Answer:
10/7 or 1 3/7. I hope this helps,
Step-by-step explanation:
Answer:
Step-by-step explanation:
a) 8.23 x 10^5 move the decimal over 5 places, 319000000 is 319 million move the decimal over until there is one number on the left side --> 3.19 x 10^8
b) 3.19 x 10^8 / 8.23 x 10^5 = 387.61 roughly 388 times larger
What a delightful little problem ! (Partly because I could see
right away how to do it, and had the answer in a few minutes,
after a lot of impressive-looking algebra on my scratch-paper.)
Three consecutive integers are . . . x, x+1, and x+2
The smallest two are . . . x and x+1
Their product is . . . . . x(x+1)
5 times the largest one is . . . 5(x+2)
5 less than that is . . . . . . 5(x+2)-5
Now, the conditions of the problem say that <u>x (x + 1) = 5 (x+2) - 5</u>
THAT's the equation we have to solve, to find 'x' .
Eliminate parentheses: x² + x = 5x + 10 - 5
Combine like terms: x² + x = 5x + 5
Subtract 5x from each side: x² - 4x = 5
Subtract 5 from each side: <u>x² - 4x - 5 = 0</u>
You could solve that by factoring it, or use the quadratic equation.
Factored, it says that (x + 1) (x - 5) = 0
From which <em>x = -1</em>
and <em>x = +5</em>
We only want the positive results, so our three consecutive integers are
5, 6, and 7 .
To answer the question, the smallest one is <em><u>5 </u></em>.
<u>Check</u>:
5 x 6 ? = ? (7 x 5) - 5
30 ? = ? (35) - 5
30 = 30
yay !
Answer:
Step-by-step explanation:
Horizontal translations = f(x ± h)
Reflection over the x-axis = - f(x)
For the function 
, translating the parabola 8 units to the right means the horizontal shift of the graph, adding (- 8) to the <em>h</em> input. This is represented by: 
.
Next, flipping the graph over the x-axis represent a reflection. Since we currently have a negative coefficient for the value of <em>a</em>, then the opposite of a negative coefficient is a positive coefficient.
Therefore, the rightward horizontal translation of 8 units, and the reflection of the graph over the x-axis is represented by:
For your reference, the three images below shows the transformations on the graph. The first image is the original function (in red parabola). The second image represents the reflection over the x-axis (green parabola). The third image shows the horizontal shift, 8 units to the right (blue parabola). If you take note of the varying values in vertices, (<em>h, k </em>) for the three graphs, you'll see that the original vertex was (4, 5) and the new vertices for the transformations are (4, -5) for the <u>reflection</u> and (12, -5) for the <u>shift</u>.
Answer:
no triangles
Step-by-step explanation:
The angles of a triangle must add to 180°
The numbers given add to 190
