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nordsb [41]
3 years ago
5

Simplify the expression 14b-2-17b

Mathematics
1 answer:
Kamila [148]3 years ago
4 0
The answer to the following question that you have asked is -2-3b
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Find three consecutive even integers such that 3 times the first is 26 less than twice the sum of the last two
Dimas [21]
Let's say our first integer is "a".

how to get the next consecutive EVEN integer?  well, just add or subtract 2 from it, therefore, the second consecutive integer will be "a + 2".

and the next after that, will then be (a + 2) + 2, or "a + 4".

so those are are 3 integers, a           a + 2           a+4

notice that, from any even or odd integer, if you hop twice either forwards or backwards, you'll land on another even or odd integer respectively.

2 + 2 is 4, or 8 + 2 is 10  some even ones

3 + 2 is 5, or 13 + 2 is 15, some odd ones

\bf \stackrel{\textit{3 times the first}}{3a}~~=~~\stackrel{\textit{26 less than twice the sum of the others}}{2[~(a+2)+(a+4)~]~~~-26}
\\\\\\
3a=2[~2a+6~]-26\implies 3a=4a+12-26\implies 3a=4a-14
\\\\\\
0=a-14\implies 14=a

what are the other two consecutive integers?  well, a + 2 and a + 4.
4 0
3 years ago
Calculate the area of the irregular polygon shown below:
Vladimir79 [104]
The answer is C. 3×4 = 12. There are two therefore 50-24 = 26.
7 0
3 years ago
Read 2 more answers
In a simple regression analysis (where y is a dependent and x an independent variable), if the slope is positive, then it must b
Scorpion4ik [409]

Answer:

c. there is a positive correlation in-between x and y

Step-by-step explanation:

A regression line is a line that suggests that all the points in a scatter diagram lie on or near one particular line. In a simple regression analysis in which y is the dependent variable and x is the independent variable. If the slope is positive, the bivariate data is also said to have a positive correlation. The positive correlation in-between two variables x and y implies that in general, an increase in x goes hand in hand with an increase in y.

3 0
2 years ago
The line segment has an endpoint (5,-6) and the midpoint is (-2,3). Find the other point.
gavmur [86]

Answer:

(-9,12)

Step-by-step explanation:

Endpoint\:= (5,-6) = x_1,y_1\\Midpoint = \: (-2,3)=x\:,y\\\\x = \frac{x_1+x_2}{2}\\\\ -2 = \frac{5+x_2}{2} \\-4 = 5+x_2\\-4-5=x_2\\-9 =x_2\\\\y = \frac{y_1+y_2}{2} \\\\3 = \frac{-6+y_2}{2} \\6 = -6+y_2\\6+(6)=y_2\\6+6=y_2\\12=y_2\\x_2 ,y_2=(-9,12)

4 0
3 years ago
The sides of a rhombus with angle of 60° are 6 inches. Find the area of the rhombus.
ehidna [41]
1. Check the drawing of the rhombus ABCD in the picture attached.

2. m(CDA)=60°, and AC and BD be the diagonals and let their intersection point be O.

3. The diagonals:
     i) bisect the angles so m(ODC)=60°/2=30°

     ii) are perpendicular to each other, so m(DOC)=90°

4. In a right triangle, the length of the side opposite to the 30° angle is half of the hypothenuse, so OC=3 in.

5. By the pythagorean theorem, DO= \sqrt{ DC^{2}- OC^{2} }=  \sqrt{ 6^{2}- 3^{2} }=\sqrt{ 36- 9 }=\sqrt{ 27 }= \sqrt{9*3}= 
=\sqrt{9}* \sqrt{3} =3\sqrt{3}  (in)

6. The 4 triangles formed by the diagonal are congruent, so the area of the rhombus ABCD = 4 Area (triangle DOC)=4*\frac{DO*OC}{2}=4 \frac{3 \sqrt{3} *3}{2}==2*9 \sqrt{3}=18 \sqrt{3} (in^{2})

6 0
3 years ago
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