Answer:
all real values of x where 1 < x < 4
If there is anything you don't understand let me know. Also, since the graph is supposedly shown you may even be able to get the information just by looking at the graph.
Step-by-step explanation:
A graph goes from being negative to positive (or the other way around) by passing through the x axis. Or in other words when f(x) = 0. So the trick is to find all 0s and then test if it is poitive or negative before and after the 0.
f(x) = (x+2)(x-4) is in factored form, so it gives the 0s. in factored form the 0s are the negatives of the numbers int he parenthesis. Or in other words (x+a)(x+b) would have 0s at -a and -b. Notie it is x+a but the 0 is at -a. so for (x+2)(x-4) the zeroes would be -2 and 4.
Then checking, we can say it is positive before -2, negative after -2 up until 4, then it is positive again.
For increasing and decreasing for anything other than a quadratic and linear function you need calculus. Since this is a quadratic though you don't need it.
With quadratics you need to know they have two parts. An increasing part and decreasing part. If you draw the graph of x^2 you can see it decreases until (0,0) then it starts increasing. -x^2 is the opposite. it won't always have the same changing point, but you can always tell if it increases first or decreases first. You look at if the coefficient next to x^2 is positive of negative.
In (x+2)(x-4) We have to expand first. so it becomes x^2 - 2x - 8. x^2 has 1 as its coefficent so we know it decreases first then increases. Also looking at (x+2)(x-4) you could say since the two xs have the same sign we also know it would be that. is one was positive and one negative, like (2x+1)(-3x+1) we would be able to say it increases first then decreases.
To know when it switches, since it is in factored form you find the point in the middle of the two zeroes, and that is where it switches. Since the zeroes are -2 and 4 we can say the middle (called the vertex) is at x=1 since it is 3 away from both 0s. So it decreases up until 1 then increases.
The different forms of quadratics have different easy methods of finding the vertex.
We could also actually use this information to say, since it is decreasing first we know it is positive before the first 0, then negative until the second 0, then positive again. Still would have to find the 0s though.
So now we know it is positive and decreasing until x=-2, negative and decreasing until 1, negative and increasing until 4, then increasing after that.
Since you want negative and increasing, that is 1 < x < 4
How do I generate equivalent expressions by combining like terms, simplifying, or factoring this? ( 4b + 8) =
Answer:
4(b + 2)
Step-by-step explanation:
Given data
The expression is
( 4b + 8)
Looking at the expression, 4 is common
factor 4 out
4(b + 2)
Hence the equivalent expression is
4(b + 2)
Which number is between
Answer:
D
Step-by-step explanation:
7.17 x 10(4) = 71,700
8.17 x 10(5) = 817,000
Any numbers between 71,700 and 817,000 is obv the answer
I did the math
A 69,200
B 7,200,000,000
C 7,570
D 80,530
Pretty obv that D be the only one that is inbetween 71,700-817,000
(excuse my spelling pls)
Evaluate (-362) + 9 ÷ 10
PLEASE HELP ME PLS U WOULD BE A LIFE SAVER AND ILL GIVE U BRAINLY PLS
In a game of chance, players spin a pointer on the spinner with eight equal-sized sections.
The sample space is 1,1,2,3,3,4,5,5
What are the probabilities of each outcome in the sample space? ( write each answer in fraction form) p.s the answer is supposed to be more than one fraction.
Step-by-step explanation:
a) Since there are 2 #1 in the spinner, the probability of landing on a 1 is 2/8 or 1/4
b) Since there is only one #2, the probability is only 1/8.
c) Probability of landing on #3 is 2/8 or 1/4.
d) Probability of landing on a #4 is 1/8
e) Just like the case of #1 & #3, there are 2 chances out of eight that it will land on a #5 so the probability is 2/8 or 1/4
Write the additive inverse of -1/3
Write the additive inverse of [tex]\frac{ - 1}{3} [/tex].
➼ The additive inverse of [tex] \frac{ - 1}{3} [/tex] is [tex]\frac{+ 1}{3} [/tex].
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Someone please help me ASAP!
Answer:
x + 1 y+1
Step-by-step explanation:
it translated 1 unit up the x axis and 1 unit y axis
Answer:
reflected across the y-axis and translated 1 to the right and 1 up
Step-by-step explanation:
Dominic wants to find the distance between his house on one side of the park and his school on the other side. He marks off a third point forming a right triangle, as shown in the diagram. The distances in the diagram are measured in yards. Use the Pythagorean Theorem to find the distance from Dominic’s house to the school. Sho
Answer:
The distance from the house to the school is 500 units
Step-by-step explanation:
The distance we want to calculate represents the hypotenuse of the right triangle
So, to use the Pythagoras’ theorem, we need the two other side lengths apart from the hypotenuse
The base side measures (350-50 = 300 units)
The measure of the height is (450-50 = 400 units)
Mathematically, the theorem states that the square of the hypotenuse equals the sum of the squares of the two other sides
Thus, we have it that;
h^2 = 300^2 + 400^2
h^2 = 90,000 + 160,000
h^2 = 250,000
h = √250,000
h = 500 units
ILL GIVE BRAINLIEST!!
Pam is looking for a new car. She has test-driven two cars but can only purchase one. The probability that she will purchase car A is 0.46, and the probability that she will purchase car B is 0.34. What is the probability that she will not purchase either car A or car B? (1 point)
The total of the two cars is 0.46 + 0.34 = 0.8
The total of all probabilities needs to equal 1
The probability of not buying either car is 1 - the sum of the two probabilities
1-0.8 = 0.20
The probability of not buying either car is 0.20
what is the length of the diagonal of the screen,in feet?
Answer:
12.2
Step-by-step explanation:
Help me to do this question
Answer:
Step-by-step explanation:
1) Vertically opposite angles are equal.
x + 30 = 180 - 2x
Add '2x' to both sides
x + 30 +2x = 180
3x + 30 = 180
Subtract 30 from both sides
3x = 180 - 30
3x = 150
x = 150/3
x = 50
2) Let the angle be x
It's complement angle = 90 - x
[tex]x = \frac{2}{3}(90-x)\\\\x = \frac{2}{3}*90 - \frac{2}{3}*x\\\\x =2*30 - \frac{2}{3}x\\\\x +\frac{2}{3}x = 60\\\\\frac{3}{3}x+\frac{2}{3}x=60\\\\\frac{5}{3}x =60\\\\x = 60*\frac{3}{5}\\\\x = 12*3\\x = 36[/tex]
The angles are : 36 , 54
3) Let the angle be x
It's supplement = 180 - x
[tex]x = \frac{1}{5}(180-x)\\\\x =\frac{1}{5}*180 - \frac{1}{5}x\\\\x + \frac{1}{5}x= 36\\\\\frac{5}{5}x +\frac{1}{5}x = 36\\\\\frac{6}{5}x = 36\\\\x = 36*\frac{5}{6}\\\\x = 6*5 = 30\\[/tex]
Angles are 30 , 150
4) Ratio = 7 : 3
The angles are = 7x , 3x
7x + 3x = 180
10x = 180
x = 180/10
x = 18
7x = 7 * 18 = 126
3x = 3 * 18 = 54
Angles are 126 , 54
1. Intersecting lines are lines that cross each other. When two lines intersect, the opposite angles are equal.
Given: x + 30° and 180° - 2x are vertically opposite angles
⇒ x + 30° = 180° - 2x
⇒ 3x = 150°
⇒ x = 50°
2. Let the complement be : C
Given : The other angle is two third of its complement
[tex]\sf{\implies Other \ angle = \dfrac{2}{3} \times C}[/tex]
Two angles are said to be Complementary if their sum is equal to 90°
[tex]\sf{\implies C + \dfrac{2C}{3} = 90}[/tex]
[tex]\sf{\implies \dfrac{5C}{3} = 90}[/tex]
[tex]\sf{\implies 5C = 270}[/tex]
[tex]\sf{\implies C = 54}[/tex]
[tex]\sf{\implies Other \ angle = \bigg(\dfrac{2}{3} \times C\bigg) = \bigg(\dfrac{2}{3} \times 54\bigg) = 36 }[/tex]
Answer: The size of the angle which is two third of its complement is 36°
3. Let the supplement be : S
Given : The other angle is one fifth of its supplement
[tex]\sf{\implies Other \ angle = \dfrac{1}{5} \times S}[/tex]
Two angles are said to be Supplementary if their sum is equal to 180°
[tex]\sf{\implies S + \dfrac{S}{5} = 180}[/tex]
[tex]\sf{\implies \dfrac{6S}{5} = 180}[/tex]
[tex]\sf{\implies 6S = 900}[/tex]
[tex]\sf{\implies S = 150}[/tex]
[tex]\sf{\implies Other \ angle = \bigg(\dfrac{1}{5} \times S\bigg) = \bigg(\dfrac{1}{5} \times 150\bigg) = 30 }[/tex]
Answer: The size of the angle which is one fifth of its supplement is 30°
4. Two supplementary angles are in the ratio 7 : 3
Let the supplementary angles be : 7S and 3S
Two angles are said to be Supplementary if their sum is equal to 180°
⇒ 7S + 3S = 180°
⇒ 10S = 180°
⇒ S = 18°
First Angle : 7S = (7 × 18) = 126°
Second Angle : 3S = (3 × 18) = 54°
A survey asked 25 students about their favorite sport. A frequency table of their responses is below.
Basketball
4.
Football
7
Lacrosse
3
Soccer
8
Volleyball
3
Which of the following is the correct relative frequency table for the students' favorite sport?
Basketball
0.16
Football
0.32
Lacrosse
0.12
Soccer
0.28
Volleyball
0.12
Basketball
0.16
Football
0.28
Lacrosse
0.12
Soccer
0.32
Volleyball
0.12
Basketball
0.04
Football
0.07
Lacrosse
0.03
Soccer
0.08
Volleyball
0.03
Basketball
4.
Football
7
Lacrosse
3
Soccer
8
Volleyball
3
Answer:
25.5 / 3 = 8.5
Step-by-step explanation:
8.5 times more student prefer basketball over soccer
Answer:
d
Step-by-step explanation:
What is the radius of a hemisphere with a volume of 920 ft^3 to the nearest tenth of a foot?
Answer:
7.6 ft
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
A hemisphere is 1/2 of a sphere
V = 1/2 (4/3 pi r^3)
V = 2/3 pi r^3
920 = 2/3 pi r^3
Multiply each side by 3/2
920 * 3/2 = 3/2 * 2/3 pi r^3
1380 = pi r^3
Divide each side by pi
1380/pi = pi r^3 / pi
1380/ pi = r^3
Using pi as 3.14
1380/3.14 = r^3
439.4904459= r^3
Taking the cube root of each side
(439.4904459)^(1/3)= r^3^(1/3)
7.602967711=r
To the nearest tenth
7.6 = r
radius=7.6ft
Answer:
Solution given:
radius [r]=?
Volume of hemisphere=920ft³
⅔*πr³=920
r³=920*3/(2π)
r³=439.267
r=[tex]\sqrt[3]{439.267}=7.6ft[/tex]
4,756 rounded to the nearest thousand is
4,756 rounded to the nearest thousand is 5,000.
Answer:
rounded to the nearest thousands 4,756 is 5,000 since 7 is higher then 4 so it rounds up
What’s 1/2 + 1/3? Y’all please help me . And when or if you can give me the answer can you do step-by-step on how you did that so I can do it myself next time?
[tex]\longrightarrow{\green{\frac{5}{6}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{1}{2} + \frac{1}{3} [/tex]
Since the denominators are unequal, we find the L.C.M (lowest common multiple) for both denominators.
The L. C. M for 2 and 3 is 6.
Now, multiply the L.C.M. with both numerator & denominator.
[tex] = \frac{1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} [/tex]
[tex]= \frac{3}{6} + \frac{2}{6} [/tex]
Now that the denominators are equal, we can add them.
[tex]= \frac{3 + 2}{6} \\ \\ = \frac{5}{6} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
I need help or my math teacher will call my parents up about it and I will die
Answer:
113mm^2
Step-by-step explanation:
Firstly work out the area of the pink circle using πr^2, which is the area of a process.
So we do πx12^2, which gives us 144π mm we have to divide this by two to get half of a circle hence giving us the area of the semi-circle. 72π mm is the area of the semicircle.
Then we must find the area of the white circle to subtract it from our semicircle. Since we know the radius is 12 from the center to anywhere, we know that the white circles diameter is 12, using our formula for the area all we need to do is πx6^2. This gives us 36π.
72π - 36π = 36π
36π is equal to 113.0973355 and since we need it too 3sf it will be 113mm^2
If 2 is subtracted from 3 times a number , the result is 25.Find the number?
Answer:
3x-2=25
x=9. .
Answer:
9
Step-by-step explanation:
answer plz plz plz plz plz
C. 270
Hope this helps! :)
Answer:
A.)90 degrees
Step-by-step explanation:
You want to buy the largest pizza in Northern Utah. You find a pizza that measures
75.36in around. What is the area that the pizza covers?
Answer:
451.7in^2
Step-by-step explanation:
You first need to determine the radius of the circle. This can be done by taking the circumference and dividing it by 2pi:
[tex]r=\frac{75.36in}{2\pi } = 11.99 in[/tex]
Now that you have the radius, you can plug it into the formula for the area of a circle (this is assuming the pizza is perfectly round):
[tex]A=\pi r^2=\pi (11.99^2)=451.7in^2[/tex]
The area that covers the circular pizza is: 451.64 in.²
What is the Area and Perimter of a Circle?Area = πr²
Perimeter = 2πr, where r is the radius of the circle.
Given the following:
Perimeter of the circular pizza = 75.36 in.
Find the radius:
2πr = 75.36
r = 75.36/2π
r = 11.99 in.
Find the area:
Area = π(11.99)²
Area = 451.64 in.²
Learn more about the area of a circle on:
https://brainly.com/question/12269818
One afternoon, Olive, who is 2 feet 3 inches tall, casts a shadow that is 6 feet 1 inch long. At the same time of
the day, a nearby tree casts a shadow that is 12 feet long. Olive reasons she can figure out the height of the
tree.
What is the height of the tree in feet? Round your answer to the nearest tenth of a foot.
2×12=24
24+3= 27
12*12=144
144/24=6
HELP! Drag each value to the correct location on the equation. Not all values will be used.
The number of archaeological sites discovered in a country over time, x, can be represented by the function S(x) = 2(1.1)x. The approximate number of artifacts found in each site over time, x, can be represented by the function A(x) = (1.1)5x + 2.
Create the function, T(x), that best describes the total number of artifacts found in archaeological sites in the country after x years.
Answer:
huh
Step-by-step explanation:
?
The exponential function that best describes the total number of artifacts found in archaeological sites in the country after x years = T(x) = [tex]2(1.1)^{6x+2}[/tex]
What is exponential function?An exponential function is defined by the formula f(x) = a×, where the input variable x occurs as an exponent.
Time period = x years
The number of archaeological sites discovered in a country in x years = S(x) = [tex]2(1.1)^{x}[/tex]
The approximate number of artifacts found in each site over time = A(x) = [tex](1.1)^{5x+2}[/tex]
The total number of artifacts found in archaeological sites in the country after x years = T(x) = S(x).A(x) = [tex]2(1.1)^{x}(1.1)^{5x+2} = 2(1.1)^{6x+2}[/tex]
Learn more about exponential function here
https://brainly.com/question/11487261
#SPJ2
I need help with basic geometry please help !
Answer:
Step-by-step explanation:
take 50 degree as reference angle
using sin rule
sin 50 = opposite/hypotenuse
0.766 = x /3
0.766*3 = x
2.298 = x
2.30 = x
Pls help not sure how to answer
Answer:
i think its yz but not sure
Step-by-step explanation:
What are the amplitude and midline?
A. Amplitude: 1; midline: y = 1
B. Amplitude: 0; midline: y = 0
C. Amplitude: 2; midline: y = 1
D. Amplitude: 2; midline: y = 0
Answer:
A. Amplitude: 1; midline: y = 1
Answer:
A. Amplitude: 1; midline: y = 1
Step-by-step explanation:
i took the test
please answer thisss <3
Answer:
i think . it is c
Step-by-step explanation:
y=3x-1
Help pleaseeeeee
Answer:
y=3x-1
Step-by-step explanation:
Not enough context
Hope this helps!
:)
if p (x) = 3x^3+2x^2+4x^4+3 and q (x) = 3x^4-2-x+5^2 .find p (x) - q (x)
Answer:
4x⁴-3x⁴+5x³-3x²+1
Step-by-step explanation:
Given that p (x) = 3x^3+2x^2+4x^4+3 and q (x) = 3x^4-2-x+5x^2
p (x) - q (x) = 3x^3+2x^2+4x^4+3 - (3x^4-2-x+5x^2)
p (x) - q (x) = 3x^3+2x^2+4x^4+3 - 3x^4 + 2 + x - 5x^2
Collect the like terms
p (x) - q (x) = 4x⁴-3x⁴+3x³+2x²-5x²+x+3-2
p (x) - q (x) = 4x⁴-3x⁴+5x³-3x²+1
This givess the difference
Can someone please help me? need this done ASAP!!!!
Answer:
They are not similar
Step-by-step explanation:
Angles dont match
what is the value of the expression 6ab - b3 , if a=1 and b=2?
Answer:
6
Step-by-step explanation:
6(1×2) - 3(2)
6×2 - 6
12-6
= 6
here you go
please help with mine
NEED HELP ASAP !!!! SOMEONE HELP ME
Answer:
A
Step-by-step explanation:
cos(71)x19=6.1
6.1 =6
Answer:
ladder is 20 feet long.So answer is option c.
Step-by-step explanation:
let the length of a ladder be x
take 71 degree as reference angle
using sin rule
sin 71 =opposite/hypotenuse
0.94=19/x
x=19/0.94
x=20.21
x=20 feet
ASAP
Help pls
Answer as fast as you can
Plsss help
Thank you
Answer:
42
Step-by-step explanation:
From the question, we have it that 63 cups were emptied
That means the sum of both cup sizes is 63
Thus;
x + y = 63 ••••••(i)
Since each small cup is of size 8 oz and a total of x was used. The total volume from the small sized cup is 8 * x = 8x oz
similarly for the medium sized, we have 12 * y = 12y oz
The sum of both is 4(147)
8x + 12y = 4(147 )•••••(ii)
We want to get the value of x
from equation i;
y = 63-x
Substitute this into equation ii
8x + 12(63-x) = 4(147)
8x + 756 - 12x = 4(147)
12x-8x = 756-4(147)
4x = 168
x = 168/4
x = 42 small sized cups
