Answer:
A. f(2k)=0
Step-by-step explanation:
The factor theorem states that a polynomial f(x) has a factor (x−k) if and only if f(k)=0 (i.e. k is a root).
If (x – 2k) is a factor of f(x), then by the factor theorem f(2k)=0 (i.e. 2k is a root).
Option A is true, f(2k)=0
Option B is false, it should be like in option A, f(2k)=0
Option C is false, because x=2k is a root, not x=-2k
Option D is false, because x-intercept of f(x) is x=2k, not y-intercept.
Answer:
A. f(2k) = 0
Step-by-step explanation:
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything to the right of the line is shaded. Which linear inequality is represented by the graph? y ≤ One-halfx + 2 y ≥ One-halfx + 2 y ≤ One-thirdx + 2 y ≥ One-thirdx + 2
Answer:
[tex]y\le\dfrac{1}{2}x+2[/tex]
Step-by-step explanation:
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). This line has the equation
[tex]y-0=\dfrac{2-0}{0-(-4)}(x-(-4))\\ \\y=\dfrac{1}{2}(x+4)\\ \\y=\dfrac{1}{2}x+2[/tex]
The origin belongs to the shaded region, so its coordinates must satisfy the inequality. Since
[tex]\dfrac{1}{2}\cdot 0+2=2\ge 0,[/tex]
then the correct inequality is
[tex]y\le\dfrac{1}{2}x+2[/tex]
Answer:
A
y ≤ [tex]\frac{1}{2}[/tex]x + 2
Step-by-step explanation:
. In an encyclopedia of language, the author presents five sentences that make a reasonable paragraph regardless of their order. The sentences are listed below. Mark had told him about the foxes. John looked out of the window. Could it be a fox? However, nobody had seen one for months. He thought he saw a shape in the bushes. In how many different orders can the five sentences be arranged?
Answer:
the 1st & last paras are fixed.
that leaves 3 to be put in any order
there are 3 choices for the 1st,
2 choices left for the 2nd
and just 1 choice for the last
multiply to get
3*2*1
= 6 ways
We want to find the total number of orders in which we can order the given sentences.
We will see that there are 120 different orders.
There are 5 sentences, let's define them as:
s₁ = Mark had told him about the foxes.s₂ = John looked out of the window.s₃ = Could it be a fox? s₄ = However, nobody had seen one for months.s₅ = He thought he saw a shape in the bushes.We know that we can order these in any order, so we can think of the situation as 5 empty slots, in each slot, we can put one of the previous statements.
Let's count the number of options for each one of these slots.
On the first one, we have 5 options (5 sentences)
On the second one we have 4, because we already used one on the first slot.
On the third, we have 3 options.
On the fourth, we have 2 options.
On the fifth, we have 1 option.
The total number of combinations is given by the product of these numbers of options.
Combinations = 5*4*3*2*1 = 120
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Help me please with question 4 b
Answer:
see explanation
Step-by-step explanation:
The second term of sequence P is 2a + b
The third term of sequence Q is 3b + a
Equating gives
2a + b = 3b + a ( subtract a from both sides )
a + b = 3b ( subtract b from both sides )
a = 2b ← as required
Good evening ,
Step-by-step explanation:
4 (b)
The 2nd term of sequence P is 2a+b
The 3rd term of sequence Q is 3b+a
2a+b=3b+a ⇌ (2a-a) = (3b-b) ⇌ a=2b.
:)
Three fifths of the members of a hiking club went
on the last hiking trip. It 39 people went on the
trip, how many are in the club?
There are 65 people in the club.
Step-by-step explanation:
Given,
Fraction of people went on hiking = [tex]\frac{3}{5}[/tex]
No. of people went on hiking = 39
Let,
x be the number of people at club.
According to given statement;
[tex]\frac{3}{5}\ of\ x = 39\\\\\frac{3}{5}x=39\\0.6x=39\\[/tex]
Dividing both sides by 0.6
[tex]\frac{0.6x}{0.6}=\frac{39}{0.6}\\x=65[/tex]
There are 65 people in the club.
Keywords: fractions, division
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solve the inequality and enter your solution as an inequality comparing the variable to the solution
-19>x-26
Answer:
x < 7
Step-by-step explanation:
We are given an equation of inequality and we have to solve the equation as an inequality.
The given equation is - 19 > x - 26
⇒ - 19 + 26 > x
⇒ 7 > x
⇒ x < 7 {Since, if a > b then we can write b < a, as they are equivalent}
Hence,the solution of the equation of the inequality is x < 7. (Answer)
A textbook costs $65.49 before tax. The tax on the textbook is 6.5%.
What is the total cost of the textbook?
Round your answer to the nearest cent.
Enter your answer in the box.
Answer:
$69.75
Step-by-step explanation:
Given: Cost of textbook before tax=$65.49
The tax on the textbook = 6.5%
The tax amount = 6.5% of $65.49
=\frac{65}{1000}\times65.49=4.25685\approx4.26
⇒The tax amount = $4.26
The total cost of the textbook=Cost of textbook before tax+tax amount
=$65.49+$4.26
=$69.75
The total cost of the textbook is $69.75.
Credit goes to @JeanaShupp
Answer:
Answer is69.75
Step-by-step explanation:
find the slope and the y-intercept of y=9x-2
Answer:
The Slope is 9 and the y-intercept is -2
Step-by-step explanation:
Answer: slope=9
Y-intercept=-2
Step-by-step explanation:
Use y=mx+b where m equals slope and b equals y-intercept
At a music festival, T-shirts are sold for $15 and sweatshirts are sold for $20. The festival organizers pay x dollars for each T-shirt and y dollars for each sweatshirt. The festival sells 53 T-shirts and 39 sweatshirts.
Write and simplify an expression that represents the profit.
Answer:
38.0
Step-by-step explanation:
you have to you's the part and whole number ≤Answer:
53(15) + 39(20) = x
795 + 780
=1,575
Step-by-step explanation:
there are 53 t-shirts 15$ each. Then 39 sweatshirts each 20$. so 53*15 + 39*20 will be your final solution.
Five tenths in standard and expanded form
Answer:
Standard form: 5 x 10^-1
Expanded form: 0.5
Step-by-step explanation:
hope this helps
What is the value of the expression if m=3 and n=2?
2(m3) + (6-n)n
Be sure to explain all of the steps you used in solving this problem.
Step-by-step explanation:
So fill it in
2(3 times 3)+(6-2)2
so
2(9)+(4)2
then
18+8=26
Answer: 26
hope that is right
Answer:
First plug in for m and n
2(3)(3) +(6-2)(2)
Next solve
18 + 8
Answer= 10
Step-by-step explanation:
What is 8.4 x 10^12/4.2 x 10^6
Answer:
2 × [tex]10^{6}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]
Split the fraction into a product, that is
= [tex]\frac{8.4}{4.2}[/tex] × [tex]\frac{10^{12} }{10^{6} }[/tex]
= 2 × [tex]10^{(12-6)}[/tex]
= 2 × [tex]10^{6}[/tex]
For apples 2 lb for $3.38 unite rate___ cost___
Answer:
1.69
Step-by-step explanation:
well to find out the unit rate that would be a pound now we need to find out how much it would cost for 1 lb which would be 3.38 / 2 which would be 1.69 as your answer
Answer:
$1.69 per pound
Step-by-step explanation:
3.38/2=1.69
plz help me plz I will mark brainlest for the person who answer first
Answer:
[tex] \frac{16}{20} [/tex]
Step-by-step explanation:
he sold 16 and he was supposed to sell 20. therefore it's 16/20. not relevant, but he sold 80% of the tickets
Answer:
I don't know why but I personally think its 1/4 I'm probably wrong but I'm trying my best well I hope dis helps and stay safe :3
Which three comparisons are true?
1/2 = 2/4
6/8 = 1/4
3/6 = 2/4
2/4 = 4/6
4/8 = 2/4
Answer:
The answer is 4/8=2/4 because 4/8 simplifying is 2/4 or 1/2
The true fraction comparisons are 1/2 = 2/4 and 4/8 = 2/4. The other comparisons are false. Simplifying fractions helps determine their equality.
Comparing Fractions:
Let's determine which of the given fraction comparisons are true:
1/2 = 2/4: To check this, we can simplify 2/4. Dividing both the numerator and the denominator by 2, we get 1/2. Thus, 1/2 equals 2/4. This is a true statement.6/8 = 1/4: We simplify 6/8 by dividing both the numerator and the denominator by 2, which gives us 3/4. This does not equal 1/4. This is a false statement.3/6 = 2/4: Simplifying 3/6 by dividing both the numerator and the denominator by 3, we get 1/2. Simplifying 2/4 gives us 1/2 as well. Therefore, 3/6 equals 2/4. This is a true statement.2/4 = 4/6: Simplifying 2/4 to 1/2 and simplifying 4/6 to 2/3 shows that 2/4 does not equal 4/6. This is a false statement.4/8 = 2/4: Simplifying 4/8 by dividing both the numerator and the denominator by 4, we get 1/2. Simplifying 2/4 also gives us 1/2. Thus, 4/8 equals 2/4. This is a true statement.The three true comparisons are: 1/2 = 2/4, 3/6 = 2/4, 4/8 = 2/4, and none from the rest.
2. Use the linear combination method to solve the system of equations. Explain each step of your solution
3x - By = 7
x +2y = -7
x = - 3
y = -2
Step-by-step explanation:
3x - 8y = 7
x +2y = -7
We standardize the coefficient of one variable such that it addition will result to zero;
3x - 8y = 7
(x +2y = -7)4
Then multiply the one equation with a constant (this case 4) to get;
3x – 8y = 7
4x + 8y = - 28
We add the two equations;
3x – 8y = 7
+
4x + 8y = - 28
=
7x = - 21
x = -21 / 7
x = - 3
Now we evaluate y by replacing the value of x with -4 in one of the equation;
x +2y = -7
-3 +2y = -7
2y = -7 + 3
2y = - 4
y = -2
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There's 5 trees fill with apples. Alex wants 2 off each tree. How much apples do she have?
Answer:
10
Step-by-step explanation:
5 trees * 2 from each = 10 apples
Answer:
10
Step-by-step explanation:
5*2=10
What is the exact volume of the cone?
108π cm3
162π cm3
18π cm3
486π cm3
V = π·r²·h/3 = π·81·6/3 = 2·81·π = 162π cm³
35 is 51% of what number?
Answer:
68.627
Step-by-step explanation:
51%=0.51
35/0.51=68.627
Answer:
68.627 is the answer!
Step-by-step explanation: I just took a test on it like 5 minutes ago!PLEASE MARK BRAINLIEST!!!! PLEASE!!! HAVE A NICE DAY!!!!
If 6 + 2 = 8, does 6+2 +3= 8+3? Why or
why not?
Answer:
yes
Step-by-step explanation:
Because 6+ 2 equals 8 then plus 3 equals 11 and 11 equals 8+3
Amit built a sand castle that measured 600 centimeters by 600 centimeters, and dug a moat around it.
Afterward, he decided to change the castle size, making it 8 meters by 6 meters.
How much longer will the new moat be than the old one?
Answer:
4 meters longer.
Step-by-step explanation:
Amit built a sandcastle that measured 600 cm by 600 cm i.e. 6 meters by 6 meters.
Therefore, its perimeter is 2(6 + 6) = 24 meters
Now, afterward, he decided to change the castle size, making it 8 meters by 6 meters.
Therefore, its perimeter is 2(6 + 8) = 28 meters
Therefore, the perimeter of the new castle is increased by (28 - 24) = 4 meters.
If Amit dug a moat around his castle then the new moat will be 4 meters longer than the old one. (Answer)
As the moat is dug around the castle, its length will be the same as the perimeter of the castle.
A restaurant manager can spend at most $400 a day for operating costs and payroll. It costs $100 each day to operate the bank and $50 dollars a day for each employee. Use the following inequality to determine how many employees the manager can afford for the day, at most: 50x + 100 ≤ 600
Answer:
The restaurant Manager can afford 6 employees for the day.
Step-by-step explanation:
Manager can spend at most of $400.
Total Money ≤ $400
Cost to operate bank = $100
Cost for each employee = $50
Let number of employees for the day be[tex]x[/tex]
Hence the equation will become;
[tex]50x + 100 \leq 400[/tex]
Solving this equation we get;
[tex]50x + 100 \leq 400\\50x \leq 400-100\\50x \leq 300\\x\leq \frac{300}{50}\\\\x\leq 6[/tex]
Hence, The restaurant Manager can afford 6 employees for the day.
Answer:
x < = 10
Step-by-step explanation:
i did it on photo math so yah
Benjamin drove a distance of 301.5 miles in
4.5 h. If Benjamin drove at a constant rate, how
many miles per h did he drive?
Answer: 67 miles per hour
Step-by-step explanation: [tex]v = \frac{s}{t}[/tex] where v is velocity, s is space and t is time;
[tex]\frac{301.5 miles}{4.5 h}[/tex] = 67
What is the product?
(negative 3 s + 2 t)(4 s minus t)
negative 12 s squared minus 2 t squared
negative 12 s squared + 2 t squared
negative 12 s squared + 8 s t minus 2 t squared
negative 12 s squared + 11 s t minus 2 t squared
Answer:
(d) negative 12 s squared + 11 s t minus 2 t squared is the PRODUCT.
Step-by-step explanation:
Here, the given expression is:
(negative 3 s + 2 t)(4 s minus t) = (- 3s + 2t) (4s - t)
Now, by DISTRIBUTIVE PROPERTY:
A(B-C) = AB - AC
Simplifying the given expression ,we get:
[tex](- 3s + 2t) (4s - t) = -3s(4s-t) + 2t(4s -t)\\= -3s(4s) -3s(-t) + 2t(4s) + 2t(-t) = -12s^2 + 3st + 8 st - 2t^2\\= -12s^2 + 11st - 2t^2\\\implies (- 3s + 2t) (4s - t) = -12s^2 + 11st - 2t^2[/tex]
Now, the resultant expression can also be written as
[tex]-12s^2 + 11st - 2t^2[/tex] = negative 12 s squared + 11 s t minus 2 t squared.
Hence, the option (4) is the correct option.
Answer:
option 4 is the answer
Step-by-step explanation:
❤❤Solve for the unknown by using the additive inverse. Type the FULL answer in the box, without using any spaces (ex., X=5).
–X + 4 = –2X – 6
Answer:
Please help solve with steps: Order of operation with integers.
6 (divide by ) (-3) - (-9)
Answer:
7Step-by-step explanation:
Use PEMDAS:
P Parentheses first
E Exponents
MD Multiplication and Division
AS Addition and Subtraction
[tex]6:(-3)-(-9)[/tex] first - division
[tex]=-2+9[/tex] use commutative property a + b = b + a
[tex]=9+(-2)=9-2=7[/tex]
Complete this statement:
45x^3a + 27xa^2= 9xa
Enter the correct answer.
0000
DO
Clear all
DOO
Answer:
[tex]45x^3a+27xa^2= 9xa(5x^2+3a)[/tex]
Step-by-step explanation:
Given:
[tex]45x^3a+27xa^2= 9xa[/tex]
We need to complete this Statement.
By Solving the above equation we get;
We will take some common factor out so we will get;
[tex]45x^3a+27xa^2= 9xa(5x^2+3a)[/tex]
Hence the Complete statement is [tex]45x^3a+27xa^2= 9xa(5x^2+3a)[/tex]
What is the final step in solving the inequality -2(5 - 4x)
Step 1: -10 + 8x < 6x - 4
Step 2: -10 <-2x - 4
Step 3: -6<-2x
Step 4
AVA
Step-by-step explanation:
[tex]-2(5-4x)<6x-4\qquad\text{use the distributive property}\\\\(-2)(5)+(-2)(-4x)<6x-4\\\\-10+8x<6x-4\qquad\text{subtract}\ 8x\ \text{from both sides}\\\\-10+8x-8x<6x-8x-4\\\\-10<-2x-4\qquad\text{add 4 to both sides}\\\\-10+4<-2x-4+4\\\\-6<-2x\qquad\text{divide both sides by (-2)}\\_{\text{by dividing by a negative number, flip the inequality sign}}\\\\3>x[/tex]
The graphs below have the same shape. What is the equation of the blue graph?
Answer:
Option C. [tex]g(x)=(x+5)^{2}[/tex]
Step-by-step explanation:
we know that
The equation of the parent function f(x) (red graph) is
[tex]f(x)=x^{2}[/tex]
This is a vertical parabola open upward
The vertex is the point (0,0) (the origin)
The function g(x) (blue graph) is a vertical parabola open upward
The vertex is the point (-5,0)
The transformation of f(x) to g(x) has the following rule
f(x) -----> g(x)
(0,0) ----> (-5,0)
(x,y) ----> (x-5,y)
That means----> The transformation is a translation of 5 units at left
therefore
The equation of g(x) is
[tex]g(x)=(x+5)^{2}[/tex]
Simultaneous equations !
Who can help
The cost of glass is: £4
The cost of mug = £2
Step-by-step explanation:
Let g be the number of glasses and
m be the number of mugs
[tex]3g+3m = 18\ \ \ \ \ Eqn\ 1\\6g+4m=32\ \ \ \ \ Eqn\ 2[/tex]
Multiplying equation 1 by 2
[tex]6g+6m=36\ \ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex]6g+6m - (6g+4m) = 36-32\\6g+6m-6g-4m=4\\2m=4[/tex]
Dividing both sides by 2
[tex]\frac{2m}{2} = \frac{4}{2}\\m = 2[/tex]
Putting m=2 in eqn 1
[tex]3g+3(2) = 18\\3g+6 = 18\\3g = 18-6\\3g = 12[/tex]
Dividing both sides by 3
[tex]\frac{3g}{3} = \frac{12}{3}\\g = 4[/tex]
Hence,
The cost of glass is: £4
The cost of mug = £2
Keywords: Linear Equation, simultaneous equations
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Karen bought a coat for 20% more than the price she wanted to pay. If she paid $150, how much was she looking to pay?
The first one to get both correct will be brainiest!!!!!!!
120% = $150
divide both sides by 6
20% = $25
We want the regular price, so 100%.
multiply both sides by 5
100% = $125
Answer:125
Step-by-step explanation:
150/1.20
=125