Answers
Answer:
b. linear; y +2 = -5/4(x +9)
Step-by-step explanation:
From the first line of the table to the second, we have ...
slope = (change in y)/(change in x) = (-7-(-2))/(-5-(-9)) = -5/4
Only one equation shows a slope of -5/4: the second one.
__
We know the relation is linear because the same slope can be computed from any pair of lines of the table. In particular, from one row to the next, x changes by the constant value +4 and y changes by the constant value -5.
Related Questions
Factor the expression over the complex numbers.
x^2+50
Answers
Answer:
[tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]
Step-by-step explanation:
The factorization is in the form (x-a)(x-b) where a,b are zeros of the equation [tex]x^{2} +50=0[/tex].
[tex]x^{2} =-50[/tex]
[tex]x =\sqrt{-50}[/tex]
[tex]x =\sqrt{50}i = 5\sqrt{2}i[/tex] and [tex]x =-\sqrt{50}i = -5\sqrt{2}i[/tex]
So, the factorization is [tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]
Complex numbers are numbers with real and imaginary part.
The factorized expression is [tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]
The expression is given as:
[tex]\mathbf{x^2 + 50}[/tex]
Set to 0
[tex]\mathbf{x^2 + 50 = 0}[/tex]
Subtract 50 from both sides
[tex]\mathbf{x^2 = -50}[/tex]
Take square roots
[tex]\mathbf{x = \sqrt{-50}}[/tex]
Expand
[tex]\mathbf{x = \sqrt{25 \times -2}}[/tex]
Take square roots of 25
[tex]\mathbf{x =\pm 5\sqrt{-2}}[/tex]
Expand
[tex]\mathbf{x = \pm5\sqrt{2 \times -1}}[/tex]
Split
[tex]\mathbf{x =\pm 5\sqrt{2} \times \sqrt{-1}}[/tex]
In complex numbers,
[tex]\mathbf{\sqrt{-1} = i}[/tex]
So, we have:
[tex]\mathbf{x = \pm5i\sqrt{2}}[/tex]
So, we have:
[tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]
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1=logx solve this equation for x. Round your answer to the nearest hundred.
Answers
10¹=x
x= 10
that's the answer
Last Saturday there were 1486 people at a cinema. There were about the same number of people in each of the 6 theaters. Between which 2 numbers does the number of people fall?
Answers
What is the slope of the graph?
slope = -3
slope = -1/3
slope = 1/3
slope = 3
Answers
Answer:
slope = -3
Step-by-step explanation:
To find the slope of the graphed line, we can use the slope formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope formula}}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\textsf{where:}\\\phantom{w}\bullet\;\;m\; \textsf{is the slope.}\\\phantom{w}\bullet\;\;(x_1,y_1)\;\textsf{and}\;(x_2,y_2)\;\textsf{are two points on the line.}\end{array}}[/tex]
First, identify two points on the line:
(x₁, y₁) = (0, 3)(x₂, y₂) = (1, 0)Substitute the coordinates into the slope formula:
[tex]m=\dfrac{0-3}{1-0}=\dfrac{-3}{1}=-3[/tex]
Therefore, the slope of the graphed line is:
[tex]\Large\boxed{\boxed{\textsf{slope}=-3}}[/tex]
Find the measure of ∠D if ∠A = 5 2 x + 30 ∠B = 7 2 x + 40 ∠C = 9 2 x + 10 ∠D = 5 2 x + 20
Answers
<A= 52x+30
<B= 72x+40
<C= 92x+10
<D= 52x+20
I put <A and <B together and <C and <D together<A and <B :
52x+30 = 72x+40
-52 -52 30 = 20x+40 -40 -40
-10 = 20x/20 /20-0.5 = xwhen you put it into the equation as 52(-0.5)+30 you get 4, and when you put it in 72x+40 you also get four.
Now for <C and <D 92x+10 = 52x+20-52 -5240x+10 = 20 -10 -1040x = 10/10 /10x=4
For anyone who needs the measure itself, it's 70.
which property is illustrated the following statement? 3z+4=4+3z
Answers
Answer:
Commutative additive property.
Step-by-step explanation:
Given : 3z+4=4+3z
To find : which property is illustrated the following statement.
Solution : We have given
3z + 4 = 4 + 3z.
Commutative additive property : a + b = b + a .
Example : 2 + 3 = 3 +2 = 5.
Hence this the commutative additive property 3z + 4 = 4 + 3z.
Therefore, Commutative additive property.
There is a large bag with marbles in it. there are 23 red ones, 16 black ones, 5 blue ones, 17 orange ones, 4 white ones, and 15 purple ones. juanita reaches in without looking and selects one marble. what is the probability that it is purple? 1 15 1 80 7 3 16
Answers
for a total of : 80 marbles
the probability of picking a purple one is 15/80 which reduces to 3/16 <=
Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of fat? what would a proportion be for this problem?
Answers
1/5+1/5+1/5+1/5+1/5=1
1/5+1/5+1/5+1/5+1/5=1
1/5+1/5+1/5+1/5+1/5=1
Now since its 2 apples per 1/5 then u multiply 20 by 2 so ur answer would be 40
40 apples = 4 grams of fat
The coordinates of the vertices of a polygon are (−2,−2), (3,−3), (4,−6), (1,−6), and (−2,−4).
What is the perimeter of the polygon to the nearest tenth of a unit?
15.3 units
16.9 units
17.5 units
17.9 units
Answers
The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{16.9{\text{ units}}}.[/tex] Option (b) is correct.
Further explanation:
The distance between the two points can be calculated as follows,
[tex]\boxed{{\text{Distance}}=\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}}}[/tex]
Given:
The coordinates of the vertices of the polygon are [tex]\left({ - 2, - 2}\right),\left( {3, - 3}\right),\left( {4, - 6}\right),\left( {1, - 6}\right)[/tex] and [tex]\left( { - 2, - 4}\right).[/tex]
Explanation:
Consider the points as A [tex]\left( { - 2, - 2} \right), B\left( {3, - 3} \right), C\left( {4, - 6} \right), D\left( {1, - 6} \right)[/tex] and [tex]E\left({ - 2, - 4} \right).[/tex]
The distance between point A and point B can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {3 + 2} \right)}^2} + {{\left( { - 3 + 2}\right)}^2}}\\ &= \sqrt {25 + 1}\\&= \sqrt {26}\\&= 5.2\\\end{aligned}[/tex]
The distance between point B and point C can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {4 - 3} \right)}^2} + {{\left( { - 6 + 3} \right)}^2}}\\&= \sqrt {{1^2} + 9}\\&= \sqrt {10}\\&= 3.17\\\end{aligned}[/tex]
The distance between point C and point D can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left({1 - 4} \right)}^2} + {{\left( { - 6 + 6}\right)}^2}} \\&=\sqrt {{3^2} + 0}\\&= \sqrt9\\&= 3\\\end{aligned}[/tex]
The distance between point D and point E can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( { - 2 - 1}\right)}^2} + {{\left( { - 4 + 6}\right)}^2}}\\&= \sqrt{ - {3^2} + {2^2}}\\&= \sqrt {9 + 4}\\&= \sqrt {13}\\&= 3.61\\\end{aligned}[/tex]
The distance between point E and point A can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 2 + 2} \right)}^2} + {{\left( { - 4 + 2} \right)}^2}}\\ &= \sqrt {{0^2} + {2^2}}\\&=\sqrt4\\&= 2\\\end{aligned}[/tex]
The perimeter of the polygon can be calculated as follows,
[tex]\begin{aligned}{\text{Perimeter}}&= 5.12 + 3.17 + 3 + 3.61 + 2\\&= 16.9\\\end{aligned}[/tex]
Option (a) is not correct.
Option (b) is correct.
Option (c) is not correct.
Option (d) is not correct.
The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{16.9{\text{ units}}}.[/tex] Option (b) is correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Coordinate geometry
Keywords: Coordinates, vertices, polygon, x-coordinate, y-coordinate, perimeter, circumference, nearest tenth unit, distance formula.
Answer:
here is the answer
Step-by-step explanation:
whats 6.3 x 10^-5 in standard notation
Answers
Since the exponent of the scientific notation is -5, we have to move the decimal point 5 places to the left to get this answer.
A barrel of oil contains 42.0 gallons. how many liters is this? (1 gal = 3.785 l)
Answers
Final answer:
A 42.0-gallon barrel of oil is equivalent to 158.97 liters, calculated by multiplying the number of gallons by the conversion factor of 3.785 liters per gallon.
Explanation:
To discover out how numerous liters are in 42.0 gallons of oil, given that 1 gallon is proportionate to 3.785 liters, you'd perform the taking after calculation:
Multiply the number of gallons by the conversion factor from gallons to liters.
42.0 gallons × 3.785 liters/gallon = 158.97 liters.
Therefore, a barrel of oil, which contains 42.0 gallons, is equivalent to 158.97 liters.
For his long distance phone service, Rafael pays a $5 monthly fee plus 9 cents per minute. Last month, Rafael long distance bill was $10.94. For how many minutes was Rafael billed?
Answers
The function, f(x)=45/x models the volume of a gas in a balloon under xx units of pressure at a constant temperature. Which best describes the domain of f(x) ?
Answers
Given: Triangles ABC and DBC are isosceles, m∠BDC = 30°, and m∠ABD = 155°.
Find m∠ABC, m∠BAC, and m∠DBC.
Answers
Answer:
- m∠ABC = m∠ACB = 25° (as triangle ABC is isosceles).
- m∠BAC = 130°.
- m∠BDC = m∠DCB = 30° (as triangle DBC is isosceles).
Explanation:
We can solve this problem by using the properties of isosceles triangles and the fact that the sum of angles in a triangle is 180 degrees.
1. Since triangle DBC is isosceles, m∠DBC = m∠DCB.
Therefore, m∠DCB = 30°.
2. In triangle ABC, since it's isosceles, m∠ABC = m∠ACB.
3. We know that m∠ABD = 155°. Since triangle ABD is a triangle, the sum of its angles is 180 degrees. So, m∠ABD + m∠BAD + m∠ADB = 180°. Therefore, m∠BAD + m∠ADB = 180° - 155° = 25°.
4. Since triangle ABC is isosceles, m∠ABC = m∠ACB = 25°.
5. In triangle ABC, the sum of its angles is 180 degrees. So, m∠ABC + m∠BAC + m∠ACB = 180°. Substituting the known values, we get 25° + m∠BAC + 25° = 180°. Solving for m∠BAC,
we find m∠BAC = 180° - 25° - 25° = 130°.
If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is
Answers
The probability of heads on the fifth trial is still 0.5, just like any other coin flip.
Explanation:The probability of heads on the fifth trial is still 0.5, just like any other coin flip. The outcome of each coin flip is independent of the previous flips, so each trial has the same probability of resulting in heads or tails.
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There are 4 dogs, 6 cats, a rooster and 8 pigs on a farm. What is the ratio of pigs to all the other animals?
Answers
Answer:
Its 8:11 because theres eleven animals and 8 pigs
Step-by-step explanation:
Complete the indirect proof to show that two supplementary angles cannot both be obtuse angles. given: angle1 and angle2 are supplementary. prove: angle1 and angle2 cannot both be obtuse. assume that two supplementary angles can both be obtuse angles. so, assume that angle1 and angle2 are obtuse. then mangle1 > 90° (equation 1) and mangle2 > ° (equation 2) by the definition of angles. adding the two inequalities, mangle1 + mangle2 > ° (equation 3). however, by the definition of supplementary angles, mangle1 + mangle2 = (equation 4). so equation 3 contradicts the given information. this means the assumption is , and therefore angle1 and angle2 both be obtuse.
Answers
The proof was completed by assuming that two supplementary angles could both be obtuse, which would mean that their sum is more than 180°. This contradicts the definition of supplementary angles, where their sum should always be exactly 180°, and hence proves that two supplementary angles cannot both be obtuse.
Explanation:To complete the indirect proof, we start by assuming that two supplementary angles, let's call them angle1 and angle2, can indeed both be obtuse angles. An obtuse angle is defined as an angle which measures more than 90°. Therefore, if both angle1 and angle2 are obtuse, they would each measure more than 90°, meaning that their sum (angle1 + angle2) would measure more than 180°.
However, the definition of supplementary angles is such that their sum should always be exactly 180°. Therefore, we reach a contradiction in our assumed scenario: the sum of angle1 and angle2 cannot be both more than 180° (by our assumption that they are both obtuse) and exactly 180° (by the known definition of supplementary angles).
This contradiction means that our initial assumption was incorrect, thus completing the proof. In other words, two supplementary angles cannot both be obtuse, as it would contradict the definition of supplementary angles.
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2(x+14)+(2x-14)= do you know this
Answers
The simplified form of the expression 2(x+14)+(2x-14) is 4x + 14.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
Given:
An expression,
2(x+14)+(2x-14).
Simplifying,
2(x+14)+(2x-14),
= 2x + 28 + 2x - 14
= 4x + 28 - 14
= 4x + 14
Therefore, the solution is 4x + 14.
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524127 Add mathematical signs (+, -, ), (*, /) in between all or some oft he above digits so the result of the created mathematical equation will be 100
Answers
524127 = 100
5 x (-2 +4 ) x (1+2+7)
=5x2 x 10
=10 x 10
=100
A stock value doubles every 42 days. If the stocks start out with $5.00, what will the value of the stock be in 18 weeks?
A.)$125.00
B.)$15.00
C.)$30.00
D.)$40.00
Answers
We should find the value of the stock in 18 weeks. Let us denote this value with S.
One week has 7 days, so 18 weeks have: 18*7=126 days.
In order to find how many times the stocks value was doubled we should divide this number of days with 42: 126/42=3
So, after 18 weeks the value of the stock would be: 5->5*2->(5*2)*2=40
answer:
D.)$40.00
Write an equation for each
1. 10
2. 12
4. 16
6. 20
Answers
x(10) = y
When x is 2 and y is 12
x(6) = y
when x is 4 and y is 16
x(4) = y
When x is 6 and y is 20
x(4) - 4 = y
hope this helps
Patty has 8 flowerpots, and she wants to plant a different type of flower in each pot. There are 11 types of flower available at the garden shop. How many different ways can choose the flowers?
Answers
C(n, r) = [tex] \frac{n!}{(n-r)!r!} [/tex]
C(11, 8) = [tex] \frac{11!}{(11-8)!8!} [/tex]
C(11, 8) = 165
So, there are 165 ways of choosing 8 flowers out of 11 flowers
how do you factor 2x^3+5y^3
Answers
[tex]\mathrm{Apply\:sum\:of\:cubes\:rule:\:}x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)[/tex]
[tex]2x^3+5y^3=\left(\sqrt[3]{2}x+\sqrt[3]{5}y\right)\left(\left(\sqrt[3]{2}\right)^2x^2-\sqrt[3]{2}\sqrt[3]{5}xy+\left(\sqrt[3]{5}\right)^2y^2\right)[/tex]
[tex]\left(\sqrt[3]{2}x+\sqrt[3]{5}y\right)\left(\left(\sqrt[3]{2}\right)^2x^2-\sqrt[3]{2}\sqrt[3]{5}xy+\left(\sqrt[3]{5}\right)^2y^2\right) \ \textgreater \ Refine[/tex]
[tex]\left(\sqrt[3]{2}x+\sqrt[3]{5}y\right)\left(2^{\frac{2}{3}}x^2-\sqrt[3]{10}xy+5^{\frac{2}{3}}y^2\right)[/tex]
Hope this helps!
For a cylinder open at one end with radius r cm and height h cm, find the dimensions giving the minimum surface area, given that the volume is 44 cm3.
Answers
To find the dimensions of a cylinder with one open end that minimizes its surface area given a volume of 44 cm³, use calculus and the formulas for the cylinder's volume and surface area. The solution results in radius r ≈ 1.34 cm and height h ≈ 9.87 cm.
Explanation:For a cylinder open at one end, the surface area is given by the formula A = πr² + πrh, where r is the radius and h is the height.
The volume of a cylinder is given by the formula V = πr²h. Given that V=44 cm³, we can write the volume equation as h = V / (πr²).
Substituting this into the surface area equation, we get A = πr² + πr(V / (πr²)) = πr² + V/r.
We want to minimize the surface area, so we take the derivative of A with respect to r, set it equal to zero and solve for r.
Doing this gives us: dA/dr = 2πr - V/r² = 0 => r = cuberoot(V/2π).
Substituting V=44 cm³ into this, we get r = cuberoot(22/π) ≈ 1.34 cm.
Substituting r back into h = V / (πr²), we derive that h = 44 / (π * (1.34)²) ≈ 9.87 cm.
Therefore, the dimensions that will minimize the surface area of the cylinder given that the volume is 44 cm³, are approximately r = 1.34 cm and h = 9.87 cm.
This is a classic problem of optimization in calculus.
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Peter begins his kindergarten year able to spell 10 words. He is going to learn to spell 2 new words every day. Determine the minimum number of whole days it will take for him to be able to spell at least 75 words.
Answers
Hope this helped :D
Peter needs 33 whole days to be able to speak 75 words.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Peter begins his kindergarten year able to spell 10 words.
He is going to learn to spell 2 new words every day.
Assuming no. of days it will take him to be able to spell at least 75 words
is d.
∴ The inequality that represents this scenario is 2d + 10 ≥ 75.
2d ≥ 65.
d ≥ 32.5 but it will take him 33 whole days to learn 75 words.'
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what is the perimeter of a polygon with sides measuring; (a) cm,(a+1) cm;(a+2) cm and 3(a+3)?
Answers
Here, the sides are: a, a+1, a+2, and 3(a+3)
So,
[tex]a+(a+1)+(a+2)+3(a+3)[/tex]
Now, do the distributive property and combine like terms,[tex]a+a+1+a+2+3a+9[/tex][tex]6a+12[/tex]
The answer is 6a + 12. Hope this helps and have a terrific day!
What is the distance between the two endpoints in the graph below? If necessary, round your answer to two decimal places.
Answers
How to multiply fractions with a mixed number?
Answers
So Multiple
7/2*1/2
Refine the fractions
7/2*2
Multiple the numbers 2*2=4 to get
7/4
and that equals 1, 3/4
A cell phone company charges a monthly fee plus $0.25$0.25 for each text message. The monthly fee is $30.00$30.00 and you owe $59.50$59.50. Write and solve an equation to find how many text messages xx you had.An equation is
Answers
the difference between the measures of two supplementary angles is 42. find both
Answers
x - (180 - x) = 42
x - 180 + x = 42
2x - 180 = 42
2x = 42 + 180
2x = 222
x = 222/2
x = 111
180 - x =
180 - 111 =
69
ur angles are : 69 and 111
Answer:
69 and 11, took me 1 hour to slove this
Step-by-step explanation: