[tex]35pq^2=5\cdot7\cdot p\cdot q^2\\-14pq^2=-1 \cdot 2\cdot 7\cdot p \cdot q^2\\-21p^2q^3=-1\cdot 3\cdot 7\cdot p^2 \cdot q^3\\\\\text{hcf}(35pq^2,-14pq^2,-21p^2q^3)=7\cdot p \cdot q^2=7pq^2[/tex]
Niko is 3 times as old as Lila. Niko's age is the same as adding Lila's age to the product of 3 and Amber's age. Niko is 45 years old. Kameron's age is equal to 2 times the sum of Amber's age and Lila's age. How old is Kameron? years old
Answer:
Kameron is 50 years old.
Step-by-step explanation:
We can make equations and start filling in what we already know, assuming [tex]n[/tex] is Niko's age, [tex]L[/tex] is Lila's age, [tex]a[/tex] is Amber's age, and [tex]k[/tex] is Kamerons age.
Our first equation:
n = 3L
We know that Niko is 45, so
45 = 3L
Divide both sides by 3:
L = 15
So, Lila is 15 years old.
Another equation:
n = L + 3a
We already know Niko and Lila's age:
45 = 15 + 3a
Subtract 15 from both sides:
30 = 3a
Divide both sides by 3:
a = 10
So Amber is 10 years old.
Another equation:
k = 2(a + L)
We know Amber and Lila's age:
k = 2(10 + 15)
k = 2(25)
k = 50
So Kameron is 50 years old.
Hope this helped!
Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф
Answer:
a) From A ∩ A' = ∅, we have;
A ∩ (A' ∪ B) = A ∩ B
b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;
A ∩ (A ∪ B)' = ∅
Step-by-step explanation:
a) By distributive law of sets, we have;
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
From the complementary law of sets, we have;
A ∩ A' = ∅
Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have
A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)
A ∩ A' = ∅ (complementary law of sets)
Therefore;
(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B) = (A ∩ B) (Addition to zero identity property)
∴ A ∩ (A' ∪ B) = A ∩ B
b) By De Morgan's law
(A ∪ B)' = A' ∩ B'
Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')
By associative law of sets, we have;
A ∩ (A' ∩ B') = (A ∩ A') ∩ B'
A ∩ A' = ∅ (complementary law of sets)
Therefore, (A ∩ A') ∩ B' = ∅ ∩ B' = ∅
Which gives;
A ∩ (A ∪ B)' = ∅.
Please help for 10 points and 5 stars with 1 thanks! :]
probability = favourable outcomes/total outcomes
you need 1 banana, out of 4 and there are total of 6 items so probability will be 4/6
when you take out 1 banana, there are 3 banana left and total of 5 items
so probability of this action will be 3/5
now, next action is taking out another banana.
this is NOT an independent event.
so by we will multiply the probabilities of these events according to rule of products.
so the answer is [tex] \frac{4\cdot3}{6\cdot5}=\frac25[/tex]
or 2×100/5=40%
Compute the value of each expression: |−12|−2|−6|
Answer:
12, 2, 6
Step-by-step explanation:
if the cost of a notebook is 2x-3 express the cost of five books
Answer:
10x - 15
Step-by-step explanation:
5(2x-3) = 10x - 15
I am an odd two-digit number. The sum of my two digits is 10 and the difference of my two digits is 0. What number am I?
Plz Help I Will Mark Brainliest If Right f(x) = x^2 + 3 A). y > -3 B). All real numbers C). y ≥ 3 D). y ≤ 3
Answer:
C) y ≥ 3
Step-by-step explanation:
The answer choices suggest that you're interested in the range of the function. x^2 cannot be negative, so its value will be 0 or greater. Adding 3 to x^2 ensures that the value of f(x) will be 3 or greater.
y ≥ 3 . . . . matches C
You see Bonnie rock climbing El Capitan. On your telescope is a clinometer. The angle
of elevation is 20 degrees. You know you are standing 950 feet away from El Capitan.
How high up is Bonnie?
Answer:
≈ 345.8 ft
Step-by-step explanation:
There is a right triangle formed by Bonnie's height (h) the ground and the angle of elevation.
Using the tangent ratio in the right triangle
tan20° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{950}[/tex] ( multiply both sides by 950 )
950 × tan20° = h , thus
h ≈ 345.8 ft ( to 1 dec. place )
Which of the following sets represents a function? {(1, 2), (3, 2), (5, 7)} {(3, 5), (-1, 7), (3, 9)} {(1, 2), (1, 4), (1, 6)}
Answer:
{(1, 2), (3, 2), (5, 7)}
Step-by-step explanation:
A function has a one to one correspondence
Each x can go to only 1 y value
{(1, 2), (3, 2), (5, 7)} function
{(3, 5), (-1, 7), (3, 9)} 3 goes to more than 1 y value
{(1, 2), (1, 4), (1, 6)} 1 goes to more than 1 y value
Answer:
[tex]\huge \boxed{ \{(1, 2), (3, 2), (5, 7)\} }[/tex]
Step-by-step explanation:
[tex]\sf A \ function \ is \ a \ relation \ if \ each \ x \ value \ is \ for \ each \ y \ value.[/tex]
[tex]\{(1, 2), (3, 2), (5, 7)\} \ \sf represents \ a \ function.[/tex]
[tex]\{(3, 5), (-1, 7), (3, 9)\} \ \sf does \ not \ represent \ a \ function.[/tex]
[tex]\{(1, 2), (1, 4), (1, 6)\} \ \sf does \ not \ represent \ a \ function.[/tex]
please answer the question
Answer is C
Step-by-step explanation:
I assure you that if you check a,b,c, and d by putting them into desmos graphing calculator you can find which graph it is. I plugged the third equation in and found that they were exact. If you want to do it the "smart" way that I teacher would show you, as you look at the answers and determine by certain points on the graph which one lines up. You start with 1/x.
Good Luck
What is the difference between a matrix and a determinant?
Answer:
Step-by-step explanation:
A matrix is a set of numbers organized in rows and columns to represent the variables in a situation, and the determinant is used to find the inverse of a matrix which helps you solve for different variable values.
Answer: A matrix or matrices is a rectangular grid of numbers or symbols that is represented in a row and column format. A determinant is a component of a square matrix and it cannot be found in any other type of matrix. ... A determinant is a number that is associated with a square matrix.
Step-by-step explanation:
This is the new one! Please help I’m so lost
Answer:
(a) (f o g)(x) = x^2 - 15x + 54
(b) (g o f)(x) = x^2 + 3x - 9
(c) (f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x
(d) (g o g)(x) = x - 18
Step-by-step explanation:
f(x) = x^2 + 3x
g(x) = x - 9
(a)
(f o g)(x) = f(g(x)) = (g(x))^2 + 3(g(x)) = (x - 9)^2 + 3(x - 9)
(f o g)(x) = x^2 - 18x + 81 + 3x - 27
(f o g)(x) = x^2 - 15x + 54
(b)
(g o f)(x) = g(f(x)) = f(x) - 9 = x^2 + 3x - 9
(c)
(f o f)(x) = f(f(x)) = (x^2 + 3x)^2 + 3(x^2 + 3x)
(f o f)(x) = x^4 + 6x^3 + 9x^2 + 3x^2 + 9x
(f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x
(d)
(g o g)(x) = g(g(x)) = x - 9 - 9 = x - 18
the product of 5 and z
Answer:
5z
Step-by-step explanation:
As product = multiplication =>
5 x z --> 5(z)
[tex]\text{Find the product of 5 and z}\\\\\text{The key term in this questions is product, and in math it translates to}\\\text{the answer when multiplled}\\\\\text{In this case, you would multiply them together to get your "product"}\\\\\text{Solve:}\\\\5\cdot z\\\\\boxed{5z}[/tex]
4' 1" − 1' 10" = Subtract measurement with Same Difference Theorem
Answer:
2' 3"
Step-by-step explanation:
Here 4' 1" − 1' 10" is certainly possible, but to carry out this operation we must borrow 1', or 12", from 4' 1":
4' 1" becomes 3' 13", and so the original problem becomes
3' 13" - 1' 10"
which in turn becomes 2' 3"
Which expression, in exponential form, is equivalent to 26x3y 47z5r3 A) ( 26x3y 47z5r3 )2 B) (26xy) 1 2 (47zr) 1 2 C) 26 1 2 x 3 2 y 1 2 47 1 2 z 5 2 r 3 2 D) 26x 3 2 y 1 2 47z 5 2 r 3 2
Answer:
The answer is "all the choices were wrong"
Step-by-step explanation:
Given value:
[tex]\bold{26x^3y 47z^5r^3}[/tex]
In the given question all the choices were wrong because it is not equivalent to given equation:
In choice A) [tex]( 26x^3y 47z^5r^3 )^2[/tex] in the value is whole squared, that's why it is wrong.
In choice B) [tex](26xy)^{12} (47zr)^{12}[/tex] when we open its value it will give different values, that's why it is wrong.
In option C and D( [tex]26^{12} x^{32} y^{12} 47^{12} z^{52} r^{32}[/tex] and [tex]26x^{32} y^{12}47z^{52} r^{32}[/tex]) both values will give different values.
Answer:
it's C
Step-by-step explanation:
I just did it
Find b.
Round to the nearest tenth:
Answer:
always b is equal to 9 is rhdx forum post in is ek of
Answer:
6.7 cm
Step-by-step explanation:
A+B+C=180°
55°+B+82°=180°
B=43°
Using the formulae
(Sin A)/a = (Sin B)/b
(Sin 55)/8 = (Sin 43)/b
b = [8(Sin 43)]/(Sin 55)
b= 6.7 cm
Patrick raced round a 440 metre circular track and stopped suddenly after 900 metres . How far was she from the starting point at the 900 metre mark ? Solve
Answer:
20 meters
Step-by-step explanation:
The track is circular so it means that after Patrick raced the entire track he is back at the starting point. In other words, every 440 meters he is back to the beginning.
So we would have that, if he races round the track twice, he would run 440(2) = 880 meters and he would be back at the starting point.
The problem asks us how far is he from the starting point at the 900 meter mark. If at 880 meters he is at the starting point, then at 900 meters he would be [tex]900-880=20[/tex] meters from the starting point.
72.3 + (-39.1)
☝
Rewrite the expression by breaking up each of the place values. In this case, the place values are tens, ones, and tenths.
Answer:
72.3 - 39.1 = 4tens - 7ones + 2tenth
Step-by-step explanation:
Give the expression 72.3 + (-39.1)
opening the parenthesis:
= 72.3 + (-39.1)
= 72.3 - 39.1
Breaking the decimal values into place values
72.3 = 7tens + 2units + 3tenth
72.3 = 7(10)+2(1)+3(1/10)
72.3 =70+2+0.3
Similarly for 39.1
39.1 = 3tens + 9units + 1tenth
39.1 = 3(10)+9(1)+1(1/10)
39.1 =30+9+0.1
72.3 - 39.1 = 70+2+0.3 - (30+9+0.1)
72.3 - 39.1 = 70+2+0.3 - 30-9-0.1
72.3 - 39.1 = 70-30+2-9+0.3-0.1
72.3 - 39.1 = 40 - 7 +0.2
72.3 - 39.1 = 4tens - 7ones + 2tenth
Answer:
72.3 - 39.1 = 70 + 2 + 0.3 + (-30) +(-9) + (0.1)
Step-by-step explanation:
got it from edmentum
State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement. Triangle LKJ≈____
Answer: C) similar, SAS similarity, triangle LQR
==============================================
Explanation:
The vertical angles KLJ and QLR are congruent. This forms the "A" in "SAS". The angles in question are between the marked sides.
KL = 18 is twice that of QL = 9, or put another way, KL/QL = 18/9 = 2. The ratio of the sides is 2. Also, JL/RL = 16/8 = 2 is the same ratio. Because both pairs of sides have the same ratio, the sides are in proportion. This helps form the two "S" letters of "SAS".
The original triangle has LKJ mentioned at the top. Note the order as its important. We start with L and move to K, so LK is the first segment mentioned. LK = 18 pairs up with LQ = 9, meaning that LQ must be the first segment mentioned of the answer triangle. Therefore LQR is the correct letter sequence if we start with point L. Writing QLR is not correct because Q is the first letter here but Q does not pair up with L.
How many cubes with side lengths of \dfrac12 \text{ cm} 2 1 cmstart fraction, 1, divided by, 2, end fraction, start text, space, c, m, end text does it take to fill the prism? Cubes
Answer:
24
Step-by-step explanation:
Answer
24!
Step-by-step explanation:
Person above me is correct :)
m∠QPSm, is a straight angle m∠RPS=6x+11 m∠QPR=7x+143 ;Find RPS
Answer:
23
Step-by-step explanation:
6x + 11 + 7x + 143 = 180
13x + 154 = 180
13x = 26
x = 2
m<RPS = 6(2) + 11 = 23
An important factor in selling a residential property is the number of people who look through the home. A sample of 17 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 19 and the standard deviation of the sample was 4 people.
Develop a 98 percent confidence interval for the population mean. (Round your answers to 2 decimal places.)
Confidence interval for the population mean is between and ?
Answer:
Confidence interval for the population mean is between 15 homes and 19 homes
Step-by-step explanation:
Given that:
Sample (n) = 17 homes, mean (μ) = 19 homes, standard deviation (σ)= 4 people and confidence (C) = 98% = 0.98
α = 1 - C = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01.
The z score of 0.01 (α/2) corresponds to the z score of 0.49 (0.5 - 0.01) which from the normal distribution table is 2.33
The margin of error (E) is:
[tex]E=z_{0.01}*\frac{\sigma}{\sqrt{n} } =2.33*\frac{4}{\sqrt{19} }=2[/tex]
The confidence interval = μ ± E = 17 ± 2 = (15, 19)
Confidence interval for the population mean is between 15 homes and 19 homes
PLEASE help me with this question! This is really urgent! No nonsense answers please.
Answer:
Last statement is the true one: AH congruent with AB
Step-by-step explanation:
Since the FG is congruent with KC, then the central angles defined by this chords are the same. and since the segments AH and AB are perpendicular to the segments GF and KC respectively (intersecting them at exactly half of their length), they form right angle triangles of which the hypotenuse is the actual radius of the circle, one of the legs of these triangles is half of the segments GF and KC of equal length. Then the third legs of those right angle triangles (AH and AB) must be equal as well.
Anyone who answers will be marked brainiest answer. If u don't understand anything just ask.
Answer:
7/2 pi
or approximately 10.99557429
Step-by-step explanation:
2 pi sqrt( a/b)
let a = 49 and b = 16
2 pi sqrt( 49/16)
We know that sqrt( a/b) = sqrt(a) /sqrt(b)
2 pi sqrt(49) / sqrt(16)
2pi ( 7) / (16)
2 pi ( 7/4)
7/2 pi
This is the exact answer
We can make an approximation for pi
Using the pi button on the calculator
10.99557429
PLZ HELP !!!!!! ASAP!!!
Part (a)
BC = opposite side (furthest leg from the reference angle)
AB = adjacent side (closest leg from the reference angle)
AC = hypotenuse (always opposite the 90 degree angle)
=============================================
Part (b)
i. False. Angle B is 90 degrees as shown by the square angle marker.
ii. False. Side AB is opposite angle C. Note how "C" is part of "BC", so that means we cannot have BC be opposite C.
iii. True. Leg AB is the closer leg to angle A. We have "A" in "AB" to see this without having to draw the diagram. Refer to part (a) above.
iv. False. The longest side of any right triangle is always the hypotenuse. The longest side of any triangle is always opposite the largest angle.
==============================================
Part (c)
cos(theta) = adjacent/hypotenuse = AB/AC
tan(theta) = opposite/adjacent = BC/AB
Refer back to part (a) to determine the opposite,adjacent and hypotenuse side lengths.
==============================================
Part (d)
The reference angle has changed, so the opposite and adjacent sides swap. The hypotenuse remains the same regardless of what reference angle you pick.
sin(C) = opposite/hypotenuse = AB/AC
cos(C) = adjacent/hypotenuse = BC/AC
tan(C) = opposite/adjacent = AB/BC
Note the tangent ratio is the reciprocal of what we found back in part (c).
Answer & Step-by-step explanation:
(a)
The hypotenuse is on line CA (the hypotenuse is always opposite the 90° angle (marked by a little square))
The adjacent is on the line BA (adjacent is next to the given angle, but NOT the hypotenuse)
The opposite is on the line CB (this is opposite the given angle)
(b)
i. false (b is a right angle)
ii. false (the side opposite C is BA)
iii. true
iv. false (the side opposite B is the hypotenuse, and the hypotenuse is always the longest side in a triangle)
(c)
cosine ratio: [tex]cos=\frac{adjacent}{hypotenuse}[/tex]
tangent ratio: [tex]tan=\frac{opposite}{adjacent}[/tex]
The cosine and tangent ratios of the given angle:
[tex]cos0=\frac{AB}{CA} \\\\tan0=\frac{CB}{AB}[/tex]
(d)
Remember SOH-CAH-TOA:
Sine=Opposite/Hypotenuse
Cosine=Adjacent/Hypotenuse
Tangent=Opposite/Adjacent
Using the angle C, plug in the appropriate sides:
[tex]sinC=\frac{BA}{CA}\\\\ cosC=\frac{CB}{CA}\\\\ tanC=\frac{BA}{CB}[/tex]
:Done
hi there can you please help me
[tex]t = \sqrt{ \frac{ab - s}{r + ak} } [/tex]
[tex]t=\sqrt{\dfrac{ab-s}{r+ak}}\\\\t^2=\dfrac{ab-s}{r+ak}\\\\rt^2+akt^2=ab-s\\\\akt^2-ab=-rt^2-s\\\\a(kt^2-b)=-(rt^2+s)\\\\a=-\dfrac{rt^2+s}{kt^2-b}\\\\a=-\dfrac{rt^2+s}{-(b-kt^2)}\\\\a=\dfrac{rt^2+s}{b-kt^2}[/tex]
What is the simplified form of this expression? (2x + 9) + (11x − 4)
Answer:
Have a great rest of your day :)
Step-by-step explanation:
Please answer this question now
Answer:
76 degrees.
Step-by-step explanation:
Let as consider O is the center of the circle . So from the figure it is clear that
[tex]\angle AOB=44^{\circ}[/tex]
[tex]\angle COD=118^{\circ}[/tex]
By central angle theorem, central angle subtended by an arc is twice of inscribed angle of the same arc.
We know that, [tex]\angle BAD=97^{\circ}[/tex] and angle BOD is the central angle subtended by arc BD.
[tex]\angle BOD=2\times \angle BAD[/tex]
[tex]\angle BOD=2\times 97^{\circ}[/tex]
[tex]\angle BOD=194^{\circ}[/tex]
Now,
[tex]\angle BOD=\angle BOC+\angle COD[/tex]
[tex]194^{\circ}=\angle BOC+118^{\circ}[/tex]
[tex]194^{\circ}-118^{\circ}=\angle BOC[/tex]
[tex]76^{\circ}=\angle BOC[/tex]
[tex]m(arc(BC))=76^{\circ}[/tex]
Therefore, the measure of arc BC is 76 degrees.
What is the simplified sum of 3x/x-4 + x-3/2x
━━━━━━━☆☆━━━━━━━
▹ Answer
-1 - 1/2x
▹ Step-by-Step Explanation
3x ÷ x - 4 + x - 3 ÷ 2x
Divide and Rewrite:
3 * 1 - 4 + x - 3 ÷ 2 * x
Calculate:
3 - 4 + x - 3/2x
-1 + x - 3/2x
= -1 - 1/2x
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
Step-by-step explanation:
[tex]\frac{3x}{x-4}+\frac{x-3}{2x}[/tex]
Make them into common denominators. To do so, multiply by the LCM of the denominators. The LCM of the denominators is (x-4)(2x). Thus, we multiply 2x to the first term and (x-4) to the second:
[tex](\frac{2x}{2x}) \frac{3x}{x-4}+(\frac{x-4}{x-4}) \frac{x-3}{2x}[/tex]
Simplify:
[tex]\frac{6x^2}{2x(x-4)}+\frac{x^2-7x+12}{2x(x-4)} \\=\frac{7x^2-7x+12}{2x(x-4)}[/tex]
And this cannot be simplified further (you can also distribute the denominator if preferred).
What is the product?
8.25 x
1
5
0.82
O 1.65
0 8.25
16.5
Answer:
Answers
product, and assign a number to each person. ... 0.82. 12–13. 9. 0.18. 1.00. Total. 50. 1.00. F requency. 0. 1. 2. 3. 4. 5. 6. 7. 8 ... 3.12 (a) x = 25661.3333, ˜x = 25514.5 (b) Skewed ... N(8.25, 0.0002857).
Answer:
the answer is c
Step-by-step explanation:
i just took the test
