From the question given:
f(x) = 5x² + 40x - 3
comparing the above with ax² + bx + c
a = 5
b = 40
c=-3
The x - axis of the vertex can be gotten by simply finding the value of -b/2a
\(x=\frac{-b}{2a}\)\(=\frac{-10}{2(5)}=\frac{-40}{10}=\text{ -}4\)To get the y-axis of the vertex, simply substitute the value of x=-4 into the function given
That is ;
\(f(-1)=5(-4)^2+\text{ 40(-4) - 3}\)\(=5(16)\text{ - 160 - 3}\)\(=80\text{ - 160 - 3}\)\(=\text{ -83}\)The function has a vertex at: (-4, -83)
\(2\frac{2}{5}\)
A fraction is a way to describe a part of a whole. The decimal form of 2 2/5 is 2.4.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The decimal form of 2 2/5 can be written as,
2 2/5 = 2 + 2/5 = 2 + 0.4 = 2.4
Hence, the decimal form of 2 2/5 is 2.4.
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To visit the manila Zoo, 11 adults and 5 Children have to pay 270 whereas 14 adults and 9 children have to pay 370? Find the total amount a family of 2 adults and 3 children has to pay to visit the zoo.
Step-by-step explanation:
let adults be x and childrens be y
a/q
11x + 5y = 270
14x + 9y = 370
→ x = -5/11y + 270/11 ; 14x + 9y = 370
→ 14(-5/11y + 270/11) + 9y = 370
→ y = 10
→ x = -5/11 × 10 + 270/11
→ x = -50/11 + 270/11
→ x = 20
therefore, we got
x = 20, y = 10
each adult have to pay 20 and each children have to pay 10
so,
2 × 20 = 40
3 × 10 = 30
40 + 30 = 70
for a family of 2 adults and 3 children they have to pay 70.
hope this helps you dear.
the length and width of a rectangle whose length is 9 centimeters more than its width
Answer:
Length W+9
Width W
Step-by-step explanation:
what is the differnence between (-2)^2 and -2^2 in math
Answer:
(-2)^2 = 4-2^2 = -4Step-by-step explanation:
The first is (-2)(-2) = 4.
The second is -(2)(2) = -4.
The order of operations says exponents are evaluated first. An exponent signifies repeated multiplication of the base.
_____
If your calculator is working correctly, it will show you the difference.
__
Beware spreadsheet programs. They don't always follow the order of operations when evaluating formulas. Parentheses are often required to keep them honest.
Answer: The one with perinthesis is bigger because you would do the negative first and you would have nothing to take away from
Step-by-step explanation:
Divide and simplify the answer to lowest terms. Write the answer as a fraction or a whole number.
17/10 ÷ 11/4
17/10 ÷ 11/4=______?
When you divide by a fraction, flip the second fraction over and change divide to multiply:
17/10 / 11/4 = 17/10 x 4/11
Now multiply straight across:
(17 x 4) / (10 x 11) = 68/110
Simplify:
68/110 = 34/55
Answer: 34/55
A half circle is joined to an equilateral triangle with side lengths of 12 units.Select all the expressions that correctly calculate the perimeter of the shape.
The perimeter of the figure described in the question is 42.84cm
How to get the perimeter of the figure?The figure is defined by a half circle is joined to an equilateral triangle with side lengths of 12 units.
So the perimeter of the figure will be equal to half of the circumference of the triangle plus the length of the two exposed sides of the triangle.
The diameter of the circle will also be 12 units, remember that the circumference of a circle of diameter D is:
C = 3.14*D
In this case, the circumference of half circle is:
C = 3.14*D/2
Replacing the value of the diameter:
C = 3.14*12cm/2 = 18.84cm
Adding the two sides of the triangle we get the perimeter.
P = 18.84cm + 2*12cm = 42.84cm
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What is the slope of the line shown below?
(1,6) (-5,-7)
A. 13/6
B. -13/6
C. -6/13
D. 6/13
\((\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{1}}} \implies \cfrac{ -13 }{ -6 } \implies \cfrac{13 }{ 6 }\)
HELP PLEASE FAST ILL MARK BRAINLIEST IF CORRECT 20 points!!
Answer:
8.49
Step-by-step explanation:
6^2 + 6^2 = 72
√72 = 8.485... = 8.49
Help me please not good at math
Answer: I think option A
Step-by-step explanation:
What is 1.07 x 10^5 in standard notation?
Answer: 107,000
Step-by-step explanation:
the exponent is a positive 5, so move the decimal point 5 places right.
if exponent is negative, go the other direction
1. Global warming creates local problems. Projections forecast that even a moderate air temperature increase of only 1.8 °F could cause brook trout distributions to decrease dramatically. For example, such a temperature increase would take Washburn county's 19 ponds that support brook trout down to 10 ponds. What would be the percent decrease in the number of ponds that support brook trout?
The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.
To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.
Initial number of ponds: 19
Final number of ponds: 10
To calculate the percent decrease, we can use the following formula:
Percent Decrease = (Difference / Initial Value) * 100
Let's apply this formula to the given data:
Difference = Initial number of ponds - Final number of ponds
Difference = 19 - 10
Difference = 9
Percent Decrease = (9 / 19) * 100
Now, let's calculate the percent decrease:
Percent Decrease = (9 / 19) * 100
Percent Decrease ≈ 47.37%
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Help me !!!
Please I really need it
Answer:
i don't know
Step-by-step explanation:
A-6=13 answer........
Answer:
A = 19
Step-by-step explanation:
A - 6 = 13
19 - 6 = 13
A = 19
I hope this helps!
Answer:
19
Step-by-step explanation:
13 + 6 = 19
19 - 6 = 13
Complete the table for all the lengths and widths that are missing for
Claire's garden.
*This is only some of the table from the problem.
Answer:
Step-by-step explanation:
x is 1,2,3,4,5
y is 14,13,12,11,10
The value of a TV decreases at a constant rate.If the TV is worth $1,190 five months after its orginal purchase date and $1,142 nine months after its original purchase date, what was the value of the tv on its original purchase date?
A.) $1,240
B.) $1,250
C.) $1,260
D.) $1,280
The original Value of the TV was $1,250. Hence, option (B) is correct.
Let the original value of the TV be $x and the rate at which the value of the TV decreases be r.
Since the rate of decrease is constant, we can use the formula, Value of TV = Original value - (Rate of decrease x Time)Using the given information,
we can write two equations,
1190 = x - (r x 5) ...(1)
1142 = x - (r x 9) ...(2)
On solving these equations, we can find the values of x and r.
Substituting the value of r in any one of the above equations will help us find the value of x.
Let's use equation (1).1190 = x - (r x 5)⇒ x = 1190 + 5r ...(3)
Substituting the value of x in equation (2),
we get,1142 = (1190 + 5r) - (r x 9)
⇒1142 = 1190 - 4r
⇒ 4r = 1190 - 1142
⇒4r = 48⇒ r = 12
Substituting the value of r in equation (3),
we get,x = 1190 + 5r = 1190 + 5 x 12 = 1250
Therefore, the original value of the TV was $1,250. Hence, option (B) is correct.
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Copy and complete the statement.
1. If HG = HK, then ____ = ____
2. If KHJ = KJH, then ____ = ____
Please add explanation as to why
Answer:
If HG = HK, then HG = HK. This statement is true by definition, as both sides of the equation are equal to the same value.
If KHJ = KJH, then KHJ = KJH. This statement is also true by definition, as both sides of the equation are equal to the same combination of letters.
The cost of a first-class postage stamp in 1962 was 4. In 1999 it is 33. The cost was (and is) growing exponentially. What was the growth rate? What will be the cost of a first-class postage stamp in 2010?
Answer:
The growth rate was 5.87%
Step-by-step explanation:
Time interval is t=1999−1962=37 yearsInitial cost in 1962 was a=4 unit Final cost in 1999 was y=33 unit Exponential growth function :y=a(1+r)t;a>0,r>0,ris rate of growth in decimal form.y=a(1+r)tor33=4(1+r)37 or(1+r)37=334or(1+r)37=8.25 , taking log on bothsides we get, 37log(1+r)=log(8.25) orlog(1+r)=log(8.25)37orlog(1+r)≈0.24769(1+r)=100.24769or1+r≈1.0587∴r=0.0587 orr%=0.0587⋅100≈5.87%The growth rate was 5.87% [Ans]
Φ1 = ∬S1 (-2u^6cos(v) - 2u^3sin(v)) du dv
= ∫(0->1) ∫(0->2π) (-2u^6cos(v) - 2u^3sin(v)) dv du
\(\begin{align}\sf\:\Phi_1 &= \iint_{S_1} (-2u^6\cos(v) - 2u^3\sin(v)) \, du \, dv \\ &= \int_{0}^{1} \int_{0}^{2\pi} (-2u^6\cos(v) - 2u^3\sin(v)) \, dv \, du \end{align} \\\)
50 POINTS AND WILL MARK BRAINLYEST***GIVE A DETAILED EXPLANATION AS TO HOW YOU GOT YOUR ANSWER**
Answer:
264
Step-by-step explanation:
3 + 8 = 11
3 - 1 = 2
3 - 1 = 2
2 + 4 = 6
11 x 2 x 2 x 6 = 264
write an equation to represent the number of points receieved by the winning team on one day of the competition. remember to define your variables
An equation representing the number of points received by the winning team on one day of the competition is P = winning team's points on one day.
Here is an equation to represent the number of points received by the winning team on one day of the competition:
Let's call the number of points received by the winning team on one day of the competition "P".
Then, the equation to represent this would be:
P = winning team's points on one day of the competition
Note: This equation is only a representation, and the actual calculation of the winning team's points would depend on various factors such as the rules of the competition, the performance of the players, etc.
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This circle is centered at the origin, and the length of its radius is 10. What is
the circle's equation?
A. x+y=10
B. x¹° + y¹° = 100
C. X²+ y² =10
D. X² +y²=100
Answer:
D
Step-by-step explanation:
If you substitute the radius, 10, and the center of the circle, the origin (also known as (0,0) into the equation of a circle, you should get: \((x - 0)^{2} + (y - 0)^{2} = 10 ^{2} \)
Multiplying this out should leave you with D as your answer.
What the meaning of statement this?
The statement is asserting that the universal class (V) is defined as the collection of all sets, where every set is included. It signifies that V encompasses all possible sets within the given set theory framework.
The statement "The universal class set, or universe, is the class of all sets: V = {x: x = x}" is referring to the concept of the universal class or the universe in set theory.
In set theory, the universal class set, denoted as V, represents the collection or class that contains all sets. It includes every possible set that can be defined or exists within the context of the set theory being considered.
The notation "{x: x = x}" is used to define the elements of the universal class. Here, "x = x" represents a condition that is always true for any object or element, regardless of its nature. In other words, this condition holds for everything in the universe, as anything is equal to itself.
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In the underlined section, what do the colonists promise to do?
Answer:
obey the law :)
Step-by-step explanation:
Answer: Obey the law
Step-by-step explanation:
Find the value of the expression below for x=10
x ^2 - 2 (x + 5)
Answer:
20
Step-by-step explanation:
your welcome!!
Cube A has an edge length of 3 inches. Cube B has an edge length double that of Cube A.
What is the volume, in cubic inches, of Cube B?
A. 27in^3
B. 36in^3
C. 216in^3
D. 729in^3
Answer:
216
Step-by-step explanation:
Cube A volume
3*3*3=27
Cube B volume
6*6*6=216
Edge length of cube B=2(3)=6in
Volume:-
\(\\ \sf\longmapsto V=(6)^3\)
\(\\ \sf\longmapsto V=6(6)(6)\)
\(\\ \sf\longmapsto V=216in^3\)
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?
About 80 necklaces have more than 28 beads. Then the correct option is C.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.
P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)
P(x > 28) = P(x - 24 / 4 > 1)
P(x > 28) = 1 - ∅1
P(x > 28) = 1 - 0.8413
P(x > 28) = 0.1587
Multiply both sides by 500, then we have
500 P(x > 28) = 0.1587 × 500
500 P(x > 28) = 79.35
500 P(x > 28) ≈ 80
About 80 necklaces have more than 28 beads. Then the correct option is C.
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The missing options are given below.
A. About 24 devices have more than 28 beads.
B. About 48 necklaces have more than 28 beads.
C. About 80 necklaces have more than 28 beads.
D. About 96 necklaces have more than 28 beads.
MULTIPLE CHOICE. Choose the inequality that describes the following
1) A
the lowest number is -3 and as it goes on, the number gets bigger and bigger therefore x must be larger than -4 but not equal to it.
2) D
the largest number is 9 and as it goes on, the number gets smaller therefore x must equal to and less than 9.
3) D
the largest number is 0 and the arrows points towards the negative numbers and the solid dot tells us that x can be equal to the number therefore the x must be equal to or less than 0.
4) A
the smallest number is -6 and the arrow points towards the positive numbers and the open dot tells us that x does not equal that number therefore x must be greater than -6 but not equal to it.
The table shows Molly and Myles's ages.
Molly's Age
Which expression best represents Myles's age in terms of Molly's age?
Answer:
y=10x
Step-by-step explanation:
myles age is 10 times the age of molly's age
2x10=20
3x10=30
4x10=40
5x10=50
solve the system of equations
y-5=x
x=-2-y y = ( , )
Answer:
y=1.5
x=-3.5
Our answer is (-3.5,1.5)
Step-by-step explanation:
y-5=x
x=-2-y
y=?
--------
Using substitution,
y-5=-2-y
Solve:
2y-5=-2
2y=3
y=1.5
We can enter 1.5 into the equation:
1.5-5=x
-3.5=x
There are five roses in a vase of 14 flowers. The rest are daisies.
(a) what is the ratio of all flowers in the vase daisies?
(B) What is the ratio of daisies to roses?
The required solution is as follows,
(a) The ratio of all flowers in the vase daisies is 14: 9
(b) The ratio of daisies to roses 9:5
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Number of daises in vase = 14 - 5 = 9
(a) The ratio of all flowers in the vase daisies,
= 14 / 9 or 14:9
(a) The ratio of daisies to roses,
= 9 / 5 or 9 : 5
Thus, the required ratio of flowers is given above.
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