Answer:
(-6,2)
Step-by-step explanation:
[tex]f(x)<0[/tex]
We are given [tex]f(x)=x^2+4x-12[/tex].
So we need to solve:
[tex]x^2+4x-12<0[/tex]
First let's find when the expression on the left is 0.
[tex]x^2+4x-12=0[/tex].
The expression on the left is factorable.
Given the coefficient of [tex]x^2[/tex] is 1, all we have to do is see if there are two numbers that multiply to be -12 and add to be 4.
Those numbers are 6 and -2 so the factored form is:
[tex](x+6)(x-2)=0[/tex]
So the solutions can be found be solving the following linear equations:
[tex]x+6=0[/tex] and [tex]x-2=0[/tex].
First equation, you just need to subtract 6 on both sides. [tex]x=-6[/tex]
Second equation, you just need to add 2 on both sides. [tex]x=2[/tex]
So draw a number line with those on it and test the intervals they divide.
--------(-6)--------(2)----------
So we need to test three intervals.
*Plug in a number before -6 to see if that piece of the function is above the x-axis or below. We are looking for below since we want [tex]f(x)<0[/tex].
Let's plug in x=-8
[tex]f(x)=(x+6)(x-2)[/tex] or use [tex]f(x)=x^2+4x-12[/tex].
[tex]f(-8)=(-8+6)(-8-2)[/tex]
[tex]f(-8)=(-2)(-10)[/tex]
[tex]f(-8)=20[/tex] so this piece is above since 20 is positive and not negative.
So we will not include this interval in our answer.
*Plug in a number between -6 and 2 like 0.
[tex]f(x)=(x+6)(x-2)[/tex]
[tex]f(0)=(0+6)(0-2)[/tex]
[tex]f(0)=(6)(-2)[/tex]
[tex]f(0)=-12[/tex] so this piece is under since -12 is negative and not positive.
So our solution includes the interval (-6,2).
*Plug in a number after 2 like 5.
[tex]f(x)=(x+6)(x-2)[/tex]
[tex]f(5)=(5+6)(5-2)[/tex]
[tex]f(5)=(11)(3)[/tex]
[tex]f(5)=33[/tex] so this piece is above since 33 is positive and not negative.
The answer only includes the interval (-6,2).
Caylan is making bakes goose for a charity bake sale ha places a tray of scones a tray of muffing and a tray of cookies in the oven the second bake for 15 the muffins bake for 12 minutes and the cookies bake for 10 minutes when one tray is done he removes it a replaces it with another tray of the same item how many minutes after caylan puts the trays in the oven will he first remove the scones muffins and cookies at the same miinutes
Answer:
Step-by-step explanation:
an hour, or 60 minutes
Answer:
60 minutes
Step-by-step explanation:
i d 1 0 t
3 − 3k + 7k = 5b find the equation for k
Answer:k=5b/4 - 3/4
Step-by-step explanation:
Answer:
[tex]k=\frac{5}{4}b - \frac{3}{4}[/tex]
Step-by-step explanation:
-3k + 7k = 5b - 3
4k = 5b - 3
[tex]k=\frac{5}{4}b - \frac{3}{4}[/tex]
please help me!
Decrease £40 by 10%
Answer:
36
Step-by-step explanation:
40 * .10 = 4
40-4 = 36
The diagram shows a triangle.
45°
38°
What is the value of s?
Answer:
97 degrees
Step-by-step explanation:
If 45 + 38 = 83
A triangle is 180 always
so 180-83=97
Abby earned $56 in 7 hours at her job today. She wants to know how much she could earn tomorrow if she works 34 hours at the same hourly rate.
How much will Rachel earn in 34 hours? please help me !!!
Answer:
It will be $85, 34÷ 4
will give you 8.5 then you multiply it by 10,× 10=85
Answer:
272
Step-by-step explanation:
56:7=8 (she earns 8$ in 1 hour)
8×34=272
Mr. Barnes hired a plumber to fix a leak. The total cost, in dollars, that the plumber charges for a job can be modeled by the function p(x)= 45+35x , where x represents the time, in hours, that the plumber used to complete the job. Mr. Barnes budgeted $220 to pay the plumber for the job. After how many hours will the cost of the job exceed Mr. Barnes's budget?
WILL PICK THE BRAINLEST.
What is the slope of 3x-2y=7?
Answer:
The slope is -3/2
Step-by-step explanation:
Hope this helped have a good day!
Y'all I need major help! This is due soon!! Just match up the points with an equation.
Write an equation of the line that passes through the given point and has the given slope, m.
1.(5,-2); m=4 2.(7,-2); m=2 3.(-3,-5); m=-3 4.(-8,-2); m=4 5.(0,0); m=1
y=-3x-14 y=2x-16 y=x y=4x+30 y=4x-22
Can someone help me with 5-6
Answer:
B, C
Step-by-step explanation:
I love slope
how many unique 3 digit codes can be created from the 5 digits {1, 2, 3, 4, 5} if repeats are possible?
Answer:
53
Step-by-step explanation:
5 choices × 5 choices × 5 choices = 53 possible 3 digit codes including repeats
[tex]\boldsymbol{125}[/tex] unique [tex]3[/tex] digit codes can be created from the [tex]5[/tex] digits.
Number of arrangementsGiven that digits are [tex]=\boldsymbol{\{1,2,3,4,5 \}}[/tex].
Number of digits [tex]=\boldsymbol{5}[/tex]
With repetition" means that repetition is allowed. Thus, in each of the three places, we have five choices.
Therefore,
Number of unique three digit codes can be created from the five digits [tex]=5\times 5\times 5[/tex]
[tex]=\boldsymbol{125}[/tex]
So, [tex]\boldsymbol{125}[/tex] unique [tex]3[/tex] digit codes can be created from the [tex]5[/tex] digits.
Find out more information about permutations here:
https://brainly.com/question/26852614?referrer=searchResults
What is the answer to this
2(x-5)-6=-18
x=___
Answer:
x= -1
Step-by-step explanation:
Distribute:2(x -5) -6 = -18
2x -10 -6 =-18
Subtract the numbers:2x -10 -6 =-18
2x -16 = -18
Add 16 to both sides of the equation:2x =16 += -18
2x -16 +16 = -18 +16
Simplify:2x = -2
Divide both sides of the equation by the same term:2x/2 = -2/2
Simplify:x=-1
Answer:x = -1
Sal invests $16,000 at age 35. He hopes the investment will be worth $320,000 when he turns 40. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
59.9%
Sorry I don’t have time to explain in the middle of an exam
The rate of growth needs to be 59.9%.
The formula used to determine the future value of an investment when interest is compounded continuously is:
FV = A x [tex]e^{r}[/tex] x N
A= amounte = 2.7182818 N = number of years r = interest rateFV = future value$320,000 = $16,000 x [tex]e^{r}[/tex] x 5
Divide both sides by $16,000
20 = 5[tex]e^{r}[/tex]
Take the In of both sides
In(20) = 5r
Divide both sides by 5
r = 59.9%
To learn, please check: https://brainly.com/question/14640433
can you help me with sas and sss congruent criteria please?
Hi can someone please tell me what the answer is thanks!
Answer:
B. 6
Step-by-step explanation:
50 times 3/5 = 150/5 = 30
30 times 4/5 = 120/5 = 24
24 times 1/4 = 24/4 = 6
How do you write 352 in expanded form
Answer:
300+ 50 + 2
Step-by-step explanation:
If you add 300+50+2 you get 352 all you need to do is break down the number to pieces! :)
Explanation:
The number 352 has 3 in the hundreds place, 5 in the tens place, and 2 in the ones place.
So that's why 352 = 300 + 50 + 2
5. The side of a square is (3x - y). What is the perimeter of the square?
a. 12x - 4y
b. 12x -Y
c. 6x-2y
d. 12x + 4y
I need help plzzz
Answer:
A) 12x-4y
Step-by-step explanation:
Since a square has a perimeter of P=4s, then P=4(3x-y)=12x-4y, therefore A is the correct option.
3/4
(x−12)=12
will mark brainlyest
Answer:
x = 24, if thats wat ur asking.
Answer:
x = 28
Step-by-step explanation:
its division come on
8(-4a + 8b) = 240please
Answer:
= -32a+64b
Step-by-step explanation:
thats the answer
Help please it’s needed!
Which relation is a function?( click all that apply)
Solve for x.
9(x + 1) = 25 + x
O x= 2
O x = 3
0 x = 4
O x = 5
Answer:
Step-by-step explanation:
9(x+1)=25+x
9x+9=25+x subtract x both sides
8x+9=25 subtract 9 both sides
8x=16 divide by 8
x=2
Solve for x in the equation: 2x-7=14
Answer: x=10.5
Step-by-step explanation:
To solve for x, we want to use our properties to isolate x.
2x-7=14 [add both sides by 7]
2x=21 [divide both sides by 2]
x=10.5
Now, we know that x=10.5.
Help!!Find the y-intercept of the line on the graph.
Enter the correct answer.
The y-intercept of the graph is -3
How to find the y-intercept of a graph?The y-intercept is the point where the line intersects the y-axis. This is the value of y when x is equals to zero.
Using slope intercept formula,
y = mx + b
where
m = slopeb = y-interceptNow, let's trace the value of y when x = 0 in the graph.
Therefore,
when x = 0, y = -3
Hence, the y-intercept of the graph is -3
learn more on y-intercept here: https://brainly.com/question/20759265
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Quiz 3-3 Parallel and Perpendicular Lines on the Coordinate Plane (Gina Wilson All Things Algebra 2014-2019) need these for a quiz please!
Answer:
14. [tex]y = -2x -1[/tex]
15. [tex]y = -\frac{3}{4}x +3[/tex]
16. [tex]y= 4x + 9[/tex]
17. [tex]y = -\frac{5}{3}x -2[/tex]
18. [tex]y= -\frac{2}{3}x -5[/tex]
19. [tex]y = 4x -3[/tex]
20. [tex]y = -3x -7[/tex]
Step-by-step explanation:
Solving (14):
Given
[tex](x_1,y_1) = (-7,13)[/tex]
[tex]Slope (m) = -2[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - 13 = -2(x -(-7))[/tex]
[tex]y - 13 = -2(x +7)[/tex]
[tex]y - 13 = -2x -14[/tex]
Collect Like Terms
[tex]y = -2x -14 + 13[/tex]
[tex]y = -2x -1[/tex]
Solving (15):
Given
[tex](x_1,y_1) = (-4,6)[/tex]
[tex]Slope (m) = -\frac{3}{4}[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - 6 = -\frac{3}{4}(x - (-4))[/tex]
[tex]y - 6 = -\frac{3}{4}(x +4)[/tex]
[tex]y - 6 = -\frac{3}{4}x -3[/tex]
Collect Like Terms
[tex]y = -\frac{3}{4}x -3 + 6[/tex]
[tex]y = -\frac{3}{4}x +3[/tex]
Solving (16):
Given
[tex](x_1,y_1) = (-5,-11)[/tex]
[tex](x_2,y_2) = (-2,1)[/tex]
First, we need to calculate the [tex]slope\ (m)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{1 - (-11)}{-2 - (-5)}[/tex]
[tex]m = \frac{1 +11}{-2 +5}[/tex]
[tex]m = \frac{12}{3}[/tex]
[tex]m = 4[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - (-11) = 4(x -(-5))[/tex]
[tex]y +11 = 4(x+5)[/tex]
[tex]y +11 = 4x+20[/tex]
Collect Like Terms
[tex]y= 4x + 20 - 11[/tex]
[tex]y= 4x + 9[/tex]
Solving (17):
Given
[tex](x_1,y_1) = (-6,8)[/tex]
[tex](x_2,y_2) = (3,-7)[/tex]
First, we need to calculate the [tex]slope\ (m)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-7 - 8}{3- (-6)}[/tex]
[tex]m = \frac{-7 - 8}{3+6}[/tex]
[tex]m = \frac{-15}{9}[/tex]
[tex]m = -\frac{5}{3}[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - 8 = -\frac{5}{3}(x -(-6))[/tex]
[tex]y - 8 = -\frac{5}{3}(x +6)[/tex]
[tex]y - 8 = -\frac{5}{3}x -10[/tex]
Collect Like Terms
[tex]y = -\frac{5}{3}x -10 + 8[/tex]
[tex]y = -\frac{5}{3}x -2[/tex]
18.
Given
[tex](x_1,y_1) = (-6,-1)[/tex]
[tex]y = -\frac{2}{3}x+1[/tex]
Since the given point is parallel to the line equation, then the slope of the point is calculated as:
[tex]m_1 = m_2[/tex]
Where [tex]m_2[/tex] represents the slope
Going by the format of an equation, [tex]y = mx + b[/tex]; by comparison
[tex]m = -\frac{2}{3}[/tex]
and
[tex]m_1 = m_2 = -\frac{2}{3}[/tex]
Equation in [tex]slope\ intercept\ form[/tex] is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - (-1) = -\frac{2}{3}(x - (-6))[/tex]
[tex]y +1 = -\frac{2}{3}(x +6)[/tex]
[tex]y +1 = -\frac{2}{3}x -4[/tex]
[tex]y= -\frac{2}{3}x -4 - 1[/tex]
[tex]y= -\frac{2}{3}x -5[/tex]
19.
Given
[tex](x_1,y_1) = (-2,-11)[/tex]
[tex]y = -\frac{1}{4}x+2[/tex]
Since the given point is parallel to the line equation, then the slope of the point is calculated as:
[tex]m_1 = -\frac{1}{m_2}[/tex]
Where [tex]m_2[/tex] represents the slope
Going by the format of an equation, [tex]y = mx + b[/tex]; by comparison
[tex]m_2 = -\frac{1}{4}[/tex]
and
[tex]m_1 = -\frac{1}{m_2}[/tex]
[tex]m_1 = -1/\frac{-1}{4}[/tex]
[tex]m_1 = -1*\frac{-4}{1}[/tex]
[tex]m_1 = 4[/tex]
Equation in [tex]slope\ intercept\ form[/tex] is:
[tex]y - y_1 = m(x-x_1)[/tex]
[tex](x_1,y_1) = (-2,-11)[/tex]
Substitute values for y1, m and x1
[tex]y - (-11) = 4(x - (-2))[/tex]
[tex]y +11 = 4(x +2)[/tex]
[tex]y +11 = 4x +8[/tex]
Collect Like Terms
[tex]y = 4x + 8 - 11[/tex]
[tex]y = 4x -3[/tex]
20.
Given
[tex](x_1,y_1) = (-10,3)[/tex]
[tex](x_2,y_2) = (2,7)[/tex]
First, we need to calculate the slope of the given points
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{7 - 3}{2 - (-10)}[/tex]
[tex]m = \frac{7 - 3}{2 +10}[/tex]
[tex]m = \frac{4}{12}[/tex]
[tex]m = \frac{1}{3}[/tex]
Next, we determine the slope of the perpendicular bisector using:
[tex]m_1 = -\frac{1}{m_2}[/tex]
[tex]m_1 = -1/\frac{1}{3}[/tex]
[tex]m_1 = -3[/tex]
Next, is to determine the coordinates of the bisector.
To bisect means to divide into equal parts.
So the coordinates of the bisector is the midpoint of the given points;
[tex]Midpoint = [\frac{1}{2}(x_1+x_2),\frac{1}{2}(y_1+y_2)][/tex]
[tex]Midpoint = [\frac{1}{2}(-10+2),\frac{1}{2}(3+7)][/tex]
[tex]Midpoint = [\frac{1}{2}(-8),\frac{1}{2}(10)][/tex]
[tex]Midpoint = (-4,5)[/tex]
So, the coordinates of the midpoint is:
[tex](x_1,y_1) = (-4,5)[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1: [tex]m_1 = -3[/tex] & [tex](x_1,y_1) = (-4,5)[/tex]
[tex]y - 5 = -3(x - (-4))[/tex]
[tex]y - 5 = -3(x +4)[/tex]
[tex]y - 5 = -3x-12[/tex]
Collect Like Terms
[tex]y = -3x - 12 +5[/tex]
[tex]y = -3x -7[/tex]
(PLEASEEE HELP) Which graph of which line represents a
proportional relationship?
Graph A
Graph B
Graph C
Graph D
Look carefully at the graph of multiple graphs shown below. Which of the graphs
represents or shows a proportional relationship?
Answer:
B
a proportional relationship in a graph needs to go through the 0.0, and also needs to be a stright line.
what are the three products of celullar respiration
Answer:
Cellular respiration is this process in which oxygen and glucose are used to create ATP, carbon dioxide, and water. ATP, carbon dioxide, and water are all products of this process because they are what is created.
Step-by-step explanation:
PLEASE HELP ME
What is the simplified form of
the quantity of x plus 6, all over 3 − the quantity of x plus 2, all over 3
The function g(x)=2x^2+16x+31 is at a minimum when x=-4. True or False?
Answer:
The answer is true.
Step-by-step explanation:
In Joey's neighborhood the ratio of families with dogs to families with cats is 5 to 2. There are 15 more families with dogs than families with cats. How many families have cats, and how many families have dogs?
Answer:
10 families have cats
25 families have dogs
Step-by-step explanation:
The difference of ratio units is 5-2 = 3. The difference in pet counts is 15, so we can see that each ratio unit stands for 15/3 = 5 pets. Then ...
dogs : cats = 5 : 2 = (5·5) : (2·5) = 25 : 10
There are 10 families with cats and 25 families with dogs.
Answer:
B D and E.
Step-by-step explanation:
What is the equation of the linear function?
= -x + 6
A
y = -2x + 3
y=-3x +3
y = ;& + 3
Done