Answer:
1) What does it mean when a polynomial equation is in standard form?
All terms are on one side of the equation, and zero is on the other side.
2) When factoring 6x2−7x−20 by grouping, how should the middle term be rewritten?
It should be written as 8x−15x.
3) Is the given equation a quadratic equation? Explain.
x(x−6)=−5
The equation is a quadratic equation because there is an x2-term.
4) Which of the following factored forms given below represent the correct factorization of the trinomial x2+10x+16?
(2+x)(8+x)
5) Which of the following is an example of the difference of two squares?
x2−9
Step-by-step explanation:
I hope this helps you out ☺
A binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:
A. [tex]x^2 - 9[/tex]
Recall:
Difference of two squares is when you have a binomial that is expressed as [tex]x^2 - y^2[/tex].The first and second term of the binomial will have an exponential of 2 wile the subtraction sign will be in the middle.Thus, from the options given, option A: [tex]x^2 - 9[/tex] is an example of a binomial that is the difference of two squares.
This is why:9 can be expressed as [tex]3^2[/tex].
In summary, a binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:
A. [tex]x^2 - 9[/tex]
Learn more here:
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-104=8x what is the answer?
Answer:
x=-12
Step-by-step explanation:
8x=-104
8x÷8=-104÷8
x=-104÷8
x=-13
Step-by-step explanation:
8x:-104
8÷8x:-104÷8
x:13
solve the multi step literal equation: solve equation for A b^2A^2-3g=q
Answer:
A = ± [tex]\sqrt{\frac{q+3g}{b^2} }[/tex]
Step-by-step explanation:
Given
b²A² - 3g = q ( add 3g to both sides )
b²A² = q + 3g ( divide both sides by b² )
A² = [tex]\frac{q+3g}{b^2}[/tex] ( take the square root of both sides )
A = ± [tex]\sqrt{\frac{q+3g}{b^2} }[/tex]
What is the justification for step 2 in the solution process? 12 − x = 7x + 32 Step 1: -x = 7x + 20 Step 2: -8x = 20
A. the division property of equality
B.the addition property of equality
C. the subtraction property of equality
D. the multiplication property of equality
Answer:
C. the subtraction property of equality
Step-by-step explanation:
given
12 − x = 7x + 32
Subtract 12 from each side using the subtraction property of equality
Step 1: -x = 7x + 20
Subtract -7x from each side using the subtraction property of equality
Step 2: -8x = 20
Write an equation for the line in the graph that passes through the points (0,4) and (12,16).
Answer:
We have,
y-y1=m(x-x1)
or,y-4=-1(x-0)
or,y-4=-x
or,x+y=4 is the required equation
Step-by-step explanation:
it it helps u ...plz mark it as brainliest
roberta is 6 times danielles age. in 12 years, roberta will only be 2 times danielles age. how old is danielle now?
Answer:
the answer is 3
Step-by-step explanation:
PLS HELP I WILL GIVE BRAINLIST AND A THANK YOU!!!!!!!! Pls help me :)
Answer:
67°
Step-by-step explanation:
CGE + AGC + AGG = 180 (angles on a straight line)
23°+90°+x=180°
x=67°
The average weight of the top 5 fish caught at a fishing tournament was 12.3 pounds. Some of the weights of the fish are shown in the table.
What was the weight of the heaviest fish?
Answer:
14.6
Step-by-step explanation:
It is given that,
The average weight of the top 5 fish caught at a fishing tournament was 12.3 pounds. From the attached figure, the weight of 5 fish are given. We need to find the weight of Wayne S. fish.
Average = sum of terms/no of terms
Let the weight of Wayne S. is x. So,
Here the sum of terms is x+12.8+12.6+11.8+9.7 and the number of terms is 5.
[tex]12.3=\dfrac{x+12.8+12.6+11.8+9.7}{5}\\\\61.5=x+12.8+12.6+11.8+9.7\\\\61.5=x+46.9\\\\x=14.6[/tex]
So, the weight of the heaviest fish is 14.6.
Please help!
Match each system on the left with the number of solutions that it has on the right.
Answer:
1. No solution
2. Infinitely many solutions
3. Infinitely many solutions
4. One solution
Step-by-step explanation:
1.
x=y-3
2x-2y=6
Substitute x=y-3 in (2)
2(y-3)-2y=6
2y-6-2y=6
2y-2y=6+6
0=12
No solution
2.
5x+2y=-7
10x+4y=-14
Multiply (1) by 2 and (2) by 1
10x+4y=-14
10x+4y=-14
Subtract (3) from (4)
0+0=0
0=0
Infinitely many solutions
3.
y=2x+1
4x-2y=-2
Substitute y=2x+1 into (2)
4x-2(2x+1)=-2
4x-4x-2=-2
4x-4x=-2+2
0=0
Infinitely many solutions
4.
9x+6y=15
2y= -1+3x
From 2
2y+1-3x=0
-3x+2y=-1
9x+6y=15 (1)
-3x+2y=-1 (2)
Multiply (2) by 3
-9x+6y=-3
9x+6y=15
Subtract (3) from (1)
9x-(-9x)=15-(-3)
9x+9x=15+3
18x=18
x=18/18
=1
x=1
Substitute x=1 into (1)
9x+6y=15
9(1)+6y=15
9+6y=15
6y=15-9
6y=6
y=6/6
=1
One solution
5. The volleyball team has a double-header on Friday. The probability that they
will win both games is 38%. The probability that they will win just the first game is
70%, What is the probability that the team will win the second game given that
they have already won the first game?
Answer: 54.29%
Step-by-step explanation:
Given: The probability that they will win both games is 38%.
i.e. P( both games will win) =0.38
The probability that they will win just the first game is 70%.
P(first game will win) = 0.70
To find : P(second game will win| first game will win)
Using formula: [tex]P(B|A)=\dfrac{P(\text{both A and B})}{P(A)}[/tex]
So, P(second game will win| first game will win) = [tex]\dfrac{\text{ P( both games will win)}}{\text{P(first game will win)}}[/tex]
[tex]=\frac{0.38}{0.70}\approx0.5429=54.29\%[/tex]
Hence, the required probability = 54.29%
What x value solves the equation? 3x – 5 = 1 x =
Answer:
x = 2
Step-by-step explanation:
3x - 5 = 1
Adding 5 to both sides gives us:
3x - 5 + 5 = 1 + 5
3x = 6
Dividing the equation by 3 gives us:
3x / 3 = 6 / 3
x = 2
Answer:
x = 2 Hfizfifsits96eotst9s
square root of 324 ,576 and 704(show all steps)
Answer:
Step-by-step explanation:
√324=18
√576=24
√704=26.532....
The slope of the line below is -3. Which of the following is the point-slope
form of the line?
13
A. ¥+ 2 = -3(x-6)
© B. y-6--3(x + 2)
© C. y. 2 = -3(x + 6)
D) D. y + 6 = -3(x-2)
Answer:
[tex]\boxed{D. y + 6 = -3(x - 2)}[/tex]
Step-by-step explanation:
Hey there!
Well given point,
(2,-6)
Point slope form is,
y - y1 = m(x - x1)
Plug in the given point
y + 6 = m(x - 2)
Plug in slope
y + 6 = -3(x - 2)
So choice D. y + 6 = -3(x - 2) is correct.
Hope this helps :)
A researcher obtained M = 27 for a sample of n = 36 scores selected from a population with µ = 30 and σ = 18. This sample mean corresponds to a z-score of z = –1.00.
Answer:
True
Step-by-step explanation:
Given that:
M = 27, sample of n = 36 scores, µ = 30 and σ = 18.
The z score is used in statistics to determine by how many standard deviations the raw score is above or below the mean. If the z score is positive, the raw score is greater than the mean and if the z score is negative the raw score is less than the mean. The z score is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that M = 27, this means that x = 27. Therefore:
[tex]z=\frac{x-\mu}{\sigma}\\\\for \ a\ sample\ size(n):z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\z=\frac{27-30}{18/\sqrt{36} } =\frac{-3}{3}=-1[/tex]
This sample mean corresponds to a z-score of z = –1.00.
i’m pretty bad at math
Answer:
2m - 3
Step-by-step explanation:
We know that Jim ran m miles. Twice that amount is simply 2 times that, or 2 * m which simplifies to 2m. 3 miles fewer means that we have to subtract 3 from that quantity, so the answer is 2m - 3.
Answer:
2m - 3
Step-by-step explanation:
Distance ran by Jim = m
Twice as far as Jim : 2 * m = 2m
3 miles fewer than '2m' = 2m - 3
Distance ran by Kelly = 2m - 3
6) 8x+y=-16
-3x+y=-5
Solve each system by elimination?
Answer:
x=-2.2 y=-1.6
Step-by-step explanation:
8x+y=-16
-3x+y=5
5x=-11
x=-11/5 or -2.2
-3x+y=5
-3(-2.2)+y=5
6.6+y=5
-6.6+y=-6.6
y=-1.6
Answer:
(−1, −8)
Step-by-step explanation:
(8x+y=−16)−1(−3x+y=−5)Becomes:8x+y=−163x−y=5Add these equations to eliminate y:11x=−11Then solve11x=−11for x:11x=−1111x11=−1111(Divide both sides by 11)x=−1
Now that we've found x let's plug it back in to solve for y.Write down an original equation:8x+y=−16Substitute−1forxin8x+y=−16:(8)(−1)+y=−16y−8=−16(Simplify both sides of the equation)y−8+8=−16+8(Add 8 to both sides)y=−8
How do I do this? All of em
Answer:
Hey there!
The equation of all of these problems should be in slope-intercept, or, y=mx+b form.
In y=mx+b form, the m is the gradient, and y intercept is the b value.
a) y=2x+4
b) y=-2x-4
c) y=1x-1/5 (But as you may know, 1x=x, because one times any number is just that number, so we can actually have: y=x-1/5.)
d) y=-x+3.78
e) y=-2/3x+0 (Can be simplified to y=-2/3x)
f) y=0x-2/3 (Can be simplified to y=-2/3)
This can be confusing, especially if you're new to the topic. Let me know if you need more help :)
I am thinking of 3 consecutive numbers. The first is a multiple of 4, the second is a multiple of 5 and the third is a multiple of 6." What could the numbers be? Can you find 3 possible sets of numbers
Answer:
{4, 5, 6}, {64, 65, 66}, {124, 125, 126}
Step-by-step explanation:
x = 1st number
x + 1 = 2nd number
x + 2 = 3rd number
{4, 5, 6}, {64, 65, 66}, {124, 125, 126}
The possible set of numbers are {4,5,6}, {64,65,66} and {124,125,126}
What are consecutive number?Consecutive numbers are the numbers which follow each other in order from small to greater number.
Let three consecutive numbers are, x ,x+1 and x+2.
According to given condition,
The first number is a multiple of 4,
The second number is a multiple of 5,
And The second number is a multiple of 6.
Start from 4 and then try to find out sequence,
The numbers can be 4, 5 and 6.
Further, the number can be 64,65 and66
And The numbers can be 124,125 and 126
So, three sets of numbers are {4,5,6}, {64,65,66} and {124,125,126}
To know more about Consecutive number on:
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PLZ HELP MEH:(
Mean, Median, and Mode
quenage
Find the mean, median, mode and range for each set of data.
1. 6. 9, 2, 4, 3, 6,5
2. 25, 18, 14, 27, 25, 14, 18, 25, 23
3. 453, 345, 543, 345, 534
4. 13, 6, 7, 13,6
5. 8, 2,9, 4, 6, 8,5
6. 13, 7, 17, 19, 7, 15, 11, 7
7. 1, 15, 9, 12, 18, 9, 5, 14, 7
8. 28, 32, 23, 43, 32, 27, 21, 34
9. 3,9, 4, 3, 9, 4, 2, 3, 8
10. 42, 35, 27, 42, 38, 35, 29, 24
11. 157, 124, 157, 124, 157, 139
Answer:
to find the mean add all numbers the divide by the ammount of numbers given
Step-by-step explanation:
ex: 1 , 2 , 3
add:
1+2+3=6
divide:
6 / 3 = 2
your mean is 2
all good?
Answer: to find the mean add up all numbers and divide them by the amount of numbers there and to find the median that is the middle number write it on a piece of paper and cross out the beginning and end till you get the to the middle that is your median
Step-by-step explanation:
Find the value of x in the triangle
Answer:
x=62
Step-by-step explanation:
a triangle equals 180
so knowing that you subtract 56 from 180
That gives you 124
Then you divide it by 2 because the sides are equal.
That gives you 62
so x=62
Kite WXYZ is graphed on a coordinate plane.
What is the area of the kite ?
Answer: 14 units^2
Step-by-step explanation: 2 times 3 is 6, 2 times 4 is 8, 6+8=14.
Compute the value of each expression |-1||-||5|
Answer:
5
Step-by-step explanation:
The absolute value is the distance between a number and zero. The distance between − 1 and 0 is 1
1 |-5|
Multiply | − 5 | by 1
The absolute value is the distance between a number and zero. The distance between − 5 and 0 is 5
Hope this can help
kofi and kweku are two brothers. Kofi is older than kweku. Given that kofi's age is (5x-4) years and kweku's age is (2x+1) years.
a. write down an expression, interns of x,for how much old is Kofi than kweku.
b. if Kofi is tens years older than kweku, find the value of x and the ages of Kofi and kweku
Answer:
Kindly check explanation
Step-by-step explanation:
Given the details :
Kofi is older than kweku
kofi's age = (5x-4) years
kweku's age = (2x+1) years
a. write down an expression, interns of x,for how much old is Kofi than kweku
Equate the ages of Kofi and kweku
(5x - 4) = (2x + 1)
5x - 4 = 2x + 1
5x - 2x = 1 + 4
3x = 5
3x - 5
B.) if Kofi is tens years older than kweku, find the value of x and the ages of Kofi and kweku
Then,
(5x-4) = (2x + 1) + 10
5x - 4 = 2x + 1 + 10
5x - 2x = 1 + 10 + 4
3x = 15
x = 5
Kofi's age : 5x - 4
5(5) - 4 = 25 - 4 = 21 years
Kweku's age : (2x + 1)
2(5) + 1 = 10 + 1 = 11 years
-4(2x-3) simplified
Answer:
-8x + 12
Step-by-step explanation:
Distribute -4 to the parentheses:
-4(2x - 3)
-4(2x) = -8x
-4(-3) = 12
-8x + 12
Answer:
-8x +12
Step-by-step explanation:
-4(2x-3)
Distribute
-4* 2x -4 *-3
-8x +12
Points C and D are on a number line (not shown).
The coordinate of point C is -16 and the coordi-
nate of point D is 14. Point E is a point on line
segment CD. If the distance from point E to point C
is 1
4
the distance from point E to point D, what is
the coordinate of point E?
Answer:
17
Step-by-step explanation:
A triangle and the coordinates of its vertices is shown in the coordinate plane below. Enter the area of this triangle in square units, rounded to the nearest tenth. square units
Answer:
22 units²
Step-by-step explanation:
1/2b*h=area
You can either count the units or use the distance formula.
[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
b = 4 units
h = 11 units
area = (1/2*4)*11 = 22 units²
You land a job as an police officer. Your salary for the 1st year is $43,125. You will receive a 7% increase every year. How much will your salary be at the start of year six?
Answer:
Salary after 5 year(A) = $60,485 (Approx)
Step-by-step explanation:
Given:
Staring salary(P) = $43,125
Growth rate(r) = 7%
Number of year (n) = (6-1) = 5
Find:
Salary after 5 year(A)
Computation:
[tex]A=P(1+r)^n \\\\ A = 43125(1+0.07)^5 \\\\ A = 60485[/tex]
Salary after 5 year(A) = $60,485 (Approx)
plz help.. plzz if you can
Answer:
C is a function
Step-by-step explanation:
We can use the vertical line test. If a vertical straight lines passes through the graph more than one, it is not a function
A and B are not functions
C is a function
Solve logs (8 - 3x) = log20 for x.
A. X = 14
B. X = -13
C.x = -8
D. X= -4
Answer:
x = -4
Step-by-step explanation:
logs (8 - 3x) = log20
Since we are taking the log on each side
log a = log b then a = b
8 -3x = 20
Subtract 8 from each side
8 -3x-8 =20 -8
-3x = 12
Divide by -3
-3x/-3 = 12/-3
x = -4
Answer:
[tex] \boxed{\sf x = -4} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: x \: over \: the \: r eal \: numbers:[/tex]
[tex] \sf \implies log(8 - 3x) = log 20[/tex]
[tex] \sf Cancel \: logarithms \: by \: taking \: exp \: of \: both \: sides:[/tex]
[tex] \sf \implies 8 - 3x = 20[/tex]
[tex] \sf Subtract \: 8 \: from \: both \: sides:[/tex]
[tex] \sf \implies 8 - 3x - 8 = 20 - 8 [/tex]
[tex] \sf \implies - 3x = 12 [/tex]
[tex] \sf Divide \: both \: sides \: by \: - 3:[/tex]
[tex] \sf \implies \frac{-3x}{-3} = \frac{12}{-3} [/tex]
[tex] \sf \implies x = - 4[/tex]
PLEASE ANSWER QUICKLY ASAP
ANSWER QUESTION A AND B
Answer:
a) [tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]
b) (i) [tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]
(ii) [tex]k=2[/tex]
Step-by-step explanation:
It is given that,
[tex]a=\begin{pmatrix}4\\-10\end{pmatrix},b=\begin{pmatrix}-2\\1\end{pmatrix},c=\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
a)
We need to find the value of a+b+c.
[tex]a+b+c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
[tex]a+b+c=\begin{pmatrix}4+(-2)+(-4)\\-10+1+6\end{pmatrix}[/tex]
[tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]
b)
(i) We need to find the value of a+2c.
[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+2\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-8\\12\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}4+(-8)\\-10+12\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]
(ii) It is given that a+2c=kb, where k is an integer. We need to find the value of k.
[tex]a+2c=k\begin{pmatrix}-2\\1\end{pmatrix}[/tex]
[tex]\begin{pmatrix}-4\\2\end{pmatrix}=\begin{pmatrix}-2k\\k\end{pmatrix}[/tex]
On comparing both sides, we get
[tex]k=2[/tex]
solve for z -0.25z= -1.25
Answer:
z = 5Step-by-step explanation:
-0.25z= -1.25
Convert the decimals to improper fractions
That's
[tex] - 1.25 = - \frac{5}{4} [/tex][tex] - 0.25 = - \frac{1}{4} [/tex]So we have
[tex] - \frac{1}{4} z = - \frac{5}{4} [/tex]Multiply through by 4
We have
- z = - 5
Divide both sides by - 1
the final answer is
z = 5Hope this helps you
Answer:
[tex] \boxed{ \bold{ \purple{z = 5}}}[/tex]Step-by-step explanation:
[tex] \mathsf{ - 0.25z = - 1.25}[/tex]
Divide both sides of the equation by -0.25
[tex] \mathsf{ \frac{ - 0.25z}{ - 0.25} = \frac{ - 1.25}{ - 0.25} }[/tex]
Calculate
[tex] \mathsf{z = 5}[/tex]
Hope I helped !
Best regards!
