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wariber [46]
3 years ago
15

The graph of y = 1/2 x2 + 2x + 3 is shown. What are the solutions to the equation 1/2 x2 + 2x + 3 = x + 7?

Mathematics
1 answer:
kirill [66]3 years ago
3 0

Answer:

Step-by-step explanation:

Let's organise our information :

  • the function is (1/2)x²+2x+3

we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7

Now the trick is to write this expression as a quadratic equation with zero at one side :

  • (1/2)x²+2x+3=x+7
  • (1/2)x²+2x+3-x-7=0
  • (1/2)x²+x-4=0

Now let's solve this equation :

  • a= 1/2
  • b= 1
  • c= -4

Δ=1²-4*(1/2)*(-4)

 = 9

So we have two solutions :

  • \left \{ {{y=\frac{-1-3}{2*0.5} } \atop {x=\frac{-1+3}{2*0.5} }} \right.
  • y= -4
  • x= 2

So the solutions are -4 and 2

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Answer:

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8(15)+(10)+(20)=

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6 0
3 years ago
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How to do this question plz answer my question step by step plzz plz plz plz ​
never [62]

Answer:

40°, 95°, 105°, and 160°

Step-by-step explanation:

Let the smallest angle be x.

Measures of the 3 angles can be expressed as:

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The sum of all angles in a quadrilateral = 360°.

Therefore, (x + 55) + (x + 65) + (x + 120) = 360

Solve for x

x + 55 + x + 65 + x + 120 = 360

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3x + 240 - 240 = 360 - 240

3x = 120

\frac{3x}{3} = \frac{120}{3}

x = 40

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Plug in the value of x in the earlier stated expressions to find the measure of the other angles:

x + 55 = 40 + 55 = 95

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3 0
3 years ago
Use the standard norml distribution or the t-distribution to construct a 99% confidence interval for the population mean. Justif
dalvyx [7]

Answer:

E) we will use t- distribution because is un-known,n<30

the confidence interval is (0.0338,0.0392)

Step-by-step explanation:

<u>Step:-1</u>

Given sample size is n = 23<30 mortgage institutions

The mean interest rate 'x' = 0.0365

The standard deviation 'S' = 0.0046

the degree of freedom = n-1 = 23-1=22

99% of confidence intervals t_{0.01} =2.82  (from tabulated value).

The mean value = 0.0365

x±t_{0.01} \frac{S}{\sqrt{n-1} }

0.0365±2.82 \frac{0.0046}{\sqrt{23-1} }

0.0365±2.82 \frac{0.0046}{\sqrt{22} }

0.0365±2.82 \frac{0.0046}{4.690 }

using calculator

0.0365±0.00276

Confidence interval is

(0.0365-0.00276,0.0365+0.00276)

(0.0338,0.0392)

the mean value is lies between in this confidence interval

(0.0338,0.0392).

<u>Answer:-</u>

<u>using t- distribution because is unknown,n<30,and the interest rates are not normally distributed.</u>

4 0
3 years ago
If the area of a triangular garden is 156 sq ft, and the base of this garden is 13 feet wide, what is the height?
Ilia_Sergeevich [38]

Answer:

height is =area  dived by base

Step-by-step explanation:

156 divide 13 is 12

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2 years ago
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I am having an issue in figuring out how the answer is 247,700. ​
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