recall that an absolute value expression is in effect a piece-wise with a ± version.
[tex]\bf |x-1| > 2\implies \begin{cases} +(x-1)>2\implies x-1>2\\\\ ~\hfill x>3\\ \cline{1-1} -(x-1)>2\implies x-1\stackrel{\downarrow }{<}-2\\\\ ~\hfill x<-1 \end{cases}[/tex]
Check the picture below.
Answer:
|x - 1| > 2Step-by-step explanation:
[tex]x< -1\ or\ x>3\\\\\dfrac{-1+3}{2}=\dfrac{2}{2}=1\\\\x<-1\ or\ x>3\qquad\text{subtract 1 from all sides}\\\\x-1<-2\ or\ x-1>2\to|x-1|>2[/tex]
Translate the word phrase into a math expression: nine more than the quotient of a number and five
Answer: [tex]\frac{x}{5}+9[/tex]
Step-by-step explanation:
Let be "x" the number mentioned in the given phrase.
"...the quotient of a number and five" indicates a division. In other words, the number "x" is divided by 5. This can represented as:
[tex]\frac{x}{5}[/tex]
Now, "Nine more than the quotient of a number and five" indicates that you need to add 9 to the quotient of a number and five ( [tex]\frac{x}{5}[/tex]).
Knowing this, you can conclude that the translation of "Nine more than the quotient of a number and five" into a math expression is:
[tex]\frac{x}{5}+9[/tex]
Final answer:
The word phrase 'nine more than the quotient of a number and five' translates to the math expression '(x/5) + 9', where 'x' represents the number.
Explanation:
To translate the word phrase 'nine more than the quotient of a number and five' into a math expression, we first identify the quotient of a number and five, which is denoted as ‘x ÷ 5’ or ‘x/5’ where x represents the number. Next, we address the phrase 'nine more than', which indicates that we need to add nine to that quotient. So, the phrase translates to the algebraic expression ‘(x/5) + 9’.
Therefore, as per the above explaination, the correct answer is (x/5) + 9
Simplify the given expression.
Answer:
C. [tex]\frac{32g^2}{3h^4}[/tex]
Step-by-step explanation:
Answer:
Option C is correct
Step-by-step explanation:
[tex]\frac{\frac{h}{3g^2}}{\frac{h^5}{32g^7}}[/tex]
We need to simplify the above expression.
We can write the above expression as:
[tex]\frac{h}{3g^2}\div\frac{h^5}{32g^7}[/tex]
Changing division sign into multiplication and reciprocating the second term we get,
[tex]\frac{h}{3g^2}*\frac{32g^7}{h^5}[/tex]
Applying the power rule: a^m/a^n = a^{m-n}
Solving:
[tex]\frac{h*32g^7}{3g^2*h^5}\\\\\frac{32g^{7-2}}{3h^{5-1}}\\\frac{32g^5}{3h^4}[/tex]
So, Option C is correct.
Which two cloud numbers round to 8 7.66 7.19 9.47
Answer:
It would be 7.66 and 7.19 because you can not round downward although I am a little confused on how 7.19 is able to round upwards But I am positive 7.66 rounds up to 8
Step-by-step explanation:
What is the following difference 11 square root 45 -4 square root 5
Your problem looks like this
[tex]11\sqrt{45} - 4\sqrt{5}[/tex]
To make this problem easier, we need to simplify these square roots
[tex]11\sqrt{45}[/tex] can be simplified
Here's how :
The factors of 45 are 9 and 5
9 is a perfect square root, but 5 is not
Think of the problem like this
[tex]\sqrt{9} × \sqrt{5}[/tex]
The square root of 9 is 3, but 5 has no perfect square root
Now [tex]11\sqrt{45}[/tex] is simplified to [tex]33\sqrt{5}[/tex]
Now let's solve the problem, because we have a common square root of 5
[tex]33\sqrt{5}[/tex] - 4\sqrt{5}[/tex]
Our final answer is
[tex]29\sqrt{5}[/tex]
Feel free to ask questions if you are confused! Hope I helped :)
For this case we must simplify the following expression:
[tex]11 \sqrt {45} -4 \sqrt {5}[/tex]
So, we rewrite 45 as [tex]3 ^ 2 * 5[/tex]:
[tex]11 \sqrt {3 ^ 2 * 5} -4 \sqrt {5} =[/tex]
We have by definition of properties of powers and roots that:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]11 * 3 \sqrt {5} -4 \sqrt {5} =\\33 \sqrt {5} -4 \sqrt {5} =\\29 \sqrt {5}[/tex]
Answer:
[tex]29 \sqrt {5}[/tex]
Which is the standard form of the equation of a parabola with a focus of (0, –3) and its vertex at the origin?
Answer:
A : x^2 = -12y
Step-by-step explanation:
TO ALL MY EDGE PEOPLE
Answer:
a) x^2=-12y
Step-by-step explanation:
Which property of addition is shown below?
If x= a + bi and y=-a-bi, x + y = 0.
O commutative property
identity property
associative property
inverse property
Answer: Last option
inverse property
Step-by-step explanation:
The property of the inverse sum says that if we have a number b and we add it with its negative -b then
[tex]b - b = 0[/tex]
In this case we have that:
[tex]x = a + bi[/tex]
and
[tex]y = -b - bi[/tex]
Note that
[tex]y = -x[/tex]
Therefore:
[tex]x + y = x -x= a + bi - a - bi = 0[/tex]
the answer is the last option
Select the correct answer from each drop-down menu.
Answer:
q(x)= 2x+5
r(x)= 6
Step-by-step explanation:
Given:
2x^2+13x+26 /x+4
Re-writing in the form of q(x) + r(x)/d(x)
Let
Polynomial P(x)= 2x^2+13x+26
Polynomial d(x)= x+4
Using remainder theorem, putting -4 in P(x) to find r(x)
P(-4)= 2(-4)^2+13(-4)+26
=6
i.e r(x)= 6
Finding q(x) by long division
q(x)= 2x+5
Hence given expression in the form q(x) + r(x)/d(x)
= (2x+5) + 6/x+4 !
what ratio is the same as 2/3?
The ratios 4/6 and 8/12 are equivalent ratio of 2/3 which we obtain by multiplying or dividing both numerator and denominator by same number.
To find a ratio that is the same as 2/3, we can multiply or divide both the numerator and the denominator by the same non-zero number.
This will result in an equivalent ratio.
If we multiply both the numerator and denominator of 2/3 by 2, we get:
(2 × 2) / (3 × 2)
= 4/6
Therefore, the ratio 4/6 is the same as 2/3.
Similarly, if we multiply both the numerator and denominator of 2/3 by 2, we get:
8/12
So, the ratio 8/12 is also the same as 2/3.
To learn more on Ratios click:
https://brainly.com/question/1504221
#SPJ6
The population of a specific strain of bacteria in a culture medium is given by f(x) = x + 3 where f(x)is the population in millions and x
is the time in hours. Find the piecewise function that matches this absolute value function. Then, graph the function using a graphing calculator
and describe what you see.
Answer:
Step-by-step explanation:
f(x) = { 0, x<0; 0 <= x, (x +3) * 1000000 }
(Note the graph ought to flatten to zero for x < 0)
ANSWER:
You need to write it’s piecewise function if
x < -3, the term x+3 becomes negative. So , for all values of x < -3 , the term becomes -(x+3)
Piecewise will be
F(x) = square root of (x+3) when x is greater than or equal to -3
F(x) = square root of -(x+3) when x less than or equal to -3
why is the answer actually 1 not 0
-2^2÷ -2^2=1
(-2)(-2)÷ (-2)(-2)=1
4 ÷4=1
Answer is 1
Answer:
Any number divided by itself is 1.
Step-by-step explanation:
One of the nice parts about algebra is that -- if a number appears more than once -- you can make things a lot cleaner looking by throwing them in a variable. Let's let x = -2² . Our equation then becomes x ÷ x = 1, and it's much clearer here that, since we're dividing x by itself, the answer should clearly be one.
What is the domain of the function shown in the mapping?
{x | x = –5, –3, 1, 2, 6}
{y | y = –9, –6, 0, 2, 4}
{x | x = –9, –6, –5, –3, 0, 1, 2, 4, 6}
{y | y = –9, –6, –5, –3, 0, 1, 2, 4, 6}
Answer:
x verse y on the map
Step-by-step explanation:
It shows what the x and the y cordinates are
You are try to dunk a basketball. You need to jump 2.5 feet in the air to dunk the ball. The height that your feet need to be of the ground is given by the function h(t)= _ 16t2+12r. What is the maximum height your feet will be above the ground? Will you be able to dunk the ball?
Answer:
1)he maximum height your feet will be above the ground is 2.25
2)Will you be able to dunk the ball= No
Step-by-step explanation:
Given:
In order to dunk the basket ball, height needed to jump= 2.5 feet
The height that your feet need to be of the ground is given by the function h(t)= -16t^2+12t
1) the maximum height your feet will be above the ground=?
Given function of height,h(x)=-16t^2+12t
finding maximun of the above function
The maximum of any function written in form of ax^2+bx+c is given by
max= c - (b2 / 4a)
Putting values c=0, b=12 and a=16, we get
max= 0-(12^2/4(-16))
= 144/64
=2.25 feet
he maximum height your feet will be above the ground is 2.25 feet.
2) Will you be able to dunk the ball=?
As the height needed to jump in the air to dunk the ball is 2.5 feet which is greater than the maximum height the feet will be above the ground i.e.
2.5>2.25
hence No you will not be able to dunk the ball !
The maximum height your feet will be above the ground is 2.25 feet. No, you will not be able to dunk the ball.
Explanation:To find the maximum height your feet will be above the ground, we need to determine the vertex of the quadratic function h(t) = -16t^2 + 12t.
The vertex of a quadratic function of the form h(t) = at^2 + bt + c is given by the formula t = -b/2a. In this case, a = -16 and b = 12, so the vertex is t = -12/(2*(-16)) = 0.375 seconds.
Substituting this value back into the function h(t), we get h(0.375) = -16(0.375)^2 + 12(0.375) = 2.25 feet. Therefore, the maximum height your feet will be above the ground is 2.25 feet.
Since you need to jump 2.5 feet in the air to dunk the ball and the maximum height your feet will reach is only 2.25 feet, you will not be able to dunk the ball.
Learn more about Quadratic functions here:https://brainly.com/question/35505962
#SPJ3
i have trouble so cn anybody help me?
Greg walked 610 of a mile and hopped 34100 of a mile.
How far did Greg travel?
Answer:
The correct answer is for sure 100 % =33,490
Step-by-step explanation:
34,100-610= 33,490
610+33,490=34,100
PLLZZZZ MARK ME BRAINLIST PLZZZZ!!!
(HELP ASAP PLEASE!!)
Two brothers went shopping at a back-to-school sale where all shirts were the same price, and all the shorts too. The younger brother spent $79 on 4 new shirts and 3 pairs of shorts. The older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185. How much did each item cost?
Each shirt cost $ ___ and each pair of shorts cost $ ___ .
Answer:
Shirts = $7
Shorts $17
Step-by-step explanation:
Let:
T - shirts
S - shorts
We can make two equations out of this problem:
4T + 3S = $79
7T + 8S = $185
Through substitution we can solve for one of the unknowns. We make one equation to solve for an unknown
[tex]4T+3S=\$79\\\\3S = \$79-4T\\\\S=\dfrac{\$79-4T}{3}[/tex]
We use the formula of S and insert it into the other equation:
[tex]7T+8(\dfrac{\$79-4T}{3}) = \$185\\\\7T + \dfrac{\$632-32T}{3}=\$185\\\\\dfrac{\$632-32T}{3}=\$185-7T\\\\\$632-32T=3(\$185-7T)\\\\$632-32T=\$555 - 21T\\\\-32T+21T=\$555-\$632\\\\-11T=-\$77\\\\\dfrac{-11T}{11}=\dfrac{-\$77}{11}\\\\T = \$7[/tex]
Thus T-shirts are $7 each.
Now that we know T, we can use it to solve for the other unknown. You can use it on any of the formulas.
[tex]4T+3S=\$79\\\\4(\$7) + 3S = \$79\\\\\$28+3S =\$79\\\\3S=\$79-\$28\\\\3S=\$51\\\\S=\dfrac{\$51}{3}\\\\S = \$17[/tex]
We know then that Shorts are $17 each.
how much is 5/9 of -3/5
a.1/2
b.-1/3
c.1/7
d.-25/27
Answer:
b.-1/3
Step-by-step explanation:
Is means equals and of means multiply
W =5/9 * (-3/5)
W = -3/9
W = -1/3
Solve please I need help
Answer:
28
Step-by-step explanation:
We can see that all the angles are inside of a triangle and the sum of the interior angle of the triangle is 180 degrees.
Knowing this, we know that the sum of all the angles present is 180 degrees.
1st angle can be seen as 90 degrees, 2nd angle is x+6 and the 3rd is 2x.
The sum can be written as ( 90 + x + 6 + 2x ) and this equals to 180 degrees.
90 + x + 6 + 2x = 180
96 + 3x = 180
( subtract 96 on both sides )
3x = 180 - 96
3x = 84
( divide by 3 on both sides )
x = 84 / 3
x = 28
Answer:
x = 28
Step-by-step explanation:
Consider the lower right triangle
The 2 given angles sum to 90° ( sum of angles in a triangle = 180° )
Hence
x + 6 + 2x = 90
3x + 6 = 90 ( subtract 6 from both sides )
3x = 84 ( divide both sides by 3 )
x = 28
Which transformations will produce similar, but not congruent, figure
Rotations, translations and reflections are transformations that preserve areas, so they always produce congruent figures.
So, the only way you have to produce a similar but not congruent figure is to use dilation with a scale different than 1.
2. What is the experimental probability of rolling a 4
3. Getting at least one tail
Experimental and theoretical
Answer:
1. 40%
2. The theoretical probability is 3% greater than the experimental probability.
Step-by-step explanation:
We are informed that a number cube is rolled 20 times and the number 4 is rolled 8 times. The experimental probability of rolling a 4 is;
(the number of times a 4 was rolled)/(total number of rolls)
8/20 = 0.4
0.4*100 = 40%
The experimental probability of obtaining at least one tails, one or more tails, is represented in mathematical notation as;
P(HT or TH or TT)
The above events are mutually exclusive, thus;
P(HT or TH or TT) = P(HT) + P(TH) + P( TT)
= (22+34+16)/(28+22+34+16)
= 0.72 = 72%
On the other hand, the theoretical probability of obtaining at least one tails,
P(HT or TH or TT) = 3/4
= 75%
This is because there is at least one tail in 3 out of 4 possible outcomes.
Therefore, it is true to say that the theoretical probability is 3% greater than the experimental probability.
Answer:
1. 40%
2. The theoretical probability is 3% greater than the experimental probability.
Step-by-step explanation:
1. Lets define experimental probability first.
Experimental probability is the probability of an event's occurrence when the experiment was conducted.
The number cube is rolled 20 times, so our sample space is 20.
And the number 4 came in result 8 times, so the the event space is 8.
So,
Experimental Probability = 8/20
=> 0.4
Converting into percentage will give:
=> 40%
So the first option is correct.
2. First we have to find the theoretical probability of getting at least one tail when two coins are tossed
The sample space is {HH, HT, TH, TT}
3 out of these 4 outcomes contain at least one tail
So the theoretical probability of getting at least one tail is: 3/4
=> 0.75 or 75%
Now for the experimental probability,
The total sample space is 28+22+34+16 = 100
The number of favorable outcomes are(Which contain at least one tail):
22+34+16 = 72
So, experimental probability of getting at least one tail = 72/100
=> 0.72 or 72%
We can see that the theoretical probability is 3% greater than the experimental probability. So second option is correct..
Solve the following inequality. Then place the correct number in the box provided. 3x < 18
For this case we must solve the following inequality:
[tex]3x <18[/tex]
Dividing between 3 on both sides of the inequality we have:
[tex]x <\frac {18} {3}\\x <6[/tex]
Thus, the solution of the variable "x" is given by all the numbers smaller than 6.
Answer:
All values of "x" less than 6.
(-∞, 6)
slope of the line 4x−8y=20
Answer:
y=1/2x-2.5
Step-by-step explanation:
4x-8y=20
Subtract 4x from both sides to get the 8y on on side.
-8y=-4x+20
divide -8 from both sides to get the y by itself.
y=1/2x-2.5
idk the equation is
[tex]\bf \textit{area of a square}\\\\ A=s^2~~ \begin{cases} s=&sides'\\ &length\\ \cline{1-2} A=&150 \end{cases}\implies 150=s^2\implies \sqrt{150}=s~~ \begin{cases} 150=&2\cdot 3\cdot 5\cdot 5\\ &2\cdot 3\cdot 5^2 \end{cases} \\\\\\ \sqrt{2\cdot 3\cdot 5^2}=s\implies 5\sqrt{2\cdot 3}=s\implies 5\sqrt{2}\cdot \sqrt{3}=s[/tex]
well then, we have a couple of known fellows, √2 and √3.
now, let's bear in mind that 2 and 3 are both prime numbers, a prime number is not divisible by anything but itself or 1, so we will never find two same-values that will give us either 2 or 3, namely, there's no exact root for √2 or √3, which means they're both irrationals, and therefore since they're factors of the answer, the answer is irrational.
2{[11(a-2)+12]-[2(5a-3)+a)}. Help me solve this please
Let's simplify step-by-step.
2(11(a−2)+12)−(2(5a−3)+a)
Distribute the Negative Sign:
=2(11(a−2)+12)+−1(2(5a−3)+a)
=2(11(a−2)+12)+−1(2(5a−3))+−1a
=2(11(a−2)+12)+−10a+6+−a
Distribute:
=(2)(11(a−2))+(2)(12)+−10a+6+−a
=22a+−44+24+−10a+6+−a
Combine Like Terms:
=22a+−44+24+−10a+6+−a
=(22a+−10a+−a)+(−44+24+6)
=11a+−14
Answer:
=11a−14
each leg of a 45-45-90 triangle measures 14 cm what is the length of the hypotenuse
ANSWER
The hypotenuse is 14√2 units.
EXPLANATION
Let the hypotenuse be x, then we can use the Pythagoras Theorem to find the length of the hypotenuse.
We have from the question that, each leg of the 45-45-90 triangle measures 14 cm.
Then, the Pythagorean Theorem, gives:
[tex] {x}^{2} = {14}^{2} + {14}^{2} [/tex]
[tex] {x}^{2} = 2 \times {14}^{2} [/tex]
Take positive square root to obtain;
[tex]x = \sqrt{ {14}^{2} \times 2} [/tex]
This simplifies to
[tex]x = 14 \sqrt{2} [/tex]
The length of the hypotenuse of the 45-45-90 triangle is 19.796 cm.
In a 45-45-90 triangle, the two legs are congruent (they have the same length) and the length of the hypotenuse is equal to the length of the legs multiplied by the square root of 2.
Given that each leg of the triangle measures 14 cm, the length of the hypotenuse can be calculated as follows:
Length of hypotenuse = Length of leg × √2
Length of hypotenuse = 14 cm × √2
Using a calculator or approximating the square root of 2 to 1.414, we can find:
Length of hypotenuse ≈ 14 cm × 1.414
Length of hypotenuse ≈ 19.796 cm (rounded to three decimal places)
Therefore, the length of the hypotenuse of the 45-45-90 triangle is approximately 19.796 cm.
To learn more about equilateral triangles click:
https://brainly.com/question/17824549
#SPJ6
A group of 40 students went on a field trip. Exactly 8 students wore blue shirts. What percent of the students on the field trip wore a blue shirt?
20% of the students wore blue shirts
40 x 0.08 = 3.2
3.2% out of the 40 students wore blue shirts.
Find the center, vertices, and foci of the ellipse. Simplify your answers as much as possible.
Answer:
1)center =(-2,3)
2) Vertices = (8,3) and (-12,3)
3) foci =(4,3) and (-8,3)
Step-by-step explanation:
As the general equation of ellipse with center at (h,k) is given by:
(x-h)^2/a^2 +(y-k)^2/b^2 = 1
where a=radius of the ellipse along the x-axis
b=radius of the ellipse along the y-axis
h, k= the x and y coordinates of the center of the ellipse.
Given equation of ellipse:
(x+2)^2/100 + (y-3)^2/64 = 1
1)
Finding center:
comparing with the general formula
h=-2 and k=3
Center of given ellipse is at (-2,3)
2)
Finding vertices:
comparing given equation of ellipse with the general formula:
a^2= 100 and b^2=64
then a = 10 and b=8
As a>b, it means the ellipse is parallel to x-axis
hence vertices along the x-axis are a = 10 units to either side of the center i.e (8,3) and (-12,3)
The co-vertices along the y-axis are b=8 units above and below the center i.e (-2,11) and (-2,-5)
3)
Finding Foci, c:
From equations of general ellipse we have a^2 - c^2=b^2
Putting values of a^2=100 and b^2=64 in above
100-c^2=64
c^2=100-64
= 36
taking square root on both sides
c=6
foci of given ellipse is either side of the center (-2,3) that is (4,3) and (-8,3)!
How do I solve (x-8)(2x+5=0
Answer:
x = 8 , x = - 2.5
Step-by-step explanation:
( x - 8 ) ( 2 x + 5 ) = 0
1. x - 8 = 0
2. 2 x + 5 = 0
x - 8 = 0
( + 8 on both sides )
x = 8
2. 2 x + 5 = 0
( - 5 from both sides )
2 x = - 5
( ÷ 5 on both sides )
x = - 2.5
10. A cliff on the seashore is eroding at the rate of 17 centimeters per year. Write and solve an equation to find the number of
years in which the cliff will erode 85 centimeters.
Answer: 17x = 85
Step-by-step explanation:
X is the number in which you'd multiply 17 by to equal 85, therefore x = the number of years.
Answer: Equation would be,
17x = 85
Where, x represents the number of year.
Step-by-step explanation:
Let x represents the number of year after which the cliff erodes 85 centimeters,
Since, the cliff on the seashore is eroding at the rate of 17 centimeters per year,
So, the total eroding of cliff after x years = 17x
[tex]\implies 17x = 85[/tex]
Which is the required equation..
The transformation (x,y) -> (x + 4,y – 3) is performed on the line segment AB.
The image is the line segment A' B' where point A' = (3, -3) and point B' = (5,-3).
What are the coordinates of A and B in line segment AB?
A. A=(-1,6), B = (1,-6)
B. A= (-1,0), B = (1,0)
C. A = (7,6), B = (9,–6)
D. A = (7,0), B = (9,0)
It’s either d or A but I’m sure it’s A
Simplify: a + 2a + 3a + 4a
A)
9a
B)
10a4
C)
9a4
D)
10a
You just need to factor a to get
[tex]a(1+2+3+4) = 10a[/tex]
Please help I’m very confused
Hello! The interquartile range would be 5°
You must subtract Quartile one from quartile 3 to find iqr