The two numbers that we requires are; y=−3+3√5 or y=−3−3√5
What are the two numbers?We know that in this question, we are required to obtain the two numbers that multiply to -36 and add up to -6. Now we have to write the problem into a system of simultaneous equations.
Thus;
Let the numbers by x and y
x + y = -6 ---- (1)
xy = -36 ------ (2)
x = -36/y ------ (3)
If we substitute (3) into (1)
-36/y + y = -6
-36 + y^2/y = -6
Multiply through by y
-36 + y^2 = -6y
Forming a proper quadratic;
y^2 + 6y - 36 = 0
Solving the quadratic for y
y=−3+3√5 or y=−3−3√5
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Samuel has a collection of toy cars. His favorites are the 27 red ones, which make up 60, percent of his collection.
The total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.
What is percentageIt's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Samuel has a collection of toy cars. His favorites are the 27 red ones.
Let Samuel has x number of toys:
From the equation:
60% of x = 27
(60/100)x = 27
0.6x = 27
x = 27/0.6
x = 45
Thus, the total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.
The complete question is:
Samuel has a collection of toy cars. His favorites are the 27 red ones which make up 60% of his collection. How many toy cars does Samuel have?
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P(4.-7) is reflected across the x-axis, what is the
coordinate of P?
Answer:
9
Step-by-step explanation:
guess
The students at Gotham Elementary want to raise $500 for charity. They have raised $337 so far. How much more money do the students need to raise?
Responses
A ? + 337 = 500 or ? − 500 = 337? + 337 = 500 or ? − 500 = 337
B 337 + ? = 500 or 500 – 337 = ?337 + ? = 500 or 500 – 337 = ?
C ? − 337 = 500 or 500 + 337 = ?? − 337 = 500 or 500 + 337 = ?
D 337 + 500 = ? or 500 − ? = 337
Answer: 163$
Step-by-step explanation:
Use the diagram to find the measure of angle 2
The measure of angle 2 is 75°
From the question, we have
∠1= 105°
∠2= 180°- 105° (Linear pair)
∠2=75°
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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A person who weighs 150 pounds weighs 25 pounds on the Moon. Suppose an object weighs 80 pounds on the Moon. What’s the objects weight on the Earth?
Answer:
480 lbs
Step-by-step explanation:
First, find the ratio of weight on the moon to weight on the earth. I will put the two known values in a fraction like this:
[tex]\frac{25}{150}[/tex]
Now, I can create a proportion, making sure to keep the same types of measurements in the numerator and denominator. I will use w for the unknown weight on earth.
[tex]\frac{25}{150}=\frac{80}{m}[/tex]
Now, I will simplify the fractions as much as I can.
[tex]\frac{1}{6}=\frac{80}{m}[/tex]
Now, I can see a correlation. 1 times 80 is 80, so 6 times 80 is m. Simplified, here is the answer!
[tex]6*80=m\\480=m\\m=480[/tex]
Answer:
480 pounds
Step-by-step explanation:
we times for objects on earth and divide for objects on the moon by the same number
150
[tex]150 \div x = 25[/tex]
150/-25=-x
-6/-1= -x/-1
6=x
[tex]150 \div 6 = 25[/tex]
so when in object is on earth you multiple by x Wich 6
[tex]80 \times 6 = 480[/tex]
you can also cross multiply
How many solutions does 5 + x/3 = x/3 + 6 + x/9
A. Infinitely many solutions
B. Two solutions
C. No solutions
D. One solution
========================================================
Explanation:
A thing that jumps out at me right away is the presence of x/3 on both sides. When subtracting x/3 from both sides, these terms cancel out and we're left with this equation
5 = 6 + (x/9)
Let's say w = x/9. We now have this equation 5 = 6 + w. Subtract 6 from both sides to isolate w and you should get w = -1
Then plug in w = x/9 and solve for x.
w = -1
x/9 = -1
x = 9*(-1)
x = -9
We get exactly one solution and it is x = -9
--------------
Check:
5 + x/3 = x/3 + 6 + x/9
5 + (-9)/3 = (-9)/3 + 6 + (-9)/9
5 - 3 = -3 + 6 - 1
2 = 3 - 1
2 = 2
We get the same thing on both sides, which leads to a true statement. This causes a domino effect to lead the first equation to be true when x = -9. Therefore, the solution is confirmed.
Barbara drew a scale drawing of a game room. The scale she used was 2 inches : 1 foot. If the actual length of the pool table is 6 feet, how long is the pool table in the drawing?
If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches .
In the question,
it is given that ,
Barbara drew an scale drawing of the game room.
the scale that she used is 1 feet in the actual length is represented by 2 inches in the drawing ,
which means ,
1 feet = 2 inches
to find the length of 6 feet in the drawing ,
6 feet = 6 × 2 inches
= 12 inches
Therefore , If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches .
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at the lone butte ranch 6 goats and 5 sheep sell for 305 while 2 goats and 9 sheep sell for 285. Find the cost of a single goat and a single sheep.
By solving a system of equations we can see that each goat costs $30 and each sheep costs $25.
How to find the cost of each animal?Let's define the variables:
x = cost of a goat
y = cost of a sheep.
We can write the system of equations with the given info:
6*x + 5*y = 305
2*x + 9*y = 285
If we subtract 3 times the second equation from the first one, we get:
(6*x + 5*y) - 3*(2*x + 9*y) = 305 - 3*285
-22*y = -550
y = -550/-22 = 25
Now that we know the value of y we can try to find the value of x:
2*x +9*25 = 285
2*x = 285 - 9*25 = 60
x = 60/2 = 30
These are the costs of each animal.
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A machine in a factory make 3 1/2 pound of nail in 1 1⁄4 hour. At what rate, in pound per hour, doe the machine make nail?
Answer:
2.8 pounds per hour
Step-by-step explanation:
[tex] \frac{3.5}{1.25} = \frac{350}{125} = \frac{14}{5} = 2.8[/tex]
consider following recurrence relation. what will be the number next in series in place of question mark? 0, 3, 8, 15, 24, 35, 48, ?
The number that will be next in the series will be 63 .
In the question ,
a recurrence relation is given that is 0, 3, 8, 15, 24, 35, 48, ? .
we have to find the number that will come in place of question mark .
On carefully examining the series , we can see that
3 - 0 = 3
8 - 3 = 5
15 - 8 = 7
24 - 15 = 9
35 - 24 = 11
48 - 35 = 13
we can se that increments 3,5,7,9,11,13,... form an Arithmetic Progression
with first term as 3 and common difference as 2 ,
So ,the next increment will be 13+2 = 15
let the next term be "x" .
x - 48 = 15
x = 15 + 48 = 63
the number in place of ? is 63 .
Therefore , The number that will be next in the series will be 63 .
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Solve 2y + x + 3 = 0 and 3y - x + 1 = 0 graphically using -4 ≤x ≤ 2
help pls
Answer:
Step-by-step explanation:
We have to the graph from x = -4 to x = 2
2y + x + 3 = 0
Rearrange the equation to make y the subject
2y = -x - 3
y = (-1/2)x -3/2
-3/2 is the y intercept
the gradients is -1/2
since the value is negative, the graph will be sloping downwards
Point your pen at y = -3/2 on the y axis (-3/2 is -1.5)
go 1 point down and 2 points to the right, make a point and connect these 2 dots and make a line across the graph.
Do the same with the other equation:
3y - x + 1 = 0
3y = x - 1
y = (1/3)x -1/3
y intercept is -1/3
gradient is 1/3
point your pen at -1/3 on the y axis, go 1 point up and 3 points to the right
and mark this point and connect these 2 points and make a line across the graph.
Which of the following measures examine the spread of different values around the measures of central tendency? A. Measures of central tendency B. Measures of variability C. Measures of frequency D. Measures of percentile
Measures which examine the spread of different values around the measures of central tendency is measures of variability.
Define central tendency.A central tendency in statistics is a typical or characteristic value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most popular ways to measure central tendency. The number used to represent the center or middle of a set of data values is known as the central tendency measure.
Given,
Measures which examine the spread of different values around the measures of central tendency:
B. Measures of variability
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5a<−35 or a−14>1
Algebra 1, high school
Answer:156
Step-by-step explanation:
The average annual rainfall for a town is 43.2 inches. The average monthly rainfall for the previous 9 months was 4 inches. Did the town exceed its average annual rainfall? If so, by how much?
Answer:
Yes, the town exceeded the average annual rainfall by 0.4 inchesStep-by-step explanation:
The average annual rainfall for a town is 43.2 inches.
This is converted to average monthly as:
43.2 in / 12 = 3.6 inThe difference is:
4 in - 3.6 in = 0.4 inAnswer:
Yeah, they exceeded by 0.4 inches.
Step-by-step explanation:
It is given that,
→ the average monthly rainfall for the previous 9 months was 4 inches.
The monthly rainfall in 12 months,
→ 43.2 inches ÷ 12 months
→ 43.2/12
→ 3.6 inches
Then the difference will be,
→ 4 inches - 3.6 inches
→ 4 - 3.6
→ 0.4 inches
Hence, the difference is 0.4 inches.
A scale on a map is 1 200 000. Work out the distance on the map, in cm, if the real distance is 10 km 15 km 4 km
The distance on the map, in cm, given the real distances, and the scale of the map are:
10 km = 5 cm15 km = 7.5 cm4 km = 2 cmHow to find the distance on the map?A scale of 1 : 200, 000 means that every 1 cm on the map is 200, 000 cm on the ground.
To find the distance on the map of 10 km, first convert it to cm:
= 10 km x 100, 000 cm per km
= 1, 000, 000 cm
The distance on the map is therefore:
= 1, 000, 000 / 200, 000 cm scale
= 5 cm on map
The distance of 15 km on the map is:
= (15 km x 100, 000) / 200, 000
= 7.5 cm
The distance of 4 km is:
= (4 x 100, 000) / 200, 000
= 2 cm
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Andrew has picked out some party favors. He calculates that they will cost $7 per guest.
Write an equation that shows how the total cost of the party favors, y, depends on the number of guests, x
Do not include dollar signs in the equation. what does y equal?
Answer:
Step-by-step explanation:
y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Andrew has picked out some party favors.
He calculates that they will cost $7 per guest.
We need to find the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
So y=7x where y is the total cost and x is the number of guests and 7 is the cost per guest.
If there are 2 guests then the total cost will be 14.
Hence y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
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Determine whether the following sequence is arithmetic, geometric, or neither. 12,17,22,27
Answer:
Arithmetic
Step-by-step explanation:
The difference between consecutive terms is 5. Thus, this is an arithmetic sequence with a common difference of 5.
can someone please help me with this
Answer:
B
Step-by-step explanation:
given 1 pound = 16 ounces , then
5 pounds = 5 × 16 = 80 ounces
-4(w + 5) + 2w simplify
Answer:
-2w-20
Step-by-step explanation:
When 6 less than 3 times a number is increased by 2 it's at least 5 times the same number decreased by 8
Answer: 2>=n
Step-by-step explanation:
3n-6 +2 >= 5n-8
3n-4 >= 5n-8
-4>= 2n -8
4>=2
2>=n
Hope this helped!!
How do I solve this problem?
PLEASE HURRY
I am having trouble
You got to set it up to boys to girls
Answer:
0,1
Step-by-step explanation:
simplest form
The perimeter of an isosceles triangle is 380 cm and it’s unequal side is 150 find the area of triangle (by Heron’s formula)
Answer:
A ≈ 6538.35 cm²
Step-by-step explanation:
Calculating the area (A) using Heron's formula
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where s is the semi perimeter and a, b, c the 3 sides
here
s = 380 ÷ 2 = 190
given perimeter = 380 and unequal side is 150 , then
equal sides = (380 - 150) ÷ 2 = 230 ÷ 2 = 115 cm
then a = 150, b = 115 , c = 115
A = [tex]\sqrt{190(190-150)(190-115)(190-115)}[/tex]
= [tex]\sqrt{190(40)(75)(75)}[/tex]
= [tex]\sqrt{42750000}[/tex]
≈ 6538.35 cm² ( to 2 dec. places )
Raman purchased books and stationery items and paid the total amount of rupees 963 if he paid 7% tax what was the net value of the item purchased.
The net value of the items purchased is ₹ 900.
Raman purchased books and stationery items and paid the total amount of rupees 963.
Paid tax = 7%
Let the net value of the items purchased be `x.
VAT = 7%
Selling price = ₹x + (7% of x)
= ₹x+ ₹ ( 7/100 * x)
=₹( x +7 x /100)
= ₹ 107 x /100
But Raman purchased books and stationery items for ₹963.
107x/100 = ₹963
x = 963 x 100/107
x = 900
Hence the answer is the net value of the items purchased is ₹ 900.
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which of the following ratios are connected to 5/20?
multiple choice
a 1/5
b1/4
c 20/100
d 25/100
Answer:
which of the following ratios are connected to 5/20?
multiple choice
a 1/5
c 20/100
d 25/100
d is the option 25/100 and
b 1/4
Which of the following rules describes the function graphed below? On a coordinate plane, points are at (negative 1, 1), (1, 2), (3, 3), (5, 4). a. Output = Input c. Output = (0.5)(Input) + 1.5 b. Output = (2)(Input) – 3 d. Output = (1.5)(Input) + 3
The rule that describes ( -1, 1), (1, 2), (3, 3), (5, 4) is c. Output = (0.5)(Input) + 1.5
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, On a coordinate plane, points are at ( -1, 1), (1, 2), (3, 3), (5, 4).
By observing the given options we conclude that it is Output = (0.5)(Input) + 1.5 to confirm let's put the values.
Given when input is - 1 output is 1.
∴ 1 = 0.5(-1) + 1.5.
1 = - 0.5 + 1.5.
1 = 1 ( satisfied).
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help pls what are the number of hours i need this before 11/20/22
a. Creating a system of equations, the length of each plan A's workout is 3/4 hour, while the length of each plan B's workout is 3/4 hour.
b. x = -8, y = 2.
How to Solve a System of Equations?Write equations of a system that represents the information given and solve accordingly.
Let the length of plan A = x
Length of plan B = y
Equation for Monday would be:
9x + 7y = 12 --> eqn. 1
Equation for Tuesday:
3x + 5y = 6 --> eqn. 2
Multiply eqn. 1 by 3 and eqn. 2 by 9
27x + 21y = 36 --> eqn. 3
27x + 45y = 54 --> eqn. 4
Subtract the equations:
-24y = -18
y = -18/-24
y = 3/4
Plan B's length of workout is: 3/4 hour.
Substitute y = 3/4 into equation 2:
3x + 5(3/4) = 6
3x + 15/4 = 6
3x = 6 - 15/4
3x = 9/4
12x = 9
x = 9/12
x = 3/4
Length of plan A's workout is: 3/4 hour.
b. 2x + 4y = -8 --> eqn. 1
-2x + 3y = 22 --> eqn. 2
Add both equations together:
7y = 14
y = 2
Substitute y = 2 into equation 1:
2x + 4(2) = -8
2x + 8 = -8
2x = -8 - 8
2x = -16
x = -16/2
x = -8
The solution is: x = -8, y = 2.
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What expressions represents the multiplex version of the expression below ?
(6x^2 +5) (2x^3+3)
Answer:
12x^5+18x^2+10x^3+15
Step-by-step explanation:
first you apply the distribution property (FOIL) and you get
12x^5+18x^2+10x^3+15
Giving brainliest to the person who give a right answer with a clear explanation
Answer:
33. AB = √45. CD = √40. Not congruent. AB is greater.
34. EF = 5. GH = √41. Not congruent. GH is greater.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Question 33Given endpoints:
A = (0, 2)B = (-3, 8)Substitute the given endpoints into the formula and solve:
[tex]\begin{aligned}\overline{AB}&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(-3-0)^2+(8-2)^2}\\&=\sqrt{(-3)^2+(6)^2}\\&=\sqrt{9+36}\\&=\sqrt{45}\\& \approx 6.7\; \sf (1 \; d.p.)\end{aligned}[/tex]
Given endpoints:
C = (-2, 2)D = (0, -4)Substitute the given endpoints into the formula and solve:
[tex]\begin{aligned}\overline{CD}&=\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\&=\sqrt{(0-(-2))^2+(-4-2)^2}\\&=\sqrt{(2)^2+(-6)^2}\\&=\sqrt{4+36}\\&=\sqrt{40}\\& \approx 6.3\; \sf (1 \; d.p.)\end{aligned}[/tex]
Therefore, the segments at not congruent.
[tex]\textsf{As\; $\sqrt{45} > \sqrt{40}$ \; then \; $\overline{AB} > \overline{CD}$}.[/tex]
Therefore, the length of segment AB is greater.
Question 34Given endpoints:
E = (1, 4)F = (5, 1)Substitute the given endpoints into the formula and solve:
[tex]\begin{aligned}\overline{EF}&=\sqrt{(x_F-x_E)^2+(y_F-y_E)^2}\\&=\sqrt{(5-1)^2+(1-4)^2}\\&=\sqrt{(4)^2+(-3)^2}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}[/tex]
Given endpoints:
G = (-3, 1)H = (1, 6)Substitute the given endpoints into the formula and solve:
[tex]\begin{aligned}\overline{GH}&=\sqrt{(x_H-x_G)^2+(y_H-y_G)^2}\\&=\sqrt{(1-(-3))^2+(6-1)^2}\\&=\sqrt{(4)^2+(5)^2}\\&=\sqrt{16+25}\\&=\sqrt{41}\\& \approx 6.4\; \sf (1 \; d.p.)\end{aligned}[/tex]
Therefore, the segments at not congruent.
[tex]\textsf{As\; $\sqrt{41} > 5$ \; then \; $\overline{GH} > \overline{EF}$}.[/tex]
Therefore, the length of segment GH is greater.
I need help again please.:)
Answer:
D
Step-by-step explanation:
D) 1755 yards is the closest amount to 1760 yards, which is how much is in a mile