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3 years ago

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On the same set of axes, use slope and y-intercept to graph each line in the system shown at right then find the points of inter

section if one or more exists y= – x + 2 y = 3x +6

1 answer:

anygoal [31]3 years ago

6 0

Answer:

Step-by-step explanation:

-x + 2 = 3x + 6

3x + 6 = -x + 2

4x + 6 = 2

4x = -4

x = -1

y = 1 + 2 = 3

(-1, 3)

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a grocer stacks apples in a pyramid-like stack whose rectangular base is 7 apples by 5 apples. each apple above the first level

g100num [7]

The arrangement of the apples in the stack is in a sequence that can be

used to find the number of apples in each row and in the stack.

Correct response:

The number of apples in the stack are <u>85 apples</u>

<h3>How to find the sum of a sequence</h3>

The given parameters are;

Dimensions of apples in the rectangular base = 7 apples by 5 apples

Number of apples on which each apple above rests = 4 apples

Required:

The number of apples in the stack.

Solution:

The dimensions, length and width of the apples in each row decreases

by 1 compared to the row on which the apple rests, as follows;

In the base, the dimension = 7 by 5

In the row directly above, the dimension = (7 - 1) by (5 - 1)

The number of apples sequence continues and is completed by a singles row of apples at the top, from which gives;

Number of apples in the stack = 7 × 5 + 6 × 4 + 5 × 3 + 4 × 2 + 3 × 1 = 85

The number of apples in the tack = <u>85 apples</u>

Learn more about sequence and series here:

brainly.com/question/13043887

4 0

2 years ago

13(x - 3)=39 what is answer

artcher [175]

X = 6 after distributing then adding 39 to both sides and then divide by 13

8 0

3 years ago

Read 2 more answers

What is the solution to log Subscript 2 Baseline (2 x cubed minus 8) minus 2 log Subscript 2 Baseline x

BARSIC [14]

Answer:

x=2

Step-by-step explanation:

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6 0

3 years ago

Read 2 more answers

A car travels at a speed of 85 miles per hour. How far will it travel in 15 mins?

marusya05 [52]

In this question, we're trying to find how many miles a car travels in 15 minutes.

We know that the car travels at 85 mph.

However, we need to know how many miles it travels per minute.

To find this, we would divide 85 by 60.

85 ÷ 60 = 1.4166

The car drives at a speed of about 1.42 per minute.

We need to know how far it goes in 15 minutes, so multiply 1.42 by 15.

1.42 · 15 = 21.3

The car travels at a approximately 21.3 miles in 15 minutes.

5 0

3 years ago

Find number a and k so that x-2 is afactor<br>OF F(x)=x4-2ax tax-<br>X+k and F(-1)=3

Slav-nsk [51]

Question:

Find numbers a and k so that x-2 is a factor of

$f(x)=x^4-2ax^3+ax^2- x+k$

and

$f(-1)=3$

Answer:

$k = -2$ and $a=1$

Step-by-step explanation:

Given

$f(x)=x^4-2ax^3+ax^2- x+k$

$Factor:\ x - 4$

$f(-1)=3$

Required

Find a and k

For $f(-1)=3$

Substitute -1 for x

$f(x)=x^4-2ax^3+ax^2- x+k$

$f(-1) = (-1)^4 - 2a *(-1)^3 + a*(-1)^2 - (-1) + k$

$f(-1) = 1 - 2a *-1 + a*1 +1 + k$

$f(-1) = 1 +2a + a +1 + k$

$f(-1) = 2 +3a + k$

Substitute 3 for f(-1)

$3 = 2 +3a + k$

Collect Like Terms

$3 - 2 = 3a + k$

$1 = 3a + k$

Also:

If $x - 2$ is a factor, then

$f(2) = 0$

Substitute 2 for x and 0 for f(x)

$f(x)=x^4-2ax^3+ax^2- x+k$

$0 = 2^4 - 2a * 2^3 + a * 2^2 - 2 + k$

$0 = 16 - 2a * 8 + a * 4 - 2 + k$

$0 = 16 - 16a + 4a - 2 + k$

$0 = 16 - 12a - 2 + k$

Collect Like Terms

$2 - 16 = - 12a + k$

$-14 = k - 12a$

$k = 12a - 14$

Substitute 12a - 14 for k in $1 = 3a + k$

$1 = 3a + 12a - 14$

$1 = 15a - 14$

Collect Like Terms

$15a = 1 + 14$

$15a = 15$

Solve for a

$a = \frac{15}{15}$

$a=1$

Substitute 1 for a in $k = 12a - 14$

$k = 12 * 1 - 14$

$k = 12 - 14$

$k = -2$

3 0

3 years ago