"Given expression: [tex]\( b(-3) \cdot (2a+b) - 4(b-a) \)[/tex] simplifies to[tex]\( -6ab - 3b^2 - 4b + 4a \)[/tex]after distributing and combining like terms."
let's simplify the expression step by step:
Given expression: [tex]\( b(-3) \cdot (2a+b) - 4(b-a) \)[/tex]
Step 1: Distribute the[tex]\( b(-3) \) and \( -4 \)[/tex] across their respective terms:
[tex]\( -3b \cdot (2a+b) - 4b + 4a \)[/tex]
Step 2: Distribute [tex]\( -3b \) across \( (2a+b) \)[/tex] using the distributive property:
[tex]\( -6ab - 3b^2 - 4b + 4a \)[/tex]
Step 3: Combine like terms. We have[tex]\( -3b^2 \) and \( -4b \)[/tex] as like terms:
[tex]\( -6ab - 3b^2 - 4b + 4a \)[/tex] can be rewritten as [tex]\( -6ab - 3b^2 - 4b + 4a \)[/tex]
So, the simplified expression is: [tex]\( -6ab - 3b^2 - 4b + 4a \)[/tex]
Which of the following is equal to the expression below?
(8*320)1/3
Answer:
[tex]\sqrt[3]{8*320} = \sqrt[3]{2,560} = 13.67[/tex]
Step-by-step explanation:
To find an equal or equivalent expression, simplify the expression by applying order of operations.
8*320 = 2,560
Now apply the exponent of 1/3. A fraction exponent is a radical where the denominator is the index.
[tex]\sqrt[3]{2,560} = 13.67[/tex]
Answer:
Have a great rest of your day :)
Step-by-step explanation:
Sanjay needs 90 meters of fence to go around a rectangular garden.
The length l of the garden is three times its width w.
Three of these equations give the correct value for w.
Which equation does NOT?
Answer:
Option A is incorrect.
Step-by-step explanation:
Length of the given parts is l and width is w meters.
It is given in the question that Sanjay needs 90 meters of fence to go around the rectangular park.
It means perimeter of the park is 90 meters.
Since perimeter of a rectangle = 2(length + width)
= 2(L + w)
It is given that length of garden is three times of width so l = 300
therefore, equation will be
Perimeter = 2[3w + w]
90 = 2[3w + w]
Option A ⇒ w + 3w = 90 ⇒ incorrect
Option B ⇒ w + 3w + w + 3w = 90
2(w + 3w) = 90 ⇒ Correct option
Option C ⇒ 2w + 2 (3w) = 90
2 [w + 3w] = 90 ⇒ Correct option
Option D ⇒ 2(3w + w) = 90 ⇒ Correct option
therefore Option A is incorrect option.
Answer:
w+3w+w+3w=90
Step-by-step explanation:
correct
Which is the best estimate of 111/5*2/34
Answer:
4/3 or 1.33333333333333333333.....
Step-by-step explanation:
Jeremy made 2 quarts of lemonade. Which expression can be used to find the number of fluid ounces of lemonade, Jeremy made.
A: 2×2×2
B:2×2×8
C: 2×2×2×2
D:2×2×2×8
The correct answer is D.
There are 32 fluid ounces in a quart so 2 quarts would have 64 fluid ounces and the last equation represents this.
I hope this makes sense and is helpful.
Answer:
D
Step-by-step explanation:
Determine the x-intercept for 3x + 2y = 14. A) (7, 0) B) (0, 7) C) ( 14 3 , 0) D) (0, 14 3 )
Answer:
[tex]\large\boxed{C.\ \left(\dfrac{14}{3},\ 0\right)}[/tex]
Step-by-step explanation:
[tex]\text{The x-intercept is for y = 0.}\\\\\text{Put y= 0 to the equation}\ 3x + 3y = 14:\\\\3x + 3(0) = 14\\\\3x + 0 = 14\\\\3x = 14\qquad\text{divide both sides by 3}\\\\x =\dfrac{14}{3}[/tex]
Y = 2 cm x = 75 grams
Answer:
Step-by-step explanation:
answer quick before I fail :)
I’m not 100% sure but I think it’s 14/49
The graph of a system of parallel lines will have no solutions. (1 point) Select one: a. Always b. Sometimes c. Never
Answer:
Always
Step-by-step explanation:
They never intersect
Answer:
Always
Step-by-step explanation:
The solution to a system of equations graphically is at the point of intersection of the graphs.
If the lines are parallel then they never intersect and so there is no solution.
IN A RUSH PLZ HELP!!!!! ASAP
Evaluate 49/81−−√ .
Enter your answer, as a fraction in simplest term, in the box.
Answer: [tex]\bold{\dfrac{7}{9}}[/tex]
Step-by-step explanation:
[tex]\sqrt{\dfrac{49}{81}}=\dfrac{\sqrt{49}}{\sqrt{81}}=\large \boxed{\dfrac{7}{9}}[/tex]
What multiples to 42 and adds to -2
Answer:
Step-by-step explanation:
xy = 42
x+y = - 2 Substitute into the top equation
y = -2 - x Put in for y
x(-2 - x) = 42 Remove the brackets
-2x - x^2 = 42 Subtract 42 from both sides.
-2x - x^2 - 42 = 0 Put in the more normal order.
-x^2 - 2x - 42 = 0 Multiply by -1
x^2 + 2x + 42 = 0
This cannot be factored. It gives complex roots as it is written. I will give you the answer but I kind of doubt the question is correct.
x1 = - 1 + 6.40i
x2 = -1 - 6.40i
Leave a comment if you have a correction.
Plz help me i need it
Answer: a) k(x) = 2ˣ
Step-by-step explanation:
[tex]g(x) = 3(2^x)\qquad h(x)=2^{x+1}\\\\k(x) = (g-h)(x)\\.\qquad =3(2^x)-2^{x+1}\\.\qquad =3(2^x)-2^x\cdot 2^1\\.\qquad =3(2^x)-2(2^x)\\.\qquad =1(2^x)\\.\qquad =\large\boxed{2^x}[/tex]
Find the distance between 2-3i and 9+21i
Answer:
25Step-by-step explanation:
[tex]d(z_1,\ z_2)=|z_1-z_2|\\\\z=a+bi\to|z|=\sqrt{a^2+b^2}\\------------------\\\\\text{We have:}\\\\z_1=2-3i,\ z_2=9+21i\\\\\text{substitute:}\\\\|(2-3i)-(9+21i)|=|2-3i-9-21i|\\\\=|(2-9)+(-3i-21i)|=|-7-24i|\\\\=\sqrt{(-7)^2+(-24)^2}=\sqrt{49+576}=\sqrt{625}=25[/tex]
Answer:
25.
Step-by-step explanation:
For two complex numbers z=([tex]x_{1},y_{1}[/tex]) and w=([tex]x_{2},y_{2}[/tex]) we have that the distance between z and w is equal to
|z-w| = [tex]\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}[/tex]
So, in this case we have that [tex](x_{1},y_{1})=(2,-3)[/tex] and [tex](x_{2},y_{2})=(9,21)[/tex], then the distance
|z-w| = [tex]\sqrt{(2-9)^{2}+(-3-21)^{2}}[/tex]
= [tex]\sqrt{(-7)^{2}+(-24)^{2}}[/tex]
= [tex]\sqrt{49+576}[/tex]
= [tex]\sqrt{625}[/tex]
= 25.
which equation can be represented using the number line?
Answer:
First Equation: [tex]\frac{3}{4} \div \frac{1}{8} =6[/tex]
Step-by-step explanation:
From the given number line we can see that there are 6 arrows/jumps of equal sizes to reach from 0 to [tex]\frac{3}{4}[/tex]
Each small jump is equivalent to [tex]\frac{1}{8}[/tex]. This is because from 0 to [tex]\frac{1}{4}[/tex] there are 2 jumps, so 1 jump will be equal to [tex]\frac{1}{4}[/tex] divided by 2 which is equal to [tex]\frac{1}{8}[/tex]
From 0 to [tex]\frac{3}{4}[/tex], 6 jumps of [tex]\frac{1}{8}[/tex] are made. In other words we can say [tex]\frac{1}{8}[/tex] is added to itself 6 times to reach to [tex]\frac{3}{4}[/tex].
Adding [tex]\frac{1}{8}[/tex] 6 times to itself also means multiplying [tex]\frac{1}{8}[/tex] by 6. So we can set up the equation as:
[tex]\frac{1}{8} \times 6 = \frac{3}{4}[/tex]
Dividing both sides by [tex]\frac{1}{8}[/tex] we get:
[tex]6=\frac{3}{4} \div \frac{1}{8} \\\\ or\\\\ \frac{3}{4} \div \frac{1}{8} =6[/tex]
Hence, the first equation represents the given number line.
Answer:
A
Step-by-step explanation:
a bag contains 6 red balls,and 4 green balls,and 3 blue balls.if we choose a ball,then another ball without putting the first one back in the bag,what is the probability that the first ball will be green and the second will be red?
Answer: the probability of green would be 4/13 the probability of red would be 6/12
Step-by-step explanation:
The probability of green would be 4/13 the probability of red would be 6/12.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of samples
Given that a bag contains 6 red balls, 4 green balls, and 3 blue balls. If we choose a ball, then another ball without putting the first one back in the bag.
Total outcomes for green ball = 6 + 4 + 3 = 13
The probability of choosing a green ball is,
Probability = 4 / 13
The probability of choosing the red ball is,
Probability = 6 / 12
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What is the value of x and y? What is the relationship between the angles?
Answer:
180 degrees and interior
Step-by-step explanation:
X and y equal 180 and make the shape C therefor are interior angles
Without specific details like an equation or diagram, we can't find the actual values of x and y. But we can talk about how angles can relate to each other generally - they can be complementary (add up to 90 degrees), supplementary (add up to 180 degrees), or vertical (equal when two lines intersect).
Explanation:The question is missing specific details like an equation or a diagram that we can use to find the actual values of x and y. Without these, it's not possible to provide a direct answer. However, we can discuss how angles relate to each other in a general sense.
These are just a few examples of the relationship between angles that could help guide your understanding. If you have a specific problem involving angles and variables, please provide it so we can assist you more accurately.
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The graphs below have the same shape. What is the equation of the blue graph?
Answer: OPTION B
Step-by-step explanation:
The red graph shows the parent function of a quadratic function (which is the simplest form of a quadratic function), whose vertex is at the origin.
The function g(x) is the result of shift the parent function 2 units to the right and shift it 1 unit up.
Therefore, keeping the above on mind you have that the transformation has the following form:
[tex]g(x)=(x-h)^2+k[/tex]
Where the horizontal shift depends on the value of h and the vertical shift depends on the value of k.
Therefore, you obtain the function:
[tex]g(x)=(x-2)^2+1[/tex]
Answer:
B. [tex]g(x)=(x-2)^2+1[/tex]
Step-by-step explanation:
The equation of the red graph is [tex]f(x)=x^2[/tex].
The blue graph has its vertex at (2,1)
Hence its equation is of the form;
[tex]g(x)=a(x-2)^2+1[/tex]
This graph has y-intercept (0,5).
[tex]5=a(0-2)^2+1[/tex]
[tex]5-1=a(-2)^2[/tex]
[tex]4=4a[/tex]
[tex]1=a[/tex]
The blue graph therefore has equation;
[tex]g(x)=(x-2)^2+1[/tex]
what is the distance ?
Pythagoras' Theorem
[tex]c^{2} =\sqrt{a^{2}+b^{2}}[/tex]
a = 5
b = 7
[tex]c^{2} =\sqrt{5^{2}+7^{2}}[/tex]
[tex]c^{2} =\sqrt{25+49}[/tex]
[tex]c^{2} =\sqrt{74}[/tex]
c = 8.6023252627c = 8.6 to 1d.p.
The distance is 8.6 units
Step-by-step explanation:see the image
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 4. If there were 6125 yes votes, what was the total number of votes?
Answer:
3,500 no votes
Step-by-step explanation:
There were 7 yes votes to every 4 no votes. There were a total of 6,125 yes votes, so set up a proportion to find the number of no votes
Let x represent the number of no votes
7 is to 4 as 6,125 is to x
We get
7/4 = 6,125/x
Now solve for x
First cross multiply
7x = 24,500
Divide both sides by 7 to isolate x..
x = 3,500 no votes
Two equations are given below:
m + 4n = 8
m = n − 2
What is the solution to the set of equations in the form (m, n)?
(4, 6)
(2, 4)
(0, 2)
(6, 8)
The solution to the set of equations is (0,2).
Reasoning:
m + 4n = 8 -> 0 + 4(2) = 8
m = n - 2 -> 0 = 2 - 2
Answer:
Yes, B is correct.
Step-by-step explanation:
aidan wants to run 10 miles. So far he has run 3/5 of those 10 miles. how many miles has aidan run
Answer:
6 miles
Step-by-step explanation:
PLS HELP! FREE POINTS! I NEED THIS QUESTION ANSWERED AS QUICK AS POSSIBLE!
What is the simplest form of the ratio 40 : 16?
A. 20 : 8
B. 10 : 4
C. 5 : 4
D. 5 : 2
E. 10 : 8
The answer is D 5:2
4:16
10:4
5:2
I just need to know if it’s right. Thanks!
You are correct! It’s C
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Check all that apply. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: 10/20 = x/1,500. 10x30/20x30=x/1,500. 300=x He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20x75=1,500
Answer:
1) He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
2) He did not multiply the numerator and denominator by the correct number to equal 1,500.
5) He should have multiplied the numerator and denominator by 75, not 30, because 20 x 75 = 1,500.
Step-by-step explanation:
Final answer:
Josiah made errors in predicting the number of rock songs on his MP3 player by not averaging the samples correctly and by using the wrong multiplication factor in his proportion calculation. The correct average should be 5, and he should have used a factor of 75 to scale his samples up to the total number of songs.
Explanation:
The student has used a proportion to predict the number of rock songs on his MP3 player based on a sample. However, the prediction method has a few mistakes that should be corrected for an accurate estimate.
Josiah's initial prediction did not consider averaging the number of rock songs from both samples, which would have given a better representation of the average occurrence in the sample set. The correct average is (4+6)/2 = 5 rock songs per sample.
The proportion set up by Josiah is 10/20 = x/1,500, which implies that the 10 rock songs in his samples represent half of all songs played. This should have been compared to the total number of songs on the MP3 player, 1,500, requiring him to multiply by a specific number. Yet, the multiplication factor used (30) was incorrect. To scale up 20 to 1,500, he should use the factor of 75, because 20 × 75 = 1,500.
The correct proportion should be 5/20 = x/1,500, which simplifies to 1/4 = x/1,500, and then x = 1,500/4 = 375. Hence, the predicted number of rock songs based on the sample should be 375.
The scatterplot shows the distance (in feet) that a person was from a motion sensor during an experiment in math class. Use the labeled points to create a linear model. About what distance in feet (y) would a person be 8 seconds after the experiment begins?
A.) 21ft
B.) 27ft
C.) 30ft
D.) 57ft
Answer:
B.) 27ft
Step-by-step explanation:
The labeled points given: (5,18) and (1.5, 7.5)
Slope = (18 - 7.5)/(5-1.5) = 10.5 / 3.5 = 3
A linear model:
y - 18 = 3(x - 5)
y - 18 = 3x - 15
y = 3x + 3
If x = 8 seconds then the distance in feet (y) would be: (plug in x = 8 into the equation y = 3x + 3)
y = 3(8) + 3
y = 24 + 3
y = 27 ft
Answer:
B.) 27ft
A person would be at a distance of 27 feet, 8 seconds after the experiment begins.
What is a scatter plot?A scatter plot diagram is a graph in which the coordinates of a point are marked and the regression or correlation between these points is observed.
A linear model for the given scatter plot can be made as shown below:The labeled points that are given are (5,18) and (1.5, 7.5)
m = Slope of the given scatter plot = (18 - 7.5)/(5 - 1.5)
= 10.5 / 3.5
= 3
The linear model of the scatter plot can be found by substituting the values of x and y using the labelled coordinates.
y - y_1 = m( x - x_1 )
y - 7.5 = 3(x - 1.5)
y - 7.5 = 3x - 4.5
y = 3x - 4.5 + 7.5
y = 3x - 3
The value of x is given as 8. Substitute x in the equation above:
y = 3(8) + 3
y = 24 + 3
y = 27 feet
Therefore, a person would be at a distance of 27 feet, 8 seconds after the experiment begins. The correct answer is option B.
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Simplify (x-5)(x^2-2x-6)
Answer:
x³ - 7x² + 4x + 30
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
x(x² - 2x - 6) - 5(x² - 2x - 6) ← distribute both parenthesis
= x³ - 2x² - 6x - 5x² + 10x + 30 ← collect like terms
= x³ - 7x² + 4x + 30
Anyone know how to solve this ?? I need help
Answer:
x = - 7, x = - 4
Step-by-step explanation:
To factor the quadratic
Consider the factors of the constant term ( + 28) which sum to give the coefficient of the x- term ( + 11)
The factors are + 7 and + 4, since
7 × 4 = 28 and 7 + 4 = 11, hence
(x + 7)(x + 4) = 0
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x + 4 = 0 ⇒ x = - 4
Which system of linear inequalities is represented by the graph?
Answer:
The system of inequalities is
[tex]y\leq -\frac{1}{3}x+2[/tex]
[tex]y>\frac{2}{3}x+3[/tex]
Step-by-step explanation:
step 1
Find the equation of the solid red line
Let
[tex]A(0,2),B(3,1)[/tex]
Find the slope
[tex]m=(1-2)/(3-0)=-1/3[/tex]
The equation of the line is
[tex]y=-\frac{1}{3}x+2[/tex]
The solution of the inequality is the shaded area below the solid red line
therefore
The inequality is
[tex]y\leq -\frac{1}{3}x+2[/tex]
step 2
Find the equation of the dashed blue line
Let
[tex]A(0,3),B(3,5)[/tex]
Find the slope
[tex]m=(5-3)/(3-0)=2/3[/tex]
The equation of the line is
[tex]y=\frac{2}{3}x+3[/tex]
The solution of the inequality is the shaded area above the dashed blue line
therefore
The inequality is
[tex]y>\frac{2}{3}x+3[/tex]
The system of inequalities is
[tex]y\leq -\frac{1}{3}x+2[/tex]
[tex]y>\frac{2}{3}x+3[/tex]
What is the value of X? show all of your work
Answer:
5
Step-by-step explanation:
We need to use Pythagoras' theorem.
For this we can use the pythagoras formula a^2+b^2=c^2 and rearrange this
We then will have 8^2+b^2=89
(because 89(sqrt) squared is 89)
We can then solve for what x is.
We take away 64 from 89 which is 25
the square root of 25 is 5
Therefore x=5
Examine the equation: 4x = 2 − y Which equation represents the equivalent equation in slope-intercept form?
Answer:
2 - y = 4x
y - 2 = -4x
y = -4x + 2
which number sentence is true?
Answer:
C
Step-by-step explanation:
You can reason your way through this without a calculator:
A: the absolute function turns everything positive, then you can see that 5/6 cannot be larger than 1 5/6
B: Realizing that √25=5, √18 cannot be larger than 5
C: 5.6x10³ means shifting to the left 3 positions: 5600 > 1000 so this one is true.
D: A negative number is always smaller than a positive number.
Answer:
Your answer would be C because simplified:
5,600 is greater than 1,00
Step-by-step explanation:
Your answer wouldn't be A because simplified:
0.833 > 1.833 is an incorrect statement.
Your answer wouldn't be B because simplified:
4.243 > 5.875 is an incorrect statement.
Your answer WOULD be C because simplified:
5,600 > 1,000 is a true statement
Your answer wouldn't be D because simplified:
-2.45 > 4.4 is an incorrect statement
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