A ball is thrown vertically upward from the top of a building 224 feet tall with an initial velocity of 80 feet per second. The distance ​s ​ (in feet) of the ball from the ground after ​t ​seconds is 224 0t 6ts = +8 −1 2a) After how many seconds does the ball pass the top of the building? b) After how many seconds does the ball strike the ground?

Answer:

C. JK and LM are congruent

Step-by-step explanation:

Given the coordinates J(-2,8), K(0,8), L(1,0), and M(1,-2), in other to determine whether JK is congruent to LM, we need to determine if the length of side JK and LM are equal i.e JK = LM

To get JK:

We will find the distance between the coordinates J(-2,8), K(0,8) to get the length JK using the formula:

JK =√(x2-x1)²+(y2-y1)²

JK = √(0-(-2))²+(8-8)²

JK = √2²+0²

JK = √4

JK = 2

For the length of LM with coordinate L(1,0), and M(1,-2)

LM = √(1-1)²+(-2-0)²

LM = √0²+(-2)²

LM = √0²+2²

LM = √0+4

LM =√4

LM = 2

Since JK = LM = 2 units, this means that JK and LM are congruent.

Step-by-step explanation:

Hey there!

Given;

[tex] {2}^{4x - 1} =32 [/tex]

[tex] {2}^{4x} . {2}^{ - 1} = {2}^{5} [/tex]

[tex] {2}^{4x} . \frac{1}{2} = {2}^{5} [/tex]

[tex] {2}^{4x} = {2}^{5} . {2}^{1} [/tex]

[tex] {2}^{4x} = {2}^{6} [/tex]

[tex]4x = 6[/tex]

[tex]x = \frac{6}{4} [/tex]

[tex]x = \frac{3}{2} [/tex]

7.)

[tex] \sqrt{x} - 3 = 7[/tex]

[tex] \sqrt{x} = 7 + 3[/tex]

[tex]( { \sqrt{x}) }^{2} = {(10)}^{2} [/tex]

X= 100

8.)

[tex]( {x + 1)}^{2} = 81[/tex]

[tex](x + 1) = \sqrt{81} [/tex]

[tex]x + 1 = \sqrt{ {9}^{2} } [/tex]

[tex]x + 1 = 9[/tex]

[tex]x = 9 - 1[/tex]

X=8

Hope it helps...

Answer:

u + 15

Step-by-step explanation:

Since we don't know the value of u, we have to put the equation like this.

Hope I helped :)

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[tex] {1000}^{ \frac{2}{3} } = {10}^{ {3}^{ \frac{2}{3} } } = {10}^{3 \times \frac{2}{3} } = {10}^{2} = 100 \\ [/tex]

Answer:

D

Step-by-step explanation:

Δ CED and Δ CAB are similar thus the ratios of corresponding sides are equal, that is

[tex]\frac{CE}{CA}[/tex] = [tex]\frac{ED}{AB}[/tex] , substitute values

[tex]\frac{x}{156-x}[/tex] = [tex]\frac{7}{84}[/tex] = [tex]\frac{1}{12}[/tex] ( cross- multiply )

12x = 156 - x ( add x to both sides )

13x = 156 ( divide both sides by 13 )

x = 12

Thus

AC = 156 - x = 156 - 12 = 144 → D

Answer:

D.  144

Step-by-step explanation:

Triangle BAC is similar to triangle DEC, so you can set up a ratio:

[tex]\frac{84}{156-x} = \frac{7}{x}[/tex]

Then cross multiply

84x = 7 (156 - x)

84x = 1092 - 7x

Add 7x to both sides.

91x = 1092

Divide both sides by 91.

x = 12

AC = 156 - x

AC = 156 - 12

AC = 144

Answer:

y= 3/4z + 25/4

Step-by-step explanation:

Answer:

x = -3 (yes that's negative 3)

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

[tex] \sf \: x = - 3[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ -6 + x + 4 = -5

Then the value of x will be,

→ -6 + x + 4 = -5

→ x + (-6 + 4) = -5

→ x + (-2) = -5

→ x - 2 = -5

→ x = -5 + 2

→ [ x = -3 ]

Hence, the value of x is -3.

Answer:

just fill in -4 for x so it would be g(-4)

Step-by-step explanation:

Happy Halloween

Answer:

×=11/4

Step-by-step explanation:

0=-2x+6x-11

0=4x-11

-4x=-11

x=11/4

Answer:

I got 1.19446588127

Answer:

Step-by-step explanation:

P(y) = y³ + 2y² + 2y + 1  

P(-1) = (-1)³ + 2*(-1)² + 2*(-1) + 1

      = -1 + 2 - 2 + 1

      = 0

As, P(-1) = 0, (y + 1) is a factor.

  Use synthetic division or remainder theorem.

-1        1          2           2           1

           0        -1            -1         -1        

           1          1            1            0

quotient = y² + y + 1

y³ + 2y² + 2y + 1  = ( y + 1) (y² + y + 1)

Answer:

Gabriela Mistral works as a humanitarian for [tex]8[/tex] days.

Step-by-step explanation:

Gabriela Mistral was a poet, diplomat, teacher and humanitarian such that each week she worked a certain amount of days as a poet diplomat teacher and humanitarian.

Ratio is [tex]1:1:3:2[/tex]

Let [tex]x[/tex] denotes total number of days Gabriela Mistral work.

As she works 12 days as a teacher,

[tex]\frac{3}{7}x=12\\ x=\frac{7}{3}(12)\\ x=28[/tex]

Total number of days [tex]=x=28[/tex]

So,

she works as a humanitarian for [tex]\frac{2}{7}x=\frac{2}{7}(28)=8[/tex] days.

Answer:

If 16 quarters is equal to 2 toonies, then 1 quarter is;

16 : 2

1 : x

16x = 2

x = 2/16

x = 1/8 toonies

20 quarters would therefore be;

= 1/8 * 20

= 2.5 toonies

24 quarters would be;

= 1/8 * 24

= 3 toonies

Answer:

2

Step-by-step explanation:

slope= change of y/change of x

slope=6/3=2

Answer:

Step-by-step explanation:

[tex]-3x + 15 > 102\\\\\mathrm{Subtract\:}15\mathrm{\:from\:both\:sides}\\\\-3x+15-15>102-15\\\\Simplify\\\\-3x>87\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\left(-3x\right)\left(-1\right)<87\left(-1\right)\\\\Simplify\\\\3x<-87\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3x}{3}<\frac{-87}{3}\\\\Simplify\\\\x<-29[/tex]

Answer:

m = 2 and n = 3

Step-by-step explanation:

We want to find the value of the integers m and n that will make the given expression true

(2x^ny^2)^m = 4x^6y^4

We can rewrite the left hand side of the equation as follows;

(2x^3y^2)^2

we can proceed to use inspection to ind the value of m and n

Through inspection since the left hand side of the equation now looks like the right hand side;

Then;

m= 2 and n = 3

Answer/Step-by-step explanation:

Given:

m<9 = 80°,

m<5 = 68°

Lines w and v are parallel to each other.

m<1 = m<9 (corresponding angles theorem)

m<1 = 80°

m<2 + m<1 = 180° (linear pair)

m<2 + 80° = 180° (substitution)

m<2 = 180° - 80°

m<2 = 100°

m<3 = m<1 (vertical angles are congruent)

m<3 = 80°

m<4 = m<2 (vertical angles are congruent)

m<4 = 100°

m<6 + m<5 = 180° (linear pair)

m<6 + 68° = 180° (substitution)

m<6 = 180° - 68°

m<6 = 112°

m<7 = m<5 (vertical angles)

m<7 = 68°

m<8 = m<6 (vertical angles)

m<8 = 112°

m<10 = m<2 (corresponding angles)

m<10 = 100°

m<11 = m<9 (vertical angles)

m<7 = 80°

m<12 = m<10 (vertical angles)

m<12 = 100°

m<13 = m<5 (corresponding angles)

m<13 = 68°

m<14 = m<6 (corresponding angles)

m<14 = 112°

m<15 = m<13 (vertical angles)

m<15 = 68°

m<16 = m<14 (vertical angles)

m<16 = 112°

Answer:

2.14159265358979323846264338327930288419716939937510582097494459230

Step-by-step explanation:

there's a song that I know

Answer:

its a anwser

Step-by-step explanation:

22+2 = 187

Answer:

The point (1 | 6) is on the graph.

Step-by-step explanation:

Answer:

it is 1/6

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

make 8 bouquets: Each bouquet will have 2 red flowers and 3 yellow flowers.

Answer:

[tex]h = \frac{2x+y}{r}[/tex]

Answer:

we know that

volume of a grain silo=volume of a cylinder+volume of a hemisphere

volume of a grain silo=17000 ft³

volume of a cylinder=pi*r²*h

h=30 ft

volume of a cylinder=pi*r²*30----> 30*pi*r² ft³

volume of a hemisphere=(2/3)*pi*r³

so

17000=30*pi*r²+(2/3)*pi*r³-----> multiply by 3---> 51000=282.60*r²+6.28*r³

6.28*r³+282.60*r²-51000=0

using a graph tool

see the attached figure

the solution is  

r=11.942 ft-------> r=11.9 ft

the answer is

The radius of the silo is 11.9 ft

Answer:

B)[tex]\frac{-3}{4}[/tex]

Step-by-step explanation:

We are supposed to find the difference of the fractions

a) [tex]-2\frac{1}{2}-(-1\frac{3}{4})[/tex]

[tex]=\frac{-5}{2}+\frac{7}{4}[/tex]

Using equivalent fraction

[tex]-\frac{5}{2} \times \frac{2}{2} = \frac{-10}{4}\\\Rightarrow \frac{-10}{4}+\frac{7}{4}[/tex]

Plot both fractions on number lines

So Using number line

[tex]\frac{-10}{4}+\frac{7}{4}=\frac{-5}{2}+\frac{7}{4}=\frac{-3}{4}[/tex]

So, Option B is true

Answer:

f(- 3) = - 14

Step-by-step explanation:

To evaluate f(- 3) substitute x = - 3 into f(x), that is

f(- 3) = (- 3)³ + 2(- 3)² - 5 = - 27 + 2(9) - 5 = 27 + 18 - 5 = - 14

Answer:

To be honest i dont even know

Step-by-step explanation:

ummmm