Correct Question : The sum of squares of two consecutive positive odd numbers is 514. Find the numbers.
[tex]\rule{130}1[/tex]
Solution :
Let the two consecutive positive odd numbers be x and (x + 2)
[tex]\rule{130}1[/tex]
☯ [tex]\underline{\boldsymbol{According\: to \:the\: Question\:now :}}[/tex]
[tex]:\implies\sf x^2 + (x + 2)^{2} = 514 \\\\\\:\implies\sf x^2 + x^2 + 4x + 4 = 514\\\\\\:\implies\sf 2x^2 + 4x + 4 = 514 \\\\\\:\implies\sf 2x^2 + 4x = 514 - 4\\\\\\:\implies\sf 2x^2 + 4x = 510 \\\\\\:\implies\sf 2x^2 + 4x - 510 = 0\\\\\\:\implies\sf x^2 + 2x - 255 = 0 \:\:\:\:\:\Bigg\lgroup \bf{Dividing\:by\:2}\Bigg\rgroup\\\\\\:\implies\sf x^2 + 17x - 15x - 255 = 0\\\\\\:\implies\sf x(x + 17) - 15(x + 17) = 0\\\\\\:\implies\sf (x + 17) (x - 15)\\\\\\:\implies\sf x = - 17\:or\:x = 15\\\\\\:\implies\underline{\boxed {\sf x = 15}}\:\:\:\:\:\Bigg\lgroup \bf{Positive\:odd\: number}\Bigg\rgroup[/tex]
When,
[tex]\bullet\: \textsf {x = } \textbf {15} [/tex]
[tex]\bullet\: \sf x + 2 = 15 + 2 =\textbf{ 17} [/tex]
[tex]\therefore\:\underline{\textsf{The required positive integer is \textbf{15 and 17}}}.[/tex]
Solve for bbb. \dfrac23b + 5 = 20 - b 3 2 b+5=20−bstart fraction, 2, divided by, 3, end fraction, b, plus, 5, equals, 20, minus, b b =b=b, equals
This question was not written properly.
Complete Question
Solve for b.
2/3b + 5 = 20 - b
Answer:
b = 9
Step-by-step explanation:
We are given the algebraic expression
2/3b + 5 = 20 - b
Step 1
Collect like terms
2/3b + b = 20 - 5
Step 2
Solve for the left hand side of the equation
2/3b + b = 15
(5/3)b = 15
Step 3
Cross multiply
5b = 15 × 3
Step 4
Divide both sides by 5
5b/5 = 45/5
b = 9
Answer: b=9
Step-by-step explanation:bc khan +]
Recycle, reuse, and reduce are referred to as the three R's. Which sequence shows the three R's in order from most to least desirable
Answer:
(1) Reuse; (2) Recycle ; (3) Reduce
Step-by-step explanation:
The ideal sequence would be:
1) Use it again (reuse) if the object still serves its intended purpose/s
2) If not possible to the used again, send it to a recycling plant to extract from it items/parts/substance of utility for other new products
3) if it cannot be reused or recycled, the last option will be to reduce it completely.
Janet deducted $5 on Monday and another $6 on Tuesday from her savings account. write an expression that represents the change in her account balance after the deductions . How much money did Janet deduct?
Answer: x -11 is the expression and she deducted 11 dollars
Step-by-step explanation:
Let's say x represent the the total amount of money in her savings account.So if 5 and 6 dollars we deducted will have the expression
x - 5 -6 or x -11
In this case Janet deducted 11 dollars.
question is in the image
Answer:
10 minutes
Step-by-step explanation:
Is it rational? -8/5
Answer:
yes
Step-by-step explanation:
A rational number is a number that can be written as a ratio of integers
-8/5 is a ratio of integers so it is rational
Answer:
Yes.
Step-by-step explanation:
Rational numbers you can solve. They have a solution.
What is 3.242424 as a mixed number
Answer:
Step-by-step explanation:
The answer is 3 /8/33.
step by step explanation
First, we can write:
x
=
3
.
¯¯¯¯
24
Next, we can multiply each side by
100
giving:
100
x
=
324
.
¯¯¯¯
24
Then we can subtract each side of the first equation from each side of the second equation giving:
100
x
−
x
=
324
.
¯¯¯¯
24
−
3
.
¯¯¯¯
24
We can now solve for
x
as follows:
100
x
−
1
x
=
(
324
+
0
.
¯¯¯¯
24
)
−
(
3
+
0
.
¯¯¯¯
24
)
(
100
−
1
)
x
=
324
+
0
.
¯¯¯¯
24
−
3
−
0
.
¯¯¯¯
24
99
x
=
(
324
−
3
)
+
(
0
.
¯¯¯¯
24
−
0
.
¯¯¯¯
24
)
99
x
=
321
+
0
99
x
=
321
99
x
99
=
321
99
99
x
99
=
3
×
107
3
×
33
x
=
3
×
107
3
×
33
x
=
107
33
Now, we can convert this improper fraction to a mixed number:
x
=
107
33
=
99
+
8
33
=
99
33
+
8
33
=
3
+
8
33
=
3
8
33
3
.
¯¯¯¯
24
=
3
8
33
HOW DO I DO NUMBER 7 SOMEONE HELPP
Answer:
Hey there!
p(x)=7x+25
7x+25=60
7x=35
x=5
Let me know if this helps :)
Today you will need to look at the following problem and explain what Susan did incorrectly.
Answer:
see explanation
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x - 3)² + (y + 4)² = 36 ← is in standard form
with (h, k) = (3, - 4 ) = centre and r = [tex]\sqrt{36}[/tex] = 6
Susan interpreted the values of h and k incorrectly by using the values - 3 and 4 instead of taking the negative of them.
She also divided 36 by 2 , thus omitting the root of 36
there are 18 girls and 22 boys in a class that has a letter the probability that the owner of the letter is a boy
18 + 22 = 40 total kids.
22 are boys
Probability the letter is with a boy would be 22/40 = 11/20
An article that is marked $500 was sold for $450 after a discount is given. Calculate the percentage discount given
Answer:
10% discounted
Step-by-step explanation:
500× X = 450
while X is the sale price
so we solve for X
(500X)÷500 = 450 ÷ 500
X = 0.9
then we turn that into percentage
0.9 × 100 = 90%
finding the discount percentage
100% - 90% = 10%
hello! I’m very confused on this question, I want to know if my format is good? I currently have x^2-14x=16 Am I on the right track?
Answer:
according to me
Step-by-step explanation:
yes u r correct
;]
Solve the equation x+5=8
Answer:
x=3
Step-by-step explanation:
Answer:
x = 3
Step-by-step explanation:
8 - 5 = 3
(Checking v)
3 + 5 = 8
Find the value of b. A. 75 B. 72.5 C. 145 D. 65
Answer:
B. 72.5
Step-by-step explanation:
b° = 1/2(180° - 35°)
b° = 1/2 * 145°
b° = 72.5°
b = 72.5
The value of angle b will be 72.5°. Then the correct option is B.
What is a circle?It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The angle that the very same arc subtends at any point around the circle's periphery is the double of the angle that same arc subtends at the center.
The central angle is 35°. Then the angle at the periphery will be
⇒ 35 / 2
⇒ 17.5°
We know that the radius of the circle and tangent of the circle makes 90°.
Then the angle b is given as
b + 17.5 + 90 = 180
b = 180 – 107.5
b = 72.5°
Thus, the value of angle b will be 72.5°.
Then the correct option is B.
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ2
solve the simultaneous equations
2p- 3q= 4
3p + 2q= 9
Answer:
q = 6/13, p = 35/13
Step-by-step explanation:
3p + 2q = 9
2p - 3q = 4
_________ (subtract the two equation from each other.)
p + 5q = 5
p = 5 - 5q
2(5 - 5q) - 3q = 4 (substitute value of p into equation)
10 - 10q - 3q = 4
10 - 13q = 4
-13q = -6
q = 6/13
3p + 2(6/13) = 9 (substitute value of q into equation)
3p + 12/13 = 9
3p = 105/13
p = 35/13
A ball is dropped from the top of a
building. The expression 4.9x2 gives the distance in meters the ball
has fallen after x seconds. Write and simplify an expression that gives the
distance in meters the ball has fallen after x2 seconds. after x3 seconds.
Clear question is;
A ball is dropped from the top of a
building. The expression 4.9x² gives the distance in meters the ball
has fallen after x seconds. Write and simplify an expression that gives the
distance in meters the ball has fallen after x² seconds. after x³ seconds.
Answer:
A) Distance = 4.9x⁴
B) Distance = 4.9x^(6)
Step-by-step explanation:
We are given the expression 4.9x² which is the distance in meters the ball
has fallen after x seconds.
Thus,
A) after x² seconds, we have;
Distance = 4.9(x²)²
Distance = 4.9 * (x²) * (x²)
When we have to multiply 2 same numbers with the same power, the powers add up. Thus, we now have;
Distance = 4.9x⁴
B) after x³ seconds, we have;
Distance = 4.9(x³)²
Distance = 4.9 * (x³) * (x³)
When we have to multiply 2 same numbers with the same power, the powers add up. Thus, we now have;
Distance = 4.9x^(6)
Solve the equation for y. y +4x=11;x= -1,0,3
Answer:
y = 15, 11, and -1 when x = -1, 0, and 3 (respectively). Together, we have the points (-1, 15), (0, 11), and (3, -1).
Step-by-step explanation:
Assuming you want to find the values of y for each evaluated x, we will simply plug in the values into the equation.
y + 4x = 11
y = 11 - 4x
For x = -1
y = 11 - 4(-1)
y = 15
For x = 0
y = 11 - 4(0)
y = 11
For x = 3
y = 11 - 4(3)
y = -1
Thus, we have the points, (-1, 15), (0, 11), and (3, -1).
Cheers.
somebody please help me on this geometry it is urgent!! i’ll mark you the brainliest please don’t waste answers
87 2/3 written as a decimal
Answer:
2/3= 0.666666666667
Step-by-step explanation:
Evaluate each expression. Name the property used in each step.
1. (1 / 5)5 * 14 = 14 because 1/5 multplied by 5 is equal to 1. I believe this is called reciprocals.
2. 6 + 4 (19 - 5) = 6 + 4(19) - 4(5) = 6 + 76 - 20 = 62. This is called the distributive property.
3. 5 (14 - 5) + 6 (3 + 7) = 5(14) - 5(5) + 6(3) + 6(7) = 70 - 25 + 18 + 42 = 105. We also used the distributive property in this question.
Complete the statement below. The expression illustrates the commutative property of multiplication.
Answer:
Option A
Step-by-step explanation:
The expression that completes the blank is A. 11 x w * x 3 = 11 x 3 x w.
What is the cumulative property of multiplication?The commutative property is a mathematical concept that states that the order in which we multiply the factors does not affect the product.
According to the commutative property, a mathematical principle, the product is unaffected by the order in which we multiply the integers.
According to the above, the example of a commutative property is:
11 x w x 3 = 11 x 3 x w
This expression is the one with the commutative property because it has the same factors on both sides of the equation in a different order and that does not affect the result.
Therefore, the correct answer is A.
This question is incomplete because you are missing the options, here are the options:
A. 11 x w x 3 = 11 x 3 x w
B. 11 x w x 3 = 11 x w x 3
C. (11 x w) x 3 = 11 x (w x 3)
D. 11 x (w x 3) = (11 x w) + (11 x 3)
To know more about cumulative property follow
https://brainly.com/question/2475734
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You win the lottery and decide to impress your friends by exhibiting a million-dollar cube of gold. At the time, gold is selling for $1282 per troy ounce, and 1.0000 troy ounce equals 31.1035 g. How tall would your million-dollar cube be?
Answer:
The million dollar cube will be 10.79 cm tall
Step-by-step explanation:
Let the sides of the gold cube representing the tallness of the cube be s
volume of the gold cube V = s³
Then :
[tex]\mathbf{s = \sqrt[3]{V} }[/tex] --- (1)
Similarly; we know that , density ρ = mass m/Volume V
making volume the subject of the formula, then ;
V = m/ρ
Replacing that into (1) above , we have:
[tex]\mathbf{s = \sqrt[3]{\dfrac{m}{\rho}} }[/tex]
Given that:
At the time, gold is selling for $1282 per troy ounce
∴ In a million-dollar cube of gold, the number of troy ounce that can be bought with a million dollar = 1000000/1282 = 780.03 troy ounce
Since 1.0000 troy ounce equals 31.1035 g
∴ 780.03 troy ounce = 780.03 × 31.1035 g
= 24261.66 g
From the tables 12.1 of Gold , the density of Gold is obtained as 19.3 g/cm³
∴
[tex]\mathbf{s = \sqrt[3]{\dfrac{m}{\rho}} }[/tex]
[tex]\mathbf{s = \sqrt[3]{\dfrac{24261.66}{19.3}} }[/tex]
[tex]\mathbf{s = \sqrt[3]{1257.080829} }[/tex]
[tex]\mathbf{s = 10.79 \ cm }}[/tex]
The million dollar cube will be 10.79 cm tall
what does GEMDAS stand for
Answer: Hi!
GEMDAS is the guideline that you would use to solve a algebraic expression. It tells you the order of which things you should solve or simplify first.
G. Groupings. (There is a similar expression called PEMDAS that is a bit easier to understand, where the P stands for parentheses, brackets, etc.)
E. Exponents.
MD. Multiplication and Division, right to left.
AS. Addition and Subtraction, right to left.
Hope this helps!
-8x+3=8x+27 I need help plz I’m trash at math
Answer:
-1.5
Step-by-step explanation:
See steps below:
-8x+3=8x+27-8x + 3 - 8x - 3 = 8x+ 27 - 8x - 3 ⇒ add -8x - 3 to both sides in order to collect like terms in the different sides of equation-16x = 24 ⇒ simplifiedx= 24/-16 ⇒ dividex= - 1.5 ⇒ answerWhich pair of angles is supplementary?
Answer:
180° angle is supplementry angle
Step-by-step explanation:
180°
Answer:
Option a) ∠RXZ & ∠YXZ
Step-by-step explanation:
If sum of two angles are 180°, then the two angles are called supplementary.
∠RXZ & ∠YXZ forms a straight line and sum of ∠RXZ & ∠YXZ
will be 180. So, they are supplementary
Translate the phrase into a variable expression.Use the letter p to name the variable the total number of plants divided among 8 yards.
I need some help
Answer:
p/8
Step-by-step explanation:
⛅️ + ⛅️+ ⛅️= 30
⛅️ + ❄️+ ❄️= 20
❄️ + + = 13
⛅️+ ❄️ x = ??
Answer:
I GOT YOU!
Step-by-step explanation:
⛅️= 10
❄️= 5
x = 8
So,
10+10+10=30
10+5+5=20
5+8= 13
10+5+8=23
I hope I helped...
A point A (x, y) is translated 6 units to the right and 4 units down. What is the mapping to the new point A'? (x-4, y+6) (x+6, y-4) (x+6, y+4) (x+4, y-6)
Answer:
New point (x+6, y-4)
Step-by-step explanation:
Given:
Points = (x , y)
Mapping
6 units to the right
4 units down
Find:
New point
Computation:
On line X, numbers are add on move right side
So,
x+6
On line Y, numbers are subtract on move down
So,
y-4
New point (x+6, y-4)
Please help me all I need is 41,42,43. Also could u friend me I just sighned up
Answer:
trailing zeros are dropped1846 beats42×(selling price for 1 tin)Step-by-step explanation:
41. The product of 0.25 and 0.4 is 0.100, with three decimal places. Trailing zeros are usually dropped--except when they are used to indicate significant digits in a calculation. Hence, the usual presentation of the result is ...
0.25 × 0.4 = 0.1
__
42. To find total beats, multiply beats per second by seconds.
(52 beats/second)(35.5 seconds) = (52)(35.5) beats = 1846 beats
The hummingbird's wings will beat 1846 times in 35.5 seconds.
__
43. To find total sales for the week, multiply the price of a tin of popcorn by the number sold in the week (42).
Answer:
41) 0.25 × 0.4 = 0.1
It has only one decimal place in the product because 0.25 has two significant figures and 0.4 has one significant figure. When multiplying, the product will always match with the number that has the least amount of significant figures. Since 0.4 has one significant figure, the product, 0.1, will also have one significant figure.
42) 35.5 s × 52 times/s = 1,846 times
43) 42 tins × $9.25/tin = $388.50
Hope that helps.
Find the volume of the composite figure formed by a hemisphere with the radius
r = 10 cm and a cube with the side length L=
20 cm.
Answer:
8209.44
Step-by-step explanation:
CUBE: 20x20x20=8000
HEMISPHERE=2/3[tex]\pi[/tex]r²=
2/3[tex]\pi[/tex](10)²=209.44
8000+209.44=8209.44
Which of the following expressions are equivalent to 6.53−(−4.11)+7.92
Answer:
C -(-6.53)+4.11-(-7.92)−(−6.53 )+4.11−(−7.92)minus, left parenthesis, minus, 6, point, ...
Answer: Choice B and Choise C.Step-by-step explanation: Equivalent expressions are those expressions that have the same value but they look different.