The equation of the line passing through the points (3, 3) and (4, 5) is:
y = 2x - 3
How to solve equation?
To find the equation of the line passing through the points (3, 3) and (4, 5), we can use the point-slope form of the equation of a line:
y - y₁= m(x - x₁)
where m is the slope of the line and (x₁, y₁) is one of the points on the line.
First, we need to find the slope of the line. We can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) = (3, 3) and (x₂, y₂) = (4, 5):
m = (5 - 3) / (4 - 3) = 2
Now we have the slope, we can use the point-slope form of the equation of a line with (x₁, y₁) = (3, 3) and m = 2:
y - 3 = 2(x - 3)
Expanding the right-hand side:
y - 3 = 2x - 6
Adding 3 to both sides:
y = 2x - 3
Therefore, the equation of the line passing through the points (3, 3) and (4, 5) is:
y = 2x - 3
This is the slope-intercept form of the equation of a line, which is in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the y-intercept is -3, which is the y-coordinate where the line crosses the y-axis. The slope of 2 indicates that the line is rising at a rate of 2 units for every 1 unit it moves to the right.
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Find the value of x in the figure.
Triangle XYZ is rotated 90° counterclockwise about the origin to produce X'Y'Z'. What are the coordinates of X'Y'Z'?
Answer:
59
Step-by-step explanation:
6 plus 4 equals 8 plus 9
The state fair is a popular field trip destination. This year the senior class at Lakota West and Lakota East both planned trips there. The senior class at Lakota West rented and filled 8 vans and 8 buses with 240 students. Lakota East rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
Answer:
For High School A, the equation is 8x+8y=240, with x representing number of students in a van and y representing the number of students in a bus. For High school B, the equation is 4x+y=54.
Now solve the system of equations to find the values of your variables.
4x+y=54 means that y=54-4x.
Now plug in this value of y into the equation for High School A.
8x+8(54-4x)=240
8x+432-32x=240
192=24x
8=x
Now that you have solved for x, plug this value in to one of the equations to solve for y.
4(8)+y=54
y=22
To check this solution of x=8 and y=22, plug these values into the other equation
8(8)+8(22)=240
Because this is correct, you know that each van holds 8 students and each bus holds 22 students.
Cakculate the Length of line x
The length of line x in the figure of the cube given is 19.
Calculate the length of the base of the cube, which is the diagonal of the lower sides :
base length = √10² + 6²
base length = √136
The length of x is the diagonal of the cube
x = √baselength² + 15²x = √(√136)² + 15²
x = √136 + 225
x = √361
x = 19
Therefore, the length of line x in the figure given is 19.
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Someone please help me!!
For the given equation, what is the step to clear the fractions and what is the result?
O Multiply both sides by 6 to get 4y - 1 = 21.
O Multiply both sides by 18 to get 12y - 3 = 7.
O Multiply both sides by 6 to get 2y - 1 = 7.
Multiply both sides by 12 to get 2y - 1 = 7
Answer:
The first choice
Step-by-step explanation:
Multiplyil by 6 to get 4y - 1 =21
In Lixue’s garden, the green pepper plants grew 5 inches in 34 month. At this rate, how many feet can they grow in one month? (Let 1 month = 4 weeks)
Answer:
0.15 inches per monthStep-by-step explanation:
step one:
This problem is focused on the growth rate of a plant.
given data
the plants grow 5 inches in 34 months
and also that 1 month= 4 weeks
step two:
We can still say that
if 34 months see a growth of 5 inches
then 1 months will be X inches
cross multiply we have
X= 5/32 inches
step three:
converting this number to decimal we have
X= 0.15 inches per month
Therefore the growth rate would be
0.15 inches per month
196.80/720 long division I will choose brainlist
Historically, the average diameter of the holes drilled has been 0.25 cm and the average range has been 0.10 cm. Samples of size 4 will be collected. For the R-chart, what is the value of upper control limit
Solution :
Given the average range of the holes drilled = 0.10 cm
The average diameter of the holes drilled = 0.25 cm
The sample size = 4
For the sample size of 4, the factor for control limit for the range (\(D_4\)) = 2.28 (From the table of constants for X-bar and R-chart)
The upper control limit for the R-chart = R-bar x \(D_4\)
= 0.10 x 2.28
= 0.228
Therefore, the answer is greater than 0.202 but less than or equal to 0.302
Victoria correctly determined the area of this parallelogram by adding the areas of the rectangle and triangles.
How did Victoria determine the area?
Enter your answer by filling in the boxes.
Victoria determined that the area of the rectangle is
m² and that the area of each triangle is
m². She added the areas of the rectangle and the two triangles for a total area of
Answer:
56 m²
16 m²
88 m²
Step-by-step explanation:
The formula for the area of a rectangle is:
A=L×W (area=length × width)
A=7×8
A=56m²
The formula for the area of triangle is:
1/2×b×h (1/2 × base × height)
A=1/2×4×8
A=2×8
A=16m²
For the total area you will now add the area of each shape. We will multiply triangle area by 2 because there is 2 triangles.
A=56+2(16)
A=56+32
A=88m²
Answer:
I got the Answer:
56 m²
16 m²
88 m²
Solve for measure of angle a.
55°
a = [?]°
25° ат
Check the picture below.
Which expression is equal to the polynomial below 2x^4+5x^3-8x-20
The expression that is equal to the given Polynomial expression is (x^3-4)(2x+5).
The polynomial expression given is 2x^4+5x^3-8x-20. We have to identify the expression that is equal to this given polynomial expression.
We will factor the given polynomial expression to determine the equivalent expression. We can use factorization by grouping to factor the expression completely and determine the equivalent expression .
Factorization by grouping:
We can group the first two terms 2x^4 and 5x^3 together and factor out x^3 from them. We can also group the last two terms -8x and -20 together and factor out -4 from them.
This gives us;2x^4+5x^3-8x-20= x^3(2x+5)-4(2x+5) =(x^3-4)(2x+5)
Therefore, the expression that is equal to the given polynomial expression is (x^3-4)(2x+5).
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i need help with this slope...
Answer:
The slope is 3/2
Step-by-step explanation:
(x1,y1)=(12,16)
(x2,y2)=(34,49)
m= y2−y1 /x2−x1
49−16 /34−12
33 /22
3 /2
Answer:
-3/2
Step-by-step explanation:
y1-y2 / x1-x2
16- 49/12-34
33/22 or -3/2
I hope this helped, Have a Wonderful Day!!
please help me I'm confused .-.
write a compound inequality for each situation
14. Children and senior citizens receive a discount on tickets at the movie theater. To receive a discount, a person must be under 10 years old, or 65 years or older.
15. The scores on the last test ranged from 65% to 100%.
16. Mercury is one of only 2 elements that are liquid at room temperature. Mercury is nonliquid for temperatures less than -38°F or greater than 673.8°F. Write a compound inequality for the temperatures at which mercury in nonliquid.
Answer:
14)A compound inequality is \(10>x\geq 65\)
15)A compound inequality is \(65\% <x< 100\%\)
16)A compound inequality for the temperatures at which mercury in nonliquid. is \(-38^{\circ} F>x> 673.8^{\circ}F\)
Step-by-step explanation:
14)
Let x be the age of person
We are given To receive a discount, a person must be under 10 years old, or 65 years or older.
So, \(x<10\) or \(x \geq 65\)
So, a compound inequality is \(10>x\geq 65\)
15) Let x be the percentage scored
We are given that The scores on the last test ranged from 65% to 100%.
So,\(65\% <x< 100\%\)
So, a compound inequality is \(65\% <x< 100\%\)
16)
Let x be the temperature
We are given that Mercury is nonliquid for temperatures less than -38°F or greater than 673.8°F
So,\(x< -38^{\circ} F\) or \(x > 673.8^{\circ}F\)
\(-38^{\circ} F>x> 673.8^{\circ}F\)
So, a compound inequality for the temperatures at which mercury in nonliquid. is \(-38^{\circ} F>x> 673.8^{\circ}F\)
Answer:
Too ride the roller coaster, one must be at least 4 feet tall.
Step-by-step explanation:
can someone help me solve and graph this equation on the number line.
This is a simple question to solve.
First let's solve the first equation as follows:
As we can see above, first we bring -4 to the first side, and when we do that is changes its sign. After the third line, we multiply both sides per (-1) because we want the x to be positive, and when we do that, the inequality changes its direction (from < to >). And finally, we have -7>x that is the same as x < - 7. As we can see, the graph shows a highlighted piece that represents all the values for x < - 7.
Now let's solve the second equation following the same logic:
Following the same logic we found x >11 and we were able to draw the graph that represents all the values for x > 11.
Can someone please explain step by step on the problem so I could get the answer! If so I’ll mark you brainliest
Answer:
Rewrite 4 as a fraction with a denominator of 11 (make it easier when subtracting).
3 11/11 - 2 7/11
Subtract the fraction part first and then the whole number part.
1 4/11
:)
52% of 225
A-117
B-89
C-50
D-65
Current spot rate EUR/USD = 1.3272. 3-month forward rate EUR/USD = 1.2728. If you expect the spot rate in the next 3 months EUR/USD = 1.15. Suppose you have 1000 EUR in the next 3 months will you?
A. Set up a EUR forward contract, if your prediction is correct, you will make a profit: 12380 USD
B. Set up a EUR forward contract, if you predict correctly, you will make a profit: 12280 USD
C. Set up a EUR forward contract, if you predict correctly, you will profit: 12380 USD
D. Set up a EUR forward contract, if your prediction is correct, you will profit: 12380 USD
Answer:
C. Set up a EUR forward contract, if you predict correctly, you will profit: 123.97 USD.
Step-by-step explanation:
To determine whether setting up a EUR forward contract would result in a profit, we need to compare the potential outcomes based on the given information.
1. Spot Rate: EUR/USD = 1.3272
2. 3-month Forward Rate: EUR/USD = 1.2728
3. Expected Spot Rate in 3 months: EUR/USD = 1.15
To calculate the potential profit or loss, we need to consider the difference between the forward rate and the expected spot rate.
Difference = Forward Rate - Expected Spot Rate
Difference = 1.2728 - 1.15
Difference = 0.1228
Since the forward rate is higher than the expected spot rate, there is a potential for profit if the forward contract is set up and the prediction is correct.
Now, let's calculate the potential profit in USD:
Profit = Difference * Amount in EUR * Forward Rate
Profit = 0.1228 * 1000 EUR * 1.2728 USD/EUR
Profit ≈ 156.97 USD
Based on the calculation, the potential profit from setting up a EUR forward contract, if the prediction is correct, would be approximately 156.97 USD.
None of the given options match this calculated amount exactly. However, option C is the closest option stating a profit of 12380 USD, which may be a typographical error.
Therefore, the most accurate option would be:
C. Set up a EUR forward contract, if you predict correctly, you will profit: 123.97 USD.
PLEASE HELP
Two projectiles are shot vertically upward at the same instant.
Projectile A's height in feet, f(t), is represented in the table, where t is the seconds since the projectile was shot off
Projectile B's height at any time t is modeled by the function
h (t)=-16t^2 +96t
How do the times at which the projectiles begin their descents compare?
SEE PHOTO
Projectile B begins its descent 1 seconds before Projectile A does.
What is y-intercept?In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).
By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:
y-intercept = (0, 44).
Maximum height = (4, 300).
When t = 0, the y-intercept of Projectile B can be calculated as follows;
h(t) = -16t² + 96t
h(0) = -16(0)² + 96(0)
h(0) = 0.
For the maximum height, we have:
h(t) = -16t² + 96t
h'(t) = -32t + 96
32t = 96
t = 96/32
t = 3
Difference in time = 4 - 3
Difference in time = 1 seconds.
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Twelve cards are numbered from 1 to 12 and placed in a box. One card is selected at random and not replaced. Another is randomly selected. What is the probability of selecting two even numbers?
In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:
In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).
The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22
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Which transformation would take Figure A to Figure B?
Answer:.......................
Work out the value of 408 5
Give your answer as a decimal.
The value of 408^5 is approximately 273,539,283,056,896. This is a large number that can be accurately calculated using a calculator or computer program.
To work out the value of 408^5, we need to perform the exponentiation calculation. In this case, 408 is the base, and 5 is the exponent.
Calculating large exponentiations like this can be time-consuming and prone to error if done manually. However, with the help of a calculator or computer, we can easily find the result.
Using a calculator or computer program, we can calculate 408^5 and obtain the value. The result is a very large number:
408^5 ≈ 273,539,283,056,896
Therefore, the value of 408^5 is approximately 273,539,283,056,896.
In decimal notation, the value is written as:
273,539,283,056,896
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HELP PLEASE!!
Create and solve your own one step equation that requires either multiplying or dividing to solve
Answer:
15x12
Step-by-step explanation:
no example heeeeewweee
Answer:
Jack worked at a phone shop. He sold 7 phones each day for 12 days. How many phones did he sell in total?
12x7=84
pls mark brainliest
When constructing a perpendicular bisector of a segment, why should you make arcs with the same radius from each endpoint? Select the true statement.
a. this makes the arcs perpendicular to each other
b. this makes the arcs equidistant from each other
c. this makes the intersections of the arcs equidistant from the endpoints
d. this makes the arcs parallel to the segment
When constructing a perpendicular bisector of a segment, you should make arcs with the same radius from each endpoint as D. this makes the arcs parallel to the segment
What is a perpendicular bisector?A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other words, a perpendicular bisector divides a line segment into two equal parts by intersecting it at a 90-degree angle.
A line segment known as a perpendicular bisector divides a straight line segment into two congruent or equal segments. At the exact midpoint of the line segment, they divide it. The arcs with the same radius from each endpoint is important as this makes the arcs parallel.
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John bought a shirt at ksh 500 and marked it at Ksh 600. A customer bought it at ksh 550. What was the percentage discount?
Answer:
The original price of the shirt was Ksh 500 and it was sold for Ksh 550.
The discount is the difference between the original price and the selling price, which is Ksh 500 - Ksh 550 = Ksh -50.
To find the percentage discount, we can use the formula:
percentage discount = (discount ÷ original price) × 100%
percentage discount = (-50 ÷ 500) × 100%
percentage discount = -10%
Therefore, the percentage discount is 10%.
determine the values of the missing entries. reduce all fractions to the lowest terms
9x-6y= 18
By evaluating the given linear relation, we conclude that the complete table is:
x: 2, 0, 1, 14/3
y: 0, -3, -3/2, 4
How to determine the values of the missing entries?Here we have the linear relation:
9x - 6y = 18
And we want to complete the given table, to do so, we just need to evaluate the relation in the given values and with that we can find the missing ones.
For example, the first pair has y = 0.
Evaluating that we get:
9x - 6*0 = 18
9x = 18
x = 18/9 = 2
Then we have the pair (2, 0).
The second has x = 0, replacing that we get:
9*0 - 6*y = 18
y = 18/-6 = -3
So we have the pair (0, -3)
The third has x = 1, replacing that:
9*1 - 6y = 18
-6y = 18 - 9 = 9
y = 9/-6 = -3/2
So we have the pair (1, -3/2)
The last value on the table is y = 4, replacing that:
9x - 6*4 = 18
9x - 24 = 18
9x = 18 + 24 = 42
x = 42/9 = 14/3
Then the complete table is:
x: 2, 0, 1, 14/3
y: 0, -3, -3/2, 4
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Based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number.
PLEASE ANSWER!!!
The number of students that bike to school is 18
How to determine the valueThe median is described as the middle number of a set of data when the values are arranged in an ascending order from the least to the greatest.
We should also know that the median is one of the measures of central tendency.
From the information given, we have that the data set representing the number of students is;
10, 11, 12 , 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
Then, we have that the median number is;
Median = 17 + 18/2
add the values
Median = 35/2
Divide the values
Median = 18 students
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I need help on this for real
Answer:
x < 3
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
Gang ima just take them points tbh
Step-by-step explanation:
i need help with this one
The value of x from the given figure is 8
How to calculate the interior angle of a triangleA triangle is a 2-dimensional shape with 3 sides an interior angle
Since the sum of the interior angles of a triangle is 180 degrees, hence;
8x - 4 + 76 + 44 = 180
8x + 116 = 180
8x = 180 - 116
8x = 64
x = 64/8
x = 8
Hence the value of x from the given figure is 8
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Nvm I found the answer
Ethan decides to type up some documents while waiting the meeting to start.He can type 2 pages every 1/8 hour.If the meeting started 3/4 hour later than the scheduled time,how many pages can he type before the meeting starts?
Answer: 4 pages
Step-by-step explanation:
To solve this problem, we need to use the formula:
Rate = Output/Time
Let's use "p" to represent the number of pages Ethan can type and "t" to represent the time he has before the meeting starts.
Rate = 2 pages/(1/8 hour) = 16 pages/hour
Since the meeting starts 3/4 hour later than the scheduled time, Ethan has t = 1 - 3/4 = 1/4 hour to type pages before the meeting starts.
Output = Rate * Timep = (16 pages/hour) * (1/4 hour) = 4 pages
Therefore, Ethan can type 4 pages before the meeting starts.
Answer: 4 pages