Answer:
If the discrimination of a quadratic function is 13, then the function will have two distinct real roots.
Step-by-step explanation:
Given the quadratic function
[tex]y=ax^2+bx+c[/tex]
where D = b²-4ac is called the discrimination of a quadratic function.
The discriminant D=b²-4ac indicates the type of roots the equation may have.
If D > 0, then the equation has two distinct real roots.
Given that the discrimination of a quadratic function is 13.
i.e. D = 13
As D > 0, so the function will have two distinct real roots.Thus, we conclude that if the discrimination of a quadratic function is 13, then the function will have two distinct real roots.
Suppose that y varies directly with x, and y = 10 when x = 25.
(a) Write a direct variation equation that relates x and y.
Equation:
(b) Find y when x = 6.
y =
Answer:
Equation: y = 0.4x
y = 2.4
Step-by-step explanation:
Use the direct variation equation, y = kx, where k is a constant
Plug in x and y:
y = kx
10 = k(25)
Solve for k:
0.4 = k
So, the equation is y = 0.4x
Then, use this equation to find y when x = 6:
y = 0.4x
y = 0.4(6)
y = 2.4
A direct proportion is a proportion such that the ratio between both variables remains constant thus the given proportion will be y = 04x and the value of y at x = 6 will be 2.4.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
a)
Let's say the direct proportion as,
y = kx
Given that y = 10 when x = 25.
10 = k(25)
Solve for k,
0.4 = k
Therefore, the equation will be y = 0.4x
y = 0.4x
b)
The value of y when x = 6
y = 0.4(6)
y = 2.4
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The graph below shows where the two functions y = f(x) and y = g(x) intersect. Solve the equation f(x) = g(x).
The solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).
We have a graphical representation of two functions f(x) and g(x) and where they intersect.
We have to solve the equation f(x) = g(x)
Two functions A(x) and B(x) are plotted on the graph such that these these two functions intersect each other at three different coordinates. The total number of solutions possible for - A(x) = B(x) is ?The total number of solutions can be calculated by counting the points at which these curves intersect each other. Hence, the total number of possible solutions are 3.
In the question given - We have a straight line and a parabola -
Now, we just have to look at the points at which these two graphs intersect each other. It can be seen that - both the graphs cut each other at coordinates - (4, 8) and (-2, 2).
Hence, the solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).
Alternative Method -
The general equation of straight line is : y = mx + c and that of parabola is : y = [tex]\sqrt{4ax}[/tex]
The solution can be calculated by equating both of the above expressions and solving them.
mx + c = [tex]\sqrt{4ax}[/tex]
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Helpppppppppppppppppp
Answer:
ik that problem gimmie a sec
Step-by-step explanation:
Step-by-step explanation:
since 1 and 2 are same the lines which create 1(g and p) and 2(h and r)
the lines g h and p r shoul be parallel. we also know that g h is parallel which proves that p and r should be parallel as well
PLEASE EXPLAIN STEPS
Answer:
C. m<C = m<F
Step-by-step explanation:
this is because in their triangle names, they are in the same spot (third letter of the name)
if they are in the same spot, they have to be congruent
same goes for the other letters, <A has to be congruent to <D and <B has to be congruent to <E
Which of the fractions is equivalent to 2/5 ?
5/2
4/25
12/15
4/10
Answer:
4/10
Step-by-step explanation:
4/10 simplifies to 2/5
4/2 = 2
10/2 = 5
help as fast as you can!!!!!! Any living thing is called an organism,no matter if it is one-celled or many-celled. True or False?.
Answer:
true
Step-by-step explanation:
Answer:
TRUE.
Step-by-step explanation:
How much of a circle does a 100-degree angle turn through?
1. 1
2. 100/180
3. 50/360
4. 100/360
What’s the answer to the problem Help me
Answer:
$2000 can get 250000 sheets of papers
Step-by-step explanation:
[tex]500/4=125[/tex]
[tex]125*2000=250000[/tex]
What is the quotient in simplest form? 4/5 ÷ 8 a. 1/10 b. 1/2 c.8 d. 20
Answer:
1/10
Step-by-step explanation:
Answer:
4/5 divided by 8 is 4/40 and 1/10 if simplified.
Step-by-step explanation:
It was cloudy 12 out of 30 days in April. Which value is equivalent to the fraction of
days it was cloudy in April?
Answer:
any of the below:
Step-by-step explanation:
12/30
6/15
2/5
Answer:
2/5, or 40%.
Step-by-step explanation:
Write it as a fraction first, then reduce it to simplest form.
12/30
Simplest form is 2/5, or 40%
Kelsey must pay $200 to rent a booth at the craft fair. The materials for each pendant cost $7.80, and she plans to sell each pendant for $13.50. To make a profit, she must make more money than she spends. Kelsey has already made 10 pendants.
Part A
Given that Kelsey has already made 10 pendants, how many additional pendants must she make and sell to make a profit of $50?
Answer:
25 more
Step-by-step explanation:
Which two expressions are equivalent?
(F was wrong) H 7(x − 3) and 7x − 7 • 3
g 7(x − 3) and 7x − 4 j 7(x − 3) and 7x + 7 • 3
Answer:
The correct answer is:
Option H: 7(x − 3) and 7x − 7 • 3
Step-by-step explanation:
Equivalent expressions are those expressions that simplify to the same expression i.e. the result of both expressions is the same. There is no change of sign or variable or any quantity.
Option H:
The two expressions are:
7(x − 3) and 7x − 7 • 3
[tex]7(x-3) = 7x - 21\\7x - 7.3 = 7x-21[/tex]
It can clearly be seen that both the expressions result in same expression
Hence,
The correct answer is:
Option H: 7(x − 3) and 7x − 7 • 3
could you please help with this equation:
Simplify the algebraic expression: 4(3x + y) – 2(x – 5y)
Answer: 10x + 14y
Step-by-step explanation: just simplify it
Answer:
10x+14y
Step-by-step explanation:
A test of a new car results in 300 miles on 10 gallons of gas. How far could you drive on 45 gallons of gas?
Question 5 options:
1350 miles
67 miles
670 miles
135,000 miles
Answer:
1350
Step-by-step explanation:
300x4=1200
300×.5=150
1200+150=1350
Jake has a piece of rope that is 5.5 yards long. What is the length, in inches, of Jake's rope?
O 180.5 inches
O 187.2 inches
O 186 inches
O 198 inches
a flour company in minneapolis wants to know what percent of local households bake at least twice a week. A company representative calls 500 randomly selected local households from 8am to 5pm during the week and finds that 56% of them bake at least twice a week
Answer:
Step-by-step explanation:
The response of this would be to say that those people without daytime jobs that are outside the home, are more likely to be home and thus, have more time on their hands to attempt to bake. So basically, the quoted 56% is definitely going to be higher than the population percentage.
A parabola can be drawn given a focus of (-4, -5) and a directrix of y=3. Write the equation of the parabola in any form.
Answer:
The equation of the parabola is (x + 4)² = -16(y + 1)
Step-by-step explanation:
The standard form of the equation of the parabola is (x - h)² = 4p(y - k), where
The vertex of the parabola is (h, k)The focus is (h, k + p)The directrix is at y = k - p∵ The focus at (-4, -5)
∴ h = -4
∴ k + p = -5 ⇒ (1)
∵ The directrix at y = 3
∴ k - p = 3 ⇒ (2)
→ Add equations (1) and (2) to find k
∴ 2k = -2
→ Divide both sides by 2 to find k
∴ k = -1
→ Substitute it in equation (1) to find p
∵ -1 + p = -5
→ Add both sides by 1
∴ -1 + 1 + p = -5 + 1
∴ p = -4
→ Substitute the values of h, k, and p in the formula above
∵ (x - -4)² = 4(-4)(y - -1)
∴ (x + 4)² = -16(y + 1)
∴ The equation of the parabola is (x + 4)² = -16(y + 1)
for algebra 2 please help <3
Answer:
A. 1
Step-by-step explanation:
✔️To find f(g(1)), first find g(1).
From the mapping given for g(x), the corresponding value of x = 1, is 0.
That is,
g(1) = 0
✔️Next is to find f(g(1)) by replacing x with 0 in f(x) = 3√x + 1
Thus:
f(g(1)) = 3√0 + 1
f(g(1)) = 0 + 1
f(g(1)) = 1
the radius of a circle is 7 kilometers. What is the circle’s area?
Is precipitation a function of month? Explain why or why not, in at least
two full sentences.
Answer:
I cannot see the question
Step-by-step explanation:
A baker has three banana muffin recipes. Recipe AAA uses 333 bananas to make 121212 muffins. Recipe BBB uses 555 bananas to make 242424 muffins. Recipe CCC uses 111111 bananas to make 484848 muffins.
Order the recipes by number of bananas per muffin from least to greatest.
Answer: Recipe Buses 5 bananas to make 24 muffins. Recipe C uses 11 bananas to make 48 muffins.
Step-by-step explanation:
Which of the following is a proportional relationship? SELECT ALL THAT APPLY
A)
[tex] \frac{2}{3} = \frac{8}{12} [/tex]
B)
[tex] \frac{6}{7} = \frac{12}{13} [/tex]
C)
[tex] \frac{15}{20} = \frac{9}{12} [/tex]
D) None of the above
Answer:
a
Step-by-step explanation:
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What is the slope and y-intercept of these equations?
y=-2/3x-6
y=3x-6
Answer:
slope=-2/3 y inter= -6
slope= 3 y inter= -6
Step-by-step explanation:
A business person is desperate to better organize their business. They hire you to act as an efficiency expert. As you review their situation, you notice they file all of their receipts and documents into one overflowing folder. Their workspace is very messy with many piles of papers and useless knick-knacks. They mention difficulty finding important documents and have forgotten important dates and events due to their clutter. Write a formal letter to your client offering tips on ways to make their business more organized and efficient. Make sure your letter has specific examples which can improve the business' organization.
Answer:
Simply have neat and organized ways to save files. You can do this with file cabinets or by having digital copies of all the files to get rid of the clutter. I would recommend the second option.
Step-by-step explanation:
I got it right
The formal letter to the client offering tips on ways to make his business more organized and efficient is;
51, broad street,
Times Square Church,
New York City.
2/12/2021
The General Manager,
Clad financial services Ltd,
Brooklyn, New York city.
Dear Mr. Bill Wilkinson,
Letter of advice on more organized and efficient business.
I am writing with respect to the need to have a more organized and efficient office. Since resumption into this role as an efficiency expert, I have noticed that specific files and documents are very difficult to locate due to unorganization and untidiness.
With respect to the issue of unorganization and untidiness, I have some neat and organized ideas that can be used to save files. This can be can done by making use of file cabinets and also by creating and saving digital copies of all the files in order to get rid of some of the files and documents occupying a lot of space in the office.
Secondly, I will also like to add that unwanted papers or files should be thrown away and the files on the shelf should be properly labeled for easy identification.
Regards.
Frank Johnson,
Efficiency Expert.
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Kenny is on the local swim team for the summer and has swim practice
five days per week. The schedule is the same each day. The team swims in
the morning and then again for 3 hours in the evening. If he swims 30
hours per week, how long does he swim each morning. Write and solve
the equation. You must show the equation and solved solution in order to
receive credit. *
Answer:
She swims for 3 hours each morning.
Step-by-step explanation:
To determine the number of hours that Kenny swims in the morning, it is necessary to perform the following equation, taking into account that he swims 5 days a week for a total of 30 hours a week, and that in the afternoon he swims for 3 hours:
X + 3 x 5 = 30
X + 3 = 30/5
X = 6 - 3
X = 3
Therefore, Kenny swims for 3 hours in the morning.
is 9.68888888... a rational number
Answer:
rational
Step-by-step explanation:
because of the dec
You have $40 to start a savings account. You plan to put $10 in the account each month.
Write an equation that represents the relationship in the story.
solve for x.
x/6 =2
A.x=3
B.x=-12
C.x=12
Answer:
C. x=12
Step-by-step explanation:
PLEASE HELP MEH ON THIS ASAP!!!!
Answer:
b
Step-by-step explanation:
Answer:
option B
Step-by-step explanation:
a is located in the left side of 0 . HENCE IT IS A NEGATIVE NUMBER . b & c are on the right side of 0. HENCE BOTH ARE POSITIVE NUMBER
In option B , it's given that -a > -c . If we'll verify this statement , we'll find that when we put the negative sign in a , the all totla value of a becomes positive BECAUSE 'a' WAS A NEGATIVE NUMBER.
Now if we put a negative sign in c , the all total value becomes negative BECAUSE 'c' WAS A POSITIVE NUMBER.
By comparing -a & -c , we'll get to know that :-
-a > -c
Helen borrowed money from her aunt to pay for college expenses. The graph below shows the amount left
on the loan as it is paid off over time. Write a linear equation that describes the amount, A, that Helen owes her
aunt to the number of months, n, since she borrowed the money. Show your work that supports your answer
Answer:
[tex]y = -100x + 13000[/tex]
Step-by-step explanation:
See attachment for graph
First, we need to take any corresponding values of x and y
[tex](x_1,y_1) = (0,13000)[/tex]
[tex](x_2,y_2) = (130,0)[/tex]
Next, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{0 - 13000}{130 - 0}[/tex]
[tex]m = \frac{- 13000}{130}[/tex]
[tex]m = -100[/tex]
Next, we calculate the line equation using:
[tex]y - y_1=m(x-x_1)[/tex]
[tex]y - 13000 = -100(x - 0)[/tex]
[tex]y - 13000 = -100x[/tex]
Make y the subject
[tex]y = -100x + 13000[/tex]
Hence, the line equation is:
[tex]y = -100x + 13000[/tex]