Answer:
a
x
2
+
b
x
+
c
=
0
the two roots of the equation take the form
x
1
,
2
=
−
b
±
√
b
2
−
4
a
c
2
a
So, start by adding
−
5
to both sides of the equation to get
2
x
2
+
x
−
5
=
5
−
5
2
x
2
+
x
−
5
=
0
Notice that you have
a
=
2
,
b
=
1
, and
c
=
−
5
. This means that the two solutions will be
x
1
,
2
=
−
1
±
√
1
2
−
4
⋅
2
⋅
(
−
5
)
2
⋅
2
x
1
,
2
=
−
1
±
√
41
4
You can simplify this if you want to get
x
1
=
−
1
+
√
41
4
≅
1.35078
and
x
2
=
−
1
−
√
41
4
≅
−
1.85078
Answer:
The correct option is B.
Step-by-step explanation:
Given information: AB\parallel DCAB∥DC and BC\parallel ADBC∥AD .
Draw a diagonal AC.
In triangle BCA and DAC,
AC\cong ACAC≅AC (Reflexive Property of Equality)
\angle BAC\cong \angle DCA∠BAC≅∠DCA ( Alternate Interior Angles Theorem)
\angle BCA\cong \angle DAC∠BCA≅∠DAC ( Alternate Interior Angles Theorem)
The ASA (Angle-Side-Angle) postulate states that two triangles are congruent if two corresponding angles and the included side of are congruent.
By ASA postulate,
\triangle BCA\cong \triangle DAC△BCA≅△DAC
Therefore option B is correct
<h2>Question 9:</h2>
1. Use Pythagorean Theorem (a²+b²=c²) to solve for missing side of triangle and rectangle. x²+16²=20², or x²+256=400. So, x²=144, and x=12
2. Use formula: 1/2(h)(b1+b2). 1/2 (12) (30+14).
3. Simplify: 1/2 (12) (44)=1/2(528)=264
Area of whole figure is 264 square mm.
<h2>Question 10:</h2>
Literally same thing but with trigonometry.
1. Use sine to find out length of dotted line: sin(60°)=x/12
2: Simplify: 12*sin(60°)=x. x≈10.4 (rounded to the nearest tenth)
3. Use Pythagorean Theorem to find out last leg of triangle: 10.4²+x²=12²
4: Simplify: 108.16 +x²=144. x²=35.84 ≈ 6
5: Use formula: 1/2(h)(b1+b2). 1/2 (10.4) (30+36)
6: Simplify: 1/2 (10.4) (66) =343.2
7: Area of figure is about 343.2
Remember, this is an approximate answer with rounding, so it might not be what your teacher wants. The best thing to do is do it yourself again.
Let's use tenths.
1/10 = 0.10
5/10 = 0.50
<span>1/10 + 5/10 = 6/10 = 0.6</span>
Answer:
b) y = 289.815 when 
Step-by-step explanation:
We are given the following information in the question:
where y is the dependent variable,
are the independent variable.
The multiple regression equation is of the form:
where,
: is the intercept of the equation and is the value of dependent variable when all the independent variable are zero.
: It is the slope coefficient of the independent variable 
.
: It is the slope coefficient of the independent variable 
.
- The regression coefficient in multiple regression is the slope of the linear relationship between the dependent and the part of a predictor variable that is independent of all other predictor variables.
Comparing the equations, we get:
- This means holding constant, a change of one in is associated with a change of 0.5906 in the dependent variable.
- This means holding constant, a change of 1 in is associated with a change of 0.4980 in the dependent variable.
b) We have to estimate the value of y
