Step-by-step explanation:
5⁵/5⁸
= 5^5-8
= 5^-3
or
(-5)×(-5)×(-5)
= -125
By the law
a^m÷ a^n = a^m-n
Wages and salaries
Kelly earns a salary of $68 430 pa how much does he earn each week, each fortnight and each month?
Answer:
Each week = $ 1311.41
Each fortnight = $ 2622.84
Each month = $ 5702.5
Step-by-step explanation:
Given that,
Annual salary of Kelly = $ 68,430
As we know,
There are 52.18 weeks in a year.
So,
Weekly income = Annual salary ÷ no. of weeks in the year
= $ 68,430 ÷ 52.18
= $ 1311.42
Fortnight income = 2 * weekly income
= 2 * $ 1311.42
= $ 2622.84
Each month's income = Annual income ÷ 12(no. of months)
= $ 68,430 ÷ 12
= $ 5702.5
How does the graph of g(x)=2⌈x⌉ differ from the graph of f(x)=⌈x⌉?
A) Multiplying by 2 compresses the graph of g(x)=2⌈x⌉vertically by a factor of 2.
B) Multiplying by 2 stretches the graph of g(x)=2⌈x⌉ vertically by a factor of 2.
C) Multiplying by 2 shifts the graph of g(x)=2⌈x⌉ up 2 units.
D) Multiplying by 2 shifts the graph of g(x)=2⌈x⌉ down 2 units.
Answer:
B is the Answer.
Step-by-step explanation:
A transformation of a function can be represented by
[tex]a(bx - h) + k[/tex]
where a is the vertical stretch or compression, b is the horizontal stretch or compression. H is the shift horizontally and k is the shift vertically.
The new function has a 2 instead of 1 on the orginally function. The function will stretch since 2 is greater than 1.
B is the answer.
A survey was done that asked students to indicate whether they enjoy reading or playing video games.
What is the ratio of those who do not enjoy reading and those who do not enjoy playing video games?
Enter your answer, in simplified form without using decimals, in the boxes.
please help me :D
Answer:
9 to 3
Step-by-step explanation:
Those who don't enjoy reading: 8+1=9
Those who don't enjoy playing video games: 1+2=3
Ratio is 9 to 3.
One number is larger than another by 9. If the greater number is increased by 10, and the lesser number is tripled, the sum of the two would be -41. What are the two numbers
Answer:
The larger number is -6, the smaller number is -15
Step-by-step explanation:
We have two numbers, a and b.
We know that one number is larger than another by 9.
Then we can write:
a = b + 9
then a is larger than b by 9 units.
If the greater number is increased by 10 (a + 10) and the lesser number is tripled (3*b), the sum of the two would be -41:
(a + 10) + 3*b = -41
So we got two equations:
a = b + 9
(a + 10) + 3*b = -41
This is a system of equations.
One way to solve this is first isolate one variable in one of the two equations:
But we can see that the variable "a" is already isolated in the first equation, so we have:
a = b + 9
now we can replace that in the other equation:
(a + 10) + 3*b = -41
(b + 9) + 10 + 3*b = -41
now we can solve this for b.
9 + b + 10 + 3b = -41
(9 + 10) + (3b + b) = -41
19 + 4b = -41
4b = -41 -19 = -60
b = -60/4 = -15
b = -15
then:
a = b + 9
a = -15 + 9 = -6
a = -6
help me pleaseeeeeeee!!!!!!!!
Answer:
8
Step-by-step explanation:
Using the chord chord theorem
10(4) = 5x
Solve for x
Simplify multiplication
40 = 5x
Divide both sides by 5
40/5 = 8
5x/5 = x
We're left with x = 8
Note:
Chord chord theorem states that if two chords intersect then the product of the measures of each part of one chord is equal to the product of the measures of the parts of the other chord.
Because the chords shown intersect the product of the parts of each chord should be equal to each other ( 4 * 10 = 5x )
Source: https://www.dummies.com/education/math/geometry/how-to-use-the-chord-chord-power-theorem
Albert, Imran and Siti invested $427000, $671000 and $305000 in a property respectively and they agreed to share the profitable n the ratio of their investments. After a few years, they sold the property for $1897500. Find the profit each of them received.
Answer:
1757200Step-by-step explanation:
42000+67000+305000=1403000(1897500-140300=1757200
The profit each of them received is $150500,$236500 and $107500
It is given that Albert, Imran and Siti invested $427000, $671000 and $305000 in a property respectively and they agreed to share the profitable n the ratio of their investments. After a few years, they sold the property for $1897500, we have to find the profit each of them received
What is Profit?
Profit= Selling Price - Cost price
Total Investment= $427000+$671000+$305000
=$1403000
Profit=$1897500-$1403000=$494500
Profit share=(Investment/Total Investment)*Total Profit
Albert Profit=($427000/$1403000)*$494500=$150500
Imran Profit=($671000/$1403000)*$494500=$236500
Siti Profit=($305000/$1403000)*$494500=$107500
Therefore profit each of them received is $150,500, $236500, $107500
To know more about profit click here:https://brainly.com/question/15036999
#SPJ2
Use trigonometric identities to solve each equation within the given domain.
4cos4(x) – 5cos2(x) + 1 = 0 from [0, 2π). PLEASE SHOW WORK!!!
Simplify each of the following:
a) root25 + root50 - root24 + root49
b) root2(2root8 – 3root32 + 4roor50)
Show your work
Answer:
a)
√25 + √50 - √24 + √49 =5 + 5√2 - 2√6 + 7 = 12 + 5√2 - 2√6b)
√2(2√8 – 3√32 + 4√50) =2√16 - 3√64 + 4√100 = 2*4 - 3*8 + 4*10 = 8 - 24 + 40 = 24Answer:
a.) 12 + 5√2 - 2√6
b.) 24
Step-by-step explanation:
a) √25 + √50 - √24 + √49
√25 + √50 - √24 + √49Calculate the square root .
5 + √50 - √24 + 7Simplify the radical expression.
5 + 5√2 - 2√6 + 7Combine like terms.
5 + 7 + 5√2 - 2√6 12 + 5√2 - 2√6b.) √2 ( 2√8 - 3√32 + 4√50 )
√2 ( 2√8 - 3√32 + 4√50 )Simplify the radical expression.
√2 ( 4√2 - 3 × 2²√2 + 20√2)Evaluate the power.
√2 ( 4√2 - 3 × 4√2 + 20√2)Calculate the products.
√2 ( 4√2 -12√2 + 20√2)Combine like terms.
√2 × (4 - 12 + 20 )√2√2 × 12 √ 2Multiply.
2 × 12 24The quadratic formula can be used to solve any quadratic equation in standard form.
True or False
Answer:
True
Step-by-step explanation:
The quadratic formula can be applied to any quadratic equation in the form [tex]ax^2+bx+c=0[/tex] (standard form).
The quadratic formula: [tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
I hope this helps!
Answer:
its true
Step-by-step explanation:
The dot plot above identifies the number of pets living with each of 20 families in an apartment building. What
fraction of the families have more than two pets?
Answer:
1/5
Step-by-step explanation:
1. The position of a particle moving along a coordinate axis is given by: s(t) = t^2 - 5t + 1. Find the speed of the particle
Answer:
[tex]v(t) = 2t - 5[/tex]
Step-by-step explanation:
Given
[tex]s(t) = t^2 - 5t + 1[/tex]
Required
The speed of the particle
To do this, we simply differentiate the position function
i.e.
[tex]v(t) = s'(t)[/tex]
So, we have:
[tex]s(t) = t^2 - 5t + 1[/tex]
Differentiate
[tex]s'(t) = 2t - 5 + 0[/tex]
[tex]s'(t) = 2t - 5[/tex]
So, the speed function is:
[tex]v(t) = 2t - 5[/tex]
Given P(B | A)=0.75, P(A ∩ B)=0.15, P(B’)=0.7, find P(A ∪ B)
By definition of conditional probability,
P(B | A) = P(A ∩ B) / P(A)
==> P(A) = P(A ∩ B) / P(B | A) = 0.15/0.75 = 0.2
By definition of complement,
P(B') = 1 - P(B)
==> P(B) = 1 - P(B') = 1 - 0.7 = 0.3
Now by the inclusion/exlcusion principle, we have
P(A U B) = P(A) + P(B) - P(A ∩ B)
==> P(A U B) = 0.2 + 0.3 - 0.15 = 0.35
last question pls answer
Answer:
30 min
Step-by-step explanation:
60 divided by 20= 30min
How do I do this question
Answer:
Step-by-step explanation:
Join OB.
∠A=∠A (common)
[tex]\frac{AP}{AO} =\frac{\frac{1}{2} AO}{AO} =\frac{1}{2} \\\frac{AQ}{AB} =\frac{\frac{1}{2} AB}{AB} =\frac{1}{2} \\\frac{AP}{AO} =\frac{AQ}{AB}[/tex]
∴ ΔAPO and ΔAOB are similar.
[tex]\frac{PQ}{OB} =\frac{1}{2} \\[/tex]
∠P=∠O
∠Q=∠B
So PQ║OB
Similarly RS║OB
∴PQ║RS
The vertex of this parabola is at (-3,-2). Which of the following could be its equation?
Answer:
B x = -2(y+2)^2 -3
Step-by-step explanation:
The vertex form of a sideways parabola is
x = a(y-k)^2+h where (h,k) is the vertex and a is a constant
x = a(y--2)^2 -3
x = a(y+2)^2 -3
B is the only option with +2 and -3in the proper postion
x = -2(y+2)^2 -3
What is the tangent ratio of angle x?
tan x= 20/21
tan x= 21/29
tan x= 20/29
tan x= 21/20
Answer:
[tex]\tan x=21/20[/tex]
Step-by-step explanation:
In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. (o/a)
For angle [tex]x[/tex], its opposite side is 21 feet and its adjacent side is 20 feet. Therefore, we have:
[tex]\boxed{\tan x=21/20}[/tex]
Explainnnnnn help me please
Answer:
99cm²
Step-by-step explanation:
area for a triangle = 1/2 x b x h
area = 1/2 x 11 x 18
area = 99cm²
WILL MARK BRAINLIEST
picture included^^^^
need help asap please n thank you!
^^^^
Answer:
14
Step-by-step explanation:
The a value is from the center to the maximum
We want from minimum to max so we need 2 times the amplitude
a = 7
2 *7 = 14
Given the triangle below is m
A. 68.6
B. 82.8
C. 74.4
D. 80.6
Answer:
B. 82.8
Step-by-step explanation:
3. Rita is applying for a job as an engineer. Hier starting salary at Company will be $30,000 a $300 yearly
raise. Her starting salary at company will be $65.000 with a 5% increase sach year. If Rata is working at a
company for 5 years. Which company should she pick?
Answer:
The 65,000 salary
Step-by-step explanation:
Because the 30,000 salary after 5 years would be 31,500.
30,000+300=30,300
30,300+300=30,600
30,600+300=30,900
30,900+300=31,200
31,200+300=31,500
The 65,000 paying company
65,000x1.05=68,250
68,250x1.05=71.662.5
71,662.5x1.05=75,245.625
75,245.625x1.05=79,007.90625
79,007.90625x1.05=82,958.3015625
her salary after 5 years would be 82,958.3015625
What is the answer? How to solve?
Answer:
a +73°=90°
a= 90°-73°
a =17°
d+18°=90°
d=90°-18°
d =72 °
please solve this please
Answer:
3
Step-by-step explanation:
Pls help me this is my homework
Answer:
C) 840
C) 87
D) 3000-150n
Step-by-step explanation:
Answer:
c
c
d
Step-by-step explanation:
The circle centered at $(2,-1)$ and with radius $4$ intersects the circle centered at $(2,5)$ and with radius $\sqrt{10}$ at two points $A$ and $B$. Find $(AB)^2$.
The first circle has equation
(x - 2)² + (y + 1)² = 4²
and the second has equation
(x - 2)² + (y - 5)² = (√10)²
Solve for (x - 2)² :
(x - 2)² + (y + 1)² = 4² ==> (x - 2)² = 16 - (y + 1)²
(x - 2)² + (y - 5)² = (√10)² ==> (x - 2)² = 10 - (y - 5)²
Then
16 - (y + 1)² = 10 - (y - 5)²
16 - (y ² + 2y + 1) = 10 - (y ² - 10y + 25)
15 - 2y - y ² = -15 + 10y - y ²
30 - 12y = 0
12y = 30
y = 30/12 = 5/2
(this is the y coordinate of A and B)
Then solve for x :
(x - 2)² = 16 - (5/2 + 1)²
(x - 2)² = 15/4
x - 2 = ± √(15/4) = ±√15/2
x = 2 ± √15/2
(these are the x coordinates for either A or B)
The intersections are the points A = (2 - √15/2, 5/2) and B = (2 + √15/2, 5/2). We want to find the squared distance between them:
(AB)² = [(2 - √15/2) - (2 + √15/2)]² + (5/2 - 5/2)²
(AB)² = (-√15)² + 0²
(AB)² = 15
Problema 6 Descompongan los siguientes números en factores primos. ¿Es posible encontrar, para cada número, más de una descomposición en factores primos? a. 42 b. 31 c. 36 d. 45
Answer:
a: 42 = 2*3*7
b: 31 = 31*1
c: 36 = 2*2*3*3
d: 45 = 3*3*5
Cada descomposición es unica.
Step-by-step explanation:
Sabemos que todo número entero puede ser reescrito como un producto de números primos.
Esta descomposición es única, dado que una vez tenemos un número escrito como producto de primos, esos números primos no pueden descomponerse en otra cosa, por lo que se concluye que una descomposición en primos es única.
a: 42
Para obtener la descomposición, podemos comenzar dividiendo por primos, comenzando por los más bajos.
En este caso, podemos comenzar por 2:
42/2 = 21
asi, podemos reescribir:
42 = 2*21
Ahora ya tenemos un factor que es primo, el 2, y un factor que no lo es, el 21.
Asi que debemos reescribir el 21 como producto de primos.
Y sabemos que 3*7 = 21, donde ambos 3 y 7 son primos, entonces:
42 = 2*21 = 2*3*7
42 = 2*3*7
así hemos reescrito 42 como un producto entre números primos.
b. 31
31 es un número primo, por lo que su descomposición es:
31 = 31*1
c. 36
Comenzamos dividiendo por 2.
36/2 = 18
36 = 2*18
Volvemos a dividir por 2 el 18.
18/2 = 9
18 = 2*9
reemplazando eso en nuestra descomposición obtenemos:
36 = 2*18 = 2*2*9
9 es impar así que no podemos dividir por 2, pasamos al próximo número primo, el 3.
9/3 = 3
9 = 3*3
Reemplazando eso, obtenemos:
36 = 2*2*3*3
d. 45
no podemos dividir por 2, puesto que es un número impar, así que pasamos al próximo primo, el 3.
45/3 = 15
45 = 3*15
Ahora descompongamos el 15.
15/3 = 5
15 = 3*5 (notar que 3 y 5 son primos)
Reemplazando eso, obtenemos:
45 = 3*15 = 3*3*5
45 = 3*3*5
graphical representation of 2x – 1 = 3?
Answer:
[tex]2x - 1 = 3 \\ 2x = 3 + 1 \\ 2x = 4 \\ x = \frac{4}{2} \\ x = 2[/tex]
An airplane from Singapore to Melbourne takes about 7 1/2 hours to cover a distance of 6057 km. What is the average speed of the airplane.
Answer: 13.46 km/h
Step-by-step explanation:
7 1/2 hr= 450 min
6057/450= 13.46
Mary is on the Barracudas swim team. Each practice, Mary has to swim a target number of laps. Today, Mary swam 34 laps before taking a snack break. She had 41 laps left to reach her target number after the snack break.
Answer:
75
Step-by-step explanation:
I'm assuming it is asking for how many laps does she need for her target because you haven't included the whole question.
34+41=75
Step-by-step explanation:
what is the question ?
just in case : I assume you want to know how many laps she had to swim overall today ?
you really need help with that ? you have no calculator ?
she needed to swim 34 + 41 = 75 laps.
Quick! HELP! THANK YOU SO MUCH!
If the difference between the interior and exterior angles of a regular polygon is 100°, how many sides does the polygon have?
Answer:
9 sides
Step-by-step explanation:
Sum of the measures of the interior angle of a polygon with n sides:
(n - 2)180
Measure of 1 interior angle of a regular polygon of n sides:
(n - 2)180/n
Sum of the measures of the exterior angles of a polygon, one per vertex:
360
Measure of 1 exterior angle of a regular polygon of n sides:
360/n
(n - 2)180/n = 360/n + 100
Multiply both sides by n.
(n - 2)180 = 360 + 100n
Distribute on left side.
180n - 360 = 360 + 100n
Subtract 100n from both sides.
80n - 360 = 360
Add 360 to both sides.
80n = 720
Divide both sides by 80.
n = 9
Answer: 9 sides
The area of a rectangle is 105 square units. Its width measures 7 units. Find the length of its diagonal. Round to the nearest tenth of a unit.
Answer:
16.6
Step-by-step explanation:
The rectangle has an area of 105. It's width is 7.
1: Find the length
[tex]\frac{area}{width}[/tex]=length
[tex]\frac{105}{7}[/tex]= 15
Length=15
2: Pythagorean theorem
[tex]a^{2} +b^2=c^2[/tex]
[tex]7^{2}[/tex]+[tex]15^2=c^2[/tex]
49+225=[tex]c^2[/tex]
275=[tex]c^2[/tex]
[tex]\sqrt{275}[/tex] = [tex]\sqrt{c^2\\}[/tex]
16.55≈c
Rounded to nearest tenth
16.6
