A.) Yes you can, the expression would be (2.95 x Y) + 4 = X
B.) (2.95 x 24) + 4 = $74.80
C.) (2.95 x 57) + 4 = X
2.95 x 57 = 168.15 + 4 = 172.15
so basically they can buy 57 books without going over $175
Answer:
The area of triangles are 16 cm^2 and 49 cm^2
Step-by-step explanation:
we know that
If two figures are similar, the ratio of its perimeters is equal to the scale factor and the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x ----> the area of the smaller triangle in square centimeters
y ----> the area of the larger triangle in square centimeters
we know that
so
-----> equation A
----> equation B
solve the system by substitution
substitute equation A in equation B
solve for y
Find the value of x
therefore
The area of triangles are 16 cm^2 and 49 cm^2
Answer:
Not possible
Step-by-step explanation:
Since the triangular base has not a right-angled form. That is, the longest side is greater than value of hypotenuse, meaning that triangular base has a form of a obtuse-angle triangle.
- 10² + 12² = 18² It is not possible because they dont equal
- 100+ 144= 324
- 244≠ 324
Given three points
P1(-2,8)
P2(0,-4)
P3(4,68)
We need the quadratic equation that passes through all three points.
Solution:
We first assume the final equation to be
f(x)=ax^2+bx+c .............................(0)
Observations:
1. Points are not symmetric, so cannot find vertex visually.
2. Using the point (0,-4) we substitute x=0 into f(x) to get
f(0)=0+0+c=-4, hence c=-4.
3. We will use the two other points (P1 & P3) to set up a system of two equations to find a and b.
f(-2)=a(-2)^2+b(-2)-4=8 => 4a-2b-4=8.................(1)
f(4)=a(4^2)+b(4)-4=68 => 16a+4b-4=68.............(2)
4. Solve system
2(1)+(2) => 24a+0b-12=84 => 24a=96 => a=96/24 => a=4 ......(3)
substitute (3) in (2) => 16(4)+4b-4=68 => b=8/4 => b=2 ..........(4)
5. Put values c=-4, a=4, b=2 into equation (0) to get
f(x)=4x^2+2x-4
Check:
f(-2)=4((-2)^2)+2(-2)-4=16-4-4=8
f(0)=0+0-4 = -4
f(4)=4(4^2)+2(4)-4=64+8-4=68
So all consistent, => solution ok.
Answer: x < -4 and -4 > x
x < -4 would be one of the two options.
This means that any number less than -4 is a solution.
This is shown by drawing an open dot on -4 and then
drawing an arrow to the left shows all answer less tan 4.
-4 > x would be our second option.
We can change it to say x < -4.
All I did was changed the order of numbers and switched the sign.
So x < -4 is the same as the first option.
