The difference of two numbers is 15, and their product is 700. The numbers are 25 and 10.
The two numbers are 25 and 10.
Let's denote the two numbers as x and y.From the given information, we have the equations x - y = 15 and xy = 700.Solving these simultaneous equations, we find x = 25 and y = 10.The two numbers are 35 and 20, or -20 and -35.
The problem states that the difference of two numbers is 15, and their product is 700. Let's denote the two numbers as x and y.
We have the following system of equations:
1) x - y = 152) x * y = 700From equation (1), we can express x in terms of y:
x = y + 15Substituting this into equation (2) gives:
(y + 15) * y = 700y^2 + 15y - 700 = 0To solve this quadratic equation, we use the quadratic formula: y = (-b ± √(b² - 4ac)) / 2a
Here, a = 1, b = 15, and c = -700. Plugging in these values, we get:
y = (-15 ± √(15² - 4 * 1 * -700)) / 2 * 1y = (-15 ± √(225 + 2800)) / 2y = (-15 ± √3025) / 2y = (-15 ± 55) / 2We have two solutions:
y = (40) / 2 = 20y = (-70) / 2 = -35The corresponding values for x are:
When y = 20, x = y + 15 = 35When y = -35, x = y + 15 = -20Therefore, the two pairs of numbers are (35, 20) and (-20, -35).
To rationalize the denominator of 2/square 13+ squared 11 , you should multiply the expression by which fraction?
Answer:
You should multiply the expression by [tex]\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex]
Explanation:
To rationalize any expression, you must multiply it by its conjugate. A conjugate is defined as a similar expression to the original one but with an opposite sign
This means that:
The conjugate of a + b would be a - b
Now, the given expression is [tex]\frac{2}{\sqrt{13}+\sqrt{11}}[/tex]
Consider the denominator:
From the above, we can conclude that the conjugate of [tex]\sqrt{13}+\sqrt{11}[/tex] is [tex]\sqrt{13}-\sqrt{11}[/tex]
And, remember that we need to keep the value of the expression unchanged. This means that we must multiply both the numerator and the denominator by the same value
Therefore:
You should multiply the expression by [tex]\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex] in order to rationalize the denominator
Hope this helps :)
Answer:
[tex] \frac { \sqrt { 13 } - \sqrt { 11 } } { \sqrt { 13 } - \sqrt { 11 } } [/tex]
Step-by-step explanation:
We are given the following expression and we are to determine the expression that we need to multiply it with in order to rationalize the denominator:
[tex] \frac { 2 } { \sqrt { 13 } + \sqrt { 11 } } [/tex]
To rationalize its denominator, we must multiply it with its conjugate.
For the denominator of the given expression, its conjugate would be [tex] \sqrt { 13 } - \sqrt { 11 } [/tex].
So to rationalize the expression, we would multiply it with:
[tex] \frac { \sqrt { 13 } - \sqrt { 11 } } { \sqrt { 13 } - \sqrt { 11 } } [/tex]
There are 56 students going on a field trip to the science center. The students tour the center in groups of 8 how many groups of students are there
Answer:
There would be 7 groups of students because 56 divided by 8 students gives you 7 groups.
Step-by-step explanation:
Answer:
7 groups 56÷8=7 that is the answer
What is the area of the polygon? Please help me.
Break it down into shapes you know. There's a triangle and a rectangle. The area of a rectangle is l*w and in this case it's 5*6 or 30 units². The area of a triangle is 1/2b*h and in this case that is 1/2 * 6 * 3 or 9 units². Add the areas together to find the total area, which is 39 units².
The following figure is a trapezoid. The top base is 18 inches, and the bottom base is 22 inches. The height of the trapezoid is 8.5 inches. Find the area of the trapezoid. Explain or show how you got your answer.
Answer:
The area would be 170 cubic inches.
Step-by-step explanation:
To find the area, use the area of a trapezoid formula.
A = (a + b)/2*h
Now input the values
A = (18 + 22)/2 * 8.5
A = 40/2 * 8.5
A = 20 * 8.5
A = 170
If there is a 25% discount, what percent of the original price must a customer pay
Answer: 75% Of the original price
Step-by-step explanation:
Find the area of the shaded region
you are making a fresh fruit salad using cantaloupe how much cantaloupe (AP) would you have to order if you needed 15 pounds (EP) and if canaloupe has a 55 percent yield?
Answer:
You would need to order 28 pounds. (27.27...)
Step-by-step explanation:
Let x be the number of cantaloupe. Then, 0.55x-=15.
0.55x=15
55x=1500
11x=300
x=300/11
x=27.27...
To make fruit salad using cantaloupe, you would need to order 28 pounds (AP) if you only need 15 pounds (EP) and the cantaloupe has a 55% yield.
Explanation:To determine how much cantaloupe (AP) you would need to order, you need to consider the yield percentage. If the cantaloupe has a 55% yield, it means that 55% of the cantaloupe will be usable. So, you need to order more than 15 pounds (EP) to account for the reduced yield.
To calculate the amount of cantaloupe (AP) to order, you can use the formula:
AP = EP / Yield Percentage
Using the given values, the calculation would be:
AP = 15 pounds / 55% = 27.27 pounds
Rounded up to the nearest whole number, you would need to order 28 pounds of cantaloupe (AP) to obtain 15 pounds (EP) with a 55% yield.
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What is the solution to the equation 1 over 2 multiplied by n equals 8 ? (5 points) n = 10 n = 6 n = 4 n = 16
Answer: n=16
Step-by-step explanation:
The solution to the equation is n = 16.
The equation 1/2 * n = 8 can be solved by multiplying both sides by 2 to find n = 16.
To solve the equation 1/2 * n = 8:
Multiply both sides by 2 to isolate n: n = 8 * 2 = 16.
Therefore, the solution to the equation is n = 16.
Use logarithmic regression to find an equation of the form y= a+b In(x) to model the data
Answer:
-76.204
37.673
Step-by-step explanation:
ur welcome :0
Final answer:
To find an equation of the form y = a + b ln(x) to model the data, follow these steps: Enter the data into a calculator and make a scatter plot, use the calculator's regression function to find the equation of the least-squares regression line, and add the equation of the regression line to the scatter plot.
Explanation:
Logarithmic Regression
To find an equation of the form y = a + b ln(x) to model the data, follow these steps:
First, enter the data into a calculator and make a scatter plot.Next, use the calculator's regression function to find the equation of the least-squares regression line.Add the equation of the regression line to the scatter plot from Step 1.By doing this, you will obtain the equation that models the data using logarithmic regression.
a small airplane flies 750 miles with an average speed of 300 miles per hour. 1 hour after the plane leaves, a Boeing 747 leaves from the same point. both planes arrive at the same time, what was the average speed of the 747
Final answer:
To calculate the Boeing 747's average speed, you subtract the one hour it departs after the small plane from the total travel time of the small plane and divide the same distance of 750 miles by this new time. The 747's average speed is found to be 500 mph.
Explanation:
The question asks for the average speed of a Boeing 747 that departs one hour after a small airplane and arrives at the same time. The small airplane travels 750 miles at an average speed of 300 miles per hour (mph). To find the average speed of the 747, we first calculate the time it takes for the small airplane to reach the destination:
Time = Distance ÷ Speed = 750 miles ÷ 300 mph = 2.5 hours
The 747 leaves an hour later, so its travel time is 2.5 hours - 1 hour = 1.5 hours. The 747 covers the same 750 miles in this shorter time frame:
Average speed of 747 = Distance ÷ Time = 750 miles ÷ 1.5 hours = 500 mph
The computed result is that the 747's average speed is 500 mph to cover the same distance and arrive simultaneously with the small airplane.
Write an algebraic expression for “12 less than the quotient of 12 and a number z.”
[tex] \frac{12}{n} - 12[/tex]
Final answer:
An algebraic expression for '12 less than the quotient of 12 and a number z' is represented by the mathematical expression (12/z) - 12.
Explanation:
To write an algebraic expression for "12 less than the quotient of 12 and a number z," you need to understand how to translate the words into a mathematical expression. The quotient of 12 and a number z is written as 12/z. To represent 12 less than this quotient, you simply subtract 12 from it, thus the expression becomes (12/z) - 12.
what percent of 5 is 7.4
148% soooo yeah that is the answer
Answer:
Step-by-step explanation:
(X+1)^3/2-2=25 solve
Answer:8
Step-by-step explanation:
Move all terms not containing x to the right side of the equation.Raise each side of the equation to the 2 /3 power to eliminate the fractional exponent on the left side.
Solve the equation for x .
Answer:
[tex] x = 8 [/tex]
Step-by-step explanation:
[tex] (x + 1)^\frac{3}{2} - 2 = 25 [/tex]
[tex] (x + 1)^\frac{3}{2} = 27 [/tex]
[tex] \left((x + 1)^\frac{3}{2} \right)^\frac{2}{3} = 27^\frac{2}{3} [/tex]
[tex] x + 1 = 3^2 [/tex]
[tex] x + 1 = 9 [/tex]
[tex] x = 8 [/tex]
Plzzzzzzzzz Help meeeee
Answer:
circumference so with all the diameters and stuff it would be 4[tex]\pi[/tex] or 12.56
6 is what percent of 8
The number 6 is 75 percent of 8
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a' the percent that considered thing is of "a" is b%. Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts.
We need to find the number that is state 25% of number is 1.
Let the unknown number is represneted by b.
It can be written by;
x% x 8 = 6
6/8 = 0.75
0.75 x 100
x= 75%
Therefore, the percent would be 75%
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If the sum of two congruent lengths equal the length of a third side,then the triangle created is isosceles. Is this a true statement?
Answer:
False
Step-by-step explanation:
To form a triangle, the sum of any two sides must be LARGER than the length of the third side.
This question says the sum of two sides are equal to the length of the third side. This wouldn't form a triangle.
Final answer:
Yes, the statement is true. If the sum of two congruent lengths is equal to the length of a third side in a triangle, then the triangle is isosceles.
Explanation:
Yes, the statement is true. If the sum of two congruent lengths is equal to the length of a third side in a triangle, then the triangle is isosceles.
In an isosceles triangle, two sides have the same length (congruent sides) and the remaining side is different (non-congruent side).
For example, if we have a triangle ABC where AB = BC (congruent sides) and AC is a different length (non-congruent side), then the triangle ABC is isosceles.
Pick the correct description of the line y=-5/3x
This line is in slope intercept form y = mx+b
Since we can write it as y = (-5/3)x + 0
m = -5/3 is the slope
b = 0 is the y intercept
The two points (0,0) and (3,-5) are on the straight line.
The graph models which linear equation?
3x + 5y = 10
v-2x-2
3x - 5y = 10
Answer:
a
Step-by-step explanation:
Based on the slope and y-intercept, the graph most closely models the linear equation 3x + 5y = 10.
Out of the three choices you provided, the graph most closely resembles the equation 3x + 5y = 10. Here's why:
Slope: The slope of the line in the graph is positive. This means that as x increases, y also increases. The equation 3x + 5y = 10 has a positive slope of [tex]$\dfrac{3}{5}$[/tex], which matches the slope of the line in the graph.Y-intercept: The y-intercept of the line in the graph is 2. This means that the line passes through the point (0, 2). When you plug x = 0 into the equation 3x + 5y = 10, you get 5y = 10, which means y = 2.So, the equation 3x + 5y = 10 also has a y-intercept of 2.
The other two equations do not match the graph as well:
The equation v - 2x - 2 does not have a positive slope.The equation 3x - 5y = 10 has a negative slope and a different y-intercept.
I need to know what this is please help me
the answer is D. Multiply by 2 to get the next term
Answer:
It is D, multiply by 2 to get the next term.
Step-by-step explanation:
1 x 2 = 2
2 x 2 = 4
4 x 2 = 8
and so on.....
See an algebraic equation to solve the problem. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if that perimeter of the triangle is 90 cm?
Answer:
22.5
30
37.5
Step-by-step explanation:
You have to multiply each ratio part by x to get them properly set up to add to 90.
3x + 4x + 5x = 90 Combine the left side
12x = 90 Divide by 12
12x/12 =90/12 Do the division
x = 7.5
3x = 3*7.5 = 22.5
4x = 4*7.5 = 30
5x = 5*7.5 = 37.5
Total 90
Final answer:
The lengths of the sides of the triangle with a perimeter of 90 cm and sides in the ratio 3:4:5 are 22.5 cm, 30 cm, and 37.5 cm. This is found by setting up an equation with variable x representing the common multiplier for the ratio, solving for x, and then calculating each side's length.
Explanation:
To solve the problem of finding the length of each side of a triangle with sides in the ratio 3:4:5 and a perimeter of 90 cm, we first set up an algebraic equation. Let the sides of the triangle be 3x, 4x, and 5x, respectively. The perimeter is the sum of these sides, so we have the equation 3x + 4x + 5x = 90 cm. Simplifying this gives us 12x = 90 cm. To find the value of x, we divide both sides of the equation by 12, resulting in x = 90 cm / 12, which simplifies to x = 7.5 cm. Subsequently, the lengths of the sides are 3x = 22.5 cm, 4x = 30 cm, and 5x = 37.5 cm.
a biologist wants to estimate the median with of over two hundred oak trees in a forest
Answer:
47 cm
Step-by-step explanation:
its really simple just put them in from least to greatest then cross one off from each side until you get your middle number.
How many thirds are in 1/3
?
I believe that the answer is there is 1 thirds in 1/3 I hope this helps
Answer:
one
Step-by-step explanation:
There is only one third is 1/3.
If you enjoy baking, think of it in the sense of a recipe calling for 4/3 cups of sugar. You grab a 1/3 cup and you would scoop four times in order to have 4/3 cups of sugar.
however since your recipe only calls for 1/3, you will only need one scoop.
write an expression for the calculation the difference of the products 5 and 2 and 5 and 1
Answer: 5
Step-by-step explanation: The first piece of information that you need to know is that the product is the answer when two numbers are multiplied. Therefore, you need to multiply the two sets of numbers, and then subtract.
The formula will be:
(5 x 2) - (5 x 1)=
First, do what is inside the parentheses:
10 - 5=
And solve...
5
The expression for the calculation the difference of the products 5 and 2 and 5 and 1 is (5 x 2) - (5 x 1).
What are arithmetic Operation?Addition (Finding the Sum; '+') Subtraction (Finding the difference; '-') Multiplication (Finding the product; '×' ) Division (Finding the quotient; '÷')
The first thing you should be aware of is that the result of multiplying two integers is the product.
The two sets of numbers must therefore be multiplied before being subtracted.
The Expression will be:
(5 x 2) - (5 x 1)
First, work on the brackets separately
(5 x 2) = 10
(5 x 1)= 5
So, (5 x 2) - (5 x 1)
= 10 - 5
=5
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5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5
Answer:
152,587,890,625
Step-by-step explanation:
5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5=[tex]5^{16}[/tex]
[tex]5^{16}[/tex]=152,587,890,625
Answer:
152,587,890,625
Step-by-step explanation:
I don't know if your joking nor not but this is the answer if your weren't <#3
Hazel and Jody received their monthly cell phone bills on Thursday.
Hazel's bill showed that she had a balance of -14 minutes of talk time remaining, which meant she went over her limit.
Jody's bill showed that he had a balance of 20 minutes of talk time remaining.
What is the difference between the remaining number of minutes?
A.
34 min
B.
6 min
C.
3 min
D.
39 min
✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧
Hello!
✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧
❖ The correct answer choice is A. 34 min.
Find the difference (subtraction):
20 - -14 = 34
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I think it’s D. But I’m not 100 sure
sara works at a local hotdog stand. she makes $5.00 per hour (h) and $1 per hot dog (d) that she sells. write an equation that sara could use to determine her pay check.
Answer: 5h + d
Step-by-step explanation: The equation that Sara could use to determine her pay check is 5h + d = amount she will earn.
Help need ASAP!! Thanks!! Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the squares share one side with the rectangle. The total area of the constructed figure is 120 cm2. What is the perimeter of the rectangle?
Answer:
The perimeter of rectangle is [tex]18\ cm[/tex]
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
[tex]x=y+5[/tex] ----> equation A
[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)
substitute the equation A in equation B
[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}[/tex]
[tex]120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]
using a graphing tool -----> solve the quadratic equation
see the attached figure
The solution is
[tex]y=2\ cm[/tex]
Find the value of x
[tex]x=y+5[/tex] ----> [tex]x=2+5=7\ cm[/tex]
Find the perimeter of rectangle
[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]
Solve. 90^x = 27. Explain every step.
Answer:
The answer is ⇒ x = 0.73244
Step-by-step explanation:
∵ 90^x = 27 ⇒ insert log in both sides
∴ [tex]log(90)^{x}=log(27)[/tex]
∵ 90 = 9 × 10 , 27 = 3³
∵ log(a)^b = b log(a)
∴ log(9 × 10)^x = x log(9 × 10)
∴ [tex]xlog(9*10)=log(3^{3})[/tex]
∵ log(a × b) = log(a) + log(b)⇒log(9 × 10) = log(9) + log(10)
∴ [tex]x[log(9)+log(10)]=3log(3)[/tex]
∵ log(10) = 1 , 9 = 3²
∴ [tex]x[log(3)^{2}+1]=3log(3)[/tex]
∴ [tex]x[2log(3)+1] = 3log(3)[/tex]
∴ x = (3log3)/[2log(3)+1]
∴ x = 0.73244
ANSWER
[tex]x \approx0.732[/tex]
EXPLANATION
The given exponential equation is
[tex] {90}^{x} = 27[/tex]
We take natural log of both sides
[tex] ln( {90}^{x} ) = ln(27) [/tex]
Recall and the following property of logarithms.
[tex] ln( {a}^{n} ) = n \: ln(a) [/tex]
This implies that;
[tex]x ln(90) = ln(27) [/tex]
Solve for x.
[tex]x = \frac{ ln(27) }{ ln(90) } [/tex]
[tex]x \approx0.732[/tex]
Plz help me get the right answer for these I hate math -.-
Answer:
The answer C. y=60x+120
Step-by-step explanation:
By using desmos, you can see the plotted points and what goes correctly into the line.
which describes the type of sequence in 99, 89.9, 78.8, 68.7, . . . . . ?
a) neither geometric nor arithmetic
b) geometric
c) arithmetic
d) both arithmetic and geometric
(pLeAsE TelL mE wHY yOu PIcKeD YoUr AnSwER)
Answer:
Step-by-step explanation:
The is neither geometric nor arithmetic. The differences have to be the same.
99 - 89.9 = 9.1
89.9 - 78.8 = 11.1
78.8 - 68.7 = 10.1
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