Answer:
-6 and -1
Step-by-step explanation:
let's suppose there are two numbers x and y so that it that works that would give the following equations
[tex]x*y=6 \\ x+y =-7[/tex]
now let'S rewrite the first to the form y =
[tex]y=\frac{6}{x}[/tex]
and plug that into the second one
[tex]x+\frac{x}{6} = -7|*6\\6x+x=-42\\7x=-42|:7\\x=-6[/tex]
use that to find out what y is
[tex]-6+y=-7|+6\\y=-1[/tex]
you can check that with the first equation
What is the probability that either event will occur?
Now, find the probability of event A and event B.
A
B
6
6
20
20
P(A and B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
Answer:
0.12
Step-by-step explanation:
Given the frequencies of occurrence in the diagram, you want to know the probability of A and B.
ProbabilityThe probability of an event is the ratio of the number of times it occurs to the total number of trials.
The diagram shows the event (A and B) occurs 6 times out of a total of 6+6+20+20 = 52 trials.
P(A and B) = 6/52
P(A and B) ≈ 0.12
<95141404393>
I attached the question
Following a translation of (x, y) (x - 1, y + 2) and a dilation by a scale factor of 2 centred at the origin, the coordinates of T are T''(8, 8).
Following translation and dilation, we must take the following actions to determine the new coordinates of point T:
1) Translation: (x, y) = (x - 1, y + 2).
T' = (5 - 1, 2 + 2)
= (4, 4) applies the translation to the original coordinates of T.
2) Dilation: Scale factor of 2 centered at the origin
Multiply the translated coordinates by the scale factor of 2:
T'' = (2 × 4, 2 × 4)
= (8, 8)
Therefore, the coordinates of T after the translation (x, y) → (x - 1, y + 2) followed by a dilation by a scale factor of 2 centered at the origin are T''(8, 8).
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Given m ∥ n, find the value of x.
given that m is parallel to n,
the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.
using the corresponding angle rule we know that:
2x + 16 = 96
2x = 80
so x = 40
HELP ASAP PHOTO INCLUDED
The volume of the shape for Jackson's ice cream is given as follows:
11.85 in³.
How to obtain the volume?The volume of a cone of radius r and height h is given by the equation presented as follows:
V = πr²h/3.
Hence the volume of the cone in this problem is given as follows:
V = 3.14 x 1.5² x 5/3
V = 11.78 in³.
The volume of an hemisphere of radius r is given as follows:
V = 2πr³/3.
Hence the volume of sphere is:
V = 2π x 1.5³/3
V = 7.07 in³.
Hence the total volume is given as follows:
11.78 + 7.07 = 11.85 in³.
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A random survey of 495 adults found that 59 had dietes. Which of the following is a 98% confidence interval for the population proportion of adults with diabetes?
Answer:
{0.0853,0.1531}
Step-by-step explanation:
[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}\bigr(1-\hat{p}\bigr)}{n}}[/tex]
[tex]\displaystyle CI_{98\%}=\frac{59}{495}\pm2.326\sqrt{\frac{\frac{59}{495}\bigr(1-\frac{59}{495}\bigr)}{495}}\approx\{0.0853,0.1531\}[/tex]
principal $45,687.23 annual interest rate 7.555% interest period monthly. What is the first period interest?
The interest rate for the first period is $287.22
Using the Simple Interest PrincipleTo obtain the first period interest, we use simple interest formula;
Simple Interest = Principal * Rate * Time
Given:
Principal = $45,687.23
Annual interest rate = 7.555%
Interest period = Monthly
Convert the annual interest rate to a monthly interest rate.
Monthly interest = Annual interest/ 12 = 7.555/12 = 0.6295%
First period interest:Interest = Principal * Monthly interest rate * Time
Since it's the first period, the time is 1 month:
Interest = $45,687.23 * 0.62958333% * 1
Interest = $45,687.23 * 0.0062958333
Interest ≈ $287.22
Therefore, the first period interest is $287.22.
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zeus industries bought a conputer for $2500. it is ecpected to depreciate at a eate of 20% per year. what will the e value of the computers be in 2 years
Answer: Let me explain!
Step-by-step explanation:
Well, this is easy, I’ll explain it.
We know the value of these computers are going to go down 20% each year. So since we know that, we can multiply 20 percent by the amount of years, which is 2, so 20 times 2 is 40, so the computers decreased in value by 40 percent!
Now that that’s established, we need to subtract forty percent of 2500, from the original price, 2500.
(To do that, move the decimal place over one to get 250, which is 10%, then multiply by 4, to get 40 percent of 2500, which is 1000, in case you weren’t sure on how to do that :)
Then, subtract 1000 from 2500, and that is your answer!
$1,500
Enter the correct answer in the box. Write the sum of 12\sqrt{23x^{13}}+14\sqrt{23x^{13}} in simplest form, if x > 0.
The sum of the expressions 12√23x¹³ + 14√23x¹³ is in its simplest form if x > 0 is 26x⁶√23x
Calculating the sum of the radical expressionFrom the question, we have the following parameters that can be used in our computation:
12\sqrt{23x^{13}}+14\sqrt{23x^{13}}
Express the summation expression, properly
So, we have
12√23x¹³ + 14√23x¹³
Next, we add the terms of teh expression
Using the above as a guide, we have the following:
12√23x¹³ + 14√23x¹³ = 26√23x¹³
Take the square root of x¹³
12√23x¹³ + 14√23x¹³ = 26x⁶√23x
The above expression is in its simplest form if x > 0.
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What is the product of 12 and 4 decreased by 15
The results of the product of 12 and 4 decreased by 15 is 33
How to solve product of numbers?Product refers to another term which means multiplication of numbers.
product of 12 and 4
= (12 × 4)
decreased by 15 means 15 is subtracted from the expression
= (12 × 4) - 15
Following the rules of PEMDAS
P = parenthesis
E = exponents
M = multiplication
D = Division
A = addition
S =subtraction
So,
(12 × 4) - 15
= 48 - 15
= 33
Hence, 33 is the product of 12 and 4 decreased by 15
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The value of the product of 12 and 4 decreased by 15 is 33
How to determine the product of 12 and 4 decreased by 15From the question, we have the following parameters that can be used in our computation:
The product of 12 and 4 decreased by 15
The product of 12 and 4 is expressed as
12 * 4
Evaluate
12 * 4 = 48
When decreased by 15, we subtract 15 from both sides of the equation
using the above as a guide, we have the following:
12 * 4 - 15 = 48 - 15
Evaluate
12 * 4 - 15 = 33
Hence, the product of 12 and 4 decreased by 15 is 33
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
KL = 7, so B is the correct answer.
Use the diagram to find x and y
The values of x and y is x=8 and y=12.
We are given that;
The dimensions=7 and 24
Now,
(x+y)^2= 7^2 + 24^2
x^2+y^2+2ab=49+416
x^2+y^2+2xy=465
Also, 7^2=x2+h2
49=x2+15
x2=49+15
x2=64
x=8
Substituting the values of x
8+y=20
y=12
Therefore, by Pythagoras theorem the answer will be x=8 and y=12.
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hey i have a question about this assignment and want to check if my answers are right
The lengths of the sides and angles of the triangles, obtained using Pythagorean Theorem and trigonometric ratios are;
D. 19.2
C. 5.3
F. 2·√5
G. √3
H. 8·√3
K. 18.9
O. 15.5
N. 14.5
M. 41.4°
I. 74.1°
What is the Pythagorean Theorem?The Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the legs of the triangle.
D. x = √(15² + 12²) ≈ 19.2
C. x = √(10² - 8.5²) ≈ 5.3
F. x = 2·√(5) (Special triangles)
G. tan (60°) = 30/x = √3
x = 30/√3 = 10·√3
H. x/16 = (√3)/2
x = 16 × (√3)/2 = 8·√3
x = 8·√3
K. tan(34°) = x/28
x = 28 × tan(34°) ≈ 18.9
O. cos(55°) = x/27
x = 27 × cos(55) ≈ 15.5
N. sin(16°) = 4/x
x = 4/(sin(16°) ≈ 14.5
M. x = arccos(9/12) ≈ 41.4°
I. x = arcsin(25/26) ≈ 74.1°
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his composite figure is made of two identical pyramids attached at their bases. Each pyramid has a height of 2 units. 2 identical pyramids with rectangular bases are connected at their base. The height of the pyramid is 2. The lengths of the sides of the rectangle are 5 and 0.25 units. Which expression represents the volume, in cubic units, of the composite figure? One-half (One-third (5) (0.25) (2) ) One-half (One-third (5) (0.25) (4) ) 2(One-third (5) (0.25) (2) ) 2(One-third (5) (0.25) (4) )
The expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.
How to evaluate the expression for the volume of the identical pyramidTo calculate for the volume of a rectangular base pyramid, we use the formula:
volume = 1/3 × area of base rectangle × height
volume of one identical pyramid = (1/3 × 5 × 0.5 × 2)cubic units
volume of the two identical pyramid = 2(1/3 × 5 × 0.5 × 2)cubic units.
Therefore, the expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.
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A company packs its fruit salad in
containers that hold 1 5/8 pounds
How many containers does it
need to hold 585 pounds of fruit
salad?
Answer: 360 containers
Step-by-step explanation: 1 5/8 in decimal form is 1.625 pounds. Divide 585 by 1.625 pounds you get 360. It takes 360 containers to hold 585 pounds of fruit
.....................................................................................
Answer:
(-6,0)
Step-by-step explanation:
An equation of a line can be modeled as y = mx + b where m is slope and b is y-intercept.
For the line r, we can model the equation as y = mx + 3 since the line intersects y-axis at (0,3) as seen in the attachment.
For the line t, we can model the equation as y = mx - 6 as the problem gives y-intercept for line t equal to -6. Hence, the line t intersects y-axis at (0,6)
Next, we have to find the slope of line t by finding the slope of line r in the attachment. Apply the rise over run by counting the steps, you can see in the attachment that I put to learn how to count rise and run of a line. Also note that the value in attachment here is a scalar quantity, meaning only magnitude, no direction.
So we will have the slope of -1 since a line graph is heading down so the output decreases as input increases. Therefore, we know that m = -1 for both lines. Therefore, for the line t, we can model the new equation to:
[tex]\displaystyle{y=-x-6}[/tex]
Then we find the x-intercept of the line by letting y = 0. Thus,
[tex]\displaystyle{0=-x-6}\\\\\displaystyle{x=-6}[/tex]
Therefore, the x-intercept of line t is at (-6,0).
Answer:
(-6,0)
Step-by-step explanation:
We need to determine the equation of line r first to find the x-intercept of line t.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
[tex]slope = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
For line r passing through (3, 0) and (0, 3), the slope is:
[tex]slope = \frac{3 - 0}{0 - 3} = -1[/tex]
Since line t has the same slope as line r, its slope is also -1.
The equation of a line in slope-intercept form (y = mx + b) is determined by its slope (m) and y-intercept (b).
We know that the slope (m) of line t is -1, and the y-intercept (b) is -6. Substituting these values into the slope-intercept form, we get:
y = -x - 6
To find the x-intercept, we set y = 0 and solve for x:
0 = -x - 6
Adding x to both sides:
x = -6
Therefore, the x-intercept of line t is (-6,0).
i need help with this
3:7 = ___: 49
Answer:
3 : 7 = 21 : 49
Step-by-step explanation:
i need help with this
3:7 = ___: 49
3 : 7 = x : 49
x = 3 × 49 ÷ 7
x = 147 ÷ 7
x = 21
3 : 7 = 21 : 49 (your answer)
-5-15x-10=-4x-8x
How do I do the is step by step?
Answer:
x = -5
Step-by-step explanation:
-5 - 15x - 10 = -4x - 8x
-5 - 10 = -4x - 8x + 15x
-15 = -12x + 15x
-15 = 3x
x = -5
#CMIIWRebecca takes out a loan that gathers compound interest. The bullet points below show the value of the loan over time.
Start = £2500.00
After 1 year = £2630.00
After 2 years = £2766.76
a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p.
b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p.
The rate is 5.2%
After 10 years, the money will amount to £4150.
What is compound interest?We know that the compound interest can be obtained from;
[tex]A = P(1 + r/n)^{nt}[/tex]
The rate is obtained from;
I = A - P
I = interest
A = amount
P = principal
r = rate
n = Number of times compounded
t = time in years
Then;
I = £2630.00 - £2500.00
I = £130
I = PRT/100
130 = 2500 * R * 1/100
R = 130 * 100/2500
R = 5.2%
After 10 years;
[tex]A = 2500 ( 1 + 0.052)^{10}[/tex]
A = £4150
Thus this is the amount after 10 years
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10. Find measure of arc JK
pls help ASAP
The value of arc JK is determined as arc JK = 28⁰.
What is the value of arc JK?
The value of arc JK is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
arc JK = m∠JNK
From the diagram, we have N = 152⁰
m∠JNK = ¹/₂ ( 360 - (152 + 152) (sum of angles at a point)
m∠JNK = 28⁰
The value of arc JK is calculated as follows;
arc JK = 28⁰
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Solve and graph on number line. |6x-3|<21
The solution of the given inequality is -3<x<4.
The given inequality is,
|6x-3| < 21
Here absolute function is applied in the given expression,
Therefore,
Case 1
⇒ (6x-3) > -21
⇒ 6x-3 > -21
Add 3 both sides,
⇒ 6x > -18
⇒ 6x > -3
Divide by 6 both sides we get,
⇒ x > -3
Case 2:
⇒ (6x-3) < 21
⇒ 6x-3 < 21
Add 3 both sides,
⇒ 6x-3+3 < 21+3
⇒ 6x < 21+3
⇒ 6x < 24
Divide by 6 both sides we get,
⇒ x < 4
Now plotting the graph of this inequality we get:
-3<x<4 is the solution.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
subtraction property of equality
multiplication property of equality
17
3
3
4
3
X-
Step
3
X=
17 3 17
7--7-x+5-77
3
5x.-
4
4
-2/x-12x X=
1 2
X= X-
2
X=-
4
5
-
-
X=
division property of equality
X+5
2
-/3/33
addition property of equality
2
3
8
15
-²333
x-²/3-1/2 x
-
17
4
5
3
given
simplification
Justification
The required justification for the solution to the equation is shown in the solution part.
As per the given equation, the required solution would be as follows:
Given:
17/3 - (3/4)x = 1(/2)x + 5
Subtraction property of equality:
17/3 - (3/4)x - 17/3 = 1(/2)x + 5 - 17/3
- (3/4)x = 1(/2)x - 2/3
Addition property of equality:
- (3/4)x - 1(/2)x = 1(/2)x - 2/3 - 1(/2)x
-(5/4)x = -2/3
Multiplication property of equality:
-(5/4)x × -4/5 = -2/3 × -4/5
Simplification:
x = 8/15
The required justification for the solution to the equation is shown in the solution part.
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Answer:
Answer shown in picture.
What is the height, in meters, of a cylinder with surface area 104π m2 and radius 4 m?
PLEASE SOMONE HELP
The height h of the cylinder is 9 meters.
What is the height of the cylinder?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The surface area of a cylinder is expressed as;
Surface Area = 2πrh + 2πr²
Given that; the surface area is 104π m² and the radius as 4 m.
We need to solve for the height (h).
Plug the values into the above formula:
Surface Area = 2πrh + 2πr²
104π = 2πrh + 2πr²
104π = 2π( rh + r² )
Divide through by 2π
52 = rh + r²
52 = ( 4 × h) + ( 4² )
52 = 4h + 16
Subtract 16 from both sides
52 - 16 = 4h + 16 - 16
52 - 16 = 4h
36 = 4h
4h = 36
h = 36/4
h = 9 meters
Therefore, the height is 9 meters.
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Please solve this question
The expression that represents a purely imaginary number is:
[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]
Option D is the correct answer.
We have,
A pure imaginary number is a number that does not have a real part and can be written in the form of bi, where b is a real number and i is the imaginary unit (√(-1)).
We have,
[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]
In this expression, we can simplify and rewrite it as:
[tex]3i^5 + i(2 - 4i^3) + 6 - 2i[/tex]
Now, let's evaluate the powers of i:
[tex]i^5 = i^{4 + 1} = i^4 \times i = 1 \times i = i\\i^3 = i^{2 + 1} = i^2 \times i = (-1) \times i = -i[/tex]
Substituting these values back into the expression:
[tex]3i^5 + i(2 - 4i^3) + 6 - 2i = 3i + i(2 - 4(-i)) + 6 - 2i[/tex]
= 3i + i(2 + 4i) + 6 - 2i
= 3i + 2i + 4i² + 6 - 2i
= 3i + 2i + 4(-1) + 6 - 2i
= 5i - 4 + 6 - 2i
= 5i - 2i - 4 + 6
= 3i + 2
The expression 3i + 2 represents a pure imaginary number, as it has no real part (the constant term is 2 and does not involve the imaginary unit i).
Thus,
The expression that represents a purely imaginary number is:
[tex]3i^5 + i (2 - 4i^3) - 2 (-3 + i)[/tex]
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please helppppppppppppppppppppppp
Answer:
last option
Step-by-step explanation:
let g = 3,
9/5 + 7/2(3)
9/5 + 21/2
adjust to a common denominator of ten to get;
18/10 + 105/10
= 123/10 = 12 3/10
so the last option !
Convert from radians to degrees.
1/4π
1/4π radians is approximately equal to 45 degrees.
To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.
Degrees = Radians × 180/π.
Therefore, to convert 1/4π radians to degrees, we have:
Degrees = (1/4π) × (180/π) ≈ 45°
Hence, 1/4π radians is approximately equal to 45 degrees.
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PLS HELP! What is the domain and Rage of the given below?
And is it a Function or not?
X /-2/-2 /-1 /-1 /0
Y/ 5/-5/ 3/-3/-1
In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above. We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.
Diagram of how a function relates two relations.
We can visualize the domain as a “holding area” that contains “raw materials” for a “function machine” and the range as another “holding area” for the machine’s products.
We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded. For example, if a person has $100 to spend, he or she would need to express the interval that is more than 0 and less than or equal to 100 and write
(
0
,
100
]
. We will discuss interval notation in greater detail later.
Let’s turn our attention to finding the domain of a function whose equation is provided. Oftentimes, finding the domain of such functions involves remembering three different forms. First, if the function has no denominator or an even root, consider whether the domain could be all real numbers. Second, if there is a denominator in the function’s equation, exclude values in the domain that force the denominator to be zero. Third, if there is an even root, consider excluding values that would make the radicand negative.
Before we begin, let us review the conventions of interval notation:
The smallest term from the interval is written first.
The largest term in the interval is written second, following a comma.
Parentheses, ( or ), are used to signify that an endpoint is not included, called exclusive.
Brackets, [ or ], are used to indicate that an endpoint is included, called inclusive.
What is the measurement of N?
a snail is 20 inches about the ground. It slips down 6 inches and the creeps up 12 inches. what is the snails height now?
Answer:
26 inches
Step-by-step explanation:
The snail starts 20 inches above the ground: +20
The snail slips (goes down) 6 inches: 20 - 6 = 14
The snail goes up 12 inches: 14 + 12 = 28
The snail is 28 inches above the ground.
Hope this helps!
how are the shapes alikei need to know
The similarity between the cube and cuboid is that both have 12 edges.
option C.
What is a cube and cuboid?A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
So a cube is a three-dimensional solid figure, having 6 square faces and 12 edges.
A cuboid is a three-dimensional geometric shape that looks like a book or a rectangular box.
A cuboid can be defined as a three-dimensional solid shape that has 12 edges, 8 vertices, and 6 faces and each of its faces is rectangular in shape.
So the similarity between a cube and cuboid is that both have 6 faces and 12 edges.
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