Answer:
1) For [tex]a = 1[/tex]: [tex]b = 6[/tex] and [tex]k = 6[/tex], 2) For [tex]a = 3[/tex]: [tex]b = 4[/tex] and [tex]k = 12[/tex]
Step-by-step explanation:
The polynomial [tex]y = x^{2} - 7\cdot x + k[/tex] is a second-order polynomial of the form [tex](x-a)\cdot (x-b) = x^{2}-(a+b)\cdot x + a\cdot b[/tex]. By direct comparison, we construct the following system of equations:
[tex]a + b = 7[/tex] (1)
[tex]a\cdot b = k[/tex] (2)
By (1) we know that there are a family of pairs such that the system of equations is satisfied. Let suppose that both [tex]a[/tex] and [tex]b[/tex] are integers. We assume two arbitrary integers for [tex]a[/tex]:
1) [tex]a = 1[/tex]
[tex]b = 7 - a[/tex]
[tex]b = 6[/tex]
[tex]a\cdot b = k[/tex]
[tex]k = (6)\cdot (1)[/tex]
[tex]k = 6[/tex]
2) [tex]a = 3[/tex]
[tex]b = 7 - a[/tex]
[tex]b = 4[/tex]
[tex]a\cdot b = k[/tex]
[tex]k = (3)\cdot (4)[/tex]
[tex]k = 12[/tex]
The lateral area of a cylinder is 100pi in^2. If its dimensions are reduced to one-fifth their original length, what would its new area be?
Answer:
4pi in^2
Step-by-step explanation:
Lateral surface area of a cylinder = 2πrh
π = pi
r = radius
h = height
Let me illustrate with an example
A cylinder has the following dimensions
r = radius = 20
h = height = 10
lateral area = 2 x π x 20 x 10 = 400π
If dimensions are reduced to one-fifth their original length, new dimensions are
r = radius = 20 x 1/5 = 4
h = height = 10 x 1/5 = 2
New lateral area = 2 x 4 x 2 x π = 16π
change in lateral area = 400π / 16π = 25
If dimensions are reduced by 1/5, lateral area would reduce by 25
100 pi / 25 = 4
HELP WILL GIVE BRAINLIEST!!!!!
Write an inequality for the situation.
Karen has at least 7 dresses.
Answer:
At least 7 < She had 15
3(m - n + 2) + 6 - m
Step-by-step explanation:
A(n) _______ is a mapping that does not change the size of the original figure.
A. Isometry
B. Mapping
C. Image
D. Preimage
Answer:
A(n) isometry is a mapping that does not change the size of the original figure.
Answer:
Isometry
Step-by-step explanation:
Isometry is a mapping that does not change the size of the original figure.
WILL MARK BRAINLIEST
Let Events A and B be described as follows:
P(A) = doing yard work
P(B) = it raining
The probability that it will rain this weekend is 68% The probability of doing yard work this weekend and it raining is15%. If the probability of doing yard work is 53%, are doing yard work and it raining independent?
Which graph represents this table of an arithmetic sequence?
Answer:
the x axis contains the arithmetic sequence
a circle is drawn in a coordinate plane centered at (8,15) and a radius of 3 units.
Answer:
(x - 8)² + (y - 15)² = 9
Step-by-step explanation:
Assuming you want the equation.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (8, 15 ) and r = 3 , then
(x - 8)² + (y - 15)² = 9
Jane found 5 seashells on the beach. Ruby found twice as many as Jane. How many shells did they find together?
Answer:
They found 15 shells
Step-by-step explanation:
First, multiply. 5 × 2 = 10
Then, add. 5 + 10 = 15
Lastly, have a great day!
whats the quadratic curve of best fit for the data. estimate what the value of will be when = −4.
(−3,2), (0,5), (1,7.3), (−1,3.3), (−6,5), (−7,7.3)
Answer:
64 is 4 times the difference between Sarah's age, a, and 44Assume Sarah is older than 44
Step-by-step explanation:
The school library has 300 books on the topic of
sports. Students have checked out seventy-four
of those books. How many books on the topic
of sports still remain in the library?
Step-by-step explanation:
226 sports book have a good day
Help pls guy I love you that was along time it since I just want to review
What is 2 2/3 in radical form step by step
hi! please help i’ll give brainliest
Answer:
A because the river is fastest at that shore
Step-by-step explanation:
how do i do c? helppppppppppppppp
Answer:
Step-by-step explanation:
Please help me with this.
Answer: Angles: 42°, 114°, 24°, 30°, 150°.
Step-by-step explanation:
I don't have a clue! I WILL MARE BRAINLIST
Answer:
r= 5
Step-by-step explanation:
because 5^3 = 125 or 5*5*5 = 125
When the function is given in vertex form y = a(x-h)? + k, how is the vertex found?
a. (kh)
b. (x,y)
c. (h,k)
d. (y,x)
Answer:
c. (h, k)
Step-by-step explanation:
Choose the best selection for the
quadrilateral with vertices at the
following points:
(0,0), (0,3), (4,0), (4,3)
Answer: rectangle not sure tho
Step-by-step explanation:
Answer:
Step-by-step explanation:
i chose B:square, i out in the points and that what shape came up. srry if im wrong
solve for the value of y
Answer:
y=8
Step-by-step explanation:
the sum of the three angles is 180
57 + 90 + 5y-7 = 180
5y + 140 = 180
5y = 40
y = 8
Please help What is the value of x. Look at picture.
Answer:
x = 50
Step-by-step explanation:
3x - 10 and 2(x + 10) are vertical angles and congruent , so
3x - 30 = 2(x + 10)
3x - 30 = 2x + 20 ( subtract 2x from both sides )
x - 30 = 20 ( add 30 to both sides )
x = 50
Awnser and show your work <3
Answer:
-14
Step-by-step explanation:
isolate x's on one side so subtract 8.5x and add 1 on both sides
[tex]-14 = 1x[/tex]
simplifies to
x = -14
A circular sheet was cut to make cone without a base of slant height equal to 7 m. If the net of the cone has a perimeter of 47 m, what percentage of the circular sheet of paper was used to make the cone?
a. 80%
b. 25%
c. 75%
d. 60%
Answer:
75%
Step-by-step explanation:
find YZ pls fast correct
Answer:
44Step-by-step explanation:
According to intersecting chords theorem:
21(2x - 6) = 30(x + 1)42x - 126 = 30x + 3042x - 30x = 126 + 3012x = 156x = 156/12x = 13Find the value of YZ:
YZ = 30 + 13 + 1 = 44[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{21(2x - 6) = 30(x + 1)}[/tex]
[tex]\large\textsf{21(2x) + 21(-6) = 30(x) + 30(1)}[/tex]
[tex]\large\textsf{21(2x) = 42x}[/tex]
[tex]\large\textsf{21(-6) = -126}[/tex]
[tex]\large\textsf{30(x) = 30x}[/tex]
[tex]\large\textsf{30(1) = 30}[/tex]
[tex]\large\textsf{42x - 126 = 30x + 30}[/tex]
[tex]\large\text{Put ALL your LIKE TERMS TOGETHER}[/tex]
[tex]\large\text{NEW EQUATION: \textsf {42x - 30x = 126 + 30}}[/tex]
[tex]\large\textsf{42x - 30x = 12x}[/tex]
[tex]\large\textsf{126 + 30 = 156}[/tex]
[tex]\large\text{NEW EQUATION: \textsf{12x = 156}}[/tex]
[tex]\large\text{DIVIDE 12 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{12x}{12}=\dfrac{156}{12}}[/tex]
[tex]\large\text{CANCEL out: } \mathsf{\dfrac{12}{12}}\large\text{ because that gives you 1}[/tex]
[tex]\large\text{KEEP: }\mathsf{\dfrac{156}{12}}\large\text{ because that helps you solve for your the given equation} \\\\\large\text{and your YZ result}[/tex]
[tex]\mathsf{\dfrac{156}{12}=\bf 13}[/tex]
[tex]\large\text{NEW and FINAL EQUATION: \textsf{30 + 1 + 13}}[/tex]
[tex]\large\textsf{30 + 1 + 13}[/tex]
[tex]\large\textsf{30 + 1 = \bf 31}[/tex]
[tex]\large\textsf{= 31 + 13}[/tex]
[tex]\large\textsf{= \bf 44}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf YZ = 44 }}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Adam is helping make mashed potatoes for Thanksgiving. He plans to add 4 fluid ounces of heavy cream to his potatoes. If he buys 1-pint carton, how many fluid ounces will he have left?
Right answer gets brainliest!! :)
may someone help me please and thank you, how do u find an equivalent fraction?? :)
Here are the ways that you can find an equivalent fraction:
Multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.
Answer:
You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction.
Step-by-step explanation:
can someone please answer all 3 parts to this question with work? will give brainliest
See above to see question
Answer:
A)65°
B)110°
C)50°
D)55°
E)80°
Step-by-step explanation:
Since the angle on a straight line should be 180, you simply subtract the given angles from 180
hope I helped
At local bakery Jonah decorated 3 cakes at a time. Ellen decorated 7 at a time. If they ended up decorating the same number of cakes by the end of the day, what is the smallest number of cakes that each must have decorated?
The first row of a theater has 16 seats. There are 3 more seats in each row thereafter. How many seats are in the 25th row/
Answer: 88
Step-by-step explanation:
Given
The first row has 16 seats
then there are 3 more seats in each row
this follows an AP with the first term [tex]a=16[/tex] and common difference [tex]d=3[/tex]
So, no of seats in the 25 th row is
[tex]\Rightarrow a_{25}=a+24d\\\Rightarrow a_{25}=16+3\times 24\\\Rightarrow a_{25}=88[/tex]
Thus, there are 88 seats in the 25 th row
Yan is climbing down a ladder. Each time he descends 4 rungs on the ladder, he stops to see how much farther he has to go. If Yan made 8 stops with no extra steps, which expression best shows another way to write the product of the number of ladder rungs that Yan climbed?
Answer:not A
Step-by-step explanation:
Answer:
stop waiting and do the next question
Step-by-step explanation:
common sense