[tex]x+2y=8[/tex] can be written in a slope-intercept form as [tex]y = 4-\dfrac{x}{2}[/tex].
SlopeA slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
Given to us,[tex]x+2y=8[/tex]
To find the slope-intercept formTo find the function, simply isolate y.
[tex]x+2y=8\\2y = 8-x\\y = \dfrac{8-x}{2}\\\\y = \dfrac{8}{2}-\dfrac{x}{2}\\\\y = 4-\dfrac{x}{2}[/tex]
Hence, [tex]x+2y=8[/tex] can be written in a slope-intercept form as [tex]y = 4-\dfrac{x}{2}[/tex].
Learn more about Graph and slope:
https://brainly.com/question/7588291
Given the functions f(x) = −2x − 1 and g(x) = −3x + 4, which operation results in the smallest coefficient on the x term?
clay is reading a map to decide his vacation route. The map has a scale of 1cm equals 18miles. If he estimates the length of his vacation route on a map is 14 centimeters what is the length in miles
Using the map scale of 1cm equals 18 miles, the actual length of Clay's vacation route is calculated as 252 miles by multiplying 14 centimeters (the length on the map) by 18 miles (the scale conversion factor).
Clay is using a map scale to plan his vacation route. The scale of the map is given as 1cm equals 18 miles. To calculate the actual length of Clay's vacation route in miles, we can set up a simple proportion. Since 1cm on the map represents 18 miles in reality, we multiply the length on the map, which is 14 centimeters, by 18 to find out how many miles this length represents:
Length in miles = 14 cm * 18 miles/cm
After performing the multiplication, we get:
Length in miles = 252 miles
Therefore, Clay’s vacation route is 252 miles long according to the map's scale.
The answer because I don’t know it
The value V of a square glass varies directly as the square of its length X cm. If the value of a square glass with length 3 cm is $243, find the value of a glass with length 5 cm
The value V of a square glass varies directly as the square of its length X cm. This means that V is proportional to [tex]X^2[/tex], which can be expressed as:
[tex]\[ V = kX^2 \][/tex]
where k is the constant of proportionality.
Given that the value of a square glass with length 3 cm is $243, we can use this information to find the constant k:
[tex]\[ 243 = k(3)^2 \][/tex]
[tex]\[ 243 = 9k \][/tex]
[tex]\[ k = \frac{243}{9} \][/tex]
[tex]\[ k = 27 \][/tex]
Now that we have the value of k, we can find the value of a glass with length 5 cm by substituting X = 5 into the original equation:
[tex]\[ V = 27(5)^2 \][/tex]
[tex]\[ V = 27 \times 25 \][/tex]
[tex]\[ V = 675 \][/tex]
Therefore, the value of a glass with length 5 cm is $675.
The answer is: 675.
What is the unit rate 3 for $5 4 for$6
Write the equation of a vertical line containing (5,-8)
A pair of parallel lines is cut by a transversal:
A pair of parallel lines is cut by a transversal. The interior angle made on the left by the intersection of the upper parallel line and the transversal is divided into 2 parts by a slanting line. One part of this angle is labeled as x, and the other part is labeled as 30 degrees. The interior angle made on the right by the intersection of the lower parallel line and the transversal is labeled as 75 degrees.
What is the measure of angle x?
Answer:
x = 45°
Step-by-step explanation:
It a transversal line intersect two parallel lines, then alternative interior angles are congruent.
From the below graph it is clear that the line m and n are two parallel lines and l is a transversal line.
[tex]\angle ABC\cong \angle BCD[/tex] (Alternative interior angles)
[tex]m\angle ABC=m\angle BCD[/tex] (Definition of congruent angles)
[tex]x+30^{\circ}=75^{\circ}[/tex]
Subtract 30° from both sides.
[tex]x+30^{\circ}-30^{\circ}=75^{\circ}-30^{\circ}[/tex]
[tex]x=45^{\circ}[/tex]
Therefore the measure of angle x is 45°.
Ella has 50 stacks of ten pennies in each stack. Describe how to find how many pennies ella has in all
The Red Sox have won 3 World Series titles in the last 11 years. At this rate, how long will it take them to win 20 World Series?
Interest of $1,632 with principal of $16,000 for 306 days(ordinary interest) results in a rate of
3. Find the scale factor using the given scale drawings and measurement below
The question asks to find the scale factor for given scale drawings and measurements. A scale factor is computed by creating a ratio comparing the measurement of the scale drawing to the actual measurement, simplifying that ratio to find the scale factor.
Explanation:The subject of the question is concerned with finding the scale factor from a given scale drawing and measurements. In mathematics, particularly in geometry, a scale factor is used to transform the size of a figure without altering its shape.
Step-by-Step ExplanationTo find the scale factor for each given scale drawing, you will need to create a ratio or a fraction that compares the scale measurement to the actual measurement. Here’s how you might solve one of the problems:
Example: What is the scale factor if 3 inches is equal to 12 feet?
Solution:
Convert all measurements to the same unit, for instance, turn feet into inches (1 foot = 12 inches).Write the ratio of the scale drawing to the actual measurement.Reduce the ratio to its simplest form to find the scale factor.How are the variables on the graph related?
Answer choices:
A. As speed decreases, height stays constant.
B. As speed decreases, height increases.
C. As speed increases, height decreases.
D. As speed increases, height increases.
Brooke bought all seven members of her family a chocolate bar at the chocolate factory in Hershey, Pennsylvania. Each chocolate bar was .8 ounces. How many ounces of chocolate did Brooke buy?
Write ratio in simplest form
6:3/5
Find the volume of the solid whose base is the circle x^2+y^2=81 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.
Find the area of the vertical cross section A at the level x=6.
The volume of the cone will be 1526.8 cubic units. The area of the vertical cross-section A at level x = 6 will be 72 square units.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The equation of the base circle is given below.
x² + y² = 81
x² + y² = 9²
Then the radius of the circle is 9 units. Then the height of the cone is the same as the diameter of the circle.
h = 2r
h = 2 x 9 = 18
The volume of the cone will be
V = (1/3)πr²h
V = (1/3) × π × 9² × 18
V = 1526.8 cubic units
The area of the vertical cross-section A at the level x = 6 will be
A = (1/2) x (18 - 6) x (18 - 6)
A = (1/2) x 12²
A = (1/2) x 144
A = 72 square units
More about the geometry link is given below.
https://brainly.com/question/7558603
#SPJ2
Find the largest odd number that divides the product of 16*24*60 evenly
Find the tangent plane to z 2 = x 3 + 2xy + y 3 at x, y = 1, 1.
Find the opposite of −8c3−10c2+6c+5
Final answer:
To find the opposite of the expression [tex]-8c^3-10c^2+6c+5[/tex], change the sign of each term to get [tex]8c^3+10c^2-6c-5.[/tex].
Explanation:
The opposite of any algebraic expression is found by changing the sign of each term within the expression. To find the opposite of the expression [tex]-8c^3-10c^2+6c+5[/tex], simply change the signs of each term:
The opposite of −[tex]8c^3[/tex] is [tex]8c^3[/tex]The opposite of −10[tex]c^2[/tex] is +10[tex]c^2[/tex]The opposite of +6c is −6cThe opposite of +5 is −5Putting it all together, the opposite of the expression [tex]-8c^3-10c^2+6c+5[/tex] is [tex]8c^3+10c^2-6c-5.[/tex]
In essence, each term in the original expression is multiplied by -1 to obtain its opposite. This operation changes all positive terms to negative and all negative terms to positive.
The concept of taking the opposite is fundamental in algebra and is often used in simplifying expressions, solving equations, and manipulating mathematical statements.
If a project is handed in late you receive 8/9 of your earned points. You received 72 points on your late project. How many points did you lose
In this situation, because the project was handed in late, you lost a total of 9 points. The full score was 81, and you got 72 after a deduction.
Explanation:The principal in this problem is understanding proportion. Given that handing in a project late results in receiving 8/9, or approximately 88.88%, of the total points, we'll figure out the total possible score by dividing the received points (72) by the portion of the full score you got for handing in the project late, which is 8/9. So, 72 ÷ 8/9 = 81. This would be the original points you could have received. You can then subtract the received points (72) from the original points (81) to ascertain the number of points lost. Therefore, 81 - 72 = 9. Consequently, you lost 9 points because the project was handed in late.
Learn more about Proportion here:https://brainly.com/question/34018947
#SPJ12
24 loaves of bread cost 48 dollars how much does 10 loaves cost?
Which equation represents a linear function? A) y – 2 = –5(x – 2) B) x + 7 = –4(x + 8) C) y – 3 = y(x + 4) D) y + 9 = x(x – 1)
i believe its the option A
a cereal box contains 15 3/4 ounces of cereal. If a bowl holds 2 2/5 ounces of cereal how many bowls are in 1 box
Given the equation D =m/v if D=2/3 and v=m+1., then m=
-3
2
1
The sum of the square of two consecutive whole number is 25. Find the numbers
Tom received a coupon in the mail for 30%off one regular priced item for a local sporting goods store He wishes tp purchase a soccer ball for 22.50 and shin guards for 17.00 which item would he use his coupon justify your answer by comparing the discount taken for each item
it should be used on the higher priced item to get a bigger discount.
So it should be used on the soccer ball
soccer ball: 22.50 * 0.30 = 6.75 discount
shin guards: 17.00 * 0.30 = 5.10 discount
6.75 is greater than 5.10
rewrite 8/9 with a denominator of 63
Final answer:
To rewrite the fraction 8/9 with a denominator of 63, multiply both the numerator and denominator by 7 to get 56/63.
Explanation:
To rewrite 8/9 with a denominator of 63, you need to find a number that you can multiply both the numerator (8) and the denominator (9) of the original fraction by, so that the denominator becomes 63. To do this, divide 63 by the original denominator, 9, which gives you 7. Thus, the number you need to multiply by is 7.
Multiply both the numerator and the denominator by 7:
Numerator: 8 times 7 = 56
Denominator: 9 times 7 = 63
Therefore, the fraction 8/9 with a denominator of 63 is 56/63.
A total of 29,183 votes were casted I’m an election. The winning candidate in the election received 61.3% of the votes. Which of the following is closest to the number of votes received by the winning candidate
A single 6-sided die is rolled twice. find the probability of getting a 55 the first time and a 11 the second time. express the probability as a simplified fraction.
Evaluate 4x-3 when x=_3
To evaluate the expression 4x-3 for x = -3, we substitute -3 into the expression and follow the order of operations, resulting in a value of -15.
Explanation:To evaluate the expression 4x-3 when x is -3, we simply substitute -3 in place of x and calculate the result as follows:
Replace x with -3: 4(-3) - 3.Multiply 4 by -3: -12 - 3.Finally, subtract 3 from -12 to get: -15.Therefore, evaluating 4x-3 when x is -3 gives us -15.
A 1950 kg car moves with a velocity of 11 m/s. What is its kinetic energy? Joules