Answer with explanation:
The given expression is
[tex]x=\frac{1}{2}\times y[/tex]
Which is equation in two variables , x and y , representing a line.
The general form of line is,
Ax +B y +C=0
Writing the above equation symmetrical to general form of line
→ 2 x=y
→2 x-y=0, is the general form.
(1-sin squared times tan is equal to ?
5. Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work. a. 3in, 4in, 5 in b. 5in, 6in, 7in c. 8in, 9in, 12in
From the information, A is a right triangle, B is an acute triangle and C is an acute angle.
What are triangles?A polygon with three sides, angles, and vertices is called a triangle.
Given that, triangle side lengths, we need to identify the triangle as acute, right or obtuse,
How to solve the triangle?
It will be a right triangle if a² + b² = c², It will be аcute if a² + b² > c² and it'll be obtuse if a² + b² < c².
1) a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25
25 = 25
This is a right triangle.
2) a² + b² = 5² + 6²
= 25 + 36 = 61
c² = 7² = 49
61 > 49 = аcute triangle.
3) a² + b² = 8² + 9²
= 64 + 81 = 145
c² = 12² = 144
145 > 144 = аcute triangle.
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Two sides of a triangle are 9 cm and 12 cm long. What is the range of possible lengths for the third side? Enter your answer in the boxes below.
Answer:
Possible length range of third side is between 3<x<21.
Step-by-step explanation:
Sum of two sides of triangle cannot be equal or less than third side. Therefore, one side length of a triangle must be between subtract and sum of other two sides. Than, range of third side is:
[tex](12-9)<x<(12+9)\\3<x<21[/tex]
Which explains why the graphs of geometric sequences are a series of unconnected points rather than a smooth curve?
The range contains only natural numbers.
The domain contains only natural numbers.
Exponential bases must be whole numbers.
Initial values must be whole numbers.
The correct answer is:
The domain contains only natural numbers.
Step-by-step explanation:The graphs of geometric sequences are a series of unconnected points rather than a smooth curve because:
The domain contains only natural numbers.
As the geometric sequence us given as:
[tex]a_1=a,a_2=ar,a_3=ar^2,....[/tex]
where a is the first term of the sequence and r is the common ratio of the geometric sequence.
Also [tex]a_n[/tex] denotes the nth term of the sequence where n belongs to natural numbers that is the domain of the function is natural numbers.
The reason why the graphs of geometric sequences are a series of unconnected points rather than a smooth curve is because: B. The domain contains only natural numbers.
What is a geometric sequence?A geometric sequence is typically a series of real and natural numbers that are calculated by multiplying the next number by the same number each time.
Mathematically, a geometric sequence is given by the expression:
[tex]a, \;ar, \; ar^{2} ....a_n[/tex]
Where:
r is the common ratio.a is the first term of a geometric sequence.In a geometric sequence, the graphs of geometric sequences comprises a series of unconnected points rather than a smooth curve is because the domain is made up of only natural numbers.
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Please help me!
Write and solve the compound inequality
A student scored a 73 and 81 on their first
two tests. Write and solve a compound
inequality to find the possible values for a
3rd quiz score that would give them an
average between 80 and 85
my answer is 86<=x<=101, but I don't know if it is right
Solve the following equation 5x+3(x-1)=8(x+2)-10
The sum of two numbers is
40
. One number is
4
times as large as the other.
Please help! The very last question has 2 answers.
A square piece of tile with sides 12 inches is cut along a diagonal, What is the length of the diagonal rounded to the nearest inch?
To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. Given that the side length of the tile is 12 inches, the length of the diagonal is approximately 17 inches when rounded to the nearest inch.
Explanation:To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the two sides of the right triangle are the sides of the square tile, and the hypotenuse is the diagonal. Given that the side length of the tile is 12 inches, we can calculate the length of the diagonal as follows:
Square the length of one side: 12 x 12 = 144
Multiply the result by 2: 144 x 2 = 288
Take the square root of the result: √288 ≈ 16.97 inches
Rounded to the nearest inch, the length of the diagonal of the square tile is 17 inches.
Final answer:
The length of the diagonal of the square, rounded to the nearest inch, is 17 inches.
Explanation:
The length of the diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two sides of the square are both 12 inches long. So, we have:
hypotenuse² = side1² + side2²
hypotenuse² = 12² + 12²
hypotenuse² = 144 + 144
hypotenuse² = 288
To find the length of the hypotenuse (or the diagonal), we take the square root of both sides:
hypotenuse = √(288)
hypotenuse = 16.97 inches (rounded to the nearest inch)
How to solve for quadratic equations with inequalities?
q, and p
First write the ratio as a fraction. make sure both terms have the same unit of measure. note that 1 foot equals 12 inches 1 foot=12 inches. then divide the numerator and denominator by their greatest common factor (gcf) to write the ratio in simplest form. ok
2X +105+ 8X -20+10 X +94+12 X -15=900 solve for x
Find the inverse of g(x)
Eric has a gift card to his favorite restaurant. Every Tuesday he has the same meal at the restaurant. This table shows the balance of money in dollars left on Eric’s gift card at different times. Time (weeks) 2, 4 ,6 ,8 Balance ($) 125, 100, 75, 50 What is the equation that represents Eric’s gift card balance, where x represents the time and y represents the balance?
Answer:
y − 100 = -12.5 (x − 4)
Step-by-step explanation:
Pick two points on the line to calculate the slope:
m = (y₂ − y₁) / (x₂ − x₁)
m = (100 − 125) / (4 − 2)
m = -12.5
Next, use point-slope form to write the line equation.
y − y₁ = m (x − x₁)
y − 100 = -12.5 (x − 4)
what is the approximate value of q ? q+log26=2q+2
Frank needs a total of $360 to cover his expenses of the week he earns $195 a week working at a restaurant and also walks dogs to supplement his income frank charges $15 per dog that he walks which equation can be used to find the number of dogs d that frank needs to walk to cover his expenses and how many dogs is that
you don't show the options but it should look something like this:
195 +15d = 360
answer:
subtract 195 from each side
15d = 165
d = 165/15 =11
he needs to walk 11 dogs
The equation which can be used to find the number of dogs d that frank needs to walk to cover his expenses is 15d+195=360 and number of dogs is 11.
What is an unknown variable?Unknown variables are used to find the unknown values of the problem using the algebraic expressions.
To find the values of unknown quantity, the statements of a problem is converted in the algebraic equation form using the variable in place of unknown numbers.
Frank needs a total of $360 to cover his expenses of the week. He earns $195 a week working at a restaurant and also walks dogs to supplement his income, frank charges $15 per dog that he walks.
The equation, which can be used to find the number of dogs d that frank needs to walk to cover his expenses,
[tex]15d+195=360[/tex]
Solve it further to find the number of dogs d,
[tex]15d+195=360\\15d=360-195\\d=\dfrac{165}{15}\\d=11[/tex]
Thus, the equation which can be used to find the number of dogs d that frank needs to walk to cover his expenses is 15d+195=360 and the number of dogs is 11.
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Harry enlarged a picture to a height of 30 inches. The original picture was 7" wide by 5" tall. Write a proportion to find the width of the enlargement and then solve for the width of the enlargement.
original height was 5" and it was enlarged to 30"
find the ratio by dividing 30 by 5
30 / 5 = 6
so ratio would be 1/6 meaning for every 1 inch of the original the new one is 6 inches
now you need to multiply the original width by 6 to find the new width
7" x 6 = 42"
new width = 42"
Lauren would like to have an average of 88 in her math class. There are five assignments with the following grades: 85, 100, 88, 80, 95. What grade will lauren need to make on the last assignment to meet her goal
The sum of two numbers is 67 . the smaller number is 9 less than the larger number. what are the numbers? larger number: smaller number:
To solve the problem, two equations were set up based on the conditions given. After substitution and simple algebraic operations, the larger number was found to be 38 and the smaller number to be 29.
The question involves finding two numbers where the sum is 67, and the smaller number is 9 less than the larger number.
Let's define the larger number as x and the smaller number as y. According to the problem:
x + y = 67 (Equation 1)y = x - 9 (Equation 2)Substitute Equation 2 into Equation 1:
x + (x - 9) = 67
2x - 9 = 67
2x = 67 + 9
2x = 76
x = 38
Now, we can find y using Equation 2:
y = x - 9
y = 38 - 9
y = 29
Therefore, the larger number is 38 and the smaller number is 29.
Line is parallel to line b and m<7=135. Find m<4
Let f(x)=2x-1 and g(x)=4-x^2. Find (f o g)(x).
simplify the expression (-2 -c) (-1)
How many gallons of rocket fuel containing 80% liquid oxygen must be mixed with 250 gallons containing 40% liquid oxygen to produce a mixture containing 70% oxygen?
Answer:
750
Step-by-step explanation:
for others
750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
What is Percentage?
percentage, a relative value indicating hundredth parts of any quantity
We need to find how many gallons of 80%
8x, since we don't know how many gallons
mixed with 250 gall of 40%: 0.40(250)
and we want a mix at 70%. The mix will include the 0.8x and the 0.4(250) Like this:
8x+0.4(250)=0.7x+0.7*250
Multiply on both sides of the equation
0.8x+100= 0.7x+175 Subtract 100 on both sides
0.8x= 0.7x+75
Subtract 0.7 on both sides
0.1x= 75
Divide both sides by 0.1
x= 750
You need 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
Hence, 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
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Can someone please help me?
Answer: -1.9
Step-by-step explanation:just add up the values for the weight change
(-1.8)+(0.9)+(-1.4)+(0.4)
-1.9
Prove that a parallelogram is a square iff its diagonals are both congruent and perpendicular
Write an algebraic expression to answer the question below. if 10 calculators cost d dollars, how much, in dollars, does each calculator cost?
What skills and practices were important for the growth and spread of early civilizations?
Which expression represents " 5 less than twice x " ?
1. 2x-5
2. 5-2x
3. 2(5-x)
4. 2( x-5)
The mathemtical expression for the word expression 5 less than twice x " is 2x - 5 option (A) 2x -5 is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The word expression is:
5 less than twice x
Twice the x = 2x
5 less than twice the x:
= 2x - 5
Thus, the mathematical expression for the word expression 5 less than twice x " is 2x - 5 option (A) 2x -5 is correct.
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Factoriza completamente las siguientes expresiones;
1. 3a²-a
2. 7ab³-14b
3. x³-x²+x
4. 12x³-xy²
5. 5x-6x²+7x³
6. 7a+8ab+9a²
7.3x²-3xy+6xy²
use exponential form to evaluate log8(2)
Answer: [tex]\frac{1}{3}[/tex]
Explanation:
let y = [tex]log_{8} (2)[/tex]
whenever we transfer base from log from one side to other it will remain be base after shifting to the other side.
Change log to exponent form [tex]\log_xm=n\\m =x^{n}[/tex]
here we have n = y, m=2, x=8 by substituting the values
we will get
[tex]8^{y} = 2[/tex] (1)
we can write 8 in power of 2 that is [tex]2^{3}[/tex]
we will rewrite the above equation (1) as
[tex]2^{3y} = 2[/tex]
we can equate the power when base is same then we will get
3y = 1
then
[tex]y=\frac{1}{3}[/tex]
The result of the logarithmic expression [tex]log _82=x[/tex] is 1/3
Let the given logarithmic function be x to have:
[tex]log _82=x[/tex]
This can be transformed into indices to have:
[tex]8^x = 2[/tex]
Solve the resulting indices for "x" a shown:
[tex](2^3)^x = 2^1\\2^{3x}=2^1[/tex]
Cancel the base and equate the power to have:
[tex]3x = 1\\x = \frac{1}{3}[/tex]
Hence the result of the logarithmic expression [tex]log _82=x[/tex] is 1/3
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