Answer:
x = 0.5 to the nearest 1/10.
Step-by-step explanation:
3^-x = x^3 + x
y = x^3 - 3^-x + x = 0
Using a graphing calculator to draw the graph of the above:
The graph crosses the x-axis at x = 0.4798
Answer:
sandwiches is £1.8
bottle water = £1.2
Step-by-step explanation:
Given data
let cheese sandwiches be x
and bottle water be y
3x+2y= 7.8------------1
5x+4y= 14.20---------2
solve 1 and 2
3x+2y= 7.8------------1*5
5x+4y= 14.20---------2*3
15x+10y= 39
- 15x+12y= 42.6
-2y = -3.6
y= 3.6/2
x=1.8
Put x= 1.8 in 1
3(1.8)+2y= 7.8
5.4+2y= 7.8
2y= 7.8-5.4
2y=2.4
y= 2.4/2
y= 1/2
Hence cheese sandwiches is £1.8
bottle water = £1.2
12.5 is 25% of x
percent means parts out of 100
25%=25/100=1/4
12.5=1/4 of a number
mulitply both sides by 4
50=number
the number is 50
Here, you're mixing scores 85 and 90 with weights X and Y, respectively. You are asked for the ratio of X to Y.
There's a quick way to work mixture problems of all kinds. Write the two components of the mixture on the left. Here, they are 90 and 85. (I usually put the larger one on top.) Put the mixed value in the middle, and form differences along the lines of an X, as shown. The numbers on the right give the relative contributions of the constituents at the same level in the diagram. Here, the ratio of X to Y is shown as 2 to 3.
For some mixture problems, you need to know the proportion of the constituent to the whole. In that case, add the ratio values to get the "whole". For example, here the X class students make up 2/(2+3) = 2/5 of the whole number of students.
For your problem, X/Y = 2/3, corresponding to selection D.
Answer:
m∠3 = 112° m∠5 = 38° m∠6 = 68° m∠8 = 74°
You do the others
Step-by-step explanation:
Facts you need to solve this problem.
1. Vertical angles are congruent
2. Alternate interior angles are congruent when lines are parallel
3. Sum of the measures of the angles of a triangle is 180
4. Adjacent angles are supplementary when two lines intersect
m∠3 = 112° (Reason 1 above)
m∠6 = 180 - 112 = 68° (Reason 4)
m∠6 + m∠5 + 74 = 180° (Reason 3)
68 + m∠5 + 74 = 180
142 + m∠5 = 180
m∠5 = 38°
m∠8 = 74° (Reason 2)
That gives you a start, so I will let you find all the others. OK? I know you don't want to do that, but you need to be able to do this type of problem. Now, go for it!!