Answer:
61cm
Step-by-step explanation:
A right angled triangle is given to us with two sides as 11cm and 60 cm .We need to find out the length of the third side . Here , since it is a right angle triangle we can apply the Pythagoras theorem .
Pythagoras Theorem :- In a right angle triangle sum of squares of perpendicular and base is equal to the square of hypotenuse.
[tex]\rm\implies hypontenuse^2 = base^2+perpendicular^2[/tex]
As we can see that here ,
Base = 11cm
Perpendicular = 60cm.
[tex]\rm\implies Hypontenuse^2 = Perpendicular^2+Base^2 [/tex]
Substitute the respective values ,
[tex]\rm\implies h^2 = (11cm)^2+(60cm)^2 [/tex]
Simplifying ,
[tex]\rm\implies h^2 = 121cm^2+3600cm^2 [/tex]
Add the numbers on RHS ,
[tex]\rm\implies h^2= 3721 [/tex]
Take squareroot on both sides ,
[tex]\rm\implies h =\sqrt{61\times 61}[/tex]
Simplify the squareroot ,
[tex]\rm\implies \boxed{\blue{\rm Hypontenuse= 61 cm }}[/tex]
Hence the hypontenuse of the triangle is 61cm .
Which equation is the inverse of y = 2x2 – 8?
y = plus-or-minus StartRoot StartFraction x + 8 Over 2 EndFraction EndRoot
y = StartFraction plus-or-minus StartRoot x + 8 EndRoot Over 2 EndFraction
y = plus-or-minus StartRoot StartFraction x Over 2 EndFraction + 8 EndRoot
y = StartFraction plus-or-minus StartRoot x EndRoot Over 2 EndFraction + 4
Answer:
y = (√x/2) ± 2
Step-by-step explanation:
Here, we want to get the inverse of the given function
y = 2x^2 - 8
make x the subject of the formula
y + 8 = 2x^2
Divide through by 2
y/2 + 4 = x^2
x = √y/2 ± 2
Now switch place for x and y
y = (√x/2) ± 2
Answer:
d
Step-by-step explanation:
What is the equation of the line shown in the graph?
Drag and drop the expressions to write the equation of the line in slope-intercept form.
X, 2x, -X, -2x, 1, -1, -2 -4
Y=( )+( )
Answer:
y = -x -2
Step-by-step explanation:
-1 is the slope
-2 is the y-intercept
slope = [tex]\frac{-4-1}{2-(-3)}[/tex] = [tex]\frac{-5}{5}[/tex] = [tex]\frac{-1}{1}[/tex] = -1
$4.20 × $ 5.00=
A. $12.50
B. $21.00
C. $21
Answer:
C. $21 (as well as B)
Step-by-step explanation:
→ $4.20 × $ 5.00 = ?
→ 4.20 × 5.00
→ 4.2 × 5.0
→ 21 {final answer}
Hence, option (C) is answer.
If a person is randomly selected, find the probability that his or her birthday is NOT in May. Ignore leap years.
Answer:
1/334
Step-by-step explanation:
There are 31 days in May, subtract that from 365 days and you get 334, and there is an equal chance that she is born in any one of those 334 days, thus 1/334.
angelA and angelB are complementary angles. If m angel = ( x-23)° and m angel B = (2x + 29°) then find the measure of angle B.
Answer:
The measure of angle B is 29°.
(x² - 3x)√(2x² - 3x - 2)≥0
Answer:
(-infinity, -1/2] and [3, infinity] Let e know if anything didn't make sense.
Step-by-step explanation:
A good way to think about it is a graph is either at 0, greater than 0 or less than 0. If you can find all of the zeroes then you can test each zero by checking points before and after. the graph will either cross and change signs, or stay the same.
So we want to find the zeroes.
Much like the factored form of a quadratic (x - a)(x - b) this inequality has two expressions being multiplied together, so if you can find when they are 0 you will have all the zeros. We shoudl also check when they do not exist just to be safe.
(x^2 - 3x) itself is a quadratic. so lets find its zeroes.
x^2 - 3x
x(x - 3)
So the zeroes are 0 and 3. lets find the zeroes of the other expression before checking signs.
sqrt(2x^2-3x-2) will be at 0 when the quadratic inside is at 0, and will not exist if the quadrati is negative, so let's look for both. first the 0s. I am going to complete the square
2x^2 - 3x - 2 = 0
2(x^2 - (3/2)x - 1) = 0
2[(x - 3/4)^2 - 25/16] = 0
2(x - 3/4)^2 - 25/8 = 0
2(x - 3/4)^2 = 25/8
(x - 3/4)^2 = 25/16
x - 3/4 = +/- 5/4
x = +/-5/4 + 3/4
x = -2/4 or 8/4
x = -1/2 or 2
Let me know if you couldn't follow that. Anyway, using those zeroes we can tell 2x^2 - 3x - 2 is negative between the two zeroes, since it is a parabola that opens upwards and crosses the x axis at those zeroes. this means sqrt(2x^2 - 3x - 2) does not exist from x=-1/2 and x=2. This means for the other zero above at x=0, the iequality will not exist. So now we have 3 points to look at.
-1/2 for its first 0 and where it then stops existing up to 2, which is also a 0. Finally 3 is the last 0.
at x=-1/2 all values before it are positive
x=2 has values immediately after it negative
x=3 then it switches so all values after that are positive since it is the last 0
Now we know that (x^2 - 3x) * sqrt(2x^2 - 3x - 2)is positive or equal to 0 along the intervals, (-infinity, -1/2] and [3, infinity]
What is the solution to this equation 1/2n^2+18=0
Answer:
n = ±6 .
Step-by-step explanation:
A quadratic equation is given to us and we need to find out the solution of the given equation . The given equation is ,
[tex]\rm\implies -\dfrac{1}{2}n^2+18=0 [/tex]
Subtracting 18 both sides ,
[tex]\rm\implies -\dfrac{1}{2}n^2 = -18 [/tex]
Multiplying both sides by -2 ,
[tex]\rm\implies -2\times\dfrac{1}{2}n^2 = -2\times -18 [/tex]
On simplyfing , we get ,
[tex]\rm\implies n^2= 36 [/tex]
Putting squareroot both sides ,
[tex]\rm\implies n= \sqrt{36} [/tex]
This equals to ,
[tex]\rm\implies \boxed{\quad\blue{\rm n =\pm 6 }} [/tex]
Hence the value of n is ±6 .
Can someone help me with this math homework please!
Answer: f(t) = 1.5t + 5
One year josh had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 2.89. Also,alice had the lowest ERA of any female pitcher at the school with an ERA of 3.31 . For the males, the mean ERA was 5.083 and the standard deviation was 0.672. For the females, the mean ERA was 4.032 and the standard deviation was 0.649. Find their respective z-scores. Which player had the better year relative to their peers, josh or alice ? (Note: In general, the lower the ERA, the better the pitcher.)
Answer:
Josh's ERA had a z-score of -3.26.
Alice's ERA had a z-score of -1.11.
Due to the lower z-score(ERA is a stat that the lower the better), Josh had a better year relative to his peers.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Josh:
ERA of 2.89, mean of 5.083, standard deviation of 0.672. So
[tex]X = 2.89, \mu = 5.083, \sigma = 0.672[/tex], and the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.89 - 5.083}{0.672}[/tex]
[tex]Z = -3.26[/tex]
Josh's ERA had a z-score of -3.26.
Alice:
ERA of 3.31, mean of 4.032, standard deviation of 0.649. So
[tex]X = 3.31, \mu = 4.032, \sigma = 0.649[/tex], and the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.31 - 4.032}{0.649}[/tex]
[tex]Z = -1.11[/tex]
Alice's ERA had a z-score of -1.11.
Which player had the better year relative to their peers, josh or alice ?
Due to the lower z-score(ERA is a stat that the lower the better), Josh had a better year relative to his peers.
4|x+3|<8 i need help asap
Answer:
-5 <x<-1
Step-by-step explanation:
4|x+3|<8
Divide by 4
4|x+3| /4<8/4
|x+3|<2
There are two solutions one positive and one negative, remember to flip the inequality for the negative
x+3 <2 and x+3 >-2
Subtract 3 from each side
x+3-3 <2-3 and x+3-3 >-2-3
x<-1 and x>-5
-5 <x<-1
-5(n²+9)=7.
Find n.
Answer:
Step-by-step explanation:
-5n^2-45=7--->-5n^2=52--->n^2=52÷(-5)= there is no answer for this question...I mean Paired power never has a negative answer.
Which point gives the y-intercept of ƒ(x) = –x2 + 4x – 3?
Answer:
A) (0,-3)
Step-by-step explanation:
to get the y-intercept let x = 0, then
y = 0 + 0 -3
y = -3
Answer:
(0,-3)
Step-by-step explanation:
The y intercept is where x=0
ƒ(x) = –x^2 + 4x – 3?
f(0) = -0^2 +4(0)-3
f(0) = -3
(0,-3)
Laiba, tauseef and Nadia walked 24,42 and 52 meters.What is the minimum distance that each of them can cover equally ?
Answer:
the minimum distance each of them can cover equally is 8 m.
Step-by-step explanation:
Given;
different distance covered by Laiba, tauseef and Nadia = 24 m, 42 m and 52 m
for the 24 m, distance covered by each = 24 m/3 = 8 m
for the 42 m, distance covered by each, = 42 m/3 = 14 m
for the 52 m, distance covered by each, = 52 m/3 = 17.33 m
From the results above, the minimum distance each of them can cover equally is 8 m.
Please hurry I will mark you brainliest
What is the slope of this?
Answer:
-3/2
Step-by-step explanation:
the slope of a line is expressed as ratio y/x showing how many units y changes, when x changes a certain number of units.
so, going from A to B, x changes 4 units (from -3 to +1), and y changes 6 units (down, from +3 to -3). that makes the y change negative.
so, the slope is
-6/4 = -3/2
Mr. Powell rents a storage space that is 7 feet high, 5 feet long, and 4 feet wide.
How many containers, each one cubic foot in volume, can Mr. Powell fit into the storage space?
Enter your answer in the box.
Answer: 7x5x4=140^3
140
Step-by-step explanation:
Joan spilled 750ml of fruit punch while pouring into cups from a bucket which held 3.75 litres of punch. Calculate what % of punch was spilled
Answer:
Percentage of punch spilled = 20%
Step-by-step explanation:
1 liter = 1000 ml
750 ml = 750/1000
= 0.75 liter
Quantity of fruit punch spilled = 0.75 liter
Total volume of fruit punch in the bucket = 3.75 liters
Calculate what % of punch was spilled
Percentage of punch spilled = quantity of punch spilled / Total quantity of punch × 100
= 0.75 liter / 3.75 liters × 100
= 0.2 × 100
= 20%
Percentage of punch spilled = 20%
Find the volume of this cone.
Use 3 for T.
V = Tip?h
[?]cm3
19 cm
V ~
6cm
Answer:
81 cm ^3
Step-by-step explanation:
The volume of a cone is given by
V = 1/3 pi r^2 h where r is the radius and h is the height
We are given the diameter of 6 so the radius is 1/2 the diameter
r = 1/2 (6) = 3
V = 1/3 pi r^2 h
= 1/3 ( 3) * (3) ^2 * 9
= 81 cm ^3
which of the following is a perfect square trinomial A. 16x^2 + 22xy - 49y^2
B. 16X^2 + 56xy - 49y^2
C. 16x^2 - 22xy + 49y^2
D. 16X^2 - 56xy + 49y^2
Answer:
D. [tex]16x^2}-56xy+49y^2[/tex]
Step-by-step explanation:
A and B aren't correct because the last term is negative.
The factored form of D is [tex](4x-7y)^2[/tex]
I hope this helps!
Evaluate the function.
f(x) = -3x2
Find f(-2)
Answer
f(-2)= 12
Step-by-step explanation:
f(x) = -3x2
f(-2)= -3 (-2) 2
f(-2)= 6.2
f(-2)= 12
Hope this help :)
Answer:
-12
Step-by-step explanation:
f(x) = -3x^2
f(-2) = -3(-2)^2 = -12
Help pleasee geometry is hard
Answer:
Step-by-step explanation:
The formula for arc length is
[tex]AL=\frac{\theta}{360}*\pi d[/tex] where theta is the central angle. We are given the central angle when we are told that the measure of arc EFG is 240 degrees. The diameter is given as 36, so filling in:
[tex]AL=\frac{240}{360}*\pi (36)[/tex] which can be simplified down a bit to
[tex]AL=\frac{2}{3}*\pi (36)[/tex] and a bit more to
[tex]AL=2\pi(12)[/tex] which gives us, finally,
[tex]AL=24\pi[/tex]
I can't tell which of your answers matches this one because they're much too small to read.
What is the explicit formula for this sequence?
-8,-3, 2, 7, ...
O A. an = 12 + (n - 1)5
O B. an = 5+(n-1)(-8)
O C. an=-8+ (n - 115
O D. an= -8+ (n - 1)(-5)
Answer:
[tex]\text{C. }a_n=-8+(n-1)5[/tex]
Step-by-step explanation:
The explicit formula for an arithmetic sequence is given by [tex]a_n=a_1+(n-1)d[/tex], where [tex]a_n[/tex] is the [tex]n[/tex]th, [tex]a_1[/tex] is the first them of the sequence, and [tex]d[/tex] is the common difference.
In the given sequence -8, -3, 2, 7, we can see that we're adding 5 to each term. Therefore, the common different is positive five (+5). We can also identify the first term is -8. Therefore, we have:
[tex]a_1=-8[/tex] [tex]d=5[/tex]Thus, the explicit formula for this sequence is:
[tex]\boxed{a_n=-8+(n-1)5}[/tex]
Helppppppp pleaseeee
Answer:
23 more cars than trucks.... It means you add 23 over the number of trucks
2 trucks | 2+23 =25
Do u get it
Can someone help me with this math homework please!
In case of Nina:
slope of graph = speed = 48-32/6-4 = 16/2 =8
y-32 =8(x-4)
y-32=8x-32
y=8x
d=8t
at x= 0 i.e at t= 0
d= 0m
In case of Ryan:
slope =speed = 47.5-35=6-4 = 12.5/2 =6.25
y-35=6.25(x-4)
y-35=6.25x-25
y=6.25x+10
d=6.25t+10
at t = 0, d= 10m
RYAN had a head start of 10 m
Multiply the binomials:
(a-2) • (a-8)
Answer:
a^2 -10a +16
Step-by-step explanation:
(a-2) • (a-8)
FOIL
first a*a = a^2
outer: a * -8 = -8a
inner: -2 *a = -2a
last: -2 *-8 = 16
Add them together
a^2 -8a -2a+16
Combine like terms
a^2 -10a +16
Answer:
Step-by-step explanation:
(a-2) (a-8) , distribute a over (a-8) then -2 over (a-8)
a²-8a-2a+16, combine like terms
a² -10a +16
Evaluate the expression and see if it true or false
Answer: Sam did not get the question correct.
I believe he squared it wrong.
Step-by-step explanation:
The s.s of |x-4|=-4 is
A-8
B-16
C blank
D 8
Find the factorization of the polynomal below 64x^2 + 48x + 9
Answer:
(8x + 3)²
Step-by-step explanation:
Since our polynomial is 64x² + 48x + 9, we multiply 64x² by 9 to get 64x² × 9 = 576x² since we cannot simplify the expression any further.
Next, we need to find the factors of 576x² that add up to give 48x, these are 24x and 24x.
So the expression is re-written as
64x² + 48x + 9 = 64x² + 24x + 24x + 9
Writing out all the common factors, we have,
64x² + 48x + 9 = 8x × 8x + 3 × 8x + 3 × 8x + 3 × 3
Factorizing we have
64x² + 48x + 9 = 8x(8x + 3) + 3(8x + 3)
64x² + 48x + 9 = (8x + 3)(8x + 3)
64x² + 48x + 9 = (8x + 3)²
Mr. Fischer, a bilingual teacher, teaches a mathematics class composed of native English speakers and English language learners (ELLs). He has introduced a new topic with new vocabulary words in which he presented the vocabulary words with several examples. Which of the following strategies should Mr. Fischer use next to check each student's understanding of the vocabulary words?a. having students look up the definition online to see if it matches what Mr. Fischer told themb. having students copy down the definition for each word that Mr. Fischer wrote on the board in Englishc. placing students in groups so each student can explain the vocabulary terms to their peers in Englishd. having students write a definition for each term in their own words in their native language
Answer:
D. having students write a definition for each term in their own words in their native language
Step-by-step explanation:
In Mr Fischer's mathematics class, we are presented with two categories of learners. Those that are native speakers of English and those who are learners of English.
Both categories of students would show their understanding best in this lesson if they were to write in their own native language.
The native english-speakers would have no issues writing in English, but those who are English learners would have problems communicating their understanding of the lesson in English. So it is best they give their definitions in their native language.
write the equation for the line that has a slope of -4 and passes through the point (-2, 2)
Answer:
y = -4x - 6
Step-by-step explanation:
y = -4x + b
2 = -4(-2) + b
2 = 8 + b
-6 = b
Please please help !!
