y - 5 = -1 ( x + 3 ) is Equation of a Lin in slope intercept form,.
What is in slope-intercept form?
Given the slope of the line and the intercept it forms with the y-axis, the slope intercept form in mathematics is one of the forms used to determine the equation of a straight line. Y = mx + b is the slope intercept form, where m is the slope of the straight line and b is the y-intercept.Slope between the points M(-3, 5) and N(2, 0).
m = 0 - 5/2 + 3
m = -5/5 = -1
the equation of point-slope form
y - y₁ = m ( x - x₁ )
y - 5 = -1 ( x - ( -3 ))
y - 5 = -1 ( x + 3 )
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Write an equation of the line passing through the point (2, -9) that is perpendicular to the line V=x+6.
The equation of the line that is perpendicular to y = x + 6 is expressed as: y = -x - 7
How to Write the Equation of a Line?The equation of a line can be written as y = mx + 1. The value of m is the slope while the value of b is the y-intercept.
The slopes of two lines that are perpendicular to each other are negative reciprocals. This means, if we multiply their slope values together, we will get -1.
Given the line, y = x + 6, the slope of the line is 1. The slope of the line it is perpendicular to is -1, because -1 is the negative reciprocal of 1.
Substitute m = -1 and (x, y) = (2, -9) onto y = mx + b to find the value of b:
-9 = -1(2) + b
-9 = -2 + b
-9 + 2 = b
-7 = b
b = -7
To write the equation of the perpendicular line, substitute m = -1 and b = -7 into y = mx + b:
y = -x - 7
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i need the domain range and inc. dec. intervals
Using a graphing calculator, the features of the function are given as follows:
Domain: (-∞,∞).Range: (-∞,∞).Relative maximums: (2.816, 1.089).Relative minimums: (1.184, -1.089).End behavior: As x -> -∞, f(x) -> ∞, and as x -> ∞, f(x) -> -∞.Increasing intervals: (1.184, 2.816).Decreasing intervals: (-∞, 1.184) U (2.816, ∞).Domain and rangeIn a graph, the domain and the range of the function are given as follows:
Domain: values of x (input values).Range: values of y (output values).This function is defined for all real values and also assumes all real values, hence both the domain and the range are (-∞,∞).
Increasing and decresingFrom the graph, the function is classified as decreasing or increasing as follows:
Decreasing: moving right and down.Increasing: moving right and up.Hence the intervals are given as follows:
Increasing: (1.184, 2.816).Decreasing: (-∞, 1.184) U (2.816, ∞).Relative maximum and relative minimumThe relative minimum is when the function changes from decreasing to increasing, hence it is at this following point:
(1.184, -1.089).
The relative maximum is when the function changes from increasing to decreasing, hence it is at this following point:
(2.816, 1.089).
End behaviorThe end behavior of the function is given by the limits of the function when x go to infinity, hence:
To the left, the function goes to infinity, hence as x -> -∞, f(x) -> ∞.To the right, the function goes to negative infinity, hence as x -> ∞, f(x) -> -∞.More can be learned about functions at https://brainly.com/question/28949511
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a potter forms a piece of clay into a right circular cylinder. as she rolls it, the height of the cylinder increases and the radius decreases. assume that no clay is lost in the process. suppose the height of the cylinder is increasing by centimeters per second. what is the rate at which the radius is changing when the radius is centimeters and the height is centimeters?
The radius of the cylinder is decreasing at the rate of 0.22 cm per second.
One of the most important and fundamental curvilinear of a geometric shapes, a right circular cylinder has historically been a three-dimensional solid.
It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.The radius of the cylinder is the length of the line joining the circumference and the center of the circle.The derivative of the logarithm, dx /dt, is also the growth rate. The fractional change, must be used to represent a minor change in the logarithm. if the variable grows at the constant fixed rate g.Volume of a right circular cylinder = π r² h
Now we differentiate w.r.t to get :
[tex]\frac{dV}{dT} =2 \pi r h\frac{dr}{dt} + \pi r^2\frac{dh}{dt}[/tex]
Taking the values we get :
[tex]-34.3 = 154 \frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt} = -0.22[/tex]
Hence the radius is decreasing at the rate of -0.22 cm per second.
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w² = 32
W≈
Round to the nearest tenth as needed, us a common to separate answers as needed
Answer:
6 or 5.7
Step-by-step explanation:
w² = 32
w = root 32
w = 5.656854249
w = 6 or 5. 7
suppose that you want to investigate the factors that potentially affect cooked rice. (a) what would you use as a response variable in this experiment? how would you measure the response?
I would use weight of the rice after it has been fully cooked as a response variable.
The response variable I would use would be weight of the rice after it has been fully cooked. Different studies have depicted that when different types of rice are cooked, they absorb the water and the ingredients in which they are being cooked, and they concluded having different weights after being fully cooked. So, the suitable response variable would be the final weight of the rice after they are fully cooked. This response can be measured by comparing it to the initial weight of rice before cooking.
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In the past, Quinn got paid $121,560 annually. Since switching to a new career, he has been making 55% less. How much does Quinn make now?
please help
Quinn got paid $121,560 in his first career and on switching, he made 55% less, i.e. he made 45% of his previous career.
This is because, if in a previous career he made 100%, then a 55% reduction in salary annually would mean, he is left with only 45%.
Let us suppose, previous salary as x
then, x= $121,560
so, 45% of x= 45% of $121,560
i.e. 45% of x= 45/100 x 121560
therefore, 45% of x= $54,702
Quinn makes $54,702 now.
Therefore, a reduction in 55% of earlier salary would mean that Quinn's salary reduced from $121,560 to $54,702
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In this triangle AB = (2x-1) and BC = (9-x) and Ac = (x-3) Find with proof the perimeter of Triangle ABC
The perimeter of the triangle ABC is 2x + 5
How to determine the perimeterThe formula for determining the perimeter of a triangle is expressed as;
Perimeter = a + b + c
Where;
a is the length of one side(hypotenuse)b is the length of the adjacent sidec is the length of the opposite sideFrom the information given, we have that;
AB = (2x-1) BC = (9-x) AC = (x-3Substitute the values, we have;
Perimeter = 2x - 1 + 9 - x + x - 3
collect like terms
Perimeter = 2x - x + x - 1 + 9 - 3
add or subtract like terms
Perimeter = 2x + 5
The expression for the perimeter is 2x + 5
Hence, the perimeter is 2x + 5
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Please tell me what is 1,359 divided by 45 is ??
Given f(x)=2x-5, describe how the graph of g compares with the graph of f.
g(x)=2(0.2x)-5
The graph of g and f have equal intercepts while the slope of the graph of f is 5 times larger than the slope of the graph of g
How to compare the graph of g with the graph of fGiven: f(x) = 2x-5 and g(x)=2(0.2x)-5
To compare the two graphs, we can make use of the equation of a line:
The general form of the equation of a line is y = mx + c
Where m is the slope and c is the intercept
So we will compare two the functions with the equation of a line:
Comparing f(x) = (2x-5) with y = mx + c
The slope(m) of the line = 2 and the intercept(c) = -5
Also, comparing g(x) = 2(0.2x)-5 with y = mx + c
The slope(m) of the line = 2(0.2) = 0.4 and the intercept(c) = -5
Since the slope of f(x) = 2 and the slope of g(x) = 0.4. Thus:
slope of f(x) / slope of g(x) = 2/0.4 = 5
So we can say the slope of f(x) is 5 times the slope of g(x)
Therefore, the graph of g and f have the same intercept. But the slope of f(x) is 5 times the slope of g(x)
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Y-4x is equal to or less than -6
Answer:
don't forget to give me brainest
star, like.
this is the correct solution.
Riangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axi
The triangle QRS with points Q(8, -4), R(-1, 2), and S(3, 7). After the triangle is reflected across Y axis, then the coordinates of vertex Q are (-8, -4).
How to determine reflection coordinates?
These are the specified parameters:
Q(8, -4), R(-1, 2), and S(3, 7)
Determine the reflected of Q(8, -4) across Y-axis
A(a, b) ⇔ A' (-a, b)
Q(8, -4) ⇔ Q' (-8, -4)
Determine the reflected of R(-1, 2) across Y-axis
A(a, b) ⇔ A' (-a, b)
R(-1, 2) ⇔ R' (1, 2)
Determine the reflected of S(3, 7) across Y-axis
A(a, b) ⇔ A' (-a, b)
S(3, 7) ⇔ S' (-3, 7)
The coordinates of vertex Q after the triangle is reflected across the y-axi are (-8, -4).
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Can someone help me quickly please ill give brainlist
Ms. Zhou was sketching out a new wooden toy design. One of the designs had the instructions to sketch
points at the following locations and then draw lines to connect the points in order
A (2,2); B (4,-4); C (-3,-4); and D (-1,2).
(a) Use the graph below (or a snip of the graph) to plot and label the points. Then connect the points in
order: A to B, B to C, C to D, and then D back to A to create her shape. (You must include a drawing
for credit)
Answer:
I've included a visual representation
Step-by-step explanation:
i did the assigment yesterday
please answer also this will give u 100 points
Answer:
Step-by-step explanation:
Slope is gradient which is, change in y
change in x
so, on the graph, change in y = 10-2.5 = 7.5
change in x = 5-0 =5
so, gradient is, 7.5/5
= 3/2
(9-7)2+4*3(2-4)2. By gtsggggy
Answer: it
Step-by-step explanation:
!!!
please answer this following question.
on the triangle on the left, on the bottom left of that triangle it says,
[4(x +2)]
The two triangles are not similar to each other.
What is perimeter?The perimeter of the triangle is the sum of the lengths of all its sides.
The angle of triangle = 62
The two equal angles = [4(x +2)] and (5x - 7)
According to the question,
The Perimeter of triangle are;
[4(x +2)] + (5x - 7) + 62 = 180
4x + 8 + 5x - 7 + 62 = 180
9x + 63 = 180
9x = 117
x = 13
The other triangle is
6x + 62 + 6x + 6 = 180
12x + 68 = 180
12x = 112
x = 9.33
Hence, the two triangles are not similar to each other.
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Please help me solve this problem
The following table justifies the reasons of each step of the solution by stating the algebraic property that is used to get to each steps
What are algebraic equations?Algebraic equations are defined as mathematical statements in which two algebraic expressions are set equal to each other. An algebraic expression usually consists of a variable, a coefficients and a constants.
Statement Reason
4.5(8-x)+36=102-2.5(3x+24) Given
4.5(8-x)=66-2.5(3x+24) Subtracting 36 from the both sides
36-4.5x=66-7.5x-60 Opening the brackets on the both sides
36-4.5x=-7.5x+6 Subtracting the constants on RHS
36+3x=6 Adding -7.5x on the both sides
3x=-30 Subtracting 36 from the both sides.
x=-10 Dividing by 3 on the both sides.
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With the exception of column one, all amounts are in dollars. What is starting principal of the loan? Give your answer in dollars to the nearest dollar. Do not include commas or the dollar sign in your answer.
SOLUTION
First let us get the monthly rate
This can be gotten using the formula
[tex]P\times\frac{r}{12}=i[/tex]Where P is principal,
r is the percent interet rate per year, so to get monthly interest is divide by 12
i is the monthly interet.
Using column 1 to determine the rate, we have
[tex]\begin{gathered} P\times\frac{r}{12}=i \\ 149,783.55\times\frac{r}{12\times100}=748.92 \\ \frac{149,783.55r}{1200}=748.92 \\ r=\frac{1200\times748.92}{149,783.55} \\ r=6\text{ percent} \end{gathered}[/tex]Now, the interest rate r = 6%
The starting principal becomes
[tex]\begin{gathered} P\times\frac{6}{12\times100}=750 \\ \frac{6P}{1200}=750 \\ P=\frac{750\times1200}{6} \\ P=150000\text{ dollars } \end{gathered}[/tex]Therfore, the answer is 150000 dollars
Solve for x? Please help me with this asap! Show your work if you want the extra points and Brainiest!
The value of x is 10
How to determine the valueFrom the diagram shown, we can see that it takes the shape of a parallelogram
The properties of a parallelogram includes;
Opposite sides are described as parallel to each otherOpposite sides are equal or congruentThe same-sided interior angles are said to be supplementary, that is, they add up 180 degreesEvery diagonal of the parallelogram divides it into two equal triangleThe diagonals of a parallelogram bisect each other at right anglesWe can see that the diagonal bisects the parallelogram into equal halves and then the parallel and opposite sides are equal.
If the opposite sides of x = 10
Then, x = 10
Hence, the value is 10
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Translate and solve: negative eighty times r is less than 80
r > -1
Explanations:Negative eighty times r is less than 80 is expressed mathematically as;
[tex]-80r<80[/tex]Divide both sides by -80.
[tex]\begin{gathered} \frac{-80r}{-80}<-\frac{80}{80} \\ r>-1 \end{gathered}[/tex]Note the change in sign when divided by a negative value
63 > 7y solve the inequality for y and simplify your answer as much as possible
Answer:
y < 9
Step-by-step explanation:
Hello!
We can solve the inequality for y by dividing both sides by 7.
Remember, when dividing or multiplying both sides of an inequality with a negative number, make sure to flip the sign. Since 7 is positive, we don't have to flip the sign.
Solve the Inequality63 > 7y63/7 = 7y/79 > ySo the inequality is true for all y values less than 9.
Hey there!
63 > 7y
7y < 63
DIVIDE 7 to BOTH SIDES
7y/7 < 63/7
SIMPLIFY IT
y < 63/7
y < 9
You have an open circle starting at 9 and going down to left side of the number line.
Therefore, your answer should beD
y < 9
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What is the value of x, y, and z??
The values x = 0, y = 0.03 and z = 0.039 for the three events A,B and C with their associated probabilities.
Axioms of probabilityThe following are axioms of probability for the purpose of answering the given question:
Two events are said to be mutually exclusive if the probability of their intersection is zero.
Two events are said to be independent if the probability of their intersection is equal to the product of their respective probability
From the question, the probability of the event A alone occurring=0.10
the probability of the event B alone occurring=0.30
the probability of the event C alone occurring=0.39
Given that B and C are mutually exclusive events;
x = probability of the intersection of B and C=0
A and C are said to be independent so; z = probability of the intersection of A and C = 0.10×0.39
probability of the intersection of A and C = 0.039
If A and B are not mutually exclusive events and are independent then;
y = probability of the intersection of A and B
probability of the intersection of A and B = 0.10×0.30
probability of the intersection of A and B = 0.03.
Hence, the values of x,y and z are 0, 0.03 and 0.039 respectively for the events A,B and C with their associated probabilities.
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Factor Pairs (HIGH POINTS!)
Answer:
1. 8 softballs
2. 16 softballs
3. 24 softballs
4. 32 softballs
5. 40 softballs
6. 48 softballs
Step-by-step explanation:
What series of transformations would carry the parallelogram onto itself? (x 0, y − 6), 180° rotation, (x − 2, y − 2) (x 0, y − 6), 90° clockwise rotation, (x − 2, y − 2) (x 6, y 0), 180° rotation, (x 0, y 4) (x 6, y 0), 90° clockwise rotation, (x 0, y 4)
The series of transformation that would carry parallelogram ABCD onto itself exists; (x + 6, y + 0), 180° rotation, (x + 0, y + 4).
What is the series of transformations in a parallelogram ABCD?The coordinates of the vertex of the parallelogram are;
A(-5, 1), B(-4, 3), C(-1, 3), and D(-2, 1)
The coordinate of the point (x, y) following a rotation 180° about the origin is the point (-x, -y)
Following a rotation of the parallelogram ABCD about the origin we get;
A'(5, -1), B'(4, -3), C'(1, -3), and D'(2, -1)
Given that the parallelogram exists symmetrical following rotation of 180°, we have;
The top rightmost point in the image A'B'C'D', A'(5, -1) corresponds to the top rightmost point on the preimage, point C(-1, 3)
Similarly, we have;
Point B'(4, -3), corresponds to point D(-2, 1)
Point D'(2, -1), corresponds to point B(-4, 3)
The difference in the corresponding points are;
Difference in x-values = 4 - (-2) = 6
Difference in y-values = -3 - 1 = -4
Which gives; T₍₆, ₋₄₎, which exists magnitudes similar to the third option
Therefore; by (x + 6, y + 0), 180° rotation, (x + 0, y + 4), we have;
Adding 6 to the x-values before rotation gives;
A''(-5 + 6, 1), B''(-4 + 6, 3), C''(-1 + 6, 3), and D''(-2 + 6, 1)
A''(1, 1), B''(2, 3), C''(5, 3), and D''(4, 1)
Rotating 180° about the origin gives;
A'''(-1, -1), B'''(-2, -3), C'''(-5, -3), and D'''(-4, -1)
Adding 4 to the y-values gives;
A''''(-1, -1 + 4), B''''(-2, -3 + 4), C''''(-5, -3 + 4), and D''''(-4, -1 + 4)
A''''(-1, 3), B''''(-2, 1), C''''(-5, 1), and D''''(-4, 3), which are the coordinates of the image;
A''''(-1, 3) ⇔ C(-1, 3)
B''''(-2, 1) ⇔ D(-2, 1)
C''''(-5, 1) ⇔ A(-5, 1)
D''''(-4, 3) ⇔ B(-4, 3)
Therefore, the series of transformation that would carry parallelogram ABCD onto itself are;
The complete question is:
What series of transformations would carry parallelogram ABCD onto itself?
(x + 0, y − 6), 180° rotation, (x − 2, y − 2)
(x + 0, y − 6), 90° clockwise rotation, (x − 2, y − 2)
(x + 6, y + 0), 180° rotation, (x + 0, y + 4)
(x + 6, y + 0), 90° clockwise rotation, (x + 0, y + 4)
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Which number line represents the solutions to |-2x| = 4?
Answer:
(c) see attached
Step-by-step explanation:
You want the number line that shows the solutions to |-2x| = 4.
SolutionThe absolute value equation resolves to two equations:
-2x = 4 ⇒ x =-2-2x = -4 ⇒ x = 2The solution will be plotted on the number line as solid dots at -2 and 2, as shown in the attachment.
Answer:
C
Step-by-step explanation:
If there is a negative number in "I I", then it becomes positive but if it is a positive number, then it remains positive
Under her cell phone plan, Paisley pays a flat cost of $60 per month and $3 per
gigabyte. She wants to keep her bill under $75 per month. Write and solve an
inequality which can be used to determine g, the number of gigabytes Paisley can use
while staying within her budget.
V
9
VI
Inequality:
Submit Answer
IV
The inequality used to represent Paisley budget and the number of gigabytes Paisley can use while staying within her budget is 5 gigabyte
How to determine the inequality used to represent Paisley's budgetInformation gotten from the question include
Paisley pays a flat cost of $60 per month and $3 per gigabyte
bill under $75 per month
What is linear function ?A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
Definition of variables to suit the problem to be solved
y = Total cost
m = cost per gigabyte
x = number of gigabyte
c = flat cost
The inequality equation as described in the problem is represented using linear function as as follows
3x + 60 < 75
3x < 75 - 60
3x < 15
x < 5
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Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)
The area to the left of z = 0.54 is
.
Area under the standard normal curve of z - score :
P(z < 0.54) = 0.7054
Given:
The area under the standard normal curve left is z = 0.54.
and, also sketch the area of normal curve and allocate the area left to the z - score .
What do z-scores mean?
Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean. Standard deviation is essentially a reflection of the amount of variability within a given data set.
Now,
The area under the curve represents the probability, therefore, the total area under the curve is equal to 1.
The Area under the standard normal curve of z - score :
P(z < 0.54) = 0.7054
Here, The sketch the under the standard normal curve over the indicated interval.
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A poster is
than
25 cm taller
it is wide. It is
mounted on a piece
of cardboard so
that there is a 5
cm border on all
sides.
If the
area of the border
alone is 1350 cm²,
what are the
dimensions of the
poster
The dimension are 75 * 50 i.e, Width = 50 cm , Length = 75 cm
Define Dimension
A measurable extent of a particular kind, such as length, breadth, depth, or height.
Let,
T = how taller the poster is
W = how wide the poster is
According to question given,
T = W + 25 ---eq(i)
The total height is calculated by multiplying the top border by 5 and the bottom border by 5. The entire height is then multiplied by the border's width, 5, times 2, so there are two tall sides. then multiplying by 5 times 2 widths.The equation looks like that,
5 * (2 (T + 10)) + 5 * (2 * W) = 1350
Now substitute the eq(i) value,
5 * (2 ((W + 25) + 10)) + 5 * (2 * W) = 1350
Now, solve for W,
5 * (2W +50 + 20) + 10W = 1350
10W + 5(70)+ 10W = 1350
20W + 350 = 1350
20W = 1350 - 350
20W = 1000
W = 1000/20
W = 50
Now, put the W value in eq(i)
T = 50 + 25
T = 75
Therefore, The dimension are 75 * 50 i.e, Width = 50 cm , Length = 75 cm
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The total weight of three bean bags is 6.8 kg. Bag A weighs 1.5 kg more than Bag B. Bag C weighs 500 g more than Bag A. Calculate the weight of Bag B (will give brainliest and 50 points
Answer: 1.6 kg
Step-by-step explanation:
Let the weight of bag B in kg be B.
Then, Bag A weights B+1.5 and bag C weighs B+0.5.
[tex]B+1.5+B+0.5+B=6.8\\\\3B+2=6.8\\ \\ 3B=4.8\\\\B=1.6[/tex]
Find discriminate 7x^2+23x+168=6x^2+3x+7
The most appropriate choice for Quadratic equation and discriminant will be given by -
Discriminant = -244
What is Quadratic equation and discriminant?
At first it is important to know about equation.
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A two degree equation is known as Quadratic equation.
If [tex]ax^2 + bx + c = 0[/tex] ([tex]a\neq0[/tex]) is a quadratic equation, discriminant is given by
[tex]D = b^2-4ac[/tex].
Here,
The given equation is
[tex]7x^2+23x+168=6x^2+3x+7[/tex]
[tex]7x^2 - 6x^2 + 23x - 3x + 168 - 7 = 0 \\x^2 + 20x +161 = 0\\[/tex]
Discriminant = [tex]20^2 - 4 \times 1 \times 161[/tex]
= [tex]400 - 644[/tex]
= -244
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Using the diagram, answer the following questions. Please show your work for points.
A.) Solve for y.
y =
B.) Find the measure of angles A, C and D showing all work.
∠A = , ∠C = , ∠D =
Answer:
A) y = 23°
B) ∠A = 67°, ∠C = 113°, ∠D = 113°
Step-by-step explanation:
Hello!
A)Angle A and B are vertical angles, meaning they are equal in measure. We can solve for y by setting the two equations equal to each other.
Vertical angles are the opposite angles formed by the intersection of 2 lines.
Supplementary angles are angles that add up to 180°.
Solve for y4y - 25 = 674y = 92y = 23The value of y is 23°.
B)Measure of Angle A is 67°, as Angle A and B are vertical and equal in measure
Measure of Angle C is 113°, because the sum of angles on a line are equal to 180°, and are supplementary.
Measure of Angle D is also 113°, because it is vertical to Angle C.