Answer: The two numbers are $x = 5$ and $y = 7.5$.
Step-by-step explanation:
Let the two numbers be $x$ and $y$, where $x < y$. We can write the two given statements as the following two equations:
$$2y = 3x + 15$$
$$\frac{1}{5}x + \frac{1}{9}y = 10$$
We can solve this system of equations using elimination. Multiplying the first equation by 5 and the second equation by 9, we get
$$10y = 15x + 75$$
$$9x + y = 90$$
Subtracting these equations, we get
$$8y - 9x = 15$$
Multiplying this equation by 8, we get
$$64y - 72x = 120$$
Adding this equation to 5 times the first equation, we get
$$69y - 72x = 120 + 75$$
$$69y - 72x = 195$$
Dividing both sides by 3, we get
$$23y - 24x = 65$$
Subtracting this equation from 4 times the second equation, we get
$$96y - 36x = 360 - 260$$
$$96y - 36x = 100$$
Dividing both sides by 60, we get
$$\frac{16}{3}y - \frac{6}{5}x = \frac{5}{3}$$
Substituting the expression for $y$ from the first equation, we get
$$\frac{16}{3}(3x + 15) - \frac{6}{5}x = \frac{5}{3}$$
This simplifies to
$$\frac{16}{5}x + \frac{64}{5} = \frac{5}{3}$$
Solving for $x$, we find that $x = 5$. Substituting this value into the first equation, we find that $y = 15/2 = 7.5$. Therefore, the two numbers are $x = 5$ and $y = 7.5$.
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Which values are possible rational roots of 9x3+14x2−x+18=0 according to the rational root theorem? Select each correct answer.
The possible roots of the cubic polynomial 9x³ + 14x² - x + 18 are 1, 2, and 3.
What is the rational root theorem?The rational root theorem explains how a polynomial's roots and coefficients are related. It explains the kind of rational roots that the polynomial might have in particular.
According to the rational root theorem, the possible roots of a polynomial of degree three and above are,
± (coefficient of the last term)/(coefficient of the first terms).
Given, A polynomial 9x³ + 14x² - x + 18 it is a cubic polynomial so it should have three roots they could be,
The factors of the constant term divided by the factors of the first terms,
So, 18 has factors ± (1, 2, 3, 6, 9, 18) and 9 has factors ± (1, 3, 9).
So, The possible roots are ± (1, 2, 3) and so on.
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Please help #5 only thank you !
Answer:
$4.37 is a possibility to the answer
Answer:
they ate 6 pizza
Step-by-step explanation:
༼ つ ◕‿◕ ༽つ
6
If the circumference of the circle is 50, find the approximate radius, diameter and area of the circle. (Use 3.14 for
)
5x35 65x76 what the the total
The solution to the above math arithmetic is 5115.
Addition and subtraction are what?Finding the sum and difference of two integers are the two main addition and subtraction arithmetic procedures. They are both the other's polar opposite. An ordered group of integers with a shared difference between each word is known as an arithmetic sequence. The common difference, for instance, between the mathematical series 3, 9, 15, 21, and 27 is 6.
What exactly is an algebraic question?This grouping contains percent difficulties, decimal recognition, addition, subtraction, multiplication, and division as well as fraction and percent equivalences and estimate issues.
For instance, 5 + 6 = 11 and 11 - 6 = 5.
5x35 + 65x76=5115
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Find the slope (-7,4) and (-7,-8)
Answer: The slope for this line is not defined.
Step-by-step explanation: We can find the slope of a line using the formula m = y2 -y1/x2 - x1
here, (x1,y1) = (-7,4)
and, (x2,y2) = (-7,-8)
now, m= -8-4/-7+7
m = -12/0
So, the slope for this line is not defined as we are getting zero in the denominator.
A function is shown below.
g(x) = 19.6 + 1.74x. what is the value of g (20)?
Answer:
54.4
Step-by-step explanation:
g(20) = 19.6 + 1.74 (20)
g(20) = 19.6 + 34.8
g(20) = 54.4
i tried using brainly but i couldnt find this question!
Answer:
dddd
Step-by-step explanation:
Find a quartic function
The quartic equation y = x⁴ - x³ - 5 · x² - x - 6 has x = - 2 and x = 3 as its only real zeros. (Correct choice: C)
What quartic equation contains a given set of zeros?
Quartic equations are polynomials of grade 4, whose standard form is described below:
y = a · x⁴ + b · x³ + c · x² + d · x + e
Where a, b, c, d, e are real coefficients. A value of x is a zero of a polynomial when the result is equal to zero. The quickest way to find the polynomial is by evaluating each expression at x = - 2 and x = 3:
x = - 2
y = (- 2)⁴ - (- 2)³ - 5 · (- 2)² - (- 2) - 6
y = 16 + 8 - 20 + 2 - 6
y = 0
x = 3
y = 3⁴ - 3³ - 5 · 3² - 3 - 6
y = 81 - 27 - 45 - 3 - 6
y = 0
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What is the image of the point (-7,-8) after a rotation of 180∘ counterclockwise about the origin?
can someone help will give brainliest
Answer:
For every hour, Bliqus earns $21.50
Step-by-step explanation:
$430 / 20 = $21.50
$215 / 10 = $21.50
Solve the following problem:
|2x+3|=-5
Answer:
No solution exists. Hope that helps sorry it took me long I was typing alot as you can see bye and have a great day!
Step-by-step explanation:
1. Break down the problem into these 2 equations 2x+3=-5 -(2x+3)=-5
2. Solve the 1st equation : 2x+3=-5 Subtract 3 from both side 2x=-5-3 =-8 divides both sides by 2 x= -8/2 which give you x=-4 Now solve the 2nd equation : -(2x+3)=-5 Remove parentheses -2x-3=-5 add 3 to both sides -2x=-5+3=-2 Divide both sides by -2x=-2 which would give you x=1
When x=-4x, the original equation ∣2x+3∣=−5 does not hold true.
We will drop x=-4x from the solution set.
When x=1, the original equation |2x+3|=-5 does not hold true.
We will drop x=1, from the solution set. So, No solution would be your answer.
√2 (2-2√10) how do you simplify
Answer:
2√2- 4√5
Step-by-step explanation:
√2 (2-2√10)
2√2- 2√20
2√2- 2√(4*5)
2√2- 2*2√5
2√2- 4√5
4 1/4 - 2 2/4
what is the answer?
Answer:
1 3/4
Step-by-step explanation:
[tex]4\frac{1}{4}- 2\frac{2}{4} \\\\17/4 - 10/4\\7/4\\1 3/4[/tex]
Answer:
Converting from Mixed numbers to Fraction
4¹/4 = 17/4
2²/4 = 10/4
17/4 – 10/4
= 7/4
You can also change this answer into Mixed Number
it'll be 1 3/4 (One whole number, three over four)
What are the domain and range of f(x) = x - 3| +6?
O Domain: {x|x is all real numbers}
Range: {yly ≥ 6}
O Domain: {x|x≥ 3}
Range: {y ly ≥ 6}
O Domain: {x|x is all real numbers}
Range: {yly 2-6}
O Domain: {x|x≥ 3}
Range: {yly 2-6}
The domain and range of the absolute value function are the ones in the first option.
Domain: {x|x is all real numbers}Range: {yly ≥ 6}What are the domain an range of the absolute value function?Here we have the absolute value function:
f(x) = |x - 3| + 6
The domain for all absolute value functions is the set of all real numbers, as there are no input that generates a problem with the function.
And the range, the set of the inputs, has a minimum at the vertex.
Remember that if the vertex is (h, k), then we can write the function as:
f(x) = |x - h| + k
Then in this case:
f(x) = |x - 3| + 6
The vertex is at (3, 6)
Then the range is the set of all real values equal to or larger than 6, or:
y ≥ 6
Then the correct option is the first one:
Domain: {x|x is all real numbers}
Range: {yly ≥ 6}
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Mental Math In a toy store, the ratio of the number of dolls to the number of teddy bears is . If the store has 240 dolls, how many teddy bears are in the store? Use pencil and paper. Describe the mental math steps you use to solve this problem.
Answer:
Step-by-step explanation:
Dolls:240 Teddy Bears:120
120:240
Please Describe the fraction If Possible.
please help will give brainliest
Answer:
157 cm^2
Step-by-step explanation:
1) find the radius
radius = side of the square /2 = 10 /2 = 5 cm
2) notice that four semicircles are equals to two circles
3) find the area of the shaded region
A = radius^2 x pi x 2 = 5^2 x pi x 2 = 157 cm^2 (round the nearest whole number)
Equations of Exponential Functions
Complete the table for the following function
Graph the function and describe what the graph looks like.
a. Increases in Quadrant III
b. Increases from left to right
c. Decreases from left to right
d. Decreases fin Quadrant II
Please select the best answer from the choices provided
Answer:
B. Increases from left to right
Step-by-step explanation:
I calculated it logically
9514 1404 393
Answer:
b. increases from left to right
Step-by-step explanation:
See below for a graph. The function increases at an increasing rate from left to right. It only exists in quadrants I and II.
Find the volume of the pyramid
Volume of pyramid:
= ⅓ × l × w × h
= ⅓ × 9 × 9 × 7
= 3 × 63
= 189 ft³
what is the conjugate of -5 + i /2i?
Answer:
see image below
Step-by-step explanation:
HELP QUICK!!! ANSWER A B C D OR E
Answer:
It's (E) ..................
Answer:
E
Step-by-step explanation:
In triangle JKL, angles J and L each measure 51° and JK = 18. Triangle PQR is similar to triangle JKL, where J corresponds to P, K corresponds to Q, and QR = 36. Which expression represents the length of segment PR?
Answer:
Step-by-step explanation:
Triangle JKL is a 51-51-78 triangle, since the angles in a triangle must add up to 180°. Since triangle PQR is similar to triangle JKL, it must also be a 51-51-78 triangle. Since corresponding sides in similar figures are in proportion, we can set up a proportion to find the length of PR:
(PR)/(JK) = (PQ)/(JL) = (36)/(18)
Cross multiplying and solving for PR, we find:
PR = (JK) * (PQ)/(JL) = 18 * 36/18 = 36
Which statement is true based on a graph of the line that passes through the given coordinates? (2, 1), (3,3), (5,7), (6,9) Please help
A. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
B. The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin.
C. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
D. The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
The correct statement regarding the linear function passing through the coordinates (2, 1), (3,3), (5,7), (6,9) is given as follows:
A. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
When does a linear function represents a proportional relationship?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the change in y divided by the change in x.b is the y-intercept, representing the value of y when x = 0.A linear function represents a proportional relationship if it has an intercept of zero.
For the points in this problem, when x increases by one, y increases by two, hence the slope is given as follows:
m = 2/1 = 2.
Hence:
y = 2x + b.
When x = 2, y = 1, hence the intercept b is given as follows:
1 = 2 + b
b = -1.
As the intercept is different of zero, this is not a proportional relationship, and option A is correct.
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6+√-18 simplified for edmentum
Answer:
= 18√2
decimal =25.45584412
What is the area of this shape?
Answer:
30 meters squared
Step-by-step explanation:
First of all, we need to split the shape into different shapes. In this case, two triangles and a rectangle. We know that the triangle on the left has a height of 3 meters, and a width of 3 meters, and the formula for the area of a triangle is:
(b*h)/2 = A
So, we can plug in the values:
(4*3)/2 = A
Then, solve.
12/2 = A
6 = A
So, the triangle on the left is 6 meters squared. There is another copy of that triangle, so that means that both of the triangles combined is:
6*2 = 12 meters squared
Lastly, we need to find out the middle rectangle, which is 6 meters by 3 meters. The area of a rectangle is:
L*W = A
Plug the values...
6*3 = 18 square meters
So, the rectangle is 18 meters squared.
Our last step is to add the area for all the shapes. That would be:
12 + 18 = 30 meters squared.
Therefore, the area of this shape is 30 meters squared. Hope this helps!
Draw a number line to show 2/8 and 4/16 are equivalent.
Step-by-step explanation:
think of it as a ruler the small dashes represents the 16ths and the big dashes represents the 4ths. They are on the same line therefore they are equal.
\int (2)/(\sqrt(5x^(2))+3)dx and steps
Answer:
Step-by-step explanation:
The volume of a sphere is 2304π in^3.
The radius of the sphere is ___ inches.
Answer:
The radius of the sphere is 12 inches.
Step-by-step explanation:
V = 4/3 · pi · r³
r³ = 1728
r = 12
Find the LCD for the following pair of fractions.
1/5
and
1/2
to get a B in math Alexandria pappas must average 80 on five test. scores on the first four test were 82, 76, 84, and 75. what is the lowest score that she can get on the las test and still get a B
Answer:
the lowest score that she can get on the las test and still get a B is 83
Step-by-step explanation:
x= score needed
(82+76+84+75+x) / 5 = 80
(317+x)/ 5 = 80
Cress multiplication
317 +x = 5 x 80
317 + x = 400
x = 83
317 + 83 = 400
400/5 = 80