Answer:
Center: (2,-1)
Radius: 4
Step-by-step explanation:
Circle equation: (x-h)^2 + (y-k)^2 = r^2
Finding the center:
Set to equaling 0 and solve for x and y
(x - 2)^2=0
(y + 1)^2=0
Finding the radius:
In the equation, because it's set to r^2, you would undo the square.
[tex]\sqrt{16}[/tex]=4
The denominator of a fraction is 7 more than the numerator. If both the numerator and the denominator are decreased by 3, the resulting fraction is equivalent to 5/12. Find the fraction.
Answer: The original fraction is 8/15
Step-by-step explanation:
The part about the 7 more than the numerator is not needed. All you have to do is add 3 to the numerator and 3 to the denominator.
5+3=8
&
12+3=15
So
8/15
I hope this helps!
A number is 11 more than another number. Twice the sum of the two numbers is 50 . Find the two numbers.
The first number is -4 and the second number is 7
What is word problem?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
Let first number = n
second number = n+11
2(n+n+11)= 6
expanding the bracket
2(2n+11)=6
4n+22 =6
collecting like terms
4n = -16
n=-4
The first number = n =-4
second number = n+11=-4+11=7
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A garden table and a bench cost $821 combined. The garden table costs $71 more than the bench. What is the cost of the bench?
X
The cost of the bench is $ 375 and the Cost of the garden table is $ 446.
Calculating Unknown Quantity:We can Calculate unknown quantities mathematically using Algebra Expressions. Unknown values in an equation are represented by variables, which are often represented by a letter of the alphabet like x, y, and z or a, b, and c, etc.
Here we have
A garden table and a bench cost $ 821 combined
Let x, and y be the cost of the garden table and bench
Given that
The garden table costs $71 more than the bench.
=> x = y + $ 71 ---- (1)
It is also given that
The total cost of the garden table and a bench = $ 821
=> x + y = 821
=> y + 71 + y = 821
=> 2y = 821 - 71
=> 2y = 750
=> y = 375
=> Cost of bench, y = $ 375
=> The cost of the garden table, x = $ 375 + $ 71 = $ 446
Therefore,
The cost of the bench is $ 375 and the Cost of the garden table is $ 446.
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Use the slope formula to find the slope of the line through the points (8,−3) and (−6,4)
Answer:
-1/2
Step-by-step explanation:
You want the slope of the line through points (8, -3) and (-6, 4) using the slope formula.
Slope formulaThe formula for the slope of the line through points (x1, y1) and (x2, y2) is ...
m = (y2 -y1)/(x2 -x1)
ApplicationFor the two given points, the slope is ...
m = (4 -(-3))/(-6 -8) = 7/-14 = -1/2
The slope of the line is -1/2.
The temperature in Austin is 65◦F and falling at a rate of 2 ◦F per hour. The temperature in Round Rock is 72◦F and falling at a rate of 3 ◦F per hour. Write an inequality that shows when the temperature in Round Rock is colder than that in Austin.
The inequality that shows how long the temperature in Round Rock will remain colder than that in Austin is 72 - 3t > 65 - 2t and the time is less than 13 hours
How to determine the inequality and the intervalsFrom the question, we have the following parameters that can be used in our computation:
Austin
Initial temperature = 65 degrees Fahrenheit
Rate of decrement = 2 degrees Fahrenheit
Round Rock
Initial temperature = 72 degrees Fahrenheit
Rate of decrement = 3 degrees Fahrenheit
The above parameters mean that
Current temperature = Initial temperature + Rate of increment x Number of hours
So, we have
Austin: A(t) = 65 - 2t
Round Rock: B(t) = 72 - 3t
When Round Rock is colder than Austin, we have
B(t) > A(t)
Substitute the known values in the above equation, so, we have the following representation
72 - 3t > 65 - 2t
Evaluate the like terms
-t > -13
Divide both sides by -1
t < 13
Hence, the interval is less than 13 hours
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The figure of the right is the result of a translation followed by a dilation of the figure on the left.
With the help of AA similarity rule option C,D,E,F will be the answer which is C:-∠ adc is 52.8°
D:- ∠ dac is 26.7°
E:- dac/adc = 0.506
F:- cd/bc =1.8
What is AA similarity rule?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.
Similar figures are items that feature more than two figures that are the same form but different sizes.
Despite having the same form, each might have different sizes.There are no matching angles that are not equal.Similar equivalent side ratios exist.When two triangles are comparable, all of their matching angle pairs and sides are congruent and proportionate. However, you do not necessarily need to have information about all of the sides and angles of two triangles in order to be certain that they are identical.
AA similarity rule
So, ∠ adc is 52.8°
and ∠ dac is 26.7°
So, the ratio of dac/adc = 0.506
And the ratio of side will also be equal as well which is 1.8
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Solve for x.
18
12
6.75
85.3
Step-by-step explanation:
32^2-24^2=448
square root 448=21
the small and large parallel line is 21=21
24+9=33
33^2+21^2=1530
square root 1530=39
39-32=7
~7~=6.75
x=6.75
Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a transit. Point C is 45 feet from point A and 69 feet from point B. The angle A C B is 52'. How far apart are points A and B?
Select one:
a. 93.3 feet
b. 69.8 feet
c. 76.7 feet
d. 103.5 feet
e. 54.4 feet
The value of distance between points A and B is 54.4 feet.
What is the law of cosine?
The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are known as the law of cosines states: c²=a²+b²−2ab cos C .
Solution:
Using the law of cosines we get:
(AB)²=(AC)²+(BC)²-2AC×BC×cos(C)
(AB)²= (45)²+(69)²-2(45)(69)cos(52°)
(AB)² = 2025 + 4761 - 3823.2577
∴ AB = 54.4 feet
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A boat is heading towards a lighthouse, where Jeremiah is watching from a a vertical distance of 126 feet above the water. Jeremiah measures an angle of depression to the boat at point A to be 11. The other measurement at point B is 78. Find the distance from point A to point B.
Using the given information, the distance from point A to point B is 568ft
How to find distance between two points?You should know that Distance is defined as the numerical or occasionally qualitative measurement of how far apart points are from each other.
The distance between A and B can be measured using the Trigonometric ratio of angles.
The drawing formed a right angled triangle.
Using the tangent function
Tan∅=[tex]\frac{opposite}{adjacent}[/tex]
Tan11⁰=x/126
x=126tan11⁰
Also, in the second angle of depression,
Using the tangent ratio as stated above,
y=126tan78⁰
The distance between A and B is given thus:
AB =126tan78⁰-126tan11⁰
AB =126*4.7046-126*0.1944
AB =592.78-24.4944
AB =568.28553
AB =568ft
In conclusion, the distance from point A to point B is 568ft
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The fox population in a certain region has a continuous growth rate of 9 percent per year. It is estimated that the population in the year 2000 was 21100.
(a) Find a function that models the population t years after 2000 ( t=0 for 2000).
Hint: Use an exponential function with base e.
(b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer must be an integer)
a) An exponential function to model the population of foxes in t years after 2000 is given by P(t) = 21,100 x 1.09^t.
b) From the exponential function from part (a), the estimated fox population in the year 2008 is 42,052.
What is an exponential function?An exponential function is a mathematical expression written in the form of y = ab^x.
Exponential functions can be used to model growth factors, especially the population of animals and bacteria increasing at a constant rate.
The continuous growth rate in the fox population = 9%
Estimated population of foxes in the year 2000 = 21,100
A function to model the population in t years after 2000: P(t) = 21,100 x 1.09^t
In 2008, the population function:
P(t) = 21,100 x 1.09^8
= 21,100 x 1.993
= 42,052
Thus, we can conclude that using the exponential function, the fox population growing at 9% per year reached 42,052 in 2008 from its 21,100 number in the year 2000.
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Station 2: Unit 3 and Unit Linear Functions given the table x 9,3,-3,-9 y 2,-2,-6,-10 ,
Find equation slope form answer the following questions.
Answer:
y = (2/3)x - 4
Step-by-step explanation:
To find the equation of the line in slope-intercept form given a table of values, you will need to calculate the slope of the line and the y-intercept. The slope of a line is a measure of its steepness, and it is calculated as the rise (change in y-values) divided by the run (change in x-values) between two points on the line. The y-intercept is the point at which the line crosses the y-axis.
Given the table x: 9, 3, -3, -9 and y: 2, -2, -6, -10, you can use any two points to calculate the slope. For example, you could use the points (9, 2) and (3, -2) to calculate the slope:
slope = (y2 - y1) / (x2 - x1) = (-2 - 2) / (3 - 9) = -4 / -6 = 2/3
To find the y-intercept, you can use the slope and one of the points from the table to substitute into the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Using the slope and the point (9, 2), you can solve for b:
y = mx + b
2 = (2/3) * 9 + b
2 = 6 + b
b = -4
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 4.
To answer the other questions, you can use this equation to determine the y-value for a given x-value or the x-value for a given y-value. You can also use the equation to graph the line on the coordinate plane.
Help Please!!!!!!!!!!!!
SHOW WORK PLEASE AND THANK YOU
Simplify this expression.
(4/5)² x (-25) - 4² =
Using PEMDAS, -32 is solution of (4/5)² x (-25) - 4².
Define PEMDAS.A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations. Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right). We are provided with the proper steps for solving a mathematical expression by the PEMDAS rule. Operations are carried out in parenthesis first according to the PEMDAS rule. The next step is to conduct operations on exponents or powers. Then, depending on which occurs first, the operations of multiplication and division are performed from left to right. The final step is to conduct addition or subtraction from left to right, depending on which comes first.
Given
(4/5)² x (-25) - 4²
Using PEMDAS,
Squaring the exponents,
16/25 × -25 - 16
Multiplying,
-16 - 16
Subtracting,
- 32
Using PEMDAS, -32 is solution of (4/5)² x (-25) - 4².
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Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.
The total area of the given figure is 68.56 units².
What do we mean by area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
On a sheet of paper, draw a square using a pencil.
It has two dimensions.
The area of a shape on paper is the area that it occupies.
Consider your square as being composed of smaller unit squares.
So, the total area of the given figure:
We can divide the figure into separate rectangles and circles:
Area of rectangle: l*b
14*4
56 units²
Area of circle: πr² (D = 4, R = 4/2 = 2)
πr²
3.14(2)²
3.14*4
12.56 units²
The total area of the figure:
56 units² + 12.56 units² = 68.56 units²
Therefore, the total area of the given figure is 68.56 units².
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1 - O produto das raízes reais da equação é igual a :
A) - 1,5
B) -0,5
C) 0,5
D) 1,5
Evan added -2 1/2+4 and got six 1/2 draw arrows on the number line to represent the problem and explains Evans error
Evan's error was that he subtracted [tex]-2\frac{1}{2}[/tex] from 4, and thus he got [tex]6\frac{1}{2}[/tex]. On adding he would be getting [tex]1\frac{1}{2}[/tex]
What is number line?
A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and decrease as we move to the left.
It is given that Evan added [tex]-2\frac{1}{2}[/tex] and 4 but got [tex]6\frac{1}{2}[/tex]
The mistake that Evan did was instead of adding, he substracted [tex]-2\frac{1}{2}[/tex] from 4, and thus he got [tex]6\frac{1}{2}[/tex]. This is because
4 - [tex]-2\frac{1}{2}[/tex]
= 4 + [tex]2\frac{1}{2}[/tex]
= [tex]6\frac{1}{2}[/tex]
This is wrong as he was asked to add and not to subtract.
Therefore, on adding [tex]-2\frac{1}{2}[/tex] and 4, we get,
= 4 [tex]-2\frac{1}{2}[/tex]
= [tex]1\frac{1}{2}[/tex]
Evan's error was that he subtracted [tex]-2\frac{1}{2}[/tex] from 4, and thus he got [tex]6\frac{1}{2}[/tex]. On adding he would be getting [tex]1\frac{1}{2}[/tex]
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-2\tfrac{1}{2}-\Big(-4\tfrac{3}{5}\Big)
−2 /2/1 −(−4 3/5)
The value of the fraction expression -2 1/2 - (-4 3/5) is 2 1/10
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
−2 /2/1 −(−4 3/5)
Express properly
So, we have the following representation
-2 1/2 - (-4 3/5)
Remove the brackets
This gives
-2 1/2 - (-4 3/5) = -2 1/2 + 4 3/5
Express the denominator as 10
So, we have
-2 1/2 - (-4 3/5) = -2 5/10 + 4 6/10
Evaluate the difference
-2 1/2 - (-4 3/5) = 2 1/10
Hence, the solution is 2 1/10
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You need to be at least 39.37 inches tall (about a meter) to ride on a bumper car. Diego’s cousin is 35.75 inches tall. How many more inches will he need to grow before Diego can take him on the bumper car ride? Explain or show your reasoning.
Answer: 3.62 inches
Step-by-step explanation:
Diego's cousin is too short for this ride, we know how tall he is now and what height he needs to be.
This can be solved by subtracting his needed height from his current height.
39.37-35.75=3.62 inches
solve for x. enter the solutions from least to greatest (x+7)^2-11=0
Answer:
[tex]x=-7-\sqrt{11}, -7+\sqrt{11}[/tex]
Step-by-step explanation:
[tex](x+7)^2=11 \\ \\ (x+7)=\pm \sqrt{11} \\ \\ x=-7-\sqrt{11}, -7+\sqrt{11}[/tex]
Liam works at a zoo. He was looking at some data showing the masses of their
5
55 African elephants. The mean mass of the elephants was
3
,
800
kg
3,800kg3, comma, 800, start text, k, g, end text, and the median mass was
3
,
600
kg
3,600kg3, comma, 600, start text, k, g, end text. The smallest elephant, named Lola, weighed
2
,
700
kg
2,700kg2, comma, 700, start text, k, g, end text.
Lola then got very sick and lost weight until her mass reached
1
,
800
kg
1,800kg1, comma, 800, start text, k, g, end text.
How will Lola's mass decreasing affect the mean and median?
Median won't change, however Mean will fall by 180.
What do mean and median?By summing all the numbers in a data collection and dividing by the total number of values in the set, one may get the mean (average) of the data set. When a data collection is sorted from least to largest, the median represents the midpoint value.
African elephants total 555 in number.
Elephants had a 3800 kg average mass.
Elephants had a 3600 kg median mass.
Lola, the elephant that was the smallest, weighed 2700 kg.
Later, Lola became really ill and lost a lot of weight, reaching a mass of 1800 kg.
What effect will Lola's weight loss have on the mean and median as well as Currently, the median is 3600 and the lowest is 2700.
now 2700 becomes 1800
so Median remains the same as 3600
No change in Median
The mean mass of the elephants was 3800 kg
=> total weight = 5 x 3800 = 19000 kg
2700 kg becomes 1800 kg
Hence new total mass = 19000 - 2700 + 1800 = 181000 kg
New Mean = 18100/5 = 3620 kg
Mean reduced by 3800 - 3620 = 180 kg
No change in Median weight
Mean reduced by 180 kg
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The Bateria in a culture increases according to the law [tex]\frac{ds}{dt} = \frac{N}{4}[/tex]
if intially N = 200, then what is thevalue of N when t = 200
The required value of N when t = 200 is given as 10,000.
Given that,
The Bateria in culture increases according to the law ds/dt = N/4
if intially N = 200, then what is the value of N when t = 200 is to be determined.
Rate of change is defined as the change in value with rest to the time is called rate of change.
Here,
ds/dt = N/4 = 200/4 = 50
Now,
N = 50t
N = 50[200]
N = 10,000
Thus, the required value of N when t = 200 is given as 10,000.
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Legs have length of 4 find the length of the hypotenuse
Answer:
4√2
Step-by-step explanation:
hypotenuse = [tex]\sqrt{4^2 + 4^2} = \sqrt{16 + 16} =\sqrt{2*16} = 4\sqrt{2}[/tex]
Determine whether the expressions are equivalent.
8 x+4 y is to 4(2 x+1)
Not equivalent. 8 x+4 y=6 x(4 y+2 x)
Equivalent. 8 x+4 y=8(x+4 y)
Not equivalent. 8 x+4 y=4(2 x+y)
Equivalent. 8 x+4 y=4(2 x+1)
From the given expressions the equivalent expression is,
8x + 4y = 4(2x + y).
What is equivalent expression?
Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).
Consider, the given expression
8x + 4y and 4(2x + 1)
Consider, 4(2x + 1)
Simplifying this,
4(2x + 1) = 8x + 4
8x + 4 is different from 8x + 4y.
Hence, 8x + 4y is not equivalent to 8x + 4.
Now consider, 8x + 4y = 6x(4y + 2x)
Simplifying this
8x + 4y = 24xy + 12x^2
⇒ 8x + 4y = 6x(4y + 2x) is not equivalent.
Now consider, 8x + 4y = 8(x + 4y)
(8x + 4y) = 8x + 32y
⇒ 8x + 4y = 8(x + 4y is not equivalent.
Now consider, 8x + 4y = 4(2x + y)
8x + 4y = 8x + 4y
⇒ 8x + 4y = 4(2x + y) is equivalent.
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What is 136 simplified. Use the fx button above to access the button.
Rewatch
Next question
The simplified expression of √136 is 2√34
How to determine the simplified expression?From the question, we have the following parameters that can be used in our computation:
√136
Expand the expression
So, we have the following representation
√136 = √68 * 2
Further, expand the expression
So, we have the following representation
√136 = √34 * 2 * 2
So, we have
√136 = √34 * 4
Take the square root
√136 = 2√34
The expression cannot be further simplified
Hence, the solution is 2√34
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The midpoint of AB is at (-2.3). If A=(7,-6) , find B.
Answer:
Step-by-step explanation:
mid point = a+b/2
let b(x,y)
-2 = [7+x]/2 3 = [-6+y]/2
-4 = 7 + x 6 = -6 + y
-11 = x 12 = y
Hence B is at (-11,12)
If 3000 dollars is invested in a bank account at an interest rate of 10 per cent per year, Find the amount in the bank after 10 years if interest is compounded annually:
Find the amount in the bank after 10 years if interest is compounded quaterly:
Find the amount in the bank after 10 years if interest is compounded monthly:
Answer:
Step-by-step explanation:
100%-10%=90%
90/100=0.9%
3000*0.9^10 years= 1046.04
Step-by-step explanation:
For annually,
3000×(1.10)^10= 7781.23
For quarterly,
3000×(1.10)^40= 135777.77
For montly,
3000×(1.10)^120=278127206.5
A student sees a bird on top of a 15 foot high light pole. The angle of elevation to the top of the light pole is 35 degrees. How far is the student standing from the base of the light pole?
The distance of the student from the light pole is 21.4 feet.
How to find the distance of the student from the light pole?A student sees a bird on top of a 15 foot high light pole. The angle of elevation to the top of the light pole is 35 degrees.
The distance of the student from the pole can be calculated as follows:
The situation forms a right angle triangle.
using trigonometric ratios,
tan 35 = opposite / adjacent
tan 35 = 15 / x
cross multiply
x tan 35 = 15
divide both sides by tan 35
x = 15 / tan 35
x = 15 / 0.70020753821
x = 21.4222201012
x = 21.4 feet
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please help ASP ....
Answer:
B. Reflexive Property
Step-by-step explanation:
The statement is that BC ~= BC. That is, that BC is congruent to itself. The reason is that all numbers are equal to themself. Angle measures are equal to themself. Segments are equal to themself.
Like looking at a reflection in a mirror. The word "reflection" can help you memorize the reason why something is equal to itself:
Reflexive Property
La suma del triple de un número más el doble de otro número distinto al cuadrado
Procedimiento:
Empezamos separando el problema por partes. En este caso, a "un número" le daremos el nombre "x", y al "otro número distinto" le daremos el nombre "y".
1. Entonces, "el triple de un número" significa que es el triple de "x". En otras palabras, es 3 veces "x", osea:
3x
2.Como dice "la suma", entonces sabemos que nuestro 3x se va a sumar con otro término, entonces nuestro enunciado está quedando así:
3x+
3.El segundo término de la suma es "el doble de otro número distinto al cuadrado". Si el "otro número distinto" es "y", tenemos que "el doble" de "y" es 2 veces "y", osea, "2y".
Finalmente, se explica que este término está al cuadrado, lo cual daría que nuestro segundo término sea (2y)^2.
4.Entonces, la expresión completa es:
3x+(2y)^2