1011101₂ = 1 • 2⁶ + 1 • 2⁴ + 1 • 2³ + 1 • 2² + 1 • 2⁰
1011101₂ = 64 + 16 + 8 + 4 + 1
1011101₂ = 93₁₀
For what value of k, the zeroes of x2 + kx + 12 will differ by 1?
Let a and b be the zeroes of x² + kx + 12 such that |a - b| = 1.
By the factor theorem, we can write the quadratic in terms of its zeroes as
x² + kx + 12 = (x - a) (x - b)
Expand the right side and equate the coefficients:
x² + kx + 12 = x² - (a + b) x + ab
Then
a + b = -k
ab = 12
The condition that |a - b| = 1 has two cases, so without loss of generality assume a > b, so that |a - b| = a - b.
Then if a - b = 1, we get b = a - 1. Substitute this into the equations above and solve for k :
a + (a - 1) = -k → 2a = 1 - k → a = (1 - k)/2
a (a - 1) = 12 → (1 - k)/2 • ((1 - k)/2 - 1) = 12
→ (1 - k)²/4 - (1 - k)/2 = 12
→ (1 - k)² - 2 (1 - k) = 48
→ (1 - 2k + k²) - 2 (1 - k) = 48
→ k² - 1 = 48
→ k² = 49
→ k = ± √(49) = ±7
Mandy created a treasure hunt in the sand at the beach. To keep track of where she buried four items, she graphed their locations in the coordinate plane.
Write the correct ordered pair to show the location of each item.
1. What is the location of item 1? Explain how you found its coordinates. Be sure to tell how you identified the sign of each coordinate.
Write your answer in the space below.
2. What is the location of item 2?
Write your answer in the space below.
3. What is the location of item 3?
Write your answer in the space below.
4. What is the location of item 4?
Write your answer in the space below
Answer:
attach photo of coordinate plane
Answer:
1. (-3,3 ½)
2. (2.9,1) or (2 9/10,1)
3. (-1,-2.5) or (-1,2 1/2)
4. (1.9,-1) or 1 9/10,-1)
Step-by-step explanation:
Since some points were not directly on a line, they must have not been a whole number, so I estimated and used logical reasoning to get the coordinates of the items. Hope this helps.
3. State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate
The additional information required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate is that Line ML is equivalent to line YL. Option A
What is the SSS congruence postulate?The SSS congruence theorem states that If all the sides of one triangle are equivalent to the corresponding three sides of the second triangle, then, the two triangles are said to be congruent.
From the diagram given, we have;
Triangles NLMTriangle LNYFor the three sides of triangles NLM to be equivalent to that of LNY;
Line MN must be equal to line YL
Thus, the additional information required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate is that Line ML is equivalent to line YL. Option A
Learn more about SSS congruence theorem here:
https://brainly.com/question/27997251
#SPJ1
Jamal makes $186 a week at his job. He plans to save 5% of his paycheck for a P.Y.F account. How much money will Jamal put in his P.Y.F account this week.
Answer:
$9.30
Step-by-step explanation:
Answer:
Jamal will put $9.30 in his P.Y.F. account this week.
Step-by-step explanation:
Jamal makes $186 a week. He plans to save 5% of that in his P.Y.F. account.
%5 of $186 is $9.30 ($186/20).
This week, he will put $9.30 in his P.Y.F. account.
Hope this helps!
help bro. ;;;;;;;;;;;;;;;;;;;;;;;
Answer:
Jose answered incorrectly. In his second step, where he expanded the term 5(c - 2), he multiplied the c by five, but failed to multiply the two, giving him, "5c - 2 - 2c" instead of the correct expression "5c - 10 - 2c".
Answer:
top one is right 100% right!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Rewrite the equation in slope-intercept form:
10x + 5y = - 15
The equation in slope-intercept form is y = - 2x - 3.
What is the equation of line?The general equation of a straight line is
y = mx + c,
where m is the gradient or slope, and
y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Now the given equation is,
10x + 5y = - 15
Dividing the equation by 5 we get,
2x + y = - 3
Subtracting 2x both the side we get,
2x + y - 2x = - 3 - 2x
⇒ y = - 3 - 2x
or, y = - 2x - 3
This is the required slope-intercept form.
where -2 is the slope and -3 is the intercept.
Thus, the equation in slope-intercept form is y = - 2x - 3.
To learn more about equation of line :
https://brainly.com/question/14200719
#SPJ1
I have 17 warnings how am I not banned from the app yet?
You should ask a moderator
Solve equation 6x+5=35
Can someone help me pls
Answer: 39.4784
Step-by-step explanation:
The equation for area of a circle is (3.14)r^2.
Just plug in the given radius (4) into the equation and solve.
Flagpole to the ground using a piece of rope that is 10 feet long. He is going to tie the rope to the top of the flagpole and then secure the other end of the rope to the ground. The flagpole is 8 feet high. How far out on the ground does he need to secure the rope from the flagpole so that the rope is tight?
Answer:
6 feetStep-by-step explanation
Using the pythagoras theorem;
Given
The length of the flag pole = 8 feet = opposite side
Length of the rope = 10 feet = hypotenuse
To determine how far out on the ground he need to secure the rope from the flagpole so that the rope is tight, we need to look for the adjacent. Using the equation
hyp² = opp² + adj²
10² = 8² + adj²
adj² = 100-64
adj² = 36
adj = √36
adj = 6feet
Hence the rope should be placed 6feet out of the ground
PLEASE HELP !!!!!! WILL MARK THE BRAINLIEST
Answer:
c
hope its right :)
good luck!
please help!! picture linked below.
Answer:
50y + 25x = 800
&
50x + 25y = 800
Can someone help me on this? which one is it???
i need help please: if
Answer:
If what??? can you please finish the question in the reply?
Put parenthesis around 5 + 4 × 2 + 6 - 2 × 2 + 1 to make the answer 19
Answer:4x2
Step-by-step explanation:
A side of the triangle below has been extended to form an exterior angle of 156°. Find
the value of x
Answer:
x=24
Step-by-step explanation:
again 180-156=24
super easy remember exterior +interior angles add up to 180
Brainliest please
First angle = 105
Second angle = x
Third angle = 156 - 105
= 51
_________________________________________
Three angles of the triangle:
[tex]105[/tex]
[tex]x[/tex]
[tex]51[/tex]
___________________________________________
Angle sum of triangle = 180°
[tex]105 + 51 + x = 180[/tex]
[tex]156 + x = 180[/tex]
[tex]x = 180 - 156[/tex]
[tex]x = 24[/tex]
A pair of dice is tossed. what is the probability of getting sum of 5 or 9?
A)7/9
B)5/9
C)1/9
D)2/9
Answer:
[tex]Probability = \frac{2}{9}[/tex]
Step-by-step explanation:
Given:
A pair of dice
Required
Determine the probability of a sum of 5 or 9
Let the sample space of the first die be S1 and the second, S2
[tex]S_1 = {1,2,3,4,5,6}[/tex] --- 6 outcomes
[tex]S_2 = {1,2,3,4,5,6}[/tex] --- 6 outcomes
Number of sample space, n is:
[tex]n = 6 * 6[/tex]
[tex]n = 36[/tex]
Next, we list out all possibilities of obtaining a sum of 5
[tex]Sum\ of\ 5 = \{(1,4),(2,3),(3,2),(4,1)\}[/tex]
n(Sum5 )= 4
Next, we list out all possibilities of obtaining a sum of 9
[tex]Sum\ of\ 9 = \{(3,6),(4,5),(5,4),(6,3)\}[/tex]
n(Sum9)= 4
The required probability is then calculated as:
[tex]Probability = \frac{n(Sum9)}{Total} + \frac{n(Sum5)}{Total}[/tex]
[tex]Probability = \frac{4}{36} + \frac{4}{36}[/tex]
Take LCM
[tex]Probability = \frac{4+4}{36}[/tex]
[tex]Probability = \frac{8}{36}[/tex]
Simplify
[tex]Probability = \frac{2}{9}[/tex]
DEF is a 90° clockwise rotation of ABC. Find the length of FD.
A
D
5x - 22
F
B
3x + 18
Answer:
Step-by-step explanation:
54
1. Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F + G) (2) =
a. 4
b. 5
c. 9
2. Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F - G) (6) =
a. -3
b. 3
c. -1
3. Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F G) (2) =
a. 20
b. 10
c. 40
Answer:
b.5
a-3
a.20
its korrect now
Find the measure of the missing angel
Answer:
58 degrees
Step-by-step explanation:
pls pls help, brainiest guaranteed
Yolanda's final exam has true/false questions, worth 4 points each, and multiple choice questions, worth 5 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct.
She needs more than 82 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.
Answer:
i think its
4× + 5y > = 85
Step-by-step explanation:
i hope im right or even close i tryed i should be right tho HAVE A NICE DAY!!
I Just want to make sure this is correct..
Answer:
Yes that is the right answer
Answer:
no, because each output has an input of one
Step-by-step explanation:
hope this helps...
Answer please. Correct answer
Answer:Graph A if I’m incorrect sorry
Step-by-step explanation:
24% of what number is 18
Answer:
75 is the answer to your question
Answer:
i believe its 75 my guy
Six is less than or equal to the sum of a number and 3 1/4
Answer:
x ≥ 2 3/4
Step-by-step explanation:
6 ≤ x + 3 1/4
6 - 3 1/4 ≤ x
2 3/4 ≤ x
x ≥ 2 3/4
The solution to that equation or inequality will be; x ≥ 2 3/4
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
WE have been given that Six is less than or equal to the sum of a number and 3 1/4;
Therefore, the inequality will be;
6 ≤ x + 3 1/4
6 - 3 1/4 ≤ x
2 3/4 ≤ x
x ≥ 2 3/4
Hence, The solution to that equation or inequality will be; x ≥ 2 3/4
Learn more about inequalities here:
https://brainly.com/question/27425770
#SPJ2
Answer one of them please thank you
The value of (M∪C)∩ V is { 3, 6 }
What are sets?Sets are defined as a collection of well-defined elements, numbers or objects.
It is important to note that;
Intersection of sets is denoted with the symbol '∩' and contains elements common to two or more setsUnion of sets is denoted with the symbol '∪' and contains all the elements of two or more sets without repetition14.
M = { 2. 3 , 4 , 5}
C = { 4, 6 , 8 , 10}
V = { 3, 5 , 7 , 9}
M∪ C = { 2, 3, 4 , 5 , 6 , 8 , 10}
(M∪C)∩ V = { 3, 6 }
Thus, the value of (M∪C)∩ V is { 3, 6 }
Learn more about sets here:
https://brainly.com/question/2166579
#SPJ1
8) Find x ifm/HGS = 3x + 5,
m/SGF=21x +3, and m/HGF = 176º.
The required value of x is 7.
In the given statement is:
m/HGS = 3x + 5,
m/SGF=21x +3, and m/HGF = 176º.
and, to find the value of 'x'
The two angles, ∠HGS & ∠SGF, when combined, will result in ∠HGF
m ∠HGS = 3x + 5
m ∠SGF = 21x + 3
m ∠HGF = 176°
Set the equation:
m ∠SGF + m ∠HGS = m ∠HGF
Plug in the corresponding terms to the corresponding variables:
21x + 3 + 3x + 5 = 176°
24x + 8 = 176°
24x = 176° - 8
24x = 168°
x = 168°/24
x = 7
Hence, The required value of x is 7.
Learn more about Variables at:
https://brainly.com/question/24357656
#SPJ1
**NEED THIS WITHIN 5 MINS** Stan’s employer pays for 45% of his annual health insurance premium of $4,567.00. Stan pays the remaining balance by having it deducted in equal amounts from his 26 paychecks throughout the calendar year. How much will Stan have deducted from each paycheck?
Answer:
$88.3
Step-by-step explanation:
Here 42% of annual health premium($5450)=*5450
=$2289
This amount is being paid by the company means it is deducted amount in one year.
One year has 26 paychecks so above amount divided by 26 is rebate amount in each paycheck.
Deducted amount=
=$88.30
Which option is the simplified version
Answer:
its the 2 option......................
Shelly is making an apple pie.she needs 3/4 cup of sugar for her pie.How many cups of sugar will she need if she makes 7 pies?