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3 years ago

Can some one help me set up an equation out of these word problems? PLEASE HELP!!!

Mathematics

2 answers:

charle [14.2K]3 years ago

7 0

Answer:

1 He spent 9 hours working

2. Her balance before she bought groceries is 83 + 294 = $ 377

3.He spent 16 × 3 = 48 minutes on his math homework.

4. Garden view hotel is 235 in height

Step-by-step explanation:

1. Sam spent 2/5 of his work day answering mail. He spent 3.6 hours answering email yesterday . To calculate how many hours he work let make the hours he worked yesterday = a

time he spent answering email

2/5 × a = 3.6

cross multiply

3.6 × 5 = 2a

18 = 2a

divide both sides by 2

a = 18/2

a = 9 hours

2. Elena was charged $ 83 from her credit card to buy groceries. Her final balance after buying groceries was $ 294. Her balance before she bought groceries is 83 + 294 = $ 377

3. Let say he spent a minutes long on science homework.

Time he spent on math homework = 3a

He spent a total of 64 minutes on math and sciences

3a + a = 64

4a =64

a = 64/4

a = 16

He spent 16 × 3 = 48 minutes on his math homework.

4.Let the plaza hotel height = a

garden view hotel height = b

2a - b = 17.........(i)

a + b = 361........(ii)

b = 361 - a

2a - (361 - a) = 17

2a - 361 + a = 17

3a = 17 + 361

3a = 378

divide both sides by 3

a = 378/3

a = 126

insertthe value of a in equation (ii)

a + b = 361........(ii)

126 + b = 361

b = 361 -126

b = 235

Elanso [62]3 years ago

5 0

1: 2/5=emails 3.6hrs=emails, 3.6=2/5 5-2=3 3.6•3=__hours of work

2. 294+83=$__

3. 3•x=hw 64/4=__•3=__hrs on math

4. Idk sorry

Sorry if some of these are wrong but I'm pretty sure there right.

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

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

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).