Find the slope of the line through p and q. p(5, −9), q(−5, 6)
Answers
Answer: slope = -1,5
Step-by-step explanation:
We can use slope formula to find the slope of a line that passes through two points (x₁ , y₁) and (x₂ , y₂)
m = ∆y/∆x = (y₂ - y₁)/(x₂ - x₁)
Given points are: p(x₁ , y₁) = (5 , −9) and q(x₂ , y₂) = (−5 , 6)
Substituting these two known points in the slope formula, we have:
m = (6-(-9))/(-5-5) = 15/-10 = -1,5
Therefore, the slope of this line = -1,5
Answer: slope = -1,5
Spymore
Related Questions
in a 10x10 grid that represents 800, one square represents
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10x10=100
So, the squares must equal 8 times as many as 10.
So it would be 8.
(2x^3+2x^2-16x+32)÷(x^2-3x+4) divide polynomial using long division
Answers
_________________________
x^2-3x+4 / 2x^3+2x^2-16x+32
Note that x^2 divides into 2x^3 with a partial quotient of 2x. Multiply x^2-3x+4 by this 2x and write your product under 2x^3+2x^2-16x+32:
__2x _________________________
x^2-3x+4 / 2x^3+2x^2-16x+32
2x^3 -6x^2 + 8x
----------------------- subtract
8x^2 -24x + 32
Now divide x^2 into 8x^2: result is 8.
__2x + 8_________________________
x^2-3x+4 / 2x^3+2x^2-16x+32
2x^3 -6x^2 + 8x
-----------------------
8x^2 -24x + 32
8x^2 -24x + 32
------------------------ subtract
0
So the desired quotient is 2x+8, or 2(x+4).
Geneva rode her bike a total of 2 1/2 miles from her house to school. First she rode 4/5 mile from her house to the park. Then she rode 1/5 mile from the park to her friends house . Finally she rode the rest of the way to her school? How many miles did she ride from her friends house to school
Answers
Answer:
She rode [tex]1\frac{1}{2}[/tex] miles from her friends house to school.
Step-by-step explanation:
Geneva rode her bike a total = [tex]2\frac{1}{2}[/tex] miles
She rode from her house to the park = [tex]\frac{4}{5}[/tex] miles
She rode from the park to her friend's house = [tex]\frac{1}{5}[/tex] miles
total distance from her house to her friend's house = [tex]\frac{4}{5}+\frac{1}{5}[/tex] = 1 mile
Finally she rode the rest of the way to her school.
distance between her friend's house to school = [tex]2\frac{1}{2}-1[/tex] = [tex]\frac{3}{2}[/tex] miles
[tex]1\frac{1}{2}[/tex] miles she rode from her friends house to school
Andrew believes that the probability that he will win the tennis match is 2/9. what is the probability that he will lose the tennis match?
Answers
This is because, in this scenario, a 100% probability is 9/9 and if the probability he will win is 2/9, then the probability he will lose is 9/9-2/9=7/9
Ina case whereby Andrew believes that the probability that he will win the tennis match is 2/9.the probability that he will lose the tennis match is [tex]\frac{7}{9}[/tex]
What is probability?Probability is the likelihood that something will occur. When we're not sure how something will turn out, we can discuss the likelihood of different outcomes, or their probabilities. Statistics is the study of events that follow a probability distribution.
p(he will win the tennis match )= 2/9.
P(he will lose the tennis match) =1 - 2/9
[tex]\frac{9}{9} -\frac{2}{9}[/tex]
=[tex]\frac{7}{9}[/tex]
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"isotherms are drawn at regular intervals; on this map, the interval between successive isotherms is ______ fahrenheit degrees."
Answers
An isotherm on a geographic map is a type of equal temperature at a given date or time. And if we talk about thermodynamics, it is a curve on a Pressure – Volume diagram at a constant temperature.
Basing from the graph, we can actually see that the interval is:
10 Fahrenheit degrees
If y has moment-generating function m(t) = e 6(e t −1) , what is p(|y − µ| ≤ 2σ)?
Answers
Now assuming [tex]\mu,\sigma[/tex] denote the mean and standard deviation of [tex]Y[/tex], respectively, then we know right away that [tex]\mu=6[/tex] and [tex]\sigma=\sqrt6[/tex].
So,
[tex]\mathbb P(|Y-\mu|\le2\sigma)=\mathbb P(6-2\sqrt6\le Y\le6+2\sqrt6)=\dfrac{66366}{175e^6}\approx0.940028[/tex]
50 points and brainliest
(3^8 x 2^-5 x 9^0) ^-2 x (2^-2 / 3^3) ^4 x 3^28
Write your answer in simplified form. Show all the steps
Answers
(3^8 *2^-5 *9^0)^-2 * (2^-2/3^3)^4 * 3^28 =
(6561 * 0.03125 * 1)^-2 * (0.25/27)^4 * 2.287679245x10^13 =
0.0000237881 * 0.00000000073503 * 2.287679245x10^13 =
0.40000008, round to 0.4
= 3^-16 2^10 x 1^-2 x 2^-8 x 3^-12 x 3^28
= 3^0 x 2^10 x 1^-2 x 2^-8
=1 x 2^2 x 1
= 1 x 4 x 1
= 4
One half liter of lemonade concentrate is added to 3 liters of water. how many one thirds liter servings of lemonade are made.
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so in short, how many times does 1/3 go into 3 and 1/2?
let's change the mixed to "improper" and divide then.
[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}\\\\ -------------------------------\\\\ \cfrac{\quad \frac{7}{2}\quad }{\frac{1}{3}}\implies \cfrac{7}{2}\cdot \cfrac{3}{1}\implies \cfrac{21}{2}\implies 10\frac{1}{2}[/tex]
You take a trip by air that involves three independent flights. if there is an 76% chance each specific leg of the trip is on time, what is the probability all three flights arrive on time?
Answers
After a concert for 1,200 people, only 9 people said they would not go to see the band again. What percent of the people who went to the concert said they would not go to see the band again? 0.75% 9% 75% 133%
Answers
divide 9 by 1200
9 / 1200 = 0.0075 = 0.75%
Suppose that we roll a fair die until a 6 comes up.
a.what is the probability that we roll the die n times
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1 _______=5,280 feet
Answers
hope this helps
find the sum of all 3 digit whole numbers that arw divisible by 13 ?
Answers
a0 = 1st 3-digit number divisible by 13
a0 = 104
d = 13 (why?)
last term is largest divisible by 13 = 988
how many terms? (988-104)/13 + 1 = 69
S = 69/2(104+988) = 37674
The sum of all 3-digit whole numbers that are divisible by 13 is [tex]\( \boxed{37674} \)[/tex].
To find the sum of all 3-digit whole numbers that are divisible by 13, we can use the arithmetic series formula.
1. Identify the first and last 3-digit numbers divisible by 13:
- The smallest 3-digit number divisible by 13 is 104 (since [tex]\( 13 \times 8 = 104 \)[/tex]).
- The largest 3-digit number divisible by 13 is 988 (since [tex]\( 13 \times 76 = 988 \)[/tex]).
2. Calculate the number of terms in the series:
- Use the formula for the number of terms n in an arithmetic sequence:
[tex]\[ n = \frac{\text{last term} - \text{first term}}{\text{common difference}} + 1 \][/tex]
Here, the common difference d = 13:
[tex]\[ n = \frac{988 - 104}{13} + 1 = \frac{884}{13} + 1 = 68 + 1 = 69 \][/tex]
3. Find the sum of the arithmetic series:
- The sum [tex]\( S_n \)[/tex] of the first n terms of an arithmetic series is given by:
[tex]\[ S_n = \frac{n}{2} \times (\text{first term} + \text{last term}) \][/tex]
Substitute the values:
[tex]\[ S_{69} = \frac{69}{2} \times (104 + 988) \][/tex]
Simplify the calculation:
[tex]\[ S_{69} = \frac{69}{2} \times 1092 = 34.5 \times 1092 = 37674 \][/tex]
Thus, the sum of all 3-digit whole numbers that are divisible by 13 is [tex]\( \boxed{37674} \)[/tex].
what is the domian of the function y=In (-x+3/2)
Answers
The domain of the function y = ln (-x + 3/2) is all real numbers less than 3/2, represented in interval notation as (-∞, 3/2). This is because the argument of the logarithm must be positive, leading to an inequality that restricts x to be less than 3/2.
Explanation:The domain of a function refers to the complete set of possible values of the independent variable. For the function y = ln (-x + 3/2), we must consider where the argument of the natural logarithm, -x + 3/2, is greater than zero. This is because the natural logarithm function is defined only for positive arguments.
To find the domain, set the argument of the logarithm function greater than zero: -x + 3/2 > 0. Solving this inequality, we find -x > -3/2, hence x < 3/2. This means that the domain of the function is all real numbers less than 3/2, which can be written in interval notation as (-∞, 3/2).
The domain of a function is the set of all possible input values. In the function y = ln(-x + 3/2), the natural logarithm function is defined only for positive numbers, so to find the domain, we need to identify the values of x that make the argument of the logarithm greater than zero.
Solve for the argument inside the logarithm to be greater than zero: -x + 3/2 > 0
Simplify the inequality to find the valid domain: x < 3/2
Therefore, the domain of the function y = ln(-x + 3/2) is x < 3/2.
The isosceles triangle has a perimeter of 7.5m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?
Answers
2x=7.5-2.1
2x=5.4
x=2.7
Answer:
2.1 +2x=7.5
Step-by-step explanation:
if Chelsea has 11 times as many art. Brushes and they have 60 art brushes altogether how many brushes does Chelsea have
Answers
Explain how finding 4x 384 can help you find 4 x 5,384. Then find both products
Answers
so the answer is 21,536
I HAVE 2 QUESTIONS:
1. if y = x^2 - x find the value of y when x = 3
2. if y = x^3 + x find the value of y when x = 5
Answers
1. y=6
2. =130
the ratio of girls to boys in the math club was 3.5. if there were 120 children altogether, how many girls were there?
Answers
3 girls to 5 boys
3+5 =8
120/8 = 15
3 *15 = 45 girls
One book costs 95p. How much do five books cost?
Answers
If one book costs 95p, then 5 must cost 5 times 95p.
95*5
=475
Five books would cost 475p.
Hope this helps.
-Benjamin
may i please have some help?
Answers
notice the tickmarks, thus TP = PU and TQ = QS, so the PQ segment is then a midsegment of the larger triangle, and thus the angles it makes on the small one, are exactly the same.
a right triangle has one angle that measures 23 degress.The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.What is the approximate area of the triangle?Round to the nearest tenth.Area of a triangle =1/2bh
Answers
Answer:
Area of the triangle will be 162.3 cm²
Step-by-step explanation:
From the figure attached,
In the triangle ABC angle ACB = 23°, side BC = 27.6 cm and hypotenuse AC = 30 cm
Now we have to calculate the area of the given right angle triangle.
Since area of a right angle triangle is represented by
Area = [tex]\frac{1}{2}\times b\times h[/tex]
Where b = adjacent side
h = opposite side
To calculate the opposite side of the triangle we will apply Pythagoras theorem in the ΔABC.
AC² = AB² + BC²
AB² = AC² - BC²
AB² = (30)² - (27.6)²
= 900 - 761.76
= 138.24
AB = √138.24
= 11.76
Area of the triangle = [tex]\frac{1}{2}(AB)(BC)[/tex]
= [tex]\frac{1}{2}(11.76)(27.6)[/tex]
= 162.28 cm² ≈ 162.3 cm²
the vertex of this parabola is at (3,5). When the y-value is 6, the x-value is -1. What is the coefficient of the squared term in the parabolas equation
Answers
[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ vertex \begin{cases} h=3\\ k=5 \end{cases}\implies y=a(x-3)^2+5 \\\\\\ \textit{we also know that } \begin{cases} y=6\\ x=-1 \end{cases}\implies 6=a(-1-3)^2+5 \\\\\\ 1=a(-4)^2\implies 1=16a\implies \cfrac{1}{16}=a[/tex]
The coefficient of the squared term in the parabola's equation, with a vertex at (3,5) and passing through the point (-1,6), is 1/16.
The student is asking about the coefficient of the squared term in the parabola's equation given that the vertex is at (3,5) and another point on the parabola is (-1,6). Since we know the vertex, we can write the vertex form of a parabolic equation as:
y = a(x - h)
^2 + k
Plugging the vertex into the equation, we get:
5 = a(3 - 3)
^2 + 5
This simplifies down to:
5 = a(0) + 5
So, we cannot determine 'a' from the vertex alone. However, we can use the other point to find 'a'. Plugging the coordinates (-1,6) into the vertex form, we get:
6 = a(-1 - 3)^2 + 5
6 = a(-4)^2 + 5
6 = 16a + 5
1 = 16a
a = 1/16
Therefore, the coefficient 'a' is 1/16.
Can someone help me with 2 and 4
Answers
First write down what we know:
Number of papers delivered per year
(1) 31
(2) 55
(3) 60
(4) 78
Now add 31,55,60,78 and then divide by 4
[tex] \frac{31 + 55 + 60 + 78}{4} = 56[/tex]
Answer:
For the four years Alexis delivered 56 papers per week
Number 4:
Thomas caught 24 fish in total. He then gave 6 to his mother and then divided the rest of the fish between his two aunts. It want to know how many fish did each aunt get.
He had 24 the he gave 6 away so we have 24 - 6 = 18 fish left. Now he divide the rest 18 between his two aunts so 18 / 2 = 9. This mean each aunt received 9 fish each.
explain -3 1/3, 3.3, -3 and 3/4, 3.5 from least to greatest
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Write 34 13/20 as a decimal please help!
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Use a calculator to divide 13/20.
13/20 = 0.65
34 13/20 = 34 + 13/20 = 34 + 0.65 = 34.65
The length of the base of a rectangle is 6 less than 3 times the width. The perimeter of the rectangle is 52 inches. What is the length of the base?
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what's the length? well, length = 3w - 6.
Nine fewer than half a number is a five more than a four times the number.define a varible, write an equation, and slove to find the number
Answers
0.5x-9 = 4x+5
add 9 to both sides
0.5x = 4x+14
subtract 4x from each side
-3.5x =14
x = 14/*3.5
x = -4
A sum of $5000 is invested at an interest rate of 5% per year. Find the time required for the money to double if the interest is compounded continually. A(t)=Pe^rt
Answers
The time required for the principal amount to double is 13 years 10 months and 10 days approx.
What is compound interest?Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The term "compound" is crucial here.
CI Formula. C.I. = Principal (1 + Rate)^time − Principal.
Given, A sum of $5000 is invested at an interest rate of 5% per year.
hence, principle = 5000
Amount = 10000
rate = 5%
let's assume the time is x
Let's solve for time
A(t)= 10000 = 5000* e⁵ˣ/¹⁰⁰
2 = (e)^x/20
taking logs on both sides
ln 2 = x / 20
x = 20 ln2
time required = 20 ln2 = 20 * 0.69 = 13.86
Therefore, To make the amount double at the interest rate of 5% we need time approx 13 years 10 months, and 10 days.
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Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds. suppose that to qualify for the nationals, a woman must complete the 200-meter backstroke in less than 128 seconds. what proportion of competitive female swimmers will qualify for the nationals? give your answer to four (4) decimal places.
Answers
The probability of a normally distributed data is given by:
[tex]P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\bar{x}}{\sigma} \right)[/tex]
Thus, the probability that a woman completes the 200-meter backstroke in less than 128 seconds is given by:
[tex]P(X\ \textless \ 128)=P\left(z\ \textless \ \frac{128-141}{7} \right)=P(z\ \textless \ -1.857)=0.03165[/tex]
Therefore, the proportion of competitive female swimmers who will qualify for the nationals is 0.0317 to 4 decimal places.