Answer:
To factor -3x^2 + 17x - 20 completely, we need to find two binomials that when multiplied together give us the original quadratic expression.
First, we can multiply the leading coefficient (-3) by the constant term (-20) to get -60. Then, we need to find two numbers that multiply to -60 and add up to the coefficient of the x-term (17). After some trial and error, we find that the two numbers are 12 and -5.
Now, we can rewrite the quadratic expression as:
-3x^2 + 17x - 20 = -3x^2 + 12x - 5x - 20
Next, we group the first two terms and the last two terms:
(-3x^2 + 12x) + (-5x - 20)
We can factor out 3x from the first group and -5 from the second group:
3x(x - 4) - 5(x + 4)
Now we can factor out a negative one from the second grouping:
3x(x - 4) - 5( -1)(x + 4)
And simplify:
3x(x - 4) + 5(x + 4)
Therefore, the quadratic expression -3x^2 + 17x - 20 can be factored completely as (3x - 5)(x - 4).
In AKLM, m = 63 inches, m/K=24° and m/L=42°. Find the length of 1, to
the nearest inch.
The length of side l of the triangle using sine rule is: 46 inches
How to use sine rule?Sine rule is used to show the relationship between the sides and angles of a triangle. It is given as:
a/sinA = b/sinB = c/sinC
Where A, B, C are the angles and a, b and c are the opposite sides to the angles.
Thus:
63/sin 114 = l/sin 42
(63 * sin 42)/sin 114 = 46 inches
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shawn deposits $100 every year into a savings account that pays interest at a rate of 3.5% per year, compounded annually. How much money will there be in his account at the end of 4 years
A-214.25
B-210.62
C-207
D-270
The amount of money that should be in the account at the end of 4 years of investment would be = $114.
How to calculate the amount of money in a given account?To calculate the total amount of money that will be in an account at the end of a given time can be calculated using the given formula below;
Simple interest = principal× time×rate/100
where;
principal = $100
rate = 3.5%
time = 4 years
simple interest = 100×3.5×4/100
= 14
Therefore the total amount of money that will be in the account at the end of 4 years = 100+14 = $114.
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2.1 The following task is given to Grade 8 learners:
Lerato spends 2/5 of her money and loses 1/3 of what is left. She still has
R6 left. How much money did she have to begin with?
Fath
2.1.1 Solve the problem using an illustration.
(5)
If Lerato spends ²/₅ of her money, loses ¹/₃ of what is left, and still has R6 left, the amount of money she had to begin with was R15.
How is the beginning amount determined?The beginning amount that Lerato had can be determined using fractional addition and subtraction.
Fractional addition and subtraction involve the addition and subtraction of fractional or proportional values.
The amount of money Lerato spend = ²/₅
The amount left = ³/₅ (1 - ²/₅)
The amount lost = ¹/₃ x ³/₅
= ¹/₅
The total amount spent and lost = ³/₅ (²/₅ + ¹/₅)
The amount of money left after spending and losing ³/₅ = R6
R6 = ²/₅
Proportionately, ²/₅ = R6, ⁵/₅ = R15 (R6 x ⁵/₂).
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Convert each unit. Enter your answers in the boxes.
32
yards =
feet
1
-
4
foot =
inches
3
miles =
yards
Answer:
32 yards = 96 feet (1 yard = 3 feet, so 32 yards x 3 feet/yard = 96 feet)
1 foot = 12 inches, so 4 feet = 48 inches
3 miles = 5,280 yards (1 mile = 1,760 yards, so 3 miles x 1,760 yards/mile = 5,280 yards)
Therefore, the conversions are:
32 yards = 96 feet4 feet = 48 inches3 miles = 5,280 yardsWhich is an example of a periodic event?
O A. The average human body temperature slowly rises and falls every day.
O B. The average person gradually loses bone mass as they age.
OC. The average child grows in bursts throughout childhood.
OD. A resting pulse stays steady for several hours.
A summary of the two stocks is shown.
Name of Stock Symbol Closing Price Day 1 Closing Price Day 2 Closing Price Day 3
Metropolis, Ltd MTP 17.95 18.25 18.28
Suburbia, Inc SBR 5.63 4.98 5.25
Suppose you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price. Which day, during the following two days, would be the best to sell both stocks and by how much?
Day 2 is the best by $13.00.
Day 3 is the best by $13.00.
Day 2 is the best by $2.45.
Day 3 is the best by $2.45.
The day, from the following two days, which would be the best to sell both stocks with the closing price is day 3 by an amount of $2.45.
Given are the closing prices of two stocks in three days.
If you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price,
Amount invested = (65 × 17.95) + (50 × 5.63) = $1448.25
If the stock is sold in day 2,
Amount received = (65 × 18.25) + (50 × 4.98) = $1435.25
Profit = $1435.25 - $1448.25 = -$13
If the stock is sold in day 3,
Amount received = (65 × 18.28) + (50 × 5.25) = $1450.7
Profit = $1450.7 - $1448.25 = $2.45
The profit is more for day 3 than day 2.
Hence it is best to sell on day 3 by $2.45.
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The lower a person's income, the less tax they must pay. People therefore try to lower their taxable income by claiming allowable tax deductions.
Work-related expenses such as uniforms, stationery and job-related travel expenses are all examples of allowable deductions. The income tax is therefore calculated on what we call a person's taxable income.
Taxable income =gross income − allowable tax deductions
Use the tax table below to compare the following jobs in Questions a and b
Taxable income
Tax on this income
$0−$18200
Nil
$18201−$37000
19c for each $1 over $18200
$37001−$80000
$3572 plus 32.5c for each $1 over $37000
$80001−$180000
$17547 plus 37c for each $1 over $80000
$180001+
$54547 plus 45c for each $1 over $180000
a An young accountant earns $3120 a fortnight, with no allowable tax deductions
i. What is the accountant’s taxable income?
ii. How much tax does the accountant owe in a year?
iii. What is the accountant’s annual net pay?
iv. What is the accountant’s fortnightly net pay?
Taxable income = $81,120,Total tax owed = $4,732.50 + $414.40 = $5,146.90 per year,Annual net pay = $81,120 - $5,146.90 = $75,973.10,Fortnightly net pay = $75,973.10 / 26 = $2,922.81
What does taxation mean?An amount of money that a government asks people to pay based on their income, property value, etc., and is used to pay for things that the government does.
The accountant's gross income for two weeks is $3,120, so his gross income for the year is:
3120 x 26 = $81,120
Since they are not allowed to deduct tax, their taxable income equals their gross income:
Taxable income = $81,120
ii. Using the presented tax table, we can determine the accountant's tax liability:
Taxable income = $81,120
Income tax over $80,000 = (81,120 - $80,000) x 0.37 = $414.40
Income tax over $37,000 = ($37,000 - $18,200) x 0.325 = $4,732.50
Total tax liability = $4,732.50 + 414.40 = $5,146.90 per year
iii. An accountant's annual net salary is his gross income minus tax liability:
Annual net salary = $81,120 - $5,146.90 = $75,973.10
iv. The accountant's semi-monthly net salary is the annual net salary divided by 26:
Net salary for two weeks = $75,973.10 / 26 = $2,922.81
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Find the volume of the solid
Answer:
27
Step-by-step explanation:
4.5*3*2 = 27
Find the volume of a right circular cone that has a height of 15.1 ft and a base with a radius of 10.7 ft. Round your answer to the nearest tenth of a cubic foot.
A day is equivalent to 8.64 x 104 seconds. What is this time in standard form? OA. 8,640 seconds OB. 864,000 seconds OC. 86,400 seconds OD. 864 seconds
I need help with this problem
The value of x and y in the cyclic quadrilateral are 15 and 3 respectively.
How to find the angles of a cyclic quadrilateral?A cyclic quadrilateral is a four sided shape that can be inscribed into a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.
Opposite angles of a cyclic quadrilateral is supplementary.
Hence,
6x - 8 + 31y + 5 = 180
6x + 31y = 183
26y + 5 + 6x + 7 = 180
26y + 6x = 168
6x + 26y = 168
Combine the equation
6x + 31y = 183
6x + 26y = 168
subtract the equation
5y = 15
divide both sides by 5
y = 15 /5
y = 3
6x + 31(3) = 183
6x = 183 - 93
6x = 90
divide both sides by 6
x = 90 / 6
x = 15
Therefore,
x = 15 and y = 3
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If cos A =
of sin A?
Square root of 5 divided by
3
and tan A < 0, what is the value of Sin A?
Answer: [tex]\tt{a.\fra{2}{3}}[/tex]
Step-by-step explanation:
If cos A = sqrt(5)/3 and tan A < 0, we can use the fact that:
sin^2 A + cos^2 A = 1
to find the value of sin A. First, we can square both sides of the equation cos A = sqrt(5)/3 to get:
cos^2 A = 5/9
Then, we can use the identity sin^2 A = 1 - cos^2 A to get:
sin^2 A = 1 - cos^2 A
sin^2 A = 1 - 5/9
sin^2 A = 4/9
Taking the square root of both sides gives us:
sin A = +/- 2/3
However, we know that tan A < 0, which means that the sine and cosine functions have opposite signs in the quadrant where angle A lies. Since cosine is positive (given by cos A = sqrt(5)/3), angle A must lie in either the first or fourth quadrant, where sine is positive or negative, respectively. Therefore, we can eliminate the negative solution and conclude that:
sin A = 2/3
What ratio do the triangles to rectangles show in this illustration? 100 points.
please answer i dont have much time left?
Answer: Its 5/2 or 2/5 but I think the right one is 5/2.
The answer is 5/2.
Step-by-step explanation: Please give Brainlist.
Hope this helps!!!!
I will answer more of your questions.
(Expert Answered)
Find the value of x
Answer: 60%
Step-by-step explanation: I think it was the answer to my work which is the same problem
Which does not represent a way to show 8+8+8+8+8+8+8 with multiplication?
Answer:
The answer is 50 because 8×7 is equal to 50
Step-by-step explanation:
8+8+8=21
8+8+8=21
21+21=42
42+8=50
HELPPPPPPPPPPPP and give me an accurate answer too K12 btw thanks
with geico you get a discount for being a good driver of 10% you have a six month policy for 1,025. if you pay it in full, you get another 10% discount how much would you pay per month if you choose not to pay in full?
round your answer to the nearest and do not put a dollar sign.
The monthly cost would be $138 if choose not to pay in full.
If you get a discount of 10% for being a good driver, then the cost of the policy before the full payment discount is:
1,025 × 0.9 = 922.50
If you pay the policy in full, you get an additional discount of 10%, so the cost of the policy after both discounts is:
922.50 × 0.9 = 830.25
If you choose not to pay in full, then you will not get the additional discount.
The policy cost is spread over 6 months, so the monthly cost would be:
= 830.25 / 6
= 138.38
Rounding this to the nearest dollar,
= 138
Thus, the monthly cost would be $138.
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answer this question
Answer:
The smallest angle in this quadrilateral is 36°.
Step-by-step explanation:
[tex]x + 2x + 3x + 4x = 360[/tex]
[tex]10x = 360[/tex]
[tex]x = 36[/tex]
So x, the smallest angle in this quadrilateral, is 36°.
What is the slope of the line with equation
Answer:
-7
Step-by-step explanation:
if you change the equation into y=mx +b form you get y=-7x +4 where m is -7 so the slope would be -7
suppose x~n(8,1). what value of x has a z-score of -2.25?
The value of x corresponding to a z-score of -2.25 is 5.75.
What is z-score ?
A z-score is a standardized score that expresses the distance of a data point from the mean in terms of the number of standard deviations. It indicates how many standard deviations a data point is above or below the mean of the distribution.
Given that x follows a normal distribution with mean μ = 8 and standard deviation σ = 1, we can find the z-score corresponding to a given value of x using the formula:
z = (x - μ) / σ
To find the value of x corresponding to a z-score of -2.25, we can rearrange the above formula as follows:
x = μ + z * σ
= 8 + (-2.25) * 1
= 8 - 2.25
= 5.75
Therefore, the value of x corresponding to a z-score of -2.25 is 5.75.
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USE A MODEL Noah wants to take a picture of a beachfront. He wants to make sure two palm trees located at points A and B are just inside the edges of the photograph. He walks out on a walkway that goes over the ocean to get the shot. Point A is 90 feet from the entrance of the walkway, and point B is 40 feet from the entrance. If the walkway is perpendicular to AB, and Noah’s camera has a viewing angle of 90°, at what distance down the walkway should Noah stop to take his photograph? On a separate sheet of paper, draw a diagram to model the situation.
He ought to pause 90 feet ahead in order to snap his shot while on the walkway.
How to solveTrigonometry can be used to determine the ideal spot on the walkway at which Noah must stop for his snapshot.
Since Noah's camera has a 90° viewing angle, both angles AON and BON will equate to 45° each.
Equipped with OA = 90 feet and OB = 40 feet, we can create two equations and use tan(45°) = 1:
1 = 90 / x
1 = 40 / x
Solving for x within each equation results in x = 90 and x = 40, respectively.
To secure that both palm trees are positioned within the border of the photograph, Noah should choose the larger distance: x = 90 feet.
Therefore, he ought to pause 90 feet ahead in order to snap his shot while on the walkway.
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Question 22 of 25
Suppose f(x)=x2 and g(x) = (4x)2. Which statement best compares the graph
of g(x) with the graph of f(x)?
A. The graph of g(x) is vertically stretched by a factor of 4.
B. The graph of g(x) is horizontally compressed by a factor of 4.
C. The graph of g(x) is horizontally stretched by a factor of 4.
OD. The graph of g(x) is shifted 4 units to the right.
SUBMIT
For the functions f(x)=x² and g(x) = (4x)² the best statement is the graph of g(x) is vertically stretched by a factor of 4.
The function g(x) = (4x)² can be rewritten as g(x) = 16x²
Comparing this with f(x) = x², we can see that g(x) is equal to f(x) multiplied by 16.
Therefore, the graph of g(x) is the same as the graph of f(x) except that it is vertically stretched by a factor of 16.
The graph of g(x) is vertically stretched by a factor of 4.
Hence, for the functions f(x)=x² and g(x) = (4x)² the best statement is the graph of g(x) is vertically stretched by a factor of 4.
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A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 90% confidence if (a) she uses a previous estimate of 0.58? (b) she does not use any prior estimates? refer to picture to view the table of critical values. (a) n = ? (Round up to the nearest integer.). b.) n=?
If she uses a previous estimate of 0.58, n = 733
If she does not use any prior estimates, n = 752
How to solve for the estimatesHere, E is given as 0.03
For 90% confidence level, Z* = 1.645
Using formula for margin of error we have
0.03 = 1.645 x (√0.58(1 - 0.58) / n)
n = 733
without prior estimates the value of p = 0.5
Then we have
0.03 = 1.645 x (√0.5(1 - 0.5) / n)
n = 752
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Select the correct answer from the drop-down menu. The value from the set {10, 11, 12, 13} that makes the equation 2(x − 5) = 12 true is .
The required value of x that makes the equation 2(x - 5) = 12 true when x is chosen from the set {10, 11, 12, 13} is x = 11.
To make the equation 2(x - 5) = 12 true, we need to solve for x. We can start by simplifying the equation using the distributive property:
2(x - 5) = 12
2x - 10 = 12
Next, we can isolate the variable x by adding 10 to both sides:
2x - 10 + 10 = 12 + 10
2x = 22
Finally, we can solve for x by dividing both sides by 2:
2x/2 = 22/2
x = 11
Therefore, the value of x that makes the equation 2(x - 5) = 12 true when x is chosen from the set {10, 11, 12, 13} is x = 11.
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The variables x and y vary inversely. Use x=−3 and y=4 to write an equation relating x and y. Then find y when x=6 .
Step-by-step explanation:
If x and y vary inversely, we can write the equation:
xy = k
where k is a constant of proportionality. To solve for k, we can use the values x = -3 and y = 4:
(-3)(4) = k
-12 = k
So the equation relating x and y is:
xy = -12
To find y when x = 6, we can plug in these values and solve for y:
(6)y = -12
y = -2
So when x = 6, y = -2.
A square pyramid has a base length of 6 inches and a height of 8 inches.
What is the volume of this pyramid?
Enter your answer in the box.
The volume of the pyramid will be equal to 96 in^3.
We are given that square pyramid has a base length of 6 inches and a height of 8 inches.
Suppose that the height of the pyramid is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex] is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, thus its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
Therefore, the volume of the pyramid;
V = 1/3 a^2 h
V = 1/3(6^2)(8)
V = 1/3(36)(8)
V = 96 in^3
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If the mass of a solid is 25 g and its volume is 50 cm³, what is its density?
Answer:
0.2 because Density = Mass / Volume
Density = 25 / 50
Density= 0.2 g/cubic cm
Could anyone help? Thanks
Answer:
Step-by-step explanation:
The formula for a function is in vertex form is
y=a(x-h)²+k
(h,k) is vertex
a is stretch
if it were facing down there would be a - in front
You question:
(-4,1) is vertex
it's facing up and there is no stretch
y=(x+4)+1 you can expand
y=x²+8x+17
A movie critic, rate movies on a scale of four stars to WinStar, a summary of her ratings for 20 movies as shown in the table at the critic rates a total of 100 movies where is the best prediction for the number of movies she gives exactly 3 stars.
A 47B 50 C 35D 27
Answer:
Step-by-step explanation:
you rigt
A normal distribution has a mean of 55 and a standard deviation of 3. Find the -score corresponding an -value of 64. Is this score considered to be statistically significant or statistically insignificant? Explain.
The z-score corresponding an x-value of 64 is 3
Finding the z-score corresponding an x-value of 64From the question, we have the following parameters that can be used in our computation:
x = 64
Mean = 55
Standard deviation = 3
using the above as a guide, we have the following:
z = (x - mean)/Standard deviation
Substitute the known values in the above equation, so, we have the following representation
z = (64 - 55)/3
Evaluate
z = 3
This score may or may not be considered to be statistically significant or statistically insignificant
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find other end point of mid point 3,1 and end point -2,5
The coordinate of the other endpoint (x₂, y₂) of the line segment will be (8, -3).
Given that:
Midpoint, (x, y) = (3, 1)
First endpoint, (x₁, y₁) = (-2, 5)
The coordinate of the other endpoint of the line segment is calculated as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
(3, 1) = [(-2 + x₂) / 2, (5 + y₂) / 2]
(6, 2) = [(-2 + x₂), (5 + y₂)]
(x₂, y₂) = (6 + 2, - 5 + 2)
(x₂, y₂) = (8, -3)
The coordinate of the other endpoint (x₂, y₂) of the line segment will be (8, -3).
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