Answer:
Answer is A
Step-by-step explanation:
Hope it helps
The perimeter of a rectangle is 62 cm. The diagonal and width of the rectangle are 25 cm and x cm respectively.
Form a quadratic equation in terms of x based on the situation.
Step 1:
62cm - (25*2)=12cm
62-25=37cm
Length for both sides 25
Width=37cm=x
Use the grouping method to factor x3 + x2 + 2x + 2.
[tex] x^3+x^2+2x+2[/tex]
$x^2(x+1)+2(x+1)=(x^2+2)(x+1)$
Answer:
Step-by-step explanation:
x³ + x² + 2x + 2 = x²(x + 1) + 2(x+1)
= (x + 1) (x² + 2)
AB = 3.2 cm
BC= 8.4 cm
The area of triangle ABC is 10 cm²
Calculate the perimeter of triangle ABC.
Give your answer correct to three significant figures.
Answer:
Therefore, perimeter of the given triangle is 18.300 cm.
Step-by-step explanation:
Area of the triangle ABC = [tex]\frac{1}{2}(\text{AB})(\text{BC})(\text{SinB})[/tex]
10 = [tex]\frac{1}{2}(3.2)(8.4)(\text{SinB})[/tex]
Sin(B) = [tex]\frac{10}{3.2\times 4.2}[/tex]
B = [tex]\text{Sin}^{-1}(0.74405)[/tex]
B = 48.08°
By applying Cosine rule in the given triangle,
(AC)² = (AB)² + (BC)²-2(AB)(BC)CosB
(AC)² = (3.2)² + (8.4)² - 2(3.2)(8.4)Cos(48.08)°
(AC)² = 10.24 + 70.56 - 35.9166
(AC)² = 44.88
AC = [tex]\sqrt{44.8833}[/tex]
AC = 6.6995 cm
Perimeter of the ΔABC = m(AB) + m(BC) + m(AC)
= 3.200 + 8.400 + 6.6995
= 18.2995
≈ 18.300 cm
Therefore, perimeter of the given triangle is 18.300 cm
A finite geometric series is the sum of a sequence of numbers. Take the sequence 1, 2, 4, 8, … , for example. Notice that each number is twice the value of the previous number. So, a number in the sequence can be represented by the function f(n) = 2n–1. One way to write the sum of the sequence through the 5th number in the sequence is ∑5n-12n-1. This equation can also be written as S5 = 20 + 21 + 22 + 23 + 24. If we multiply this equation by 2, the equation becomes 2(S5) = 21 + 22 + 23 + 24 + 25. What happens if you subtract the two equations and solve for S5? Can you use this information to come up with a way to find any geometric series Sn in the form ∑an-1bn-1?
hope this helps you alot
Help please!!! Thank you
Answer:
2y+6x=180
Step-by-step explanation:
Because we know that side lengths BD, DC, and AD are all congruent, we can conclude that triangles BDA and CDA are congruent because they have at least two congruent sides. Since these triangles are both 45-45-90 triangles, angle C is equal to 45 degrees, or 3x. 45/3 is 15, so x=15. Angle B is equal to 45 degrees, or y, so y=45.
From there, we plug these numbers into the equation with 2(45) + 6(15), or 90+90 = 180.
Please help. I need it. Bad.
Answer:
Option a.
Step-by-step explanation:
In the given triangle angle A is a right angle so triangle ABC is a right angled triangle.
Opposite side of right angle is hypotenuse. So, CB is hypotenuse.
From figure it is clear that CA is shorter that segment BA.
All angles are congruent to itself. So angle C is congruent to itself.
We know that, if an altitude is drawn from the right angle vertex in a right angle triangle it divide the triangle in two right angle triangles, then given triangle is similar to both new triangles.
So, triangle ABC is similar to triangle DBA if segment AD is an altitude of triangle ABC.
Therefore, the correct option is a.
Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking Last weekwalked 18 miles in 6 hours This week d = 2.5h Which statement must be true?
THIS IS THE COMPLETE QUESTION BELOW;
Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking.
Last week: walked 18 miles in 6 hours
This week: d = 2.5h
Which statement must be true?
A.This week, she walked a greater distance.
B. Last week, she walked a greater distance
C. This week, she walked at a faster pace.
D. Last week, she walked at a faster pace
Answer
OPTION B is correct
B)Last week, she walked a greater distance
Step-by-step explanation:
We were told Rosemary walks each week for exercise.
From the question,
✓d represented the distance walked
✓h represent the number of hours spent walking.
A)Last week: she walked 18 miles in 6 hours
Then, if she walks 18 miles in 6 hours, we can be expressed as (18miles/6hour)
= 3 miles per hour
B)This week: d = 2.5h
This implies that she she walked 2.5 miles per hour this week since the distance is expressed in miles and time in hours.
So we can conclude that last week she walked 3 miles per hour which is more greater than 2.5 miles per hour which she walks this week.
Therefore, OPTION B is correct, (Last week, she walked a greater distance)
Answer:
It's b
Step-by-step explanation:
Please please please please help
Answer:
[tex]x^2 +4x +3 [/tex]
Step-by-step explanation:
f(x)=x²-1
g(x)= x+2
f(g(x)) =f(x+2)
=(x+2)²-1
=x²+4x+4-1
=x²+4x+3
The radius of the circle is increasing at a rate of 1 meter per day and the sides of the square are increasing at a rate of 3 meters per day. When the radius is 3 meters, and the sides are 20 meters, then how fast is the AREA outside the circle but inside the square changing
Answer:
The area inside the square and outside the circle is changing at a rate of 101.150 square meters per day.
Step-by-step explanation:
According to the statement of the problem, the circle is inside the square and the area inside the square but outside the circle, measured in square meters, is represented by the following formula. It is worth to notice that radius ([tex]r[/tex]) is less than side ([tex]l[/tex]), both measured in meters:
[tex]A_{T} = A_{\square} -A_{\circ}[/tex]
[tex]A_{T} = l^{2}-\pi\cdot r^{2}[/tex]
Now, the rate of change of the total area is calculated after deriving previous expression in time:
[tex]\frac{dA_{T}}{dt} = 2\cdot l\cdot \frac{dl}{dt} -2\pi\cdot r\cdot \frac{dr}{dt}[/tex]
Where [tex]\frac{dl}{dt}[/tex] and [tex]\frac{dr}{dt}[/tex] are the rates of change of side and radius, measured in meters per day.
Given that [tex]l = 20\,m[/tex], [tex]r = 3\,m[/tex], [tex]\frac{dl}{dt} = 3\,\frac{m}{day}[/tex] and [tex]\frac{dr}{dt} = 1\,\frac{m}{day}[/tex], the rate of change of the total area is:
[tex]\frac{dA_{T}}{dt} = 2\cdot (20\,m)\cdot \left(3\,\frac{m}{day} \right)-2\pi\cdot (3\,m)\cdot \left(1\,\frac{m}{day} \right)[/tex]
[tex]\frac{dA_{T}}{dt} \approx 101.150\,\frac{m^{2}}{day}[/tex]
The area inside the square and outside the circle is changing at a rate of 101.150 square meters per day.
How to do this question plz answer my question plz
Answer:
£22.40
Step-by-step explanation:
60% of 12 is 7.2 (you can also write it as 7.20) so you times that by 2 to get 14.4 (you can also write it as 14.40) and [tex]\frac{1}{3}[/tex] of 24 is 8, so you add that to the 14.4 and you get 22.4 (also writen as 22.4) hope this helps!
Determine the slope of a line which contains the points (2, 4) and (-6, 9). Write your answer in simplest form.
Answer:
-5/8
Step-by-step explanation:
(2,4) (-6.9)
m= y2-y1/x2-x1
= 9-4/-6-2
=5/-8
=-5/8
We can calculate EEE, the amount of euros that has the same value as DDD U.S. Dollars, using the equation E=\dfrac{17}{20}DE= 20 17 DE, equals, start fraction, 17, divided by, 20, end fraction, D. How many euros have the same value as 111 U.S. Dollar? euros How many U.S. Dollars have the same value as 111 euro? dollars
Answer: 1 U.S.dollar = 0.85 euro.
1 euro = 1.18 dollars.
Step-by-step explanation:
The given equation: [tex]E=\dfrac{17}{20}D[/tex]
, where 'E' is the amount of euros that has the same value as 'D' U.S. Dollars.
At D= 1,
[tex]E=\dfrac{17}{20}=0.85\text{ euro}[/tex]
i.e. 1 U.S.dollar = 0.85 euro.
At E= 1 , we have
[tex]1=\dfrac{17}{20}D\\\\\Rightarrow\ D= 20/17\approx1.18\text{ dollars}[/tex]
Hence, 1 euro = 1.18 dollars.
Help, Answer ASAP; will give brainliest
Answer:
a = 2, b = 3
Step-by-step explanation:
The diagonals of a rectangle bisect each other, thus
5a² = 4a² + 4 ( subtract 4a² from both sides )
a² = 4 ( take the square root of both sides )
a = [tex]\sqrt{4}[/tex] = 2
Also
6b - 8 = 4b - 2 ( subtract 4b from both sides )
2b - 8 = - 2 ( add 8 to both sides )
2b = 6 ( divide both sides by 2 )
b = 3
i think the answer. . .is the second one please correct me if i'm wrong
Answer: You are correct, it is the second option.
Step-by-step explanation:
Volume of a cylinder formula is: pi*r^2*h. The diameter is 6 and the radius is half the diameter so we get r=3. The height is 10 inches, so h=10. pi(3)^2(10) is the volume of the vase.
Volume of a sphere (marbles) formula is: 4/3*pi*r^3
The marbles have a diameter of 3 so 3/2=1.5. r=1.5.
The volume of the marbles is 8(4/3*pi*1.5^3).
Then you subtract the volume of the marbles from the volume of the vase to find the volume of the water in the vase.
pi(3)^2(10) - 8(4/3pi(1.5)^3)
Hope this helps. :)
Answer:
You are absolutely correct, second option is the correct answer.
Step-by-step explanation:
Diameter of vase = 6 inches
Therefore, radius r = 3 inches
Diameter of marbles = 3 inches
Radius of marbles = 1. 5 inches
Height of water h = 10 inches
Volume of water in the vase = Volume of vase - 8 times the volume of one marble
[tex] = \pi r^2h - 8\times \frac{4}{3} \pi r^3 \\\\
= \pi (3\: in) ^2(10\: in) - 8( \frac{4}{3} \pi (1.5\: in) ^3) \\\\[/tex]
Given the following angles, what ray is the common side of ZCFD and ZDFE?
D
E
0
Ray FD
Ray FE
Ray FC
Answer:
ray df or ray fd because both of these letters are consecutive in both of the angles.
Step-by-step explanation:
Answer:
Answer is Ray FD
Step-by-step explanation:
Given the following angles, what ray is the common side of ∠CFD and ∠DFE?
A. Ray FC
B. Ray FE
C. Ray FD
Jeania's parents have given her a interest-free loan of $100 to buy a new pair of running shoes She has to
pay back the loan with monthly payments of $20 each.
Write a function rule for the balance of the function (p), where p represents the number of
payments Jeania has made.
Answer:
The balance on the loan f(p) = $100 - $20 × p
Step-by-step explanation:
The parameters of the question are;
The loan amount = $100
The amount of monthly payment for the loan = $20
The function rule for the balance of the function f(p) where p is the number of payments is given as follows;
The balance on the loan, f(p) = The loan amount less the total amount paid
The total amount payment Jeania has made = Amount of monthly payment × Number of months paid, p
The total amount payment Jeania has made = $20 × p
∴ The balance on the loan, f(p) = $100 - $20 × p
Which gives;
f(p) = $100 - $20 × p.
round your answer to the nearest hundredth. Find angle A=?
Answer:
A=48.81
Step-by-step explanation:
it is a right angle triangle find the hypotenuse c using Pythagorean theorem:
c²=a²+b²
c²=8²+7²
c=√64+49
c=10.63
sin A =opp/hyp
sin A=8/10.63
A= 48.81
another way :
tan A=opp/adj
tan A=8/7
A=48.81
i'm doing domain and range, and I'm kinda having a hard time with this... can someone help?
Answer:
Domain : any real number
Range : y ≥0
Step-by-step explanation:
The domain is the values that x can be
X can be any real number
The range is the values the y can be
Y can be zero or any positive value since y = x^2
Domain : any real number
Range : y ≥0
Answer:
[tex]\boxed{\sf Option \ A}[/tex]
Step-by-step explanation:
[tex]y=x^2[/tex]
[tex]\sf The \ domain \ of \ a \ function \ is \ all \ possible \ values \ for \ x.[/tex]
[tex]\sf There \ are \ no \ restrictions \ on \ the \ value \ of \ x.[/tex]
[tex]\sf The \ domain \ is \ all \ real \ numbers.[/tex]
[tex]\sf The \ range \ of \ a \ function \ is \ all \ possible \ values \ for \ y.[/tex]
[tex]\sf When \ a \ number \ is \ squared \ the \ result \ is \ always \ greater \ than \ or \ equal \ to \ 0.[/tex]
[tex]\sf The \ range \ is \ \{y:y\geq 0\}[/tex]
Find the slope and Y-Intercept of the line. 6X plus 2Y equals -88
Answer:
That’s ez pz
Step-by-step explanation:
Answer:
The slope is -3 and the y intercept is -44
Step-by-step explanation:
6X+ 2Y= -88
The slope intercept form of a line is y= mx+b where m is the slope and b is the y intercept
Solve for y
6X-6x+ 2Y= -88-6x
2y = -6x-88
Divide by 2
y = -3x -44
The slope is -3 and the y intercept is -44
Plz help me. what is 4.9 * 10^-5 +.0005
Answer:
It should be 490000.0005
Step-by-step explanation:
4.9*10^5+.0005
10^5=100000
4.9*100000=490000
490000+.0005=490000.0005
Answer:
Step-by-step explanation:
[tex]10^{-5}=\frac{1}{10^{5}}=\frac{1}{100,000}=0.00001\\\\[/tex]
4.9* 10^-5 +0.0005 = 4.9 * 0.00001 + 0.0005
= 0.000049 + 0.0005
= 0.000549
Solve for p 9(p-4)=-18
Answer:
The answer is
p = 2Step-by-step explanation:
9(p-4)=-18
First expand the terms in the bracket
that's
9p - 36 = - 18
Group like terms
Send the constants to the right side of the equation
That's
9p = - 18 + 36
9p = 18
Divide both sides by 9
That's
9p/9 = 18/9
We have the final answer as
p = 2Hope this helps you
Answer:
[tex] \boxed{p = 2}[/tex]Step-by-step explanation:
[tex] \mathsf{9(p - 4) = - 18}[/tex]
Distribute 9 through the parentheses
[tex] \mathsf{9p - 36 = - 18}[/tex]
Move constant to R.H.S and change it's sign
[tex] \mathsf{9p = - 18 + 36}[/tex]
Calculate
[tex] \mathsf{9p = 18}[/tex]
Divide both sides of the equation by 9
[tex] \mathsf{ \frac{9p}{9} = \frac{18}{9} }[/tex]
Calculate
[tex] \mathsf{p = 2}[/tex]
[tex] \mathcal{Hope \: I \: helped}[/tex]
[tex] \mathcal{Best \: regards}[/tex]
En una fábrica de automóviles que trabaja las 24 horas se arman diariamente 24
automóviles tipo Sedan, 16 camionetas tipo SUV, 12 camionetas tipo VAN, 8
Camionetas tipo Pick-up y 2 automóviles deportivos.
Cl costo de producción y el precio de venta de cada vehículo es el siguiente:
Costo de
Vehículo
Precio de
Producción Venta
SEDAN
SEDAN
DEPORTIVO
$140,000 $185.000
SUV
$250,000
$320,000
VAN
$310,000
$400,000
PICK-UP
PICK-UP
$210,000
$285,000
VAN
DEPORTIVO
$400,000
$550,000
SUV
Cada año transcurrido, posterior a su fabricación, el precio de venta de los
vehículos disminuye una octava parte de su valor.
a suponiendo que en un día se vendan los vehículos en igual cantidad de los
que se fabricaron, como podrías calcular la ganancia?
b
Si la fábrica trabajara solo 12 horas, existe una forma de calcular cuántos
vehiculos se fabrican, ¿cuantos se fabricaron en este lapso? Sustenta tu
respuesta
Answer:
a. La ganancia es de $ 4,060,000.00
b. 31 vehículos
Step-by-step explanation:
(a) Los parámetros dados son;
El número de automóviles tipo sedán fabricados = 24
El número de camiones tipo SUV fabricados = 16
El número de camiones tipo VAN fabricados = 12
El número de camionetas pick-up fabricadas = 8
El número de autos deportivos fabricados = 2
La ganancia por la venta de autos tipo sedán = $ 185,000 - $ 140,000 = $ 40,000
La ganancia por la venta de camionetas tipo SUV = $ 320,000 - $ 250,000 = $ 70,000
La ganancia por la venta de camiones tipo VAN = $ 400,000 - $ 310,000 = $ 90,000
La ganancia por la venta de las camionetas pick-up = $ 285,000 - $ 210,000 = $ 75,000
La ganancia por la venta de los autos deportivos = $ 550,000 - $ 400,000 = $ 150,000
La ganancia = 24 * $ 40 000 + 16 * $ 70 000 + 12 * $ 90 000 + 8 * $ 75 000 + 2 * $ 150 000 = $ 4060 000
(b) Por lo que hay una tasa de producción constante, solo la mitad de los automóviles se producirán dentro del período de 12 horas
Por lo tanto, tu fabricado
12 autos sedán, 8 camionetas tipo SUV, 6 camionetas tipo VAN, 4 camionetas pick-up y 1 auto deportivo para hacer un total de 31 vehículos.
Please answer answer question
Answer:
The correct answer is
Step-by-step explanation:
11 square centimeters.
Hope this helps....
Have a nice day!!!!
plz help ASAP! thank u
Answer: Choice B)
The relation is a function because there are no vertical lines that can be drawn on the graph that pass through more than one point.
This graph passes the vertical line test. Any input (x) leads to one and only one output (y). An example of a graph failing the vertical line test would be a graph that is a sideways parabola.
Juan works as a tutor for $12 an hour and as a waiter for $7 an hour. This month, he worked a combined total of 110 hours at his two jobs.
Let t be the number of hours Juan worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.
Answer:
12t+7w=D
t+w=110
Step-by-step explanation:
12t= $12 made every tutor hour
7w= $7 made every waiter hour
D= total dollars made
t+w=110 is the tutor hour and the waiter hour adding together
Answer:
12t + 7y = x
or
5t + 770 = x
Step-by-step explanation:
12t + 7y = x
t = number of hours he worked as a tutor
y = number of hours he worked as a waiter
x = the total amount of money he earned
t + y = 110
=> y = 110 - t
=> 12t + 7(110 - t) = x
=> 12t + 770 - 7t = x
=> 5t + 770 = x
what is the range and domian of y=(x-4)
Between which two integers on a number line does -√120 lie on?
Answer:
-11 and -10
Step-by-step explanation:
● -√120 = -1 × √120
● -√120 = -1 × 2√30
● 30 is close to 25 so √30 is close to five but greater than it.
Multiplying 5 by -2 gives -10
Multipluing √30 by -2 gives you a number that is close to -10 but smaller than it.
So -√120 lies between -11 and -10
Which answer choice identifies the relevant information in the problem? Sarah left the house at 12:15 p.M. To go to the store. She spent $42.20 on 2 books for her children and she spent $5.67 on a toys for her dog, Rover. Sarah arrived home at 1:00 p.M. How much did Sarah spend on each book? A. She spent $42.20 on 2 books. B. She spent $42.20 and $5.67. C. She left the house at 12:15 p.M. And arrived home at 1:00 p.M. D. You need to know how many children she has to solve the problem.
Answer:
Answer choices A, B and C identifies the relevant information in the problem
Step-by-step explanation:
Sarah left the house at 12:15 pm
She spent $42.20 on two books for her children
She spent $5.67 on a toy for her dog
Sarah arrived home at 1:00 pm
How much did Sarah spent on each book?
If she spent $42.20 on two books for her children,
Then, it means she has two children and the book cost $21.10 each
Answer choices A, B and C identifies the relevant information in the problem
Answer:
its A all the other one dont make sence sorry if im wrong but i got it right on my test
Step-by-step explanation:
DUE NOW PLEASE HELP!!!
Factor completely x2 − 10x + 25.
(x − 5)(x − 5)
(x + 5)(x + 5)
(x + 5)(x − 5)
(x − 25)(x − 1)
Answer:
(x - 5)(x - 5)
Step-by-step explanation:
[tex] {x}^{2} - 10x + 25 \: is \: the \: expansion \\ of \: {(x - 5)}^{2} \\ {(x - 5)}^{2} = (x - 5)(x - 5)[/tex]
The complete factorization of the quadratic expression x² - 10x + 25 is (x - 5)(x - 5). Hence the first option is the right choice.
How to factor a quadratic expression?A quadratic expression of the form ax² + bx + c is factored by using the mid-term factorization method, which suggests that b should be broken in such two components that their product = ac. After this, we can factorize using the grouping method.
How to solve the given question?In the question, we are asked to factor the quadratic expression x² - 10x + 25 completely.
Comparing x² - 10x + 25 to ax² + bx + c, we get a = 1, b = -10, and c = 25.
To factor the expression we will use the mid-term factorization method, and try to break b in such two numbers whose product = ac.
Now, ac = 1 * 25 = 25. b = -10, which can be broken as -5, and -5.
Therefore, we can write the given expression as:
x² - 10x + 25
= x² - 5x - 5x + 25, mid-term factorization
= x(x - 5) -5(x - 5), grouping
= (x - 5)(x - 5), grouping.
Therefore, the complete factorization of the quadratic expression x² - 10x + 25 is (x - 5)(x - 5). Hence the first option is the right choice.
Learn more about mid-term factorization at
https://brainly.com/question/25829061
#SPJ2
Keisha, Felipe, and Manuel sent a total of 100 text messages during the weekend. Keisha sent 8 more messages than Felipe. Manuel sent 2 times as many
messages as Felipe. How many messages did they each send?
Answer:
Felipe = 23 messages
Keisha = 31 messages
Manuel = 46 messages
Step-by-step explanation:
Keisha = K
Felipe = F
Manuel = M
=> There are a total of 100 messages.
=> K sent 8 +F => K = 8 + F
=> M sent 2 * F => M = 2F
=> F = F
=> 8 + F + 2F + F = 100
=> 8 + 4F = 100
=> 8 - 8 +4F = 100 -8
=> 4F = 92
=> 4F/4 = 92/4
=> F = 23
So, Felipe = 23 messages.
Keisha = 8 + F = 8 + 23 = 31 messages.
Manuel = 2F = 2* 23 = 46 messages.
46 + 31 + 23 = 77 + 23 = 100 messages.
So, the answer is correct.
