You should invite at least 23 guests to your party to have at least a 2/3 chance of having a guest with the same birthday as yours.
For your party, you need to invite at least 23 randomly chosen guests in order to have a probability of 2/3 or higher of having a guest with the same birthday as yours. This is known as the birthday paradox and it is based on the probability of two people having the same birthday. To calculate the number of guests needed for the probability of having at least one match, you can use the following formula:
P(at least one match) = 1 - (365/365)^n
where n is the number of guests you invite.
So, to solve for n, you would rearrange the equation to:
n = ln(1-P) / ln(365/365)
When P = 2/3, this equation gives us n = 23.
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If tan(theta)= 3/4 and 180 degree < theta < 270 degrees, what is sin(theta)?
Answer:
sin(theta) = -3/5.
Step-by-step explanation:
We know that tan(theta) = 3/4, which means that the ratio of the opposite side to the adjacent side of a right triangle with angle theta is 3/4. We can use the Pythagorean theorem to find the hypotenuse of the triangle:
hypotenuse^2 = opposite^2 + adjacent^2
hypotenuse^2 = (3^2) + (4^2)
hypotenuse^2 = 9 + 16
hypotenuse^2 = 25
hypotenuse = 5
Since 180 degrees < theta < 270 degrees, we know that theta is in the third quadrant, where the sine function is negative. Therefore, sin(theta) = -opposite/hypotenuse = -3/5.
So, sin(theta) = -3/5.
Find the common difference of the arithmetic sequence − 15 , − 13 , − 11 , . . . −15,−13,−11,...
Answer:
Common difference = 2
Step-by-step explanation:
We can find the common difference by subtracting any two consecutive terms with the smaller number being subtracted from the larger:
Thus, to find the common difference, d, we can subtract -13 from -15:
d = -15 - (-13) = -15 + 13 = 2
The question is in the screenshot below :)
Answer:
Step-by-step explanation:
The circumference is the perimeter of a circle, which is equal to 131.88ft.
Circumference = [tex]2\pi r^{2}[/tex]
[tex]131.88=2\pi r^{2} \\r^{2} =\frac{131.88}{2\pi } \\r=\sqrt{20.989} \\r=4.581[/tex]
This means that the diameter is:
[tex]d=2r\\d=9.163[/tex]
So our area is:
[tex]A=\pi r^{2} \\A=\pi (4.581)^{2} \\A=65.940[/tex]
Hope this helped!
A study of a local high school tried to determine the mean amount of money that each student had saved. The study surveyed a random sample of 99 students in the high school and found a mean savings of 3800 dollars with a standard deviation of 500 dollars. Determine a 95% confidence interval for the mean, rounding all values to the nearest whole number.
A 95% confidence interval for the average is 3898.
What is confidence interval ?In statistics, the confidence interval formula is used to express the degree of uncertainty surrounding a sample estimate of a population parameter.
Formula of confidence interval:
If n ≥ 30,
Confidence Interval = m ± z(SD/√n)
where,
n = Number of terms
m = Sample average
SD = Standard Deviation
Value for the confidence interval in the z table is z.
Table of Confidence interval and Z
CI z
0.70 1.04
0.75 1.15
0.80 1.28
0.85 1.44
0.90 1.645
0.92 1.75
0.95 1.96
0.96 2.05
0.98 2.33
0.99 2.58
According to the question
random sample of student (n) = 99
average savings = 3800 dollars
Standard deviation = 500 dollars
95% confidence interval for the average needed
i.e , z = 1.96
Now, By using Formula of confidence interval:
Confidence Interval = m ± z(SD/√n)
substituting the values
Confidence Interval = 3800 ± 1.96(500/√99)
= 3800 ± 98.49
= 3898.49
values to the nearest whole number
Confidence Interval = 3898
Hence, A 95% confidence interval for the average is 3898 .
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PLEASE HELP QUICK
Find the circumference. Use π = 3.14.
In the circle below, EG is a diameter. Suppose m FG = 116° and mZ GFH=69°. Find the following.
We can conclude after answering the provided question that Therefore, diameter m GFH = 21° and m GZH = 116°.
what is diameter?In geometry, the diameter of a circle is any straight line segment that has an endpoint on the circle and travels through its centre. Another way to put it is the longest chord of a circle. Either concept can be used to define the diameter of a sphere. The diameter is the length of the line that runs tangent to the two points at either end of the circle. If you consider length to be the distance between two points, diameter equals length. The diameter of a circle is the distance between its two furthest points.
We know that angle EGF is a right angle (90°) because EG is a diameter.
Given that m FG = 116°, we can calculate m FGE by subtracting it from 180° (the sum of triangle angles):
m FGE = 180 degrees - m FG = 180 degrees - 116 degrees = 64 degrees
m GFH = 180° - m ZGF - m ZGFH = 180° - 90° - 69° = 21°
Finally, we can calculate m GZH by subtracting m FGE from 180° (the sum of triangle angles):
180° m GZH - 180° m FGE - 64° = 116°
Therefore, m GFH = 21° and m GZH = 116°.
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construct a rectangle so that the diagonal is 6 cm and angle between them is 30 degree
Answer:
Let the length of the rectangle be x and the width of the rectangle be y.
Then, we can use the Pythagorean Theorem to find the value of x and y:
x2 + y2 = 62
x2 + y2 = 36
We can use trigonometry to find the value of x and y:
x = 6 sin 30°
y = 6 cos 30°
Therefore, the length of the rectangle is 6 sin 30° cm and the width of the rectangle is 6 cos 30° cm.
PR is ranger to circle Q at Point R. PS is tangent to circle Q at Point S. Find m
The value of m∠Q is 148°.
What is tangent?
The straight line that "just touches" the curve at a given location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.
Here, we have
Given: PR is ranger to circle Q at Point R. PS is tangent to circle Q at Point S.
We have to find the value of m∠Q.
We know that PR = PS
In ΔPRS
∠P + ∠R + ∠S = 180°
∴ ∠R = ∠S
∠P + ∠R + ∠R = 180°
38 + 2∠R = 180°
2∠R = 180° - 32°
2∠R = 148°
∠R = 74°
∠S = 74°
∠PRQ = 90°
In ΔSRQ
∠SRQ = 90° - 74° = 16°
∠RSQ = 90° - 74° = 16°
∴ ∠SRQ + ∠RSQ + ∠RQS = 180°
16° + 16° +∠RQS = 180°
∠RQS = 180° - 32°
∠RQS = 148°
m∠Q = 148°
Hence, the value of m∠Q is 148°.
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The measuring scale on an oil tank is shown. What fraction of the oil tank is empty? Full
Answer:
1/4
Step-by-step explanation:
As given the figure, 3 out of 4 rectangles are shaded,
So,
4/4-3/4=1/4
7 root 3 by root10 + root3 - 2 root5 by root6 +root5 -3 root 2 by root15 + 3root2
The evaluation of expression 7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2) and simplification to get the final result of 2√5 - 2√6 + 6.
To evaluate the expression is
7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2)
we need to rationalize the denominators of each fraction. To do this, we can multiply both the numerator and denominator of each fraction by the conjugate of the denominator.
For the first fraction, we can multiply the numerator and denominator by (√10 - √3):
7√3(√10 - √3) / [(√10 + √3)(√10 - √3)]
Simplifying the denominator gives:
7√3(√10 - √3) / 10 - 3
For the second fraction, we can multiply the numerator and denominator by (√6 - √5):
-2√5(√6 - √5) / [(√6 + √5)(√6 - √5)]
Simplifying the denominator gives:
-2√5(√6 - √5) / 6 - 5
For the third fraction, we can multiply the numerator and denominator by (√15 - 3√2):
-3√2(√15 - 3√2) / [(√15 + 3√2)(√15 - 3√2)]
Simplifying the denominator gives:
-3√2(√15 - 3√2) / 15 - 9
Now, we can simplify each expression separately and then combine them:
7√3(√10 - √3) / 7 = √30 - 3
-2√5(√6 - √5) / 1 = -2√6 + 2√5
-3√2(√15 - 3√2) / 6 = -√30 + 9
Combining the expressions gives:
√30 - 3 - 2√6 + 2√5 - √30 + 9
Simplifying further gives:
2√5 - 2√6 + 6
Therefore, the value of the expression 7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2) is 2√5 - 2√6 + 6.
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√16² Please help me find what the value is
Answer:
16
Step-by-step explanation:
When you square a square root (√1^2) it just cancels out. :)
Ashim draws this picture on a piece of paper measuring 12 cm by 8cm. He colours the six circles red and the rest of the paper blue. Calculate the area of the paper that is blue.
The area of the blue paper obtained by subtracting the 6 circle areas from the rectangle is 20.64 sq. cm.
Explain about the area of circle?A circle is made up of all points in a single plane that are equidistant from one another. Only the bordering points make up the circle. The radius is the distance from the centre to the outside of the circle.
The diameter is the length of a line that connects the circle's ends to its middle point. The radius is half as large as the diameter.
Given data:
length l = 12 cm
width w = 8 cm
radius r = 4/2 = 2 cm.
Area of blue page = Total area of rectangle - 6*area of circle
Area of blue page = length * width - 6*π*r²
Area of blue page = 12*8 - 6*3.14*2²
Area of blue page = 20.64 sq. cm.
Thus, the area of the blue paper obtained by subtracting the 6 circle areas from the rectangle is 20.64 sq. cm.
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The diameter of a sphere is 4 centimeters. which represents the volume of the sphere? a. startfraction 32 over 3 endfractionπ cm3 b. 8π cm3 c. startfraction 64 over 3 endfractionπ cm3 d. 16π cm3
The volume of the sphere is approximately 33.51 cubic centimeters.
The volume of a sphere can be calculated using the formula:
V = (4/3)π[tex]r^{3}[/tex]
where r is the radius of the sphere
V is the volume of the sphere
Since the diameter of the sphere is 4 centimeters, the radius is half of that, or 2 centimeters.
Plugging this value into the formula, we get:
V = (4/3)π([tex]2^{3}[/tex])
V = (4/3)π(8)
V = (32/3)π
So the answer is (a) 32/3π[tex]cm^{3}[/tex]
the volume of the sphere is approximately 33.51 cubic centimeters.
The volume of the sphere is a measure of how much space the sphere occupies. The formula for the volume of the sphere tells us that the volume is proportional to the cube of the radius. This means that as the radius increases, the volume of the sphere increases much more rapidly. This is why a small increase in the radius can result in a much larger increase in the volume of the sphere.
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Mrs. Vo, Mrs. Manuel, Ms. Soun and Mr. Lopez are contestants on a game show. In one of the rounds of the game
show, the contestants have a chance to spin a wheel up to two times in a row to try to get the highest possible sum
without going over 100. The wheel that they spin is divided into 21 equal portions, each containing one element from
the set of numbers containing 1 and all the multiples of 5 less than or equal to 100.
Mr. Lopez goes first. If he spins the wheel twice, getting a 15 and a 50, what is the probability that on Mrs. Vo's first
spin, she gets a number larger than Mr. Lopez's sum? Express your answer as a common fraction.
Therefore, the probability of Mrs. Vo winning is 1 - 91/300 - 8/21 = 11/30.
What is Probability?Probability refers to the likelihood or chance that a particular event or outcome will occur. It is a mathematical concept that quantifies the degree of uncertainty associated with an event or situation. Probability is typically expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that it is certain to occur.
by the question.
let's consider the first case: Mrs. Vo spins a number greater than 65 on her first spin. There are a total of 8 numbers greater than 65 on the wheel: 70, 75, 80, 85, 90, 95, 100. Since there are 21 sections on the wheel, the probability of spinning a number greater than 65 on the first spin is 8/21.
The number of possible outcomes for Mrs. Vo's spin is 21, since there are 21 equal portions on the wheel. However, we need to exclude the outcomes that would cause Mrs. Vo's sum to exceed 100, since that would result in an automatic loss. The largest possible outcome on the wheel is 100, so Mrs. Vo cannot spin a number greater than or equal to 35 on her first spin.
The number of outcomes that would give Mrs. Vo a winning sum of at least 66 is the number of outcomes greater than 65, which are 70, 75, 80, 85, 90, 95, and 100. There are 7 such outcomes.
If Mrs. Vo spins a number less than or equal to 65 on her first spin, the probability of this happening is 13/21. The probability of her second spin being between 1 and 35 is 35/100 (since there are 35 numbers between 1 and 35 on the wheel). So, the probability of her total sum being less than or equal to 65 is (13/21) * (35/100) = 91/300.
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A 80cm by 100cm rectangular piece of cardboard is to be made into an open top box by cutting squares out of the corners and folding up the sides. The area of the base of the box is 4000 cm?. Find its dimensions.
The dimensions of the box are 30 cm by 50 cm by 25 cm.
Define areaArea is a measure of the amount of space enclosed by a two-dimensional object, such as a shape or a surface. It is usually expressed in square units, such as square meters (m²), square inches (in²), or square centimeters (cm²), depending on the unit system used.
Let x be the side length of the squares that are cut out of each corner of the cardboard.
When the squares are cut out and the sides are folded up, the resulting box will have dimensions (80-2x) cm by (100-2x) cm by x cm.
The area of the base of the box is:
(80-2x) cm × (100-2x) cm = 8000 - 360x + 4x² cm²
We know that the area of the base is 4000 cm², so we can set this equal to the expression we just found:
8000 - 360x + 4x² cm² = 4000 cm²
Simplifying and rearranging, we get a quadratic equation:
4x² - 360x + 4000 = 0
Dividing both sides by 4, we get:
x² - 90x + 1000 = 0
This quadratic can be factored as:
(x - 40)(x - 25) = 0
Therefore, the possible values of x are x = 40 cm and x = 25 cm.
If we use x = 40 cm, then the dimensions of the box are:
Length = 80 - 2x = 0 cm (not possible)
Width = 100 - 2x = 20 cm
Height = x = 40 cm
If we use x = 25 cm, then the dimensions of the box are:
Length = 80 - 2x = 30 cm
Width = 100 - 2x = 50 cm
Height = x = 25 cm
Therefore, the dimensions of the box are 30 cm by 50 cm by 25 cm.
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With a ruler, Antonio determines the diameter of a baseball to be 6.4 centimeters
and the diameter of a bowling ball to be 12.8 centimeters. Antonio claims that the
bowling ball has twice the volume of the baseball.
In FOUR sentences, explain Antonio's misconceptions.
Use the formula for the volume of a sphere to determine the volume of both the
baseball and the bowling ball in cubic centimeters and then compare their volumes.
A sphere's volume may be calculated using the formula [tex]137.25[/tex] cm cube.
How do you determine a sphere's volume?V = 4/3 r3, where V is the volume and r is the radius, is the formula for a sphere's volume. 1/2 of a sphere's radius makes up its radius. Therefore, you may determine the radius first, followed by the volume, to get the surface of a circle given its diameter.
What are the sphere's surface area and volume?The radius of a sphere is the distance between its center and its outside surface. The amount of space a satellite's surface covers is known as its surface area, and it is equal to 4r2.
The diameter of the sphere, [tex]d = 6.4[/tex] cm
Radius,[tex]r = 3.2[/tex] cm
We need to find the volume of the sphere. The formula for the volume of a sphere is given by :
[tex]V=4/3pir^{3}[/tex]
[tex]4/3pi*(3.2)^{3}[/tex]
[tex]=137.25 cm^{3}[/tex]
The radius of the bowling ball is [tex]6.4 cm/2 = 3.2 cm[/tex], and its volume is [tex]V[/tex] bowling [tex]= 4/3 pi(3.2)^{3} * 8 = 1,100.8[/tex] cubic cm.
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Zee is a babysitter. She gets paid $25 just to show up on time. Then each hour, she
makes $8 babysitting. How many hours does she have to work to make a total of
$233?
Explain your answer to the previous question. How did you solve it? What was your procedure?
ii) The difference between Simple interest and Compound interest of a certain sum of money is 50.4 at 6% p.a. for 2 years. Find the principal.
The principal from difference between Simple interest and Compound interest of a certain sum of money is 50.4 at 6% p.a. for 2 years is $14,000.
How to calculate the principalLet the principal be P.
Simple interest = P x 0.06 x 2 = 0.12P
Compound interest = P(1 + 0.06)^2 - P = 1.1236P - P = 0.1236P
Given: Compound interest - Simple interest = 50.4
0.1236P - 0.12P = 50.4
0.0036P = 50.4
P = 50.4 / 0.0036
P = 14000
Therefore, the principal is $14,000.
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Please help me with this and show work for each question
Answer:
A
Step-by-step explanation:
Find the area of a triangle whose vertices have the coordinates (-1, 1). (-1. 5), and (4. 1).
The area of the triangle with vertices (-1, 1), (-1, 5), and (4, 1) is 10 square units.
What is the area of a triangle?The area of a triangle is a measure of the amount of space inside the triangle. It is defined as half the product of the base of the triangle and its corresponding height.
If a triangle has base length b and corresponding height h, then its area A is given by the formula:
A = (1/2) × b ×h.
In the given question,
To find the area of the triangle with vertices (-1, 1), (-1, 5), and (4, 1), we can use the formula: A = (1/2) × b ×h.
where the base is the distance between two vertices of the triangle and the height is the perpendicular distance from the third vertex to the base.
We can choose any two points as the endpoints of the base, but it may be easiest to use the points (-1, 1) and (4, 1), since the height will be the vertical distance from the third vertex (which is ( -1, 5)) to the base.
The distance between (-1, 1) and (4, 1) is: base = 4 - (-1) = 5
To find the height, we need to determine the perpendicular distance from the point (-1, 5) to the line containing the base. This can be done by finding the equation of the line containing the base and then finding the distance from the point (-1, 5) to that line.
The equation of the line containing the base is: y = 1
since the line is horizontal and passes through the point (4, 1) and (-1, 1).
The distance from the point (-1, 5) to the line y = 1 is:
height = |5 - 1| = 4
where the absolute value is taken to ensure that the height is positive.
Now, we can substitute the values of the base and height into the formula for the area:
Area = (1/2) × base × height
= (1/2) * 5 * 4
= 10
Therefore, the area of the triangle with vertices (-1, 1), (-1, 5), and (4, 1) is 10 square units.
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if a/3 = 2/b, what are the following ratios?
3a-3b/a-b
If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio and the ratio in the given situation is 3a:2b = 6:1.
What do we mean by ratios?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
A proportion is an equation that sets two ratios at the same value.
For instance, if there is 1 boy and 3 girls, you may express the ratio as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.
Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B).
So, we know that:
a+b/a-b = 5/3
Now, solve as follows:
3 ( a + b) = 5 ( a - b)
3 a + 3 b = 5 a - 5 b
5 b + 3 b = 5 a - 3 a
8 b = 2 a
2 a = 8 b
a = 4 b
3 a = 3 × 4 b
3 a = 12 b
3 a: 2 b = 12 b : 2 b
Then: 3a:2b = 6:1
Therefore, if b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio and the ratio in the given situation is 3a:2b = 6:1.
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Correct question:
A+b/a-b=5/3 what are the following ratios? 3a:2b
Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar. If the triangles are similar, write a valid similarity statement. Problems 7 & 8
The given triangles are similar by AA~, SSS~, SAS~, or not similar.
What is similar triangles in maths?
Triangles that are similar to one another in terms of shape but not necessarily size are called congruent triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size.
7. In triangles AEB & BDC
AE/BD = EB/DC
We can conclude that, the corresponding sides are in common ratio, so triangles are similar.
Hence, The given triangles are similar.
8. Given a figure of two triangles, ΔLKM and ΔLJN
Here,
LK/LJ = LM/LN
21 - 6/21 = 10/14
15/21 = 10/14
5/7 = 5/7
We can conclude that, the corresponding sides are in common ratio, so triangles are similar.
Hence, The given triangles are similar.
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Calculate the size of each exterior angle of a regular 10-sided polygon.
Answer:
The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides. The sum of exterior angles of a polygon is 360°. The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides.
Step-by-step explanation:
rectangle ABCD with diagonal AC, labeled as measuring 5 inches, angle BAC measuring 30 degrees, angle BCA measuring 60 degrees, angle DCA measuring 30 degrees, and angle DAC measuring 60 degrees. Rounded to the nearest tenth, what is the perimeter of rectangle ABCD?
Answer:
5 + 10[tex]\sqrt{3}[/tex]
= 22.3205080757
Step-by-step explanation:
Answer:
≈ 13,7 inches
Step-by-step explanation:
Just use trigonometry (sin or cos) from the right triangles ∆ABC and ∆ADC
What else would need to be congruent to show that AABC = AXYZ by ASA?
AA
C
B
A
N
OA. BC=YZ
OB. ZY ZB
OC. ZZ ZA
D. AC = XZ
Y
X
Given:
ZZZC
CB ZY
The answer is option (A) BC=YZ ,to show that AABC = AXYZ by ASA, we need to know that angle C is congruent to angle ∠Y, angle ∠Z is congruent to angle ∠B, and BC is congruent to ZY.
What are Angle?An angle is a geometric figure formed by two rays with a common endpoint, called the vertex of the angle. The two rays are called the sides of the angle, and they can be named in any order. The measure of an angle is the amount of rotation needed to bring one of the rays into alignment with the other.
To show that AABC = AXYZ by ASA, we need to show that two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle. Since we are given that ZZZC and CB ZY, we know that angle ∠C is congruent to angle ∠Y, and angle ∠Z is congruent to angle ∠B. Therefore, we need to find another piece of information that shows that the included sides are congruent.
Looking at the diagram, we can see that side BC is congruent to side ZY, since they are opposite sides of a rectangle. Therefore, we have BC = ZY, which means that statement A, BC=YZ, is true.
So, to show that AABC = AXYZ by ASA, we need to know that angle ∠C is congruent to angle ∠Y, angle ∠Z is congruent to angle ∠B, and BC is congruent to ZY. Since we have all three of these conditions, we can conclude that AABC = AXYZ by ASA.
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URGENT! Please give the correct answer (25 POINTS).
Answer:
y-y1=m(x-x1)[tex] \frac{y - y1}{m} = x - x1 \\ x1 = x - \frac{y - y1}{m} [/tex]
so,A is the correct answer...
Part B. The Cure
A doctor prescribes 500 milligrams of penicillin to treat this infection.
Each hour following the initial dose, 80% of the concentration remains in
the body from the preceding hour.
h) What type of function can be used to model this situation? Explain.
Answer:
An exponential function can be used to model this situation.
In this case, we know that each hour following the initial dose, 80% of the concentration remains in the body from the preceding hour. This means that the amount of penicillin remaining in the body is decreasing exponentially.
We can use the formula for exponential decay, which is:
A = A0 * e^(-kt)
where A is the amount of penicillin remaining in the body at time t, A0 is the initial amount of penicillin (in this case, 500 milligrams), k is the decay constant, and e is the mathematical constant approximately equal to 2.718.
The decay constant, k, can be calculated using the following formula:
k = ln(0.8)
where ln is the natural logarithm.
So the exponential function that can be used to model this situation is:
A = 500 * e^(-0.2231t)
where t is the time in hours since the initial dose was administered.
This function will give us the amount of penicillin remaining in the body at any time t, based on the initial dose and the rate of decay.
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2. Where is the point of discontinuity of y =
=
O x = 5
O x = 49
O x=-10
O x = -5
-10x+49
x-5
?
Answer:
2. Where is the point of discontinuity of y =
=
O x = 5
O x = 49
O x=-10
O x = -5
-10x+49
x-5
?
Write the equation of the line that passes through the points (-7,7) and (−2,−6). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
An equation of the line that passes through the points (-7, 7) and (−2, −6) in point-slope form is y - 7 = -13/5(x + 7).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]
Where:
m represent the slope.x and y represent the points.At data point (-7, 7), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 7 = \frac{(-6- 7)}{(-2 -(-7))}(x -(-7))\\\\y - 7 = \frac{(-6- 7)}{(-2 +7)}(x +7)[/tex]
y - 7 = -13/5(x + 7)
y = -13x/5 + 7 - 91/5.
y = -13x/5 - 56/5
In this context, we can reasonably infer and logically deduce that an equation of the line that represents this line in slope-intercept form is y = -13x/5 - 56/5.
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What are the domain and range of the inequality: y < sqrt{x + 3} + 1
A: x < -3 and y < 1
B: x < 3 and y < 1
C: x > 3 and y > 1
D: x > -3 and y > 1
After answering the provided question, we can conclude that Therefore, inequality the answer is (D) x > -3 and y > 1.
What is inequality?In mathematics, an inequality is a non-equal relationship between two expressions or values. As a result, imbalance leads to inequality. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal sign is commonly used (). Different inequalities, no matter how small or large, are used to contrast values. Many simple inequalities can be solved by modifying the two sides until only the variables remain. But a number of things contribute to inequality: Negative values are divided or added on both sides. Trade off the left and right.
domain and range of the inequality
[tex]y - 1 < \sqrt{x + 3}\\(y - 1)^2 < x + 3\\(y - 1)^2 - 3 < x\\[/tex]
Therefore, the answer is (D) x > -3 and y > 1.
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