a) Dos números enteros positivos se diferencian en 6 unidades y la suma de sus cuadrados
es 260. ¿Cuáles son esos números?
Queremos encontrar dos números enteros tales que su diferencia sea de 6 y la suma de sus cuadrados sea igual a 260.
Veremos que los dos números son 8 y 14.
Primero, podemos definir esos números como A y B.
Entonces tenemos que:
A - B = 6
A^2 + B^2 = 260
Esto es un sistema de ecuaciones.
Para resolverlo, el primer paso es aislar una de las variables en una de las ecuaciones, vamos a hacer esto en la primera.
A - B = 6
A = 6 + B
Ahora reemplazamos esto en la otra ecuación.
A^2 + B^2 = 260
(6 + B)^2 + B^2 = 260
36 + 12*B + B^2 + B^2 = 260
36 + 12*B + 2*B^2 = 260
Ahora podemos resolver esto para B:
2*B^2 + 12*B + 36 - 260 = 0
2*B^2 + 12*B - 224
Las soluciones estan dadas por la formula de Bhaskara:
[tex]B = \frac{-12\pm \sqrt{12^2 - 4*2*(-224)} }{2*2} \\\\B = \frac{-12 \pm 44 }{4}\\\\B = (-3 \pm 11)[/tex]
Entonces las dos soluciones son:
B = -3 + 11 = 8
B = -3 - 11 = -14
Sabemos que los números son positivos, asi que elejimos la primera, entonces tenemos:
B = 8.
Con esto podemos calcular el valor de A como:
A - B = 6
A = 6 + B = 6 + 8 = 14
Entonces los dos números son:
8 y 14.
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Write the slope-intercept form of the given line. Include your work in your final answer. Type your answer in the box provided to submit your solution.
Answer:
y=-1/3x+1
Step-by-step explanation:
it is negative because when you find the slope you go down instead of up
If you bought 12.6 gallons of gasoline as $1.20 per gallon, how much did the gasoline cost?
Answer:
15.12$
Step-by-step explanation:
Gallons = 12.6
Cost = $1.20
Gasoline Cost = ??
12.6 ×1.20
=15.12
Hence, gasoline will cost 15.12 $
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7x-2y=-29
9x+10y=13
emliantion substuion methd
Answer:
(-3, 4)
Step-by-step explanation:
5(7x - 2y = -29)
35x - 10y = -145
9x + 10y = 13
44x = -132
x = -3
7(-3) - 2y = -29
-21 - 2y = -29
-2y = -8
y = 4
help me please! find the angles and solve for x!!!
Answer:
x = 25; 47 degrees, 47 degrees, 86 degrees
Step-by-step explanation:
the two triangles are congruent so they have the same angles
that means 2x - 3 = x + 22
2x - 3 = x + 22
subtract x from each side
x - 3 = 22
add 3 to both sides
x = 25
and this is your answer
assuming that the triangles are isosceles triangles two of the angles are the same
the angles with the x on it are 47 after calculating
that means that the other angle across from it is also 47
a triangles angles added up is 180
47 + 47 + n = 180
the last angle after calculating is 86 degrees
a line passes through the point (10,-5) and a slope of -3/2
Write an equation in slope-intercept form for this line.
Answer:
y = -3/2x + 10
Step-by-step explanation:
The slope = -3/2
Using the slope = -3/2 and the point (10, -5) substitute into y = mx + b and solve for "b"
y = mx + b
-5 = -3/2(10) + b -3/2 · 10 = -30/2 = -15
-5 = -15 + b
-5 + 15 = b
10 = b
The equation of the line is y = -3/2x + 10
If the simple interest on $1000 for 2 years is $100, then what is the interest rate?
Answer:
R = 450%/year
Equation:
r = (1/t)(A/P - 1)
Converting r decimal to R a percentage
R = 4.5 * 100 = 450%/year
Sandra and Peter together weigh 275 pounds. Sandra and
Martin together weigh 245 pounds. All three together
weigh 410 pounds. What is Sandra's weight alone?
Answer:
110 pounds
Step-by-step explanation:
Let the weight of Sandra, Peter and Martin be S, P and M pounds respectively.
S +P= 275 -----(1)
S +M= 245 -----(2)
S +P +M= 410 -----(3)
(3) -(1):
S +P +M -(S +P)= 410 -275
S +P +M -S -P= 135
M= 135
Substitute M= 135 into (2):
S +135= 245
S= 245 -135
S= 110
Thus, Sarah weighs 110 pounds.
What was the frequency of rolling a sum greater than 5?
Answer:
on a 6-sided dice, 1/6
Step-by-step explanation:
Question 1 of 10 According to the Venn diagram below, what is P(A U B U C)?
A. 21/25
B.24/25
C.22/25
D.23/25
Answer:
D. 23/25
Step-by-step explanation:
Add all the numbers inside the venn diagram for the number of outcomes
> 10+2+8+8+6+5+7 = 46
Then add all the numbers inside and outside the venn diagram for the number of possibilities
> 10+2+8+8+6+5+7+4 = 50
[tex]p(a \: u \: b \: u \: c \: ) = \frac{total \: number \: of \: outcomes}{total \: number \: of \: possibilities} [/tex]
[tex]p( a \: u \: b \: u \: c) = \frac{46}{50} [/tex]
[tex]p(a \: u \: b \: u \: c \: ) = \frac{23}{25} [/tex]
Annette's mom made snacks for her party. She made 181 snacks and there are 27 students. How many more snacks does she need to make in order for each student to receive 7 snacks?
181 snacks
27 students
to find:How many snacks she need to make in order for each student to receive 7 snacks.
solution:[tex]7 \times 27[/tex]
[tex] = 189[/tex]
[tex]189 - 181[/tex]
[tex] = 8[/tex]
therefore, she needs to make 8 more snacks in order for each student to receive 7 snacks.
Suppose that a department contains 8 men and 17 women. How many ways are there to form a committee with 6 members if it must have strictly more women than men
Graph the following equation: y - 3 = (x - 2)
Answer:
Step-by-step explanation:
I took pictures of what I found and I think is right
Guve 2 example of measurement length
Answer:
There are inches, feet, miles, centimeters, meters, kilometers
Step-by-step explanation:
None sense >report
I. Study the situation below:
Jose wanted to construct a rectangular garden such that its perimeter is 28mn and
its length is 6 times its width.
What are the linear equations that represents the given situation?
II. Answer the following questions:
1. How do you describe a system of linear equations in two variables?
2.
Give at least two examples of systems of linear equations in two variables.
3.
How is the system of linear equations in two variables used in solving in real
life problems and in making decisio?
Answer:
Radio waves have photons with the lowest energies. Microwaves have a little more energy than radio waves. Infrared has still more, followed by visible, ultraviolet, X-rays and gamma rays.1.) What three ratios are equivalent to 3/9? *
O 1/3, 2/3, 3/3
1/3, 12/36, 15/45
6/9, 12/15, 18/21
05/12, 9/12, 3/12
Answer:
B
Step-by-step explanation:
3/9 is the same as 1/3.
It can't be D since 5/12 isn't 1/3.
It can't be A since 2/3 and 3/3 don't equal 1/3.
It can't be C since everything listed is equal to 2/3.
a path forms a diagonal of a rectangular city park. a bench is placed along the path at a point that is closest to the fountain. this point is 30 yards from one end of the path and 50 yards from the other end of the path what is the distance from the bench to the fountain to the nearest yard
The answer: 39 yards
The quotient of a number x and 4 is at most 5.
Answer:
x ÷ 4 ≤ 5
Step-by-step explanation:
Since it was 7 years ago, Mr. Ly's age was 28 years old.
Can someone please tell me what is his age at present (In now)?
Answer:
28+7=35. 35 is your answer.
Answer:
35
Step-by-step explanation:
35 because 7+28 is 35 7
28
Can you please help I can’t play in my basketball game Tuesday if I can’t pass this !
Answer:
i think its 71.1 but idrk
basically i hope you're able to play game good luck man
Brandie lives on the twelfth floor of her apartment building. She walks down 2 flights to visit a friend, then up 3 flights to
deliver a message to a neighbor. Which integer best represents the number of flights Brandie must walk to get back to
her starting point?
0-12
O-1
05
7
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the price of a machine is given as GHC 20,000 plus VAT. If the VAT rate is 12%, find the price that a customer must pay for the machine.
Answer:
Step-by-step explanation:
12/100 × 20000
= 2400
Price customer must pay = 20,000+ 2400 = 22400.
If price of a machine is given as GHC 20,000 plus VAT. If the VAT rate is 12%. Then 22400 is the price that a customer must pay for the machine.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given,
The price of a machine is given as GHC 20,000 plus VAT
The VAT rate is 12%,
We need to find how much a customer has to pay for the machine..
12% is changed to decimal number by dividing with 100.
12/100=0.12
Now multiply 20000 with 0.12 to find 12% of 20000
0.12×20000=2400
Now we have to add 2400 with 20000 to get the cost of machine after adding VTA
20000+2400=22400
Hence 22400 is the price that a customer must pay for the machine.
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what decimal is equivalent to 4/100 + 5/10
Answer: 0.54
Step-by-step explanation:
im not sure if your talking about turining the fraction into a decimal but this is how it would look as a decimal.
PLZ HELP I Will Give points if you answer correctly No links plz just the answer
Answer:
B.
Step-by-step explanation:
She has created a connection of something physical to express a similar conection with her emotions.
A hot air balloon leaves the ground and ascends at a rate of 5 feet per minute for 4 minutes.
Then descends at a rate of 2 feet per minute for 7 minutes. How far above the ground is the
balloon now?
When the balloon is on the ground, it is at point 0. It starts to go up at 5 f/m for a time of 4 minutes. So we will multiply 5 by 4 to get 20. At this point, the balloon is 20 feet off the ground. However, we now know that the balloon descends at 2 f/m at a time of 7 minutes. So we must multiply 2 by 7 to get 14. So we know it was at 20, and then it went down by 14.
20 - 14 = 6 feet
This means that the balloon is now 6 feet above the ground.
I hope I've helped! :)
if a:b=3:4 and b:c=2:5 find i)a:c and II) a:b:c
Answer:
a:c= 3/5 = 0.6
a:b:c= 3/4/5=0.15
Does someone have the answer to this??? Thank You so much
Answer:
22
Step-by-step explanation:
Answer:
f(0)=22
Step-by-step explanation:
f(0)=13(2)^0+9
f(0)=13(1)+9
f(0)=13+9
f(0)=22
(any number raised to 0 is 1)
What are the coordinates of the midpoint between the points (3,-1) and
(7,-5)
i
Answer:
(5,-3)
Step-by-step explanation:
simultaneous equations!!
solve the following pair of equations for x and y:
y + 4x = 27
xy + x = 40
Pls helppp it’s due soon!
Will give brainliest if your answer is right
Answer:
19.4
Step-by-step explanation:
This problem can be simplified to finding the diagonal of a rectangle of sides 19 and 4. Using the Pythagorean theorem gives FH = √(19^2 + 4^2) = 19.4