Answer:
[tex]y-2=3(x-3)[/tex]
Step-by-step explanation:
We want to write the equation of a line in point-slope form.
This is given by:
[tex]y-y_1=m(x-x_1)[/tex]
We have that line passes through (3,2).
Assuming the line has a slope of m=3, then the equation in point slope form is:
[tex]y-2=3(x-3).[/tex]
Final answer:
The point-slope form of the line that passes through the point (3, 2) with a slope of ½ is represented by the equation y - 2 = ½(x - 3).
Explanation:
The equation that shows the point-slope form of the line that passes through the point (3, 2) with a slope of ½ is derived from the point-slope equation format: y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope. Plugging the given point and slope into this formula, we get the equation y - 2 = ½(x - 3).
When solving for y to get the slope-intercept form, it's important to distribute the slope ½ across the (x - 3) term resulting in the equivalent equation: y = ½x + ¼.
Which three statements about the expression x² + 7x + 6 are true? Can you choose which are correct please?
x is a variable in the expression.
2 is the coefficient of one term of the expression.
The expression has three terms.
6 is a factor of the expression.
7 is the coefficient of one term of the expression.
Answer:
A, C, and E are correct
Step-by-step explanation:
B can't be right because 2 is an exponent, not a coefficient
D can't be right because 6 doesn't go into 7
Hope this helped!
1/6 / 1 2/3 divide fraction to simplest form
Answer:
1/10
Step-by-step explanation:
1/6 / 1 2/3
Convert 1 2/3 to 5/3.
1/6 / 5/3
1/6 x 3/5
3/30 or 1/10
The result of the division of 1/6 by 1 2/3 can be found by first converting 1 2/3 to an improper fraction, then taking the reciprocal of this fraction and multiplying it by 1/6. This gives the result as 1/10.
Explanation:To solve this fraction division problem, we first need to convert the mixed number 1 2/3 to an improper fraction. A mixed number like 1 2/3 means one plus 2/3, and it can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator. For 1 2/3, this means: (1*3 + 2)/3 = 5/3.
Now, we have the problem 1/6 / 5/3. In fraction division, we can replace the division with multiplication by the reciprocal of the second fraction. The reciprocal of a fraction is created by switching the numerator and the denominator. So, the reciprocal of 5/3 is 3/5.
Our equation 1/6 / 5/3 then becomes 1/6 * 3/5 = 3/30 = 1/10 when simplified. Hence, the result of 1/6 divided by 1 2/3 in its simplest form is 1/10.
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What is the value of the expression 22 + 62 ÷ 22? 10 13 16 36
Answer:10, hope it helps!! :)
Step-by-step explanation:
22 + 62 ÷ 22=
4 + 36 ÷ 4=10
I do not get how to do this problem
Answer:
Cross multiply
Step-by-step explanation:
[tex]\frac{2x+1}{3}\geq 5\\\\ 2x+1\geq 15\\2x\geq 15-1\\2x\geq 14\\\frac{2x}{2}\geq \frac{14}{2}\\ x\geq \frac{(2)(7)}{2}\\ x\geq 7[/tex]
Solve the following system of equations. What is the x-value of the solution?
3x + 2y = 7
x - y + 1 = 0
Answer:
x = 1
Step-by-step explanation:
Step 1: Choose one of the equations to solve for y:
x - y + 1 = 0
(-y) / -1 = (-1 - x) / -1
y = 1 + x
Step 2: Plug in y into either equation
3x + 2(1 + x) = 7
3x + 2 + 2x - 2= 7 - 2
5x / 5 = 5 / 5
x = 1
Answer: x = 1
1/4(10-7y)=15
Solve for y
Answer:
1/3 (39.09)=17 thats all thanks
Refer to the rectangle below. The length of the rectangle is x + 12. The width of the rectangle is x + 3.
Please determine the area of the rectangle.
Answer:x^2 +15x +36
Step-by-step explanation:
The length of a rectangle is 2 feet more than the width. If it’s perimeter is 40 feet, find the length and width
Answer:
w=9 feet
l=11 feet
Step-by-step explanation:
Let the length of the rectangle be l and width be w
Condition 1:
l=2+w --------(I)
Condition 2:
2l+2w=40--------(2)
Putting eq (1) in (2)
2(2+w)+2w=40
4+2w+2w=40
4+4w=40
4w=40-4
4w=36
Dividing both sides by 4
w=9
Now
Putting w=9 in eq (1)
l=2+9
l=11
Can someone please help me find x
Answer:
x = 17
Step-by-step explanation:
Vertical angles are congruent, so ...
5x° = 85°
x = 85°/5° . . . . . . divide by the coefficient of x
x = 17
Mr.Jenkins won $500 in a raffle. He split some of the money with his three children and had $20 left. How much money did he give each of his children?
Answer:460
Step-by-step explanation:
Answer the question below. Type your response in the space provided.
What is the answer?
12 X 4 [1 over 2]
Answer:54
Step-by-step explanation:
(12 x 4) = 48
(12 x .5) = 6
48 + 6 = 54
Which option gives f(x) = x² - 4x - 12 rewritten in vertex form as well as the function's correct axis of symmetry?
f(x) = (x -2)² - 16, x = -16
f(x) = (x + 2)(x - 6), x = 6
f(x) = (x + 2)(x - 6), x = -2
f(x) = (x - 2)² - 16, x = 2
Answer:
Part 1) [tex]f(x)=(x-2)^{2}-16[/tex]
Part 2) The function's correct axis of symmetry is x=2
Option f(x) = (x - 2)² - 16, x = 2
Step-by-step explanation:
we have
[tex]f(x)=x^{2} -4x-12[/tex]
This is a vertical parabola open upward
The vertex is the minimum
Part 1) Convert to vertex form
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]f(x)=(x^{2} -4x+2^2)-12-2^2[/tex]
[tex]f(x)=(x^{2} -4x+4)-16[/tex]
Rewrite as perfect squares
[tex]f(x)=(x-2)^{2}-16[/tex] ----> function in vertex form
Te vertex is the point (2,-16)
Part 2) Find the axis of symmetry
we know that
The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
The vertex is the point (2,-16)
therefore
The function's correct axis of symmetry is x=2
Final answer:
The function f(x) = x² - 4x - 12 rewritten in vertex form is f(x) = (x - 2)² - 16, and the axis of symmetry for this function is x = 2.
Explanation:
To rewrite the function f(x) = x² - 4x - 12 in vertex form, we need to complete the square. This involves the following steps:
Factor out the coefficient of the x² term, if it is not 1 (which it is in this case).Rearrange the equation to isolate the x-terms: x² - 4x.Find the number that completes the square for x² - 4x, which is the square of half of the coefficient of x. This number is (-4/2)² = 4.Add and subtract the determined number inside the brackets: (x² - 4x + 4) - 4.Rewrite the function in vertex form: f(x) = (x - 2)² - 16.The axis of symmetry for a parabola in the form (x - h)² is always x = h, which in this case is x = 2.
Therefore, the correct answer is f(x) = (x - 2)² - 16, x = 2.
Wskaż sumę liczb 2,5*10^10 i 7,8*10^10
odpowiedzi są takie:
A. 1,03*10^9
B. 1,03*10^10
C. 1,03*10^11
D. 10,3 * 10^20
proszę o pilną odpowiedź
To sum the numbers in scientific notation, you add the coefficients and keep the exponent. The correct sum of 2.5 \(\times\) 10^10 and 7.8 \(\times\) 10^10, expressed in proper scientific notation, is 1.03 \(\times\) 10^11.
Explanation:To find the sum of 2.5 \(\times\) 10^10 and 7.8 \(\times\) 10^10, you add the two numbers while keeping the same exponent since they are like terms in scientific notation. You calculate 2.5 + 7.8 which equals 10.3. Therefore, the sum in scientific notation is 10.3 \(\times\) 10^10.
However, in proper scientific notation, this number should have only one non-zero digit to the left of the decimal point. So, we adjust this sum by writing it as 1.03 \(\times\) 10^11 by moving the decimal one place to the left and increasing the exponent by 1. Thus, the correct answer is 1.03 \(\times\) 10^11, which correlates with option C.
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The following diagram shows that the state of Nevada is shaped somewhat like a trapezoid. Which measurement is the approximate area of the state of Nevada 320 miles, 200 miles, and 480 miles?
The area of Nevada, based on map measurements converted to actual miles using the map's scale, is calculated to be approximately 156,800 square miles.
Explanation:The question relates to finding the area of the state of Nevada using its scaled measurements from a map. Given that the scale on the map is 1/2" to 20 miles, and the physical distances measured on the map are 8" wide and 12.25" long, we need to convert these measurements into actual miles before calculating the area. To do this conversion, we set up a proportion based on the scale given:
0.5 inch/20 miles = 12.25 inches/x milesBy cross-multiplying, we find that x, the actual length in miles, is approximately 490 miles. Having converted both the width (8" which is equivalent to 320 miles) and the length, we can now calculate the area of the trapezoid that represents Nevada. Assuming the shape is close to rectangular for simplicity, the area would be width × length, or:
Area = 320 miles × 490 miles = 156,800 square miles.
5. Ms. Steinle can grade 30 tests in 75 minutes. How many tests can she get done during her 50-minute prep
period?
Answer: 20 tests
Step-by-step explanation: She does every test in 2 1/2 mins. So she can do 20 in 50 mins.
whats the answer for
2×(9×4-35)+27=
Answer:
Step-by-step explanation: 2× (9×4-35) +27
Using BODMAS
= 2× (36-35)+27
=2×(1) + 27
=2 + 27
=29
Divide. −5 5/6÷(−2 1/6)
Step-by-step explanation:
-5 5/6 ÷(-2 1/6)
Turn them into improper fractions
-35/6 and -13/6
Change the division sign to multiply
-35/6 × -13/6
Making -13/6 into -6/13
Solve
-35/6 × -6/13 = 210/78
Simplify
Answer:
35/13
Edit: if you want it to be a mixed number, it will be 2 9/13
Answer:
-5 5/6 ÷(-2 1/6)
Turn them into improper fractions
-35/6 and -13/6
Change the division sign to multiply
-35/6 × -13/6
Making -13/6 into -6/13
Solve
-35/6 × -6/13 = 210/78
Simplify explanation:
a sequence starts 1 4 9 16
the nth term is n squared
use this fact to find the nth term of the following sequences
2 5 10 17
2 8 18 32
Answer:
See the attached image for the answers and the working out.
Step-by-step explanation:
The nth term of the sequences 2, 5, 10, 17... and 2, 8, 18, 32... are n² + 1 and 2n² respectively.
What are sequences?Sequences are a group of numbers written in a specific order such that the nth term of the sequence can be determined using some logic or formula.
We can find the nth term of the given sequences as follows:It is given that the nth term of the sequence 1, 4, 9, 16... is n squared.
We can find the nth term of the sequences 2, 5, 10, 17... as shown below:2, 5, 10, 17...
1² + 1, 2² + 1, 3² + 1, 4² + 1...
This is of the form n² + 1. The nth term can be found using the formula n² + 1.
We can find the nth term of the sequences 2, 8, 18, 32... as shown below:2, 8, 18, 32...
2×1², 2×2², 2×3², 2×4²...
This is of the form 2n². The nth term can be found using the formula 2n².
Therefore, we have found that the nth term of the sequences 2, 5, 10, 17... and 2, 8, 18, 32... are n² + 1 and 2n² respectively.
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One leg of a right triangle has a length of 3. The other sides have lengths that are consecutive integers. Find these lengths.
Answer:
Therefore other two sides of the triangle are 4 and 5.
Step-by-step explanation:
Given one leg of a right triangle has a length of 3
Let other sides of the triangle be x and x+1 [ since they are consecutive]
According to the problem,
3²+x²=(x+1)²
⇔9 + x²=x²+2x+1
⇔2x+1=9
⇔2x=9-1
⇔2x=8
⇔x=4
Therefore other two sides of the triangle are 4 and 5.
To find the lengths of the other two sides of the right triangle with one leg of length 3, we can use the Pythagorean theorem. The lengths of the other two sides are 4 and 5.
Explanation:To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Since one leg has a length of 3, let's call the lengths of the other two sides x and x+1. We can set up the equation:
3^2 + x^2 = (x+1)^2
Simplifying the equation:
9 + x^2 = x^2 + 2x + 1
Subtracting x^2 from both sides:
9 = 2x + 1
Subtracting 1 from both sides:
8 = 2x
Dividing both sides by 2:
4 = x
So, the lengths of the other two sides are 4 and 5.
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Yesterday 5/7 of the 49 students in a contest gave their speeches. How many students gave their speeches? Write your Answer in simplest form.
Answer:
35
Step-by-step explanation:
given total number of students = 49
fraction of students that gave speeches = 5/7
number of students that gave speeches
= (5/7) x 49
= (5 x 49) / 7
= 245/7
= 35
Answer:35 students have their speeches
Step-by-step explanation:
1/7 of 49 is 7, so if it is 5/7 of the students multiply 5x7
PLEASE HELP!!!!!! I really need help fast
Answer:
c
Step-by-step explanation:
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
Considering the small triangle in which the one side and two angles are given:
Finding the third angle of the small triangle
Sum of angles of the triangle is [tex]180[/tex]°
as two angles are given i.e 90° and 45°, so third angle is 180°-(90°+45°)
Third angle in the small triangle is 45°.
As the opposite angles are 45° joining together to form 90° angle, therefore the small triangle is an isosceles triangle in which the opposite sides are equal.
Therefore the two sides are 7 and 7 of small triangle, so By Pythagoras theorem the third side is
[tex]H=\sqrt{P^2+B^2}\\ \\=\sqrt{7^2+7^2}\\\\=\sqrt{98} \\H=7\sqrt{2}[/tex]
Similarly the bigger triangle is also an isosceles triangle whose base is determined i.e [tex]7\sqrt{2}[/tex] = perpendicular length of bigger triangle.
Applying the Pythagoras theorem in bigger triangle:
[tex]x=\sqrt{(7\sqrt{2})^2+(7\sqrt{2})^2 }\\x=\sqrt{98+98}\\\\ x=\sqrt{196} \\\\x=14[/tex]
You roll a six-sided die. How likely is it that you roll a number less than 6?
A) certain
B) likely
C) unlikely
D) impossible
Answer:
b
Step-by-step explanation:
PLZ answer this question correctly
Jose bought a wallet for $19.95 and y hats for $5.99 each. Which of the following expressions shows the total amount of money he spent? (4 points)
Group of answer choices
19.95y + 5.99
19.95 + 5.99y
19.95 + 5.99 + y
19.95y + 5.99y
Answer:
Step-by-step explanation:
so he bought a wallet for 19.95 and y hats for 5.99
y = number of hats
19.95 + 5.99y....because each hat is 5.99
What combination equals 12345
There are 120 combination in 12345.
What is Combination?A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
To find number of combination in 12345.
Since, There 5 digits in the given number.
Hence, Possible combinations are,
⇒ 5!
⇒ 5 × 4 × 3 × 2 × 1
⇒ 120
Thus, There are 120 possible combination in 12345.
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Complete question is,
How many combinations with 12345 without repeating the numbers?
-8-w/9 + 4s use w=36 and s equal 5
Answer:
ight man that answer is 43 your welocome smart aint i
Step-by-step explanation:
Answer:
answers: 8
Step-by-step explanation:
There were 6 purple socks and 4 orange socks in a drawer. Zucky picked one sock without looking and then another without looking (or replacing the first). What is the probability that he picked 2 purple socks?
Answer: 1/3
Step-by-step explanation:
The sum of the least and greatest of 3
consecutive integers is 60. What are the
values of the 3 integers?
Answer:
Step-by-step explanation:
The the 3 consecutive numbers be
X, X + 1, X + 2
: X + X + 2 = 60
2X = 60 - 2
2X = 58
X = 58/2
X = 29
THE NUMBERS ARE 29, 30 AND 31
The graph shows a vertical translation of y = RootIndex 3 StartRoot x EndRoot.
On a coordinate plane, a cube root function goes through (negative 4, negative 4), has an inflection point at (0, negative 2.5), and goes through (4, negative 1).
What is the range of the translated function?
{y|y < 0}
{y|y ≥ 0}
{y|y is a natural number}
{y|y is a real number}
{y|y is a real number}
The range of the translated function is {[tex]y|y[/tex] is a natural number}.
What is a real number and example?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5), and irrational numbers such as √3, π(22/7), etc., are all real numbers.
What is not a real number?The numbers which are not real and are Imaginary are known as not real or non-real numbers. Non-real numbers cannot be represented on the number line. Some of the types or examples of the non-real numbers are √−2,6√−54.
What makes a real number?The real number, in mathematics, is a quantity that can be expressed as an infinite decimal expansion. Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting.
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Let’s consider all possible rectangles with the same area of 30 square inches.
Please note: the length of the sides are whole numbers.
Let the base of such a rectangle be x and the height be y. How would y depend on x?
Answer:
Given:
Area of the rectangle = 30 square inches.
length of the sides are whole numbers.
Solution:
The base of the rectangle is x and the height is y
We know that Area of the rectangle = [tex]length \times breadth[/tex]
That is
30 = [tex]x \times y[/tex]
The possible values of length and breadth
length x : 1 2 3 5 6 10 15 30
breath y: 30 15 10 6 5 3 2 1
Now
30 = xy
[tex]y = \frac{30}{x}[/tex]
when y increases x decreases and vice versa