The distance between the points B and H on the coordinate plane is 4.48 units
What is the distance between the points B and H?See below for the complete question
The coordinates of the points B and H are given as:
(-2.63, 7) and (1.85,7)
Rewrite properly as
B = (-2.63, 7)
H = (1.85,7)
The distance between any two points on a coordinate plane is calculated using the following distance formula
d = √(x2 - x1)^2 + (y2 -y1)^2
Substitute the known values in the above distance equation
So, we have
d = √(-2.63 - 1.85)^2 + (7 - 7)^2
Evaluate the exponents
So, we have
d = √20.0704 + 0
Evaluate the sum
So, we have
d = √20.0704
Evaluate the exponent
So, we have
d = 4.48
Hence, the distance between the points B and H on the coordinate plane is 4.48 units
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Possible question
Find the distance between B (-2.63, 7) and H (1.85,7)
Simplify. √75 + √125
The value of the expression √75 + √125 is 5 (√3 + √5 ).
A number is a fundamental mathematical unit. For counting, measuring, and comparing quantities, we utilize numbers. A set of symbols, or numerals, used to represent numbers is known as a number system.
A square root is a factor of a number that yields the original number when multiplied by itself.
Consider the expression √75 + √125,
Let's assume x = √75 + √125
Now,
75 = 5 × 15 = 5 × 3 × 5
125 = 5 × 25 = 5 × 5 × 5
Therefore,
x = √75 + √125
x = √ [ 5 × 3 × 5] + √ [ 5 × 5 × 5 ]
x = 5√3 + 5√5
x = 5 × [ √3 + √5 ]
x = 5 × [ 1.73 + 2.24 ]
x = 5 × 3.97
x = 19.85
√75 + √125 = 19.85
Hence, the value of √75 + √125 is equal to 19.85.
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what is the square of -3
Answer:
The square of -3 is 9
Step-by-step explanation:
(-3)^2=9
Find the center, vertices, and foci of the ellipse with equation x squared divided by 9 plus y squared divided by 25 = 1
Answer:
Center: (0,0)
Vertices: (0,-5), (0,5)
Foci: (0,-3) (0,3)
Step-by-step explanation:
Suppose you invest $ 500 in a savings account that pays 3.5 % annual interest. How much will be in the account after five years?
Amount $593.84 will be in the account after five years.
According to the question we have been given that the
amount invested initially = $500
annual interest rate = 0.035
Time = 5 years.
The formula for the future value is given as
[tex]FV = a(1 + r)^{t}[/tex] (1)
where , FV = future value
a = amount invested initially
r = annual interest rate
t = time
putting the required values in equation (1) we get
[tex]FV = 500 (1 + 0.035)^{5} \\FV = 500 ( 1.035)^{5}[/tex]
FV = 500*1.188
FV = $ 593.84
Thus, $593.84 will be the amount in the account after five years.
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Identify all rays and lines in the picture below.
According to this definition given below, we identify all lines and rays as follows, EA, EB, EC, and ED are rays, and ED and BE are, Line.
A line is, it is actually difficult to give a good mathematical definition. Roughly, we can say that a line is an infinitely thin, infinitely long collection of points extending in two opposite directions. When we draw lines in geometry, we use an arrow at each end to show that it extends infinitely.
A line can be named either using two points on the line (for example, AB←→ ) or simply by a letter, usually lowercase (for example, line m ).
A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line.
___
A segment is named by its two endpoints, for example, AB.
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.
A ray is named using its endpoint first, and then any other point on the ray (for example, BA−→− ).
according to this definition, EA EB EC ED are rays, and ED, and BE are Line
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If x= -2, the value of the expression 3x² - 5x +1/x is
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{3x^2 - 5x + 1}{x}}\\\\\mathsf{= \dfrac{3(-2)^2 - 5(-2) + 1}{-2}}\\\\\mathsf{= \dfrac{(3)(4) - (5)(-2)+1}{-2}}\\\\\mathsf{= \dfrac{12 - (5)(-2)+1}{-2}}\\\\\mathsf{= \dfrac{12 - (-10) + 1}{-2}}\\\\\mathsf{= \dfrac{12 + 10 + 1}{-2}}\\\\\mathsf{= \dfrac{22 + 1}{-2}}\\\\\mathsf{= \dfrac{23}{-2}}\\\\\mathsf{-11 \dfrac{1}{2}}\\\\\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{-11\dfrac{1}{2}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]the sum of three is 131 the second of three numbers is seven more than twice the first the third number is 12 less then the first what equation can be used to solos this problem
Answer:
4x - 5 = 131 where x is the first number.
Step-by-step explanation:
Let the first number be x.
Seconder number = 2x + 7.
Third number = x - 12.
So, the equation is :-
x + 2x + 7 + x - 12 = 131
4x - 5 = 131
4x = 136
x = 34
First number = 34, second = 2(34) + 7 = 75 and third number = 34-12 = 22.
PLease help!!!! 3( - 4y - 5) = 8y + 25, Show your work please!!
Answer:
y = -2
Step-by-step explanation:
Given equation:
[tex]3(-4y-5)=8y+25[/tex]
Distribute:
[tex]\implies 3 \cdot -4y - 3 \cdot 5=8y+25[/tex]
[tex]\implies -12y - 15=8y+25[/tex]
Add 15 to both sides:
[tex]\implies -12y - 15+15=8y+25+15[/tex]
[tex]\implies -12y =8y+40[/tex]
Subtract 8y from both sides:
[tex]\implies -12y-8y =8y+40-8y[/tex]
[tex]\implies -20y =40[/tex]
Divide both sides by -20:
[tex]\implies \dfrac{-20y}{-20} =\dfrac{40}{-20}[/tex]
[tex]\implies y =-2[/tex]
Now we have to,
→ solve for the required value of y.
Let's solve the problem,
→ 3(-4y - 5) = 8y + 25
→ -12y - 15 = 8y + 25
→ -12y - 8y = 25 + 15
→ -20y = 40
→ y = -40/20
→ [ y = -2 ]
Hence, the value of y is -2.
If an airplane can travel at 20,000 miles per hour, how many meters per second does it travel? Knowing that: 1 mi 1.609 km
Answer: 8,938 [tex]\frac{8}{9}[/tex] or 8,938.8889 meters per second
Step-by-step explanation:
To solve this problem, we will use a process called dimensional analysis (that you have probably done many times without realizing it).
What is dimensional analysis? Let's say you know there are 12 inches in a foot, and you want to know how many inches are in 2 feet. 12 * 2 = 24 inches in a foot, that's dimensional analysis!
Here is the process you would take to solve your problem:
➜ If we have the units [tex]\frac{hour}{hour}[/tex], they "cancel" out to become one. This way, we make sure we end up with the correct units, [tex]\frac{meters}{second}[/tex].
➜ We take units we know, such as 3,600 seconds in an hour, and multiply them by the original value until we end up with the measurement we want.
[tex]\displaystyle 20,000\; \frac{miles}{hour}*\frac{1 \;hour}{3,600\; seconds} *\frac{1,609\;meters}{1\;mile}=\frac{20,000*1*1,609\;meters}{3,600\;seconds} =\frac{32,180,000\;meters}{3,600\;seconds} = 8,938.89\; \frac{meters}{second}[/tex]
In other words;
8,938.89 meters per second
f(x)=10 x-10 . Find each value.
(f ⁰ f⁻¹)(-10)
The inverse function returns the original value for which the output of a function was given.
The value of f(x) = 10x - 10 is -110.
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.
Lett the function be F(x) = 10x - 10
To differentiate with respect to X
F⁻¹(x) = 10
F( f⁻¹(x)) = F(10)
F( f⁻¹(x)) = -10x -10
Substitute the value of X = 10, then we get
F( f⁻¹(x)) = -10(10)-10
simplifying the above equation, we get
F( f⁻¹(x)) = -100-10
F( f⁻¹(x)) = -110
Therefore, the value of (f ⁰ f⁻¹)(d) = -110.
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Nayeli went to the grocery store and bought bottles of soda and bottles of juice. each bottle of soda has 25 grams of sugar and each bottle of juice has 15 grams of sugar. nayeli purchased 5 more bottles of soda than bottles of juice and they all collectively contain 205 grams of sugar. write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. define the variables that you use to write the system.
The system of equations are:
25s + 15j = 205
s - j = 5
Where:
s = number of soda bought
j = number of juice bottles bought
What are the system of equations?In order to determine the number of bottles of soda and juice bought, two sets of equations would need to be formed based on the information provided in the question. The equations would be solved simultaneously.
Grams of sugar in the soda bottle + grams of sugar in the juice bottle = total grams of sugar
difference in the number of bottles bought
25s + 15j = 205
s - j = 5
The methods that can be used to solve the simultaneous equations :
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The average distance from Earth to the sun is about 9.3×107 miles. The average distance from Mars to the sun is about 1.4×108 miles. When both planets are at their average distance from the sun, how much farther is Mars from the sun than Earth?
A 79,000,000 mi
B 47,000,000 mi
C 107,000,000 mi
D 233,000,000 mi
Pre-calculus Help please
The inverse of the expression y = 5 · (x - 6)² - 5 is x = √[(y + 5) / 5] + 6. (Correct choice: D)
How to determine the inverse of a function
According to the statement we have a function of the form y = f(x) and we need to find its inverse, that is, finding the equation of x in terms of y. This can be done by using algebra properties:
y = 5 · (x - 6)² - 5 Given
y = 5 · [(x - 6)² - 1] Distributive property
y / 5 + 1 = (x - 6)² Compatibilities with multiplication and addition / Existence of additive and multiplicative inverses / Associative and modulative properties
x - 6 = √(y / 5 + 1) Definition of square root / Symmetric property
x = √(y / 5 + 1) + 6 Compatibility with addition / Existence of additive inverse / Associative, commutative and modulative properties
x = √[(y + 5) / 5] + 6 Addition of fractions with different denominators / Result
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convert 87.65 to base 8
The answer is 127.5146314631
What is 87.65 decimal in octal? 87.65 from decimal to octal is 127.5146314631. Here we show you how to write 87.6510 in octal and how to convert 87.65 from base-10 to base-8.
To convert decimal number 87.65, we convert its integer and fraction part individually and then add them to get the equivalent octal number, as below:
To convert integer 87 to octal, follow these steps:
Divide 87 by 8 keeping notice of the quotient and the remainder. Continue dividing the quotient by 2 until you get a quotient of zero.
Then just write out the remainders in the reverse order to get the equivalent octal number.
87 / 8 = 10 with remainder 7
10 / 8 = 1 with remainder 2
1 / 8 = 0 with remainder 1
Here is the answer to 87 decimal to octal number:
127
For converting decimal fraction 0.65 to octal number, follow these steps:
Multiply 0.65 by 8 keeping notice of the resulting integer and fractional part. Continue multiplying by 8 until you get a resulting fractional part equal to zero (we calcuclate upto ten digits).
Then just write out the integer parts from the results of each multiplication to get equivalent octal number.
0.65 × 8 = 5 + 0.2
0.2 × 8 = 1 + 0.6
0.6 × 8 = 4 + 0.80000000000001
0.80000000000001 × 8 = 6 + 0.40000000000009
0.40000000000009 × 8 = 3 + 0.20000000000073
0.20000000000073 × 8 = 1 + 0.60000000000582
0.60000000000582 × 8 = 4 + 0.80000000004657
0.80000000004657 × 8 = 6 + 0.40000000037253
0.40000000037253 × 8 = 3 + 0.20000000298023
0.20000000298023 × 8 = 1 + 0.60000002384186
Here is the answer to 0.65 decimal to octal number:
0.5146314631
Therefore, decimal number 87.65 converted to octal is equal:127.5146314631
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plsssssszz answerrrrrr
I think this is one of those trick questions!
I'm going to say the answer is... 90°
because it states within the question that ∠A and ∠B are vertical angles
That is my educated guess. I hope it's helpful!
Pls let me know if my answer is incorrect.
You are driving a car when a deer suddenly darts across the road in front of you. Your brain registers the emergency and sends a signal to your foot to hit the brake. The car travels a reaction distance D , in feet, during this time, where D is a function of the speed r , in miles per hour, that the car is traveling when you see the deer, given by D(r)=11 r+5/10 . Find the inverse and explain what it represents. Is the inverse a function?
The inverse of the given equation is r = (10D - 5)/11 which represents the reaction speed of the car in terms of the reaction distance.
The car travels a distance of D feet, where D is a function of the speed r miles/hour given by D(r) = (11r + 5)/10
D = (11r + 5)/10
⇒ 10D = 11r +5 (multiply by 10 on both sides)
⇒ 10D - 5 = 11r (subtracting 5 on both sides)
⇒ (10D - 5)/11 = r (dividing by 11 on both sides)
Therefore, the inverse of the given equation is r = (10D - 5)/11.
Inverse represents the speed of the car (miles/hour) in terms of the reaction distance D.
The inverse is also a function, which represents the reaction speed of the car in terms of the reaction distance.
Therefore. the inverse of the given equation is r = (10D - 5)/11 which represents the reaction speed of the car in terms of the reaction distance.
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Samantha is following a blueprint to build an addition to her house. The kitchen countertop will be 8.75 feet long. The scale of the blueprint is 1 centimeter = 1.75 feet. What is the length of the countertop on the blueprint?
The length of the countertop on the blueprint is 5 cm.
What is defined as the scale?Scale is a ratio that reflects the relation between the size of a model and the actual dimensions of a figure or object. It aids in the representation of real-world objects on paper with relatively tiny dimensions. Scale is primarily employed in maps as well as blueprints for building construction.For the given question;
The length of kitchen countertop = 8.75 feet.
The scale used in blueprint is 1 centimeter = 1.75 feet.
Thus, use the unitary method.
1.75 feet -----> 1 cm.
Divide both side by 1.75.
1 feet ------>1/1.75 cm
Multiply both side by 8.75.
8.75 feet ---> 8.75/1.75 cm
8.75 feet ------> 5 cm.
Therefore, the the length of a countertop for the blueprint is found as 5 cm.
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14. “-4 times a number plus 29”
Answer:
It depends on what that number is but -4+29 is equal to 29-4; making the answer to -4+29=5.
Step-by-step explanation:
A retail clothing store offers customers an opportunity to open up a credit card during checkout. one location of the retail clothing store states that the number of credit cards, a, that are opened t months since january can be modeled by the function a(t) = 20 4t. the number of credit cards opened at another location, b, is defined by the function b(t) = 25 − t. what is an expression that can be used to determine the total amount of credit cards opened at the two locations? (a − b)(t) = −5 5t (a − b)(t) = −5 3t (a b)(t) = 45 5t (a b)(t) = 45 3t
An expression that can be used to determine the total amount of credit cards opened at the two locations is: (a + b) (t) = 45 + 3t.
Given,
Number of credit cards opened at location a = a (t) = 20 + 4t
Number of credit cards opened at location b = b (t) = 25 - t
Hence,
Total amount of credit card:
(a + b) (t) = (20 + 4t) + (25 - t)
(a + b) (t) = 20 + 4t + 25 - t
(a + b) (t) = 45 + 3t
Therefore an expression that can be used to determine the total amount of credit cards opened at the two locations is: (a + b) (t) = 45 + 3t.
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Marta paid $53 for 4 tickets to see a ballet. each ticket cost the same amount. what was the cost each ticket for the ballet?
The cost of each ticket for the ballet is $13.25.
What is cost price?The cost price or simply the cost in retail systems represents the particular value that corresponds to the unit price paid. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.
There are numerous ways to calculate cost pricing, however it all relies on the kind of query we are asking. For instance,
If a selling price and profit are provided, then,
Cost price = Selling price (SP) − profit
If a selling price and loss are provided, then,
Cost price =Selling price + loss
In the given question,
The total amount that Marta paid is $53
=> amount = $53
and total number of tickets = 4
Now, the cost of each ticket = Total amount / number of tickets
= $53 / 4
= $ 13.25
Hence, the cost each ticket for the ballet is $13.25.
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X = 2y + 18
5x = -3y - 27
Use the substitution method to solve the system below
Answer:
(0, - 9 )
Step-by-step explanation:
x = 2y + 18 → (1)
5x = - 3y - 27 → (2)
substitute x = 2y + 18 into (2)
5(2y + 18) = - 3y - 27
10y + 90 = - 3y - 27 ( add 3y to both sides )
13y + 90 = - 27 ( subtract 90 from both sides )
13y = - 117 ( divide both sides by 13 )
y = - 9
substitute y = - 9 into (1)
x = 2(- 9) + 18 = - 18 + 18 = 0
solution is (0, - 9 )
Evaluate each logarithm.
log₅(-25)
log₅(-25) is undefined
Logarithms are another notation for exponents in mathematics. The logarithm of a number whose base is equal to another number.A logarithm is the reciprocal of a power. For example, if 10² = 100 then log₁₀ 100 = 2. The natural logarithm is called the base e logarithm. The natural logarithm is represented by ln or loge. where 'e' represents Euler's constant, which is approximately equal to 2.71828. For example, the natural logarithm of 78 is written ln 78. The natural logarithm determines how much "e" must be multiplied to get the desired output.Since the logarithmic function y = logₐ(x) is the inverse of the exponential function,
As the base is positive so x must also be positive
The logarithm of the real base of negative numbers is undefined.
Hence, log₅(-25) is undefined
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Please help me out please please please
The surface area is the sum of the area of the surfaces. The surface area of the box is 360x^2 - 216x
Surface area of a box.
The formula for calculating the surface area of a box is expressed according to the equation:
Surface area = 2(lw + wh +lh)
Given the following parameters
length = 6x
width = 12x - 9
height = 6x
Substitute
Surface area = 2(6x(12x-9) + (12x-9)(6x) +(6x)(6x))
Expand
Surface area = 2(72x^2-54x) + (72x^2-54x) + 36x^2)
Surface area = 2(180x^2-108x)
Surface area = 360x^2 - 216x
Hence the surface area of the box is 360x^2 - 216x
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find the value of 9^-1/2
Applying the negative exponent rule, the value of 9^-1/2 is calculated as: 1/3.
What is the Negative Exponent Rule?If a number has a negative exponent, i.e. a^-1/2, it can be rewritten and expressed as:
a^-1/2 = 1/a^½
1/a^½ can also be rewritten or expressed as:
1/a^½ = 1/√a
Thus, we would apply the negative exponent rule to find the value of the expression, 9^-1/2 as explained below:
9^-1/2 = 1/9^½
Rewrite 1/9^½ as 1/√a
1/9^½ = 1/√9
Take the square root of 9
1/√9 = 1/3
This implies that, the value of the expression, 9^-1/2 is 1/3.
In conclusion, applying the negative exponent rule, the value of 9^-1/2 is determined as: 1/3.
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Solve each equation by factoring. Check your answers.
x²-8 x+15=0
The factors of equation are 5 and 3.
Rewriting the equation -
x² - 8x + 15 = 0
ax² + bx + c = 0
Factorizing the equation such that -
Sum of factors is equal to middle expression (b) (8x in this case)Product of factors is equal to the numeral values (a and c) (15 in this case)The suitable factors that can be used for solving the expression are 5 and 3.
x² - 5x - 3x + 15 = 0
x(x - 5) -3 (x - 5) = 0
(x - 5) (x - 3) = 0
(x - 5)= 0
x = 5
(x - 3) = 0
x = 3
Hence, the two factors of expression are 5 and 3.
To check the factors, we will keep each value of x to see if Left Hand Side is equal to Right Hand Side or not
When x = 5
x² - 8x + 15 = 0
5² - 8×5 + 15 = 0
25 - 40 + 15 = 0
-15 + 15 = 0
0 = 0
When x = 3
x² - 8x + 15 = 0
3² - 8×3 + 15 = 0
9 - 24 + 15 = 0
- 15 + 15 = 0
0 = 0
Since for both factors Left Hand Side is equal to Right Hand Side, thus, 5 and 3 are correct factors of the equation.
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Read each question. Then write the letter of the correct answer on your paper.Let g(x)=x-3 and h(x)=x²+6 . What is h(1)xg(1) ?
We get the value of h(1) × g(1) as - 14 for the functions g (x) = x - 3 and h (x) = x² + 6.
We are given the two functions as:
g (x) = x - 3 and h (x) = x² + 6
Now, we will first find h (1)
h (1) = (1)² + 6
h(1) = 1 + 6
Add them, we get:
h (1) = 7
Now, we will find g (1):
g (1) = 1 - 3
g (1) = - 2
Now we will find the expression h(1) × g(1):
h(1) × g(1) = 7 × ( - 2 )
h(1) × g(1) = - 14
Therefore, we get the value of h(1) × g(1) as - 14 for the functions g (x) = x - 3 and h (x) = x² + 6.
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How do you answer and write this out correctly
2.
x^2-4y
/2
4^2- (4*-3)
/2
16+12
/2
28/2
14
What expression is equivalent to -3(2x-4)
The given expression , the value of x is 2.
given,
equivalent expression = -3(2x - 4)
= -6x + 12
x = 2
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18. and can also be written as 6(x2 + 2y + 1) = 6x2 + 12y + 6.you can write equivalent expressions by combining like terms. Like terms are terms that have the same variables raised to the same powers. For example, the list shows some pairs of like terms. the new coefficient is 9.Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other. In addition, you can also determine if two expressions are equivalent when values are substituted in for the variable and both arrive at the same answer.to know more about equivalent expression;
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Factories (a + b)³-3a²b(a + b)
Answer:
(a+b) (a+2ab+b2−3a2b)
Step-by-step explanation:
f(x) = 3x²5x + 20
Find f(-8)
Answer:
f(-8)= -7660
Step-by-step explanation:
f(-8)= 3(-8)^2·5(-8)+20