Answer: (3, -7) and (3, -1)
Step-by-step explanation:
Distance formula: a^2 + b^2 = c^2
c is the distance between different points which is 5 in this case
a=3-(-1)
a=3+1
a=4 ==> distance between x-coordinates
4^2+b^2=5^2
16+b^2=25
b^2=9
b=3
Distance from -4 and y-coordinate of a different point is equaled to 3.
How to express this in the form of an equation?
|-4-y|=3 ==> where y is the y-coordinate of a different point
-4-y=3
-4+4-y=3+4
-y=7
y=-7 ==> (3, -7)
-4-y=-3
-4+4-y=-3+4
-y=1
y=-1 ==> (3, -1)
(3, -7) and (3, -1)
how do you solve 13=-2(y-4)+3y in three different ways?
The required three ways of solutions are,
1 - Transposition left to right
2- Property of equality
3 - Transposition right to left
Here,
Given expression,
13=-2(y-4)+3y
Approach 1,
13 = -2 (y - 4) + 3y
13 = -2y + 8 + 3y
13 = y + 8
13 - 8 = y
5 = y
Approach 2
13 = -2 (y - 4) + 3y
13 - 3y = -2y + 8
Adding 3y both side
13 - y = +8
Subtracting 13 on both sides
-y = -5
Multiplying by -1 on both sides
y = 5
Approach 3
13 = -2 (y - 4) + 3y
transposition of the variable to the left and contents to the right
2(y - 4) - 3y = -13
2y - 8 -3y = -13
-y -8 = -13
-y = -13 + 8
-y = -5
y = 5
Thus, the required three ways of solutions are,
1 - Transposition left to right
2- Property of equality
3 - Transposition right to left
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3x - 1 = 4x+8-х what is the answer
Answer:
No Solutions
Step-by-step explanation:
Hello!
Solve for x by isolating the variable.
Solve for x3x - 1 = 4x + 8 - x3x - 1 = 3x + 8 Combine like terms-1 = -8 Subtract 3x from both sidesSince -1 does not equal to -8, there are no solutions for x that makes this equation true.
Answer:
no solution
Step-by-step explanation:
3x-1=4x+8-x
add like terms
3x-1=3x+8
add 1 to both sides
3x=3x+9
subtract 3x from both sides
0=9
no answer!
I need help with this ASSAP, it’s about math please help
Answer: 10 tutors
Step-by-step explanation:
Make the proportion:
72 students - 6 tutors
120 students - x tutors
Hence,
[tex]\displaystyle\\x=\frac{(120)(6)}{72} \\\\x=\frac{720}{72} \\\\x=\frac{(72)(10)}{72}\\\\ x=10\ tutors[/tex]
PQ has endpoints P(5, -3) and Q(2, 4).
Midpoint:
Which linear equation is being represented by the graph?
The linear equation that is being represented by the graph is y=-3x +2.
What is linear equation?A linear equation can be described as the equation that has its highest power of the variable as 1 and this is been refereed to as the one-degree equation.
It should be noted that slope, of the the equation is usually in the form y=mx+b where mx is slope, however the linear equation usually have one or two variables and when a variable in a linear equation has a power greater than 1 then it is no more linear.
Therefore, option A is correct.
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Natalie works as a playground supervisor for 8 weeks during the summer at a rate of
$15.27/h. She works a 40-hour week but averages 3 hours of overtime each week,
paid at time and a half. How much will she earn each week, and for the whole
summer?
Natalie will receive a weekly salary of $656.61 and a summer salary of $10505.76.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Natalie earns $15.27 per hour while working as a playground supervisor for 8 weeks throughout the summer. Although she works a 40-hour week, she typically puts in 3 hours of overtime.
For a week = ( 40 + 3 ) x 15.27 = $656.61
For a summer = 4 x 4 = 16 weeks
For a summer = 16 x $656.61 = $10505.76
Therefore, Natalie will be paid $656.61 for a week and for summer $10505.76.
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Write an equation in slope-intercept form for each line.
(-4,-1) and (-8,-5)
For each line, an equation in slope-intercept form :
y = (-1/4)x - 2 .
What does intercept mean in terms of slope?Summary of the lesson. The slope-intercept form is just a means of stating a line's equation so that the slope (steepness), as well as y-intercept (where the line crosses the vertical y-axis), as well as y-intercept (where the line crosses the vertical y-axis), are obvious. This form is also known as the y = MX + b form.
In a graph, what are slope as well as intercept?The slope, m, of a line represents its steepness. The slope of something like the line is however termed a gradient, sometimes. A line's y-intercept, b, represents the y-coordinate of something like the point where the line's graph intersects the y-axis.
According to the given data:To begin, use the slope formula to determine the average slope here between two points.
m = (y2-y1)/(x2-x1)
= (-1 - (-4))/ (-4-8)
= 3/(-12)
= -1/4
So the slope is -1/4.
We must now determine the y-intercept. This will be accomplished by converting a single of the points and indeed the slope through into point-slope form of something like a linear equation, which is y2-y1 = m(x2-x1).
Let’s plug in the point (8,-4).
So we get y-(-4) = (-1/4)(x-8) ⇒ y+4
= (-1/4)x + 2 ⇒ y
= (-1/4)x - 2.
So y = (-1/4)x - 2
For each line, write an equation in slope-intercept form y = (-1/4)x - 2.
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Write this from least to greatest:
0.2, 1/4, 1/12, 22%
Answer:
1/12, 0.2, 22%, 1/4
Step-by-step explanation:
1/12 = 0.083333
1/4 = 0.25
22% = 0.22
0.2
So: 1/12, 0.2, 22%, 1/4
Solve each equation or inequality.
19+|x-1|=33
After solving the equation the value of x is -23, 25 in the equation 19+|x-1|=33
How to solve an equation?
To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
⇒ 9+|x-1| = 33
For positive case
⇒ 9+|x-1| = 33
⇒ (x-1) = 33 - 9
⇒ x - 1 = 24
⇒ x = 25
For negative case
⇒9+|x-1| = 33
⇒ -(x-1) = 33 - 9
⇒ -x + 1 = 24
⇒ - x = 23
⇒ x = -23
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Given the rule (x,y) --> (x-4, y+8), describe what transformation occurs to any given point.
The description of the transformation that occurs to any given point is a 4 unit left translation and 8 units up translation
How to describe what transformation occurs to any given point?The rule is given as
(x,y) --> (x-4, y+8)
The above rule represents a translation transformation
This is evident because it has the format
(x,y) --> (x + h, y + k)
By comparison, we have
h = -4
k = 8
This represents a 4 unit left translation and 8 units up translation
Hence, the description of the transformation that occurs to any given point is a 4 unit left translation and 8 units up translation
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the sum of the measures of the angles of a triangle is 180. the sum of the measures of the second and third angles is four times the measure of the first angle. the third angle is 22 more than the second. find the measure of the three angles. let x, y and z represent the measures of the first, second, and third angles, respectively. find the measure of the three angles
Answer:
x= 36 y= 67 and z=77
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180
can be written as x+y+z=180
The sum of the measures of the second and third angles is four times the measure of the first angle.
It can be written by: x+y=4z
The third angle is 10 more than the second
It can be written as z=y+10
By solving the equations systems the above values can be determined.
x+y+z=180
x+y=4z
z=y+10
If the average metabolic rate of a pigeon is 3 j/s and that of a goose is 12 j/s, what is the ratio of the pigeon's aorta radius to that of the goose?
1:4 is the ratio of the pigeon's aorta radius to that of the goose.
What do we mean by Ratio?A ratio in mathematics indicates how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio of 4:3). Similarly, the proportion of lemons to oranges is 6:8 (or 3:4), and the proportion of oranges to total fruit is 8:14. (or 4:7).A ratio's numbers can be any quantity, such as a count of people or objects, or measurements of lengths, weights, time, and so on. In most situations, both numbers must be positive.So,
The ratio will be 3:12.Canceling it to the simplest form:
3/12 = 1/4So, the ratio is 1:4.
Therefore, 1:4 is the ratio of the pigeon's aorta radius to that of the goose.
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I need help with this ASSAP, it’s about math please help
72/6=12
that means every tutor would have 12 students. if the academy has 120 students then we divide 120 by 12 to get 10. That means the academy needs 10 tutors.
Which orders have different information between the reports? select all that apply. 101 102 103
The order number that conveys a different information between the two analytical reports presented in tabular form is Order 102
How to find the difference between the reports?
The report that accompanies a similar question consists of two tabular forms of (analytical) reports, as follows;
Report 1.
Order. Stock # Qty
101. 27–671. 1
102. 27–781. 2
103. 27–090. 3
Report 2.
Order. Stock # Qty
101. 27–671. 1
102. 27–783. 2
103. 27–090. 3
From the above reports, by examination, we have at order 102
Stock number (Stock #) for Order 102 in Report 1 = 27–781
Stock number (Stock #) for Order 102 in Report 2 = 27–783
Therefore;
The order(s) that have (has) a different information between the reports is; Order 102
The correct option is therefore;
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Write an equation in standard form for the line that is perpendicular to the
graph of 1/5x + 2/5y = 0.05 and has y-intercept -0.5.
first look at the equation you’re given. It’s in y-intercept form. The slope is 5.
A line perpendicular to it has a slope that is the opposite reciprocal, -1/5. You are told that the y-intercept of the line is 4, so the equation for the Since the slope of the line is -1/5, and the y-intercept is 4, the equation of the line is,
y = (-1/5)x + 4
Multiply both sides by 5 and put into standard form,
x + 5y = 20line in y-intercept form is y= -1/5x+4
When we have a linear equation in standard form, we can find the x- and y-intercepts of the corresponding line. This also allows us to graph it.
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the cost of 5 pens and 3 rulers is 90p
the cost of 2 pens and 1 ruler is 33p
What is the cost of 3 pens and 2 rulers
The cost of 3 pens will be 27P and the cost of 2 rulers will be 30p.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that the cost of 5 pens and 3 rulers is 90p the cost of 2 pens and 1 ruler is 33p. the cost of 3 pens and 2 rulers will be calculated as below:-
From the equations and solve:-
5p + 3r = 90p
2p + r = 33p
5p + 3r = 90p
-6p - 3r = -99p
Cost of one pen P = 9
The cost of the 1 ruler:-
2p + r = 33p
2 x 9 + r = 33
18 + r = 33
r = 33 - 18
r = 15
Cost of 3 pens = 3 x 9 = 27
Cost of 2 rulers = 2 x 15 = 30
Therefore, the cost of 3 pens will be 27P and the cost of 2 rulers will be 30p.
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Which situation shows causation?
When the number of people in a bus increases, the number of animals in a zoo also increases.
When the number of hours worked each week by an hourly employee decreases, the amount of money earned
by the employee also decreases.
When the amount of a discount for a sale increases, the number of items sold during the sale decreases.
6 When the number of bike trails in a city decreases, the amount of rainfall in the city increases.
Statements (B) and (D):
"(B) When the number of hours worked each week by an hourly employee decreases, the amount of money earned by the employee also decreases.(D) When the number of bike trails in a city decreases, the amount of rainfall in the city increases."shows causation.
What do we mean by Causation?Causation denotes that one event is the result of the other event's occurrence; that is, there is a causal relationship between the two events. This is also known as cause and effect. Causation is the process by which one variable causes another to change, implying that one variable is dependent on the other. It is also known as cause and effect. For example, as the weather warms, people get more sunburned. In this instance, the weather resulted in sunburn.In the given questions statements (B) and (D) shows causation.
Therefore, statements (B) and (D):
"(B) When the number of hours worked each week by an hourly employee decreases, the amount of money earned by the employee also decreases.(D) When the number of bike trails in a city decreases, the amount of rainfall in the city increases."shows causation.
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The correct question is given below:
Which situation shows causation?
(A) When the number of people in a bus increases, the number of animals in a zoo also increases.
(B) When the number of hours worked each week by an hourly employee decreases, the amount of money earned by the employee also decreases.
(C) When the amount of a discount for a sale increases, the number of items sold during the sale decreases.
(D) When the number of bike trails in a city decreases, the amount of rainfall in the city increases.
Refer to ®F .
If C F=14 inches, what is the diameter of the circle?
A diameter of a circle is any straight line segment that passes through the center of the circle and has endpoints on the circle.
The diameter of the circle is 28 inches.
What is meant by diameter?In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.
The diameter is twice the radius because the greatest distance between two points on a circle must be a line segment through the center of the circle.
Here, CF is a radius and the diameter is twice the radius.
Diameter of a circle = 2r
d = 2r
Where, r = 14
Diameter of a circle, d = 2r
Diameter of a circle = 2(14)
Diameter of a circle = 28
Therefore, the diameter of the circle is 28 inches.
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Choose the answer below that expresses .74 as a fraction.
A
B
с
D
74
1,000
74
74
100
10
Answer:
74/100
37/50 (this is the answer if 74/100 is simplified)
Hope this helps :)
Explanation right below.
Step-by-step explanation:
The 4 in 0.74 ends in the hundredths place, so 74 will be put over 100 in a fraction to get 74/100. If 74/100 needs to be simplified then divide the numerator and denominator by 2 to get 37/50.
This is easy but I can't find out exact answer.Plss,answer to just (b)
I've so hurry,pls help in a little time.
Answer:
Hello,
1/37
Step-by-step explanation:
Explanation on the picture
Identify another name for a reciprocal
Answer:
inverse
In math, a reciprocal is also called an inverse.
Step-by-step explanation:
Answer:
A correlative is another name for a reciprocal.
Correlative:
A degree into which 2 or more values are associated.
Given: AB CD
CF EB
Prove: AE FD
Proof:
AB CD
given
AB=CD
definition of
congruent segments
AE+EB-CFFD
segment addition
AE-FD
AE=FD
definition of
congruent segments
AB AE+EB
CD-CF FO
segment addition
CF = EB
given
CF EB
defation of
congruent segments
9
What is the missing reason in the proof?
OA segment addition
OB.
Congruent Segments Theorem
OC.
Transitive Property of Equality
OD. Subtraction Property of Equality
The figure have AE = FD
given,
AB =CD
AB = AE + EB
CD = CF + FD
AE + EB = CF + FD
CF = EB given,
AE = FD
if the triangle ABC and triangle DEF are identical. More specifically their side lengths and their angle measures are all the same, therefore we can consider them congruent figures. And that's exactly how you prove two figures are congruent by matching their corresponding parts.
SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side).
Triangles that have exactly the same size and shape are called congruent triangles.
Identifying Congruent Figures in the Real World
Two figures are congruent if and only if they have the exact same shape and the exact same size.2.If the corresponding sides of two figures with the same shape have the same length, then the two figures are congruent.
They are the same shape but not the same size. Non-congruent rectangles. These two polygons have matching sides equal but their matching angles are not equal and so they are not congruent. They are different shapes even though the sides are the same size.
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Find a slope-intercept form equation for the line through the points (-10,6) and (5,3) HELP ILL GIVE BRAINLIES
Answer:
[tex]y = - \frac{1}{5} x + 4[/tex]
Step-by-step explanation:
The slope-intercept form equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept.
Start by finding the slope.
[tex]\boxed{\text{Slope}= \frac{y_1 - y_2}{x_1 - x_2} }[/tex]
Slope of line, m
[tex] = \frac{6 - 3}{ - 10 - 5} [/tex]
[tex] = \frac{3}{ - 15} [/tex]
[tex] = - \frac{1}{5} [/tex]
Substitute value of m into equation:
[tex]y = - \frac{1}{5} x + c[/tex]
Substitute any point the line passes through into the above equation:
When x= 5, y= 3,
[tex]3 = - \frac{1}{5} (5) + c[/tex]
3= -1 +c
c= 3 +1
c= 4
Substitute the value of c into the equation:
[tex]y = - \frac{1}{5} x + 4[/tex]
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The measures of three angles of a triangle are 3x, x + 30, and x + 40. Find the measure of all three angles.
Answer: 66 degrees for 1st angle
52 degrees for 2nd angle
62 degrees for 3rd angle
Step-by-step explanation:
3x+(x + 30)+(x + 40)=180
3x+x+30+x+40=180
3x+x+x+30+40=180
5x+70=180
5x=110
x=22
3x=
3(22)=66 degrees for 1st angle
x+30=
22+30=52 degrees for 2nd angle
x+40=
22+40=62 degrees for 3rd angle
Answer:
3x=66
x+30=52
x+40=62
66,42,62
Step-by-step explanation:
(3x)+(x+30)+(x+40)=180
5x+70=180
5x=110
x=22
3x=66
x+30=52
x+40=62
Write 2% as a decimal (not as a percentage).
Answer: 2 1/2 as a decimal is 2.5
2 as a decimal is 0.02
Step-by-step explanation:
Samuel wants to buy a snake for $288 and the pet store owner wants him to make 6 equal payments of $49.
6 StartLongDivisionSymbol 288 EndLongDivisionSymbol minus 240 = 48. 48 minus 48 to get a remainder of 0 and a quotient of 49.
What error did the pet store owner make?
There is a multiplication error. The payment should be $48 per month.
There is a multiplication error. The payment should be $58 per month.
6 goes into 288 forty-six times. The answer is $46.
6 goes into 48 nine times. $49 is correct. PTS WORTH: 12
ima be up all night please help
The pet store owner made a multiplication error.
The payment should be $48 per month.
How do we calculate an equal periodic payment?An equal periodic payment can be calculated using the following formula:
P = T / N ............................................. (1)
Where, from the question:
P = periodic payment or the amount required to be paid periodically = ?
T = Total amount payable or the amount Samuel bought the snake = $288
N = Number of periods = 6
Substituting all the relevant values into equation (1), we have:
P = $288 / 6
P = $48
The P = $48 implies that $48 has to be multiplied by 6 to obtain $288.
Therefore, the pet store owner made a multiplication error.
The payment should be $48 per month.
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solve for x : 15x - 3(3x+4)=6
A diver is 25 feet below sea level. After he swims up 15 feet toward the surface, what is his elevation?
Answer:
-10.
Step-by-step explanation:
-25+15=-10.
a. What is an equation of the parabola with vertex (0,0) and focus (0,-1.5) ?
A parabola having vertex at the origin and focus at (0, -1.5) is expressed by the following equation:
y = -x²/6
What is a parabolic function?A parabolic function is one that has a quadratic variable, its shape is defined by the intersection of an inclined plane whose angle of inclination with respect to the axis of revolution of the cone is equal to that presented by its generatrix.
Since the vertex and the focal axis are on the same axis, we analyze that:
v = (0, 0)f = (0, -1.5) focus is on the negative part of the y-axis.(x - 0)² = 4p(y - 0)
Focus
f = (0, 0 + p)
0 + p = -1.5
p = 0 -1.5
p = -1.5
(x - 0)² = 4*(-1.5)(y - 0)
(x)² = -6(y)
y = -x²/6
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Peter is 3/4 as old as June and David is one and a half times as old as Peter how many times as old as June is to David write your answer as a fraction
In fraction, June is 9/8 as old as David.
What is a fraction?
A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction has a numerator above a line and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.
The required fraction is (3/4) x (3/2) = 9/8
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