Answer:
(15+x)÷4 = 80-x
by criss cross we'll get:
15+x = 4(80-x)
15+x = 320-4x
x+4x=320-15
5x = 305
x = 61
The diagram shows 3 identical circles inside a rectangle.
each circle touches the other 2 circles and the side of the rectangle, as shown in the diagram.
Radius of each circle is 28mm.
work out the area of the rectangle.
Give your answer correct to three significant figures
The area of the rectangle is 6272 mm² (to three significant figures).
What is area?Area is a physical quantity that refers to the amount of space within a two-dimensional shape or surface. It is typically measured in square units such as square meters, square centimeters, or square feet.
What is radius?Radius is a measure of the distance from the center of a circle to any point on its circumference. It is often denoted by the letter "r" and is usually expressed in units of length, such as meters or millimeters.
In the given question,
We can start by drawing lines connecting the centers of the circles and the rectangle.
Let's call the width of the rectangle "w" and the height of the rectangle "h".
Since each circle touches the side of the rectangle, we know that the diameter of each circle is equal to the width of the rectangle, so:
diameter of each circle = radius of each circle = 28 mm
Therefore, we can write:
2 x 28 mm + w + w = h
Simplifying, we get:
w + 56 mm = h/22w + 56 mm = h
Now we can find the area of the rectangle by multiplying its width and height:
Area of rectangle = w x h
Substituting for "h", we get:
Area of rectangle = w x (2w + 56 mm)
Expanding and simplifying, we get:
Area of rectangle = 2w² + 56w mm²
To find the value of "w", we can use the fact that the radius of each circle is 28 mm and the circles touch each other, so:
w + 2 x 28 mm + w = 3 x diameter of each circle
Simplifying, we get:
2w + 56 mm = 3 x 2 x 28 mm
2w + 56 mm = 168 mm
2w = 112 mmw = 56 mm
Now we can substitute this value of "w" into the formula for the area of the rectangle:
Area of rectangle = 2w² + 56w mm²
Area of rectangle = 2 x (56 mm)² + 56 mm x 56 mm
Area of rectangle = 6272 mm²
Therefore, the area of the rectangle is 6272 mm² (to three significant figures).
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A sample of 128g of an unknown substance has a half-life of 1,250
years. Approximately how long will it take for 37 grams of the substance
to remain (to the nearest year)?
The radioactive decay will take approximately 3,051 years for 37 grams of the substance to remain.
What is radioactive decay ?
Radioactive decay is the process by which an unstable atomic nucleus loses energy (in terms of mass in its rest frame) by emitting ionizing particles or radiation such as alpha particles, beta particles, gamma rays, or positrons. As a result of this decay, the nucleus may transform into a different nuclide or isotope with a different number of protons or neutrons or into a different energy state. The rate of decay of a radioactive substance is measured by its half-life, which is the amount of time it takes for half of the original amount of the substance to decay.
According to the question:
The half-life formula for radioactive decay is:
[tex]N = N0 (1/2)^{t/h}[/tex]
where N is the amount of substance remaining after time t, N0 is the initial amount of substance, h is the half-life, and t is the time elapsed.
We can use this formula to find the time it takes for 37 grams of the substance to remain. Let N0 be the initial amount of substance, which is 128 g, and N be the amount of substance remaining, which is 37 g. We know the half-life is 1,250 years. Let's plug in these values and solve for t:
[tex]37 = 128 (1/2)^{t/1250}[/tex]
Dividing both sides by 128, we get:
[tex](1/2)^{t/1250} = 37/128[/tex]
Taking the logarithm of both sides with base 1/2, we get:
t/1250 = log(37/128) / log(1/2)
Simplifying, we get:
t = 1250 log(128/37) / log(1/2)
t ≈ 3,051 years
Therefore, it will take approximately 3,051 years for 37 grams of the substance to remain.
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Imagine we have a simple linear model, with one X predicting one Y, where R-squared is equal to .81. What was the correlation between X and Y?A) .81 (or maybe -.81)B) There is not enough information to tell.C) .66 (or maybe -.66)D) .90 (or maybe -.90)
The correlation between X and Y can be calculated using the formula r = SQRT(R-squared).The correlation coefficient is a measure of the strength of the linear relationship between two variables and can range from -1 to 1
In this case, the R-squared value is 0.81, so the correlation between X and Y is r = SQRT(0.81) = 0.9 (or -0.9 depending on the direction of the relationship).The correlation between X and Y can be calculated using the formula r = SQRT(R-squared). The correlation coefficient is a measure of the strength of the linear relationship between two variables and can range from -1 to 1, where -1 is a perfectly negative linear relationship, 0 is no linear relationship, and 1 is a perfectly positive linear relationship. In this case, the correlation between X and Y was 0.9, indicating a strong linear relationship between the two variables.
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Michelle bought a new car for $25,000. She paid a 10% down payment and financed the remaining balance for 72 months with an APR of 6.5%. Assuming she makes monthly payments, determine the total interest Michelle pays over of the loan.
Answer:
Michelle paid a 10% down payment, which is:
10% of $25,000 = $2,500
So the amount she financed is:
$25,000 - $2,500 = $22,500
To calculate the monthly payment, we can use the formula for a loan payment:
P = (r * A) / (1 - (1 + r)^(-n))
where P is the monthly payment, r is the monthly interest rate (APR divided by 12), A is the amount financed, and n is the number of payments (72 in this case).
First, we need to calculate the monthly interest rate:
r = 6.5% / 12 = 0.00541667
Plugging in the values, we get:
P = (0.00541667 * $22,500) / (1 - (1 + 0.00541667)^(-72))
P = $363.12
So Michelle will pay $363.12 per month for 72 months.
To calculate the total interest paid over the life of the loan, we can multiply the monthly payment by the number of payments and subtract the amount financed:
Total interest = (P * n) - A
Total interest = ($363.12 * 72) - $22,500
Total interest = $7,111.04
Therefore, Michelle will pay a total of $7,111.04 in interest over the life of the loan
5) What is the probability of picking a vowel, replacing it
and then picking a consonant from the word "SLEEP"?
The probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is approximately 0.096 or 9.6%.
What is probability?Probability is usually expressed as a number between 0 and 1, with 0 meaning that the event is impossible and 1 meaning that the event is certain.
According to question:There are two vowels (E) and three consonants (S, L, P) in the word "SLEEP".
The probability of picking a vowel on the first draw is 2/5, because there are two vowels out of five letters total.
Since we replace the vowel we picked, the probability of picking another vowel on the second draw is also 2/5.
The probability of picking a consonant on the third draw is 3/5, because there are three consonants left out of five letters total.
Therefore, the probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is:
(2/5) x (2/5) x (3/5) = 12/125 or approximately 0.096 or 9.6%.
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2. write how many degrees are angle between.
a) North and East _______
Answer:
N and E is 90 degrees
N and S is 180 degrees
N and W is 90 degrees
Just need help on 7,8, and 9
According to the given information, the missing values in the ratio table are:
7. 6:1/3, 12:2, 6:1, 24:4
8. 1/4:3, 2:6, 1:12, 5/4:15
9. 1/3:8/3, 2/3:2/3, 1:1, 4/3:1.04
What is ratio?
A ratio is a mathematical comparison of two or more quantities. Ratios express the proportional relationship between the quantities being compared. Ratios are often written using a colon (:) or as a fraction, such as "1:2" or "1/2".
7.
We can simplify the ratio of feet to seconds by converting 1/3 to its equivalent fraction with a denominator of 3:
Ratio of feet to seconds = 6 : 1/3 = 6 : (1/3) = 6 : (1/3) x (3/3) = 6 : 1
So, the ratio of feet to seconds is 6 : 1.
Using this ratio and the other ratios given, we can create equations to solve for the missing values:
6 : 1 = 12 : x
Cross-multiplying, we get: 6x = 12
Solving for x, we get: x = 2
y : 1 = 6 : 1
Cross-multiplying, we get: y = 6
6 : 1 = 24 : z
Cross-multiplying, we get: 6z = 24
Solving for z, we get: z = 4
Therefore, the missing values are:
x = 2, y = 6, z = 4
8.
We can set up equations based on the given ratios and solve for the missing values.
1/4 : x = blue ribbon : red ribbon
y : 6 = blue ribbon : red ribbon
1 : z = blue ribbon : red ribbon
5/4 : 15 = blue ribbon : red ribbon
To find x:
1/4 : x = 1 : z (since blue ribbon : red ribbon = 1 : z)
Cross-multiplying, we get:
1z = 4x
z = 4x
To find y:
y : 6 = 1/4 : x (since blue ribbon : red ribbon = 1/4 : x)
Cross-multiplying, we get:
y * x = 6 * 1/4
y * x = 3/2
y = (3/2) / x
To find z:
1 : z = 5/4 : 15 (since blue ribbon : red ribbon = 1 : z)
Cross-multiplying, we get:
1 * 15 = 5/4 * z
z = (1 * 15 * 4) / 5
z = 12
Therefore, the values of x, y, and z are x = 3, y = 2, and z = 12.
9.
To find the values of x, y, and z, we need to first simplify the ratios given.
The ratio between orange fabrics and yellow fabric is:
1/3 : 8/3
We can simplify this ratio by multiplying both sides by 3 to get:
1 : 8
The ratio between 2/3 and x is:
2/3 : x
The ratio between 1 and y is:
1 : y
The ratio between 4/3 and z is:
4/3 : z
We can simplify this ratio by multiplying both sides by 3/4 to get:
1 : (4/3)z or 1 : 1.33z (rounded to two decimal places)
Now we have the following ratios:
Orange : Yellow = 1 : 8
2/3 : x = 2/3 : x
1 : y = 1 : y
1 : (4/3)z = 1 : 1.33z
To solve for x, y, and z, we can use cross-multiplication.
Orange : Yellow = 1 : 8
1/8 = (Orange / Yellow)
8/1 = (Yellow / Orange)
2/3 : x = 2/3 : x
This ratio is already in its simplest form, so x = 2/3.
1 : y = 1 : y
This ratio is already in its simplest form, so y = 1.
1 : (4/3)z = 1 : 1.33z
1 = (4/3)z / 1.33z
1 = 0.96z
z = 1.04
Therefore, the values of x, y, and z are:
x = 2/3, y = 1, z = 1.04
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TRUE/FALSE.In a preliminary investigation report, the findings section includes a summary of a project request and a specific recommendation.
In a preliminary investigation report, the findings section includes a summary of a project request and a specific recommendation. - False
The outcomes of the inquiry and any pertinent data or information that was gathered are normally presented in the findings section of a preliminary investigation report. This might contain a synopsis of the problem or topic under investigation, an outline of the research approach taken, and a statement of any findings or recommendations made in light of the data gathered.
On the other hand, the recommendations part often follows the results section and provides detailed ideas or plans for handling the problem or issue at hand. The conclusions of the inquiry, as well as any pertinent research or industry standards, may all be taken into consideration when making the recommendations.
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Two cars, one going due east at the rate of 90 km/hr and the other going to south at the rate of 60 km/hr are traveling toward the intersection of two roads. At what rate the two cars approaching each other at the instant when the first car is 0.2 km and the second car is 0.15 km from the intersection ?
The two cars are approaching each other at a rate of 36 km/hr at the given instant.
We can solve this problem by using the Pythagorean theorem and differentiating with respect to time. Let's call the distance of the first car from the intersection "x" and the distance of the second car from the intersection "y". We want to find the rate at which the two cars are approaching each other, which we'll call "r".
At any moment, the distance between the two cars is the hypotenuse of a right triangle with legs x and y, so we can use the Pythagorean theorem
r^2 = x^2 + y^2
To find the rates of change of x and y, we differentiate both sides of this equation with respect to time
2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)
Simplifying and plugging in the given values
dr/dt = (x(dx/dt) + y(dy/dt)) / r
dr/dt = (0.2 x 90 + 0.15 x (-60)) / sqrt((0.2)^2 + (0.15)^2)
dr/dt = (18 - 9) / sqrt(0.04 + 0.0225)
dr/dt = 9 / sqrt(0.0625)
dr/dt ≈ 36 km/hr
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Gilberto opened a savings account for his daughter and deposited $1500 on the day she was born. Each year on her birthday, he deposited another $1500. If the account pays 9% interest, compounded annually, how much is in the account at the end of the day on her 11th birthday?
Using compound interest, the amount in the account at the end of the day on her 11th birthday is $240,019.25.
To solve this problem, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^{(nt)}[/tex]
where A is the amount of money in the account at the end of the 11th year, P is the principal amount (initial deposit), r is the annual interest rate (9%), n is the number of times interest is compounded per year (once annually), and t is the number of years (11).
First, we need to calculate the total amount of money that Gilberto deposited into the account over the 11 years:
1500 + 1500 × 10 = $16,500
Next, we can plug the values into the formula and solve for A:
A = 1500[tex](1 + 0.09/1)^{(1 * 11)}[/tex] + 1500[tex](1 + 0.09/1)^{(2 * 11)}[/tex] + ... + 1500[tex](1 + 0.09/1)^{(11 * 11)}[/tex]
A = 1500 × [[tex](1.09)^{11}[/tex] + [tex](1.09)^{22}[/tex] + ... + [tex](1.09)^{121}[/tex]]
A = 1500 × [[tex](1.09^{11}[/tex] - 1)/(1.09 - 1)]
A = 1500 × [(1.315 - 1)/(0.09)]
A = $240,019.25
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Macy of New York sold LeeCo. of Chicago office equipment with a $6,300 list price. Sale terms were 3/10, n/30 FOB New York. Macy agreed to prepay the $40 freight. LeeCo. pays the invoice within the discount period. What does LeeCo. pay Macy?
The amount that LeeCo pays Macy for the office equipment at the $6,300 list price, sales terms of 3/10, n/30 FOB with payment made within the discount window, is $6,111.
What is a cash discount?A cash discount refers to a reduction in the price of an item due to payment within the discount period.
A cash discount incentivizes the customer to make prompt payments.
The list price of the equipment = $6,300
Sales terms: 3/10, n/30 FOB
Prepaid freight = $40
Cash discount = $189 ($6,300 x 3%)
Payment after the discount = $6,111 ($6,300 - $189)
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In the diagram below ijk~ljm. FIND G
As the triangles are similar to each other, using congruent theorem, we get the value of side g = 2m.
What are similar triangles?Comparable triangles are those that resemble one another but may not be precisely the same size. Comparable items are those that share the same shape but differ in size.
This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is often known as "similarity".
As per the triangles,
g/5 = 4/10
⇒ g = 4 × 5/10
⇒ g = 2m.
Therefore, we conclude that the value of g = 2m as per the similar triangles' theorem.
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Two angles of a quadrilateral measure 301° and 10°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?
Answer:
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360°. We know that the measures of two angles are 301° and 10°.
Let x be the measure of the smaller of the other two angles, and let y be the measure of the larger of the two angles.
We know that x:y = 2:5, so we can write y = (5/2)x.
Using the fact that the sum of all four angles is 360°, we can write an equation:
301° + 10° + x + y = 360°
Substituting y = (5/2)x, we get:
301° + 10° + x + (5/2)x = 360°
Combining like terms, we get:
311° + (7/2)x = 360°
Subtracting 311° from both sides, we get:
(7/2)x = 49°
Multiplying both sides by 2/7, we get:
x = 14°
So the smaller of the two angles is 14°.
Using y = (5/2)x, we get:
y = (5/2) × 14° = 35°
Therefore, the measures of the two angles are 14° and 35°.
Please help and explain what and why you did to get the answer.
For the equation complete the given ordered pairs.
x = -5
(,4), (, -3), (,0)
The ordered pairs of given equation are (3/2,4), (1/3, -3),(5/6,0)
What is ordered pairAn ordered pair is composed of the ordinate and the abscissa of the x coordinate, with two values supplied in parentheses in a specified sequence. Placing a point on the Cartesian plane could be beneficial for visual comprehension.
for example, the ordered pair (x, y) signifies an ordered pair in which 'x' is referred to as the first element and 'y' is referred to as the second element. These items, which can be either variables , have distinct names depending on the context in which they are used. In an ordered pair, the element order is quite significant.
Given Equation of Y=6x−5
First Ordered pair;(,4)
y=4
x=4+5/6
x=3/2
First Ordered pair;(, -3)
y=-3
x=-3+5/6
x=1/3
First Ordered pair; (,0)
y=0
x=5/6
The ordered pairs of given equation are
(3/2,4), (1/3, -3),(5/6,0)
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The complete question is:
For The Equation, Y=6x−5
Complete The Given Ordered Pairs (,4), (, -3), (,0)
WILL GIVE BRAINLIEST PLEASE ANSWER FAST!
In each triangle, M, N, and P are the midpoints of the sides. Name a segment parallel to the one given.
Answer: UV
Step-by-step explanation:
Find the perimeter of the triangle whose vertices are (−4,3), (−4,1), and (−5,−4). Write the exact answer. Do not round.
Answer:
2 + √[26] + √[50]
Step-by-step explanation:
To find the perimeter of a triangle with vertices given in the coordinate plane, we need to calculate the distance between each pair of vertices and then add them up.
Using the distance formula, the distance between the first two vertices is:
√[(x2 - x1)^2 + (y2 - y1)^2] =
√[(-4 - (-4))^2 + (1 - 3)^2] =
√[0 + 4] = 2
The distance between the second and third vertices is:
√[(x2 - x1)^2 + (y2 - y1)^2] =
√[(-5 - (-4))^2 + (-4 - 1)^2] =
√[1 + 25] = √[26]
Finally, the distance between the third and first vertices is:
√[(x2 - x1)^2 + (y2 - y1)^2] =
√[(-4 - (-5))^2 + (3 - (-4))^2] =
√[1 + 49] = √[50]
Therefore, the perimeter of the triangle is:
2 + √[26] + √[50]
This is the exact answer, and we cannot simplify it further.
the number of creeping bentgrass shoots on an average size (6000 square feet) well-maintained putting green can range from ______ shoots.
The total number of creeping bentgrass shoots on a 6000 square feet putting green could range from approximately 480,000 to 600,000 shoots.
The United States Golf Association (USGA) suggests that a healthy putting green, which is well-maintained, can support around 80 to 100 creeping bentgrass plants in each square foot. As the given putting green is 6000 square feet, we can calculate the total number of creeping bentgrass plants on this area by multiplying the area by the suggested number of plants per square foot. Therefore, the total number of creeping bentgrass shoots on a well-maintained 6000 square feet putting green could range from approximately 480,000 to 600,000 shoots, based on the given range of suggested plants per square foot.
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what is the domain of the function {(-1,-1),(0,1),(2,-1)}
a) (-1,1)
b) (-1,0,2)
c) (-1,0,1,2)
d) {(-1,-1),(0,1),(2,-1)}
Answer:
[tex]b) \quad(-1,0,2)[/tex]
Step-by-step explanation:
The domain is the set of all input values for a function. It can be represented as a list of values where it is countable or as a set notation
Here there are only 3 ordered pairs. The first entry in each ordered pair represents the input of the function, the second entry the corresponding output value
Looking at the first entry in all three ordered pairs we get the domain as
[tex](-1, 0 , 2)[/tex]
The weight of a goat increased by 12 pounds is 38 pounds. Write an equation to represent the situation.
The answer would be g+12=38
Answer:
x+12=38
Step-by-step explanation:
we do not know the starting weight of the goat so we can use x to represent it and then is increased by twelve so we can add that and we know the current weight is 36 pounds so x+12 with equal 36
(4) Practice: Using Visual Cues
Step-by-step explanation:
Refer to pic..........
convert 457000СМ² to M².
Answer: 45.7
Explanation:
Divide the area value by 10000
Al's total payment for his loan was $34,267. What was his monthly payment if he
paid it off after making 42 monthly payments? Round to the nearest dollar. Do not
state the units.
Answer: 816
Step-by-step explanation:
Let's denote the monthly payment by x.
Then, Al paid a total of 42x dollars over 42 months.
We know that the total payment for the loan was $34,267. Therefore, we can set up the equation:
42x = 34267
Solving for x, we get:
x = 34267/42
x ≈ 816
So Al's monthly payment was approximately $816.
Find the area of the region that is bounded by the given curve and lies in the specified sector.
r = e^ θ/2
π/6 = θ = 7π/6
The area of the region that is bounded by the given curve and lies in the specified sector is A = 2(e^(7π/12) - e^(π/12))
The polar curve r = e^(θ/2) represents a spiral that starts from the origin and gets farther away as it unwinds. We want to find the area of the region that lies inside this spiral and inside the sector defined by the angles θ = π/6 and θ = 7π/6.
To solve the problem, we need to find the points where the curve intersects the sector, which are given by plugging in the values of θ:
r(π/6) = e^(π/12)
r(7π/6) = e^(7π/12)
Then we can set up the integral for the area inside the sector:
A = 1/2 ∫[π/6, 7π/6] (r(θ))^2 dθ
Substituting the equation for r:
A = 1/2 ∫[π/6, 7π/6] e^θ/2 dθ
Using the power rule for integration:
A = 2(e^(7π/12) - e^(π/12))
This is the exact value of the area inside the sector and inside the spiral. If we want a decimal approximation, we can use a calculator or computer software to evaluate it.
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35% of households say they would feel secure if they had 50000 in savings he randomly selected 8 households and ask them if they would feel secure if they had 50000 in savings find the probability that the number that say that they would feel secure a exactly 5B more than 5 &c at most 5
Probability that precisely 5 people will respond that they would feel comfortable is 0.0808
Probability that more than 5 people will respond that they would feel comfortable is0.1061
Probability that at most 5 people will respond that they would feel comfortable is 0.9747
Probability Definition in MathProbability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence.
Solving the problem:35 percent of households claim that having $50,000 in savings would make them feel comfortable. Ask 8 homes that were chosen at random if they would feel comfortable if they had $50,000 in savings.
Binomial conundrum with p(secure) = 0.35 and n = 8.
the likelihood that the number of people who claim they would feel comfortable is
(a) The number exactly five is equal to ⁸C₅ (0.35)5×(0.65)×3=binompdf(8,0.35,5) = 0.0808.
(b) more than five = 1 - binomcdf(8,0.35,4) = 0.1061
(c) at most five = binomcdf(8,0.35,5) = 0.9747.
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what is 7 in x 3 in x 6 in x 4 in x 15 in=
Answer:
7,560 inches.
Step-by-step explanation:
Given: 7 in x 3 in x 6 in x 4 in x 15 in = ?
First, multiply 7 and 3:
21 in x 6 in x 4 in x 15 in
Then multiply 21 and 6:
126 in x 4 in x 15 in
Then multiply 4 and 15:
126 in x 60 in
Finally, multiply 126 and 60:
= 7,560 inches.
Consider points A(1,3) , B(4,-2) , and C(5,2). Let D be the midpoint of AB. How can you prove that C lies on the perpendicular bisector of AB? Complete each statement.
The coordinates of D are: B. (2.5, 0.5).
The product of the slopes of CD and AB is: C. -1.
This shows that AB is perpendicular to CD. Therefore, C lies on the perpendicular bisector of AB.
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Substituting the given parameters into the midpoint of a line segment formula, the midpoint of line AB is given by;
Midpoint AB = [(4 + 1)/2, (-2 + 3)/2]
Midpoint AB = [5/2, 1/2]
Midpoint AB = (2.5, 0.5).
5, 2
Next, we would determine the slopes of line segment CD and AB:
Slope (m) of CD = (0.5 - 2)/(2.5 - 5)
Slope (m) of CD = -1.5/-2.5 = 3/5
Slope (m) of AB = (-2 - 3)/(4 - 1)
Slope (m) of AB = -5/3 = 0.6
Product of the slopes = 3/5 × -5/3 = -3/3 = -1.
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Please select the correct answer. Which expression is equivalent to the given expression?
Answer:
[tex]5a^6b[/tex]
Step-by-step explanation:
To simplify this expression, we can divide 20a^8b^2 by 4a^2b.
First, we can simplify the numbers by dividing 20 by 4 to get 5.
Then, we can simplify the variables by subtracting the exponents of the same bases (a and b).
[tex]\frac{20}{4}[/tex] · [tex]\frac{a^8}{a^2}[/tex] · [tex]\frac{b^2}{b}[/tex]
[tex]5[/tex] · [tex]a^6[/tex] · [tex]b[/tex]
This gives us the simplified expression 5a^6b. So the answer would be the third one down, or [tex]5a^6b[/tex].
the given point is on the graph of y=f(x). Find a point on the graph of y=g(x).
g(x)=f(x−1)+3; (6,15)
The point (6, 15) on the graph of y = f(x) corresponds to the point (6, 18) on the graph of y = g(x).
What is graph?A graph is a visual representation of data, usually depicted as a set of points or lines plotted on a coordinate plane or a series of bars or other shapes displayed in a bar chart or pie chart. Graphs are used to show relationships between variables, trends over time, or comparisons between different data sets.
According to question:The problem asks us to find a point on the graph of y = g(x) given that (6, 15) is a point on the graph of y = f(x), and g(x) = f(x - 1) + 3.
To find a point on the graph of y = g(x), we need to substitute the given value of x = 6 into the formula for g(x):
g(6) = f(6 - 1) + 3
Simplifying the expression on the right-hand side, we have:
g(6) = f(5) + 3
Since (6, 15) is a point on the graph of y = f(x), we know that f(6) = 15.
g(6) = f(5) + 3
g(6) = 15 + 3
g(6) = 18
Therefore, the point (6, 15) on the graph of y = f(x) corresponds to the point (6, 18) on the graph of y = g(x).
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please find the midpoint of the following line and arc using straightedge-compass-construction method
The midpoint of a line or arc can be found using straight edge-compass-construction method by drawing two perpendicular bisectors. The intersection of these bisectors is the midpoint.
To find the midpoint of a line segment, first draw a straight line passing through both endpoints of the segment using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the line segment. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the line segment. The intersection of these bisectors is the midpoint of the line segment.
To find the midpoint of an arc, first draw a chord that intersects the arc at two points using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the chord. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the chord. The intersection of these bisectors is the center of the circle that the arc belongs to. Draw a line from the center of the circle to the midpoint of the chord. This line will intersect the arc at its midpoint.
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--The question is incomplete, answering to the question below--
"find the midpoint of a line and arc using straight edge-compass-construction method"
6th grade math, is this correct?
Answer:
No, it is y = - 3x + 7
( negative 3x not positive )
Hope this helps!
Step-by-step explanation:
1. Subtract both sides by 3x
3x + y - ( 3x ) = 7 - ( 3x )
2. Combine like terms
( 3x - 3x ) + y = 7 - ( 3x )
0 + y = 7 - ( 3x )
y = 7 - ( 3x )
y = -3x + 7