The three consecutive number are 17 , 18 and 19 respectively
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be = x
Let the second number be = ( x + 1 )
Let the third number be = ( x + 2 )
Now ,
A = 4 times the first decreased by the second is 12 more than twice the third
Substituting the values in the equation , we get
4x - ( x + 1 ) = 12 + 2 ( x + 2 )
On simplifying the equation , we get
4x - x - 1 = 12 + 2x + 4
3x - 1 = 16 + 2x
Subtracting 2x on both sides of the equation , we get
x - 1 = 16
Adding 1 on both sides of the equation , we get
x = 17
Therefore , the value of x is 17
Hence , the consecutive numbers are 17 , 18 and 19
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Determine whether the relation is a function.
Which table represents a function
Answer:
The table with (-3, 2), (0, 2), etc.
Every input has exactly one output.
Hope this helps :)
PLEASE HELP ME ASAP NOW PLEASE
The lines with a slope larger than f(x) are:
option 4) y = (25/3)*x - 1/2
option 5) (4/5)*y - 16x = -1/2
Which one is the linear equation shown on the graph?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
First, you can see that the line crosses the y-axis at y = -4, so the line is something like:
y = a*x - 4
And we can see that it crosses the x-axis at x = 2, then we can write the equation:
0 = a*2 - 4
4 = a*2
4/2 = a
2 = a
So the linear equation on the graph is:
y = 2*x - 4
The slope is 2, the linear equations with a slope larger than that are:
option 4) y = (25/3)*x - 1/2
option 5) (4/5)*y - 16x = -1/2
Which can be rewritten as:
y = (5/4)*16x - (5/4)*(1/2)
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I need the answer for 9 and 10
A right triangle with coordinates A (-2,5), B (-2, 9) and C (4,5) is first rotated 90 degrees counterclockwise and
then translated 2 units left and 3 units down to form triangle A'B'C'. What is the measure of angle B'A'C',
in degrees, in the resulting figure?
Answer:
90 degree
Step-by-step explanation:
since the original angle BAC is 90 degree, no matter the triangle is rotated or translated, the angle remain unchanged
The figure below is a scale drawing of a garden if the scale used is 1/4 inch = 3 feet then what is the peremiter of the actual garden
Answer:
if the scale used 1/4 inch = 3 feet, then what is the perimeter of the actual garden? AI Recommended Answer: The perimeter of the actual garden is 144 feet.
Step-by-step explanation:
The table describes the quadratic function p(x).
x p(x)
−1 10
0 1
1 −2
2 1
3 10
4 25
5 46
What is the equation of p(x) in vertex form?
p(x) = 2(x − 1)2 − 2
p(x) = 2(x + 1)2 − 2
p(x) = 3(x − 1)2 − 2
p(x) = 3(x + 1)2 − 2
The equation of p(x) in vertex form is p(x) = 3(x - 1)² - 2.
Option C is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
From the table,
From p(x) = 10 to p(x) = -2 the value of p(x) is decreasing and from p(x) = -2 to p(x) = 46 it is increasing.
So,
The vertex is (1, -2).
The vertex form of p(x).
p(x) = a ( x - h)² + k
Where (h, k) is the vertex.
Now,
(1, -2) = (h, k)
Make (0, 1) = (x, p(x))
1 = a (0 - 1)² + (-2)
1 = a - 2
a = 1 + 2
a = 3
Thus,
The vertex equation of p(x).
p(x) = 3(x - 1)² - 2
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Find the midpoint and distance between (-3,10) and (15,-2)
The midpoint and distance between (-3,10) and (15,-2) are ( 6,4 ) and 6√13 respectively.
What is the midpoint and distance between the given coordinates?The midpoint formula is expressed as;
[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]
The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Given the data in the question;
Point 1(-3,10)
x₁ = -3y₁ = 10Point 2( 15,-2 )
x₂ = 15y₂ = -2Plug the given values into the midpoint formula and simplify.
[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]
[ ( -3 + 15)/2, ( 10 + (-2) )/2 ]
[ ( 12)/2, ( 10 - 2 )/2 ]
[ ( 12)/2, ( 8 )/2 ]
( 12/2, 8/2 )
( 6,4 )
Therefore, the midpoint is (6,4).
Plug the given values into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
D = √( ( 15 - (-3) )² + ( -2 - 10 )² )
D = √( ( 15 + 3 )² + ( -2 - 10 )² )
D = √( ( 18 )² + ( -12 )² )
D = √( 324 + 144 )
D = √( 468 )
D = 6√13
Therefore, the distance between the points is 6√13.
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The equation of a ellipse is given below.
Graph the ellipse find the center, vertices, foci, and equation of major axis.
(y+5)^2/9 + (x+5)^2/25 = 1
Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).
Explain the equation.An equation is a mathematical representation of two identical variables, one on each side of a "equals" sign. Common difficulties can be solved using equations. We commonly seek pre algebra help to resolve problems in real life. Pre-algebra is the fundamental building block of mathematics.
Here,
[tex](x + 2)^{2}[/tex] / [tex]a^{2}[/tex] + [tex](y-5)^{2}[/tex] /[tex]b^{2}[/tex] -=1 is (h, k).
the ellipse's nucleus
The major axis is the larger of the two axes, which are 2a and 26.
(H, a, k) and (H, k, b) are the vertices. Vertices are those along the major axis in this case, and covertices are those along the minor axis.
[tex](x + 2)^{2}[/tex]/16 + [tex](y-5)^{2}[/tex] /20 =1
can be written as
[tex](x + 2)^{2}[/tex]/ [tex]4^{2}[/tex] + [tex](y-5)^{2}[/tex] /(2√/5)2
hence centre is (-2, 5), maor axis is 2 x 2√√5 = 4√√5 and minor axis
is 2 x 4 = 8
Vertices are ( 2,5 25), or ( 2,5 25) and ( 2,5 + 25), while covertices are ( 2 4, 5) and ( 6,5), respectively.
As a result of the presence of a vertical major axis, eccentricity e and focii are
(h, k ± be). e is given by the relation a2 = b2(1 − e2) i.e.
=> e = [tex]\sqrt{1 - \frac{a^{2} }{b^{2}} }[/tex]
a2= 16 and b2= 62
=> e = 1/√5
Focii (-2,5 ± (2√5 x 1/√5)
or (-2,5±2) i.e. (-2, 7) and (-2, 3).
Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).
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Tyler’s brother earns 14 per hour. The store offers him a raise a 15% increase per hour. After the raise, how much will Tyler brother make per hour
Answer: 16.10
Step-by-step explanation:
$14 + 15% increase rate = 16.10
15% = 2.10
Which integer in the set has the greatest value (7, -7, -3, 3)?
A. -7
B. -3
C. 3
D. 7
Answer:
-3
Step-by-step explanation:
i hope this helps
1.
How many degrees does the hour hand of
a clock turn in 5 minutes?
(A)1/2
(B)3 1/2
(C) 5°
(D)2 1/2
Answer:
The answer is D (2 1/2)
Hope u helped
Length of insect is 23mm and length of drawing is 85mm. So what is Magnification
Answer:
The magnification is the ratio of the size of the image to the size of the object. In this case, the length of the insect is the size of the object, and the length of the drawing is the size of the image.
To find the magnification, we can divide the size of the image by the size of the object:
Magnification = size of image / size of object
Plugging in the values, we have:
Magnification = 85mm / 23mm
Calculating, we find that the magnification is approximately 3.7. This means that the length of the drawing is 3.7 times the length of the insect.
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Write the quotient as a mixed number.
26÷3=8 R2
When we divide 26 by 3 we get 8 as a quotient and 2 as a remainder, the Mixed Fraction is [tex]8\frac{2}{3}[/tex]
What is a mixed Number ?A full number plus a legal fraction are combined to form a mixed number. Mixed numbers, commonly referred to as mixed fractions, make it easier for humans to comprehend numbers.
A full number and a legal fraction make up a mixed number. A mixed number like [tex]2\frac{x}{y}[/tex] is one where 1/4 is the correct fraction and 2 is the whole number portion. It should be emphasized that once mixed numbers are transformed into an incorrect fraction, they are simple to add, subtract, multiply, and divide.
Steps to convert Improper fraction to Mixed Fraction :
Divide the numerator by the denominator to obtain the remainder and quotient as the first step. 43 divided by 9 in this situation yields 4 as the quotient and 7 as the remainder.Step 2: This quotient (4) becomes the mixed number's whole number component. While the denominator stays the same, the remainder (7) becomes the numerator portion.Step 3: As a result, 43/9 becomes a mixed number and is written as , meaning that 43/9 = [tex]4\frac{7}{9}[/tex].So when we divide 26 by 3 we get 8 as a quotient and 2 as a remainder so the Mixed Fraction is : [tex]8\frac{2}{3}[/tex]
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Choose the expression that is equivalent to fraction with 7 raised to the negative tenth power in the numerator and 7 raised to the fourth power times seven raised to the zero power in the denominator.
negative 1 divided by 7 raised to the fourteenth power
−714
1 divided by 7 raised to the fourteenth power
714
The equation that corresponds to fraction [tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex] is [tex]\frac{1}{7^{14} }[/tex] . A phrase by itself could contain an action .
what is expression ?It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: Expression: (Math Operator, Number/Variable, Math Operator). A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence.
given
[tex]\frac{7^{-10} }{(7^{4} )(7^{0} )} \\= \frac{1}{7^{4} } *\frac{1}{7^{10} } * 1\\= \frac{1}{7^{14} }[/tex]
The equation that corresponds to fraction [tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex] is [tex]\frac{1}{7^{14} }[/tex] .
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x−2y=3
Determine the missing coordinate in the ordered pair (−4,?) so that it will satisfy the given equation.
Answer:
y=-3.5
Step-by-step explanation:
substitute -4 for x
add 4 on both sides to get rid of the -4
divide -2 on both sides to isolate y
and you get 3.5 for y
The value of y that will satisfy the equation given is -3.5.
What is an equation?Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
Given that, the missing coordinate in the ordered pair (−4, ?), we need to find the missing value that will satisfy the equation x-2y = 3,
To find the same, just replace the value of x by -4,
-4-2y = 3
-2y = 7
y = -3.5
Hence, the value of y that will satisfy the equation given is -3.5.
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Rewrite the following equation in slope-intercept form. 17x + y = –19
Answer: y = 17x - 19
Step-by-step explanation:
17x + y = -19
Subtract 17 on both sides
Y= -19 - 17x
Then put it in y= mx + b
Y= -17x - 19
Answer:
y = -17x -19
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
17x+y = -19
Solve for y
y = -17x -19
From the set {28, 56, 112}, use substitution to determine which value of x makes the equation true.
x ÷ 2 = 56
The number in the replacement set that will make the equation true is (c) 112
How to determine the solution to the expressione/equation?From the question, we have the following parameters that can be used in our computation:
x ÷ 2 = 56
Rewrite the expression properly
so, we have the following representation
x/2 = 56
Also, we have the replacement set to be
{28, 56, 112}
In the given equation, we have the variable to be
The variable is x
Multiply 2 to both sides of the expression
So, we have the following representation
2 * x/2 = 56 * 2
Evaluate the products on both sides of the equation
x = 112
Hence, the solution is x = 112
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Marathon Race. Carlos, Maura, and Jacob are running a marathon-26 miles. Carlos runs at a rate of 6 miles per hour. Carlos runs at a rate that is 25% slower than Maura's rate. Jacob takes 2 hours and 36 minutes to finish the marathon. Determine and clearly show everyone's speed. Show or explain your
calculations. Clearly show the exact time it takes for each person to finish the race.
First, let's find Maura's running speed by using the information that Carlos runs at a rate that is 25% slower than Maura's rate. If Carlos runs at a rate of 6 miles per hour, then Maura runs at a rate of 6 * 1.25 = 7.5 miles per hour.
How to calculate time?Next, let's calculate how long it takes for Carlos to finish the marathon. We know that Carlos runs at a rate of 6 miles per hour and the marathon is 26 miles long. So we can use the formula:
time = distance/rate
time = 26/6
time = 4.33 hours
Now let's find how long it takes for Maura to finish the marathon. We know that Maura runs at a rate of 7.5 miles per hour and the marathon is 26 miles long. So we can use the formula again:
time = 26/7.5
time = 3.47 hours
Finally, let's convert Jacob's time of 2 hours and 36 minutes to hours. We can use the formula:
time = 2 + (36/60)
time = 2 + 0.6
time = 2.6 hours
In conclusion, Carlos takes 4.33 hours, Maura takes 3.47 hours and Jacob takes 2.6 hours to finish the marathon.
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What is an equation for the linear function whose graph contains the points (9, 7) and (4, −8)?
Enter your answers in the boxes.
The line that passes through these two points is y=x-2
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here function whose graph contains the points (9, 7) and (4, −8)
Thus using the two point formula for a line we get the equation as y-7=(x-9)
y=x-2
Hence, The line that passes through these two points is y=x-2
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what values are solutions for inequality -3 < 2x -3
The values that are solutions to the inequality -3 < 2x -3 are all real numbers greater than 0.
What is the solution to the given inequality?Given the inequality in the question;
-3 < 2x -3
Solve for x, by making it the subject of the formula.
Subtract 2x from both sides
-3 < 2x -3
-3 - 2x < -3
Add 3 to both sides
-3 + 3 - 2x < -3 + 3
-2x < -3 + 3
-2x < -3 + 3
-2x < 0
Next, divide both sides by -2
-2x/-2 > 0/2
x > 0/2
x > 0
Therefore, the solution to the inequality is x > 0.
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What is the value of sin(7pi/4)? See attached.
Answer:
-sqrt(2)/2 , the last option of your document.
Step-by-step explanation:
sin(7pi/4) = -sin(7pi/4 - pi)
= -sin(7pi/4 - 4pi/4)
= - sin(3pi/4)
sin(3pi/4) is a special angle , which is sqrt(2)/2
Hence, sin(7pi/4) = -sin(3pi/4)
= -sqrt(2)/2
Answer:
-sqrt(2)/2
Step-by-step explanation:
did the test
Clark is building a large gazebo for his backyard. It is in the shape of a regular hexagon. Each side of the
gazebo is 12 feet long. The apothem is 10.4 feet. He needs to purchase stones for the floor. It costs $9.50
per square foot for a special type of interlocking stone. Find the cost of the gazebo's floor.
Round to the nearest ten dollars.
Total cost of gazebo's floor is $3556.8 when the gazebo has 12 feet on each side. 10.4 feet tall is the apothem.
Given that,
In Clark's backyard, a sizable gazebo is being constructed. It has a typical hexagonal form. The gazebo has 12 feet on each side. 10.4 feet tall is the apothem. He must get stones for the flooring. The price of a particular kind of interlocking stone is $9.50 per square foot.
We have to identify the gazebo's floor's cost.
We know that,
The distance from the center of the regular polygon to the mid point of the side. Here, AB is the chord and AM =BM. O is the center of the circumcircle.
Segments joining the center of a circle to the midpoint of the chord is perpendicular to the chord.
So, OM ⊥AB
In ΔOAB,
AB is the base and OM is the height.
AB = 12 feet
OM = 10.4 feet.
The area of the triangle OAB =1/2×base×height
= 1/2×12×10.4
=62.4 square feet.
A regular hexagon is divided into 6 equilateral triangle having each side 12 feet.
Area of the regular hexagon = 6× area of the one triangle
=6×62.4=374.4 square feet
Cost of inter locking stones = $9.50 per square feet.
Total cost of gazebo's floor = 374.4× 9.50 =$3556.8
Therefore, Total cost of gazebo's floor is $3556.8 when the gazebo has 12 feet on each side. 10.4 feet tall is the apothem.
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Any help pls. Question is : Find the equation of line B, which is perpendicular toy-2x=-8(x-8)and passes through the point (6,-6). Find the midpoint of the line segment AB in the following figure
Answer:
Perpendicular line ⇒ 2x + 9y + 42 = 0
midpoint: (-1,1)
Step-by-step explanation:
Let's find the coordinates of midpoint of AB
Here, from figure, A = (-3,-2), B = (1,4)
So midpoint:
[tex]P = (\frac{-3+1}{2},\frac{-2+4}{2})[/tex]
∴ P = (-1, 1)
Now, given straight line is x - 2y = -8(x-8)
⇒x - 2y = -8x+64
⇒9x - 2y - 64 = 0
Perpendicular line to 9x - 2y - 64 = 0 is 2x + 9y + k = 0
Perpendicular line passes though (6,-6)
Putting the values, we get
2(6) + 9(-6) + k = 0
⇒12 - 54 + k = 0
⇒k = 42
∴ Perpendicular line ⇒ 2x + 9y + 42 = 0
pls help due tomorrow
On solving the provided question, we can say that - by doing the equation, we have -12 +18 = p + 7 => 6 = p + 7 => p = -1
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here,
-12 +18 = p + 7
6 = p + 7
p = -1
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alex, beverly and carl live on the same straight road. alex lives 12 miles from beverly and carl 4 mies from berve,y, how far does alex live from carl?
is it possible to have an inscribed circle by using centroid as the centre ?
Answer:
Yes, it is possible
Step-by-step explanation:
whats the second step of calculating the present value of an ordinary annuity by table lookup
The second step of calculating the present value of an ordinary annuity by the table lookup is to look up the periods and rates in the PV annuity table.
What is the present value of an ordinary annuity?The present value of an ordinary annuity is the current value based on future cash inflows of the annuity, given a specified discount rate.
The present value is higher when the discount rate is lower, and vice versa.
The present value of an ordinary annuity, which discounts the annuity to the current time, is computed as Annuity Payment x Present value of the ordinary annuity table.
In conclusion, an annuity simply means a series of periodic payments and may involve payment at the beginning (annuity due) or at the end of the period (ordinary annuity).
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5x -2y = 1, 5x -6y = b
what is the value of b so that it has no solution
Answer:
DNE
Step-by-step explanation:
You want the value of 'b' so that the system of equations has no solution.
5x -2y = 15x -6y = bNo solutionIn order for the system of two linear equations to have no solution, the equations must describe parallel lines. That is, the lines must have the same slope.
SlopeThe slope of the line written in the form px -qy = c is the coefficient of x when the equation is rearranged to "y=" form. Here, that is p/q.
The slope of the first line is 5/2; the slope of the second line is 5/6. These values are different and do not depend on 'b'.
There is no value of 'b' that will make this system have no solution. It does not exist (DNE).
A 50 Gram Sample of a substance that used to treat thyroid disorders has a K-value of 0.1113. What is the half life? thanks
The half life of the iodine is obtained as 6.2 s.
What is the half life?
Let us recall that the half life would be the time that is taken for about half of the original radioactive isotope that remains in the sample, to become depleted in the thyroid treatment.
Given that we have the fact that the decay constant that we have in the process is given as 0.1113 in the question and we know that;
Half life = 0.693/K
Half life = 0.693/0.1113
Half life = 6.2 s
It would have the half life about 6.2 s.
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