The value of k in the expression is equal to 9.
The expression is in the form of Cubic polynomial. A cubic polynomial is the one which can be written in the form y = ax³ + bx² + cx + d where a, b, c and d are coefficients and x, and y are independent and dependent variables respectively. The cubic polynomial f(x) = 2x³ + (k)x - 11 has a factor equal to (x-1). If it is the factor, then x = 1 is the solution of cubic polynomial and at x = 1 the value of f(x) = 0.
2(1)³ + k(1) - 11 = 0
2 + k - 11 = 0
k - 9 = 0
=> k = 9 which is the required value.
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one number is 9 more than 3 times another. Their product is 9 more than 3 times their sum. Find the numbers. Answer in the form of paired points with the lowest of the two integers first
Let x and y be the two numbers we are trying to find.
'One number is 9 more 3 times another' is equivalent to x=9+3y
'Their product is 9 more than 3 times their sum' is equivalent to xy=9+3(x+y)
We have two equations and two unknowns; therefore, we can solve the problem
[tex]\begin{cases}x=9+3y \\ xy=9+3(x+y)\end{cases}[/tex]Solve it as shown below
[tex]\begin{gathered} x=9+3y \\ \Rightarrow xy=(9+3y)y=9y+3y^2 \\ \text{and} \\ 9+3(x+y)=9+3(9+3y+y)=9+3(9+4y)=9+27+12y=36+12y \\ \Rightarrow9y+3y^2=36+12y \\ \Rightarrow3y^2-3y-36=0 \\ \Rightarrow y^2-y-12=0 \end{gathered}[/tex]Solve the quadratic equation
[tex]\begin{gathered} y^2-y-12=0 \\ \Leftrightarrow(y-4)(y+3)=0 \\ \Rightarrow y=4,y=-3 \end{gathered}[/tex]Finally,
[tex]\begin{gathered} y=4 \\ \Rightarrow x=9+3(4)=21 \\ \Rightarrow(21,4) \\ y=-3 \\ \Rightarrow x=9+3(-3)=0 \\ \Rightarrow(0,-3) \end{gathered}[/tex]The solutions are (21,4) and (0,-3)
What is 0.044444... as a fraction?
Answer:
0.044444 = 11111/250000
Step-by-step explanation:
[tex]=\frac{44444}{1000000} =\frac{22222}{500000} =\frac{11111}{250000}[/tex]
Hope this helps
Damon drew a scale drawing of a swimming pool. The scale he used was 1 inch : 9 feet. The diving board is 2 inches long in the drawing. How long is the actual diving board?
Since the scale utilized in the draw is 1 inch : 9 feet and the diving board is 2 inches, we need to multiply the 2 inches by the scale:
[tex]2\cdot9ft=18ft[/tex]The actual diving board is 18ft long
Please help due tonight
Answer:
C.
Step-by-step explanation:
The solution to a system of equations is the point where the two lines intersect. In this case, the lines intersect at Point C.
HELP PLEASE ITS DUE BY MIDNIGHT
A rectangular park is 40 yards wide. then a city planner designs a path that is 1 yard wide to run all the way around the park.now the area of the park plus the path is 4200 square yards.how long is the park not counting the path?
The length of the park not counting the path is 98 yards
How to determine the length of the park
The formula for determining the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleFrom the information given, we have that;
The dimensions of the path having a width of 1 yard path around it are
(L+2) x (W+2)
We have to add 2 to the length and width because there will be a 1 yard path on all 4 sides of the rectangle
Given that the area is 4200 square yards; the original width is 40 yards
Now, substitute the values into the formula, we have;
Since Area = LW
4200 = (L+2)(W+2)
4200 = (L+2)(40+2)
Add the values
4200 = (L+2)(42)
expand the bracket
4200 = 42L + 84
collect like terms
4116 = 42L
Make 'L' the subject of formula
L = 98 yards
Hence, the length is 98 yards
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Answer:
98 yards
Step-by-step explanation:
PLS HELO IM MARKING BRAINLEIST!!
∠O ≅ ∠U is third statement which is congruent .
What is congruent triangle?
Two figures are said to be "congruent" if they can be placed perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to having precisely the same form and size.If all three sides of two triangles are the same, they are said to be congruent. If we have a side, an angle between the sides, and then a second side that is congruent, we know they are congruent. In other words, side, angle, side.ΔONP and ΔUTV are congruent .
By using ASA Theorem ,
NP ≅ TV
∠P ≅ ∠V
∠O ≅ ∠U
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Answer:
∠O ≅ ∠U is third statement which is congruent .
Step-by-step explanation:
What is congruent triangle?
Two figures are said to be "congruent" if they can be placed perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other.
Congruent refers to having precisely the same form and size.
If all three sides of two triangles are the same, they are said to be congruent.
If we have a side, an angle between the sides, and then a second side that is congruent, we know they are congruent. In other words, side, angle, side.
ΔONP and ΔUTV are congruent .
By using ASA Theorem ,
NP ≅ TV
∠P ≅ ∠V
∠O ≅ ∠U
BRAINLIST??
mark has 5 pants and 7 shirts in his closet. he wants to wear a different pant/shirt combination each day without buying new clothes for as long as he can. how many weeks can he do this for?
Mark has 35 unique combinations to choose from, so can he co go 5 weeks with this set of clothes
Number of pants in Mark's closet = 5
Number of shirts in Mark's closet = 7
Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.
He can choose amongst the pants in 5 ways, similarly, he can choose among the shirts in 7 ways
Total number of combinations = 5*7 = 35 unique combinations
So, if he wears one combination each day he can last 35 days or 5 weeks, without buying new clothes
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What is the slope line that passes through the points (-6,4) and (-15,4)?
Answer: the slope=0
Step-by-step explanation:
[tex]\displaystyle\\(-6,4)\ \ \ \ \ (-15,4)\\\\\boxed {The\ slope=\frac{y_2-y_1}{x_2-y_1} }\\\\The\ slope=\frac{4-4}{-15-(-6)} \\The\ slope=\frac{0}{-15+6} \\\\The\ slope=0[/tex]
BRAINLIEST will be given to the answer
Write in the form (x + p)^2 + q
x^2 - 5x + 3
Answer:[tex][x{-\frac{5}{2}] ^{2} +\frac{-12}{25}[/tex] is in the form [tex][x+p]^{2} +q[/tex]
Step-by-step explanation:
Here given is [tex]x^{2} -5x+3[/tex].................................eq [1]
now we know that [tex][x-\frac{5}{2}] ^{2}[/tex]= [tex]x^{2} -5x+\frac{25}{4}[/tex]............eq [2]
now add and subtract [tex]\frac{25}{4}[/tex] in eq 1
[tex]x^{2} -5x+3+\frac{25}{4} -\frac{25}{4}[/tex]
[tex]x^{2} -5x+\frac{25}{4}+3-\frac{25}{4}[/tex]
[tex][x-\frac{5}{2} ]^{2} +\frac{3*4-25}{4}[/tex]................................from eq[2]
[tex][x{-\frac{5}{2}] ^{2} +\frac{-12}{25}[/tex]
so comparing with the given form [tex][x+p]^{2} +q[/tex]
where p=[tex]\frac{5}{2\\}[/tex] and q=[tex]\frac{-12}{5}[/tex]
A box contains 5 reams of paper. How could you estimate the thickness of 2 sheets of paper. One ream is 500 sheets.
Answer:
If one ream is 500 sheets, then that would mean that two reams combined are 1,000 sheets, and the fact that there are 5 reams is just a random number meant to throw you off.
Work out, giving your answer in it's simplest form: 4 1/5 × 5/14
12x + 5y = -24 13x - 5y = 14 Linear Equations By Elimination
Let,
[tex]\begin{gathered} 12x+5y=-24\ldots(1) \\ 13x-5y=14\ldots(2) \end{gathered}[/tex]Perform the operation (1)+(2),
[tex]\begin{gathered} 12x+5y+(13x-5y)=-24+(14) \\ 12x+13x+5y-5y=-10 \\ 25x+0y=-10 \\ 25x=-10 \\ x=\frac{-10}{25} \\ x=\frac{-2}{5} \end{gathered}[/tex]Substitute the value of x=-2/5 in the expression (1).
[tex]\begin{gathered} 12\times\frac{-2}{5}+5y=-24 \\ 5y=-24+\frac{24}{5} \\ 5y=\frac{-96}{5} \\ y=\frac{-96}{5\times5} \\ y=\frac{-96}{25} \end{gathered}[/tex]Thus, the value of x is -2/5 and value of y is -96/25.
Given: 4+x=16
What is the value of x?
Need this answered ASAP
Answer:
To get the answer for X we have to subtract 16 from 4 which gives us 12
X=12
Hope this helps.
Answer:
4+X= 16
X=16-4
X=12
*To find X , you need to minus 16 by four. That is because you have to move (+4) to the other side (change sides,change signs). So (+4) becomes (-4) so 16-4 =12
Ben orders t-shirts for $8.00 per t-shirt. There is a $6.00 flat fee for shipping. He only has $50.00 to spend. How many t-shirts can he
buy?
PLEASE PLEASE HELP RN 20 POINTS ADDED
Answer: The answer is 5 shirts
Step-by-step explanation:
8x + 6 = 50
subtract 6 from each side:
8x +6 (-6) = 50 (-6)
8x=44
divide by 8:
8x/8=44/8
x=5.5
round to single shirts:
x=5 shirts
Answer:
Step-by-step explanation: you have to divide 50 by 8 then get your answer of 6.25, but you also have to consider two things; the extra $6.00 flat fee, and you cant buy 6.25 shirts, so what we do is multiply 8 times 6 to get 48, but we have to consider the extra $6.00, so you take away 8 which gives you 5 shirts, plus the shipping fee so in all he can buy 5 shirts.
Ron's youth group commits to making a certain number of sandwiches for a local soup
kitchen. They make 132 sandwiches, but then they run out of peanut butter. The group still
has 110 sandwiches left to make to meet their commitment.
Use an equation to find the total number of sandwiches the youth group commits to making.
sandwiches
Answer:
242 sandwiches
Step-by-step explanation:
The group wants to make x number of sandwiches.
They have already made 132 sandwiches and still have 110 sandwiches to make.
To find the total, you can add these numbers up, because:
132 + 110 = total sandwiches
This way, you get 242 sandwiches
Calculate (9.5 × 106) + (4.2 × 106)
Give your answer in standard index form.
Answer:
1.4522 x [tex]10^{3}[/tex]
HELP PLEASE I GIVE BRAINY IF U ANSWER RIGHT AND IF I CANT READ THAT THERE IS MORE THEN ONE ANSWER U WONT GET ANYTHING
ANSWER BOTH QUESTIONS PLEASE IF U DON'T I WONT GIVE U A THING
Question 1
Which ordered pairs lie on the graph of the exponential equation
f(x) = 25(2.2)^x ?
Select EACH correct answer.
A. (0, 0)
B. (0.5, 37.08)
C. (1, 55)
D. (2, 121)
THE FIRST PICTURE GOES WITH QUESTION 2 ONLY
Question 2
The function f(x) = (3/8)^x is shown on the coordinate plane.
Determine which expressions describe the end behaviors of the function.
Select EACH correct answer.
A. As x increases without bound, the graph of f(x) decreases without bound.
B. As x increases without bound, the graph of f(x) approaches y = 1.
C. As x decreases without bound, the graph of f(x) increases without bound.
D. As x decreases without bound, the graph of f(x) approaches y = 0.
The ordered pairs lie on the graph of the exponential equation is
(0.5, 37.08) (1, 55) (2, 121)What is exponential equation?Exponents are used in exponential functions, as the name indicates. But take note that an exponential function does not have a constant as its base and a variable as its exponent (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). One of the following forms can be used for an exponential function.
According to its definition, a fundamental exponential function has the formula f(x) = [tex]b^x[/tex], where b is a constant and x is a variable. The exponential function f(x) = [tex]e^x[/tex], where "e" is "Euler's number," and e = 2.718, is one of the most well-known ones. An exponential function may incorporate a constant if we expand the potential of various exponential functions.
Given function:
f(x) = 25 [tex](2.2)^x[/tex]
Now, taking x=0
y = f(x) = 25
and, x=0.5
y= f(x) = 37.08
and, x = 1
y = 55
and, x=2
y = 121
So, the ordered pairs lie on the graph of the exponential equation is
(0.5, 37.08) (1, 55) (2, 121)2. The given function is [tex]f(x)= (3/8)^x[/tex]
Now, as per the graph As x decreases without bound, the graph of f(x) approaches y = 1.
Or, As x decreases without bound, the graph of f(x) increases without bound.
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how to find the edge of a cube with the volume of 125 inches
Answer:
5 inches
Step-by-step explanation:
Hello!
The volume of a cube is simply the side length cubed, or the side lengthed multiplied by itself 3 times.
So, to find the edge, we can find the cube root of 125 to find that measure.
Find the Side Lengthx³ = 125x = ∛125x = 5The edge is 5 inches.
Calculate the surface area of the can. Area of a circle =
Height = 10cm
Diameter = 7 cm
Please help me thank you!
What is the surface area of the circle?
The surface area of the can is 220cm².
The height of the can is 10cm, and the diameter is 7cm.
height (h) = 10cm
radius(r) = 7/2 cm
The formula to find the surface area of the can = 2πrh
= 2 × 22/7 × 7/2 × 10
= 220cm²
Therefore the surface area of the can is 220cm².
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help me 20 points please
Answer:
Step-by-step explanation:
the one on top is simple it's 120
can someone please help me solve this math problem with solution too?? TYY!!
Answer: 2080
Step-by-step explanation:
62² −42²
3844−42²
3844−1764
2080
mr jeneski is preparing for a half marathon. He runs a total of 60 miles per week. Five of those miles are ran on saturday, and he takes sunday off. How many miles does he run per day, Monday-Friday
11 miles he run per day, Monday-Friday.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total distance travelled = 60 miles.
On Saturday= 5 miles
Sunday was off
So, from Monday to Friday he travelled
=60 - 5
= 55 miles.
and, per day he run
= 55/5
= 11 miles
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Answer the 4 question in the photo for EASY points ( 20 points )
The pink ribbon is shortest.
Purple > yellow > silver > pink
how would i solve this?
FIRST FIND THE EQUATION OF THE LINE
I WILL USE THE POINTS (-94,24) AND (-54,12)
TO FIND THE GRADIENT
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{12 - 24}{ - 54 - ( - 94)} \\ m = \frac{ - 24}{ - 54 + 94} \\ m = \frac{ - 24}{40} \\ m = \frac{ - 3}{5} [/tex]
THE m ABOVE IS THE GRADIENT.
I WILL USE THE POINT (-74,18) TO GET THE VALUE OF C IN THE EQUATION Y=MX+C
[tex]15 = \frac{ - 3}{5} ( - 74) + c \\ 15 = \frac{222}{5} + c \\ c = 15 - \frac{222}{5} \\ c = \frac{ - 147}{5} [/tex]
THEREFORE THE EQUATION NOW IS
[tex]y = \frac{ - 3}{5} x - \frac{147}{5} \\
FOR THE X-INTERCEPT Y=0 SINCE IN THR X-AXIS Y=0..PLUG IN 0 IN THE PLACE OF Y TO GET X-INTERCEPT.
[tex] \frac{ - 3}{5} x - \frac{147}{5} = 0 \\ \frac{ - 3}{5} x = \frac{147}{5} \\ x = \frac{147}{5} \div \frac{ - 3}{5} \\ x = - 49[/tex]
(-49,0)
NEED HELP ASAP - 100 Points (Operations with Polynomials)
In multiple sentences, create your own real-world application problem for either adding or subtracting polynomials. Include a description of how the problem can be solved.
Answer: Well we can look at whether or not cubes may or may not equal the same by using volume and surface area, where the volume can be used as x^3 and the surface area x^2, but the reason why polynomials can help us a great deal in world problems is whether or not measurements are accurate, or just in general for solving big math equations. Hope this helps.
Which ordered pairs are on the graph of 7x−y=2?
Select ALL that applies.
A. >>(−3,−19)open paren negative 3 comma negative 19 close paren
B. (−1,−9)open paren negative 1 comma negative 9 close paren
C. (0,−2)open paren 0 comma negative 2 close paren
D. (1, 9)(1, 9)
(3, 23)(3, 23)
The ordered pairs which are on the graph of 7x - y = 2 as required in the task content are; Choices B and C; (-1, -9) and (0, -2).
Which ordered pairs are on the graph of 7x - y = 2 as required in the task content?It follows from the task content that the ordered pairs which are on the graph of 7x - y = 2 be determined.
Hence, by testing each pair as follows; we have;
For (-3, -19); we have; 7(-3) - (-19) = 2; -21 + 19 = 2; -2 ≠ 2. Hence, FALSE.For (-1, -9); we have; 7(-1) - (-9) = 2; -7 + 9 = 2; 2 = 2. Hence, TRUE.For (0, -2); we have; 7(0) - (-2) = 2; 0 + 2 = 2; 2 = 2. Hence, TRUE.For (1, 9); we have; 7(1) - (9) = 2; 7 - 9 = 2; -2 ≠ 2. Hence, FALSE.For (3, 23); we have; 7(3) - (23) = 2; 21 - 23 = 2; -2 ≠ 2. Hence, FALSE.Ultimately, the required ordered pairs are; (-1, -9) and (0, -2).
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Convert the following repeating decimal to a fraction in simplest form. .07
PLS HELP ASAP THIS QUESTION IS REALLY EASY
Answer:
x = -1, y = -1
Step-by-step explanation:
[tex]4x + 3 = - 8x - 9[/tex]
[tex]12x + 3 = - 9[/tex]
[tex]12x = - 12[/tex]
[tex]x = - 1[/tex]
[tex]y = 4( - 1) + 3 = - 4 + 3 = - 1[/tex]
You can also use an area model to find the product of 253 x 34
Answer: 8602 is the answer to 253 x 34, do you want the other parts solved too?
Step-by-step explanation: