Apply exponent rule: a^b + c = a^b a^c
x^2 = xx, x^3 x/3 = xx^2, x^2 = xx
= 3xx - 3xxx - 6xx + 3x
Rewrite -6 as 2 . 3
= 3xx - 3xxx + 2 . 3xx + 3x
Factor out common term 3x
= 3x(x - x^2(x/3) -2x + 1)
= 3x(- x^3/3 - x + 1)
Multiply each factor with the highest power:
(- x^3/3 - x + 1) . 3 . (1/x - 1\) . x
Simplify
3x^2 + x^4 - x^3 + 3 - 6x
Create a line that is parallel to AB↔ and passes through point C.
Draw 2 lines parallel to each other (AB and line B). Draw a point on line B and label it "C"
3(5-4)+2(5)-5 squared
the answer should be -12 if I did the math right.
Step-by-step explanation:
3*1+10-5^2(we subtract 5 from 4 first because it was inside bracket)
3+10-25(Square of 5 is 25)
-12(subtracting the above equation 12 comes)
What's the slope of (2, 1) (4,5)
Answer:
[tex]\displaystyle m = 2[/tex]
General Formulas and Concepts:
Algebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (2, 1)
Point (4, 5)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{5 - 1}{4 - 2}[/tex]Subtract: [tex]\displaystyle m = \frac{4}{2}[/tex]Simplify: [tex]\displaystyle m = 2[/tex]Melinda walked to the mall at 4 miles per hour and then rode back home in a bus at 24 miles per hour. If her total traveling time was 14 hours, how far was it to the mall?
Given:
Melinda walked to the mall at 4 miles per hour and then rode back home in a bus at 24 miles per hour.
Total traveling time was 14 hours.
To find:
The distance between Melinda's house and mall.
Solution:
Formula used:
[tex]Time=\dfrac{Distance}{Speed}[/tex]
Let x miles be the distance between Melinda's house and mall.
Melinda walked to the mall at 4 miles per hour. So, the time taken by Melinda is [tex]\dfrac{x}{4}[/tex] hours.
Speed of bus is 24 miles per hour. So, the time taken by bus is [tex]\dfrac{x}{24}[/tex] hours.
Total traveling time was 14 hours.
[tex]\dfrac{x}{4}+\dfrac{x}{24}=14[/tex]
[tex]\dfrac{6x+x}{24}=14[/tex]
[tex]7x=14\times 24[/tex]
Divide both sides by 7.
[tex]\dfrac{7x}{7}=\dfrac{14\times 24}{7}[/tex]
[tex]x=2\times 24[/tex]
[tex]x=48[/tex]
Therefore, the mall is 48 miles far from Melinda's house.
A student buys 5-cent, 10-cent, and 15-cent stamps, with a total value of $6.70. If the
number of 5-cent stamps is 2 more than the number of 10-cent stamps, while the
number of 15-cent stamps is 5 more than one half the number of 10-cent stamps, how
many 15-cent stamps did the student obtain?
Question 8(Multiple Choice Worth 5 points) (01.01 MC) Which number line best show how to solve -4 - (-8)?
Answer:
4
Step-by-step explanation:
-4 - (-8) Note: a negative negative equals a positive. There for it is just the same as saying -4 + 8
which point is on the line that passes through point H and is perpendicular to line FG?
Answer:
The correct answer is (-6, 10).
Step-by-step explanation:
You can find the equation of the blue line and then find out which point is on the perpendicular line to that blue line but you also can figure this out visually by looking at where the points are.
Feel free to message me if you still have questions :)
Answer:
(–6, 10)
Step-by-step explanation:
Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people can be made if:
a) there must be exactly 3 students on the committee
b) there must be at least one teacher and at least one student on the committee
Answer:
a) 11,880
b) 7,770
Step-by-step explanation:
The number of teachers that volunteer = 6 teachers
The number of students that volunteer = 12 students
The number of people in the committee = 5 people
a) The exact number of student on the committee = 3 student
Therefore, the number of teachers in the committee of 5 = 5 - 3 = 2
The number of teachers in the committee = 2 teachers
We get;
The number of committees that can be made = ₁₂C₃ × ₆C₂ = 792×15 = 11,880
b) When there is at least one teacher and at least one student on the committee, we have;
₁₂C₄ × ₆C₁ + ₁₂C₃ × ₆C₂ + ₁₂C₂ × ₆C₃ + ₁₂C₁ × ₆C₄ = 7,770
The number of committees having at least one teacher and at least one student = 7,770
Derek had a bill of $29 last month on he Call-a-Lot Plan. How many minutes did he use?
1
Work out the area of the shape:
3cm
6cm
2cm
2cm
Answer:
24 cm
Step-by-step explanation:
6*2+3*4=?
12+12
24 cm
Please help
I am giving all my points for this (15 points)
Select all input values for which g(x)=8.
Choose all answers that apply:
(Choice A)
x=−4
(Choice B)
x=6
(Choice C)
x=9
(Choice D)
None of the above
Answer:
D. none of the above
Step-by-step explanation:
If g(x)=8 is the only equation, then none of the answers are correct. The correct answer would have been 8 because 8=8.
Matt is making cookies. He adds 3 over 4 cup of sugar to a bowl. He then removes two 1 over 8 cups of sugar. Which of the following best explains the amount of sugar left in the bowl?
Answer:
3/4 is equal to 6/8 2 1/8s is equal to 2/8
Find the missing segment
need help with part b of the attached screenshot please
9514 1404 393
Answer:
(b) 82.9253
Step-by-step explanation:
The first attachment shows the rectangles. The second shows the sum of their areas.
please help me out asap
(geometry)
Answer:
x = 30
Step-by-step explanation:
If A and B were parallel, then 2x + 50 and 5x - 80 are same- side interior angles and sum to 180° , then
2x + 50 + 5x - 80 = 180
7x - 30 = 180 ( add 30 to both sides )
7x = 210 ( divide both sides by 7 )
x = 30
What type of slope is demonstrated by the line below? 5 (-1,3) --5 5 (0.-2)
A. Zero slope
B. Positive slope
C. Undefined slope
D. Negative slope
Answer:
D. Negative slope
Step-by-step explanation:
The slope goes down from left to right, so it is a negative slope
Up from left to right is a positive slope
A vertical line is undefined
A horizontal line is zero slope
The fraction 9/7 is equivalent to?
9/7 is equivalent to 18/14 or 27/21 or 36/28 etc
Answered by Gauthmath must click thanks and mark brainliest
Candice bought 6 dozen eggs and broke 9 eggs how many eggs did she have left
Answer:
63
Step-by-step explanation:
12x6=72
72-9=63
the answer is 63
