Using the distributive property, we can write (z-5)(z+3) is equal to [tex]z^2[/tex] - 2z - 15.
Let us expand the expression (z-5)(z+3).
We will distribute the terms in the first set of parentheses (z-5) to the terms in the second set of parentheses (z+3) as follows -
(z-5)(z+3) = z(z+3) - 5(z+3)
Now, we will simplify the expression by distributing z to both terms inside the first set of parentheses, and then distributing -5 to both terms inside the second set of parentheses as follows -
z(z+3) - 5(z+3) = [tex]z^2[/tex] + 3z - 5z - 15
Combining the like terms, we get,
(z-5) (z+3) = [tex]z^2[/tex] - 2z - 15
Therefore, (z-5)(z+3) is equal to [tex]z^2[/tex] - 2z - 15.
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Select the correct answer.
What is the value of x in the triangle?
7√3
60°
OA. 21
OB. 10
O C.
C. 7
O D. 7√3
30%
The value of x in the triangle is equal to: A. 21.
What is a 30-60-90 triangle?In Mathematics, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the sides are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side).
Note: x is the side opposite to the 60° angle.
The side opposite to the 60° angle, x = 7√3 × √3
The side opposite to the 60° angle, x = 7 × 3
The side opposite to the 60° angle, x = 21 units.
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For which pair of functions f(x) and g(x) below will the limit as x goes to infinity of the quotient of f of x and g of x equals 0 ?
f(x) = ex; g(x) = x2
f(x) = ex; g(x) = ln(x)
f(x) = ln(x); g(x) = ex
f(x) = x; g(x) = ln(x)
The pair of functions f(x) and g(x) below that equals 0 as the limit as x goes to infinity of the quotient of f of x and g of x will be C. f(x) = ln(x); g(x) = ex
How to explain the informationFor the limit of the quotient of f(x) and g(x) to equal 0 as x approaches infinity, it is necessary for f(x) to grow more slowly than g(x).
Out of the options given, the only pair of functions where this is true is f(x) = ln(x) and g(x) = ex. As x approaches infinity, ex grows much faster than ln(x), so the limit of the quotient of these two functions as x approaches infinity is 0.
In conclusion, the correct option is C.
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George needs a string that is 4 feet long. So far history is 44 inches. Is it long enough or does he need to make it longer
If so far the George's string is 44 inches long , then his string is not long enough , so he need to make it longer .
To find whether George's string is long enough, we first convert both measurements to same unit of measurement.
that means we convert length of the string in inches to feet by dividing it by 12 ; because there are 12 inches in a feet ;
⇒ (44 inches)/(12 inches/feet)
⇒ 3.67 feet ;
The George's string is currently 3.67 feet long and he needs a string that is 4 feet long .
So , his current string is not long enough and he needs to make it longer. He needs to add another 0.33 feet to his string .
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The given question is incomplete , the complete question i
George needs a string that is 4 feet long. So far his string is 44 inches. Is it long enough or does he need to make it longer ?
A cardboard box in the shape of a rectangular prism has the
dimensions shown.
a. Write a polynomial that represents the volume of the box.
b. The volume of the box is 60 cubic inches. What are the
length, width, and height of the box?
On solving the provided question, we can say that Volume of cuboid - L X B X H=> volume = (x+6)*(x-2)*(x-1) => [tex]V = x^3 + 3x^2 - 16x + 12[/tex]
what is cuboid?A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.
The dimensions are:
Length =(x + 6), Width = (x - 2) and Height = (x -1)
Volume of cuboid - L X B X H
volume = (x+6)*(x-2)*(x-1)
[tex]V = (x+6)(x^2 - 3x +2)[/tex]
[tex]V = x^3 - 3x^2 + 2x + 6x^2 - 18x + 12[/tex]
[tex]V = x^3 + 3x^2 - 16x + 12[/tex]
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a jury of 12 people is selected from a pool 30 people that includes 12 men and 18 women. what is the probability that the jury will be composed of 12 women
The probability of selecting a jury composed of 12 women from a pool of 30 people that includes 12 men and 18 women is extremely low, only 0.0657%.
The probability of an event happening is the measure of how likely that event is to occur.
In this case, we need to find the probability of selecting a jury of 12 women from a pool of 30 people. To calculate this probability, we can use the formula:
Probability = Number of favorable outcomes / Total number of outcomes
The total number of outcomes is the number of ways in which we can select 12 people from a pool of 30. We can calculate this number using the combination formula:
Total number of outcomes = C(30,12) = 30! / (12! * (30-12)!) = 28,238,760
Now, we need to calculate the number of favorable outcomes, which is the number of ways in which we can select 12 women from a pool of 18. We can calculate this number using the combination formula as well:
Number of favorable outcomes = C(18,12) = 18! / (12! * (18-12)!) = 18,564
Therefore, the probability of selecting a jury composed of 12 women is:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 18,564 / 28,238,760
Probability = 0.000657 or 0.0657%
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Colton's gross pay is $1421.50 and his net pay is $973.48.
What percent of his gross pay is take-home pay?
31.5%
44.8%
46%
68.5%
68.5% of Colton's gross pay is take-home pay. To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and then multiply by 100 to convert the resulting decimal to a percentage.
To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and multiply the resulting decimal by 100 to express it as a percentage. Colton's gross pay is $1421.50 and his net pay is $973.48. Dividing the net pay by the gross pay gives a result of 0.685, or 68.5% when converted to a percentage. This means that 68.5% of Colton's gross pay is take-home pay, or the amount of money that he receives after deductions are made. Therefore, Colton's take-home pay is $973.48, which is 68.5% of his gross pay.
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If radius of circle is tripled then area of circle will be increased by
If radius of circle is tripled then area of circle will be increased by:9 times.
If the radius of a circle is tripled, then the new radius is three times the original radius, or R' = 3R, where R is the original radius and R' is the new radius. The area of a circle is given by the formula A = πR^2, where A is the area and R is the radius.
Substituting R' = 3R into the formula for the area of a circle, we get:
A' = πR'^2
= π(3R)^2
= 9πR^2
Therefore, the new area A' is 9 times the original area A. In other words, if the radius of a circle is tripled, the area of the circle will be increased by a factor of 9. This is because the area of a circle is proportional to the square of its radius.
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A square pyramid is shown. What is the surface area?
A square based pyramid, with bases labeled 3.5 centimeters and side length of triangle labeled 7 centimeters.
(4 points)
19.25 cm2
30.625 cm2
49.625 cm2
61.25 cm2
Answer:
61.25
Step-by-step explanation:
brainlest pls and I hope this helped u :)
Given 24.8 × 3.5, find the product.
8.68
72.4
75.64
86.8
an urn contains 3 red and 7 black balls. players a and b withdraw balls from the urn consecutively until a read ball is selected. find the probability that a selects the red ball
Players A and B withdraw balls from the urn consecutively until a read ball is selected, the probability that player A selects the red ball is approximately 0.408.
To find the probability that player A selects the red ball, we can use the law of total probability and consider all the possible ways the game could end. A selects the red ball on the first draw. The probability of this is simply the proportion of red balls in the urn, which is 3/10.
A selects a black ball on the first draw, followed by B selecting a black ball on their turn, and so on, until A finally selects the red ball. The probability of this is:
(7/10) * (6/9) * (5/8) * ... * (1/4) * (3/7)
Notice that the probability of selecting a black ball decreases by one after each turn, since the total number of balls in the urn decreases by one and the number of black balls decreases by one.
The probability of selecting the red ball on the last turn (after all the black balls have been selected) is 3/3 = 1. We multiply all these probabilities together to get the total probability of this sequence of events.
A selects a black ball on the first draw, followed by B selecting a black ball on their turn, and so on, until B finally selects the red ball. The probability of this is:
(7/10) * (6/9) * (5/8) * ... * (2/4) * (3/6)
Notice that the probability of selecting a black ball decreases by one after each turn, just like in the previous case. However, the probability of B selecting the red ball on their turn is now 3/6, since there are only six balls left in the urn at this point. We multiply all these probabilities together to get the total probability of this sequence of events.
Adding up these three probabilities, we get:
3/10 + (7/10) * (6/9) * (5/8) * ... * (1/4) * (3/7) + (7/10) * (6/9) * (5/8) * ... * (2/4) * (3/6) ≈ 0.408
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LAST TIME I NEED HELP XD
Answer:
Step-by-step explanation:
no idea. i have a idea!
do it your self
Write an equation of the line passing through point P(0,
1) that is parallel to the line y =
2x +3.
L
y =
Answer:
y = 2x + 1
Step-by-step explanation:
Parallel lines have the same slope. The slope in the equation y = 2x + 3 is 2. The slope of the parallel equation will be 2 also.
We will use the slope, and the point (0,1) to help us write the new equation.
The y intercept of the parallel line is 1. When x = 0, y is where the line will cross the y axis. So the y intercept is 1
The slope (m) is 2 and the y-intercept (b) is 1.
y = mx + b Substitute 2 for m and 1 for b.
y = 2x + 1
A triangular shaped region has side lengths of 829 miles, 911 miles, and 1,007 miles.
Does the region form a right triangle? Justify your answer.
Answer: no it does not
Step-by-step explanation: Because 1,007 squared is 1,014,049 and the sum of 911 squared is 829,921 and then 829 squared is 687,241 then add 829,921+687,241=1,517,162 when it should equal 1,014,049 which is the amount of 1,007 squared to make it a right triangle.
The solution is : no, it does not form a right triangle.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
given that,
A triangular shaped region has side lengths of 829 miles, 911 miles, and 1,007 miles.
now, we get,
Because 1,007 squared is 1,014,049
and the sum of 911 squared is 829,921
and then 829 squared is 687,241
then add 829,921+687,241=1,517,162
when it should equal 1,014,049
which is the amount of 1,007 squared to make it a right triangle.
as we know that,
in right triangle,
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a^2 + b^2 = c^2.
so, we get,
The solution is : no, it does not form a right triangle.
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The blood pressure in millimeters was measured for a large sample of people. The average pressure is 140 mm, and the SD of the measurements is 20 mm. The histogram looks reasonably like a normal curve. Use the normal curve to estimate the following percentages. Choose the answer that is closest to being correct.
a. 10.6%
b. 89.4%
c. 39.4%
d. 78.8%
e. 68.27%
Using the normal curve to estimate the following percentages. The answer that is closes to being correct is 39.4%. So, the correct answer is C.
Since the distribution is approximately normal, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentages.
a. 10.6%: This corresponds to the area under the curve that is more than 2 standard deviations below the mean. Using the rule, we know that about 2.5% of the area under the curve is more than 2 standard deviations below the mean. So 10.6% is too high. The answer is not a.
b. 89.4%: This corresponds to the area under the curve that is less than one standard deviation above the mean. Using the rule, we know that about 68% of the area under the curve is within one standard deviation of the mean. So 89.4% is too high. The answer is not b.
c. 39.4%: This corresponds to the area under the curve that is within one standard deviation of the mean. Using the rule, we know that about 68% of the area under the curve is within one standard deviation of the mean. So 39.4% is the closest to being correct. The answer is c.
d. 78.8%: This corresponds to the area under the curve that is less than two standard deviations above the mean. Using the rule, we know that about 95% of the area under the curve is within two standard deviations of the mean. So 78.8% is too high. The answer is not d.
e. 68.27%: This corresponds to the area under the curve that is within one standard deviation of the mean. This is the same as c. So e is not the correct answer.
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You deposit $200 each month into an account earning 1.25% interest compounded monthly.
How much will you have in the account in 20 years?
How much total money will you put into the account?
How much total interest will you earn?
Answer:
Step-by-step explanation:
The interest rate of 1.25% compounded monthly means that the interest earned each month is 1.25% of the current balance. Here's how you can calculate the final balance in the account after 20 years:
First, calculate the interest earned each month: $200 * 1.25% = $2.50
Then, add the interest earned to the monthly deposit to get the new balance: $200 + $2.50 = $202.50
Repeat this process for 240 months (20 years x 12 months/year).
The final balance in the account after 20 years would be approximately $71,934.24.
To find the total money you will put into the account, simply multiply the monthly deposit by the number of months: $200 * 240 = $48,000.
To find the total interest earned, subtract the initial deposit from the final balance: $71,934.24 - $48,000 = $23,934.24
So, in 20 years, you will have put a total of $48,000 into the account, and you will have earned a total of $23,934.24 in interest.
D. A car dealer purchased 40 new cars at
$6500 each. He sold 40% of them at
$8000 each and the rest at $9000 each.
What was his total profit?
40%=
5
2
5
2
⋅40=16 cars at 8000 each =128,000 in sales
40−16=
24 cars at 9000 each
=216,000 in sales
Total sales: 128,000+216,000=344,000
Total expense: 6500⋅40=260,000
Total profit: 344,000−260,000=84,000
Answer:
$84000
Step-by-step explanation:
40% of the cars would be 16 cars that are sold for $8000 each.
16×$8000=$128000
The remaining 60% of cars would be 24 cars to be sold at $9000 each.
24×$9000=$216000
The total profit = the sum - the amount he paid for all cars.
total profit = ($128000+$216000) - (40×$6500)
total profit = $344000 - $260000
total profit = $84000
Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
On solving the provided question we can say that the equations are y = 3x - 6 and y = -2x + 8
What is equation?A mathematical equatiοn is a fοrmula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the twο sentences οn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbοl, fοr instance, 2x – 4 = 2.
the equations are
y = 3x-6
y = -2x+8
3x - 6 = -2x+8
5x -6 = 8
5x = 14
x = 14/5
Now solve for y:
y = 3(14/5) - 6
y = 42/5 - 6
y=42/5 - 30/5
y = 12/5
The position 12/5 is where these two lines cοnverge. The triangle created by these two lines and the x-axis has a height equal to this.
So that we can identify the triangle's base, let's lοcate the roots of these equations (where they contact the x-axis).
Put a 0 in both equations.
(I) 0 = 3x - 6
6 = 3x
x = 2
Set the second equation equal to 0.
(II) y = -2x+8
2x = 8
x = 8/2
x = 4
The triangle has a base between the numbers (2, 0) and (4, 0), giving it a length of two units.
The triangle has a height of 12/5 units.
Area of a Triangle:
A = 1/2bh
A = (1/2) · (2) · (12/5)
A = 12/5
The region between the x-axis that is enclosed by the lines y = 3x - 6 and y = -2x + 8 has a 12/5 unit area.
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68.2 divided by 0.4 eritema full a problem
The required, 68.2 divided by 0.4 is equal to quotient 170.5, as per the given condition.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
68.2 divided by 0.4 is given as,
To divide a decimal value by another decimal value, you can use the same process as dividing whole numbers, but you need to make sure that the decimal points are lined up correctly.
= 68.2 / 0.4
= 682/4
= 170.5
Therefore, 68.2 divided by 0.4 is equal to 170.5.
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She said, " mother is cooking food. " Convert into indirect speech
The indirect speech version of the given sentence would be:
She said that her mother was cooking food.
Indirect speech (also known as reported speech) is a way of expressing what someone else said, without using their exact words. In indirect speech, we usually report the statement or question using a reporting verb like "say", "tell", "ask", or "explain", followed by a conjunction such as "that". We also need to change the tense and sometimes the pronouns to reflect the new context.
Indirect speech is often used in writing and speaking to convey someone else's message, opinion or idea. It helps us to paraphrase or summarize what someone else said, without quoting them directly. It is important to learn how to use indirect speech correctly, as it is a common feature of both formal and informal communication.
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Use the Pythagorean Theorem to find the distance between points F and C.
A. 2 √3
B. √41
C. 4 √3
D. 3 √5
A right triangle has side length 8 15 and 17 use these lengths to find Cos M Tan M and Sin M
Answer:
Cos A: [tex]\frac{15}{17}[/tex]
Tan A: [tex]\frac{8}{15}[/tex]
Sin C: [tex]\frac{8}{17}[/tex]
How I did it:
Cos A: [tex]\frac{Base}{Hypotenuse}[/tex] This is the basic " fraction "
Or in similar terms: = [tex]\frac{ab}{bc}[/tex]
Cos A = [tex]\frac{15}{17}[/tex]
Tan A = [tex]\frac{Perpendicular}{Base}[/tex]
Similar terms once again = [tex]\frac{ac}{ab}[/tex]
Tan A = [tex]\frac{8}{15}[/tex]
Sin A = [tex]\frac{Perpendicular}{Hypotnuse}[/tex]
Similar terms = [tex]\frac{ac}{bc}[/tex]
Since A = [tex]\frac{8}{17}[/tex]
Thus your answers are:
Cos A = [tex]\frac{15}{17}[/tex]
Tan A = [tex]\frac{8}{15}[/tex]
Sin A = [tex]\frac{8}{17}[/tex]
a 12-ft-by-15-gt rectangular swimming pool has a 3-ft-wide no-slip surface around it. what is the outer preimeter of the no-slip surfaec
If a 12-ft-by-15-gt rectangular swimming pool has a 3-ft-wide no-slip surface around it. The outer perimeter of the no-slip surface around the rectangular swimming pool is 78 feet.
The key idea in this problem is to recognize that the no-slip surface around the pool consists of a rectangular strip of uniform width that runs parallel to the edges of the pool. To find the outer perimeter of this strip, we need to add up the lengths of all four sides of the rectangle formed by the outermost edges of the no-slip surface.
Let's start by finding the length of the no-slip surface that runs along the length of the pool. Since the pool is 12 feet long and the no-slip surface extends 3 feet beyond each end of the pool, the total length of the no-slip surface is:
12 + 2(3) = 18 feet
The "2(3)" term in this equation represents the 3-foot-wide extension on each end of the pool. Next, we need to find the length of the no-slip surface that runs along the width of the pool. Since the pool is 15 feet wide and the no-slip surface extends 3 feet beyond each side of the pool, the total width of the no-slip surface is:
15 + 2(3) = 21 feet
Now we have the lengths of the two parallel sides of the rectangle formed by the outermost edges of the no-slip surface. To find the lengths of the other two sides, we simply add up the lengths of the corresponding sides of the pool.
Therefore, the length of the rectangle is 12 + 2(3) = 18 feet, and the width of the rectangle is 15 + 2(3) = 21 feet.
Finally, we can add up the lengths of all four sides of the rectangle to find the outer perimeter of the no-slip surface:
2(18) + 2(21) = 36 + 42 = 78 feet.
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On a test that has a normal distribution, a score of 34 falls two standard deviations above the mean, and a score of 22 falls one standard deviation below the mean. Determine the mean of this test.
The mean of this data set is 65.
What is the mean absolute deviation?The average distance between each data item and the mean is known as the mean absolute deviation.
The gap between each data value and the mean in absolute terms is represented by this average.
Let the mean be 'x' and the standard deviation be 'y'
3 standard deviations the mean means that we are taking away 3 standard deviations from the mean
Mathematically, we have that as;
x - 3y = 41...(i)
73 is 1 standard deviation above the mean
Mathematically;
x + y = 73...(ii)
So let us solve both equations simultaneously
Simply multiply equation (ii) by 3 then add to (i)
x - 3y = 41
3x + 3y =219
4x = 41 + 219
4x = 260
x = 260/4
x = 65.
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Answer: 26
Step-by-step explanation:
The key on a stem-and-leaf plot shows that 1|9 represents 19. How would the number 402 be represented?
The number 402 would be represented as 4|02.A stem-and-leaf plot is a graphical representation of a data set that is used to show its distribution.
The number 402 would be represented as 4|02. A stem-and-leaf plot is a way of organizing data into numerical order. It separates the numbers into two parts, the stem, which is the first digit or digits, and the leaf, which is the last digit or digits. The stem is listed on the left side and the leaf is listed on the right side. In this case, the stem would be 4 and the leaf would be 02, so the number 402 would be represented as 4|02.
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Answer:4l02
Step-by-step explanation: mark me brainiest ;]
Zendaya was comparing the price of grapefruit juice at two stores. The equation
y = 0.97x represents what Zendaya would pay in dollars and cents, y, for x bottles
of grapefruit juice at store A. Zendaya can buy 4 bottles of grapefruit juice at Store b
for a total cost of $6.80.
How much more is a bottle of grapefruit juice at Store B than
at Store A?
The sum of two numbers is 147 the difference of the two numbers is 25 what are the two number?
The two numbers, then, are 86 and 61.The two numbers can be found by using basic algebra.
The two numbers can be found by using basic algebra. To solve for the two numbers, we can set up two equations, one for the sum and one for the difference. For the sum, we can set up the equation: x + y = 147. For the difference, we can set up the equation: x - y = 25. We can then solve for x by adding y to both sides of the equation for the difference, so x = 25 + y. We can then substitute this value for x in the equation for the sum, so 25 + y + y = 147, or 2y = 122, and y = 61. We can then substitute this value for y in the equation for x, so x = 25 + 61, or x = 86. The two numbers, then, are 86 and 61.
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Fill in the gap in the equation below by completing the square. x² + 12x +44 = (x + 6)² +
Answer:
[tex]8[/tex]
Step-by-step explanation:
[tex]x^2+12x+44=(x^2+12x+36)+8=(x+6)^2+8[/tex]
a square with area is inscribed in a square with area with one vertex of the smaller square on each side of the larger square. a vertex of the smaller square divides a side of the larger square into two segments, one of length , and the other of length . what is the value of ?
The value of is equal to the length of the side of the larger square minus the sum of the lengths of the two segments.
The value of is equal to the length of the side of the larger square minus the sum of the lengths of the two segments. This is because the area of the smaller square inscribed in the larger square is equal to the product of the side lengths of the smaller square. If a vertex of the smaller square is located on the side of the larger square, the side of the larger square is divided into two segments with one segment having length and the other having length . The side length of the larger square is then equal to the sum of the lengths of the two segments plus the side length of the smaller square, which is . Therefore, the side length of the larger square minus the sum of the lengths of the two segments is equal to the side length of the smaller square, or the value of is equal to two segments.
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find the selling price if
cost price is R720 with a profit of 40%
Answer:
R1008
Step-by-step explanation:
720 X 1.4 = R1008
I used 1.4 because there is a 40 percent profit
Need help with this question urgent please
The equation y < - 4 · x - 1 represents the inequality seen in the figure.
How to determine an inequality
According to analytic geometry, we can derive the equation of a line from the knowledge of two points along the line. In this problem we must determine an inequality of the form:
y < m · x - b
m = Δx / Δb
Where:
m - Slopeb - InterceptWe know that points (x, y) = (- 1, 3) and (x, y) = (0, - 1) are points of the line. Now we proceed to determine the equation of the line:
m = (- 1 - 3) / [0 - (- 1)]
m = - 4
b = - 1
y < - 4 · x - 1
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