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3 years ago

Simplify the expression by combining like terms -4f-9-f+15

Mathematics

2 answers:

shusha [124]3 years ago

4 0

Answer:

-5f+6

Step-by-step explanation:

-4f-f = -5f

15-9= 6

Answer is -5f+6

Hope this helps!

oee [108]3 years ago

4 0

Answer:

-5f + 6

Step-by-step explanation:

-4f - 9 - f + 15

( -4f + -f) + (-9 + 15)

-5f + 6

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zepelin [54]

Answer:

The required equation is: $\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}$

Step-by-step explanation:

We need to find equation from the table given

x f(x)

3 -5

7 -2

11 1

15 4

We can write equation in the form of $y=mx+b$

where m is slope and b is y-intercept.

Finding Slope

We can used the slope formula to find slope: $Slope=\frac{y_2-y_1}{x_2-x_1}$

From the table we have: $x_1=3, y_1=-5, x_2=7, y_2=-2$

Putting values and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-(-5)}{7-3} \\Slope=\frac{-2+5}{7-3}\\Slope=\frac{3}{4}$

So, we get slope $m=\frac{3}{4}$

Now, finding y-intercept

Using the slope $m=\frac{3}{4}$ and point (3,-5) we can find y-intercept

$y=mx+b\\-5=\frac{3}{4}(3)+b\\-5=\frac{9}{4}+b\\b=-5-\frac{9}{4}\\b=\frac{-5*4-9}{4}\\b=\frac{-20-9}{4}\\b=\frac{-29}{4}$

The y-intercept is $b=\frac{-29}{4}$

So, the equation having slope $m=\frac{3}{4}$ and y-intercept $b=\frac{-29}{4}$ will be:

$y=mx+b\\y=\frac{3}{4}x-\frac{29}{4}$

The required equation is: $\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}$

6 0

3 years ago

Calculate the sum of the first 30 terms in the sequence that begins with 70,65,60

Afina-wow [57]

$\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle \Large \boldsymbol{} a_1=70 \ ; \ d=-5 \\\\S_n=\frac{a_1+a_n}{2} \cdot n \ ; \ a_n=a_1+(n-1)d \Longrightarrow \\\\\\ S_{30}=\frac{70+70-29\cdot5}{2} \cdot 30 =-75 \\\\\\Answer: S_{30}=-75$

4 0

3 years ago

Expand and simplify 5(3x+2)-2(4x-1)

blsea [12.9K]

5(3x+2)-2(4x-1)

= 15x+10-8x+2

= 7x+12

6 0

2 years ago

Jodie bought some shirts for $6 each. Marge bought some shirts for $8 each. The girls spent the same amount of money on shirts.

liubo4ka [24]

$24 cause 6 times 4 is 24 and 8 times 3 is 24

6 0

3 years ago

Read 2 more answers

The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the stan

torisob [31]

The point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ is $\fbox{\begin\\\ \math 2x+5y=-15\\\end{minispace}}$ i.e., $\fbox{\begin\\\ \bf option C\\\end{minispace}}$ .

Further explanation:

It is given that line passes through the points $(-5,-1)$ and $(10,-7)$ .

The objective is to determine the point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ .

The options given are as follows:

Option A: 2x-5y=-15

Option B: 2x-5y=-17

Option C: 2x+5y=-15

Option D: 2x+5y=-17

Consider the point $(-5,-1)$ as $(x_{1},y_{1})$ and $(10,-7)$ as $(x_{2},y_{2})$ .

Slope of a curve is defined as the change in the value of $y$ with respect to change in value of $x$ .

The slope of the line is calculated as follows:

$\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}$

To obtain the value of slope substitute the value of $x_{1},y_{1},x_{2},y_{2}$ in the above equation.

$\begin{aligned}m&=\dfrac{-7-(-1)}{10-(-5)}\\&=\dfrac{-6}{15}\\&=\dfrac{-2}{5}\end{aligned}$

Therefore, the slope of the line is $\fbox{\begin\\\ \math m=\dfrac{-2}{5}\\\end{minispace}}$

The general way to express the equation of a line in its point slope form is as follows:

$\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}$

To obtain the point slope form of the equation of the line substitute the value of $m$ , $x_{1}$ and $y_{1}$ in the above equation.

$\begin{aligned}(y-(-1))&=\dfrac{-2}{5}(x-(-5))\\(y+1)&=\dfrac{-2}{5}(x+5)\\5y+5&=-2x-10\\5y+2x&=-15\end{aligned}$

From the above calculation it is concluded that the point slope form the equation of a line is $\fbox{\begin\\\ \math 5y+2x=-15\\\end{minispace}}$

Figure 1 (attached in the end) represents the graph of the function $5y+2x=-15$ .

This implies that the correct option for the point slope form of the line is option C.

Therefore, the point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ is $2x+5y=-15$ i.e., option C.

Learn more:

1. A problem to complete the square of quadratic function brainly.com/question/12992613

2. A problem to determine the slope intercept form of a line brainly.com/question/1473992

3. Inverse function brainly.com/question/1632445.

Answer details

Grade: High school

Subject: Mathematics

Chapter: Linear equation

Keywords: Equation, linear equation, slope, intercept, x-intercept, y-intercept, intersect, graph, curve, slope intercept form, line, y=3x/2-3, standard form, point slope form.

6 0

3 years ago

Read 2 more answers

Simplify the expression by combining like terms -4f-9-f+15​

Simplify the expression by combining like terms -4f-9-f+15