A line with a positive slope generally moves upward from left to right, representing an increase in y-values as x-values rise.
Explanation:If a line has a positive slope, its general direction is upward from left to right. This means that as the x-values increase, the y-values also increase. The slope of a line in mathematics represents the rate at which y changes with respect to x. A positive slope indicates a direct relationship between the two variables involved; as one increases, so does the other. In the context of a graph, this manifests as a line that rises as it moves along the x-axis.
The nature of the slope determines the line's direction. A higher positive slope indicates a steeper ascent, while a smaller positive slope results in a less steep, flatter incline. The concept of slope is crucial in economics as well, as it measures the relationship between two variables, such as price and quantity supplied, where a positive slope illustrates that firms supply more as the price goes higher.
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?
What is the 214 term in the sequence 7,10,13,16?
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
Given: Triangles ABC and DBC are isosceles, m∠BDC = 30°, and m∠ABD = 155°.
Find m∠ABC, m∠BAC, and m∠DBC.
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°.
Find a number that is 24 more than its opposite
What is the probability that a roll of a pair of 6-sided dice will sum to 8?
Simplify , You may leave the numerator and denominator of your answer in factored form ?
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) ?
What is the slope of the graph?
slope = -3
slope = -1/3
slope = 1/3
slope = 3
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]
Factor the expression over the complex numbers.
x^2+50
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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the difference between the measures of two supplementary angles is 42. find both
Answer:
69 and 11, took me 1 hour to slove this
Step-by-step explanation:
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?
What operation would you use to find the next term in the sequence 96,48,24,12?
524127 Add mathematical signs (+, -, ), (*, /) in between all or some oft he above digits so the result of the created mathematical equation will be 100
what is the perimeter of a polygon with sides measuring; (a) cm,(a+1) cm;(a+2) cm and 3(a+3)?
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.
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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How to multiply fractions with a mixed number?
Is the TI-36X Pro allowed in the PSAT
Write an equation for each
1. 10
2. 12
4. 16
6. 20
What is the distance between the two endpoints in the graph below? If necessary, round your answer to two decimal places.
which property is illustrated the following statement? 3z+4=4+3z
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.
how do you factor 2x^3+5y^3
If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is
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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Russ and vickie are trying to solve a problem.There are 93 students taking buses to the museum.if each bus holds 22 students how many buses will they need? Vickie says they need 4 buses. Russ says they need 5 buses. who is correct?
whats 6.3 x 10^-5 in standard notation
2(x+14)+(2x-14)= do you know this
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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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
For anyone who needs the measure itself, it's 70.
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.
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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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?
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