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sp2606 [1]
3 years ago
6

Christopher wrote the number pattern below. The first term is 8.

Mathematics
1 answer:
REY [17]3 years ago
6 0
Subtract 2 then add 3 
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Solve the following system of equations by substitution. Show all steps.
Alinara [238K]

Answer:

Given system of equations:

\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}

To solve by substitution, equate the equations and solve for x:

\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}

Therefore, the x-values of the solution are x = 0 and x = 4.

To find the y-values of the solution, substitute the found values of x into the functions:

f(0)=-(0)^2+2(0)+3=3

g(0)=-2(0)+3=3

f(4)=-(4)^2+2(4)+3=-5

g(4)=-2(4)+3=-5

Therefore, the solutions to the given system of equations are:

(0, 3) and (4, -5)

4 0
2 years ago
Find 3x2 − y3 − y3 − z if x = 3, y = −2, and z = −5.
IceJOKER [234]
3x²-y³ - y³ - z        if x = 3, y = -2, z = -5

Simply plug in all the values :)

3(3²) - (-2³) - (-2³) - (-5)

Simplify.

3(9) + 2³ + 2³ + 5

Simplify.

27 + 8 + 8 + 5

Simplify.

35 + 13

Simplify.

48

~Hope I helped!~
4 0
3 years ago
Use the stem and leaf plot graph to answer the question.
kogti [31]
<h3>Answer:   13 days</h3>

====================================================

Explanation:

Count the number of leaves marked in green.

  1. Row One: 2 leaves (1 and 8)
  2. Row Two: 3 leaves (3, 6, and 9)
  3. Row Three: 5 leaves (2, 3, 4, 6, 7)
  4. Row Four: 3 leaves (1, 6, and 8)

There are 2+3+5+3 = 13 leaves total. This represents tickets were sold on 13 days.

Each stem and leaf combines to form a different ticket count. For instance, the stem of 1 and leaf of 8 combine to get the value 18. So 18 tickets were sold on that particular day.

7 0
1 year ago
When adding or subtracting decimals, how can you be sure to add or subtract only digits that have the same place
Igoryamba

Answer: the number that are at the left side of the decimal is the whole numbers and the ones at the right are like the ones less than the whole numbers

4 0
2 years ago
Read 2 more answers
GEOMETRY<br><br> *image is attached above*
Keith_Richards [23]

Answer:

(-9.5, -4)

Step-by-step explanation:

Given the ratio a:b (a to b) of two segments formed by a point of partition, and the endpoints of the original segment, we can calculate the point of partition using this formula:

( \frac{a }{a + b} (x_{2} - x_{1}) + x_{1}, \frac{a}{a + b} (y_{2} - y_{1})+y_{1}).

Given two endpoints of the original segment

→ (-10, -8) [(x₁, y₁)] and (-8, 8) [(x₂, y₂)]

Along with the ratio of the two partitioned segments

→ 1 to 3 = 1:3 [a:b]

Formed by the point that partitions the original segment to create the two partitioned ones

→ (x?, y?)

We can apply this formula and understand how it was derived to figure out where the point of partition is.

Here is the substitution:

x₁ = -10

y₁ = -8

x₂ = -8

y₂ = 8

a = 1

b = 3

( \frac{a }{a + b} (x_{2} - x_{1}) + x_{1}, \frac{a}{a + b} (y_{2} - y_{1})+y_{1}). →

( \frac{(1) }{(1) + (3)} ((-8) - (-10)) + (-10), \frac{(1)}{(1) + (3)} ((8) - (-8))+ (-8)) →

( \frac{1}{4} ((-8) - (-10)) + (-10), \frac{1}{4}((8) - (-8)) + (-8)) →

( \frac{1}{4} (2) + (-10), \frac{1}{4}(16) + (-8)) →

( (\frac{1}{2}) + (-10), (4) + (-8)) →

( (-\frac{19}{2}), (-4)) →

( -\frac{19}{2}, -4) →

*( -9.5, -4)*

Now the reason why this

6 0
3 years ago
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