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3 years ago

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When finding the intersection of two lines from both Algebra 1 and geometry you first set the linear equations equal to each oth

er. find the intersection points of the two lines whose equations are shown below. be sure to find the X & Y coordinates.
y=5x+1 and y=2x-11

2 answers:

Diano4ka-milaya [45]3 years ago

7 0

Answer with explanation:

The equation of twio lines are

y=5 x +1-----(1)

y=2 x-11--------(2)

Equation (1) - Equation (2)

0=5x-2x+1-(-11)

0=3 x+12

Adding , -12 on both sides

-12=3x+12-12

3x= -12

Dividing by , 3 on both sides

x=-4

Putting the value of , x in equation 1,

y= 5 × (-4)+1

y= -20 +1

y= -19

Point of intersection of two lines are = ( -4, -19)

NNADVOKAT [17]3 years ago

6 0

I really dont know so sorry

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Maria throws a softball straight up into the air with an initial velocity of 50 ft/sec. The ball leaves her hand when it is exac

Nataly_w [17]

Answer:

The equation that models the situation is $s_{f} = 4+\frac{v_{f}^{2}-2500}{64.348}$ .

Step-by-step explanation:

Let suppose that effects from air friction and Earth's rotation can be neglected, so that the softball can be modelled experiment a free fall, that is, an uniform accelerated motion due to gravity. From we know the initial velocity and position of the position and we can determine the final position of the ball as a function of the final velocity:

$v_{f}^{2} = v_{o}^{2}+2\cdot a \cdot (s_{f}-s_{o})$ (1)

Where:

$s_{o}$ , $s_{f}$ - Initial and final position of the softball, measured in feet.

$a$ - Acceleration, measured in meters per square second.

$v_{o}$ , $v_{f}$ - Initial and final velocities of the softball, measured in feet per second.

If we know that $v_{o} = 50\,\frac{ft}{s}$ , $a = -32.174\,\frac{m}{s^{2}}$ and $s_{o} = 4\,ft$ , then the equation that models the situation is:

$v_{f}^{2} = 2500-64.348\cdot (s_{f}-4)$

Then, we clear the final position of the softball:

$-\frac{v_{f}^{2}-2500}{-64.348} = s_{f}-4$

$s_{f} = 4+\frac{v_{f}^{2}-2500}{64.348}$

The equation that models the situation is $s_{f} = 4+\frac{v_{f}^{2}-2500}{64.348}$ .

8 0

2 years ago

Please solve this for me

olga_2 [115]

15/5 is 3

So then you change the equation to be 12=15z-3 ( don’t forgot the negative sign)

Move the constant to the right side and change the sign

-15z= -3 -12

-3-12 is -15

Divide -15z= -15

Your final answer will be z= 1

5 0

3 years ago

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric

Zanzabum

Answer:

a) (1215, 1297)

b) (1174, 1338)

c) (1133, 1379)

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 1256

Standard Deviation, σ = 41

Empirical Rule:

Also known as 68-95-99.7 rule.
It states that almost all the data lies within three standard deviation for a normal data.
About 68% of data lies within 1 standard deviation of mean.
About 95% of data lies within two standard deviation of mean.
About 99.7% of data lies within 3 standard deviation of mean.

a) range of years centered about the mean in which about 68% of the data lies

$\mu \pm 1(\sigma)\\=1256 \pm 41\\=(1215, 1297)$

68% of data will be found between 1215 years and 1297 years.

b) range of years centered about the mean in which about 95% of the data lies

$\mu \pm 2(\sigma)\\=1256 \pm 2(41)\\=1256 \pm 82\\=(1174, 1338)$

95% of data will be found between 1174 years and 1338 years.

c) range of years centered about the mean in which about all of the data lies

$\mu \pm 3(\sigma)\\=1256 \pm 3(41)\\=1256 \pm 123\\=(1133, 1379)$

All of data will be found between 1133 years and 1379 years.

3 0

3 years ago

Factor using the trinomial<br> 10.<br> X2 + 13x + 12

Rudik [331]

Answer:

Factoring the trinomial: $x^2+13x+12$ we get the factors $\mathbf{(x+1)(x+12)}$

Step-by-step explanation:

We need to factor the trinomial: $x^2+13x+12$

We can factor the trinomial by breaking the middle term i.e 13x

Such that adding or subtracting gets the both terms we get 13x and multiplying both terms we get 12x^2

We can break 13x as: 12x and x

Adding them we get 13x and multiplying them we get 12x^2

So,

$x^2+13x+12\\=x^2+12x+x+12\\=x(x+12)+1(x+12)\\=(x+1)(x+12)$

So, Factoring the trinomial: $x^2+13x+12$ we get the factors $\mathbf{(x+1)(x+12)}$

8 0

2 years ago

Polly buys 14 cupcakes for a party. The bakery puts them into boxes that hold 4 cupcakes each.

Temka [501]

Answer:

Part a) The number of boxes needed will be 4

part b) The fraction of the box that is empty is $\frac{1}{2}$

Part c) Are needed 2 cupcakes to fill the last box

Step-by-step explanation:

Part a) How many boxes will be needed for Polly to bring all the cupcakes to the party?

To find out the number of boxes needed, divide the total number of cupcakes by 4 (maximum number of cupcakes that fit in each box).

so

$\frac{14}{4}=3.5\ box$

Round up

The number of boxes needed will be 4

Part b) If the bakery completely fills as many boxes as possible, what fraction of the last box is empty?

we know that

The maximum number of cupcakes per box is 4

The first three boxes have 4 cupcakes

The last box has

$14-3(4)=2\ cupcakes$

The fraction of the box that is empty is equal to the number of cupcakes missing to fill the box divided by the cupcake capacity of the box

$\frac{2}{4}=\frac{1}{2}$

Part c) How many more cupcakes are needed to fill this box

Subtract the number of cupcakes in the box from the cupcake capacity of the box

The last box has 2 cupcakes

The cupcake capacity of the box is 4

so

$4-2=2\ cupcakes$

therefore

Are needed 2 cupcakes to fill the last box

8 0

3 years ago