Answer:
Step-by-step explanation:
Because of the nature of the information we are given, we have no choice but to use the equation
[tex]y=a(x-h)^2+k[/tex]
and solve for a.
We know by the info that the vertex is (0, 84). We also know that if the vertex is at the origin, and that the base is 42 feet wide, it spans 21 feet to the right of the origin and 21 feet to the left of the origin. That means that we have 2 coordinates from which we need to pick one for our x and y in the equation. I don't like negatives, so I am going to choose the coordinate (21, 0) as x and y. Because this parabola opens upside down, as archways of door openings do, our "a" value better come out algebraically as a negative. Let's see...From the vertex we have that h = 0 and k = 84. So filling in:
[tex]0=a(21-0)^2+84[/tex] and simplifying a bit:
0 = 441a + 84 and
-84 = 441a so
[tex]a=-\frac{84}{441}=-\frac{4}{21}[/tex] Good, a is negative. Your equation is, then:
[tex]y=-\frac{4}{21}x^2+84[/tex]
Answer:
x² = -21y
Step-by-step explanation:
THIS IS THE RIGHT ANSWER I TOOK THE TEST
without actually calculating the cubes find the value of each of the following (-28)^3+(12)^3+(16)^3
Answer:
-16128
Step-by-step explanation:
This expression can be calculated by algebraic means, whose process is described below:
1) [tex](-28)^{3}+(12)^{3}+(16)^{3}[/tex] Given.
2) [tex](-12-16)^{3} + (12)^{3}+(16)^{3}[/tex] Definition of addition.
3) [tex](-12)^{3} + 3\cdot (-12)^{2}\cdot (-16)+3\cdot (-12)\cdot (-16)^{2}+(-16)^{3}+(12)^{3}+(16)^{3}[/tex] Cubic perfect binomial.
4) [tex](12)^{3}+[(-1)\cdot (12)]^{3}+(16)^{3} + [(-1)\cdot (16)]^{3}+3 \cdot (-12)^{2}\cdot (-16) + 3\cdot (-12)\cdot (-16)^{2}[/tex] Commutative property/[tex](-x)\cdot y = -x\cdot y[/tex]
5) [tex](12)^{3} + (-1)^{3}\cdot (12)^{3} + 16^{3} +(-1)^{3}\cdot (16)^{3} + (-3)\cdot [(-12)^{2}\cdot (16) +(-16)^{2}\cdot (12)][/tex] Distributive property/[tex](-x)\cdot y = -x\cdot y[/tex]/[tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]
6) [tex](12)^{3} + [-(12)^{3}]+(16)^{3} + [-(16)^{3}]+ (-3)\cdot [(-12)^{2}\cdot (16)+(-16)^{2}\cdot (12)][/tex] [tex](-x)\cdot y = -x\cdot y[/tex]
7) [tex](-3)\cdot [(-12)^{2}\cdot (16) + (-16)^{2}\cdot (12)][/tex] Existence of the additive inverse/Modulative property for addition.
8) [tex](-3) \cdot [(12)^{2}\cdot (16)+(16^{2})\cdot (12)][/tex] [tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]/[tex](-x)\cdot (-y) = x\cdot y[/tex]
9) [tex](-3)\cdot (12)\cdot (16)\cdot (12+16)[/tex] Distributive property.
10) [tex]-16128[/tex] [tex](-x)\cdot y = -x\cdot y[/tex]/Definition of sum/Definition of multiplication/Result
a. Give Tommy your estimate of 0.27 probability in ratio form.
Answer:
0.27 expressed in ratio form is 27:100
Step-by-step explanation:
Before we give Tommy the estimate of 0.27 probability in ratio form, we shall need to turn 0.27 to fraction
Mathematically, that would be 27/100
Now expressing this in ratio form, we will have 27:100
The Anderson family wants to look at their cash flow over a year. They decide to write out their cash flow for 4 months as given in the spreadsheet below. In which of the months did they have the greatest net cash flow? A 5-column spreadsheet showing cash inflows and outflows over a year. Total cash inflow: January, 2,760 dollars; April, 3,060 dollars; August, 2,760 dollars; December, 2,900 dollars. Total cash outflow: January, 2,435 dollars; April, 2,675 dollars; August, 2,670 dollars; December, 3,000 dollars. a. January b. April c. August d. December
Answer:
It is B. April
Step-by-step explanation:
The Anderson family greatest cash flow for the year is April
How to find greatest cash flowTotal cash inflow:
January, 2,760 dollarsApril, 3,060 dollarsAugust, 2,760 dollarsDecember, 2,900 dollarsTotal cash outflow:
January, 2,435 dollarsApril, 2,675 dollarsAugust, 2,670 dollarsDecember, 3,000 dollarsCash flow:
January = 2,760 dollars - 2,435 dollars
= $325
April = 3,060 dollars - 2,675 dollars
= $385
August = 2,760 dollars - 2,670 dollars
= $90
December = 2,900 dollars - 3,000 dollars
= $ -100
Learn more about cash cash flow:
https://brainly.com/question/735261
Solve for x. Enter your answer using digits. 4x−14+6=12 x=
Answer:
x = 5
Step-by-step explanation:
Given
4x - 14 + 6 = 12 , that is
4x - 8 = 12 ( add 8 to both sides )
4x = 20 ( divide both sides by 4 )
x = 5
Help ASAP please show work I need this done ASAP
Answer:
Step-by-step explanation:
Graph shows the distance traveled by a biker as a function of time.
Velocity of the biker changes in the different intervals.
1). In the interval 0 < t < 2, biker is moving with a constant velocity.
Velocity = [tex]\frac{\text{Displacement}}{\text{Time}}[/tex]
= [tex]\frac{0-4}{0-2}[/tex]
= 2 km per hour
2). In the interval 2 < t < 5,
Velocity = [tex]\frac{4-4}{4-2}[/tex]
= 0
Therefore, biker stopped between 2 to 5 hours.
3). In the interval 5 < t < 6,
Velocity = [tex]\frac{\triangle x}{\triangle t}[/tex]
= [tex]\frac{4-3}{6-5}[/tex]
= 1 km per hour
4). In the interval 6 < t < 7,
Velocity = [tex]\frac{6-3}{7-6}[/tex]
= 3 km per hour
Answer this question
Answer:
[tex]\huge\boxed{width=12cm}[/tex]
Step-by-step explanation:
[tex]l-length\\w-width\\P-perimeter[/tex]
The formula of perimeter of the rectangle:
[tex]P=2l+2w=2(l+w)[/tex]
Substitute:
[tex]l=6w\\\\P=168cm[/tex]
[tex]168=2(6w+w)\\168=2(7w)\\168=14w\qquad|\text{divide both sides by 14}\\\\\dfrac{168}{14}=\dfrac{14w}{14}\\\\12=w\Rightarrow w=12(cm)[/tex]
Answer:
Width of rectangle = 12 cm
Step-by-step explanation:
Let us assume that,
→ Length = 6x
→ Width = x
→ Perimeter = 168 cm
Perimeter of rectangle,
→ P = 2(L + W)
Forming the equation,
→ 168 = 2(6x + x)
Now the value of x will be,
→ 168 = 2(6x + x)
→ 2 × 7x = 168
→ 14x = 168
→ x = 168/14
→ [ x = 12 ]
Then the length and width is,
→ Length = 6x = 6(12) = 72 cm
→ Width = x = 12 cm
Hence, required width is 12 cm.
PLZ HELP ME!!!! I NEED THE ANSWER QUICK SO IM GIVING BRAINLIEST TO THE FASTEST AND BEST ANSWER.
Answer:
f(x) = 8(1/2)^x.
Step-by-step explanation:
According to the graph, there is a point at (0, 8) and (1, 4).
That means that when x = 0, y = 8.
8 = a(b)^0
1a = 8
a = 8
That means that a = 8, and when x = 1, y = 4.
4 = 8(b)^1
4 = 8b
8b = 4
b = 4/8
b = 1/2
So, f(x) = 8(1/2)^x.
Hope this helps!
what is the area of the figure below?
Answer:
D. 72 [tex]in^2[/tex]
Step-by-step explanation:
The square is 36 in2
The 2 triangles are both 18 in2.
36+18+18=72 in2
I hope this helps!
pls ❤ and give brainliest pls
Answer:
Area is 72 in²
Step-by-step explanation:
= Area of three triangles + area of square.
[tex]{ \bf{ = 3 \times ( \frac{1}{2} b \times h) + (s \times s)}}[/tex]
substitute:
[tex]{ \sf{ = ( \frac{1}{2} \times 6 \times 6) + 2( \frac{1}{2} \times 6 \times 3) + (6 \times 6)}} \\ = { \sf{18 + 18 + 36}} \\ = { \sf{ {72 \: in}^{2} }}[/tex]
Complete the recursive formula of the geometric sequence 7, -14, 28, -56, ....
Answer:
[tex]a_{n}[/tex] = - 2[tex]a_{n-1}[/tex]
Step-by-step explanation:
A geometric recursive formula has the form
[tex]a_{n}[/tex] = r[tex]a_{n-1}[/tex]
where r is the common ratio
Here r = - 14 ÷ 7 = - 2, thus
[tex]a_{n}[/tex] = - 2[tex]a_{n-1}[/tex] with a₁ = 7
como resuelvo esto y=1+2(4/5)
Answer:
Es 2.6
Step-by-step explanation:
Answer: translate
Step-by-step explanation:
Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 80 yd from B and 104 yd from A, with angle ACB
measuring 51.2º. How far apart are A and B (to the nearest yard)?
HURRYYY GIVING 20 POINTS!!
Answer:
Step-by-step explanation:
The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The distance between A and B is 85.6 yds.
What is the Law of Cosine?The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
The three points A, B, and C will form a triangle. Therefore, using the law of cosine the measure of the third side AB can be written as,
[tex]AB =\sqrt{(AC)^2 + (BC)^2 -2(AC)(BC)\cdot \cos(51.2^o)}\\\\AB =\sqrt{(80)^2 + (104)^2 -2(80)(104)\cdot \cos(51.2^o)}\\\\AB = \sqrt{6400+10816-16640\cos51.2^o}\\\\AB = \sqrt{7328.4}\\\\AB=85.6\rm\ yd[/tex]
Hence, the distance between A and B is 85.6 yds.
Learn more about the Law of Cosine:
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#SPJ2
Can someone tell me if this is right?
Answer:
Yep
Step-by-step explanation:
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A limo is rented at a fixed cost for an evening. It is rented by 12 people, the average cost for each person will be $2 less than if it is rented by 10 people. How much does the limo cost for the evening?
Answer:
$120
Step-by-step explanation:
According to the information in the statement and taking into account that the price for renting the limo is fixed, you can say that the cost of renting the limo for 12 people is equal to the cost of renting it for ten. Then, the cost for 12 people is 12 for the cost per person which is equal to 10 for the cost per person and you can express it as follow:
x is the cost per person when the limo is rented by 10 people.
12*(x-2)=10*x
You can solve for x:
12x-24=10x
12x-10x=24
2x=24
x=24/2
x=12
Now that you have the cost per person when the limo is rented by 10 people, you can multiply this value for 10 to find the cost of renting the limo for the evening:
12*10=120
The answer is that the limo cost $120 for the evening.
Maria is installing gutters on her rectangular shed that measures 10 ft by 9 ft she has 23 ft of gutter already and need to purchase more to complete of gutter all the way around the shed the store sells gutters in length of 5 feet how many lenths of gutter does she need to buy to finish the shed
Answer:
Maria needs 3 lengths of gutter of finish the shed.
Step-by-step explanation:
We need to calculate the perimeter of the rectangular shed to know how much 5 feet gutter is needed.
The perimeter of the shed is p = 2(l + b) where l = 10ft and b = 9 ft
p = 2(10 + 9) = 2(19) = 38 ft
Now, the perimeter of the shed also equal 23 ft of gutter already installed plus 5x ft gutter where x = number of gutters.
So 23 + 5x = 38
collecting like terms, we have
5x = 38 - 23
5x = 15
dividing through by 5 we have
5x/5 = 15/5
x = 15/5
x = 3
So, Maria needs 3 lengths of gutter of finish the shed.
The length, breadth ND height of box are 32 cm 16cm, 8cm.wht is the maxim length of the string that can be used to measure the sides of the box exactly
Answer:
8 cm
Step-by-step explanation:
The maximum length of the string will be the greatest common divisor of 32 , 16 , 8
32 = 2 * 2 * 2 * 2 * 2
16 = 2 * 2 * 2 * 2
8 = 2 * 2 * 2
GCD = 2* 2 * 2 = 8
The maximum length of the string = 8 cm
**Yoxelt buys 4 1/2 gallons of soda. One-fourth of the soda he bought was Pepsi and the rest was Sprite. How many gallons of Pepsi did Yoxelt buy? Show all work below.
Answer:
1 1/8
Step-by-step explanation:
1/4 of the 4 1/2 gallons were Pepsi, so the amount is ...
(1/4)(9/2) = (1·9)/(4·2) = 9/8 = 1 1/8
Yoxelt bought 1 1/8 gallons of Pepsi.
Solve the following formula for m v2=3Pmn
Answer:
m= 0 /(−3np+v2 )
Step-by-step explanation:
Find the value of p.
Answer:
[tex]\huge\boxed{p = 3}[/tex]
Step-by-step explanation:
7p + 7 = 37 - 3p (They both are equal)
7p + 3p = 37-7
10p = 30
Dividing both sides by 10
p = 3
Answer:
p=3
Step-by-step explanation:
7p+7=37-3p
7p[+3p]+7=37-3p[+3p]
10p+7=37
10p+7[-7]=37[-7]
10p=30
10p/10=30/10
p=3
I hope this helps!
The sum of 6 consecutive integers is 519. What is the third number in this sequence?
Answer:
86
Step-by-step explanation:
x+x+1+x+2+x+3+x+4+x+5 = 519
6x+15 = 519
6x = 504
x = 84
Third number = x+2 = 86
Answer:
86
Step-by-step explanation:
khan
ate
at?
20) A triangular garden has sides that
1
5
6- 7
feet.
6
What is the perimeter of the garden?
Answer:
Since all the three sides of the triangle are of equal length, we can find the perimeter by multiplying the length of each side by 3. 20 + 20 + 20 = 3 × 20 = 60 cm.
How to do this question plz answer me step by step plzz plz
Answer:
20π cm
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = 2πr ( where r is the radius )
Here r = 10 , thus
C = 2π × 10 = 20π cm
Answer:
hope it helps
Step-by-step explanation:
circumference of a circle = 2*pi*r = 2*pi*10 =20picm
Two buildings are 12m apart on the same horizontal level. From the top of the taller building, the angle of depression of the bottom of the shorter building is 48degrees and from the bottom, the angle of of elevation of the top of the shorter building is 36 degrees. Calculate the difference in the heights of the buildings
Answer:
4.61 m
Step-by-step explanation:
The angle of depression of the bottom of the shorter building from the top of the taller building = 48° equals the angle of elevation of the top of the taller building from the bottom of the shorter building
Using trig ratios
tan48° = H/d where H = height of taller building and d = their distance apart = 12 m
H = dtan48° = 12tan48° = 13.33 m
Also, the angle of elevation of the top of the shorter building from the bottom of the taller building is 36°
Using trig ratios
tan36° = h/d where h = height of shorter building
h =dtan36° = 12tan36° = 8.72 m
Now, the difference in height of the buildings is thus H - h = 13.33 m - 8.72 m = 4.61 m
1) factories x^2+7x
2) factories 6+9x
3) factories 6y^2-9xy
Step-by-step explanation:
it was helpful to you
always be happy in your life㋛︎㋛︎☺︎︎☺︎︎☺︎︎
[tex] {x}^{2} + 7x \\ x(x + 7) \\ \\ \\ 6 + 9x \\ 3(2 + 3x) \\ \\ 6 {y}^{2} - 9xy \\ 3x(2y - 3x)[/tex]
Which could be the entire interval over which the
function, f(x), is negative?
(-8,-2)
(-8,0)
(-0, -6)
(00,-4)
b) Factor the expression completely. (1 point)
20b - 16
Answer:
20b - 16
=> 4 (5b - 4)
or
20b - 16
=> 20b/16 - 16/16
=> 1.25b - 1
Answer:
4(5b-4)
Step-by-step explanation:
To factor this you need to find a number, that 20 and 16 are divisible by. You can divide 4 from both of these.
It becomes 4(5b-4)
A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint. If a can of paint contains 75 ounces of white paint, how many ounces of blue paint are in the can?
Answer:
i think 60 parts of blue paint are in the can.
Step-by-step explanation:
ratio should be equal in both cases
therefore,let blue part in second case be x(suppose)
5÷4=75÷x
by equating this we will be able to identify the value of x
and the value of x comes 60 which is the required answer....
hope this will help you..
i try my best to give correct answer..
if i am mistake, i am sorry for that...
Help me please, IXL keeps messing me up
Circle the correct term to complete the sentence: When you dilute a solution, the resulting solution has a concentration that is (increased/decreased) and the volume is (increased/decreased).
Answer:
1st option is decreased 2nd is increased
Step-by-step explanation:
Because you add a liquid to dilute a solution, it makes the solution weaker (less concentrated) you also added more liquid which would increase the volume
Answer:
decreased; increased
Step-by-step explanation:
when you dilute something you make it less concentrated by adding something else (usually water i think). so the concentration decreases while the volume increases
What is the standard form for the quadratic function? g(x)=(x−6)2−5
Answer:
x^2-12x+31
Step-by-step explanation:
Standard form of the quadratic equation (x-6)^2-5 is x^2-12x+36-5=x^2-12x+31
Mr. Lee is 32 years older than his son. Five years later, Mr. Lee’s age will be 5 times that of his son. How old is Mr. Lee now?
Answer: mr lee is 37 year .
Step-by-step explanation:32+5=37
Answer:
Mr. lee is 35 yrs old right now. his son 3
Step-by-step explanation:
after 5 yrs, his son will be 8 and lee 40, 8×5=40