The quadratic equation with the given zeros is:
y = 2.5*x^2 - 5x - 7.5
How to find the quadratic equation?
For a quadratic equation with the zeros h and k, and a leading coefficient a is:
y = a*(x - h)*(x - k)
Here we know that the zeros are 3 and -1, replacing these values we will get:
y = a*(x - 3)*(x + 1)
Finally, we also know that the quadratic goes through (1, -10)
Replacing these values we will get:
-10 = a*(1 - 3)*(1 + 1)
-10 = a*(-2)*2
-10 = -4a
10/4 = a
5/2 = a = 2.5
Then the quadratic equation is:
y = 2.5(x - 3)*(x + 1)
Expanding that we will get:
y = 2.5*(x^2 - 3x + x - 3)
y = 2.5*x^2 - 5x - 7.5
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A farmer notes that in a field of horses and chickens there are 34 heads and 104 feet. How many of each animal are there
Answer: 18 horses and 16 chickens
Step-by-step explanation:
horses = h , chickens = c
h + c = 34
4h + 2c = 104, or simplified, 2h + c = 52
Now we just use systems of equations to solve. I will subtract the second equation from the first.
(2h + c = 52) -
(h + c = 34)
so simplified, our system becomes h = 18. Therefore, there are 18 horses. Now we can plug this value into h for any of the equations to get c, the amount of chickens.
18 + c = 34
c = 16.
Therefore, there are 18 horses and 16 chickens.
A company purchases electronic components in batches of 100 and the supplier guarantees that
there will be no more than 5 defective components in each batch. Before acceptance of a particular
batch the company has a policy of selecting without replacement two components for testing. If both
components are satisfactory the batch is accepted and if both are defective the batch is rejected.
However, if only one is defective another component is selected and if this is satisfactory the batch
is accepted while if it is defective the batch is rejected. If the probability that a component is
defective is 5% what is the probability that the batch will be accepted?
Answer:
To solve this problem, we can use conditional probability.
First, let's find the probability that both components selected for testing are satisfactory. Since we're selecting without replacement, the probability of both being satisfactory is (95% * 94%) = 90.3%.
Next, let's find the probability that both components selected for testing are defective. This is (5% * 4%) = 0.2%.
Now, let's find the probability that one component is defective and the other is satisfactory. We can find this by multiplying the probability of one component being defective (5%) by the probability of the other component being satisfactory (94%). This gives us (5% * 94%) = 4.7%.
Finally, we'll find the probability that the batch will be accepted. The batch will be accepted if both components are satisfactory or if only one component is defective and the other component selected is satisfactory. The probability of this is 90.3% + 4.7% = 95%.
So the probability that the batch will be accepted is 95%.
7. Asri spends 40% of his monthly allowance on food. He spends 20% of the remainder on transport and saves the rest. What percentage of his monthly allowance does he spend in all?
Answer:
52%
Step-by-step explanation:
First solve for the remainder:
remainder = 100% - 40%
remainder = 60% since 60% is left after 40% is spent on food.
Now solve for the percent of the total allowance spent:
20% of the remainder =
20% of 60% =
20% * 60% =
20% * 60/100 = ==> 60% = 60/100
1200% / 100 =
12 / 100 = ==> 1200% = 12 * 100%
12 * 100% = 12 * 1 = 12
12 / 100 = 12% spent on transport
Now add up the percent spent on food and the percent spent on transport:
40% + 12% = 52%
HELP PLS URGENTT
Image attached
The equation, 6(-2 + 4) = -12 + 24, illustrates E. the Distributive Property of Multiplication over Addition.
What Is Distributive Property?In this mathematical property, the multiplication of two or more addends by a number results in the same value as multiplying each addend individually by the number and then adding the products together.
For instance, 6(-2 + 4) = -12 + 24
= 12
OR:
6(-2 + 4) = 6 x 2
= 12
In this situation, we can either multiply the numbers in parenthesis individually by 6 or sum the parenthesis and then multiply the sum by 6. Either way yields the same result, showing that multiplication is distributive.
Thus, in the equation, the property illustrated is Option E, not the commutative properties of addition and multiplication, the inverse properties of addition and multiplication, the associative properties of addition and multiplication, or the identity properties of addition and addition multiplication.
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Jenny buys candy that costs $7 per pound. She will spend more than $70 on candy. What are the possible numbers of pounds she will buy?
Use p for the number of pounds Jenny will buy.
Write your answer as an inequality solved for p.
Answer: p > 10
Step-by-step explanation:
If one pound of candy is $7, then ten pounds of candy would be $70. If Jenny plans on spending more that $70, this means that she plans on buying more that ten pounds of candy, which shows that p (the number of pounds of candy she will buy) is greater than ten.
I hope this helps!!
please help due now!
Answer:
e + 8
Step-by-step explanation:
a dealer gains 7% by selling a sofa set for rs 3852 .find his gain percent if he sells it for rs 4050
The gain percentage is 12.5%
First, let`s find the Cost price (C.P) of the sofa.
Let C.P of the sofa be x.
Now, according to the question:
x+ 7% of x=Rs.3852
x + (7/100 * x) = 3852
x + 0.07x = 3852
1.07x = 3852
x=3852/1.07,
x = Rs 3600.
Now the dealer sells it for Rs 4050.
so, the Formula for gain% is=(Selling price-Cost price/Cost price)x100
Gain %= (4050-3600/3600)x100
Gain%=(450/3600)x100
Gain%=(450/36)
i.e = 12.5%.
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Find the value of x.
A.2
B.4
C.6
D.8
it's B.4 approximately .. sorry for not explaining in details
The Smith’s want to build their dog a house similar to their own house. The front door of their house measures 3 1/2 feet by 8 feet. If the scale factor from the actual house to the dog house is to be 1/6, what should the dimensions of the dog’s front door be? ( in inches)
Answer:
7 x 16 inches.
Step-by-step explanation:
Since your answer is in inches, first convert feet to inches by multiplying the value by 12.
(3 1/2) x 12 = 42 inches
(8) x 12 = 96 inches
Since the dimensions of the door of the dog's house are 1/6 that of the Smith's house, multiply each of the Smith's dimensions by 1/6 (or divide by 6)
42 / 6 = 7 inches 42 x 1/6 = 7 inches
96 / 6 = 16 inches 96 x 1/6 = 16 inches
I need help with written steps please
Answer:
a. To find the cost to surround the forest with a fence, we first need to determine the perimeter of the forest. The problem tells us that the perimeter is 45 yd. To convert this to feet, we can use the conversion factor of 3 feet per 1 yard. So, the perimeter in feet is:
45 yd x (3 ft/1 yd) = 135 ft
Next, we need to multiply the perimeter by the cost per foot to install fencing. We're told this cost is $6 per foot, so we can calculate the cost as:
135 ft x $6/ft = $810
b. To determine which region costs more to prepare, we need to calculate the cost per square yard for both the grassland and the forest. We're told that the cost to prepare 1 square yard of grassland is $15 and the cost to prepare 1 square yard of forest is $25.
To find the total cost for the grassland, we'll multiply the area of grassland with the cost per square yard:
2400 yd x $15/yd = $36,000
To find the total cost for the forest, we'll multiply the area of forest with the cost per square yard:
60 yd x $25/yd = $1,500
We can see that the grassland cost $36,000 to prepare while the forest cost $1,500 which means Grassland costs more to prepare.
NO LINKS!!
Find the area of this shape.
Answer:
54 units²---------------------------------
It is a combination of 3 rectangles.
All dimensions are given apart from the middle one. The missing dimension is:
6 - 2 = 4 unitsThe total area is:
8*2 + 5*4 + 6*3 = 16 + 20 + 18 = 54 units²Select the correct answer.Which is the correct simplified form of the expression (b^6/a^3)^1/3 ?
[tex] { (\frac{ {b}^{6} }{ {a}^{3} })}^{ \frac{1}{3} } \\ = \frac{ {b}^{6 \times \frac{1}{3} } }{ {a}^{3 \times \frac{1}{3} } } \\ = \frac{ {b}^{2} }{a} [/tex]
Answer:
b^2/a
Hope it helps.
If you have any query, feel free to ask.
Find the value of x that makes the quadrilateral a parallelogram.
Answer:
x=2/3
Step-by-step explanation:
If I am correct, I would make them both equal each other.
6x=3x+2
3x=2
x=2/3
6(2/3)=3(2/3)+2
4=2+2
4=4
Is -2 a solution of 6g-14>21
Answer:
-2 is not a solution of the inequality 6g - 14 > 21.
Step-by-step explanation:
To determine if -2 is a solution of the inequality 6g - 14 > 21, we need to substitute -2 for g in the inequality and see if it is true.
6g - 14 > 21
6(-2) - 14 > 21
-12 - 14 > 21
-26 > 21
This inequality is not true. Because -26 is not greater than 21.
[tex]6g-14 > 21[/tex]
Substitute -2 for g:
[tex]6(-2)-14 > 21[/tex]
[tex]-12-14 > 21[/tex]
[tex]-26 > 21[/tex]
-2 is not a solution because -26 is not greater than 21.
A finance charge includes which elements?
A) Interest and fees
B) Interest, fees, and principal
D
Fees and principal
192
Interest and principal
A finance charge includes Interest, fees, and principal, So the correct answer is Option (B) Interest, fees, and principal.
What Is a Finance Charge?A finance charge is a fee incurred when using a credit or extending credit that already exists. A fixed rate or a percentage of borrowings may be used to calculate finance charges; the latter is more common.
A finance charge is usually made up of the cost of carrying the debt as well as any related transaction fees, account management fees, or late fees imposed by the lender.
Finance charges are a way for a lender to get paid for giving a borrower credit or access to funds. These costs could be one-time payments, like the origination fee for a loan, or they could be interest payments that could be repaid daily or monthly. A finance charge includes Interest, fees, and principal
Therefore,
A finance charge includes Interest, fees, and principal, So the correct answer is Option (B) Interest, fees, and principal.
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Write an equation of the line passing through the given point and satisfying the given condition. Give the equation (a) in slope-intercept form and (b)
in standard form.
(8, 5); perpendicular to 4x-y=3
(a) Write the equation of the line in slope-intercept form.
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
Answer:
Slope intercept form : y = 4x -3
Step-by-step explanation:
A company will issue stock and bonds to raise
$35,000,000 to finance a project. The company will
need to pay specialty fees and service commission
as part of this process. 0.5% of the money raised
will be spent on specialty fees, and 2% of the
money raised will be spent on service commission.
Calculate the amount of money that will be spent
on specialty fees.
fees = $ [?]
Enter
PH
Skip
Answer:
$175,000.
Step-by-step explanation:
The amount of money that will be spent on specialty fees is $35,000,000 x 0.5% = $175,000.
Answer:
$175,000
Step-by-step explanation:
To calculate the amount of money that will be spent on specialty fees, we need to multiply the total amount of money raised (35,000,000) by the specialty fee percentage (0.5%).
fees = 35,000,000 * 0.005 = 175,000
So, $175,000 will be spent on specialty fees.
To calculate the amount of money that will be spent on service commission, we need to multiply the total amount of money raised (35,000,000) by the service commission percentage (2%).
commission = 35,000,000 * 0.02 = 700,000
So, $700,000 will be spent on service commission.
please help asap
• it would mean sm and make my day
Answer:
I know it
Step-by-step explanation: Btw did somone already answer this?
Mark plays field hockey. He makes a goal 55% of the time he shoots. A = the event Mark is successful on his first goal attempt. P(A) = 0.55. B = the event Mark is successful on his second goal attempt. P(B) = 0.55. Mark tends to make goals in streaks. The probability that he makes a second goal given that he made the first goal is 0.80.
Which of the following is true about A and B?
A and B are independent and mutually exclusive
A and B are neither independent nor mutually exclusive
A and B are independent, but not mutually exclusive
A and B are not independent, but mutually exclusive
A and B are disjoint
Answer: A and B are not independent, but mutually exclusive.
Step-by-step explanation:
Independence means that the probability of one event happening does not affect the probability of the other event happening. Mutual exclusivity means that the two events cannot happen at the same time.
In this case, we know that P(B|A) = 0.80, which means that the probability of Mark making a second goal given that he made the first goal is 0.80. This is different from P(B) = 0.55, the probability of Mark making a second goal without any information about whether he made the first goal. This means that the probability of event B is affected by whether event A has occurred, so A and B are not independent.
However, A and B are mutually exclusive, because Mark can either make his first goal or not, but can not make it at the same time.
Have 5 minutes left!!!!!
Which system of equations below has exactly one solution?
O y = -8x - 6 and y = -8x + 6
O y = -8x -6 and 7y = -4x - 3
O y = -8x - 6 and y = 8x - 6
Q y = -8x - 6 and -y = 8x + 6
Answer:
Y=-8x-6 and x=-8x+
Step-by-step explanation:
Write the expression 15½ in radical form.
Which set of numbers is correctly ordered from greatest to least?
221
07,207.36, 2.4-√3x
7.36, 221, 2.4-√3x
30
0 7 1,7
O 2.4√√3,7.36, 221 1,7/1/1
30
221
O
○ 2.4-√3x, 230, 7. 36,7
The set of number that is correctly ordered from the question in the attachment is option D.
How to solve for the solution in order to get the ordering1. [tex]7\frac{1}{3}[/tex] = 7 + 0.3333
= 7.3333
2. 221 / 30 = 7.3666
3. 7.36 = 7.36363636
4. [tex]2.4\sqrt{3\pi }[/tex] = 2.4 * [tex]\sqrt{9.43}[/tex]
= 7.36999
We would have to arrange all of the values from their highest to the least values
7.36999, 7.3666, 7.36363636, 7.3333
[tex]2.4\sqrt{3\pi }[/tex], 221 / 30, 7.36 , 7.3333
Hence the last option is the answer. It shows how the solution is ordered from the greatest to the smallest value
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Write an equation to represent the following: the product of the quantity
eight times a number x plus 4 and is equal to 17. Lesson 5-1
Answer:
8x+4=17
Step-by-step explanation:
The rectangle below has the dimensions 6.9 x 5.2 create another rectangle that is scaled to 4 times the size of the current rectangle I need this answer fast
A rectangle that is scaled to be 4 times the size of the given rectangle would have the dimensions of 27.6 x 20.8.
How to create the rectangle ?When a rectangle is said to be scaled to be a certain number of times more than the size of another rectangle, it means that both rectangles will have the same shape and orientation, but their dimensions will be different.
This difference will come from the change that the scale factor brought about. In this instance, the scale factor is 4 times which means that the second rectangle will be 4 times the size of the first.
The first dimension would be :
= 6 . 9 x 4
= 27.6 units
The second dimension would be:
= 5 . 2 x 4
= 20. 8 units
The dimensions would then be:
27. 6 x 20. 8
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ben has a piece of plywood that measures 1 yard on each side .he cuts the wood into 6 equal pieces .each piece is 1/3 yard wide and 1/2 yard long. what is the area of each piece that ben cuts. explain how the product 1/2x1/3 relates to the model
Answer:
Step-by-step explanation:
Ben has a piece of plywood that measures 1 yard on each side, and he cuts it into 6 equal pieces.
The width of each piece is 1/3 yard, and the length of each piece is 1/2 yard.
To find the area of each piece that Ben cuts, we can multiply the width and length of each piece:
Area = (1/3 yard) x (1/2 yard)
Area = (1/3) x (1/2)
Area = 1/6 yard^2
So each piece that Ben cuts has an area of 1/6 yard^2.
The product 1/2x1/3 relates to the model in that it represents the area of the piece. In other words, the length and width are multiplied to find the area of the piece.
In this case, we can see that Ben cuts the plywood into 6 pieces of equal area, which is 1/6 of a square yard.
Which statement about a histogram is true?
Group of answer choices
A peak is a bar that is higher than the other bars around it.
A cluster means the frequency is zero.
A mirror image of the left and right side of a histogram means there is a peak in the middle.
If the graph has a cluster, the data is evenly distributed.
The true statement about a histogram is A. A peak is a higher bar than the other bars around it.
What is a histogram?A histogram is a pictorial representation of data using vertical bars of equal width but different heights with no spaces between the bars.
Histograms are graphical representations of the frequency of numerical data using rectangular bars.
The height of the histogram represents the frequency of the variable of interest.
A Histogram as a graph shows the distribution frequency of continuous data, making it easier to interpret.
Histograms summarize and provide a visual interpretation and comparison of data.
Thus, the highest bar in height represents the peak; therefore, Option A is correct since Options B, C, and D do not refer specifically to a histogram.
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39 oz to ____ lb ____ oz
Answer:
2.4375 pounds
835 yd to km express answer using three significant figures
Answer: 835 yards is equal to 0.764 kilometer.
Step-by-step explanation: One yard is equal to about 0.0009144 kilometer. In order to answer the question, we just have to multiply this by 835. This gives us about 0.763524.
In order to round to three significant figures, we start counting from the first non-zero number within this value - which would be 7. This means that 3 is our third significant value, and because a 5 comes after it we round up to four.
Thus, our final answer is 0.764.
Which table represents the second piece of the function f(x) = StartLayout enlarged left-brace 1st Row 1st column negative 3.5 x + 0.5, 2nd column x less-than 1 2nd row 1st column 8 minus 2 x, 2nd column x greater-than-or-equal-to 1 EndLayout?
A 2-column table has 3 rows. The first column is labeled x with entries negative 1, 0, 1. The second column is labeled f (x) with entries 4, 0.5, negative 3.
A 2-column table has 3 rows. The first column is labeled x with entries negative 1, 0, 1. The second column is labeled f (x) with entries 10, 8, 6.
A 2-column table has 3 rows. The first column is labeled x with entries 1, 2, 3. The second column is labeled f (x) with entries 6, 4, 2.
A 2-column table has 3 rows. The first column is labeled x with entries negative 1, 2, 3. The second column is labeled f (x) with entries negative 3, negative 6.5, negative 10.
The values in the table that represent the second piece of the function f(x) is the option;
A 2-column table has 3 rows. The first column is labeled x with entries 1, 2, 3. The second column ism labeled f(x) with entries 6, 4, 2
What is a mathematical function?A function maps the values in the set of input variables to the values in the set of output variables.
The functions are presented as follows;
First row; f(x) = -3.5·x + 0.5; x < 1
Second row; f(x) = 8 - 2·x; When x ≥ 1
The second piece of the function is therefore;
f(x) = 8 - 2·x; When x ≥ 1
The possible values of x, which are values in the domain are; 1, 2, 3
The values of f(x), which are values in the range are therefore;
f(1) = 8 - 2 × 1 = 6
f(2) = 8 - 2 × 2 = 4
f(3) = 8 - 2 × 3 = 2
The values of x and f(x) are therefore;
x [tex]{}[/tex] f(x)
1 [tex]{}[/tex] 6
2 [tex]{}[/tex] 4
3 [tex]{}[/tex] 2
The correct option that represents table for the second piece of the function, f(x) is therefore;
A 2-column table has 3 rows. The first column is labeled x with entries 1, 2, 3. The second column is labeled f(x) with entries 6, 4, 2
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Answer: C. or third chart
Step-by-step explanation:
Got it right!!
what is 2/3x + 5 = 1 ??
Answer:
To solve for x in this equation, you can follow these steps:
Subtract 5 from both sides: 2/3x = -4
Multiply both sides by 3/2 to cancel out the denominator on the left side: x = -6
So the solution for x is -6
So, 2/3x + 5 = 1 becomes 2/3(-6) + 5 = -4 + 5 = 1
