Step-by-step explanation:
For a polynomial of the form
a
x
2
+
b
x
+
c
, rewrite the middle term as a sum of two terms whose product is
a
⋅
c
=
6
⋅
−
12
=
−
72
and whose sum is
b
=
−
1
.
−
1
out of
−
x
.
6
x
2
−
(
x
)
−
12
Rewrite
−
1
as
8
plus
−
9
6
x
2
+
(
8
−
9
)
x
−
12
Apply the distributive property.
6
x
2
+
8
x
−
9
x
−
12
Factor out the greatest common factor from each group.
Tap for more steps...
2
x
(
3
x
+
4
)
−
3
(
3
x
+
4
)
Factor the polynomial by factoring out the greatest common factor,
3
x
+
4
.
(
3
x
+
4
)
(
2
x
−
3
)
the absolute values of positive and negative integers are not always positive true or false?
Answer:
True
Step-by-step explanation:
Its true because the absolute value of integers is either its positive side or negative side. For example -4 turn into 4 and -5 turn into 5. Hope this helps!
Point N is the midpoint of FG. If FN = 2x, what expression represents FG?
The line segment FG can be represented as expression 4x whose midpoint is N
We are provided with that Point N is the midpoint of FG and FN = 2x and We need to find expression that represents FG
As N is the midpoint of line segment FG than FN = NG
Also it could be written as FG = FN + NG because FG is the broken into two different line segment FN and NG because of the midpoint N
Therefore, FN = 2x which means FN= NG=2x
So, we can write an expression that could represent FG
FG = FN + NG
FG = 2x + 2x
FG = 4x
Hence, The line segment FG can be represented as expression 4x
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Find the sum.
(3x² + x + 5) + (2x² + x - 2)
Answer:
5X2 + 2X + 3 orr 10x + 2
Step-by-step explanation:
A spinner numbered 1 through 6 is spun. Find the probability that the number spun is a 3 given that it was less than 4 .
The probability that the number spun is a 3 given that it was less than 4 is 1/6.
Let A is the event of a number less than 4.
P(A) is the probability of getting a number less than 4.
The total number less than 4 is 3
Here, the total numbers in the game are 6.
By the Formula for the probability of an event E can be observed as:
P(A)= no of favorable cases/total no. of cases = 3/6 = 1/2
B is the event of getting the number 3
P(B) be the probability of getting 3
The total possible cases is 1
Therefore , P(B)= 1/6
Now, P(B/A) is the probability of getting 3 which is an odd number.
P(B/A)= P(A ∩ B) / P(A)
=1/6 / 1/2
= 1/3
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Solve the equation
|x/7|=3
Answer:
x = 21, -21
Step-by-step explanation:
Let's solve the problem,
→ |x/7| = 3
→ x/7 = 3 ll -x/7 = 3
→ x = 3 × 7 ll -x = 3 × 7
→ [ x = 21 ] ll [ x = -21 ]
So, the value of x is 21, -21.
The midpoint M of FG has coordinates (8, 5). Point F has coordinates (6, 8). Find the
coordinates of point G.
Write the coordinates as decimals or integers.
Coordinates of point G is ( 10 , 2) in this equation.
What do mathematical point coordinates mean?
The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph. There are two coordinates in every point or ordered pair.M is the mid points of FG.
coordinates of M is ( 8,5)
coordinates of F is ( 6,8 )
Let coordinates of G point is ( x₂, y₂)
[tex]x = \frac{x_{1} + y_{1} }{2} , y = \frac{x_{2}+ y_{2} }{2}[/tex]
[tex]8 = \frac{6 + x_{2} }{2} , 5 = \frac{8 + y_{2} }{2}[/tex]
[tex]16 = 6 + x_{2} , 10 = 8 + y_{2}[/tex]
x₂ = 10 , y₂ = 2
So, coordinates of point G is ( 10 , 2)
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Please help with problem 18, Algebra 1, in the attachment
Answer:
r=2
Step-by-step explanation:
To find the slope, we take the difference in the y values over the difference in the x values
m = ( y2-y1)/(x2-x1)
2 = ( 9-3)/ (5-r)
2 = (6)/(5-r)
Multiply each side by (5-r)
2 ( 5-r) = 6
Divide each side by 2
5-r = 6/2
5-r = 3
Subtract 5 from each side
5-r-5 = 3-5
-r = -2
r = 2
Answer:
r = 2
Step-by-step explanation:
To solve this problem, we have to use the following formula for slope:
[tex]\boxed{m= \frac{y_2 - y_1}{x_2 - x_1}}[/tex],
where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the coordinates of two points.
We are given the coordinates [tex](r, 3)[/tex] and [tex](5, 9)[/tex], and told that [tex]m = 2[/tex]. To find the value of r, we have to substitute the given values into the formula and then solve for r :
[tex]2 = \frac{9 - 3}{5-r}[/tex]
⇒ [tex]2 = \frac{6}{5-r}[/tex]
⇒ [tex]2\times (5-r) = \frac{6}{5-r} \times (5 - r)[/tex] [Multiplying both sides by (5 - r)
⇒ [tex]2(5-r) = 6[/tex]
⇒ [tex]\frac{2}{2}(5-r) = \frac{6}{2}[/tex] [Dividing both sides by 2]
⇒ [tex]5- r = 3[/tex]
⇒ [tex]5 - r - 5 = 3 - 5[/tex] [Subtracting 5 from both sides]
⇒ [tex]-r = -2[/tex]
⇒ [tex]\frac{-r}{-1}= \frac{-2}{-1}[/tex] [Dividing both sides by -1]
⇒ [tex]r = \bf 2[/tex]
-4>y+2>-10
qwdasdasddddddddddddddddddddddddddddddd
If you are looking to solve the inequality for y:
_____________________________________
Inequality Form:
[tex]-12 < y < -6[/tex]
Interval Notation:
[tex](-12, -6)[/tex]
Hope this helps!
What are the solutions of x² + 6x - 16 = 0?
Step-by-step explanation:
[tex]x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:1\cdot \left(-16\right)}}{2\cdot \:1}\\\sqrt{6^2-4\cdot \:1\cdot \left(-16\right)}\\\sqrt{6^2+64}\\\sqrt{36+64}\\\sqrt{100}\\\sqrt{10^2}\\=10\\x_1=\frac{-6+10}{2\cdot \:1},\:x_2=\frac{-6-10}{2\cdot \:1}\\\\\bold{x_1:2}\\\frac{-6+10}{2\cdot \:1}\\\frac{4}{2\cdot \:1}\\\frac{4}{2}\\=2\\\\\bold{x_2:-8}\\\frac{-6-10}{2\cdot \:1}\\\frac{-16}{2\cdot \:1}\\\frac{-16}{2}\\-\frac{16}{2}\\=-8[/tex]
Answer:
x₁ = 2
x₂ = -8
Solve each equation. -y+13=-67
The solution of the given linear equation is y = 80.
According to the given question.
We have an equation.
-y + 13 = -67
Since, we have to solve the above linear equation in variable.
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable -y + 13 = -67 is given by
-y + 13 = -67
⇒ - y = -67 -13 (subtractting 13 from both the sides)
⇒ -y = -80
⇒ y = 80
Hence, the solution of the given linear equation is y = 80.
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Determine whether the events are independent or dependent. Then find the probability. You roll two dice and get a 5 each time.
The events are independent. The probability of getting 5 each dice after rolling the dice 2 times is 1/36.
As we are rolling two different die simultaneously, the events are independent.
The probability of getting a 5 in the first die = 1/6
The probability of getting a 5 in the second die = 1/6
Hence, as the events are independent, we can write :-
The probability of getting 5 each dice after rolling the dice 2 times =
probability of getting a 5 in the first die * probability of getting a 5 in the second die = (1/6)*(1/6) = 1/36
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In the final round of a singing competition, the audience voted for one of the two finalists, Luke or Sean. Luke received 25% more votes than Sean received. Altogether, the two finalists received 5175 votes. How many votes did Luke receive?
Based on the number of votes that the two finalists received, the number of votes that Luke received was 2,875 votes
What number of votes did Luke receive?Assuming that the number of Sean's votes could be shown as x, the expression for the votes would be:
x + (x + 25%) = 5,175
2.25x = 5,175
x = 5,175 / 2.25
= 2,300 votes
Luke's votes were:
= 2,300 x (1 + 25%)
= 2,875 votes
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What is the length of the unknown leg in the right triangle?
The length of the unknown leg is 8 yd in the given right triangle.
What is the Pythagoras Theorem?The Pythagoras theorem states that a right-angled triangle's hypotenuse square (90 degrees) equals the sum of the squares of its other two sides.
Let the three legs of the right triangle be a, b and c where a is the altitude, b is the base and c is hypotenuse of the given right angled triangle.
Here, a = [tex]\sqrt{23}[/tex] yd, b = ? and c = [tex]\sqrt{87}[/tex]
According to the Pythagoras theorem,
Hypotenuse² = Base² + Altitude²
c² = b² + a²
[tex](\sqrt{87})^{2}[/tex] = b² + [tex](\sqrt{23})^{2}[/tex]
87 = b² + 23
Subtracting 23 from both sides of the equation.
87 - 23 = b²
b² = 64
Taking square root of the both sides.
b = ± 8
Since the value of length can't be negative so the value of b = - 8 is rejected.
Therefore, the value of b = 8 yd.
As we have calculated above, the length of the unknown leg is 8 yd.
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12-6r=2r+36 (2-step equations)
Answer: r=-3
Step-by-step explanation:
12-6r=2r+36
12=8r+36
-24=8r
r=-3
what is the product of (x+6)(8x+7)
Answer: 8x^2 + 55x + 42
Step-by-step explanation:
(x+6)(8x+7)=
(8x*x)+(7x)+(6*8x)+(6*7)=
8x^2 + 7x + 48x + 42=8x^2 + 55x + 42
Please give me the answer for a) and b)
Answer: a) y=x²+6x+2 b) x=-3-√7, -3+√7
Step-by-step explanation:
(0,2) (-6,2) (-3,-7)
a)
y=ax²+bx+c
(0,2)
x=0 y=2
⇒ 2=a(0²)+b(0)+c
⇒ 2=0+0+c
⇒ 2=c
(-6,2)
x=-6 y=2
⇒ 2=a(-6)²+b(-6)+2
⇒ 2=36a-6b+2
⇒ 2-2=36a-6b+2-2
⇒ 0=36a-6b
⇒ 0+6b=36a-6b+6b
⇒ 6b=36a
Divide both parts of the equation by 6:
b=6
(-3,-7)
⇒ -7=a(-3)²+6(-3)+2
⇒ -7=9a-18+2
⇒ -7=9a-16
⇒ -7+16=9a-16+16
⇒ 9=9a
Divide both parts of the equation by 9:
1=a
Hence,
y=x²+6x+2
b)
x²+6x+2=0
D=(-6)²-4*1*2
D=36-8
D=28
√D=√28
√D=√(4*7)
√D=2√7
x=(-6±2√7)/2
x=-3-√7
x=-3+√7
Which of the following science and engineering practices involves studying graphs directly in order to develop initial meaning?
A) Designing solutions
B) Asking questions
C) Analyzing and interpreting data
D) Planning and carrying out investigations
The science and engineering practices involves studying graphs directly in order to develop initial meaning is c) Analyzing and Interpreting data
Analyzing and interpretation provide answers to the research questions postulated in the study.
Science and engineering practices that involves studying graphs directly in order to develop initial meaning
Analysis means the ordering, manipulating and summarizing of data to obtain answers to research questions. Its purpose is to reduce data to intelligible and interpretable form so that the relations of research problem can be sudden and tested.
Interpretation gives the results of analysis, makes inferences pertinent to the research relations studied, and draws conclusions about these relations.
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Directly analyzing graphs to get initial meaning is a practice used in research and engineering. b) Data analysis and interpretation
The research questions posed in the study are answered via analysis and interpretation.
Practices in science and engineering that need direct graph analysis to provide initial meaning
Analysis is the process of arranging, modifying, and summarizing data to find solutions to research problems. Its goal is to condense data into an understandable and interpretable form so that the connections between the research problem may be quickly and accurately verified.
The interpretation presents the findings of analysis, draws conclusions about the relations under study in the research, and makes relevant inferences.
HELP ASAP WILL MARK BRAINLEST IF RIGHT!
Which describes the range of the parent absolute value function?
{y | y is a real number}
{y | y is an integer}
{y|y > 0}
{y|y < 0}
Answer:
{y|y≥0}
Step-by-step explanation:
The parent absolute value function is
This is a V-shaped function whose vertex is at the origin.
This means that, the least y-value is 0 and there is no highest y-value.
The range refers to all y-values for which the function exists.
Therefore the range is
Or
{y|y≥0}
Answer:
{y | y is a real number}
Step-by-step explanation:
because yxy=y=2
Aisha surveyed 300 of the students in her school about their favorite color. 285 students said their favorite color was red. What percentage of the surveyed students said their favorite color was red?
Answer: 95%
Step-by-step explanation:
To find the percentage, we divide the number of students who chose red by the total number of students and then multiply by 100.
[tex]\frac{285}{300} \times 100=95[/tex]
10. Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially dangerous and
occur when a person's blood sugar fluctuates by more than 38 mg from the normal blood sugar level of
88mg. Write and solve an absolute value inequality to describe blood sugar levels that are considered
potentially dangerous.
We get the absolute value inequality as | x - 88 | > 38.
We are given that:
Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially dangerous and can occur when a person's blood sugar fluctuates by more than 38 mg from the normal blood sugar level of 88mg. We need to write an inequality for it.
We know that the blood sugar level should not be less than:
88 mg - 38 mg = 50 mg
Also, the blood sugar level should not be higher than:
88 mg + 38 mg = 126 mg
The inequality then will become:
50 mg ≤ Blood sugar level ≤ 126 mg.
The absolute value inequality will be:
| x - 88 | > 38
Therefore, we get the absolute value inequality as | x - 88 | > 38.
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Identify the pattern and find the next three terms. 5/7, 8/7, 11/7, 2, ...........
The given pattern 5/7, 8/7, 11/7, 2, ....... is in the form of the arithmetic progression AP. The next 3 terms are 17/7, 20/7, 23/7.
What is defined as the arithmetic progression AP?An arithmetic progression is a sequence whose terms continue to increase and otherwise decrease by a constant number. The common difference is the set amount through which they either increase or decrease.
The following arithmetic progression formulas are frequently utilized to solve various AP problems for the initial term 'a' of an AP and the common difference 'd'-
Common difference 'd' = a₂ - a₁ = a₃ - a₂ = a₄ - a₃ = ....= an - a(n-1).nth term : an = a + (n - 1) dSum of nth terms; Sn = n/2(2a+(n-1)d) = n/2(a + l), where 'l' is the last term of an AP.Now, as per the stated question;
The AP given as; 5/7, 8/7, 11/7, 2, ...........
The series consists of four given terms.
Consider the initial term be 'a₁' = 5/7.
Then, the second term be 'a₂' = 8/7.
And, the third term be 'a₃' = 11/7.
And, the fourth term is 'a₄' = 2.
The AP have the same common difference. so,
d = a₃ - a₂
Substitute the values.
d = 11/7 - 8/7
d = 3/7
Thus, the common difference is 3/7.
or d = a₄ - a₃ (Put the values)
d = 2 - 11/7
d = 3/7
As, a₃ - a₂ = a₄ - a₃
Thus, we can conclude that the given sequence is in AP.
The fifth term will be; a₅ = a₄ + d = 2 + 3/7
a₅ = 17/7
Now, the 6th term will be; a₆ = a₅ + d = 17/7 + 3/7
a₆ = 20/7
Similarly, the 7th term will be; a₇ = a₆ + d = 20/7 + 3/7
a₇ = 23/7
Therefore, it can be said that the given sequence is in AP next three terms be 17/7, 20/7, 23/7.
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3. If pencils cost 15 cents each, and notebooks cost 85 cents each, find the number of pencils
purchased if 50 items cost $18.00.
Answer:
Pencils = 35
Notebooks = 15
Step-by-step explanation:
15 cents = 15/100 = $0.15
85 cents = 85/100 = $0.85
p + n = 50 Eq. 1
0.15p + 0.85n = 18 Eq. 2
p = number of pencils
n = number of notebooks
From Eq. 1
p = 50 - n Eq. 3
Replacing Eq. 3 in Eq. 2:
0.15(50-n) + 0.85n = 18
(0.15*50 + 0.15*-n) + 0.85n = 18
(7.5 - 0.15n) + 0.85n = 18
7.5 + 0.7n = 18
0.7n = 18 - 7.5
0.7n = 10.5
n = 10.5 / 0.7
n = 15
From Eq. 3:
p = 50 - n
p = 50 - 15
p = 35
Check:
From Eq. 2
0.15p + 0.85n = 18
0.15*35 + 0.85*15 = 18
5.25 + 12.75 = 18
e
Question 7: Luna has consumed 900 calories so far today. She has also burned 500 calories in dance class. She wants to keep her daily calorie total to 1,500 calories per day. How many calories does she have left to consume for the day? Is 1,200 a viable solution to this problem?
No; 1,200 is more than the 500 she burned dancing.
No; 1,200 will cause her to exceed 1,500.
Yes; 1,200 is less than 1,500.
Yes; 1,100 is less than 1,500.
1,200 is not a viable solution to this problem as B.
No; 1,200 will cause her to exceed 1,500
How to calculate the value?It should be noted that Luna has consumed 900 calories so far today and has also burned 500 calories in dance class.
Therefore, the amount left will be:
= 1500 - (900 - 500)
= 1500 - 400
= 1100
Therefore, 1,200 is not a viable solution to this problem
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I WILL AWARD BRAINLIST!!! PLEASE HELP! Its A Math Question!!! Find the value of sin(A)
Thank you for your help. please take care.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
By Pythagoras theorem :
[tex]\qquad \sf \dashrightarrow \: hypotenuse = \sqrt{(perpendicular) {}^{2} + (base) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: h= \sqrt{15 {}^{2} + {8}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: h = \sqrt{225 + 64} [/tex]
[tex]\qquad \sf \dashrightarrow \: = \sqrt{289} [/tex]
[tex]\qquad \sf \dashrightarrow \: h = 17 \: \: units[/tex]
Now, we know ~
[tex]\qquad \sf \dashrightarrow \: \sin(A) = \dfrac{opposite \: \: side}{hypotenuse} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sin(A) = \dfrac{8}{17} [/tex]
hi can someone help me here
Answer:
[tex]\textsf{1.} \quad x^2-2x-1[/tex]
[tex]\textsf{2.} \quad -3x^4-5x^3+14x^2+20x-8[/tex]
[tex]\textsf{3.} \quad -\dfrac{5}{2}[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x) = x^2 - 4\\g(x) = x + 2\\h(x) = -3x + 1\end{cases}[/tex]
Question 1
The composite function (f + g - h)(x) means to add functions f(x) and g(x) then subtract function h(x):
[tex]\begin{aligned}(f+g-h)(x) & = f(x)+g(x)-h(x)\\& = (x^2-4)+(x+2)-(-3x+1)\\& = x^2-4+x+2+3x-1\\& = x^2+3x+x-4+2-1\\& = x^2+4x-3\end{aligned}[/tex]
Question 2
The composite function (fgh)(x) means to multiply functions f(x), g(x) and h(x):
[tex]\begin{aligned}(fgh)(x) & = f(x)\cdot g(x) \cdot h(x)\\& = (x^2-4)(x+2)(-3x+1)\\& = (x^2-4)(-3x^2-5x+2)\\& = -3x^4-5x^3+2x^2+12x^2+20x-8\\& = -3x^4-5x^3+14x^2+20x-8\end{aligned}[/tex]
Question 3
The composite function (f/g)(h)(1/2) means to substitute the value of function h(x) when x = 1/2 into function f(x) and function g(x) and divide the former by the latter:
[tex]\begin{aligned}\left(\dfrac{f}{g}\right)(h)\left(\dfrac{1}{2}\right) & = \dfrac{f\left(h\left(\dfrac{1}{2}\right)\right)}{g\left(h\left(\dfrac{1}{2}\right)\right)}\\\\& = \dfrac{f\left(-3\left(\dfrac{1}{2}\right)+1\right)}{g\left(-3\left(\dfrac{1}{2}\right)+1\right)}\\\\& = \dfrac{f\left(-\dfrac{1}{2}\right)}{g\left(-\dfrac{1}{2}\right)}\\\\& = \dfrac{\left(-\dfrac{1}{2}\right)^2-4}{\left(-\dfrac{1}{2}\right)+2}\\\\& = \dfrac{-\dfrac{15}{4}}{\dfrac{3}{2}}\\\\& = -\dfrac{5}{2}\end{aligned}[/tex]
Inequality
Set Notation:
Interval Notation:
14
16
18
20
22
24
26
28
The set notation will be S ∈ { 14, 16, 18, 20, 22, 24, 26, 28}.
When we have to represent set having defined specific number, we do my writing the number in curly bracket. When we have to represent the set having collection of continuous number between two specific defined number, we do by writing first and last number in small bracket.
As the terms given for the set is 14, 16, 18, 20, 22, 24, 26, 28 which are defined and specific terms so it will be represented by writing it in curly brackets
i.e. S ∈ { 14, 16, 18, 20, 22, 24, 26, 28}
Final answer, the set will be S ∈ { 14, 16, 18, 20, 22, 24, 26, 28}
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Kelsey used 2 identical stones to form a path that was 1.7 meters long. How long was each of the stones?
solve the equation v3 = 12
Answer: v= root[3] {12}=2.2894
Step-by-step explanation:
Answer:Your answer is V=4
Step-by-step explanation:Need brainliest award
How are previously decided court cases similar to theorems?
What is the value of Σ⁵n=1 (2 n-3) ?
What is the value of Σ⁵n=1 (2 n-3) ? 15
[tex]\sum_{n=1}^{5} (2 n-3)\\\\ (2 (1)-3)+ (2 (2)-3)+ (2 (3)-3)+ (2 (4)-3)+ (2 (5)-3)\\\\ -1+1+3+5+7=15[/tex]
The sum of the given expression is 15
What is summation?
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labelled "+" is defined can all be added together, in addition to numbers.To learn more about summation, refer:
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