Answers
Answer:
x = -4, -2
Step-by-step explanation:
Given equation is,
x² + 6x + 8 = 0
Let the equation to be graphed is,
y = x² + 6x + 8
y = x² + 2(3x) + 9 - 1
y = x² + 2(3x) + 3² - 1
y = (x + 3)² - 1
Table for the Input-output values
x -6 -4 -3 -2 -1 0
y 8 0 -1 0 3 8
Now we can plot these points on the graph as attached.
Since, this graph is intersecting x-axis at x = -4, -2
Therefore, solutions of the given equation will be x = -4, -2
Related Questions
solve each of the following systems, if possible. indicate whether the system has a unique solution, infinitely many solutions, or no solution.
a. 2x + 10y = 9
3x + 15y = 13
b. 2x + 8y = 5
3x + 12y = 7.5
c. y = 3-x
d. 5x -8y = -1
-5/2 x + 4y = 1/2
Answers
Answer:
(a) No solution
(b) Infinitely many solution
(c) No solution
(d) Infinitely many solution
Step-by-step explanation:
Solving (a):
[tex]2x + 10y = 9[/tex] --- (1)
[tex]3x + 15y = 13[/tex] --- (2)
Multiply (1) by 1.5
1.5 * [[tex]2x + 10y = 9[/tex]]
[tex]3x + 15y = 13.5[/tex] --- (3)
Subtract 2 and 3
[tex]3x - 3x + 15y - 15y = 13.5 - 13[/tex]
[tex]0 = 0.5[/tex]
The above is false; Hence, the system has no solution
Solving (b):
[tex]2x + 8y = 5[/tex] --- (1)
[tex]3x + 12y = 7.5[/tex] -- (2)
Multiply 1 by 1.5
1.5 * [[tex]2x + 8y = 5[/tex]]
[tex]3x + 12y = 7.5[/tex]
Subtract 2 and 3
[tex]3x - 3x + 12y - 12y = 7.5 - 7.5[/tex]
[tex]0 = 0[/tex]
The above implies that the system has infinitely many solutions
Solving (c):
[tex]y = 3 - x[/tex]
A second equation is required to solve for (c)
Solving (d):
[tex]5x - 8y = -1[/tex] --- (1)
[tex]-\frac{5}{2}x+ 4y = \frac{1}{2}[/tex] --- (2)
Multiply (2) by 2
[tex]-5x + 8y = 1[/tex] --- (3)
Add 1 and 3
[tex]5x - 5x -8y + 8y = -1 + 1[/tex]
[tex]0 = 0[/tex]
The above implies that the system has infinitely many solutions
don’t mind the pencil writing
Answers
Answer:
Length = 22 cm
Width = 4 cm
Step-by-step explanation:
Area = 88 cm²
Length = x + 7
Width = x - 11
Area of rectangle = length*width
Therefore:
(x + 7)(x - 11) = 88
x(x - 11) +7(x - 11) = 88
x² - 11x + 7x - 77 = 88
Add like terms
x² - 4x - 77 = 88
x² - 4x - 77 - 88 = 88 - 88
x² - 4x - 165 = 0
Factorize
x² - 15x + 11x - 165 = 0
x(x - 15) +11(x - 15) = 0
(x + 11)(x - 15) = 0
x = -11 or x = 15
Let's use the positive number.
Therefore:
Length = x + 7
Plug in the value of x
Length = 15 + 7 = 22 cm
Width = x - 11 = 15 - 11 = 4 cm
If you sleep 6 hrs out of 24 hrs how much percent do you sleep?
Answers
Answer:
25%
Step-by-step explanation:
I hope this helps you!!
Answer:
You sleep 25% of the day.
Step-by-step explanation:
First you change the equation into a fraction:
6 hrs out of 24 hrs = 6/24
Then you can simplify this fraction:
6/24 = 1/4
Lastly, convert the fraction to a percent:
1/4 = 25%
Brainliest would be greatly appreciated!!!!
A line that passes through points (x, 4) and (6, -1) has a slope of 5/6. What value of x will yield the given slope?
A: x = -12
B: x = 0
C: x = -6
D: x = 12
Answers
If the triangles below are similar, find the value of x. 42 х 11 22
Answers
9514 1404 393
Answer:
28
Step-by-step explanation:
Corresponding sides are proportional.
x/42 = 22/(22+11)
x = 42(2/3)
x = 28
13. Find the diagonal of a square if the lengths of its sides are each 16 mm. Round to the nearest tenth.
A. 16.0 mm
B. 45.3 mm
C. 22.6 mm
D. 32.0 mm
Answers
Answer:
[tex]C.\ 22.6mm[/tex]
Step-by-step explanation:
When one draws a diagonal in a square (a line connecting opposite corners), the halves of the square form (45-45-90) triangles. This means that the triangle follows the following ratio,
[tex](a)-(a)-(a\sqrt{2})[/tex]
Where (a) represents the legs or the sides adjacent to the right angle (angle with the box around it) and ([tex]a\sqrt{2}[/tex]) represents the hypotenuse or side opposite to the right angle.
Both legs have a length of (16)mm this is because all sides of a square are congruent, and the two sides adjacent to the right angle are both the sides of a square. One of them has the measure of (16) thus the other must have a measure of (16). This means that the diameter has the following value,
[tex]16\sqrt2}[/tex]
In numerical form,
[tex]\approx22.62[/tex]
If Rashid faces north and then turns clockwise half a turn, in which direction does he face
Answers
Answer:naneeeeee
Step-by-step explanation:
Please no troll include work
Answers
2) 40/4 = 10/1 = 10
3) 7/10
4) 48/3 = 16/1 = 16
5) 8/9
6) 32/5
if you have any questions, let me know!
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using Minitab, resulting in the accompanying output.
Variable N Mean St Dev SEMean Z P -Value
lifetime 50 738.44 38.20 5.40 -2.14 0.016
What conclusion would be appropriate for a significance level of .05? A significance level of .01? What significance level and conclusion would you recommend?
Answers
What is today date please tell me
Solve for 44.
4 4 = [?]
510
51
44/42
Answers
Angle 4 is an exterior angle which is equal to the sum of the two opposite inside angles.
The two opposite inside angles are given as 51 and 51
Angle 3 = 51 + 51 = 102 degrees.
Answer:
[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]
Step-by-step explanation:
the sum of the interior angles of a triangle is 180°
thus our equation is
[tex] \displaystyle {51}^{ \circ} + {51}^{ \circ} + \angle2 = {180}^{ \circ} [/tex]
simplify addition:
[tex] \displaystyle {102}^{ \circ} + \angle2 = {180}^{ \circ} [/tex]
cancel 102° from both sides:
[tex] \displaystyle \angle2 = {72}^{ \circ} \cdots \text{I}[/tex]
By straight line theorem we acquire:
[tex] \displaystyle \angle4 + \angle2 = {180}^{ \circ} [/tex]
substitute:
[tex] \displaystyle \angle4 + {72}^{ \circ} = {180}^{ \circ} [/tex]
cancel 72° from both sides:
[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]
hence, the measure of [tex]\angle 4[/tex] is 108°
Which statements are true about the graph of y s 3x + 1 and y 2 -x + 2? Check all that apply.
O The slope of one boundary line is 2.
O Both boundary lines are solid.
A solution to the system is (1, 3).
O Both inequalities are shaded below the boundary lines
O The boundary lines intersect.
Answers
===========================================================
Explanation:
Let's go through each of the answer choices to see which are true and which are false.
----------------
Choice A
The general slope intercept form is y = mx+b
m = slope and b = y intercept.
For y = 3x+1, the boundary line of the first inequality, the slope is 3.
For y = -x+2, the slope is -1.
None of the slopes are 2.
Choice A is false.
We'll use the concept of slope again in choice E.
----------------
Choice B
The "or equal to" part of the inequality sign is what directly determines the boundary line being solid. This is because we include points on the boundary.
Choice B is true.
----------------
Choice C
Plug x = 1 and y = 3 into the first inequality
[tex]y \le 3x+1\\\\3 \le 3(1)+1\\\\3 \le 3+1\\\\3 \le 4\\\\[/tex]
The last inequality is true, so the first inequality is true when (x,y) = (1,3). This makes (1,3) a solution to [tex]y \le 3x+1\\\\[/tex]
Repeat those steps for the other inequality given to us
[tex]y \ge -x+2\\\\3 \ge -1+2\\\\3 \ge 1\\\\[/tex]
which is also true, so that makes (1,3) also a solution to [tex]y \ge -x+2\\\\[/tex]
The point (1,3) is a solution to both inequalities at the same time, making it a solution to the system overall.
Choice C is true
----------------
Choice D
When y is fully isolated, the "less than" inequality indicates the shading is below the boundary. This is due to us considering points of y coordinates smaller than the boundary line. So we'll shade below the boundary for [tex]y \le 3x+1\\\\[/tex]
We don't do the same for [tex]y \ge -x+2\\\\[/tex]. Instead, we'll shade above the solid boundary line.
Choice D is false.
----------------
Choice E
If two lines have equal slopes, but different y intercepts, then we have parallel lines. Parallel lines never intersect.
If on the other hand, the slopes are different values, then the two lines will intersect somewhere on the xy grid. There will only be exactly one point of intersection.
The given system has boundary lines of slopes 3 and -1, for the first and second inequality respectively. Refer back to choice A. These differing slopes tell us that the boundary lines intersect somewhere.
Choice E is true
Let's go through all the options one at a time and look for the correct ones
Option 1: The slope of one boundary line is 2
We have 2 equations of lines, where the coefficients of are 3 and -1 respectively
because the coefficient of x denotes the slope of a line, we know that the lines have the slope 3 and -1, not 2
Hence, this option is Incorrect
Option 2: Both boundary lines are solid
In order for the boundary lines to be solid, the inequality must have an 'equal to', like ≤ (less than or equal to) or ≥ (greater than or equal to)
we can see that that's the case in our case and hence, this option is Correct
Option 3: A solution to the system is (1, 3)
To confirm this, we'll plug these coordinates into the given inequalities and see if it stands correct
y ≤ 3x + 1
3 ≤ 3(1) + 1
3 ≤ 4 which is correct because 3 is less than 4
Second equation:
y ≥ 2 - x
3 ≥ 2 - 1
3 ≥ 1
Which is also true because 3 is greater than 1
Now, we can say that (1 , 3) is a solution to the system because it satisfies both the equations and is Correct
Option 4: Both inequalities are shaded below the boundary lines
For an inequality to be shaded below the boundary line, it must have the ≤ inequality (in case of solid line) and < inequality (in case of dotted line)
because the second inequality listed includes the ≥ inequality, which was not mentioned above, it won't be shaded below
another way to think about it is that any 'greater than' inequality will shade everything above the line and the 'lesser than' inequality will shade below the line
which means that this option is Incorrect
Option 5: The boundary lines intersect
In order for the boundary lines to intersect, they must have have different slopes.
as we mentioned in the explanation of the first option, that the slopes of the lines is 3 and -1, which are different slopes
Therefore, this option is Correct
Help with Math Question 1
Answers
Answer:
Step-by-step explanation:
X is also 67° Like the interior angle
Find the value of x in the isosceles triangle below.
need this ASAP! Please include an explanation if possible
Answers
Answer:
x = 64
Step-by-step explanation:
Remark
The markings on the triangle tell us that the sides are equal. There is no marking on the third side, so it is not equal to the other two. The important fact is the angles opposite equal sides are also equal. That means that the angle on the lower right is equal to x.
Equation
So you have two angles = to x.
x + x + 52 = 180 All triangles have interior angles of 180
2x + 52 = 180 Combine the like terms on the left.
- 52 -52 Subtract 52 from both sides
2x = 128 Divide by 2
2x/2 = 128/2
x = 64
In square units!!! Real answers only please no links!!!!
Answers
Hurry up please timed test
Answers
Answer:
the second option
hope this helps!
f
Solve the equation + 22 = 17.
3
Answers
Answer: subtract 22 on both sides
Step-by-step explanation:
Now you would have -5 to solve take 3 and multiply on both sides to get f=-15
Hope this helps
Answer: -5
Step-by-step explanation:
Which of the following could be the equation of the function below?
y=0.5cos(2(x-pi/2))+2 y=0.5cos(4(x+pi/2))-2 y=0.5cos(4(x+pi))+2 y=0.5cos(2(x-pi))-2
Answers
Answer:
D y=0.5cos(2(x-pi))-2
Step-by-step explanation:
The Equation of the function is y=0.5 cos (4(x+π/2))-2
The correct option is B.
As, y=a cos (b(x+c))+d
Here, y max=-1.5 and y min=-2.5
So, d=(max + min)/2
d=(-1.5+(-2.5))/2
d=(-1.5-2.5)/2
d=(-4.0)/2
d=-2.0
and, the horizontal axis is
y=-2
Then, y= a cos(b(x+c))+(-2)
y=a cos (b(x+c))-2
The amplitude (a) is
a = max-d = d- min
a=-1.5-(-2)=-2-(-2.5)
a=-1.5+2=-2+2.5
a=0.5.
We have the period is π/2
P=2π/b
π/2=2π/b
πb=4π
b=4
Now, y=0.5 cos (4(x+c))-2
Thus, the required function is y=0.5 cos (4(x+π/2))-2.
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3 9 26
a. Use eoch digit once, make the smallest 4-digit number:
b. Use each digit once, moke the largest 4-digit number :
c. You can use one diga twice, make the smallest 4-digit number:
c. You con use one digit twice make the largest 4-digit number
.
Answers
b. 9632
c. 2236
d. 9963
ONLY ANSWER CORRECTLY
Select the correct answer.
Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan's father and paternal grandfather were allergic to
penicillin, Nathan has a 75% chance of having the same allergy. The doctor performed a skin test to see whether Nathan would react to it. The
test is 98% accurate. What is the probability that Nathan is not allergic to penicillin and the test predicts it?
OA. 0.005
ОВ,
0.015
Ос.
0.245
OD 0.735
Reset
Next
1071 Can Allen
app.edmentum.com/assessments delivery/ua/mt/launch/49001233/826708953/aHROCHM6Ly9mMiShcHAUZWR
ZXItdWkvdXNICI
B4MY3MDG5NTE 3de
US
10:21
DULL
Answers
Answer:
C 0.245
Step-by-step explanation:
have a good day/night sorry if wrong may i please have a bralliest
There are 44 rabbits. What is 44 rounded to the nearest 10?
Answers
Answer:
4
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
44 is closer to 40 than 50 because 44-40 = 4, 50-44=6 and 4<6
3b.) Nora is buying a used car valued at $22,730. It is expected to
depreciate an average of 9.5% each year. Predict the value of Nora's car in
6 years.
Help ??
Answers
Answer:
$12487.86
Step-by-step explanation:
Given data
Cost of car= $22,730
Rate of decrease= 9.5%
Time= 6 years
We can predict the value by using the exponential decay function'
A= P(1-r)^t
substitute
A= 22730(1-0.095)^6
A= 22730(0.905)^6
A= 22730*0.5494
A=$12487.86
Hence the value will be $12487.86
What is the probability that the card is not a heart, GIVEN that the card is a face card??
Best answer gets brainliest!!
Answers
Answer:
.75
Step-by-step explanation:
Conditonal probability formula:
A|B= (A∩B)/B
let NH= Not heart
Let F= Face
NH|F= NH∩F/F
not hearth and face is 9
face is 12
9/12=.75
Lin drew this set of axes and plotted the points A=(1,2), B=(-3, -5), C=(5,7), D=(-4, -3), and E=(-4, 6) on them. Identify her mistakes! Which points were plotted incorrectly?
Answers
Answer:
B=(-3, -5)
Step-by-step explanation:
if the radius of an argon atom is 0.0000000000098m, write in scientific notation
Answers
Answer:
90
Step-by-step explanation:
In parallelogram LMNO, the measure of N= 98° and the measure of 0= 82°. Find the measure of M.
Answers
Answer:
82
Step-by-step explanation:
180 - 98=82
The sum of two angels is 180
Jamal borrowed $316 for nine months. He paid it off by paying $38.27 monthly.
What will he pay in finance charges?
Answers
The finance charge payed by Jamal is $28.43.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Amount borrowed by Jamal for nine months = $316
His monthly payment = $38.27
Total amount payed by Jamal for nine months = [tex]9(38.27)[/tex]
⇒ [tex]\$344.43[/tex]
Thus his finance charge = [tex]344.43-316[/tex]
⇒ [tex]\$28.43[/tex]
Hence we can conclude that the finance charge payed by Jamal is $28.43.
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X-y=6, x+y=8, zx+zy=20
Answers
Answer:
Step-by-step explanation:
x = 6 + y
6 + y + y = 8
y = 1
x - 1 =6
x = 7
zx + zy = z(x + y) = 20
z = 2.5
Answer:
X = 7
Y = 1
Z = 2/5
Step-by-step explanation:
7-1 = 6
7+1 = 8
2/5 × 7 + 2/5 = 20
Answer Choices:
A. 0.26
B. 0.56
C. 0.52
D. 0.31
If you answer back with a link your comment will be reported.
Answers
x^2=-28 square root method
Answers
Answer:
2i[tex]\sqrt{7}[/tex],-2i[tex]\sqrt{7}[/tex]
Need help on this please tell me the answer
Answers
Answer:
your answere is 80 degrees
Step-by-step explanation:
the total of the inside is 180 so subtract 35 and 65 from 180 and you get 80