Answer:
[tex]\frac{2}{3}[/tex] is the Slope of a line that is perpendicular to a given line equation -2y=3x+7
Step-by-step explanation:
We are given here with the equation of the line [tex]-2y=3x+7[/tex] or we can write this equation as [tex]y=\frac{-3}{2}x+\frac{-7}{2}[/tex]
the general equation of the line [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
Compare the given equation with general equation we get,
the value of slope(m) [tex]=\frac{-3}{2}[/tex]
The slope of line perpendicular to a line is, [tex]m_{perpendicular}=\frac{-1}{m}[/tex]
Since, the slope of the given line is, m=[tex]\frac{-3}{2}[/tex]
then, [tex]m_{perpendicular}=\frac{-1}{\frac{-3}{2} }[/tex][tex]=\frac{2}{3}[/tex]
Therefore, the slope of a line that is perpendicular to a line whose equation is -2y=3x+7 is, [tex]\frac{2}{3}[/tex]
The slope of the line that is perpendicular to a line whose equation is -2y = 3x + 7 is 2/3.
For lines to be perpendicular to each other, the product of there slopes is equals to negative 1. This can be mathematically represented as follows
m₁ × m₂ = -1
where
m₁ and m₂ are slopes of the lines.
Therefore,
let's find the slope of the equation given
-2y = 3x + 7
divide both sides by -2
y = -3/2 x + 7/2
Using the slope equation model,
y = mx + c
where
m = slope
The slope in our equation will be - 3/2.
Using the first formula for perpendicular lines,
m₁ × m₂ = -1
-3/2 m₁= -1
m₁ = -2/-3
m₁ = 2/3
The slope of the line is 2/3
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How many 3 letter "words" can be created from the letters abcdefg when 1. repetition allowed,?
What does the end behavior look like of the graph of the function f(x)=-8x^4-2x^3+x?
I know what the graph itself looks like but I have trouble explain its end behavior.
Thank you.
The Sheng family had dinner at their favorite restaurant. A 4% sales tax was added to their bill. Amy paid the bill with a $25 gift certificate plus $44.80. How much did the family's dinner cost before tax? Round your answer to the nearest penny.$ 71.59$ 66.01$ 67.12$ 67.01
PLEASE HELP ME DO NOT HELP IF YOU DO NOT KNOW HOW TO DO IT
The state of Colorado had roughly the shape of a rectangle that is 3.8 x 10^2
2.8 x 10^2 miles high. What is the approximate area of Colorado? hint: the area of the rectangle is a product of its length and width.
Mrs. Sage will print a copy of the class alphabet book for each student. The book is formatted in1/2 pages with a title page, a page for each letter and an end page. If there are 70 students, how many reams of paper will Mrs. Sage need for the books?
Write -42/9 mixed in a reduced form
HELP MEH PLEZ! When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there
The equation representing the number of people, y, at the fair x hours after the gates open:
y = 68 * 1.5^(x-1)
Initial number of people: 68 (given)
Growth factor per hour: 1.5 (given)
Number of hours since gates opened: x
The equation uses the following logic:
Start with the initial number of people (68).
Multiply by the growth factor (1.5) to account for the increase after the first hour.
Since the growth factor applies after each hour, raise it to the power of (x-1) to account for the total number of times it's applied after x hours. This is because the first hour's growth is already accounted for in the initial number.
Therefore, the equation y = 68 * 1.5^(x-1) accurately represents the number of people at the fair x hours after opening.
Complete question:
When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.
Can someone please explain this in a way my dumb brain would understand? WHY does 2 - (-8) = 10? Shouldn't it be decreasing to -6?
The reasoning is because you are subtracting 2. If you were to be adding 2, then it would be -6.
Since you are subtracting 2 it = 10.
Glad to help a Senior mod out.
Thanks, Plip.
find m<G p//r. the diagram is not to scale. I believe it to be 146 but I'm not sure.
The given information is not clear enough to determine the measure of angle G p//r.
Explanation:To find m<G p//r, we need to understand the given diagram. However, the provided information is not clear enough to determine the measure of angle G p//r. More information or a clear diagram is needed to find the angle accurately. Please provide additional details or a clear diagram for further assistance.
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5377 people/km^2= how many people/m^2 ?
Answer:
0.005377 people/m²
Step-by-step explanation:
5377 people/km² can written as
5377 × [tex]\frac{people}{km^2}[/tex]
Now we have to find the value in [tex]\frac{people}{meter^2}[/tex]
Since 1 km = 1000 meter.
So 5377 × [tex]\frac{people}{km^2}[/tex] = 5377 × [tex]\frac{people}{(1000)^2met^2}[/tex]
= [tex]\frac{5377}{(1000)^2}[/tex] people per met²
= [tex]\frac{5377}{(1000000)}[/tex]
= 0.005377 people/m²
You know, this question "functions" just as well as the Kardashians. Not at all, at least to my brain! I definitely need help with this.
evaluate the expression (18-6)÷(11-5), if possible
If the intercepts of a line are (a,0) and (0,b), what is the slope of the line?
Show how you solved it.
Suppose you had d dollars in your bank account. You spent $12 but have at least $51 left. How much money did you have initially? Write and solve an inequality that represents this situation.
A.
d+12 51; d 75
B.
d + 12 51; d 75
C.
d-12 51; d 63
D.
d-12 > 51; d > 63
For the points M(-2,3), N(4,5), P(1,6) and Q(4,-3), what is the relationship between MN and PQ?
help will mark brainliest Jim Shu has the following work shown on their paper. The directions read “Simplify each radical.” Unfortunately, they have not simplified correctly.
A. Find their mistake and explain what they did wrong.
Jim Shu made two mistakes in simplifying radicals: they missed the initial steps and included an irrelevant step of checking the answer's reasonability.
Explanation:The instructions provided to Jim Shu involve simplifying radicals, but there is an omission of the initial steps in the process.
The student proceeds with step 6 without detailing the necessary earlier steps in simplifying the algebraic expression.
This misstep results in an incomplete representation of the solution process.
Furthermore, step 7 introduces an unrelated directive, advising the student to check the answer for reasonability.
This step is incongruent with the task at hand, which is the simplification of radicals.
To address this error, Jim Shu should incorporate the essential preliminary steps for simplifying radicals, ensuring a comprehensive presentation.
Additionally, the extraneous step of checking reasonability should be omitted, aligning the solution process with the given directions.
Katie jogged 2.4 miles on Monday, 3.7 miles on Tuesday, and 2.9 miles on Wednesday. How many miles did Katie jog on Thursday if she jogged a total of 12.1 miles for the four days
andy constructed a triangle angle 1 and 2 are the same but angle 3 has a measurement of 100 degrees what is the measurement of angle 1 and 2
write an equation of the line, in slope intercept form, that passes through the given point and has the given slope. point:(8,-8), slope:3
If you are dealt two cards successively (with replacement of the first) from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.
The longer leg of a right triangle is 4cm longer than the shorter leg the hypotenuse is 8 cm longer than the shorter find the side lengths of the triangle
The side lengths of the triangle are 8 cm, 12 cm, and 16 cm
To solve for the side lengths of the right triangle, we can use the Pythagorean Theorem, which states that for any right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is written as a^2 + b^2 = c^2.
Let's denote the shorter leg of the triangle as x. Then, according to the problem, the longer leg is x + 4 cm and the hypotenuse is x + 8 cm. Plugging these expressions into the Pythagorean Theorem, we have:
x^2 + (x + 4)^2 = (x + 8)^2
Expanding and simplifying the equation:
x2 + x2 + 8x + 16 = x2 + 16x + 64
2x2 + 8x + 16 = x2 + 16x + 64
x2 - 8x - 48 = 0
Solving this quadratic equation for x, we find:
x = 8 cm (shorter leg)
x + 4 = 12 cm (longer leg)
x + 8 = 16 cm (hypotenuse)
Therefore, the side lengths of the triangle are 8 cm, 12 cm, and 16 cm
Newer stocks can be bought for $8 each, while older stocks can be bought for $4 each. The total cost, in dollars, of 10 stocks is represented by the expression 8s+4(10-s), where s represents the number of new stocks bought. how does changing the value of s change the value of the term 4(10-s)?
A.) For values of s less than 10, the term 4(10-s) will be negative; for values of s greater than 10, the term will be negative; for values of s equal to 10, the term will equal 0.
B.) For values of s less than 10, the term 4(10-s) will be negative; for values of s greater than 10, the term will be positive; for values of s equal to 10, the term will equal 0.
C.) For values of s less than 10, the term 4(10-s) will be positive; for values of s greater than 10, the term will be positive; for values of s equal to 10, the term will equal 0.
D.) For values of s less than 10, the term 4(10-s) will be positive; for values of s greater than 10, the term will be negative; for values of s equal to 10, the term will equal 0.
a fishing lake was stocked with 300 bass. Each year, the population decreases by 25. the population of bass in the lake after x years is represented by the function f(x)=300-25x
The function f(x)=300-25x represents the decline of population in a fishing lake that was initially stocked with 300 bass. Each year, the population reduces by 25. For instance, after 4 years, the number of bass left in the lake would be 200.
Explanation:The question is about a fishing lake that was initially stocked with 300 bass. As per the information given, the population of bass in the lake decreases by 25 each year. Therefore, if we let x represent the number of years, then every year, the number of bass decreases by 25x. This relationship is represented by the algebraic function f(x)=300-25x.
To provide a practical understanding, suppose you want to calculate the number of bass remaining after 4 years. You just substitute '4' in place of x in the equation. Hence, f(4) = 300 - 25 * 4 = 300 - 100 = 200. So, after 4 years, there would be 200 bass remaining in the lake.
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1. Write the expression in simplified radical form. Show your work. 3 – 2√11/ 2 +√11
Suppose a parabola has vertex (-3,7) and pass throught the point (-2,11). write the equation of the parabola in vertex form.
Parabola is a plane curve with a U shape.
The parabola equation is given as:
y = a (x – h)² + k
The equation of a parabola that has a vertex (-3, 7) and passes through the point (-2, 11) is y = 11.
What is a parabola?Parabola is a plane curve with a U shape.
The parabola equation is given as:
y = a (x – h)² + k
(h, k) is the vertex.
We have,
Parabola:
Vertex = (-3, 7)
Passes through the point = (-2, 11)
The equation of the parabola is y = a (x - h)² + k
(-3, 7) = (h, k)
Since the parabola passes through the point (-2, 11) we get,
11 = a (-2 - (-3))² + 11
11 = a (-2 + 3)² + 11
11 = a x 1 + 11
11 = a + 11
Subtract 11 on both sides.
0 = a
a = 0
Now,
y = 0 (x + 3)² + 11
y = 0 + 11
y = 11
Thus,
The equation of a parabola that has a vertex (-3, 7) and passes through the point (-2, 11) is y = 11.
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John buys big ice-cream cylindrical Jar and sells it for $1 each ice-cream cone.
Each cone has around 30 cubic cm of ice-cream in it.
Jar has diagonal 20 cm. and its height is 3 times of width.
If he sells the whole jar, and He originally bought it for $7 does he make profit out of selling the jar?
John can make a profit by selling ice cream from the cylindrical jar. After calculating the volume, he would earn approximately $15.70 in revenue, and by deducting the initial cost ($7), he makes a profit of around $8.70.
To determine if John will make a profit by selling the entire ice-cream cylindrical jar, we first need to calculate the volume of the jar to find out how many cones he can fill. The jar has a diagonal of 20 cm and a height that is three times its width. Assuming the width is 'w' and height is '3w', we can use the Pythagorean theorem with the jar's diagonal to find 'w', since the diagonal forms a right triangle with the width and height of the cylinder.
The formula for the Pythagorean theorem is diagonal^2 = width^2 + height^2, which gives us 20^2 = w^2 + (3w)^2. Solving for 'w', we get w = 4 cm and height = 12 cm. The volume 'V' of the cylinder is given by V = π * radius^2 * height, which gives us V = π * 2^2 * 12, therefore, V = 48π cm^3. Then, we divide the jar's volume by the volume of each ice cream cone to find the number of cones, 48π cm^3 / 30 cm^3/cone ≈ 5π cones.
Given that John sells each cone for $1, the total revenue from selling all the ice-cream cones would be approximately $5π. Since π is approximately 3.14, his total revenue would be about $15.70. Subtracting the initial cost of the jar ($7), we find that John would make a profit of approximately $8.70.
Therefore, John will indeed make a profit out of selling the jar of ice cream.
There are 20 girls on the basketball team. of these, 17 are over 16 years old, 12 are taller than 170 cm, and 9 are both older than 16 and taller than 170 cm. how many of the girls are older than 16 or taller than 170 cm?
Final answer:
By using the principle of inclusion-exclusion, we calculate that all 20 girls on the basketball team are either over 16 years old or taller than 170 cm, as the sum of the individual criteria minus the intersection equals the total number of girls on the team.
Explanation:
To determine how many of the girls on the basketball team are either over 16 years old or taller than 170 cm, we can use the principle of inclusion-exclusion. According to the information provided, there are 20 girls on the team in total, of which 17 are over 16 years old, 12 are taller than 170 cm, and 9 satisfy both criteria. The principle of inclusion-exclusion states that the number of elements in the union of two sets is equal to the sum of the sizes of each set minus the size of their intersection.
Using this principle:
Number of girls over 16 years old: 17
Number of girls taller than 170 cm: 12
Number of girls who are both over 16 and taller than 170 cm: 9
The calculation would be as follows:
17 (over 16) + 12 (taller than 170 cm) - 9 (both) = 20
Therefore, there are 20 girls on the team who are either older than 16 or taller than 170 cm.
Find the next term of the following sequence.
25, 10, 4,
The given sequence is 25, 10, 4.
Notice that this is a geometric sequence because here we have equal common ratio.
So, common ratio : r = [tex] \frac{a_{2}}{a_{1}} [/tex]
= [tex] \frac{10}{25} [/tex]
= 0.4
So, each term is 0.4 times of it's previous term.
Hence, to get the next term of this sequence, multiply 0.4 with the third term 4.
So, fourth / next term = 4* 0.4 =1.6
Hence, next term of this sequence is 1.6.
Hope this helps you!
Answer:
Step-by-step explanation:
the answer is 8/5 i just did it on my quiz and got it right.
If sin theta = 3/5 and cos theta <0 find tan theta
Help please I’ll mark you brainliest