Answer:
5x+7
Step-by-step explanation:
The area of a triangle formed by points of intersection of parabola y=a(x−1)(x−4) with the coordinate axes is 3. Find a if it is known that parabola opens downward.
Answer:
[tex]a=-\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given the parabola
[tex]y=a(x-1)(x-4)[/tex]
To find y-intercept, substitute [tex]x=0:[/tex]
[tex]y=a(0-1)(0-4)\\ \\y=4a[/tex]
Hence, [tex](0,-4a)[/tex] is the point of intersection with y-axis.
To find x-intercept, substitute [tex]y=0:[/tex]
[tex]0=a(x-1)(x-4)\\ \\x_1=1\ \text{or}\ x_2=4[/tex]
Hence, points [tex](1,0)[/tex] and [tex](4,0)[/tex] are the points of intersection with x-axis.
Find the area of the triangle formed:
[tex]A_{\triangle}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}\\ \\\text{Base}=|4-1|=3\\ \\\text{Height}=|4a|\\ \\A_{\triangle }=\dfrac{1}{2}\cdot 3\cdot |4a|=6|a|[/tex]
Since the area of the triangle is 3, you have
[tex]6|a|=3\\ \\6a=-3\ [\text{Parabola goes downward}]\\ \\a=-\dfrac{1}{2}[/tex]
The middle school golf team is selling golf balls to raise $850 for new equipment. They sell golf balls for two dollars each. A case has 24 packs of golf balls. Each pack has six golf balls. How many cases of golf balls does the team need to sell to raise enough money for new equipment.
Answer:
3 cases
Step-by-step explanation:
Total Money Needed = $850
Each Golf Ball = $2
Total Balls needed = 850/2 = 425 balls
Case = 24 Pack
Pack = 6 balls
So a Case has:
24 * 6 = 144 balls
They need 425 balls to sell and each case has 144 balls, so number of case needed would be:
425/144 = 2.95
We can't have 2.95 cases, so we round up to 3 cases
If a = b and e = f, what is the value of y
A. 87
B.88
C. 91
D. 92
Answer:
it’s 92 on edge
Step-by-step explanation:
is 40% of a class are girls. and 25% of girls play tennis, what is the percent of the class play tennis?
a. 10%
b. 15%
c. 20%
d. 40%
Answer: a. 10%
Step-by-step explanation:
Girls in the class = 40%
Girls play tennis = 25%
Percentage of class play tennis = 40%*25% = 0.4*0.25 = 0.1
Percentage of class play tennis = 10%
The percentage of the class that plays tennis is 70%.
What is a percentage?The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying by 100.
The percentage change is also calculated using the same method.
In percentage change we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We
If 40% of a class is girls, then 60% of the class must be boys.
Let's say there are 100 students in the class, so 40 of them are girls, and 60 are boys.
If 25% of the girls play tennis, that means 25% of 40, which is 10 girls, play tennis.
Therefore, the total number of students who play tennis is 10 girls + some number of boys.
We don't know how many boys play tennis, but we can find out what percentage of the whole class plays tennis by dividing the total number of tennis players by the total number of students:
(10 girls + X boys) / 100 total students
We know that 40% of the class is girls, so:
X boys = 60% of 100 total students = 60 students
So the total number of students who play tennis is:
10 girls + 60 boys = 70 students
And the percentage of the class that plays tennis is:
70 students / 100 total students = 70%
Therefore,
The percentage of the class that plays tennis is 70%.
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The table above represents what type of function?
A.
nonlinear
B.
linear
C.
linear and nonlinear
D.
neither linear nor nonlinear
Answer:
A
Step-by-step explanation:
I’m confused on what’s going on here, so if someone could explain it I would be super grateful.
Given AB = 4x + 5, BC = 3x - 2 and AC 9x -5
The sum of the length of any two sides of a triangle is greater than the length of third side.
Case I
AB + BC > AC
⇔4x +5 +3x -2 > 9x -5
⇔7x + 3 >9x - 5
⇔ 7x -9x > -5 -3
⇔-2x > -8
⇔x <4
Case II
if AB+AC > BC
4x +5 +9x -5> 3x -2
⇔13x >3x -2
⇔ 13x -3x> -2
⇔10x > -2
⇔x >[tex]-\frac{1}{5}[/tex]
Case III
AC+BC > AB
⇔9x - 5 +3x - 2 > 4x +5
⇔6x -7 > 4x +5
⇔6x -4x >5+7
⇔2x > 12
⇔x > 6
Which form of equation models the data if a is a negative integer and b is a positive integer?
A.) b = ax/y
B.) y = ab^x
C.) y = ax+b
D.) y = ab^-x
* ^ = exponent *
Answer:
y=ax+b
Step-by-step explanation:
i got it right on TTM
Answer:
C
Step-by-step explanation:
the 17th term of an A.P is 13 times the second term.prove that the twelve term is five term the third term.
Answer:
T_12 = 5(T_3)
Step-by-step explanation
T_17 = 13(T_2)
T_n = a + (n-1)d; where a=first term and d=common difference
T_17 = a + 16d
T_2 = a + d
Therefore,
a + 16d = 13(a + d)
a + 16d = 13a + 13d
16d - 13d = 13a - a
3d = 12a
d = 4a
To prove that T_12 = 5(T_3)
a + 11d = 5(a + 2d)
a + 11d = 5a + 10d
since d = 4a
a + 11(4a) = 5a + 10(4a)
a + 44a = 5a + 40a
45a = 45a
Since LHS = RHS
Therefore; T_12 = 5(T_3)
find the slope between points (1,3) and (4,5)
Answer:
2/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(5-3)/(4-1)
m=2/3
Equation that would have infinitely many solutions with 5x+3y=12
Which shows the correct first step to solving the system of equations in the most efficient manner ? 3x+2y=17 x+4y=19
The correct answer is option 1: x = -4y+19
Step-by-step explanation:
Given equations are:
[tex]3x+2y=17\ \ \ Eqn1\\x+4y=19\ \ \ \ Eqn2[/tex]
When we have to solve a system of equations using substitution method we look for a variable in both of equations that is without any co-efficient as it is easy to isolate that variable in the equation and then using substitution method to solve it
We can see that in equation 2, x is without any co-efficient
So,
[tex]x+4y = 19[/tex]
Subtracting 4y from both sides
[tex]x+4y-4y = 19-4y\\x = 19-4y\\[/tex]
Can also be written as:
[tex]x = -4y+19[/tex]
Hence,
The correct answer is option 1: x = -4y+19
Keywords: Linear equations, variables
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Answer:
The correct answer is option 1: x = -4y+19
Step-by-step explanation:
If you know a point on a line and you know the equation of a line parallel to this line, explain how to write the line’s equation.
Answer:
Step-by-step explanation:
First, parallel lines have the same slope, so the slopes should be the same , and then you use the given point to find the y intercept
EX:
y=x+1
find equation of line the is parallel and passes through (1, 1)
Same slope, so y=x+b
then plug in the point
1=1+b
b=0
our line would be y=x
To write the equation of a line when you know a point on the line and have the equation of a line parallel to it, use the point-slope form of a linear equation. Substitute the values and simplify to get the equation.
Explanation:To write the equation of a line when you know a point on the line and have the equation of a line parallel to it, you can use the point-slope form of a linear equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the known point and m is the slope of the parallel line. Substitute the values into the equation and simplify to get the equation of the line.
For example, if you know a point on the line is (2, 5) and you have the equation of a line parallel to it as y = 2x + 3, the slope of the parallel line is 2. Substitute the values of the known point and the slope into the point-slope form: y - 5 = 2(x - 2). Simplify the equation to get the equation of the line: y - 5 = 2x - 4.
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A. (5, 7) and (-4,-2)
find the slope of a line
Answer: m = 1
Step-by-step explanation: Use the slope formula to find the slope m.
Hope this helps you out! ☺
Answer:
m = 1
Step-by-step explanation:
refer to attached picture for reference
we are given 2 points
(x₁, y₁) = (5,7)
(x₂,y₂) = (-4,-2)
simply substitute these into the given equation for slope
m = (y₂ - y₁)/(x₂-x₁)
= (-2 -7) / (-4 - 5)
= -9 / -9
= 1
If you want to make 2 1/2 Batches of cookies and you need one and 1 2/3 cups of flour per cookie batch how much flower do you need
Answer:
you need 4 1/3 cups of flower
A real estate agent received a 1.5% commission for a house that sold for $250,000. How much was the agent's commission?
Answer:
$3,750
Step-by-step explanation:
1.5% of 250,000 is 3,750
The question does NOT ask for the total price. It is just asking for commission.
Find the slope determined by the following pair of points
(19/4,2) , (1,3/4)
Answer:
1/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3/4-2)/(1-19/4)
m=(3/4-8/4)/(4/4-19/4)
m=(-5/4)/(-15/4)
m=(-5/4)(-4/15)
m=20/60
m=2/6
m=1/3
Answer:
1/3
Step-by-step explanation:
fred thinks of a number that is greater than 110 and less than 120. he can make his number with same number of hundreds,tens and ones. what is freds number?
The number Fred thinks of is 111
Solution:
Given that, Fred thinks of a number that is greater than 110 and less than 120
He can make his number with same number of hundreds,tens and ones
To find: Fred's number
Given that the number is greater than 110 and less than 120
The possible numbers are:
111 , 112, 113, 114, 115, 116, 117, 118, 119
But he can make his number with same number of hundreds,tens and ones
So the numbers in ones, tens and hundreds place are same
So the only possible number is 111
Thus the number Fred thinks of is 111
Final answer:
Fred's number is 111, as it is the only number that is greater than 110 and less than 120 and has the same number of hundreds, tens, and ones.
Explanation:
The number Fred thinks of must be greater than 110 and less than 120. Additionally, it must have the same number of hundreds, tens, and ones. To meet these conditions, the only number that fulfills this is 111. This is because it's the only number between 110 and 120 that has the same digit in the hundreds, tens, and ones place.
Fred's number is unique in this range because it is represented with three identical digits, showcasing an interesting property of numbers in our base-ten system where a digit's value depends on its position. Hence, 111 is the number Fred is thinking of, which consists of one hundred, one ten, and one one.
41,464,700+?=50,000,000
Answer:
8,535,300
Step-by-step explanation:
the answer is 41,464,700 + 8,535,300 = 50,000,000
A real estate sales agent receives a salary of $250 per week plus a commission of 2% of sales.Write an equation that gives the weekly income y in terms of sales x.
The equation y=0.02x+250 gives the weekly income y in terms of sales x.
Step-by-step explanation:
Given,
Weekly salary of real estate agent = $250
Commission rate = 2%
Let,
x be the sales per week.
y be the total weekly income.
Amount of commission = 2% of sales per week
Amount of commission = [tex]\frac{2}{100}*x[/tex]
Amount of commission = 0.02x
Total weekly income = Amount of commission + Weekly salary
[tex]y=0.02x+250[/tex]
The equation y=0.02x+250 gives the weekly income y in terms of sales x.
Keywords: equation, percentage
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The weekly income y of a real estate agent can be calculated using the equation y = 250 + 0.02x where 'y' is the weekly income, 'x' is the sales amount, '250' is the fixed salary and '0.02x' is the commission on sales.
Explanation:The weekly income y of a real estate agent is comprised of a fixed salary and a variable part which is a commission based on the amount of sales done. Given the fixed salary is $250 and the commission is 2% of sales, we can represent this as a mathematical equation:
y = 250 + 0.02x
Here, 'y' represents the weekly income, 'x' represents the amount of sales and '250' is the fixed salary. The term '0.02x' is the 2% commission of sales. So, for a given sales amount 'x', the weekly income 'y' can be computed using this equation.
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triangle ABC has AB=5, BC=7, and AC=9. D is on AC with BD=5. Find the length of DC
Answer:
[tex]DC=\frac{8}{3}\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The triangle ABD is an isosceles triangle
because
AB=BD
The segment BM is a perpendicular bisector segment AD
so
In the right triangle ABM
Applying the Pythagorean Theorem
[tex]BM^2=AB^2-AM^2[/tex]
we have
[tex]AB=5\ units\\AM=x\ units[/tex]
substitute
[tex]BM^2=5^2-x^2[/tex]
[tex]BM^2=25-x^2[/tex] -----> equation A
In the right triangle BMC
Applying the Pythagorean Theorem
[tex]BM^2=BC^2-MC^2[/tex]
we have
[tex]BC=7\ units\\MC=AC-AM=(9-x)\ units[/tex]
substitute
[tex]BM^2=7^2-(9-x)^2[/tex]
[tex]BM^2=49-(81-18x+x^2)[/tex]
[tex]BM^2=49-81+18x-x^2[/tex]
[tex]BM^2=-x^2+18x-32[/tex] ----> equation B
equate equation A and equation B
[tex]-x^2+18x-32=25-x^2[/tex]
solve for x
[tex]18x=25+32\\18x=57\\\\x=\frac{57}{18}[/tex]
Simplify
[tex]x=\frac{19}{6}[/tex]
Find the length of DC
[tex]DC=AC-2x[/tex]
substitute the given values
[tex]DC=9-2(\frac{19}{6})[/tex]
[tex]DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units[/tex]
what is the answer to 6y2−24y+18
13.) Springfield Elementary is putting on a school play
to raise money for their field trip. They are selling
adult's tickets for $6 and children's tickets for $3.50.
They made a total of $550 for selling 125 tickets. Write
and solve a system to determine how many of each
type they sold.
45 adult tickets and 80 children tickets were sold
Solution:
Let "a" be the number of adult tickets sold
Let "c" be the number of children tickets sold
Cost of 1 adult ticket = $ 6
Cost of 1 children ticket = $ 3.50
They sold a total of 125 tickets
Therefore,
a + c = 125
c = 125 - a --------- eqn 1
They made a total of $550. Therefore, frame a equation as:
number of adult tickets sold x Cost of 1 adult ticket + number of children tickets sold x Cost of 1 children ticket = 550
[tex]a \times 6 + c \times 3.50 = 550\\[/tex]
6a + 3.50c = 550 ----------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
6a + 3.50(125 - a) = 550
6a + 437.5 - 3.50a = 550
2.5a = 112.5
a = 45Substitute a = 45 in eqn 1
c = 125 - 45
c = 80Thus 45 adult tickets and 80 children tickets were sold
what is the square root of 56
Answer:
7.48331477355
Step-by-step explanation:
Answer:
(7.48331)
Step-by-step explanation:
The equation of a line is x + 3y = 14. What is the y-intercept of the line?
Answer:
First of all, before writing the y-intercept you need to make sure that the equation is in slope intercept form.
x + 3y = 14
3y = 14 - x
y = 14/3 -x/3
y= -x/3 + 14/3
14/3 is the y-intercept
The y-intercept of the line with equation x + 3y = 14 is 4.67.
Explanation:The equation of the line is in the form x + 3y = 14. To find the y-intercept, we need to set x = 0 and solve for y. Plugging in x = 0, we get 0 + 3y = 14. Simplifying the equation gives us 3y = 14. Dividing both sides by 3, we find that y = 4.67. Therefore, the y-intercept of the line is 4.67.
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What is the area of this parallelogram?
A.
2.9 cm2
B.
5.8 cm2
C.
8.7 cm2
D.
6.0 cm2
Answer:
5.8
Step-by-step explanation:
easy question plz help
darren got 42 out of the 56 question correct on the test. what percent of the questions did he get correct? please help ....
Answer:
75%
Step-by-step explanation:
42/56 = [tex]\frac{42}{56}[/tex]
Convert to decimal form:
42÷56 = 0.75
= 75%
Darren got 75% of the questions correct on his test, as 42 out of 56 simplifies to 3/4 or 75%. This percentage might place him in a higher percentile, indicating good performance.
Explanation:Darren scored 42 out of 56 questions correctly on his test. To find what percent of the questions he got correct, you set up a fraction of correct answers over the total number of questions and then convert it to a percentage. The fraction for Darren's test is 42/56, which simplifies to 3/4 or 0.75 when divided. To convert this to a percentage, you multiply by 100, giving Darren a score of 75% correct on his test.
Some students might be interested in how this compares to percentile ranks. For example, if the 70th percentile for a test is 16 correct answers out of 20, this means that 70% of the students answered 16 or fewer questions correctly. Darren's score of 75% would likely place him in a higher percentile since he got a larger proportion of the questions correct, which is generally considered good.
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what is 40 percdnt of 30? plz hel will give brainliest
Answer:
12
Step-by-step explanation:
30 times .40 =12
Answer:
Step-by-step explanation:
To calculate %, or to find x% of y, use
xy/100
(30)(40)/ 100
1200/100
12
Therefore, 40% of 30 = 12
Help please I need the area and perimeter
Perform the indicated operation.
h(x) = 3x - 1
g(x) = 2x – 4
Find (hog)(x)
Answer:
[tex]\large\boxed{(h\circ g)(x)=6x-16}[/tex]
Step-by-step explanation:
[tex]h(x)=3x-1\\\\g(x)=2x-4\\\\(h\circ g)(x)=h\bigg(g(x)\bigg)\\\\\text{Substitute instead of x the expression (2x - 4) to h (x):}\\\\(h\circ g)(x)=3(2x-4)-4\qquad\text{use the distributive property}\\\\(h\circ g)(x)=(3)(2x)+(3)(-4)-4\\\\(h\circ g)(x)=6x-12-4\\\\(h\circ g)(x)=6x-16[/tex]