Answer:
[tex]\large\boxed{y+3=\dfrac{3}{2}(x+4)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have
[tex]m=\dfrac{3}{2},\ (-4,\ -3)[/tex]
Substitute:
[tex]y-(-3)=\dfrac{3}{2}(x-(-4))\\\\y+3=\dfrac{3}{2}(x+4)[/tex]
The volume of a rectangular prism is (x3 – 3x2 + 5x – 3), and the area of its base is (x2 – 2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
Answer:
height = (x^3 – 3x^2 + 5x – 3) / (x^2 – 2)
Step-by-step explanation:
We know that the volume of a rectangular prism is the product of its base area and height
Volume_prism = area_base * height
height = Volume_prism / area_base
Volume_prism = (x^3 – 3x^2 + 5x – 3)
area_base = (x^2 – 2)
height = Volume_prism / area_base
height = (x^3 – 3x^2 + 5x – 3) / (x^2 – 2)
Please see attached image
Answer:
The answer is A
Step-by-step explanation:
The way that you get this answer is by divided x2 to x3 and you get x and then you multiply x to x2-2 and you get x3-2x and the you subtract that from x3-3x2+5x-3 and then you repeat that process and the final answer is x-3 + 7x-9/x2-2
the length and width of a rectangle are consecutive even integers. the area of the rectangle is 120 square units. what are the length and width of the rectangle
The length and width of the rectangle is 12 and 10 respectively.
Let the consecutive integers be :
a ; a+2Area of rectangle = Length × width
120 = a(a + 2)
120 = a² + 2a
a² + 2a - 120 = 0
a² - 10a + 12a + 120 = 0
a(a - 10) + 12(a - 10)
a = 10 or a = -12
The width cannot be negative, Hence, width = 10
Length = a + 2
Length = 10 + 2
Length = 12
The length and width of the rectangle is 12 and 10 respectively.
At summer camp the kids preformed 6 times over the last two days if the camp theater holds 35 people wich is the maximum number of people who watched the play
Answer:
35x6=210
Step-by-step explanation:
The 5 in 35 and times that by 6 is 30. So the ones place is 0.
Set aside the 3 and do 3x6 which is 18. but add 3 is 21. So the answer is 210.
Answer:
The answer is 420 people.
Step-by-step explanation:
Over the course of two days, the play was performed 6 times. So multiply 6 times 2 to get 12. The play was performed a total of 12 times in two days. Now multiply 12 times the number of maximum people who watched on both days to get 420.
What is the domain of the function y=2 sqrt x-6 ?
Answer
Domain of the function:
In interval notation: [6, ∞)
In set notation: {x: x∈R, x≥6}
Explanation
Remember that the the domain of the square root function are all the values such is is bigger than zero. We can express the later in set notation: {x: x∈R, x≥0}, or in interval notation: [0, ∞)
This is because the square root is not defined, in the real numbers, for negative values.
So, to find the domain of our function, we just need to set the thing inside the radical grater or equal than zero and solve for x:
The domain of the function is all the numbers bigger than 6, including 6.
Answer:
[6, infinity (use the symbol)
Step-by-step explanation:
i got this answer by graphing
How to do this question?
Answer:
D
Step-by-step explanation:
The answer is D, since there is no correlation in the data (meaning that it is scattered all over the plot with no pattern or anything).
Aisha has 45 books to place on a bookcase. She is told to place the same number of books on each of the 5 shelves. How many books should she place on each shelf ?
Answer: The correct answer is 9.
Step-by-step explanation: In order to solve this problem you need to divide the 45 books by the 5 book shelves. 45 / 5 = 9. Divided equally, there will be 9 books on each shelf.
[tex]45 \div 5 = 9[/tex]
Aisha can place 9 books on each shelf.
The vertex of this parabola is at (-1,-3). Which of the following could be it’s equation?
Answer:D
Step-by-step explanation: The vertex is (-1, -3), and since it's in terms of y, the y-coordinate is in the parentheses. D is the only choice with -3 as the y-coordinate.
The equation of the parabola with vertex (-1, -3) is y = a(x + 1)^2 - 3.
Explanation:The equation of a parabola in vertex form is y = a(x - h)^2 + k, where the vertex is (h, k). In this case, the vertex is (-1, -3), so the equation could be y = a(x + 1)^2 - 3. The coefficient a determines the shape of the parabola.The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape. If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.
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Simply the expression given below. x^2+x-2/x^3-x^2+2x-2
Answer:
Step-by-step explanation:
(x-1)(x+2)/x^2(x-1)+2(x-1)
(x-1)(x+2)/(x-1)(x^2+2)
(x+2)/(x^2+2)
Answer:
[tex]\frac{(x+2)}{(x^2+2)}[/tex]
Step-by-step explanation:
[tex]\frac{x^2+x-2}{x^3-x^2+2x-2}[/tex]
To simplify the given expression , factor both numerator and denominator
Numerator : [tex]x^2+x-2[/tex]
Product is -2 and sum is +1. factors are 2 and -1
[tex]x^2+x-2=(x+2)(x-1)[/tex]
Denominator : [tex]x^3-x^2+2x-2[/tex]
Group first two terms and last two terms
Factor out GCF from each term
[tex](x^3-x^2)+(2x-2)[/tex]
[tex]x^2(x-1)+2(x-1)[/tex]
[tex](x^2+2)(x-1)[/tex]
Replace the factors in the given expression
[tex]\frac{(x+2)(x-1)}{(x^2+2)(x-1)}[/tex]
Cancel out x-1 at the top and bottom
[tex]\frac{(x+2)}{(x^2+2)}[/tex]
Five people each write a positive integer on a piece of paper. If the average of these five integers is 8, what is the greatest possible value of one of these integers?
A. 36
B. 38
C. 39
D. 40
Answer:
Option D. [tex]40[/tex]
Step-by-step explanation:
Let
x------>the greatest possible value
we know that
If four people write the number zero, then the average will be
[tex]8=(0+0+0+0+x)/5\\ \\40=0+x\\ \\x=40[/tex]
Answer: 36
Step-by-step explanation:
Which range is the best estimate for capacity in the fluid ounces of a water bottle
Answer:
K is the best estimate.
Step-by-step explanation:
This is just common sense, not much math.
J: No, that is smaller than an essential oils bottle, which is as tall as a finger.
K: Probably, the range is from the size of a medicine bottle to a small/medium water bottle.
L: No, that much is the size of a bottle of detergent.
M: No, that much water is 6 kg.
What is the standard form equation of the line shown below?
Which function is shown on the graph?
ANSWER
The correct choice is C.
EXPLANATION
The given graph has vertical asymptote at x=1.
Therefore , the denominator of the function represented by the graph should be 1-x
The graph also has a horizontal asymptote at y=-6. The numerator should be of the form
b+6x,
where b is a constant.
So that the horizontal asymptote will be
[tex]y = \frac{6}{ - 1} = - 6[/tex]
Our rational function now becomes
[tex]y = \frac{b + 6x}{1 - x} [/tex]
The function also has a y-intercept of 3,
[tex]3 = \frac{b + 6(0)}{1 - 0} = b[/tex]
Therefore the required function is
[tex]y = \frac{3 + 6x}{1 - x} [/tex]
When developing a plan for a proof, it is important to look at the "given" information. True False
Answer:
Yeah true
Step-by-step explanation:
Because it makes sense
It is true that when developing a proof, focusing on the "given" information is crucial as it forms the foundation of the logical argument leading to the conclusion that needs to be proven.
When developing a plan for a proof, it is indeed important to look at the "given" information. This is true because in the context of mathematical proofs, the "given" information represents the starting point from which you will build you argument to reach a conclusion. These are the facts, definitions, or previously proven theorems that can be used in establishing the validity of the statement you are tasked to prove.
To develop a successful proof, one generally follows a systematic approach:
Identify the given information in the problem.Analyze what the problem is asking you to find or prove.Consider what principles, theorems, or rules apply based on the given information.Develop a logical sequence of steps that connects the given information to the conclusion you are trying to reach.This structured approach to problem-solving involves using what you know to logically arrive at a conclusion that was previously unknown or needs to be proven. This method not only applies to mathematics but also to other fields that require logical reasoning and evidence-based conclusions.
A $1508 award is shared equally by 8 people. What is each persons share of the award
Answer:
$188.50
Step-by-step explanation:
i got this answer by dividing $1,508 by 8 and you would get 188.5 which would turn into $188.50 and that is how much each person would get.
I hope this helps.
Carrie started a 12 ounces of water when finish drinking she had 2 1/4 how much did she srink
Answer:
She drank 12 ounces so, 12 minus 2 1/4 = 9 3/4 ounces of water.
Step-by-step explanation:
Help pleaseee! Relationships within triangles posttest
It’s 88 cause if you see in the other side is 44+44 and what does That Equal =88
HELP ASAP!! GIVING BRAINLIEST!
ABC goes through a sequence of transformations to form A’B’C’. The sequence of transformations involved is a:
A) rotation 180 degrees counterclockwise about the origin
B) translation 2 units to the right
C) translation 4 units to the left
D) reflection across the line y=x
followed by a:
A) reflection across the x-axis
B) reflection across the y-axis
C) rotation 90 degrees clockwise about the origin
D) translation 4 units to the right
Answer:
B) translation 2 units to the right
B) reflection across the y-axis
Step-by-step explanation:
If you move ABCD over to the right by 2, then reflect it over the y axis. Then you get the A'BCD.
ABC goes through a sequence of transformations to form A'B'C'. The sequence of transformations involved are
B) translation 2 units to the right and followed by a
B) reflection across the y-axis
This can be explained by using the graph and the definition of transformation
Transformations:Transformations are changes done in the shapes on a coordinate plane There are four types of transformations. They are translation, rotation, reflection, and dilationThe translation is moving a function in a specific direction, rotation is spinning the function about a point, reflection is the mirror image of the function, and dilation is the scaling of a functionThe translation, rotation, and reflection are called rigid transformations wherein the image is congruent to its pre-image. These are isometric transformationsDilation stretches or shrinks the pre-image i.e., expands or contracts the shape. It is non-isometric.The sequence of transformations involved:From all the information given above, it came to know that the sequence of transformations involved in transforming ABC to A'B'C' is translation and reflection.ABC is translated by 2 units to the right, it is shown in the graphAnd followed by a reflection across the y-axisThere is no rotation happenedThus, from the graph it is clear that the sequence of transformations involved is B) translation by 2 units to the right and followed by a B) reflection across the y-axis.
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find the area of each figure. round to the nearest tenth if necessary .
We first would divide the Pentagon into two shapes, one a square and the other a triangle. To find the height of the triangle we must minus the 15cm to the 10cm, which gives us 5cm.
5cm= height of triangle
7cm= base of triangle
Then, apply the area of triangle formula
which is: A=(b×h)÷2
so the area would be 17.5cm squared.
For the square, 10= height and the 7=base
The formula for rectangles is:
A=b×h
so, the area is 70cm squared.
if you want the total area add the two area together, which equals 87.5cm squared.
I hope this helps.
To find the area of each figure, we can use different formulas depending on the shape. If the figure is a square or rectangle, we can use the formula A = length x width. If the figure is a circle, we can use the formula A = πr², where r is the radius.
Explanation:To find the area of each figure, we can use different formulas depending on the shape. If the figure is a square or rectangle, we can use the formula A = length × width. If the figure is a circle, we can use the formula A = πr², where r is the radius. For triangles, we can use the formula A = ½base × height. For irregular shapes, we can approximate the area by breaking it down into simpler shapes and summing up their areas.
Let's say we have a square with side length 5 cm. Using the formula A = length × width, the area would be A = 5 cm × 5 cm = 25 cm². If we have a circle with a radius of 2 cm, using the formula A = πr², the area would be A = 3.14 × 2 cm × 2 cm = 12.56 cm² (rounded to the nearest tenth).
is 0.64 rational ....
yes, 0.64 is a rational number. it can be expressed as the fractions 64/100, 32/50, 16/25.
Answer:
yes 0.64 is a rational number
Step-by-step explanation:
1) 0.64 = 64/100
2) Divide by 4
64 divided by 4 is 16 (Numerator)
100 divided by 4 is 25 (Denominator)
3) 16/25
It is a rational number because it can be written as a fraction.
Hopes this helps!
which of the following is the solution to |10x|>-2
Let's reason through it.
We are given the inequality that says, in English, that the absolute value of ten times x is greater than -2.
Let's consider three cases:
x is negative
- When x is negative the number in the absolute value will be negative. But because it is inside the absolute value, the number becomes positive. Therefore, for any x that is negative (however small or large), the left side will be positive. Any positive value (however small) is greater than a negative value, so the inequality is satisfied in this case.
x is positive
- When x is positive, the number inside the absolute value will be positive. The absolute value of a positive number is itself, so the left hand side will be positive again. Then, for all positive values of x (however small or large), the inequality will be satisfied because any positive value is larger than -2.
x is zero
- Even in the case of zero, when the left hand side will be zero, the equality is satisfied. This is because zero is greater than -2. If this doesn't immediately make sense, imagine the two numbers on the number line. 0 is to the right of -2, so it is larger.
Since we cannot find a value for x that does not satisfy the inequality, the solution to the inequality is all values of x. See the attached image.
Answer:
All values are solutions
Step-by-step explanation:
How many unique ways are there to arrange the letters in the word SONG
Words you can make with the word SONG:
Snog
Nogs
m–[(m–n)÷(−2)](−5), if m=−4, n=−6
[tex] - 4 - (( - 4 + 6) \div ( - 2))( - 5) = \\ = - 4 - (2 \div ( - 2))( - 5) = \\ = - 4 - ( - 1)( - 5) = - 4 - 5 = \\ = - 9[/tex]
The answer is M-5
Step-by-step explanation:See the image
A rectangle has a perimeter of p centimeters. Its width is b centimeters. Its length is double its width. Express p in terms of b.
Answer:
[tex]p=6b[/tex]
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
The perimeter of rectangle is equal to
[tex]P=2(x+y)[/tex]
[tex]P=p\ cm[/tex]
so
[tex]p=2(x+y)[/tex] -----> equation A
[tex]y=b\ cm[/tex] ----> given problem
[tex]x=2y[/tex] -------> [tex]x=2b\ cm[/tex]
substitute the value of x and the value of y in the equation A
[tex]p=2(2b+b)[/tex]
[tex]p=2(3b)[/tex]
[tex]p=6b[/tex]
Ray's Car Wash received $25 for washing 5 cars. How much money does Ray's Car Wash earn per car?
Answer:
$5
Step-by-step explanation:
25/5=5
$5
Wouldn’t it be 5$ a person to pay for a car wash? Because if you think of it this way they made 25$ and it cost 5$ so you would take 25 divided by five . Please correct me if I’m wrong
If g=26.4 and f=35 degrees, find h. round to the nearest tenth
Answer:
Option b. [tex]h=21.6\ units[/tex]
Step-by-step explanation:
we know that
In the right triangle FGH
The function cosine of angle F is equal to divide the adjacent side angle F by the hypotenuse
[tex]cos(F)=\frac{FG}{FH}[/tex]
substitute the values and solve for h
[tex]cos(35\°)=\frac{h}{26.4}[/tex]
[tex]h=(26.4)cos(35\°)=21.6\ units[/tex]
Rewrite the equation 2x + 3y = 6 in slope-intercept form. 3y = -2x + 6 y = -2x + 6 y = -2/3x + 2 y = 2x + 6
Answer:
y = -2/3x + 2
Step-by-step explanation:
2x + 3y = 6 to y = mx + b form.
1. Subtract 2x from both sides.
3y = -2x + 6
2. Divide each side by 3.
y = -2/3x + 2
Answer:
y = -2/3x + 2
Please help!! I’ll mark brainliest
The triangle was only rotated. The size did not change, so the corresponding angles would remain identical.
Because C is 28 degrees C' would also be 28 degrees.
Which expression would provide the measure of angle N?
A) tan (7/6)
B) tan (6/7)
C) tan -1(7/6)
D) tan -1(6/7)
Answer:
[tex]N = { \tan }^{ - 1} \frac{6}{7} [/tex]
The correct answer is D.
Which function represents the sequence?
11
Question 11 options:
f(n)=n+3
f(n)=7n−4
f(n)=3n+7
f(n)=n+7
Answer: SECOND OPTION
Step-by-step explanation:
Substitute any value of n shown in the table attached into each function given in the options, and observe if you obtain the value of [tex]a_n[/tex] shown in the table.
Let's substitute n=1 (According to the table, you need to obtain [tex]a_n=3[/tex]):
For the first option:
[tex]f(1)=1+3=4[/tex]
For the second option:
[tex]f(1)=7(1)-4=3[/tex] THIS IS THE FUNCTION
For the third option:
[tex]f(1)=3(1)+7=10[/tex]
For the fourth option:
[tex]f(1)=1+7=8[/tex]
Therefore, the answer is the second option.
ANSWER
[tex]f(n) = 7n - 4[/tex]
EXPLANATION
The terms of the sequence are;
[tex]3,10,17,24,31,...[/tex]
This implies that,
[tex]a_1=3[/tex]
The constant difference is
[tex]d = 10 - 3 = 7[/tex]
The nth term of the sequence is;
[tex]a_n=a_1+d(n-1)[/tex]
[tex]a_n=3+7(n-1)[/tex]
[tex]a_n=3+7n - 7[/tex]
[tex]a_n=7n-4[/tex]
Or
[tex]f(n) = 7n - 4[/tex]
The correct choice is B.
dry cleaning bill is shown by y equals 1.50 x + 4.50 y is the total cost and x is the number of shirts graph this equation
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
y------> the total cost
x------> the number of shirts
we know that
The linear equation is
[tex]y=1.50x+4.50[/tex] ------> equation of the line
To graph the line find the intercepts
The y-intercept is the value of y when the value of x is equal to zero
The x-intercept is the value of x when the value of y is equal to zero
Find the y-intercept
For x=0
[tex]y=1.50(0)+4.50=4.50[/tex]
The y-intercept is the point (0,4.50)
Find the x-intercept
For y=0
[tex]0=1.50x+4.50[/tex]
[tex]1.50x=-4.50[/tex]
[tex]x=-4.50/1.50=-3[/tex]
The x-intercept is the point (-3,0)
Plot the intercepts to graph the line
see the attached figure