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3 years ago

How many more buttons will Teresa need to make 12 puppets ? Explain

Mathematics

1 answer:

Dominik [7]3 years ago

3 0

Please go into more detail about the question then u will be able to help you

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1. -8(1+4x)+7x=-25-8x 2. -5+6(x-7)=-40+5x Could you show the work?

chubhunter [2.5K]

Answer:

1. x=1

2. x=7

Step-by-step explanation:

1. -8(1+4x)+7x=-25-8x

-8-32x+7x=-25-8x

8x-32x+7x=-25+8

-17x=-25+8

-17x=-17

$\frac{-17x}{-17} =\frac{-17}{-17} \\x=1$

2. -5+6(x-7)=-40+5x

-5+6x-42=-40+5x

-47+6x=-40+5x

x=47-40

x=7

5 0

3 years ago

Solve the equation 2 sec² x = 3 - tan x for the domain 0° ≤ x ≤ 360°

vodka [1.7K]

$2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\$

$\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\$

$x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\$

$\text{In degrees,}~ x = 135^{\circ},~315^{\circ},~\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]$

4 0

2 years ago

Use the parabola tool to graph the quadratic function. f(x)=2x^2 +12x+16 Graph the parabola by first plotting its vertex and the

givi [52]

(-3, -2) is the vertex.

You can find this by plugging into -b/2a to find the x value and using the x value to find the y value.

And another spot on the vertex would be (0, 16), which is the y intercept.

8 0

3 years ago

one bus leaves a stop every 9 minutes a second bus leaves every 15 minutes if they both leave at 1:25 at what time will they nex

aleksandrvk [35]

In this question you need to find the lowest common multiple. I like to do it the factor tree way:
 15 9
/ \ / \
3 5 3 3
See how there are both a 3 in the 15 factor tree and there is at least on three in the 9 factor tree. So when you find the LCM, you combine the two threes from the different factor trees like this:
3 x 5 x 3 = 45
So every 45 minutes the bus would be at the bus stop together

Now simply add the 45mins onto the 1:25

Answer: 2:10

3 0

3 years ago

Read 2 more answers

Tiffany is filling her daughter's pool with water from a hose she can fill the water at a rate of 1/10 gallons/second. Create at

s2008m [1.1K]

Answer:

Three equivalent ratios that are associated with this rate would be 6 gallons/1min, 360gallons/1 hour and 720 gallons/2hours.

I'm sorry but I can't explain or show how to use a double number line for this question.

Step-by-step explanation:

4 0

3 years ago