Answer:
C
Step-by-step explanation:
use a proportion
( 3/4 ) / 1 1/8 = ( 4/4) / x teaspoons
x = 1.5
Answer: The length of the base is 10.
Step-by-step explanation:
You can draw an isosceles triangle like the one shown attached.
An isosceles triangle has two equal sides. Then, you can divide it into two right triangles, where the base of each one of them will be:
![b'=\frac{2x}{2}=x](https://tex.z-dn.net/?f=b%27%3D%5Cfrac%7B2x%7D%7B2%7D%3Dx)
The hypotenuse of each right triangle shown is 13 and the other legs are (x+7) and x, therefore you can apply the Pythagorean Theorem:
![13^2=x^2+(x+7)^2](https://tex.z-dn.net/?f=13%5E2%3Dx%5E2%2B%28x%2B7%29%5E2)
Simplify the expression:
![169=x^2+(x^{2}+2(x)(7)+7^2)\\169=x^{2}+x^{2}+14x+49\\0=2x^{2}+14x-120](https://tex.z-dn.net/?f=169%3Dx%5E2%2B%28x%5E%7B2%7D%2B2%28x%29%287%29%2B7%5E2%29%5C%5C169%3Dx%5E%7B2%7D%2Bx%5E%7B2%7D%2B14x%2B49%5C%5C0%3D2x%5E%7B2%7D%2B14x-120)
Use the quadratic formula, where:
![a=2\\b=14\\c=-120](https://tex.z-dn.net/?f=a%3D2%5C%5Cb%3D14%5C%5Cc%3D-120)
![x=\frac{-b\±\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Then:
![x=\frac{-14\±\sqrt{14^2-4(2)(-120)}}{2+2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-14%5C%C2%B1%5Csqrt%7B14%5E2-4%282%29%28-120%29%7D%7D%7B2%2B2%7D)
![x_1=5\\x_2=-12](https://tex.z-dn.net/?f=x_1%3D5%5C%5Cx_2%3D-12)
Choose the positive value, because lengths are not negative.
Substitute the value of x into the base 2x. Therefore, the answer is:
![b=2x=2(5)=10](https://tex.z-dn.net/?f=b%3D2x%3D2%285%29%3D10)
Answer:
2 7/16
Step-by-step explanation:
2 3/4 - 5/16 → 11/4 - 5/16 (convert 2 3/4 into an improper or top-heavy fraction)
11/4 - 5/16 → 44/16 - 5/16 (multiply 11/4 by 4/4 to make a common denominator)
44/16 - 5/16 = 39/16 (Subtract 44 - 5 = 39)
Simplify (convert back into mixed number)
39/16 = 2 7/16
Hope this helps!
I have attached n image showing this dot plot.
Answer:
Median
Step-by-step explanation:
In measures of centre of data are usually; mean, median and mode.
Now, mean is the best measure of centre to use when the data set is symmetric or approximately normal.
Secondly, the best to use when the data is asymmetric as a result of having outliers would be median due to the fact that it exhibits robustness to the outliers.
Since the dot plot contains 2 extreme values which are known as outliers, from the definition given earlier, we can say that the best measure of centre to use will be "median"
Answer:
x=-5/8, y=15/2, z=-10. (-5/8, 15/2, -10).
Step-by-step explanation:
4x-7y=5
8x+3z=-35
6y+3z=15
----------------
4x=7y+5
2(4x)=2(7y+5)
8x=14y+10
14y+10+3z=-35
14y+3z=-35-10
14y+3z=-45
-----------------------
14y+3z=-45
6y+3z=15
------------------
14y+3z=-45
-(6y+3z)=-15
---------------------
14y+3z=-45
-6y-3z=-15
--------------------
8y=-60
simplify,
y=15/2
6(15/2)+3z=15
45+3z=15
3z=15-45
3z=-30
z=-30/3
z=-10
8x+3(-10)=-35
8x-30=-35
8x=-35+30
8x=-5
x=-5/8
x=-5/8, y=15/2, z=-10.