The lines, y = -1 and x = 1 are perpendicular lines.
What are Perpendicular Lines?If two lines are perpendicular to each other, it means they form right angle at the point of intersection, and also, they have slopes that are negative reciprocals to each other.
Also, vertical and horizontal lines are perpendicular to each other because horizontal line has a slope that is zero while vertical line has an undefined slope.
y = -1 is a horizontal line, while x = 1 is a vertical line. Therefore, we can concluded that, they are perpendicular to each other.
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100 POINTS! How many roots does the polynomial equation have?
0=x^3(x+3)(x−1)^2
Answer: There are none
Step-by-step explanation:
A persons blood has a pH of 7.371 and a carbonic acid concentration of 1.5, Approximate the concentration of bicarbonate in the persons blood.
Answer: The pH of blood is a measure of its acidity or basicity and is related to the concentration of hydrogen ions (H+) in the blood. The pH of 7.371 indicates that the blood is slightly basic. Carbonic acid (H2CO3) is a weak acid that dissociates into bicarbonate (HCO3-) and hydrogen ions (H+) in water. The carbonic acid concentration of 1.5 indicates the concentration of H2CO3 in the blood.
The concentration of bicarbonate (HCO3-) in the blood can be approximated by using the relationship between the pH, carbonic acid concentration and the bicarbonate concentration. The Henderson-Hasselbalch equation, which relates the pH and the pK of a buffer, to the ratio of the buffer's conjugate base to its acid form is:
pH = pK + log [HCO3-]/[H2CO3]
The pK of carbonic acid is 6.1 and the concentration of H2CO3 is given as 1.5.
Plugging these values into the Henderson-Hasselbalch equation,
7.371 = 6.1 + log [HCO3-]/1.5
Solving for [HCO3-],
[HCO3-] ≈ 25.8 mM
The approximate concentration of bicarbonate (HCO3-) in the person's blood is 25.8 mM.
Please note that this is an approximation, the actual value may vary depending on the person's health condition.
Step-by-step explanation:
Given the scatter plot, choose the function that best fits the data.
f(x) = 2^x
f(x) = 2x
f(x) = −2x
f(x) = 2x^2
The given scatter plot depicts the exponential function. Therefore, option 1 f(x) = 2ˣ is the correct one.
A scatter plot is a particular kind of graphic diagram that uses Cartesian coordinates to show the values of two variables for a collection of data.
We write y as the function of x as y=f(x). Here, f is considered the name of the function and x is the value of the function. To check which function depicts the given scatter plot, we have to substitute the values for x and find the function. Then, plot the graph.
By doing we get, the plot for f(x) = 2ˣ is equivalent to the given scatter plot. Because this graph depicts the exponential function where the graph passes through the point (0,1). Therefore, option 1 correctly depicts the given plot. Option 2 depicts the identity function and 4 depicts squaring or quadratic function.
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A rectangle has dimensions of x + 3 and x - 4. Find the area and the perimeter.
Step-by-step explanation:
The area of a rectangle is given by the formula:
Area = length * width
In this case, the length of the rectangle is given by x + 3 and the width is given by x - 4.
Therefore, the area of the rectangle is:
Area = (x + 3) * (x - 4)
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
In this case, the length of the rectangle is given by x + 3 and the width is given by x - 4.
Therefore, the perimeter of the rectangle is:
Perimeter = 2 * ((x + 3) + (x - 4)) = 2x - 2
So the area of the rectangle is (x + 3)(x - 4) and the perimeter is 2x - 2.
give me brainlist
Answer: Area= x^2-x-12 , Perimeter = 4x-2
Step-by-step explanation: According to the question,
Length = x+3
Breadth = x-4
Area of a rectangle = Length * breadth
Area = (x+3)(x-4)
Area = x^2-x-12
Perimeter of rectangle = 2*(length+ breadth)
Perimeter = 2* (x+3+x-4)
= 2*(2x-1)
= 4x-2
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Prove that circle A with center (1, 1) and radius 4 is similar to circle B with center (–4, –2) and radius 3
Since they are not the same, they are not the exact same circles. In other words they are similar.
Since the center point does not affect the size of the circle.
Now, According to the question:
Figures can be proven similar if one, or more, similarity transformations
reflections, translations, rotations, dilations can be found that map one
figure onto another.
To prove all circles are similar, a translation and a scale factor from a
dilation will be found to map one circle onto another
Lets solve the problem
Circle A has center (1 , 1) and radius 4
The standard form of the equation of the circle is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex] , where (h , k) are the coordinates the center
and r is the radius
Equation circle A is [tex](x -1)^2 + (y - 1)^2 = (4)^2[/tex]
Equation circle A is : [tex](x -1)^2 + (y - 1)^2 = 16[/tex]
[tex]x^{2} +1-2x+y^2+1-2y=16\\\\x^2 +y^2-2x-2y+2=16\\\\x^2 +y^2-2x-2y-14=0\\\\x^2+y^2= 14+2x+2y[/tex]
Circle B has center (-4 , -2) and radius 3
Equation circle B is [tex](x - (-4))^2 + (y - (-2))^2 = (3)^2[/tex]
Equation circle B is [tex](x +4)^2 + (y +2)^2 = 9[/tex]
[tex]x^2+16+8x+y^2+4+4y=9\\\\x^{2} +y^2+20+8x+4y=9\\\\x^2+y^2+8x+4y+11=0[/tex]
By comparing between the equations of circle A and circle B
As you can see, if we try to equate the [tex](x^2 + y^2)'s[/tex], the values of them are not the same. Since they are not the same, they are not the exact same circles. In other words they are similar.
You can also compare the radii as well, since the center point does not affect the size of the circle.
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Factored form of 6+27 using GCF
The factored form of 6 + 27 is 3(2 + 9) using GCF.
What is GCF?The greatest common factor, which is the product of two or more numbers, is the biggest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's components have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF)
The given expression is:
6 + 27
Take the factors of the individual numbers:
6 = 1, 2, 3, 6
27 = 1, 3, 9, 17
Take the common factor from both the numbers, in this case it is 3.
Now, factor out the number from the given expression:
6 + 27
3(2 + 9)
Hence, the factored form of 6 + 27 is 3(2 + 9) using GCF.
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why use the sum function with a range of cells when adding the values together accomplishes the same thing?
It saves time, doesn't need to be changed if a row or column is added to the range, and adjusts the range when the function is copied to another cell.
Based on the values in another column, we'll discover how to add up a column of numerical data. We are attempting, for instance, to assess product sales based on the typical customer rating. Thus, each of our products has an average rating of 9.8, 7.2, 6.1, and so on because customers score our products on a scale of 1 to 10. The sales totals for goods with ratings of 9 to 10, 7 to 8, and so forth should be calculated.
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The temperature of one furnace is 1,200°C and cools at a rate of 3.5°C per minute. The temperature of another furnace is 900°C and is heated at a rate of 0.5°C per minute. After how many minutes will the furnaces be the same temperature?
Answer:
525 minutes
Step-by-step explanation:
Let us find the temperature of each furnace after 't' minutes.
Furnace1:
Temperature in furnace1 is reducing at rate of 3.5°C per minute.
Rate of cooling after t minute = 3.5*t = 3.5t
We have to subtract 3.5t from 1200°C as it is cooling.
Temperature of furnace1 after 't' minutes = 1200 - 3.5t
Furance2:
Temperature in furnace2 is increasing at rate of 0.5°C per minute.
Rate of heating after t minute = 0.5*t = 0.5t
We have to add 3.5t from 900°C as it is getting heated.
Temperature of furnace1 after 't' minutes = 900 +0.5t
After some minutes, both furnace reach the same temperature.
900 + 0.5t = 1200 - 3.5t
900 + 0.5t + 3.5t = 1200
4t = 1200 + 900
4t = 2100
t = 2100 ÷ 4
[tex]\boxed{t = 525 \ minutes}[/tex]
3/4 + 1/3 what is it
Answer:
[tex] \frac{3}{4} + \frac{1}{3} \\ \frac{ \: \: 9 \: \: + \: \: 4 \: \: }{12} \\ \frac{13}{12} [/tex]
Please help like ASAP find the value of X please ASAP
The value of x is 15 and the angles in the pentagon are 105,49,90,33,83
What is interior angles in a pentagon ?
The interior angles in a pentagon are the angles which are inside the pentagon and sum of the interior angles in a pentagon is 540 degrees.
Given ,
From the figure we can say that it is pentagon.
And the sum of exterior angles in a pentagon is always 360 degrees.
SO,
7x+49+6x+33+83 = 360
13x + 165 = 360
13x = 360 - 165
13x = 195
x = 195 / 13
x = 15
So, the angles could be 7x = 7*15 = 105 and 6x = 6*15 = 90
Therefore, The value of x is 15 and the angles in the pentagon are 105,49,90,33,83 .
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If f(x)=2x^3+6x^2+18x-26f(x)=2x
3
+6x
2
+18x−26 and x-1x−1 is a factor of f(x)f(x), then find all of the zeros of f(x)f(x) algebraically.
Upon factorization, The factors of the equation be x = 1, x = -2 + 3i, x = -2 - 3i and x = 1.
What does "factorizing method" mean?In mathematics, factorization or factoring is the process of breaking down one entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication produces the original number, matrix, etc.
Factorization is the process of shrinking the bracket of a quadratic equation, as opposed to widening the bracket and turning the equation into a product of factors that cannot be further reduced.
To solve a quadratic equation by factoring, factor the expression, set each factor equal to 0, and then solve each equation. To accomplish this, set up the terms in the equation so that the other side equals 0.
Let the given equation be f(x) = 2x³ + 6x² + 18 x - 26 and x - 1 then
2x³ + 6x² + 18x - 26 = 0
Factor 2x³ +6x² +18x-26: 2(x-1) (x²+4x+13)
2(x-1) (x²+4x+13) = 0
Using the Zero Factor Principle: If ab=0 then a=0 or b=0, x-1=0 or
Solve - 1=0:
x = 1
Solve x² + 4x + 13 = 0: x² + 3i, x = - 2 - 3i
The solutions are
x = 1, x = -2+31, x = -2 - 31
The given equation be x - 1,
x-1= 0 then x = 1.
Therefore, the factors of the equation be x = 1, x = -2 + 3i, x = -2 - 3i and x = 1.
The complete question is:
If f(x) = 2x²+6x²+18x-26 and x-1 is a factor of f(x), then find all of the zeros of f(x) algebraically.
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a college has 10 time slots for its courses, and blithely assigns courses to completely random time slots, independently. the college offers exactly 3 statistics courses. what is the probability that 2 or more of the statistics courses are in the same time slot?
Probability that 2 or more of the statistics courses are in same slot is 0.28.
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
probability that 2 or more of the statistics courses are in same slot
=1-P(all 3 are in different slots)
=1-P(select 3 from 10 slots and arrange them)
=1-(10*9*8)/10^3
=0.28
Therefore, probability that 2 or more of the statistics courses are in same slot is 0.28.
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The constant of the polynomial function f(x)=-(x+3(x+7)²(x-1)⁵(x+1)⁷(x-4) is
Answer:
The constant of a polynomial function is the coefficient of the term with the highest degree (the term with the highest power of x), which in this case is 0. Therefore, the constant of the polynomial function f(x)=-(x+3(x+7)²(x-1)⁵(x+1)⁷(x-4) is 0.
−9(5 − 6x)
answers:
A 45 − 54x45 − 54x
B −45 − 54x−45 − 54x
C 45 + 54x45 + 54x
D −45 + 54x
Answer:
[D] -45 + 54x
Step-by-step explanation:
Base on the given we can use the distributive property to solve this:
Distributive property ⇒ Multiply outside numbers with each term inside the parenthesis.
-9 (5 - 6 x ) → {-9 × 5 = -45 } {-9 × -6x = 54x}
Now let's put it together;
-45 + 54x
Hence, [D] -45 + 54x is the correct answer.
RevyBreeze
A 5. 5kg bowling ball initially at rest is dropped from the top of a 12 m building. It hits the ground 1. 75s later. Find the net external force on the falling ball?
The net external force acting on the freely falling ball is 43.12 N.
We are provided with the following information:
Mass of bowling ball (m) = 5.5kg
Distance travelled by the ball (h) = 12m
Time taken by the ball = 1.75 s
To calculate the net force acting on the ball, we first need to calculate the acceleration experienced by the ball under free fall.
We can determine the acceleration using the formula,
d= ut + (1/2)at^2
since, the ball was initially at rest, u=0.
Thus, formula becomes,
d= (1/2)at^2.
Therefore, a= 2d/t^2
=> a= 2*12/(1.75)^2
=> a=24/ 3.0625
=> a= 7.84 m/s^2
Now, according to Newton's 2nd law of Motion,
[tex]F_{net} = mass * acceleration[/tex]
[tex]F_{net}[/tex] = 5.5 * 7.84 N = 43.12 N
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Your cousin is building a new house. The layout of the first floor is shown in the diagram above. Using the
diagram and knowledge of polynomials find the following:
1. Write a polynomial that represents the length of the north side of the house. Then simplify the
expression.
2. Write a polynomial expression that represents the area of the kitchen. Then multiply to put the
polynomial in standard form.
3. Write a polynomial expression that represents the area of the bedroom. Then multiply to put the
polynomial in standard form.
4. Find the dimensions of the bathroom in terms of x. (Hint the west and east side of the house
should be equal.)
The polynomial for the north side of the house will be 2x^2+9x-32.
What are polynomials?
Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.
Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.
Now,
As the north side will be the sum of 5x-4,x^2-23 and 4x-5
so the polynomial for north will also be the sum of 5x-4,x^2-23 and 4x-5.
Hence,
Polynomial for north side= 5x-4 + x^2-23 + 4x-5
Polynomial for north side =2x^2+9x-32
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You spent $250 on your credit card. It has been 5 years and you have a 3.75% interest rate. How much interest do you owe?
Answer:
1050$
Step-by-step explanation:
HELP!!!!!!
50 POINTS
Answer:
see explanation
Step-by-step explanation:
1
20% of 35
= [tex]\frac{20}{100}[/tex] × 35
= 0.2 × 35
= 7
(2)
60% of 70
= [tex]\frac{60}{100}[/tex] × 70
= 0.6 × 70
= 42
(3)
45% of 80
= [tex]\frac{45}{100}[/tex] × 80
= 0.45 × 80
= 36
Answer:
busy work lol. its = not smart
Step-by-step explanation:
Carver's Auto Custom has two potential retail spaces to choose from.
Warehouse Space A: Includes 8000 sq. Ft. Of showroom and workshop space. It rents for. 85 cents
ar safl per month and an additional 25. Cents per sq. Ft, per month for operations expenses. One
half of this warehouse space will be used to stock paint cans and rims.
According to the area value, the amount required to be paid for the showroom is $2000.85
The term area in math is known as the region bounded by the shape of an object or it is the space covered by the figure or any two-dimensional geometric shape.
Here we have know that Warehouse Space A Includes 8000 sq. Ft. Of showroom and workshop space and it rents for. 85 cents per month and an additional 25. Cents per sq. Ft, per month for operations expenses.
While we looking into the question, we know that the following are known,
Area = 8000 square feet.
Rent = 85 cents.
Additional expenses = 25 cent per square feet.
Then the total expense is calculated as,
=> 85 + (8000 x 25)
=> 200085 cents.
When we convert into dollars, then we get,
=> One dollar = 100 cents.
Then the resulting value is
=> $2000.85
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substitute 6x-5y=-1 and 6x+4y=-10
Answer:
x=-1 y=-1
Step-by-step explanation:
i am lazy to type
Answer:{x = -1}{y = -1}
Step-by-step explanation:
subtract the two equations
{6x - 5y = -1 ^
{6x + 4y = -10 ^
determine the sign
6x - 5y - (6x +4y) = -1 - (-10) ^
simplify
6x - 5y - 6x - 4y = -1 + 10 ^
substitute
y = -1 ^
solve the equation
6x + 4 x (-1) = -10 ^
write the solution
x = -1 ^
Select one or more expressions that together represent all solutions to the equation. Your answer should be in degrees.
Assume
�
nn is any integer.
7
cos
(
9
�
)
−
1
=
1
7cos(9x)−1=17, cosine, left parenthesis, 9, x, right parenthesis, minus, 1, equals, 1
The trigonometric equation 7cos(9x) - 1 = 17 has an undefined solution.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
7cos(9x) - 1 = 17
Isolating the cosine, we have that:
7cos(9x) = 18
cos(9x) = 18/7
Now we isolate x applying the arc cosine, which is the inverse of the cosine, as follows:
9x = arccos(18/7)
9x = undefined.
The solution is undefined because the arccosine only exists for values between -1 and 1, as the cosine of an angle is always going to assume a value between -1 and 1.
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4% of what number is 77
Answer:
1935
Step-by-step explanation:
Step 1: If 4% of a number is 77, then what is 100% of that number? Setup the equation.
77
4% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
4Y = 77 x 100
4Y = 7700
Y = 7700
100 = 1,925
The population of alaska is approximently 6. 5 x 10^5 people. The population of illinois is about 1. 3 x 10^7 people. How many times greater is the population of illinois than alaska
After finding the ratio, the population of Illinois than Alaska is 20 times greater.
The population of Alaska is approximately 6.5 x [tex]10^5[/tex] people.
The population of Illinois is about 1.3 x [tex]10^7[/tex] people.
We have to find how many times greater is the population of Illinois than Alaska.
We will use their population ratio to determine how many times the population of Illinois is greater than the population of Alaska.
Ratio = Population of Illinois's /Population of Alaska
Ratio = 1.3 x [tex]10^7[/tex]/6.5 x [tex]10^5[/tex]
Now simplifying.
Ratio = 0.2 x [tex]10^2[/tex]
Ratio = 20
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a pitcher won 75%of the games she pitched. she pitched 60 games. how many games did she win
= 75
75 ___ × 60
75 ___ × 60 100
75 ___ × 60 100= 3
75 ___ × 60 100= 3 ___ × 60
75 ___ × 60 100= 3 ___ × 60
75 ___ × 60 100= 3 ___ × 60 4
75 ___ × 60 100= 3 ___ × 60 4= 45
the area of four walls of room is 90m if the rom is 7 m long and 2m wide , then find the height of the room
The height of the room is 5 m.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Length = 7 m
Width = 2 m
Height = x
Four walls of a room will have,
Two walls of length x height.
Two walls of Width x height.
Now,
Area four walls of the room = 90 m
2 (length x height) + 2 (Width x height) = 90
2 (7x) + 2 (2x) = 90
14x + 4x = 90
18x = 90
x = 5
Thus,
Height of the room = 5 m.
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Daniel mows lawns on the weekends. He graphed his earnings below.
What is the rate he charges to mow?
A.
$11.50 per lawn
B.
$13.00 per lawn
C.
$30.00 per lawn
D.
$7.50 per lawn
Answer:
where's the graph?
Step-by-step explanation:
Which number is less than 5/8 but greater than 1/9?
A number that is less than 5 / 8 but is greater than 1 / 9 is A. 0. 5.
How to find the number ?To find the number that is less than 5 / 8 but greater than 1 / 9, first convert both fractions to decimals.
5 / 8 in decimals is:
= 5 / 8
= 0. 625
1 / 9 in decimals is:
= 1 / 9
= 0. 111
The number from the given options that is less than 5/8 but greater than 1/9 is therefore 0. 5 as it is less than 5 / 8 but more than 1 / 9.
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The options for the question include:
0.50.80.90.05Consider the equations f(x)=1/x and g(x) = (x-1)^2-1. To the nearest tenth, what is the solution of f(x)=g(x)?
The solution of equation f(x)=g(x) is 2.
How do equations work?a formula that illustrates the relationship between the two expressions on either side of a sign. Usually, it has one variable and an equal sign. similar to 2. 2x - 4 = 2. The equals sign (=) in equations indicates that two expressions are equal. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.
The "left hand side" and "right hand side" of the equation refer to the expressions on each side of the equals sign. The right side of an equation is frequently thought of as zero.
Given : f(x)=g(x)
1/x = (x-1)^2-1
1 = x (x-1)² - 1
x (x-1)² = 2
x ( x² + 1 - 2x ) = 2
x³ + x - 2x² = 2
x³ + x - 2x² - 2 = 0
x³ - 2x² + x - 2= 0
x²(x-2) + 1(x-2) = 0
(x² +1) + (x-2) = 0
So, x = 2 .
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Brad is standing on a hill which places him at the same height as a nearby flagpole.
The flagpole is 15 ft. High and Brad is 20 ft. Horizontally from the top of the pole.
Brad can see the bottom of the flag pole.
What is the length in feet of Brad's "line of sight" to the base of the flagpole?
As per the Pythagoras theorem the length in feet of Brad's "line of sight" to the base of the flagpole 25 feet².
In math the term called Pythagoras theorem is states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
The standard form of the Pythagoras theorem is written with the help of the triangle ABC as,
=> AC² = AB² + BC²
where AC refers the hypotenuse and AB and BC refers the sides of the triangle.
Here we know that it follows from the task content that the length in feet of Brad's line of sight to the base of the flag pole is to be determined.
And here we also know that the flag pole in discuss is said to be 15 feet high.
And here we have also identified that Brad is at the same height as the pole and is at a horizontal distance of 20 feet from the top of the pole.
Then the length is calculated as,
=> l² = 15² + 20²
=> l² = 225 + 400
=> l² = 625
=> l = 25.
Hence the length of the line of sight is 25 feet.
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how do you prove an angle is a right angle when the other 2 angles are complementary in a triangle theorem
The two non-right angles in a right angled triangle balance each other out because the right angle already takes up 90 degrees of the triangle's 180 total angles. We refer to two angles as complementing each other when their sums equal 90 degrees.
The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The sum of the other two inner angles is 90 degrees. Base and perpendicular are the names of the other two sides that are close to the right angle. The Pythagorean Theorem is a triangle formula.
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