the answer is b= a+ c+d
Answer:
b = \(\frac{d-c}{a}\)
Step-by-step explanation:
ab + c = d
-c -c
ab = d - c
÷a ÷a
b = \(\frac{d-c}{a}\)
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Avery checked her outdoor thermometer below on a cold winter morning.
What is the opposite of this temperature?
Answer:
5 degrees Fahrenheit.
Step-by-step explanation:
The temperature shows -5 degrees Fahrenheit. The opposite of a negative number is a positive number, so the opposite of the temperature is 5 degrees.
What is the first common factor of 6 and 8.25?
Answer:
omo
___
Step-by-step explanation:
1 PROBLEM *BRAINLIEST* FOR CORRECT ANSWER
this is graphing quadratic equations. use an x/y chart to graph with 5+ points on it.
problem: y = x^2 + 4x + 6
there's an image with the problem as well as the graph if that helps you. i know how to graph, i really just need those five points (if yk what you're doing, this should make sense)
THANK YOU!!!!
To graph y = x² + 4x + 6 with 5+ points using an x/y chart, follow these steps:
Step 1: Create an x/y chart with five rows and two columns. Label the first column x and the second column y.
Step 2: Choose five values for x. You can choose any values you want as long as you plug them into the equation in the next step. In this example, we will use -3, -2, -1, 0, and 1. Write these values in the first column of your chart.
Step 3: Plug each value of x into the equation y = x² + 4x + 6 to find the corresponding value of y. Write these values in the second column of your chart. To make it simpler, here are the calculations for each point:When x = -3: y = (-3)² + 4(-3) + 6 = 3When x = -2: y = (-2)² + 4(-2) + 6 = 2When x = -1: y = (-1)² + 4(-1) + 6 = 1When x = 0: y = (0)² + 4(0) + 6 = 6When x = 1: y = (1)² + 4(1) + 6 = 11
Step 4: Plot each point on the x/y chart. The x value goes on the horizontal axis (x-axis) and the y value goes on the vertical axis (y-axis). Once you have plotted all five points, connect them with a smooth curve to create the graph of y = x² + 4x + 6. The graph is shown in the figure below.
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For these problems, determine the number of zeros using the discriminant, then solve using the quadratic formula. Leave your answer in simplified radical form, if necessary.
1. y = x^2 + 5x - 15
2. y = 2x^2 + 16x + 32
3. y = x^2 + 18x + 4
4. y = x^2 - 24x - 6
1. The number of zeros for y = x² + 5x - 15 is 2 zeros and the solution is x = (-5 ± √85)/2.
2. The number of zeros for y = 2x² + 16x + 32 is 1 zero and the solution is x = -4.
3. The number of zeros for y = x² + 18x + 4 is 2 zeros and the solution is x = -9 ± √308/2.
4. The number of zeros for y = x² - 24x - 6 is 2 zeros and the solution is x = 12 ± √600/2.
What is a quadratic equation?In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
In this scenario, we would determine the number of zeros by using the discriminant formula as follows;
Discriminant, D = b² - 4ac
Question 1:
y = x² + 5x - 15
Discriminant, D = 5² - 4(1)(-15)
Discriminant, D = 25 + 60
Discriminant, D = 85
85 > 0 (2 zeros).
For the solution, we have:
\(x = \frac{-(5)\; \pm \;\sqrt{(5)^2 - 4(1)(-15)}}{2(1)}\)
x = (-5 ± √85)/2.
Question 2:
y = 2x² + 16x + 32
Discriminant, D = 16² - 4(2)(32)
Discriminant, D = 256 - 256
Discriminant, D = 0
0 = 0 (1 zero).
For the solution, we have:
\(x = \frac{-(16)\; \pm \;\sqrt{(16)^2 - 4(2)(32)}}{2(2)}\)
x =-16/4
x = -4
Question 3:
y = x² + 18x + 4
Discriminant, D = 18² - 4(1)(4)
Discriminant, D = 324 - 16
Discriminant, D = 308
308 > 0 (2 zeros).
For the solution, we have:
\(x = \frac{-(18)\; \pm \;\sqrt{(18)^2 - 4(1)(4)}}{2(1)}\)
x = (-18 ± √308)/2.
x = -9 ± √308/2
Question 4:
y = x² - 24x - 6
Discriminant, D = (-24)² - 4(1)(-6)
Discriminant, D = 576 + 24
Discriminant, D = 600
600 > 0 (2 zeros).
For the solution, we have:
\(x = \frac{-(-24)\; \pm \;\sqrt{(-24)^2 - 4(1)(-6)}}{2(1)}\)
x = (24 ± √600)/2.
x = 12 ± √600/2
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7. Find the value of x.
Help please??
Answer: which one
Step-by-step explanation:
13. The grocery store sells 4 donuts for $3.00. The gas station sells a dozen for $8.75.
a) What is the price per donut at the grocery store?
0.75
b) What is the price per donut at the gas station?
13
c) Which store has the better deal?
The gas station has a better deal because if you got 12 donuts from the grocery store you would spend $9 but to get 12 donuts from the gas station it is only $8.75
If anyone knows please help asap!!
Answer:
u
Step-by-step explanation:
it is undefined because its a vertical line.
Answer:
slope is undefined u
Step-by-step explanation:
Calculate the slope m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (1, - 3 ) and (x₂, y₂ ) = (1, 0 )
m = \(\frac{0-(-3)}{1-1}\) = \(\frac{0+3}{0}\) = \(\frac{3}{0}\)
Since division by zero is undefined then the slope of the line is undefined
when group a loses an item or items to group b even though group a's population grew at a faster rate than group b's, the _______ paradox occurs.
When Group A loses an item or items to Group B even though Group A's population grew at a faster rate than Group B's, the Simpson's Paradox occurs.
This statistical anomaly happens when a trend appears in different groups of data, but disappears or reverses when the groups are combined. It is crucial to consider the context and variables involved when analyzing data, as the Simpson's Paradox may lead to incorrect conclusions if only aggregate data is examined.
This paradox serves as a reminder to always investigate the underlying factors that may influence statistical results.
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find the scalar and vector projection of the vector b=⟨−3,−1,4⟩ onto the vector a=⟨−3,1,−5⟩ . scalar projection (i.e., component): vector projection ⟨ , ,
The scalar projection of b onto a is: Scalar projection -2.
The vector projection of b onto a is: Vector projection ⟨6/7, -2/7, -20/7⟩.
What are the scalar and vector projections of the vector b onto the vector a?First, we can find the scalar projection (or component) of b onto a using the formula:
proj_a(b) = (b . a) / ||a||
where "b . a" represents the dot product of vectors b and a,
and "||a||" is the magnitude of vector a.
We have:
b . a = (-3)(-3) + (-1)(1) + (4)(-5) = 9 - 1 - 20 = -12||a|| =√((-3)² + 1² + (-5)²) = √(35)So, the scalar projection of b onto a is:
proj_a(b) = (-12) /√(35)
To find the vector projection of b onto a, we can use the formula:
proj_v(a, b) = (b . a / ||a||²) * a
Using the values we found earlier, we get:
proj_v(a, b) = ((-12) / 35) * ⟨-3, 1, -5⟩
Simplifying, we get:
proj_v(a, b) = ⟨36/35, -12/35, 60/35⟩ = ⟨(12/35) * 3, (-12/35) * 1, (12/7) * 5⟩
So, the vector projection of b onto a is ⟨(12/35) * -3, (-12/35) * 1, (12/7) * -5⟩, which simplifies to ⟨-36/35, -12/35, -60/7⟩.
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What is the median of the data shown?
Heights of the Members of Ms. Smith's Class
(in inches)
68
69
71
71
71
73
74
75
75
78
71
72.5
72
78
Simplify following:
(5X^6×p^2)×(9xp^3)
The simplified form of the given expression is 45 \(x^{6} p^{5}\) .
What is an expression?
One or more arithmetic operations, at least two additional variables or integers, and the expression's own elements make up a mathematical expression.
We are given an expression which is as follows :
(5\(x^{6}\)\(p^{2}\)) × (9\(p^{3}\))
Now, on simplifying this, we get
⇒ 45 \(x^{6} p^{2} p^{3}\) (By multiplying the two terms)
We know that exponents which have the same base can be added.
So, in the expression p is the same base with powers 2 and 3.
So, on adding the powers, we get
45 \(x^{6} p^{5}\)
Hence, the simplified form of the given expression is 45 \(x^{6} p^{5}\) .
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Can someone please help me
Answer:
x, 4 y, 3, z2
Step-by-step explanation:
When children create an imaginary town with various blocks and figurines, they are learning:
When children create an imaginary town with various blocks and figurines, they are learning through play and engaging in important cognitive and social development processes.
1. Imagination and Creativity: Building an imaginary town involves using their imagination and creativity to create a world of their own. This helps children develop their cognitive skills by coming up with ideas, planning and problem-solving.
2. Language and Communication: During play, children may engage in pretend conversations and storytelling, which helps enhance their language skills and vocabulary. They may also negotiate and cooperate with others, improving their social communication skills.
3. Fine Motor Skills: Manipulating blocks and figurines requires the use of fine motor skills. Children practice hand-eye coordination, dexterity, and control while building and arranging their town.
4. Social Skills: Collaborating with others in creating the town encourages teamwork, sharing, and turn-taking. Children learn to negotiate, compromise, and solve conflicts, promoting social and emotional development.
5. Cognitive Development: Creating an imaginary town involves categorization, spatial awareness, and problem-solving skills. Children learn to organize and categorize blocks, create different structures, and explore cause-and-effect relationships.
In conclusion, when children engage in creating an imaginary town with blocks and figurines, they develop various skills such as imagination, creativity, language, fine motor, social, and cognitive skills. Through this play activity, children learn and grow in multiple ways, contributing to their overall development.
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determine f(x) and f(x) for the following function. then give the horizontal asymptotes of f, if any. f(x)=4x/8x 6
The function f(x) is defined as f(x) = 4x/8x-6.
This can be simplified to f(x) = 1/2x-3. The horizontal asymptote for this function is y = 0, as its denominator approaches 0 as x approaches infinity or negative infinity.The function f(x) is defined as f(x) = 4x/8x-6. To find the vertical asymptote, we need to set the denominator to 0. We can solve this equation to find that the vertical asymptote of f(x) is x = 6. This means that as x approaches the value of 6, the function approaches infinity. Therefore, the horizontal asymptote of this function is y = 0 and the vertical asymptote is x = 6.
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simplified ration of squares to total shapes is 6:16 for every 3 squares there are how many total shapes there fore the simplified ratio of squares to total shape is what
For every 3 squares, there are 5 total shapes. Therefore, the simplified ratio of squares to total shapes is 3 : 5.
What is the simplified ratio of squares to total shapes?If the unsimplified ratio of squares to total shapes is 6 : 16, then we can express this as 6/16, then,we can simplify this ratio by dividing both the numerator and denominator by 2, giving us 3/8.
This means that for every 3 squares, there are 5 total shapes. Therefore, the simplified ratio of squares to total shapes is 3 : 5.
Full question "Unsimplified ratio of squares to total shapes: 6 : 16. For every 3 squares, there are ____ total shapes; Therefore, the simplified ratio of squares to total shapes is __ : __.
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Four friends all five each other presents
The total cost of presents is £80.52
Work out the mean cost of presents in pounds
Step-by-step explanation:
Four friends all give each other presents. The total cost of the presents is £80.52. We need to find the mean cost of a present in pounds. So, the mean cost of a present is equal to 20.13 .
a rectangle has a length m less than twice its width. when m are added to the width, the resulting figure is a square with an area of . find the dimensions of the original rectangle.
Let's start by setting up some equations based on the given information.
Let's call the width of the rectangle "w" and the length "l". We know that:
l = 2w - m (since the length is "m less than twice its width")
When we add "m" to the width, we get a square with an area of:
(w + m)^2 =
We can set up another equation based on the fact that the area of the original rectangle is:
A = lw =
Now, we can use the information we have to solve for the dimensions of the original rectangle. We can start by simplifying the equation for the area of the square:
(w + m)^2 =
w^2 + 2wm + m^2 =
Now we can substitute our expression for "l" in terms of "w" and "m":
w(2w - m) =
Expanding this out gives us:
2w^2 - wm =
We can substitute this expression for "lw" in our equation for the area of the square:
2w^2 - wm =
w^2 + 2wm + m^2 =
Now we can simplify this equation by expanding out the square on the left side:
2w^2 - wm =
w^2 + 2wm + m^2 =
2w^2 - wm =
w^2 + 2wm + m^2 =
w^2 + wm + m^2 =
Now we can solve for "m" by subtracting the first equation from the second:
3wm + m^2 =
Subtracting "w^2" from both sides gives us:
wm + m^2 =
Now we can solve for "m" using the quadratic formula:
m =
We can use this value for "m" to solve for the dimensions of the original rectangle. Substituting into our equation for "l" in terms of "w" and "m", we get:
l = 2w - m =
And substituting into our equation for the area of the rectangle, we get:
A = lw =
So the dimensions of the original rectangle are:
Width: w =
Length: l =
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Which represents a function ?
Answer:
The answer is A. Both 1 and 4
Step-by-step explanation:
The equation of line u is y = 9/2x+1. Line v is perpendicular to u. What is the slope of line v
Answer:
Step-by-step explanation:
The slope of line u is 9/2; the line perpendicular to that is the opposite reciprocal...opposite sign and the flip of the fraction. The perpendicular slope is -2/9
What is the equation of the line that passes through the point (4, -6) and has a
slope of -5/2?
Answer:
In slope-intercept form:
\( y = - \frac{5}{2} x + 4\)
In standard form:
\(5x + 2y = 8\)
Step-by-step explanation:
\( - 6 = - \frac{5}{2} (4) + b\)
\( - 6 = - 10 + b\)
\(b = 4\)
\(y = - \frac{5}{2} x + 4\)
\( - 2y = 5x - 8\)
\( - 5x - 2y = - 8\)
\(5x + 2y = 8\)
Solve step by step 249×625
Answer:
155625 is the answer.
Step-by-step explanation:
add astre#6666 on discord for the step by step
A roller coaster can hold 32 people at a time. There are 275 people waiting to ride the roller coaster. How many trips will the roller coaster have to make for all the people to ride?
Answer:
9
Step-by-step explanation:
275 divided by 32 in equal to 8.59, so you just have to round up but that last trip just wont be full
Answer:
9 roller coaster rides. hope this helps!
Step-by-step explanation:
A roller coaster can hold 32 people at a time.
there are 275 people waiting in line.
How many trips will it take for there to be 0 people waiting in line?
We know the roller coaster can hold 32 people at a time, and 275 people are waiting in line.
275/32=8 rides and 19 people left.
If you don't know how to do that: 275 people at first. 275-32 because the roller coaster can only hold 32. Repeat that process untill you find your answer.
So we have 8 rides, and 19 people left? It doesn't matter, It will not take, half the time left, or more time to get it done. So anything below or equal to 32 people will take the same amount of time. So our final answer is 9 rides. Not 8.59375.
Which equation can be used to find y, the year in which both bodies of water have the same amount of mercury? 0.05 – 0.1y = 0.12 – 0.06y 0.05y 0.1 = 0.12y 0.06 0.05 0.1y = 0.12 0.06y 0.05y – 0.1 = 0.12y – 0.06
The equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.
In the question, we have been asked for the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury.
First, we will find the equations showing the level of mercury in each body of water.
For the first water body:
Initial measure of mercury = 0.05 ppb.
Rate of rising = 0.1 ppb each year.
Number of years = y.
Thus, the equation showing level of mercury = 0.05 + 0.1y.
For the second water body:
Initial measure of mercury = 0.12 ppb.
Rate of rising = 0.06 ppb each year.
Number of years = y.
Thus, the equation showing level of mercury = 0.12 + 0.06y.
We are looking for the equation, to find y, the year in which both bodies of water have the same amount of mercury.
As they will have the same amount of mercury, their respective equations showing the level of mercury should be equal, that is:
0.05 + 0.1y = 0.12 + 0.06y, which is the required equation.
Thus, the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.
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For the complete question, refer to the attachment.
Look at pic for question and answer choices.
Natalie is completing construction of an equilateral triangle inscribed in a circle, as shown below. What should be the next step in her construction?
B
O Construct a line perpendicular to the line AB to create four congruent quadrants.
O Construct six equal sections around the circle using the original radius as a guide.
O Construct another point C anywhere on the circle to be the third vertex of her triangle.
O Draw arcs above and below line AB to show where the triangle sides meet.
Z
The next step she should take is to draw arcs above and or below line AB to show where the triangles sides meet.
Steps in construction of an equilateral triangleThe steps involved in the construction of an a equilateral triangle are:
Place the compass point on A and measure the distance to point BSwing an arc of this size above or below of the segment.Do not change the span on the compassThen place the compass point on B and swing the same arc, intersecting with the first arcLabel the point of intersection as the third vertex of the equilateral triangle.Thus, the next step she should take is to draw arcs above and or below line AB to show where the triangles sides meet.
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ow many groups of
1
5
5
1
start fraction, 1, divided by, 5, end fraction are in
4
44?
By the calculations below, there are 20 groups of 1/5 in 4.
Division of Fractions: Finding GroupsTo find out how many groups of 1/5 are in 4, we can use the concept of division of fractions.
Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the problem as:
4 ÷ 1/5
To find the reciprocal of 1/5, we flip the fraction:
1/5 → 5/1
Now, we can rewrite the division problem as multiplication:
4 ÷ 1/5 = 4 × 5/1
Multiplying across gives:
4 × 5/1 = 20
Therefore, there are 20 groups of 1/5 in 4.
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The probability of a student spending time reading is 0.59, and the probability of a student doing well on an exam and spending time reading is 0.58. What is the probability of a student doing well on an exam given that the student spends time reading
The probability of a student doing well on an exam given that they spend time reading is approximately 0.983 or 98.3%.
To calculate the probability of a student doing well on an exam given that the student spends time reading, we need to use conditional probability.
Let's denote:
P(R) as the probability of a student spending time reading (P(R) = 0.59),
P(E) as the probability of a student doing well on an exam (P(E)),
P(E|R) as the probability of a student doing well on an exam given that they spend time reading (P(E|R) = 0.58).
The formula for conditional probability is:
P(E|R) = P(E and R) / P(R).
Given that P(E and R) = 0.58 (the probability of a student doing well on an exam and spending time reading) and P(R) = 0.59 (the probability of a student spending time reading), we can substitute these values into the formula:
P(E|R) = 0.58 / 0.59 = 0.983.
Therefore, the probability of a student doing well on an exam given that the student spends time reading is approximately 0.983 or 98.3%.
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Determine the measure of angle j 10x-20
Therefore, both angles have a measure of 60 degrees.
What is angle?An angle is a geometric figure formed by two rays (or two line segments) that share a common endpoint, called the vertex of the angle. The rays or line segments that form the angle are called the sides of the angle. The size of an angle is measured in degrees, where one degree is 1/360th of a full rotation around a point. Angles are commonly used in geometry, trigonometry, and many other areas of mathematics and science.
Here,
To find the measure of each angle, we need to solve the equation:
10x - 20 = 7x + 4
First, we can simplify the equation by combining like terms:
10x - 7x = 4 + 20
3x = 24
Next, we can solve for x by dividing both sides by 3:
x = 8
Now that we know x, we can find the measure of each angle by substituting x = 8 into the expressions given:
10x - 20 = 10(8) - 20 = 60
7x + 4 = 7(8) + 4 = 60
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Complete question:
Find the measure of each angle.
10x - 20= 7x + 4
ASAP HELP
Find the variance and standard deviation of the data set below:
0 0.107
1 0.352
2 0.400
3 0.141
If the standard deviation of a set of data is 6, then the value of variance is 36
The formula for determining variance is variance = √Standard deviation
Variance of a set of data is equal to square of the standard deviation.
If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula
variance = √Standard deviation
Take square root on both sides
Standard deviation² = 6²
Standard deviation= 36
Hence, standard deviation of a set of data is 6, then the value of variance is 36
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Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4.
After she rolls it 20 times, how many times does she roll the number 3?
A. 3
B. 5
C. 6
D. It is impossible to tell.
To find the expected number of times Joan rolls a 3, we use the formula for mean of a binomial distribution.
The correct option is, option (C) 6.
The probability of rolling a number 3 on any given roll is 1/4
If Joan rolls the die 20 times, the number of times she rolls a 3 will follow a binomial distribution with n = 20 (number of trials) and p = 1/4 (probability of success).
The formula for the probability mass function of a binomial distribution is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where X is the random variable representing the number of successes (the number of times Joan rolls a 3), k is the number of successes, n is the number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.
Using this formula, we can calculate the probability of rolling a 3 exactly k times out of 20 rolls:
P(X=k) = (20 choose k) * (1/4)^k * (3/4)^(20-k)
To find the expected number of times Joan rolls a 3, we can use the formula for the mean of a binomial distribution:
E(X) = n * p
In this case, E(X) = 20 * 1/4 = 5
Therefore, the expected number of times Joan rolls a 3 is 5.
Since the possible answers are integers, the closest answer to 5 is 6. Therefore, the answer is (C) 6.
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