Determine the parent function.

Answer:

30 seconds.

Step-by-step explanation:

So, we have the equation:

[tex]h(t)=-16t^2+h[/tex]

Where t is the time in seconds and h is the initial height.

A barometer falls from a weather balloon at a height of 14,400 feet. In other words, the initial height is 14,400. Substitute for h:

[tex]h(t)=-16t^2+14400[/tex]

We need to find when the barometer hits the ground. Ground level is 0 feet. Therefore, we can substitute h(t) for 0 and solve for the equation (solve for t) in order to find how long (in seconds) it took for the barometer to fall:

[tex]0=-16t^2+14400\\-14400=-16t^2\\900=t^2\\t=\pm\sqrt{900} \\\text{Time cannot be negative.}\\t=\sqrt{900}\\ t=30 \text{ seconds}[/tex]

Therefore, it took 30 seconds for the barometer to hit the ground when it fell at a height of 14,400 feet.

Edit: Spelling.

Answer:

Step-by-step explanation:

We will make a table and fill it in according to the information provided. What this question is asking us to find, in the end, is how long did it take the cars to travel the same distance. In other words, how long, t, til car 1's distance = car 2's distance. The table looks like this:

              d     =      r     *     t

car1

car2

We can fill in the rates right away:

             d       =      r     *     t

car1                       40

car2                       60

Now it tells us that car 2 leaves 3 hours after car 1, so logically that means that car 1 has been driving 3 hours longer than car 2:

            d     =      r      *      t

car1                     40         t + 3

car2                     60           t

Because distance = rate * time, the distances fill in like this:

                   d      =      r      *      t

car1    40(t + 3)    =      40        t+3

car2          60t     =       60         t

Going back to the interpretation of the original question, I am looking to solve for t when the distance of car 1 = the distance of car 2. Therefore,

40(t+3) = 60t and

40t + 120 = 60t and

120 = 20t so

t = 6 hours.

Answer:

[tex]\large \boxed{\sf \ \ a = 2, \ b = -2, \ c = -3 \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]2x^2 - 8x + 5=2(x^2-4x)+5\\\\\text{*** We notice that *** }\\\\\text{*** } x^2-4x=(x-2)^2-2^2=(x-2)^2-4\\\\\text{*** So we can write ***}\\\\2x^2 - 8x + 5=2(x^2-4x)+5=2\left( (x-2)^2-4\right)+5\\\\=2\left(x-2\right)^2-8+5=\boxed{2\left(x-2\right)^2-3}[/tex]

So a = 2, b = -2, c = -3

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

x=5,y=-1

Step-by-step explanation:

5x– 2y = 27

-3x +2y=-17

Add the two equations together to eliminate y

5x– 2y = 27

-3x +2y=-17

----------------------

2x  = 10

Divide by 2

2x/2 = 10/2

x = 5

Now find y

-3x +2y = -17

-3(5)+2y = -17

-15+2y =-17

Add 15 to each side

-15+15 +2y = -17+15

2y = -2

Divide by 2

2y/2 = -2/2

y =-1

Answer:

2 / 5.

Step-by-step explanation:

The slope is the rise over the run.

In this case, the rise is 2 - (-6) = 2 + 6 = 8.

The run is 4 - (-16) = 4 + 16 = 20.

So, the slope is 8 / 20 = 4 / 10 = 2 / 5.

Hope this helps!

Answer:

the slope of the line that goes through (4,2) and (-16,-6) is 2/5

m= 2/5

Step-by-step explanation:

in order to find the slope we use the ∆y/∆x which is really the change in y over the change in x.

so all you have to do is find your y's and X's.

your y's are -6 and 2

your X's are -16 and 4

now in order to find the change in y and x you subtract your y's and x'x

the formula for this is:

∆y/∆x = y1-y2/x1-x2= (m aka the slope)

y1 is -6

and y2 is 2

-6 - 2 = -8

now do the X's

X1 is -16

and X2 is 4

-16 - 4 = -20

put that in fraction form and it's -8/-20

simplify that you get 2/5

Answer:

If x=7 that means that if 7 substitute r which is 7^2 and 7*7=49 and 49/4

=12 1/4

So the remainder is 1

Step-by-step explanation:

Answer:

3x^2 -4

Step-by-step explanation:

f(x) = 2x^2 +3

g(x) = x^2 -7

(f+g) (x) =  2x^2 +3 +  x^2 -7

 Combine like terms

            = 3x^2 -4

Answer:

[tex]\boxed{3x^2-4}[/tex]

Step-by-step explanation:

[tex](f+g)(x)[/tex]

Rewrite.

[tex]f(x)+g(x)[/tex]

[tex](2x^2 +3)+(x^2-7)[/tex]

Combine like terms and simplify.

[tex](2x^2 +x^2 )+(3-7)[/tex]

[tex](3x^2 )+(-4)[/tex]

[tex]3x^2 +-4[/tex]

Answer:

=360

explanation:

When you’re talking about rotation you go counterclockwise and each quadrant is another 90 degrees.

Answer:

360

Step-by-step explanation:

Answer:

it is 3.375

Step-by-step explanation:

The volume inside the giant sugar cube is of 3.375m³.

To solve this question, we first find the side of the cube, given it's surface area, and with the side, we find the volume.

-----------------------------------

Finding the side:

Considering it took 13.5 m² of material to build the cube, we have that it's surface area is of 13.5m².

The surface area of a cube of side s is:

[tex]S_A = 6s^2[/tex]

In this question:

[tex]6s^2 = 13.5[/tex]

[tex]s^2 = \frac{13.5}{6}[/tex]

[tex]s = \sqrt{\frac{13.5}{6}}[/tex]

[tex]s = 1.5[/tex]

-----------------------------------

Volume:

The volume of a cube of side s is:

[tex]V = s^3[/tex]

In this question, [tex]s = 1.5[/tex], so:

[tex]V = 1.5^3 = 3.375[/tex]

The volume inside the giant sugar cube is of 3.375m³.

A similar question is found at https://brainly.com/question/11862932

Answer:

Alternate Exterior Angles theorem

Answer:

alternate exterior angles

Step-by-step explanation:

alternate exterior angles are when two angles are on the far side of two lines and are not on the same side of the line cutting through the two parallel lines

Hope this is not redundunt or anything because I thought maybe I should just explain it so you would understand it next time :)

Answer:  b) {-3, 0.5}

Step-by-step explanation:

The new equation is the original equation plus 6.  Move the original graph UP 6 units.  The solutions are where it crosses the x-axis.

[tex]\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6[/tex]

+6 means it is a transformation UP 6 units.  

Solutions are where it crosses the x-axis.

The curve now crosses the x-axis at x = -3 and x = 0.5.

Answer:

11 cars

Step-by-step explanation:

There are 20 cars in my building's parking lot, 15 cars are 4-door, then

20 - 15 = 5 cars are 2-door.

5 cars are 2-door, 4 of them are 2-door and white, then

5 - 4 = 1 car is 2-door and red.

12 cars are red, 1 car is 2-door and red, then

12 - 1 = 11 cars are 4-door and red.

plz give me brianlist

Answer:

n = -15 and n = 9. n = -15 is not reasonable because you can't have negative boxes or negative units of measurement.

Step-by-step explanation:

8(n + 2)(n + 4) = 1,144

(n + 2)(n + 4) = 143

n^2 + 2n + 4n + 8 = 143

n^2 + 6n - 135 = 0

(n + 15)(n - 9) = 0

n + 15 = 0

n = -15

n - 9 = 0

n = 9

I got two solutions: n = -15 and n = 9. Only one is reasonable because you cannot have a negative number of boxes or negative weight.

Hope this helps!

Simplify the equation, and set it equal to zero to prepare for factoring.

Multiply the two factors in parentheses using the distributive property:

8(n2 + 2n + 4n + 8) = 1,144

Combine like terms inside the parentheses:

8(n2 + 6n + 8) = 1,144

Multiply the terms inside the parentheses by 8 using the distributive property:

8n2 + 48n + 64 = 1,144

Set the equation equal to zero by subtracting 1,144 from each side:

8n2 + 48n − 1,080 = 0

Factor out the GCF, which is 8:

8n2 + 48n − 1,080 = 0

8(n2 + 6n − 135) = 0

Divide both sides of the equation by 8:

n2 + 6n − 135 = 0

Compare the equation with the standard form ax2 + bx + c = 0, and get a, b, and c:

a = 1, b = 6, c = -135

The leading coefficient of the equation is 1. So, find two numbers that have a sum of 6 and a product of -135:

6 = -9 + 15

-135 = -9 • 15

The two numbers are -9 and 15. Use the two numbers to write the factors of the quadratic expression:

(n − 9)(n + 15) = 0

Use the zero product property, and solve for n:

n − 9 = 0 or n + 15 = 0

n = 9 or n = -15

There are two solutions for n. But since n represents the width of the helmet box, it can’t be negative. Therefore, the only reasonable solution is n = 9

Answer:

125

Step-by-step explanation:

Add all the angles then subtract by 360.

Answer:

Vp-by-step explanation:

Answer:

5

Step-by-step explanation:

5

Step-by-step explanation:

[tex]6x - 30 = 5(x - 4)[/tex]

[tex]6x - 30 = 5x - 20[/tex]

[tex]6x - 30 - 5x = - 20[/tex]

[tex]x - 30 = - 20[/tex]

[tex]x = - 20 + 30[/tex]

[tex]x = 10[/tex]

Hope this is correct and helpful

HAVE A GOOD DAY!

You answer is 10404 to get this answer multiply the 102 double time

Answer: m∠PNO =16.25°  , m∠ONM=57.5°

Step-by-step explanation:

Given: Circle k(O), m NM =65° ∠PNO≅∠PMO

To find: m∠PNO, m∠ONM.

Since, central angle is equal to the measure of minor arc.

⇒∠MON = m NM =65°

In Δ MON , ON = OM [Radii of circle]

⇒ ∠ONM = ∠NMO   (i)   [Angle apposite to equal side of triangle are equal]

In Δ MON , ∠ONM + ∠NMO+∠MON =180°

⇒ ∠ONM + ∠ONM+65°=180°  [from (i)]

⇒ 2∠ONM=115°

⇒ ∠ONM=57.5°

⇒ ∠ONM = ∠NMO =57.5°

Also, an inscribed angle is half of a central angle that subtends the same arc.

⇒∠MPN =half of∠MON

=  [tex]\dfrac{65^{\circ}}{2}=32.5^{\circ}[/tex]

Also, ∠PNO≅∠PMO  [Given]

⇒∠PNO =∠PMO

⇒ ∠PNO +∠ONM =∠PMO+∠NMO   [∵∠ONM = ∠NMO]

⇒∠PNM=∠PMN

In ΔNPM

⇒ ∠MPN +∠PNM+∠PMN = 180°

⇒ 32.5° +∠PNM + ∠PNM= 180°

⇒ 2(∠PNM)= 147.5°

⇒ ∠PNM = 73.75°

Also,  ∠PNM = ∠PNO+∠ONM

⇒73.75°= ∠PNO+57.5°

⇒ ∠PNO =16.25°

Hence, m∠PNO =16.25°  , m∠ONM=57.5°

Answer:

Answer: m∠PNO =16.25°  , m∠ONM=57.5°

Step-by-step explanation:

Given: Circle k(O), m NM =65° ∠PNO≅∠PMO

To find: m∠PNO, m∠ONM.

Since, central angle is equal to the measure of minor arc.

⇒∠MON = m NM =65°

In Δ MON , ON = OM [Radii of circle]

⇒ ∠ONM = ∠NMO   (i)   [Angle apposite to equal side of triangle are equal]

In Δ MON , ∠ONM + ∠NMO+∠MON =180°

⇒ ∠ONM + ∠ONM+65°=180°  [from (i)]

⇒ 2∠ONM=115°

⇒ ∠ONM=57.5°

⇒ ∠ONM = ∠NMO =57.5°

Also, an inscribed angle is half of a central angle that subtends the same arc.

⇒∠MPN =half of∠MON

=  

Also, ∠PNO≅∠PMO  [Given]

⇒∠PNO =∠PMO

⇒ ∠PNO +∠ONM =∠PMO+∠NMO   [∵∠ONM = ∠NMO]

⇒∠PNM=∠PMN

In ΔNPM

⇒ ∠MPN +∠PNM+∠PMN = 180°

⇒ 32.5° +∠PNM + ∠PNM= 180°

⇒ 2(∠PNM)= 147.5°

⇒ ∠PNM = 73.75°

Also,  ∠PNM = ∠PNO+∠ONM

⇒73.75°= ∠PNO+57.5°

⇒ ∠PNO =16.25°

Hence, m∠PNO =16.25°  , m∠ONM=57.5°

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let side of the square = a

The , Area of square = a²

Now, Midpoint of Diagonal DB is E

And DE = 2 units

So, DB = 2 DE = 2 × 2 = 4 units

Now, using Pythagoras theorem in ∆ BCD

DB² = DC² + BC²

plug the values

[tex] {4}^{2} = {a}^{2} + {a}^{2} [/tex]

Collect like terms

[tex] {4}^{2} = 2 {a}^{2} [/tex]

Evaluate the power

[tex]16 = 2 {a}^{2} [/tex]

Swipe the side of the equation

[tex]2 {a}^{2} = 16[/tex]

Divide both sides of the equation by 2

[tex] \frac{2 {a}^{2} }{ 2 } = \frac{16}{2} [/tex]

Calculate

[tex] {a}^{2} = 8[/tex]

Therefore, The area of the square is 8 sq.units.

Hope this helps..

Best regards!!

The area of the square is 8 square units.

Let's assume that the side length of the square is "s". Since the midpoint of the diagonal is 2 units from the vertex of the square, the diagonal of the square is 4 units (twice the distance from the vertex to the midpoint).

We can use the Pythagorean theorem to find the side length "s" of the square:

[tex]s^2 + s^2 = 4^2\\2s^2 = 16[/tex]

Divide both sides by 2:

[tex]s^2 = 8[/tex]

Now, to find the area of the square, we use the formula:

[tex]Area = side length^2\\Area = s^2 = 8[/tex]

So, the area of the square is 8 square units.

To know more about area:

https://brainly.com/question/33403734

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Answer:

(0, –2)

Step-by-step explanation:

I am assuming that point 'B' is (-5 , 0).

The translation rule is: [tex](x,y)\rightarrow(x+5,y-2)[/tex].

Apply the rule to point 'B':

[tex]\frac{(-5,0)\rightarrow(-5+5,0-2)}{(x,y)\rightarrow(x+5,y-2)}\rightarrow\boxed{(0,-2)}[/tex]

B' should be (0, -2).

Answer:

Guy above me might be right but Im not sure. Im on the cumulative exam on edge.

Step-by-step explanation:

Answer:

The answer to this question can be defined as follows:

In option 1, She buys 4 memory cards.

In option 2, The cost of memory is $40  

Step-by-step explanation:

Given:

Available space is = 105 GB

required space = 1000 GB

256 GB memory cost $10.

Find needed memory:

=  1000 GB - 105 GB

= 895 GB

∴ the available memory is 256 GB.

∵ 256 × 4 = 1024  GB

The total memory she have = 1024 + 105 = 1129 GB

And  she needs to buy 4 memory cards.

The cost of the four memory cards is= 4 ×10 =  $40.

Using proportions, it is found that the least  amount of money Nancy can spend to get the storage she needs is of $40.

------------------------------

The rule of three is of:

1 card - 256 GB

x cards - 895 GB

Applying cross multiplication:

[tex]256x = 895[/tex]

[tex]x = \frac{895}{256}[/tex]

[tex]x = 3.5[/tex]

Rounding, she has to buy 4 cards.

A similar problem is given at https://brainly.com/question/17594062

Answer:

(-2, -8/3)

Step-by-step explanation:

2(-2) - 6y = 12

-4 -6y = 12

-6y = 16

y = -16/6 = -8/3

Answer:

dependent, 1/11

Step-by-step explanation:

the probability of picking a white ribbon at first is 1/3

the probability of picking a white ribbon next is 3/11

1/3 * 3/11 = 3/33 = 1/11

it is dependent because picking the first ribbon affects picking the second.

Answer:

7.8

Step-by-step explanation:

To do this problem you need to know Pythagorean Theorem which is also known as [tex]a^{2} +b^{2} =c^{2}[/tex].

In this problem 6 would be a, 5 would be b, and d would be c. So to do this we would do 5 squared (which is 25)+ 6 squared which is 36) and you would get 61 and when you do that you will just take the square root of that which is 7.81 and round it to the nearest tenth which is 7.8 and that would be the final answer

Answer:

b

Step-by-step explanation:

edg 2020

The smallest measure of angle is angle ∠ V due to opposite angle of smallest side which is correct option(B).

A triangle is defined as simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol of Δ and consists of three connected vertices. Triangles can be categorized into a number of different varieties according on their sides and angles.

A triangle has three sides, three vertices, and three interior angles.

The angle sum property of a triangle states that the sum of the three interior angles of a triangle is always 180°

In ΔTUV,

Length of Side TU = 5 units

Length of Side UV = 8 units

Length of Side TV = 11 units

Side TU is opposite of angle ∠ V

Side UV is opposite of angle ∠ T

Side TV is opposite of angle ∠ U

The sides in order from longest to shortest :  Side TV > Side UV = Side TU

The longest side is always opposite of the largest angle, and the smallest side is always opposite of the smallest angle.

Hence, the angle in order from longest to shortest :  angle ∠ U > angle ∠ T > angle ∠ V

Thus, the smallest measure of angle is angle ∠ V.

Learn more about triangle here :

brainly.com/question/2773823

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Three different whole numbers whose sum and product are equal are 1, 2, and 3.

1 + 2 + 3 = 6

1 x 2 x 3 = 6

As demonstrated above, the sum and product of 1, 2, and 3 is the same.

Hope this helps!! :)

Answer:

1 2 and 3

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

Let the numerator = n.

Let the denominator = d.

The fraction is

n/d

"The denominator of a rational number is greater than its numerator by 3."

d = n + 3

The fraction is

n/(n + 3)

"If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5."

(n - 3)/(n + 3 + 2) = 1/5

(n - 3)/(n + 5) = 1/5

Cross multiply.

5(n - 3) = 1(n + 5)

5n - 15 = n + 5

4n = 20

n = 5

d = n + 3 = 5 + 3 = 8

n/d = 5/8

The original number is 5/8.

Answer:

25°

Step-by-step explanation:

Since ∠DBC = 130°, ∠DBC + ∠ABD = 180° (sum of angles on a straight line is 180°). Solving for ∠ABD:

∠DBC + ∠ABD = 180°

130 + ∠ABD  = 180°

∠ABD = 180° - 130°

∠ABD = 50°

∠ABD  is bisected by line BE, therefore ∠ABD = ∠EBA + ∠DBE (angle addition postulate).

The angle addition postulate states that if w is the interior of xyz then ∠XYZ = ∠XYW + ∠ZYW

Since E is the interior of ∠ABD, then:

∠ABD = ∠EBA + ∠DBE

But ∠EBA = ∠DBE

∠ABD = 2∠EBA

50 = 2∠EBA

∠EBA = 25°

Answer:

Answer:

Lines r and s are parallel as Corresponding Angles given. There are four pairs of corresponding angles: angle 1 and angle 5, angle 2 and angle 6, angle 3 and angle 7, and angle 4 and angle 8. Since r and s are parallel, the slope of r is equal to the slope of s. Since t is a straight line, the slope of t is the same at both intersections, by the definition of a straight line. Thus, the corresponding angles created at both intersections must have the same measure, since the difference of the slopes at each intersection is the same, and the intersections share a common line. So, corresponding angles must have equal measure. Therefore, by definition of congruent angles, corresponding angles are congruent: angle 1 is congruent to angle 5, angle 2 is congruent to angle 6, angle 3 is congruent to angle 7, and angle 4 is congruent to angle 8.

Step-by-step explanation

answer from haven

Answer:

184 cm²

Step-by-step explanation:

Surface area of the rectangular box is expressed as S = 2(LW+LH+WH)

L is the length of the box = 90 cm

W is the width of the box = 50 cm

H is the height of the box= 90 cm

If there are error of at most 0.2 cm in each measurement, then the total surface area using differential estimate will be expressed as shown;

S = 2{(LdW+WdL) + (LdH+HdL) + (WdH+HdW)

Note that dL = dW = dH = 0.2 cm

Substituting the given values into the formula to estimate the maximum error in calculating the surface area of the box

S = 2{(90(0.2)+50(0.2)) + (90(0.2)+90(0.2)) + (50(0.2)+90(0.2))

S = 2{18+10+18+18+10+18}

S = 2(92)

S = 184 cm²

Hence, the maximum error in calculating the surface area of the box is 184cm²