The best approximation for the solution to the system of equation is option C) (-2.2 , -3)
According to the question we have been given two system of linear equation which are:
y = -3 (1)
and y = x - 0.8 (2)
Now solving these two equation and find the value of x
Substituting the value of y from equation (1) to the equation (2) we get
-3 = x - 0.8
-3 + 0.8 = x
x = -2.2
Thus the best approximation for the solution to the system of equation is option C) (-2.2 , -3)
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Refer
to the rectangle at the right. Suppose the side lengths
are doubled.
a.
Find the percent of change
in the perimeter.
in the area.
b. Find the percent of change
Given the measures of three angles of a triangle, explain how to find the ratio of the lengths of two sides of the triangle.
You can let the sides be a and b. You can then use the Law of Sines to create an equation relating the two sides and the angles opposite them, and finally isolate a/b.
I need help with this today please!
Answer:
kevin ate 1/6 more than Kathy or un simplified, 2/12
Step-by-step explanation:
least common denominator
Find the distance.
1. (-2,2) (4, -1)
2. (-3,-5) (2, 5)
3. (-4,0). (2, 3)
Answer:
1)3√5
2)5√5
3)3√5
2/3x - 5/8 = 1
pls help asap
Solve. Check for extraneous solutions. √-3 x-5=x+3
-7 = extraneous solution
The equation is
[tex]\sqrt{-3x - 5}[/tex] = x + 3
To find the value of x we need to square both sides of the equation
[tex](\sqrt{-3x - 5})^{2}[/tex] = [tex](x + 3)^{2}[/tex]
- 3x -5 = [tex]x^{2}[/tex] + 6x + 9
[tex]x^{2}[/tex] + 9x + 14 = 0
[tex]x^{2}[/tex] + 7x + 2x + 14 =0
x( x + 7) + 2( x + 7) = 0
(x + 7) (x + 2 ) = 0
x = -2, -7
To find the extraneous solution we have to put both the value of x in the equation.
x=-2
[tex]\sqrt{(-3 * -2) - 5}[/tex] = -2 +3
[tex]\sqrt{1}[/tex] = 1
1 = 1
x = -7
[tex]\sqrt{(-3 * -7) - 5}[/tex] = -7 +3
[tex]\sqrt{16}[/tex] = -4
4 = -4
The extraneous solution of the equation is -7 and -2 is the solution of the equation
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In holly jewelry box 50% of the jewelry is bracelets and the rest is necklaces.If holly has 30 bracelets,How many pieces of jewelry is in her jewelry box
HELP MEEEEEE ❓❓❓⁉️⁉️⁉️⁉️⁉️
A) two rational roots
B) two unrational roots
C) two equal roots
D) two unequal real roots
E) two non real complex roots
The nature of the roots in the given quadratic equation (x - 3)² + (x - 4)² = 0 is; A: two rational roots
What are the roots of the Quadratic Equation?We are given the quadratic equation;
(x - 3)² + (x - 4)² = 0
Now, some of the rules in naming the roots are;
If b² – 4ac > 0, then the roots are real and unequal
If b² – 4ac = 0, then the roots are real and equal
If b² – 4ac < 0 then the roots are unequal and Imaginary
If b² – 4ac > 0 (is a perfect square), then the roots are real, rational and unequal
If b² – 4ac > 0 (is not a perfect square), then the roots are real, irrational and unequal
From the above rules and comparing to our given equations, it is clear that we have two rational roots which are x = 3 and x = 4.
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Im not sure how to do this one
Answer:
B
Step-by-step explanation:
6x - 8x - 4 = - 2x - 2 , that is
- 2x - 4 = - 2x - 2 ( add 4 to both sides )
- 2x = - 2x + 2 ( add 2x to both sides )
0 = 2 ← not possible
this indicates the equation has no solution
Answer:
6x-8x-4=-2x-2 (group the like terms)
6x-8x+2x= 4-2 (-8x+2x= -6x and 6x-6x=0) (4-2=2)
answer= 0=2
,therefore: it has no solution
Step-by-step explanation:
the answer is 0=2 which mean there is nothing that 2 is equivalent to because when you group the like terms and work out the answer the x in the equation will be canceled.
If x and y vary inversely and x = 2.5 when y = 100 find x when y = 25
Answer:
the answer is b
Step-by-step explanation:
thnx
How many zeros does this 7.185629 x 10^2985 have?
Answer: 2979 Zeroes
Step-by-step explanation:
1. Figure out what 10^2985 is. (It's one followed by 2985 zeroes).
2. Using that knowledge, make 7.185629 a whole number. To do that, you need to multiply it by a number that has the same number of zeroes as it does to move the decimal place one by one to the right. In this case, it is 1,000,000, because it has 6 zeroes and you need to move the decimal point past 6 numbers (after 7 in 7.185629).
3. Subtract 2985 by 6, because you used 6 zeroes.
4. This gives you the answer 2979 zeroes because 2985 zeroes - 6 zeroes= 2979 zeroes.
There are between 50and 60 eggs in a basket when mohammed counts by 3's,there are 2egg left left over when he counts by 5's there are 4 left over how many eggs are there in the basket
Answer: 59 eggs
Step-by-step explanation: Dividing 3 will get you 19 eggs with 2 left over. Dividing 59 by 5 will get you 11 eggs and 4 left over
Aidan is doing a multiple choice test with 20 questions he scores 3 marks for a correct answer and loses 1 mark if the answer is incorrect he answered all questions and scored 40 marks how many we questions were correct
Answer: 10 answers correct and 10 answers incorrect
Step-by-step explanation:
60 is the highest total assuming every one was correct
20 is the lowest total assuming every one was incorrect
40 is the middle meaning he got half write half wrong
Half of 20 is (10) (10 x 3 = 30 ) + ( 10 x 1 = 10 ) 30 + 10 = 40
Answer: 13.3 repeating is what I got see if it make sense according to my work
Step-by-step explanation: 20x3=60, and one mark per wrong answer, so 60-40=20 wrong. So, 40 divided by 3=13.3 repeating
Write a polynomial function with rational coefficients and the given roots.
-√7, 1+2 i
The polynomial function is [tex]x^{2}-x-2ix+\sqrt{7}x-\sqrt{7}-2\sqrt{7}i[/tex]
What are polynomial functions ?In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear Polynomial Quadratic PolynomialSome examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³According to question,
roots are -√7 , 1+2i
Thus the factors are :
(x - (-√7)) (x-(1+2i))
=> (x+√7)(x-1-2i)
=>x²-x-2ix+√7x-√7-√7.2i
Thus polynomial function for given roots is x²-x-2ix+√7x-√7-√7.2i.
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Find each product or quotient. 7√7 . 3√7
The given expression can be solved by determining the product of irrational numbers.
Irrational number is a real number that cannot be expressed as the quotient of two integers. If a square root of a number is not a perfect square root, then it is an irrational number.
In the given expression, there are two rational numbers 7 and 3 while two irrational numbers √7 and √7.
The integer 7 and 3 can be multiplied. Hence,
7√7*3√7=7*3*√7*√7=21*√7*√7
When multiplying terms in square root, √a*√b=√ab. Hence,
21*√7*√7=21√7*7
As square root of a number is the number multiplying itself i.e., √a*a=a
21√7*7= 21*7=147
The product of the expression 7√7.3√7 is 147
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show work please
2x + 3(4x – 1)
2) The area of my best friend's pool is 121ft2. What is the width of the pool if the length is 12ft?
Answer:
10.083333...ft
Step-by-step explanation:
length = 12ft
area = 121sqft
area = length * width
121sqft = 12ft * width
width = 121sqft / 12ft
[tex]width = 10\frac{1}{12}\mathrm{ft}[/tex]
width = 10.08(3)ft
simplify -x^2(3x^2-2x-4)
Answer:
-3x^{4}+2x^{3}+4x^{2}
Step-by-step explanation:
Re-order terms so constants are on the left
-x^{2}\left( 3x^{2}-2x-4\right)
-x^{2}\left( 3x^{2}-2x-4\right)
2
Distribute
-\textcolor{#C58AF9}{x^{2}\left( 3x^{2}-2x-4\right) }
-\left( \textcolor{#C58AF9}{3x^{4}-2x^{3}-4x^{2}}\right)
3
Distribute
-\left( 3x^{4}-2x^{3}-4x^{2}\right)
-3x^{4}+2x^{3}+4x^{2}
10.
Ginnie and her cousin went to a restaurant for dinner. Ginnie dinner cost
$15 more than her cousin's. If their combined bill was under $65, which
inequality best describes the cost of their dinners?
The cost of the Ginnie's dinner is a $40 and the cost of his cousin's dinner is $25.
According to the statement
We have to find that the cost of their dinners.
So, For this purpose, we all know that the
The cost function may be wont to find the common cost, which is that the average amount of cash it costs to provide a unit.
From the given information:
Ginnie dinner cost $15 over her cousin's. If their combined bill was under $65.
Then
Let Ginnie dinner is x and his cousin's be y.
Then
x+y = 65 And x = y+15
Then
Substitute the values then y+15+y = 652
y+15 = 652
y = 65-152
y = 50
[tex]y = \frac{50}{2}[/tex]
y = 25.
Then x = y+15
x = 25+15
x = 40.
So, The cost of the Ginnie's dinner is a $40 and the cost of his cousin's dinner is $25.
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Please help me fill in the blanks
A line with a positive slope slants (blank) and to the right. A line with a negative slope slants (blank) and to the right. A (blank) line has zero slopes. A (blank) line has an undefined slope.
Answer:
Find the Slope from a Graph
Identify rise and run from a graph
Distinguish between graphs of lines with negative and positive slopes
Find the Slope from Two Points
Use the formula for slope to define the slope of a line through two points
Find the Slope of Horizontal and Vertical Lines
Find the slope of the lines
x
=
a
and
y
=
b
Recognize that horizontal lines have slope = 0
Recognize that vertical lines have slopes that are undefined
Identify slopes of parallel and perpendicular lines
Given a line, identify the slope of another line that is parallel to it
Given a line, identify the slope of another line that is perpendicular to it
Interpret slope in equations and graphs
Verify the slope of a linear equation given a dataset
Interpret the slope of a linear equation as it applies to a real situation
Identify slope from a graph
The mathematical definition of slope is very similar to our everyday one. In math, slope is used to describe the steepness and direction of lines. By just looking at the graph of a line, you can learn some things about its slope, especially relative to other lines graphed on the same coordinate plane. Consider the graphs of the three lines shown below:
You can determine the slope of a line from its graph by looking at the rise and run. One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope. Let’s look at an example.
EXAMPLE
Use the graph to find the slope of the line.
A line that crosses the points (2,1) and (6,3). A blue line labeled Rise goes up two units from the point (2,1). A red line labeled Run goes left from the point (6,3) so that it forms a triangle with the main line and the Rise line. A formula says slope equals rise over run.
Show Solution
This line will have a slope of
1
2
no matter which two points you pick on the line. Try measuring the slope from the origin,
(
0
,
0
)
, to the point
(
6
,
3
)
. You will find that the
rise
=
3
and the
run
=
6
. The slope is
rise
run
=
3
6
=
1
2
. It is the same!
Let’s look at another example.
EXAMPLE
Use the graph to find the slope of the two lines.
A graph showing two lines with their rise and run. The first line is drawn through the points (-2,1) and (-1,5). The rise goes up from the point (-2,1) to join with the run line that goes right to the point (-1,5). The second line is drawn through the points (-1,-2) and (3,-1). The rise goes up from the point (-1,-2) to join with the run to go right to the point (3,-1).
Show Solution
When you look at the two lines, you can see that the blue line is steeper than the red line. It makes sense the value of the slope of the blue line, 4, is greater than the value of the slope of the red line,
1
4
. The greater the slope, the steeper the li
Step-by-step explanation:
Convenient store sold 8.5 pounds 6.26 Ibs 9.2 Ibs and 4.54 Ibs of apples each week during one month is the store started at out the month with an inventory of 46.2 Ibs of apples how many were left at the end of the month
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Round 4328 to 1 significant figure
Round 25446 to 1 significant figure
Round 38562.7 to 1 significant figure
Round 87600.2 to 1 significant figure
1) Rounding up 4328 to 1 significant figure will give us; 4000
2) Rounding up 25446 to 1 significant figure will give us 30000.
3) Rounding up 38562.7 to 1 significant figure will give us; 40000
4) Rounding up 87600.2 to 1 significant figure will give us; 90000
When talking about significant figures with whole numbers, we mean all non - zero whole numbers. They include;
Any non-zero digit.Zeros between non-zero digits such as 4004 or 98.50007.Trailing zeros only when there is a decimal point as in 7580. or 394.2200.1) Rounding up 4328 to 1 significant figure will give us; 4000
2) Rounding up 25446 to 1 significant figure will give us 30000.
3) Rounding up 38562.7 to 1 significant figure will give us; 40000
4) Rounding up 87600.2 to 1 significant figure will give us; 90000
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Solve. Check for extraneous solutions. (7 x+6)¹/₂-(9+4 x)¹/₂=0
No Extraneous solution
The given equation is
( 7x + 6 ) ^ 1/2 - (9 + 4x ) ^ 1/2 = 0
We have to find the value of x
[tex]\sqrt{7x + 6}[/tex] = [tex]\sqrt{9 + 4x}[/tex]
Squaring both sides of the equation
[tex](\sqrt{ 7x + 6} )^{2}[/tex] = [tex](\sqrt{9 + 4x})^{2}[/tex]
7x + 6 = 9 +4x
3x = 3
x = 1
To know whether the value of x is the extraneous solution or not, put the value of x in the equation
[tex]\sqrt{7 * 1 + 6}[/tex] -[tex]\sqrt{ 9 + 4 * 1}[/tex] = 0
[tex]\sqrt{13}[/tex] - [tex]\sqrt{13}[/tex] =0
0 = 0
Therefore there is no extraneous solution to the equation as x = 0 is the solution of the equation.
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Solve. Check for extraneous solutions. 3 √2x -3=9
No extraneous solution to the equation.
The equation is:
3[tex]\sqrt{2x}[/tex] - 3= 9
To know whether the equation has an extraneous solution, first we need to find the value of x.
[tex]3\sqrt{2x}[/tex] = 12
[tex]\sqrt{2x}[/tex] = 4
2x = 16
x = 8
Now put the value of x in the equation.
3[tex]\sqrt{2 * 8}[/tex] - 3 = 9
3× 4 - 3 = 9
12 - 3= 9
9 = 9
Therefore there is no extraneous solution to the equation, x = 8 is the solution of the equation.
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PLEASE HELP QUICK TYSM
Answer:
Step-by-step explanation:oooooooooooooooooooooooooooooooooooooo
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Bill weighs 53kg.This is more than Juan. How much does Juan weigh
Answer:
Step-by-step explanation:
Answer:
This is more than Juan
Step-by-step explanation:
Divide and simplify. √36 x⁴ / √9 x⁶
The divide and simplify of the equation √36 x⁴ / √9 x⁶ will result to [tex]\frac{2}{x^{2} }[/tex]
Let's begin by simplifying the equation;
Simplify the equation by finding the square root of both 36 and 9
The square root of 36= 6
The square root of 9= 3
= [tex]\frac{6x^{4} }{3x^{6} }[/tex]
The above equation can also be written as;
= [tex]6x^{4} * 3x^{-6}[/tex]
The next step is to solve the powers, that is,
= [tex]\frac{6x^{4} }{3x^{6} }[/tex]
Cancel out 6 by 3 and get 2
The result is,
= [tex]\frac{2}{x^{6-4} }[/tex]
The final submission result is,
= [tex]\frac{2}{x^{2} }[/tex]
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Maxwell drives 45 miles/hour for 0.4 hours. Bianca drives 65 miles/hour for 0.25 hours.
Who drove farther?
Answer:
D Maxwell drove further. He drove 18 miles.
Step-by-step explanation:
Distance = Speed × Time
Maxwell:
Distance = 45 × 0.4
Distance = 18 miles
Bianca:
Distance = 65 ×0.25
Distance = 16.25 miles
18 > 16.25
Maxwell drove further. He drove 18 miles.
Answer:
D. Maxwell. He drove 18 miles,
Step-by-step explanation:
Distance = speed * time
Maxwell drives:
45 * 0.4 = 18 miles.
Bianca drove:
65 * 0.25 = 16.25 miles.
Somebody please solve the Absolute Value Inequality.: |-7b+1|-8<-70
Answer: the answer is no solution
Step-by-step explanation:
Answer:
No Solution
Step-by-step explanation:
An absolute value will always have a positive value. If you isolate the absolute value it shows the abs val LESS THAN a negative number. Its not possible to have a positive less than a negative.
If you just go on and do the problem in auto-pilot, the answers don't check. ALSO since it it a LESS THAN inequality statement BOTH of the inequalities have to be true at the same time which is not possible.
See image.
Is y=e (x+7) a natural base exponential function?
We need to know about natural exponential function to solve the problem. The given function is a natural base exponential function.
An exponential function is a function in which x is an exponent. An exponential function has an exponential graph that keeps growing. A natural base exponential function is one where the base of the function is e which is a mathematical constant and is approximately equal to 2.71828. The inverse of a natural exponential function is a logarithmic function. An exponential function is of the form y=[tex]b^{x}[/tex] where b is the base, in a natural base exponential function, the b is replaced by e which means y=[tex]e^{x}[/tex]. In the given question y=[tex]e^{x+7}[/tex] is a natural base exponential function since the base is the natural base.
Therefore we found that the given function is a natural base exponential function.
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