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Explain how you know the following system of equations has at most 2 solutions.
Solve the system algebraically. Show your work.
Solve the system by graphing.
y= 2x-1
y= x^2-9
Answers
Answer:
Step-by-step explanation:
Answer:
The said explanation is the answer.
Step-by-step explanation:
1) Graphing the first function (y = 2x-1). When the exponents of the variables are all 1, that is there are no square, cubes, etc. the equation is a line. Then it is enough to find two points to draw it. We can calculate two points assigning a number to x and calculating the corresponding number for y. For example, when x= 0 y= 2 times 0 -1 = -1. Then the line will pass from the point (0,-1). We need a second point, we can take x=1, then y = 2 times 1 -1 = 1. The line will pass from (1,1). We can mark the two points on the plane and draw the line from these two points.
2) Graphing the second function (y = x^2-9). A quadratic equation is of the form: ax^2+bx+c= 0. We have: y= f(x) -9. Set y=0. We have the quadratic equation: x^2-9=0. Using the algebraic identity: a^2-b^2=(a+b)(a-b). We can rewrite x^2-9=0 as x^2-3^2=0: [(x+3)(x-3)=0] - [(x+3)=0,(x-3)=0] - [x= -3, x= 3]. Hence, there are two solutions for x. So we have two x-intercepts: (-3,0) and (3,0). To find the y-intercept, set x=0: [(y = (0)^2-9=0)] - [(y=-9)]. Hence the y-intercept: (0,-9)
In conclusion, this system of equations at most has two real solutions, since two points of both functions intersect each other.
Here's the graph:
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I provided what I thought the answer is, so if someone would be kind enough to help me clarify!!
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Answer: [tex]90\leq 2x-44\leq 95[/tex]
Step-by-step explanation:
Graph the line through 2,3 that is Parallel to the line with the equation 3x-y=2
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Answer:
y=3x-3
Step-by-step explanation:
first we turn in the stander from to y incept form
then you plug in the x and y, for time here, i am not goona put the steps more
msg me if you need steps
Olivia is cutting a 1 \dfrac12 \text{ m}1 2 1 m1, start fraction, 1, divided by, 2, end fraction, start text, space, m, end text by \dfrac34\text{ m} 4 3 mstart fraction, 3, divided by, 4, end fraction, start text, space, m, end text piece of rectangular paper into two pieces along its diagonal.
Answers
Answer:
The answer is "[tex]0.375 \ m^2 \ \ and \ \ 0.1875 \ m^2[/tex]".
Step-by-step explanation:
A rectangular paper on the side is given by Olivia:
[tex]a= \frac{1}{2} \ m \\\\b= \frac{3}{4} \ m[/tex]
On the diagonal she cuts paper. A paper parts which results would be about half the original field.
Area of origin:
[tex]A= a\times b[/tex]
[tex]= \frac{1}{2} \times \frac{3}{4} \\\\= \frac{3}{8} \ m^2\\\\ = 0.375 \ m^2[/tex]
The resulting parts area:
[tex]A_2 =\frac{A}{2} = \frac{\frac{3}{8}}{2}[/tex]
[tex]=\frac{3}{16} \ m^2 \\\\= 0.1875 \ m^2[/tex]
Chloe was given a box of assorted chocolates for her birthday. Each night, Chloe treated herself to some chocolates. There were originally 30 chocolates in the box and after 2 nights, there were 24 chocolates remaining in the box. Write an equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Chloe's birthday.
Answers
Answer:
C=-3t+30
Step-by-step explanation:
67. Find all points on the x-axis that are 5 units from the point
(4, -3).
Answers
Answer:(9,2) I assume I don’t really understand the question
Step-by-step explanation:
Find the value of x
(9x-38)+(4x+23)=180
Answers
Answer:
x=15
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
9x−38+4x+23=180
9x+−38+4x+23=180
(9x+4x)+(−38+23)=180(Combine Like Terms)
13x+−15=180
13x−15=180
Step 2: Add 15 to both sides.
13x−15+15=180+15
13x=195
Step 3: Divide both sides by 13.
13x/13=195/13
Answer:
15
Step-by-step explanation:
9x-38+4+23=180
13x-15=180
13x=195
x=15
Find the slope of (-2,1),(-2,2)
Answers
Answer:
there is no slope its undefined
Step-by-step explanation:
if f(×)=3×/2+× find the exact value of f(-4)
Answers
-8x + 14 = -2(4x - 7) what is the value of x
Answers
Answer:
Step-by-step explanation:
-8x + 14 = -2(4x - 7)
use the distributive property to get rid of the parentheses (-2 x 4x and -2 x -7) (negative times negative equals positive)
-8x + 14 = -4x + 14
subtract 14 on both sides to cancel out 14
-8x is not equal to -4x
although this may seem like a weird answer, if x is the same variable (pretend it's one) 1 multiplied with -8 will not equal 1 multiplied with -4
Answer:
all real numbers
Step-by-step explanation:
Given
- 8x + 14 = - 2(4x - 7) ← distribute parenthesis
- 8x + 14 = - 8x + 14
Since both sides are equal, then any real value of x is a solution of the equation.
Reciprocal for one as a fraction please help fast
Answers
Answer:
the reciprocal of one is [tex]\frac{1}{1}[/tex] it doesn't really make a difference it's still 1
Step-by-step explanation:
640 divided by one hundred
Answers
Answer:
6.4
Step-by-step explanation:
the correct answer is 6.4
Convert
40.7% to fraction
Answers
Answer:
Decimal Fraction Percentage
0.407 407/1000 40.7
Step-by-step explanation:
Maria makes $6.00 an hour plus 5% commission for telephone sales. Yesterday, Maria worked 8 hours and had sales of $600.00. How much did Maria make yesterday? Explain your answer.
Answers
Given:
Maria makes $6.00 an hour plus 5% commission for telephone sales.
Working time = 8 hours
Sales = $600.00.
To find:
The amount that Maria make yesterday.
Solution:
We know that,
1 hour = $6.00
8 hour = 8 × $6.00 = $48.00
Commission = 5% of telephone sales
Sales = $600.00.
[tex]Commission=5\times 6[/tex]
[tex]Commission=30[/tex]
Total amount that Maria make yesterday is the sum of total hourly changes plus commission.
[tex]\$48.00+\$30.00=\$78.00[/tex]
Therefore, the required amount is $78.00.
A number line going from negative 3 to positive 5. An open circle is at 1.5. Everything to the right of the circle is shaded. Which symbol completes the inequality represented on the graph? z _____ 1.5 > Greater-than-or-equal-to < Less-than-or-equal-to
Answers
Answer:
>
Step-by-step explanation:
Which symbol completes the inequality represented on the graph?
z _____ 1.5
>
Greater-than-or-equal-to
<
Less-than-or-equal-to
The required inequality is given as Z Greater than or equal(≥) to 1.5.
Number line from -3 to 5 is given and a open circle at 1.5.
Right of the circle is shaded and the inequality for the shaded portion to be determine.
Inequality is when the equations contain [≤ , ≥ <, >] is termed as inequalities.
Here, in the given numerical shaded potion of Z is beyond 1.5 to the right so their must be an greater than equal to (≥) after z. i.e. z ≥ 1.5.
Thus, the required inequality is given as Z Greater than or equal(≥) to 1.5.
Learn more about Inequality here:
https://brainly.com/question/20383699
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Identify the vertex for the given function. 2(x-1)^2 + 8
Answers
Answer:
(1,8)
Step-by-step explanation:
PLEASE HELP ME. Select Function or Not A Function.
Answers
Answer:
a and c are functions b is not
Step-by-step explanation:
a and c are both functions
while b, is not
Translate the sentence into an inequality.
A number w divided by 5 is less then 20.
Answers
Answer:
x/5<20
Step-by-step explanation:
The value of yvaries directly with x. If x= 3, then y= 21.
What is the value of x when y= 105?
Answers
Answer:
If y = 105, x should be 15: x =15
Step-by-step explanation:
Simplify the expression using the order of operations.
(12 − 9)3 − 2 × 7 =
Answers
Answer:
-5
Step-by-step explanation:
Parentheses
Exponents
Multiply
Divide
Add
Subtract
(12-9)3-2x7=
(3)3-2x7=
9-14= -5
Answer:
-5 I used pemdas
Step-by-step explanation:
Brainliest please
What is the range of this data set?
A.) 53
B.) 60
C.) 100
D.) 40
Answers
Answer:
53 or A
Step-by-step explanation:
Range would be 75 - 22 = 53
Answer:
A
Step-by-step explanation:
Simplify.
2+{8−2[32+5(1+2)]}
Answers
Answer:
2+{8-2[32+5(1+2)]} = −84
Work:
2+{8-2[32+5(1+2)]}
Add (1+2)
2+{8-2[32+5+3]}
Add [32+5+3]
2+{8-2+40}
Add 8-2+40
2+{46}
Times 1{46} because there is a 1 in front of parentheses; if there wasn’t a 1 it would look like 2{46} instead of 2+{46}
2{46}
Times 2{46}
92
I hope that makes sense?!
Find the slope of the line that passes through:
(-4,7) and (-6, -4)
Answers
Answer:
Ok:
Step-by-step explanation:
The formula is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. Here, we can plug in values where x2 = -6, x1 = -4, y2=-4, and y1 = 7. Solving, we get the slope is 11/2 or 5.5.
How do I find the area of a triangle if I only have the angle and 1 side length?
Answers
Answer:
5.4
Step-by-step explanation:
Use the pythagorean theorem a^2 + b^2 = c^2
4 more than one third of a number n is 6. An equation is? The solution is n =?
Answers
Answer:
[tex]\frac{1}{3}[/tex]n + 4 = 6
6
Step-by-step explanation:
Given problem:
4 more than one third of a number n is 6
Unknown:
The equation = ?
Solution of the number = ?
Solution:
let the number = n
So, 4 more than one third of a number;
One third of n = [tex]\frac{1}{3}[/tex]n
4 more;
[tex]\frac{1}{3}[/tex]n + 4
is 6;
[tex]\frac{1}{3}[/tex]n + 4 = 6 (equation of the expression)
Let us now solve the equation:
[tex]\frac{1}{3}[/tex]n + 4 = 6
[tex]\frac{1}{3}[/tex]n = 6 - 4
[tex]\frac{1}{3}[/tex]n = 2
n = 6
which number is a multiple of 7
Answers
Answer:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70...
Step-by-step explanation:
HELP NEEDED ASAP WILL GIVE YOU BRAINLIEST AND 5 STARS RATE
Answers
Answer:
A) - .5
B) 7
C) - 2
Step-by-step explanation:
8n +7(2n-4)=4(7 + 3n) - 6
Answers
Answer:
n=5 hope this helps
Step-by-step explanation:
HELPPPPPPPPPP!!!!!!!!!!!!!!! plss help meh Please and Thank you for your time
Simplify the expression.
3/2(4f - 10)
Answers
Derivative of 6^(4x)
Add step by step explanation
Answers
Answer:
4*6^4x ln(6)
Step-by-step explanation:
6^(4x)
6^4x
-d/dx[6^4x]
ln(6)*6^4x*d/dx[4x]
ln(6)*6^4x*4*d/dx[x]
4ln(6)*6^4x*1
4ln(6)*6^4x
4*6^4x ln(6)
Find the next number in the sequence: "-1, 1, 4, 8, 13, ..."
Answers
Answer:
19
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
because the more you go up the amount increases
