The expanded and simplified form of the expression (x + 5)(x - 1) is x² - x + 5x - 5.
What is the expanded form of the expression?Given the expression in the question;
(x + 5)(x - 1)
To expand and simplify the expression (x+5)(x-1),
we use the distributive property:
(x + 5)(x - 1)
x(x - 1) + 5(x - 1)
Now we can simplify each term by using the distributive property again:
x(x - 1) = x² - x
5(x - 1) = 5x - 5
Putting these terms back together, we have:
(x+5)(x-1) = x² - x + 5x - 5
Combining like terms, we get:
(x+5)(x-1) = x² + 4x - 5
Therefore, (x+5)(x-1) simplifies to the quadratic expression x² + 4x - 5.
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The diagram below shows a large square with two smaller squares within it.
(Diagram)
Write an expression, involving exponents, to calculate the shaded area, in square inches, of the diagram. Then use that expression to calculate the shaded area, in square inches, of the diagram.
The shaded area of the diagram is 23 square inches when side of large square is 6 inches.
What is square ?
A square is a geometrical shape that has four sides of equal length and four angles of 90 degrees each. It is a two-dimensional polygon with four vertices or corners. The area of a square can be calculated by multiplying the length of one of its sides by itself (i.e., squaring it) using the formula
[tex]A = s^2[/tex] , where A is the area and s is the length of one side of the square.
To calculate the shaded area, we need to subtract the area of the two small squares from the area of the large square and then subtract the area of the unshaded region (which is the area of the two overlapping squares).
The area of the large square is:
[tex]$(6\text{ in})^2 = 36\text{ in}^2$[/tex]
The area of the two small squares is:
[tex]$(2\text{ in})^2 + (3\text{ in})^2 = 4\text{ in}^2 + 9\text{ in}^2 = 13\text{ in}^2$[/tex]
Therefore, the expression for the shaded area is:
[tex]$36\text{ in}^2 - 13\text{ in}^2[/tex]
Simplifying this expression, we get:
[tex]$23\text{ in}^2$[/tex]
Therefore, the shaded area of the diagram is 23 square inches.
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In a class of 70 students, 10 students passed mathematics, biology or chemistry, 30 pass mathematics, 30 pass biologi, and 25 pass mathematics if 11 pass mathematics or biology 10 pass biology and chemistry and 7 pass mathematics and. Chemistry how many pass all three subjects
Answer:
We can use a Venn diagram to visualize the information given in the problem.
Let M, B, and C represent the sets of students who pass mathematics, biology, and chemistry, respectively. We are given the following information:
|M| = 10 (the number of students who pass mathematics)
|B| = 30 (the number of students who pass biology)
|C| = 25 (the number of students who pass chemistry)
|M ∩ B| = 11 (the number of students who pass both mathematics and biology)
|B ∩ C| = 10 (the number of students who pass both biology and chemistry)
|M ∩ C| = 7 (the number of students who pass both mathematics and chemistry)
|M ∩ B ∩ C| = ? (the number of students who pass all three subjects)
We know that:
| M ∪ B ∪ C | = |M| + |B| + |C| - |M ∩ B| - |B ∩ C| - |M ∩ C| + |M ∩ B ∩ C|
Substituting the given values:
| M ∪ B ∪ C | = 10 + 30 + 25 - 11 - 10 - 7 + |M ∩ B ∩ C|
Simplifying:
| M ∪ B ∪ C | = 37 + |M ∩ B ∩ C|
We also know that:
| M ∪ B ∪ C | = 70 (the total number of students)
Substituting the value:
70 = 37 + |M ∩ B ∩ C|
Simplifying:
|M ∩ B ∩ C| = 33
Therefore, 33 students pass all three subjects.
Step-by-step explanation:
pls mark branliest i beggggg u
A fair 6-sided die is rolled 550 times. What is a reasonable prediction for the number of times the event of landing on an even number will occur?
92
150
275
325
A reasonable prediction for the number of times the event of landing on an even number will occur in 550 rolls is 275.
When rolling a fair 6-sided die, there are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5). Therefore, the probability of rolling an even number is 3/6 or 1/2.
To predict the number of times the event of landing on an even number will occur in 550 rolls, we can multiply the probability of rolling an even number by the total number of rolls:
Expected number of even rolls = Probability of rolling an even number x Total number of rolls
Expected number of even rolls = (1/2) x 550
Expected number of even rolls = 275
Therefore, a reasonable prediction for the number of times the event of landing on an even number will occur in 550 rolls is 275.
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Which statement is true?
A.The given sides and angles cannot be used to show similarity by either the SSS or SAS similarity theorems.
B.The given sides and angles can be used to show similarity by the SSS similarity theorem only.
C.The given sides and angles can be used to show similarity by the SAS similarity theorem only.
D.The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems
The triangles ΔFGH and ΔLJK are similar triangles. Then the correct option is B.
Given that:
The diagram is shown.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The ratio of the corresponding sides of the triangle ΔFGH and ΔLJK is given as,
FG / JL = HF / LK = GH / JK
32/8 = 36/9 = 48/12
4 = 4 = 4
The ratio of the corresponding side will be equal. Then the triangles ΔFGH and ΔLJK are similar triangles. Then the correct option is B.
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MARKING AS BRAINLIST PLS HELP!! 15 points ASAP
The missing angle C of the given triangle using law of cosine is: 62.1°
How to use law of cosine?The Law of Cosines is defined as a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.
Numerically, the Law of Cosines can be communicated as:
c² = a² + b² - 2abcos(C),
where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.
Thus:
90² = 55² + 50² - 2(55 * 50)cos(C),
2575 = 5500 cos C
2575/5500 = cos C
cos C = 0.4682
C = cos⁻¹0.4682
C = 62.1°
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PLEASE HURRY DUE TONIGHT
Mary is babysitting a 4-year-old. The little boy wants to play in the kiddie pool in the backyard. Mary knows that using the hose that is near the kiddie pool will take 30 minutes to fill up. The little boy has already asked 17 times if the pool is ready but she hasn't even turned on the water yet. Mary also knows that the hose from the front yard works faster and can fill the pool in 1/2 the time as the hose in the back yard. If she can use both hoses at the same time, how long will it take for the pool to fill up?
(PLEASE SHOW YOUR WORK)(I saw other people get 7.5 min and 75 min but those answers are incorrect.)
A. 5 minutes
B. 10 minutes
C. 22.5 minutes
Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.
To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).
The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.
We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.
Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.
To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)
Density = 600g / 600 cubic feet = 1g/cubic foot
Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.
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.......................
Answer:
about 80.03 feet
Step-by-step explanation:
You want the change in height of a bridge with a span of 1068.5 feet and a grade of 7.49%.
GradeThe grade of a roadway is the ratio of rise to run:
grade = rise/run
7.49% = rise/(1068.5 ft)
Solving for the rise, we have ...
rise = (1068.5 ft)(0.0749) ≈ 80.03 ft
The height change is about 80.03 feet.
__
Additional comment
Your problem statement tells you to round this value. We cannot see what precision it is asking for, so you'll have to figure the rounded value yourself. The attachment shows the value you'll be rounding.
find the surface area of the right prism.
8 ft
2 ft
3 ft
Answer: 92 ft²
Step-by-step explanation:
To find the surface area of a right prism, we will find the area of each side and add them together. We have three sets of two congruent sides. We will write an equation representing the area of these sides, set it equal to the surface area, and solve by simplifying.
2(8 ft * 3 ft) + 2(3 ft * 2 ft) + 2(8 ft * 2 ft) = Surface Area
2(24 ft²) + 2(6 ft²) + 2(16 ft²) = Surface Area
48 ft² + 12 ft² + 32 ft² = Surface Area
92 ft² = Surface Area
Which is the missing section?
391283
9??219
1 ??391
219382
839128
382193
Please teach me reason. Thank you for help :)
Based on the pattern, the missing section in the middle row is:
9282
The sequence seems to move in a clockwise or counter-clockwise fashion, filling in the digits. Some observations:
• The first and last rows are mirror images of each other, just reversed. So the middle section should continue that pattern.
• Going clockwise, 2 comes before 8. So 9282 fits.
• The digits in each section increase (or decrease) by 1 each time, except for the overlaps at the corners. So 9282 maintains that incremental pattern.
• The total sum of each row is the same: 391283, 9282? 1??391, 219382, 839128, 382193. Filling in 9282 for the middle section keeps the same overall sum.
• No other combination of 2 digits in that range (92-99 or 20-29) fits the pattern on both sides of the missing section. 9282 is the only logical choice.
So with all these clues pointing to 9282, that is the number that belongs in the missing section of the middle row. Let me know if any additional explanation is needed! I can also re-layout the pattern with the missing section filled in if that would be helpful.
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Randy and angela each graph the solution set for the inequality -3x+18.≤
Note that the graph of the solution presented by Randy and Angela will be given as a straight line graph as attached. The solution is x ≥ 6.
What is the step by step for the above solution?Let's take a step by step approach.
-3x + 18 ≤ 0
Subtracting 18 from both sides, we have:
-3x + 18 -18 ≤ 0 -18
-3x ≤ -18
To find x , we must divide both sides by -3
x ≤ 6
Hence, the solution of the inequality by Randy and Angela is x ≤ 6. See this in the attached Line Graph.
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Which equations are correct?
Select each correct answer.
Responses
3a3(−3a4)=−9a7
3 a cubed end power left parenthesis negative 3 a to the power of 4 right parenthesis equals negative 9 a to the power of 7
8x3(3x2)=24x6
8 x cubed end power left parenthesis 3 x squared right parenthesis equals 24 x to the power of 6
6b3(−2b3)=−12b6
6 b cubed end power left parenthesis negative 2 b cubed right parenthesis equals negative 12 b to the power of 6
4x3(6x2)=24x6
Answer:
Step-by-step explanation:
Responses 1 and 3 are correct.
When you multiply an exponent by an exponent, like x-squared times x-squared, you'll add the two exponents. That means x-squared times x-squared is x to the fourth power.
If you look at responses 1 and 3, the exponents were added correctly and the coefficients were multiplied correctly.
However, if you look at responses 2 and 4, the exponents were multiplied instead of added, making those two expressions incorrect.
pls answer
worth 25 points!!!!!
Answer:
[tex] \sf \: c \: = \: 28.3[/tex]
Step-by-step explanation:
To find the circumference of a circle .
We have to use the formula,
Where, C = [tex] 2 \pi r [/tex]
[tex] \pi [/tex] = 3.142
[tex] r [/tex] = 4.5m
So,
C = 2 × 3.142 × 4.5
C = 28.278 ≈ 28.3
Answer: 28.3
Step-by-step explanation:
C=2[tex]\pi r[/tex]
=2[tex]\pi[/tex](4.5)
=28.3 m
A lorry left town a for town b at 6.50 pm at an average speed of 60 km/hr. After 1 hour 45 minutes a car left town A for B at an average speed of 90 km/hr. if A is 317 km from B determine:
a)The distance of the lorry from town B when the car took off
b)The distance the car travelled to catch up to the lorry
c)What time of the day did the car catch up with the lorry (Give your answer in 24 hour system)
Can anyone help me to solve this differentiation.
y = (sin ² x - e²x)^ln x
regrisson for the equation
Answer:
A. Quadratic
Step-by-step explanation:
The equation y=x^2+7x-15 is a quadratic equation. It might be the result of a quadratic regression.
_____
The descriptors "linear," "quadratic," "exponential," and "power" describe the sort of equation that is used to try to match the data. Quadratic regression returns a quadratic equation.
There are 148 cars in front of a department store. If each car has 4 wheels, estimate the number of wheels in front of the store by rounding the larger number to the nearest ten.
Billy wants to estimate the percentage of students who live more than three miles from the school. He wants to create a 95% confidence interval which has an error bound of at most 3%. How many students should be polled to create the confidence interval?
z0.10 z0.05 z0.025 z0.01 z0.005
1.282 1.645 1.960 2.326 2.576
The percentage with a 95% confidence interval that has an error bound of at most 3%.
What is percentage?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". For example, if there are 20 red marbles out of 100 marbles in a jar, we can say that the percentage of red marbles is 20%. Similarly, if a store offers a 10% discount on a $50 item, the discounted price would be $45.
Percentages are commonly used to represent proportions or rates in various contexts, such as finance, and science. They allow us to easily compare and communicate numbers on a standardized scale, making it easier to interpret and analyze data.
To estimate the required sample size, we need to use the following formula:
n = (z*σ / E)^2
where:
n is the sample size we need to estimate the percentage with the desired error bound
z is the z-score for the desired level of confidence (95% in this case), which is 1.96
σ is the standard deviation of the population (unknown)
E is the desired margin of error, which is 3% of the percentage we are trying to estimate
Since we do not know the standard deviation of the population, we can use a conservative estimate of 0.5 (which gives the largest possible sample size).
Substituting the values we have:
n = (1.96 * 0.5 / 0.03)^2
n = 1067.11
So we would need to poll at least 1068 students to estimate the percentage with a 95% confidence interval that has an error bound of at most 3%.
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A funnel has a diameter of 9 in. and is 16 in. deep. What is the volume of the funnel to the nearest tenth of a unit?
The volume of the funnel to the nearest tenth of a unit is approximately 341.4 cubic inches.
What is volume?
Volume is a measure of the amount of space that a three-dimensional object occupies. It is the quantity of space that is enclosed within a closed surface, and is typically measured in cubic units, such as cubic meters ([tex]m^3[/tex]), cubic centimeters ([tex]cm^3[/tex]), cubic feet ([tex]ft^3[/tex]), or gallons (gal).
We can use the formula for the volume of a cone to find the volume of the funnel, since a funnel is essentially a cone with a hole at the top. The formula for the volume of a cone is:
[tex]V = (1/3)\pi r^2h[/tex]
where V is the volume, r is the radius of the circular base, and h is the height of the cone.
Since the funnel has a diameter of 9 inches, its radius is half of that, or 4.5 inches. The height of the funnel is given as 16 inches.
Plugging these values into the formula, we get:
[tex]V = (1/3)\pi(4.5 in)^2(16 in)\\\\= (1/3)\pi(20.25 in^2)(16 in)[/tex]
≈ [tex]341.4 in^3[/tex]
Rounding this answer to the nearest tenth of a unit, we get:
V ≈ [tex]341.4 in^3[/tex]
Therefore, the volume of the funnel to the nearest tenth of a unit is approximately 341.4 cubic inches.
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What is the slope of the line that contains the points (−3, −1) and (3, 3)?
Undefined
0
two thirds
three halves
Answer:
3/2
Step-by-step explanation:
Answer:
(c) 2/3
Step-by-step explanation:
You want the slope of the line through points (-3, -1) and (3, 3).
SlopeThe slope is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (3 -(-1))/(3 -(-3)) = 4/6 = 2/3
The slope of the line is two thirds, choice C.
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Harold and Bradley took a trip to the local farmer’s market. Harold bought 5 tomatoes and 12
cucumbers and spent $16.45. Bradley bought 8 tomatoes and 6 cucumbers and spent $15.10.
How much was each tomato and cucumber?
QUICK I’ll MARK YOU BRAINLIEST!! HELP ME SOLVE THIS EQUATION!!
The change in price can be expressed using any of 6/5, 1.2 and 120%
Explaining the expression in this situationGiven that
12.5x = 15
This means that the increment factor in the price is x
Solving for xWe have
12.5x = 15
The value of x is
x = 15/12.5
Evaluate
x = 1.2 as decimal
As fraction, we have
x = 6/5
As percentage, we have
x = 120%
Describing the situationSee attachment for the description of the figure
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Assuming that x \neq -3, simplify (8x - 4)(x + 3) - (4x - 44)(2x + 6).
Answer: Your answer is 504 or if you want it differently it's 84x+252
Hope it helped :D
Sketch the graph of the following system of equations and label at least 3 points on each graph. At what point do the equations intersect ?
x + y = 4
2x + 3y = 18
PLEASE HELP TIMED QUIZ!! 25 POINTS!
The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.
The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.
The point of intersection is (-6, 10).
We have,
To sketch the graph of the system of equations:
x + y = 4
2x + 3y = 18
We can start by solving each equation for y:
y = -x + 4
y = (-2/3)x + 6
Then, we can plot a few points on each graph by choosing values of x and solving for y.
Here are three points for each graph:
x + y = 4:
x = -4, y = 8: (-4, 8)
x = 0, y = 4: (0, 4)
x = 4, y = 0: (4, 0)
2x + 3y = 18:
x = 0, y = 6: (0, 6)
x = 3, y = 4: (3, 4)
x = 9, y = 0: (9, 0)
To plot the graphs, we can use these points and draw a straight line through each set of three points.
The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.
The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.
To find the point of intersection, we can solve the system of equations:
x + y = 4
2x + 3y = 18
One way to solve this system is to use substitution.
We can solve the first equation for x:
x = 4 - y
Then we can substitute this expression for x into the second equation and solve for y:
2(4 - y) + 3y = 18
8 - 2y + 3y = 18
y = 10
Now that we know that y = 10, we can substitute this value into either equation to solve for x:
x + y = 4
x + 10 = 4
x = -6
So the point of intersection is (-6, 10).
Thus,
The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.
The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.
The point of intersection is (-6, 10).
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calculate the volume of a cone (π=22/7) base radius 1.4and height radius 1.8
The volume of the cone is 4.2 units cube.
How to find the volume of a cone?The volume of a cone can be calculated as follows:
Therefore,
volume of a cone = 1 / 3 πr²h
where
r = radius of the coneh = height of the coneTherefore,
r = 1.5 units
h = 1.8 units
volume of a cone = 1 / 3 × 22 / 7 × (1.5)² × 1.8
volume of a cone = 1 / 3 × 89.1 / 7
volume of a cone = 89.1 / 21
volume of a cone = 4.24285714286
volume of the cone = 4.2 units cube
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Find the volume of figure one using the volume formula. Make sure to identify length width and height
Answer:
Step-by-step explanation:
In a right triangle, the length of one leg is 6 units. The length of the other leg is 8 units. What is the length of the hypotenuse?
Answer:
Step-by-step explanation:
Using the Pythagorean Theorem, we can find the length of the hypotenuse.
a² + b² = c²
6² + 8² = c²
36 + 64 = c²
100 = c²
√100 = c
10 = c
Answer: 10 units
Step-by-step explanation:
To find the hypotenuse of a triangle, use the Pythagorean Theorem (A² + B² = C²).
In this equation, A is 6, B is 8, and C is x, or the hypotenuse.
1. 6² + 8² = x²
2. 36 + 64 = x²
3. 100 = x²
4. √100 = √x²
(Taking the square root of both sides, cancelling out x²)
5. 10 = x
convert 300° to radius
Answer:
radians = degrees x π/180
Therefore, to convert 300 degrees to radians, we have:
radians = 300 x π/180
radians = 5π/3
So, 300 degrees is equal to 5π/3 radians.
Please help I just need number 8
Answer:
Step-by-step explanation:
P=10.1
A=3.08
P=4.7+3.2+2.2 =10.1
A=1/2 b h = 1/2 (2.2)(2.8)
Question 5 of 8 At what rate in milliliters per hour will an infusion be set if a nurse is administering 150 mL of dextrose 5% in lactated Ringer (D5LR) over 2 hours? Record your answer using a whole number.
Step-by-step explanation:
150 ml / ( 2 hr) = 75 ml/hr
Lester got $50 for his birthday, so his mom took him to the bank to open a savings account. Going forward, Lester also plans to deposit all of his income into his savings account each week. He has two sources of weekly income: his $10 allowance and the $15 he makes from delivering newspapers
Answer: (11) Julius asks Rachel if she would like to sell her boat. Rachel privately has no interest in selling her boat and believes that Julius can't afford her boat anyway. Rachel says, "I'd sell my boat to you for $20,000." To Rachel's surprise, Julius responds "Ok, it's a deal." Rachel does not want to sell the boat to Julius for any price. Julius and Rachel have:
