Hello, we know that for a and b real numbers
[tex]a^2-b^2=(a-b)(a+b)[/tex]
So,
[tex](2a-b)^2-(a-2b)^2=(2a-b-a+2b)(2a-b+a-2b)\\\\=(a+b)(3a-3b)\\\\\boxed{=3(a+b)(a-b)}[/tex]
Thank you.
The domain of this function is {-12, -6, 3, 15}. y=-2/3x+7 Complete the table based on the given domain.
Answer:
Step-by-step explanation:
Domain of a function represents the set of x-values (input values) and y-values (output values) of the function represent the Range of the function.
Given function is,
[tex]y=-\frac{2}{3}x+7[/tex]
If Domain (input values) of this function is,
{-12, -6, 3, 15}
Table for the input-output values of this function,
x -6 3 15 -12
y 11 5 -3 15
Answer:
Step-by-step explanation:
Vanessa uses the expressions (3x2 + 5x + 10) and (x2 – 3x – 1) to represent the length and width of her patio. Which expression represents the area (lw) of Vanessa’s patio?
To get the area simply multiply the length by the width.
(3x^2+5x+10)(x^2-3x-1) = 3x^4 - 4x^3 - 8x^2 - 35x - 10
Answer:
the answer is A
Step-by-step explanation:
got it right on edge
The circle shown below is a unit circle, where ∠a=π/3 and the radius of the circle is 1.
Answer:
Step-by-step explanation:
What is the rule for the transformation below?
=================================================
Explanation:
The translation notation T(-5, 3) looks like an ordered pair point, but it is not. Instead, it is a rule to tell you how to shift any point left/right and up/down. The first number is the left/right shifting as its done along the x axis. The negative value means we shift left, so we shift 5 units to the left. The positive 3 in the y coordinate place means we shift 3 units up.
We see this shifting happen when we go from
A = (-1, -1) to A ' = (-6, 2) B = (2, 3) to B ' = (-3, 6)C = (5, -3) to C ' = (0, 0)The translation notation T(-5, 3) is the same as writing [tex](x,y) \to (x-5, y+3)[/tex] which may be a more descriptive notation to use, and it would avoid confusion with ordered pair point notation.
The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of days and a standard deviation of days. (a) What is the minimum pregnancy length that can be in the top % of pregnancy lengths? (b) What is the maximum pregnancy length that can be in the bottom % of pregnancy lengths? (a) The minimum pregnancy length is 280 days.
Answer:
(a) 283 days
(b) 248 days
Step-by-step explanation:
The complete question is:
The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 268 days and a standard deviation of 12 days. (a) What is the minimum pregnancy length that can be in the top 11% of pregnancy lengths? (b) What is the maximum pregnancy length that can be in the bottom 5% of pregnancy lengths?
Solution:
The random variable X can be defined as the pregnancy length in days.
Then, from the provided information [tex]X\sim N(\mu=268, \sigma^{2}=12^{2})[/tex].
(a)
The minimum pregnancy length that can be in the top 11% of pregnancy lengths implies that:
P (X > x) = 0.11
⇒ P (Z > z) = 0.11
⇒ z = 1.23
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\1.23=\frac{x-268}{12}\\\\x=268+(12\times 1.23)\\\\x=282.76\\\\x\approx 283[/tex]
Thus, the minimum pregnancy length that can be in the top 11% of pregnancy lengths is 283 days.
(b)
The maximum pregnancy length that can be in the bottom 5% of pregnancy lengths implies that:
P (X < x) = 0.05
⇒ P (Z < z) = 0.05
⇒ z = -1.645
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.645=\frac{x-268}{12}\\\\x=268-(12\times 1.645)\\\\x=248.26\\\\x\approx 248[/tex]
Thus, the maximum pregnancy length that can be in the bottom 5% of pregnancy lengths is 248 days.
Multiply and simplify. (1 − 5i)(1 − 2i) A) 1 + 7i B) 9 − 7i C) 1 − 7i D) − 9 − 7i
Answer:
The product renders: [tex]-9-7\,i[/tex]
Step-by-step explanation:
Recall that the product of the imaginary unit i by itself renders -1
Now proceed with the product of the two complex numbers using distributive property:
[tex](1-5\,i)\,(1-2\,i)=1-2\,i-5\,i+10\,i^2=1-7\,i-10=-9-7\,i[/tex]
A stone is thrown downward straightly its speed at speed of 20 second what and it reaches the ground at 40 metre second what will be the height of building
Answer:
[tex]\Huge \boxed{\mathrm{61.22 \ m}}[/tex]
Step-by-step explanation:
A stone is thrown downward straightly with the velocity of 20 m/s and it reaches the ground at the velocity of 40 m/s. What will be the height of building? (Question)
The initial velocity ⇒ 20 m/s
The final velocity ⇒ 40 m/s
We can apply a formula to solve for the height of the building.
[tex](V_f)2 - (V_i)^2 =2gh[/tex]
[tex]V_f = \sf final \ velocity \ (m/s)[/tex]
[tex]V_i = \sf initial \ velocity \ (m /s)[/tex]
[tex]g = \sf acceleration \ due \ to \ gravity \ (m/s^2 )[/tex]
[tex]h = \sf height \ (m)[/tex]
Plugging in the values.
Acceleration due to gravity is 9.8 m/s².
[tex](40)^2 - (20)^2 =2(9.8)h[/tex]
Solve for [tex]h[/tex].
[tex]1600 - 400 =19.6h[/tex]
[tex]1200 =19.6h[/tex]
[tex]\displaystyle h=\frac{1200}{19.6}[/tex]
[tex]h= 61.22449[/tex]
The height of the building is 61.22 meters.
To get from home to work, Felix can either take a bike path through the rectangular park or ride his bike along two sides of the park. How much farther would Felix travel by riding along two sides of the park than he would by taking the path through the park?
Answer:
c=5.9/6(G)
Step-by-step explanation:
first find the 2 distances.
a^2+b^2=c^2 c=2.4+.7
7^2+2.4^2=c^2 c=3.1
.49+5.85=c^2
c^2=6.34
c=√6.34
c=2.51.
next subtract the two distances to find the difference.
c=2.51-3.1
c=.59
so the distance would be .59 which can be rounded up to .60/G
explanation on how I knew the answer.
Im reviewing for the math 8th grade staar.
Why the answer question now correct
Answer:
461.58 in²
Step-by-step explanation:
The surface area (A) is calculated as
A = area of base + area of curved surface
= πr² + πrl ( r is the radius of base and l is slant height )
= 3.14 × 7² + 3.14 × 7 × 14
= 3.14 × 49 + 3.14 × 98
= 3.14(49 + 98)
= 3.14 ×147
= 461.58 in²
find the exterior angle of a triangle whose interior opposite angles are 43 degree and 27 degree
Answer:
[tex]\huge\boxed{Exterior\ angle = 70\°}[/tex]
Step-by-step explanation:
The measure of exterior angle is equal to the sum of opposite interior angles.
So,
Exterior angle = 43+27
Exterior angle = 70°
ux=x+y/k, solve for x
Answer:
x = y/( ku-1)
Step-by-step explanation:
Here in this question, we are asked to solve for x.
we have;
Ux = x+ u/ k
cross multiply;
k * Ux = x + y
kUx = x + y
kUx- x = y
x(KU-1) = y
x = y/( ku-1)
really urgent...i need the working also ...pls help me
Answer:
See below.
Step-by-step explanation:
In each case, you are looking for time. We know speed is distance divided by time. Lets start with the speed formula.
speed = distance/time
Now we solve it for time. Multiply both sides by time and divide both sides by speed.
speed * time = distance
time = distance/speed
Time is distance divided by speed. In each problem, you have a speed and a distance. Divide the distance by the speed to to find the time.
1) speed = 44.1 km/h; distance = 150 km
time = distance/speed = 150 km/(44.1 km/h) =
= 3.401 hours = 3 hours + 0.401 hour * 60 min/hour = 3 hours 24 minutes
2) speed = 120 km/h; distance = 90 km
time = distance/speed = 90 km/(120 km/h) =
= 0.75 hours = 0.75 hour * 60 min/hour = 45 minutes
3) speed = 125 m/s; distance = 500 m
time = distance/speed = 500 m/(125 m/s) =
= 4 seconds
WILL GIVE BRAINLIEST!!!!!! Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown: Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer, stating the theorem you used. Show all your work. Part B: The length of rod PR is adjusted to 17 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work.
A) Here, We'll use "Pythagoras Theorem" which tells:
a² + b² = c²
So, PR² = PQ² + QR²
PR² = 14² + 9²
PR² = 196 + 81
PR = √277
In short, Your Answer would be 16.64 Feet
B) Again, Use the Pythagoras Theorem,
c² - a² = b²
18² - 14² = b²
b² = 324 - 196
b = √128
b = 11.31
In short, Your Answer would be 11.31 Feet
Part A: Using the Pythagorean Theorem. a^2 + b^2 = c^2
PQ^2 + QR^2 = PR^2 (The rods make a right triangle, where PR would be the hypotenuse, and QR and PQ would be legs a and b.)
14^2 + 9^2 = PR^2
196 + 81 = PR^2
Square root of 277 = PR
16.64 = PR
So, the hypotenuse would be equal to 16.64 ft.
Part B: Using the Pythagorean Theorem. a^2 + b^2 = c^2
PR^2 - PQ^2 = QR^2 (Trying to find the height of QR this time, not the hypotenuse, since we know what it is already. Subtracting the value of leg a from the hypotenuse will give us the value of leg b, QR.)
18^2 - 14^2 = QR^2
324 - 196 = QR^2
Square root of 128 = QR
So, the new height of QR would be 11.31 ft.
Michael is using a number line to evaluate the expression –8 – 3. A number line going from negative 12 to positive 12. A point is at negative 8. After locating –8 on the number line, which step could Michael complete to evaluate the expression?
Answer:
move to the left 3 more spaces
Step-by-step explanation:
you are at -8 already. Therefore, you (-3) more spaces, so you go to the left three more spaces. Use the saying keep change change to help with this.
Keep the first number sign, change the next sign, and the next sign.
Answer:
d
Step-by-step explanation:
I NEED HELP ANSWERING THESE QUESTIONS FIRST ANSWER GET BRAINLIEST!
Answer:
3 - b=12
4- b=14.1
Step-by-step explanation:
Area of the bookshelf=864 square inches
the book shelf is a rectangular prism
if we have height=4b, width=3b, length=b
then the area=length * width
A=(l*w)*2 ( we have 2 shelves)
864=(b*3b)*2
864=6b²
b²=864/6=144
b=√144= 12 inches
4- to cover the sides :
(height * length)*2 ( we have 2 sides)
(4b*b)×2=1600
8b²=1600
b²=1600/8=200
b=√200=14.1
Answer:
Question #3: b = 12 in
Question #4: b = 14.1 in
Step-by-step explanation:
Please see in the image attached the actual proportions that the furniture manufacturer uses to build the furniture in question:
Height = 4 b
Width = 3 b
Depth = b
So for question #3, given that the customer wants a total surface of the shaded shelves to be 864 [tex]in^2[/tex]
we can write that one wants twice the area of each rectangle of width 3 b and depth b to total 864:
[tex]2\,(3b\,*\,b)=864\\6 b^2=864\\b^2=864/6\\b^2=144\\b=12\,\,in[/tex]
Question # 4:
The total lateral surface to be covered by the silk is 1600 [tex]in^2[/tex], therefore if we consider the surface of each lateral plank as:
Area of each lateral plank :
[tex](4b)\,(b) = 4\,b^2[/tex]
Then twice these is: [tex]8\, b^2[/tex]
So we can solve for be requesting that these total surface equal the amount of silk:
[tex]8\,b^2=1600\\b^2=1600/8\\b^2=200\\b=\sqrt{200} \\b\approx 14.1421\,\,in[/tex]
which rounded to the nearest tenth of an inch gives:
[tex]b\approx 14.1\,\,in[/tex]
Sarah has $20 saved. She gets $10 per week for her allowance, and she saves her allowance for the next 3 weeks. At the end of the week, she gets $150 in birthday money. How much money will she have after the 3 weeks? Which of the following sets of equations represents this problem?
Answer:
$200
Step-by-step explanation:
We know that she already has $20. And we know that every week, for three weeks she gets $10.
20+3(10)+150=m
We add all of this up, and we find that at the end of 3 weeks Sarah has $200 saved.
Given an angle of a triangle and the opposite side length; which trigonometric function would you use to find the hypotenuse? a TAN b COS c SIN d Not enough information
Answer:
Sin
Step-by-step explanation:
Sin < = opposite/hypotenuse
Someone pls help thank you sm ..
Answer:
15 lawns
Step-by-step explanation:
The Xbox costs $400 and his parents gave him $100. He needs to earn $300 more. $20 each lawn so $100 for 5 lawns. 5 lawns times three.
Xbox cost =400
Daniel's money =100
Xbox cost - Daniel money=300
yard cost =20
therefore 400 -100 /20
Daniel's need 15 yards to get the xbox
Please explain and help
Answer:
y=-x+2
Step-by-step explanation:
it is linear equation y=mx+b two points (0,2),(1,1)
find m ( slope)=y2-y1/x2-x1 ⇒1-2/1-0⇒-1
y=mx+b choosea point from graph :(0,2)\when x =0 the y=b=2
y=-x+2
evaluate 15.2% of a 726 + 12.8% of 673
Answer:
196.496
Step-by-step explanation:
0.152x726+0.128x673
110.352+86.144
=196.496
Mildred’s salary has increased from £24,600 to £25,338. By what percentage has her salary increase?
Answer:
The answer is 3%Step-by-step explanation:
To find the percentage increase we use the formula
[tex]Percentage \: change = \frac{ change}{original \: quantity} \times 100[/tex]
To find the change subtract the smaller quantity from the bigger one
From the question
original price = $24,600
Current price = $ 25,338
Change = $25,338 - $ 24,600
Change = $ 738
So the percentage increase is
[tex] \frac{738}{24600} \times 100[/tex]
[tex] = \frac{3}{100} \times 100[/tex]
We have the final answer as
Percentage increase = 3%Hope this helps you
Triangle A' B' C' is a dilation of a triangle ABC. The scale factor is [tex]\frac{3}{4}[/tex]. Point B is 11 inches away from the center of dilation is point B'?
Answer:
None of the options are correct
Step-by-step explanation:
Let us assume point B is at (x, y) and the center of dilation is at (a, b). Therefore the distance between the two points is:
[tex]Distance =\sqrt{(b-y)^2+(a-x)^2}=11 \\\\\sqrt{(b-y)^2+(a-x)^2}=11[/tex]
If Triangle ABC is then dilated by 3/4, the new coordinate is B'(3/4 (x-a) + a, 3/4 (y - b) + b). The distance between B' and the center of dilation would be:
[tex]Distance =\sqrt{(b-[\frac{3}{4}( y-b)+b])^2+(a-[\frac{3}{4} (x-a)+a])^2}[/tex]
Therefore the distance cannot be gotten until the center of dilation is given
Arnold made the following grades on his quizzes and assignments: 80, 92, 88, 90, 75, 38, 92, 95 2. Arnold wants to present his scores as advantageously as possible. Should he use the mean or the median of this data set? What other strategies could he employ to yield a more favorable measure of center?
Answer:
Step-by-step explanation:
If he were to find the mean then he would need to add all the numbers up and divide by the number of numbers. The answer of this would 69.1
If you find the median you would need to put the numbers in order,
2, 38, 75, 80, 88, 90, 92, 92, 95, then find the middle which would be 88.
So the better option would be finding the median. I think that this would be the best way to get the the most favorable measure of center.
I hope this helps.
Find the value of x. A. 53–√ m B. 241−−√ m C. 6 m D. 6+35–√ m
Answer:
x = 2√41 mStep-by-step explanation:
Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x
Using Pythagoras theorem we have
a² = b² + c²
where a is the hypotenuse
From the question x is the hypotenuse
So we have
[tex] {x}^{2} = {8}^{2} + {10}^{2} [/tex][tex] {x}^{2} = 64 + 100[/tex][tex] {x}^{2} = 164[/tex]Find the square root of both sides
We have the final answer as
x = 2√41 mHope this helps you
Answer:
2 sqrt(41) =c
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
8^2 + 10^2 = c^2
64+ 100 = c^2
164 = c^2
take the square root of each side
sqrt(164) = sqrt(c^2)
sqrt(4*41) = c
2 sqrt(41) =c
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The two inequalities that show the solution to these equations are n ≥ 55 and y ≥ 6
Step-by-step explanation:
We are given two inequalities that we have to solve. We can solve these inequalities as if we are solving for the variable.
n/5 ≥ 11
Multiply by 5 on both sides.
n ≥ 55
Now, let's do the second one.
-3y ≤ -18
Divide by -3 on both sides. When we divide by a negative in inequalities, then the sign is going to flip to its other side. So, this sign (≤) becomes this sign (≥)
y ≥ 6
In the diagram of the right triangle shown find the value of c.
Answer:
Hey there!
20^2+25^2=c^2
400+625=c^2
1025=c^2
Square root 1025 is the correct answer, so option C.
Let me know if this helps :)
Answer: B
Step-by-step explanation:
a broker gets rs 20000 as commission from sale of a piece of land which costs rs 8000000. Find the rate of commission.
Answer:
0.25%
Step-by-step explanation:
Rate of commission
= (commission*100)/cost of land
=( 20000*100)/8000000
= 2000000/8000000
=2/8
= 0.25%
someone please expain how to do this, i’m really confused.
Answer:
13
Step-by-step explanation:
Basically, we have to plug in 4 for r into g(r). Doing so gives us g(4) = 25 - 3 * 4 = 25 - 12 = 13.
Some more examples:
g(6) = 25 - 3 * 6 = 25 - 18 = 7
g(1) = 25 - 3 * 1 = 25 - 3 = 22
Answer:g(4)=13
Step-by-step explanation:
g(4)=25-3r
25-3(4)
25-12
g(4)=13
A line passes (-8,-2) and has a slope of 5/4. Write an equation in Ax + By=C
Answer:
5x-4y = -32
Step-by-step explanation:
First write the equation in point slope form
y-y1 = m(x-x1)
y - -2 = 5/4 ( x- -8)
y+2 = 5/4 (x+8)
Multiply each side by 4 to clear the fraction
4( y+2 )= 4*5/4 (x+8)
4y +8 = 5(x+8)
4y+8 = 5x+40
Subtract 4y from each side
8 = 5x-4y +40
Subtract 40 from each side
-32 = 5x-4y
5x-4y = -32
Answer:
The answer is
5x - 4y = -32Step-by-step explanation:
To write an equation of a line given a point and slope use the formula
y - y1 = m( x - x1)
where
m is the slope
( x1 , y1) is the point
From the question
slope = 5/4
point (-8 , -2)
So the equation of the line is
[tex]y + 2 = \frac{5}{4} (x + 8)[/tex]Multiply through by 4
4y + 8 = 5( x + 8)
4y + 8 = 5x + 40
5x - 4y = 8 - 40
We have the final answer as
5x - 4y = -32Hope this helps you
Pregunta N° 1: ¿Cuántas fracciones propias e irreductibles con denominador 24 existen? 1 punto A) 2 B) 4 C) 6 D) 8 E) 10 Pregunta N° 2: ¿Cuántas fracciones impropias e irreductibles con numerador 25 existen? 1 punto A) 19 B) 21 C) 25 D) 29 E) 33 Pregunta N° 3: La edad de Miguel es 4/5 de la edad de su novia. Si las edades de los dos suman 63 años, calcule la edad de la novia de Miguel. 1 punto A) 20 años B) 26 años C) 32 años D) 35 años E) 40 años Pregunta N° 4: Si son las 8 a. m., ¿qué fracción del día ha transcurrido? 1 punto A) 1 B) 2 C) 1/2 D) 1/3 E) 1/5
ayuden porfavor
Answer:
Pregunta 1: Opcion D. 8
Pregunta 2: Opción A. 19 (aunque lo correcto es decir que son 20)
Pregunta 3: 28 años (no está como opción)
Pregunta 4: Opción D. 1/3
Step-by-step explanation:
Las fracciones irreductibles son aquellas que después de dividirlas por un común divisor, una vez que no se pueden dividir más se dice que son irreducibles, por lo tanto no existe ningún número que sea divisor común del numerador y del denominador más que 1.
Fracciones irreductibles con común denominador 24.
Como máximo divisor tenemos el 24 y como mínimo el 1
entre 1/24 y 1 estarán nuestras fracciones o sea:
1/24 < x/24 < 1. Ahora convertimos el 1 en fracción de 24, lo que sería 24/24 para igualar el numerador en ambos lados de la ecuación, para poder determinar x
1/24 < x/24 < 24/24
Como vemos que x tiene que estar entre 1 y 24, las respuestas serán:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 y 23
Eliminamos los números divisores de 24, aquellos pares, y nos focalizamos en los que no podriamos dividir por nada con 24, o sea los números primos
5, 7, 11, 13, 17, 19, 23. Como nos falta el 1, obtenemos un total de 8 fracciones: 1/24, 5/24, 7/24, 11/24, 13/24, 17/24, 19/24, 23/24
Mismo procedimiento para el 25:
1/25 es una de las fracciones irreductibles. Pensamos en los valores de x
1/25 < x/25 < 25/25
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
Los números divisibles por 25, son los multiplos de 5, asi que esas respuestas no irían. Las fracciones irreductibles son:
1/25, 2/25, 3/25, 4/25, 6/25, 7/25, 8/25, 9/25, 11/25, 12/25, 13/25, 14/25, 16/25, 17/25, 18/25, 19/25, 21/25, 22/25, 23/25 y 24/25 haciendo un total de
20. Por alguna razón está mal formulada la pregunta, son 20 pero no está como opción y como te piden fraccion impropia (numerador > denominador), contamos a partir de 26. FIjate que hasta el proximo entero que sería 50/25, también son 20 fracciones (irreductibles e impropias)
26/25, 27/25, 28/25, 29/25, 31/25, 32/25, 33/25, 34/25, 36/25, 37/25, 38/25, 39/25, 41/25, 42/25, 43/25, 44/25, 46/25, 47/25, 48/25, 49/25
Próxima pregunta:
Miguel tiene 4/5 de la edad de la novia, y ambas edades suman 63.
Plantiemos la siguiente ecuacion donde x es la edad de la novia
4/5x + x = 63
9/5x = 63
x = 63 . 5/9 (como 9/5 pasa al otro lado de la igualdad dividiendo, damos vuelta la fraccion multiplicandola)
x = 35
Si la novia tiene 35 años y la edad de Miguel es 4/5 de esa edad
4/5 .35 = (35 .4) /5 = 28
Es raro porque no está la respuesta como tal.
Próxima pregunta:
Al ser las 8 am, quiere decir que han pasado 8 horas de que empezó el día
y el día tiene 24 horas.
8 horas transcurridas / 24 horas totales = 1/3
