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3 years ago

17−5r+9r=12+6r−1 what is r?

Mathematics

1 answer:

jonny [76]3 years ago

7 0

Answer:

r=3

Step-by-step explanation:

simplify each side

4r+17=6r+11

Subtract 4r from both sides.

17=2r+11

Subtract 11 from both sides

6=2r

divide both sides by 2

3=r

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(08.07 HC)

andreev551 [17]

Answer:

$\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}$

$\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

C) See attachment.

Step-by-step explanation:

Given function:

$f(x)=2x^2-x-10$

To factor a <u>quadratic</u> in the form $ax^2+bx+c$ <em> , </em>find two numbers that multiply to $ac$ and sum to $b$ :

$\implies ac=2 \cdot -10=-20$

$\implies b=-1$

Therefore, the two numbers are -5 and 4.

Rewrite $b$ as the sum of these two numbers:

$\implies f(x)=2x^2-5x+4x-10$

Factor the first two terms and the last two terms separately:

$\implies f(x)=x(2x-5)+2(2x-5)$

Factor out the common term (2x - 5):

$\implies f(x)=(x+2)(2x-5)$

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

$\implies (x+2)(2x-5)=0$

Therefore:

$\implies (x+2)=0 \implies x=-2$

$\implies (2x-5)=0 \implies x=\dfrac{5}{2}$

So the x-intercepts are:

$x=-2, \:\:x=\dfrac{5}{2}$

The x-value of the vertex is:

$\implies x=\dfrac{-b}{2a}$

Therefore, the x-value of the vertex of the given function is:

$\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}$

To find the y-value of the vertex, substitute the found value of x into the function:

$\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}$

Therefore, the vertex of the function is:

$\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the <u>leading coefficient</u> of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.

The axis of symmetry is the <u>x-value</u> of the <u>vertex</u>. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is <u>symmetrical</u>.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

5 0

2 years ago

Please help with all of these 5 points per question

liberstina [14]

Answer:

1. C = $100 = .25(m)

2. C = $150

3. 800 = m

Step-by-step explanation:

1. C = $100 (flat fee rate) + .25m

2. c = $100 + .25(200 miles)

↓

c = $100 + 50

↓

c = 150

3. 300 = 100 + .25(m)

-100 -100 (subtract on both sides)

--------------------------------

200 = .25(m)

------------------- (divide by .25 to get m by itself)

.25

Therefore being 800 = m

5 0

4 years ago

Please show work it’s due tommorow I will give 35 Brainly

SCORPION-xisa [38]

Answer:

Step-by-step explanation:Worked out on paper shown below

Also I recommended a online app called (it has wierd name but it’s helpful for algebra) mathpapa

Also I do math in pen so the last answer is messed up it’s 4c^2d and then the rest of the parentheses.Sorry for that.

5 0

2 years ago

I need help with this problem.

MariettaO [177]

Answer:

the numbers next to a variable is a coefficient, for instance in 2x 2 would be the coefficient.

the constants are the numbers without variables next to them, just numbers

like terms are the term that are similar like 2x and 8x or even 5 and 3

lm not exactly sure what they mean when asking for constant terms.

4 0

3 years ago

11. Let f(x) = 2x² + 7x + 5

Lady_Fox [76]

Answer:

(x+1)(2x+5)

Step-by-step explanation:

f(x) = 2x² + 7x + 5

Factor the expression by grouping. First, the expression needs to be rewritten as 2x²+ax+bx+5. To find a and b, set up a system to be solved.

a+b=7

ab=2×5=10

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 10.

1,10

2,5

Calculate the sum for each pair.

1+10=11

2+5=7

The solution is the pair that gives sum 7.

a=2

b=5

2x²+7x+5 as (2x²+2x)+(5x+5).

(2x²+2x)+(5x+5)

Factor out 2x in the first and 5 in the second group.

2x(x+1)+5(x+1)

Factor out common term x+1 by using distributive property.

(x+1)(2x+5)

7 0

3 years ago