Answer:
Step-by-step explanation:
At the point where two line cut across, the vertically opposite angles formed are equal. This means that
2x degrees = 78 degrees
Dividing the left hand side and the right hand side of the equation by 2, it becomes
2x/2 = 78/2
x = 39
Checking,
The sum of the angles on a straight line is 180 degrees.
180 - 78 = 102 degrees
2x + 102 = 180
2x = 180 - 102 = 78
x = 78/2 = 39
Answer:
25 sq feet
Step-by-step explanation:
Length = 5 feet
Area = (Length)²
= 5²
= 25 sq feet
Given the equation:
We will use the following rule to find the solution to the equation:
![x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
From the given equation: a = 6, b = 7, c = 2
So,
![\begin{gathered} x=\frac{-7\pm\sqrt[]{7^2-4\cdot6\cdot2}}{2\cdot6}=\frac{-7\pm\sqrt[]{1}}{12}=\frac{-7\pm1}{12} \\ x=\frac{-7-1}{12}=-\frac{8}{12}=-\frac{2}{3} \\ or,x=\frac{-7+1}{12}=-\frac{6}{12}=-\frac{1}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D%5Cfrac%7B-7%5Cpm%5Csqrt%5B%5D%7B7%5E2-4%5Ccdot6%5Ccdot2%7D%7D%7B2%5Ccdot6%7D%3D%5Cfrac%7B-7%5Cpm%5Csqrt%5B%5D%7B1%7D%7D%7B12%7D%3D%5Cfrac%7B-7%5Cpm1%7D%7B12%7D%20%5C%5C%20x%3D%5Cfrac%7B-7-1%7D%7B12%7D%3D-%5Cfrac%7B8%7D%7B12%7D%3D-%5Cfrac%7B2%7D%7B3%7D%20%5C%5C%20or%2Cx%3D%5Cfrac%7B-7%2B1%7D%7B12%7D%3D-%5Cfrac%7B6%7D%7B12%7D%3D-%5Cfrac%7B1%7D%7B2%7D%20%5Cend%7Bgathered%7D)
So, the answer will be option B) x = -1/2, -2/3
Answer:
(d) (4x² +7)(x -3)
Step-by-step explanation:
This polynomial can be factored by factoring pairs of terms.
= (4x³ -12x²) +(7x -21)
= 4x²(x -3) +7(x -3)
= (4x² +7)(x -3)
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<em>Additional comment</em>
The answer choices suggest we're not interested in irrational or complex factors. The quadratic (4x² +7) could be factored into linear terms involving irrational complex numbers. The form for "difference of squares" would be used for the purpose.
Answer:
A) 40
B) length = 4.275 km; not quite true. See below for explanation.
Step-by-step explanation:
A) Your calculator can tell you the ratio ...
(national pennies)/(local pennies) = (8×10⁶)/(2×10⁵)
= (8/2)×10⁶⁻⁵ = 4×10¹ = 40
The national drive collected 40 times as many pennies as the Valley Stream Central goal.
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B) Multiplying the number of pennies by the diameter of each will tell the length of the line of pennies. That length can be compared to the 5 km distance to determine if the reporter's statement is true. (It is <em>not</em> true.)
length of string = (length of penny) × (number of pennies)
= (19×10⁻⁶ km) × (2.25×10⁵) = 42.75×10⁻¹ km = 4.275 km
The length of the pennies laid side-to-side is less than 5.0 km. The reporter's statement is not true.
_____
All scientific and graphing calculators and many 4-function calculators will let you enter numbers in scientific notation.
