Answer:
use a calculator
Answer:
Step-by-step explanation:
For example, if you had 2 3/4, you would change the mixed number into an improper fraction. That would equal 11/4 (4 times 2 is 8 and 8 + 3 is 11). Then, you would divide 11 by 4, which equals 2.75 (2 and 75 hundredths).
For negative fractions, you would take the numerator divided by the denominator (3/4= 3 divided by 4= 0.75). You would then put the negative sign in front of the decimal.
1. Name the vertex of angle 2.
2. Name the sides of angle 4.
3. Write another name for angle 3.
4. Classify each angle.
-angle YTW
-angle XTU
-angle YTU
-angle WTX
5. Name an angle bisector.
Answer:
1) YTW
2) WT, TZ
3) UTZ
4) Right angle
Acute angle
Obtuse angle
Right angle
5) TU
The ratio of the numerator and denominator of a rational number is 2 : 7 and
if 4 is added to the numerator and 2 is subtracted from denominator, the
rational number becomes 10
19
. Find the original rational number.
Answer:
6/21.
Step-by-step explanation:
let the rational number be 2x/7x.
2x + 4 / 7x - 2 = 10 /19
Cross multiply:
19(2x + 4) = 10(7x - 2)
38x + 76 = 70x - 20
96 = 70x - 38x
32x = 96
x = 3.
So the rational number is 2*3/ 7*3
= 6/21.
1.1.17
Question Help
Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
6/7
Answer:
whole number is the answer
Find t12 for a geometric sequence where t1=2+2i and r=3
Answer:
[tex]T_{12} = 354294 + 354294i[/tex]
Step-by-step explanation:
Given
Geometric Sequence (GP)
[tex]T_1 = 2 + 2i[/tex]
[tex]r = 3[/tex]
Required
Determine T₁₂
The nth term of a GP is calculated as thus;
[tex]T_n = ar^{n-1}[/tex]
In this case;
[tex]n = 12[/tex]; [tex]r = 3[/tex] and [tex]a = T_1 = 2 + 2i[/tex]
Substitute these values in the above formula
[tex]T_{12} = (2 + 2i) * 3^{12-1}[/tex]
[tex]T_{12} = (2 + 2i) * 3^{11}[/tex]
[tex]T_{12} = (2 + 2i) * 177147[/tex]
Open the bracket
[tex]T_{12} = 177147 * 2 + 177147 * 2i[/tex]
[tex]T_{12} = 354294 + 354294i[/tex]
Hence, the 12th term of the sequence is [tex]T_{12} = 354294 + 354294i[/tex]
Find the sum and Express it in simplest form. (-8n^3 + 4n - 8) + (7n^3 - 2n + 6)
Please Help !
Answer:
n^3 + 2n -2
Step-by-step explanation:
Remove the parentheses and simplify:
-8n^3 + 4n - 8 + 7n^3 - 2n + 6
n^3 + 2n -2.
Answer:
Step-by-step explanation:
We have to add the like terms. Like terms are with variables of same power.
-8n³ and 7n³ are like terms , now add the coefficient of n³ , -8 + 7 = -1
-8n³ + 7n³ = -1n³
(-8n³ + 4n - 8) + (7n³ - 2n + 6 )
Combine like terms
= -8n³ + 7n³ + 4n - 2n - 8 + 6
= -1n³ + 2n - 2
What is two and one-fourth subtracted by one-eighth?
Please help ASAP!!!!!
Answer:
The answer is -14/25 or - 0.56
3. Which of these will DEFINITELY be true about any number between -35 and -15? (A) It will be equal to -25. (B)It will be less than -20. (c) It will be more than -10. (D)It will be less than -10
Answer:
(A) It will be equal to -25
Step-by-step explanation:
Given a number between -35 and -15.
To find:
A statement always true about the number.
(A) It will be equal to -25.
(B)It will be less than -20.
(c) It will be more than -10.
(D)It will be less than -10
Solution:
First of all, let us represent the given numbers on number line.
Please refer to the attached diagram for the number line representation of the numbers.
When we move towards left from 0, the numbers decrease.
Therefore, -15 is a value greater than -35.
-15 > -35
When we move towards right from 0, the numbers increase.
So, statement "A)It will be equal to -25" is true.
-25 will always be in between -15 and -35.
Option B:
Less than -20.
-40 is also lesser than -20 but is not in between -35 and -15.
So not true.
Option C:
More than -10.
-8 is also more than -10 but not in between -35 and -15.
So not true.
Option D:
Less than -10.
-11 is also lesser than -10 but is not in between -35 and -15.
So not true.
4. Using the digits 1 to 9, at most one time each, fill in the boxes to
make a result that has the greatest value possible. HELP PLEASE
Answer:
9^3
Step-by-step explanation:
9x9x9= 729
1/9 as a percent? Rounded to the nearest hundreth.
Answer:
11.11%
Step-by-step explanation:
We can first convert the fraction [tex]\frac{1}{9}[/tex] into a decimal.
We know that a number over 9 will be 0.(that number repeating), for example, [tex]\frac{4}{9}[/tex] is 0.444444...
So this means that [tex]\frac{1}{9}[/tex] will be 0.11111...
Converting [tex]0.\overline{11}[/tex] into a percentage is easy - we just multiply by 100.
This get us [tex]11.\overline{11}[/tex]%, which rounds to 11.11%.
Hope this helped!
HELP WILL GIVE 40 POINTS AND BRAINLIEST!!!! Solve these two (second-degree) quadratic equations by factoring. [tex]2x^{2}+6x=0[/tex] & [tex]x^{2}+9x+14=0[/tex]
Answer:
Step-by-step explanation:
First equation: 2x^2 + 6x = 0 factors into 2x(x + 3) = 0, so either x = 0 or x = -3.
Second equation: x^2 + 9x + 14 = 0 factors into (x + 2)(x + 7) = 0. Thus, either x = -2 or x = -7
Hi there! Hopefully this helps!
---------------------------------------------------------------------------------------------------------
Answer for [tex]2x^{2} + 6x = 0[/tex]: x = 0x = -3|
|[tex]2x^{2} + 6x = 0[/tex]
|
|First we factor out x
\/
[tex]x(2x+6)=0[/tex]
To find equation solutions, solve [tex]x = 0[/tex] and [tex]2x+6 = 0[/tex]
|
\/
[tex]x = 0[/tex]
[tex]x = -3[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer for [tex]x^{2}+ 9x + 14 = 0[/tex]:x = -2x = -7|
|
|[tex]x^{2}+ 9x + 14 = 0[/tex]
|
|To solve the equation, factor [tex]x^{2}+ 9x + 14[/tex] using formula [tex]x^{2} + (a + b)x + ab = (x+a) (x+b).[/tex] To find [tex]a[/tex] and [tex]b[/tex], set up a system to be solved.
|
\/
[tex]a + b = 9[/tex]
[tex]ab = 14[/tex]
|
\/
Since [tex]ab[/tex] is positive, [tex]a[/tex] and [tex]b[/tex] have the same sign. Since [tex]a + b[/tex] is positive, [tex]a[/tex] and [tex]b[/tex] are both positive. List all such integer pairs that give product 14.
1, 14
2, 7
|
\/
Calculate the sum for each pair.
1 + 14 = 15
2 + 7 = 9
|
\/
The solution is the pair that gives sum 9.
[tex]a = 2[/tex]
[tex]b = 7[/tex].
|
\/
Rewrite factored expression [tex](x+a)(x+b)[/tex] using the obtained values.
[tex](x+2)(x+7)[/tex]
|
\/
To find equation solutions, solve [tex]x + 2 = 0[/tex] and [tex]x + 7 = 0[/tex].
|
\/
[tex]x = -2[/tex]
[tex]x = -7[/tex]
I need the answer ASAP!:/
Answer:
-2
Step-by-step explanation:
At first, you might think that -5 is bigger than -2 because 5 > 2, right? Actually, no, that's not how it works. The "rules" for numbers are flipped when you are dealing with negative numbers, so therefore, -2 is bigger. Basically, what I'm saying is that the smaller the number after the negative sign, the bigger the number is and vice versa.
Answer:
Answer is - 2
Step-by-step explanation:
Because in case of negative numbers the number which is smaller in negative no is bigger in negative
numbers I hope you understand....Mark me as brainliest
Brainlist! :c y no one helping
For which function is f(-x) = f(x)?
(A) f(x) = sqaure root x
(B) f(x) = 2x
(C) f(x) = x2
(D) f(x) = x2
(E) f(x) = 2^x
Answer:
C and D are same options
(D)[tex] f(x) = x^2 [/tex]
Step-by-step explanation:
[tex]f(x) = {x}^{2} \\ plug \: x = - x \\ f( - x) = {( - x)}^{2} = {x}^{2} \\ f( - x) = f(x)[/tex]
Solve the following equation for the variable.
x + 7 = 12
Answer:
x=5
Step-by-step explanation:
i took 12 and subtracted 7 to see what i got and to check my answer i added 5 to 7 to see if i got 12
1. Simplify the following a) 4√12 - √50 -5√48 b) √8 × √5 ×√10 c) √45 + √180 + √80
Answer:
-12√3 - 5√22013√5Step-by-step explanation:
1.
[tex]4\sqrt{12}-\sqrt{50}-5\sqrt{48}\\\\4\sqrt{12}=8\sqrt{3}\\\\\sqrt{50}=5\sqrt{2}\\\\5\sqrt{48}=20\sqrt{3}\\\\=8\sqrt{3}-5\sqrt{2}-20\sqrt{3}\\\\\mathrm{Add\:similar\:elements:}\:8\sqrt{3}-20\sqrt{3}=-12\sqrt{3}\\\\=-12\sqrt{3}-5\sqrt{2}[/tex]
2.
[tex]\sqrt{8}\sqrt{5}\sqrt{10}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{b}=\sqrt{a\times b}\\\\=\sqrt{8\times \:5\times \:10}\\\\=\sqrt{400}\\\\\mathrm{Factor\:the\:number:\:}\:400=20^2\\\\=\sqrt{20^2}\\\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a\\\\\sqrt{20^2}=20[/tex]
3.
[tex]\sqrt{45}+\sqrt{180}+\sqrt{80}\\\\\sqrt{45}=3\sqrt{5}\\\\\sqrt{180}=6\sqrt{5}\\\\\sqrt{80}=4\sqrt{5}\\\\=3\sqrt{5}+6\sqrt{5}+4\sqrt{5}\\\\\mathrm{Add\:similar\:elements:}\:3\sqrt{5}+6\sqrt{5}+4\sqrt{5}\\\\=13\sqrt{5}[/tex]
Find the center of a circle with the equation:
x² + y² + 2x -20y – 20 = 0
===============================================
Explanation:
If we had x^2+2x + ___, then 1 must go in the blank so that we have x^2+2x+1 = (x+1)^2
So we must add 1 to both sides to complete the square for the x terms. To find this value '1' we take half of the x coefficient 2 to get 1, then square it to get 1^2 = 1.
We have
x^2+y^2 + 2x - 20y - 20 = 0
x^2+y^2 + 2x - 20y - 20 + 1 = 0 + 1
(x^2+2x+1) + y^2 - 20y - 20 = 1
(x^2+2x+1) + y^2 - 20y = 1 + 20
(x+1)^2 + y^2 - 20y = 21
After completing the square for the x terms. Repeat for the y terms. Take half of -20 to get -10, which squares to 100. Add this to both sides
(x+1)^2 + y^2 - 20y = 21
(x+1)^2 + y^2 - 20y + 100 = 21+100
(x+1)^2 + (y - 10)^2 = 121
The equation is in the form (x-h)^2 + (y-k)^2 = r^2 where
h = -1k = 10r = 11The center is (h, k) = (-1, 10). The radius is r = 11.
simplify- 13= 7x + 4 - 4x simplify- b - 6 + 6b = 27 simplify- 5(5x - 2) = 65 URGENT please answer i will give brainliest
Step-by-step explanation:
1: - 13= 7x + 4 - 4x
Isolate variables.
- 13= 7x + 4 - 4x
-13 = 3x + 4
-3x = 13+4
-3x = 17
x = -17/3
2: - b - 6 + 6b = 27
5b - 6 = 27
5b = 33
b = 33/5
3: - 5(5x - 2) = 65
-25x + 10 = 65
-25x = 55
x = -55/25
x = -11/5
What is the maximum value of this function? f(x)=−16x²+32x+20
Answer: The maximum value is 35.94
Step-by-step explanation:
We have the function:
f(x) = -16*x^2 + 34*x + 20
This is a quadratic equation, and the first thing we can see is that the leading coefficient is smaller than zero, which means that the "arms" of the graph will go downwards, which means that the maximum of our function will be at the vertex.
First, we know that the vertex of a quadratic function is when f'(x) = 0.
f'(x) = 2*(-16*x) + 34 = 0.
x = -34/(-2*16) = 34/32 = 17/16.
Now we evaluate our function in the point x = 17/16.
f(17/16) = -16*(17/16)^2 + 32*(17/16) + 20 = 35.94
The maximum value is 35.94
Using the vertex, it is found that the maximum value of the function is of 36.
The function is given by:
[tex]f(x) = -16x^2 + 32x + 20[/tex]
Which is a quadratic function with coefficients [tex]a = -16, b = 32, c = 20[/tex].
The maximum value of a quadratic function with [tex]a < 0[/tex] is at the vertex, in which the value is:
[tex]f_{MAX} = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]
Hence, in this problem:
[tex]f_{MAX} = -\frac{(32)^2 - 4(-16)(20)}{4(-16)} = 36[/tex]
The maximum value of the function is of 36.
A similar problem is given at https://brainly.com/question/16858635
PLEASE HELP ME ASAP ILL MARK BRIANLIEST!!!!!!!!! ANSWER THE QUESTIONS AND DO THE STEPS TOO PLEASEE
Answer:
1). t ≥ -[tex]\frac{3}{2}[/tex]
2). k ≥ [tex]\frac{16}{3}[/tex]
3). y < -[tex]\frac{1}{2}[/tex]
4). b > [tex]\frac{250}{9}[/tex]
5). w ≤ 0
Step-by-step explanation:
1). [tex]14(\frac{1}{2}-t)\leq 28[/tex]
[tex]\frac{14}{14}(\frac{1}{2}-t)\leq \frac{28}{14}[/tex]
[tex]\frac{1}{2}-t\leq 2[/tex]
[tex]-t\leq 2-\frac{1}{2}[/tex]
[tex]-t\leq \frac{3}{2}[/tex]
t ≥ -[tex]\frac{3}{2}[/tex]
2). 15k + 11 ≤ 18k - 5
15k - 18k ≤ -5 - 11
-3k ≤ - 16
3k ≥ 16
k ≥ [tex]\frac{16}{3}[/tex]
3). 44y > 11 + 88y - 22y
44y > 11 + 66y
44y - 66y > 11
-22y > 11
22y < -11
[tex]\frac{22y}{22}<-\frac{11}{22}[/tex]
y < [tex]-\frac{1}{2}[/tex]
4). [tex]\frac{7}{9}(b - 27) > \frac{49}{81}[/tex]
[tex]\frac{7}{9}(b - 27)\times \frac{9}{7} > \frac{49}{81}\times \frac{9}{7}[/tex]
(b - 27) > [tex]\frac{7}{9}[/tex]
b > [tex]\frac{7}{9}+27[/tex]
b > [tex]\frac{250}{9}[/tex]
5). 11w - 8w ≥ 14w
3w - 14w ≥ 0
-11w ≥ 0
w ≤ 0
The Robinson family goes to the library. There are 5 people in the
family. Each person borrows 2 books. How many books does the
family borrow in all?
What is the unknown in this problem?
number of people in the family
number of books for each person
number of books in all
Answer:
10 books
Step-by-step explanation:
5 × 2 = 10
unknown in this problem is number of books in all
You spend 30 minutes reading emails. You then spend 2 hours playing video games . Write the ratio of the amount of time reading emails to the amount of time spent playing on video games as a fraction in a simple form.
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Step 1: State what is given
2 hours playing games or 120 minutes
30 minutes reading email
Step 2: Put information into fraction
[tex]\frac{email}{games} = \frac{30}{120}[/tex]
Step 3: Simplify the fraction by 30
[tex]\frac{30}{120}=\frac{1}{4}[/tex]
Therefore the fraction representing how long he plays games and reads email is [tex]\frac{1}{4}[/tex]
In the image, mZHKM = 155° and mZJKL = (5x + 15)°.
H
What is the value of x?
OA. 8
OB.
34
OC. 28
D.
2
Answer:
Option C. 28
Step-by-step explanation:
From the question given,
m<HKM = 155°
m<JKL = (5x + 15)°
From the diagram,
m<HKM = m<JKL (since they are directly opposite)
Inputting the value of m<HKM and m<JKL into the above expression, we have:
m<HKM = m<JKL
m<HKM = 155°
m<JKL = (5x + 15)°
155 = 5x + 15
Collect like terms
155 – 15 = 5x
140 = 5x
Divide both side by 5
x = 140/5
x = 28
Therefore, the value of x is 28.
Answer: C. 28
Step-by-step explanation:
how to do this question plz answer me step by step plzz
Answer:
Not enough tables.
Step-by-step explanation:
Circumference is 2*pi*r
The diameter is 2 times the radius or 2r, if the table diameter is 180cm. All we need to do is multiply by pi (3.14159) to get the circumference.
180*pi = 556.48cm
If each guest needs 70cm then we divide the circumference by 70
556.48/70 = 8.08 but we cant have a portion of a person so we can fit 8 people per table.
18 tables with 8 at a table is 8 x 18 = 144
If 145 guests are attending then there aren't enough tables, you are 1 table short.
What is the answer to the equation 2x = -10
Answer:
-5 homie
Step-by-step explanation:
-5 times 2 is -10
What is the Factor:X^2-x-12 ?
Start by setting up your two sets of parenthses.
Inside, we have the terms that compose each binomial.
Since x² breaks down into x · x, we use an x in each binomial.
The second term is the factors of -12 that add to the coefficient
of the middle term but what is the coefficient of the middle term?
If there is nothing written there, it's understood to be 1.
So factors of -12 that add to -1 are 4 and -4.
So we have (x + 4)(x - 3) which is our answer.
Answer:
x = 4 , x = -3
Step-by-step explanation:
x^2 - x - 12 = ( x - 4) ( x + 3)
x - 4 = 0 or x + 3 = 0
x = 4 or x = -3
Hi . I'm kinda stuck on this question .
Help please.
Workings please
Answer:
[tex]\large \boxed{\text{Q31, D. 6.00 F; 32. C. N21.75; Q33. A. 168.00 F}}[/tex]
Step-by-step explanation:
Your graph is hard to read, so I re-drew it as best I could.
You must first develop an equation relating francs and naira.
The line goes through the origin, so the general equation is
y = kx
One of the points is (40,240).
[tex]\begin{array}{rcl}F & = &k \times N\\240 & = &k \times 40\\k & = & \dfrac{240}{40}\\\\k&=&\textbf{6 F/N}\\\end{array}\\\text{The equation is $\large \boxed{\mathtbf{F = 6 N}}$}[/tex]
Q 31.
[tex]\begin{array}{rcl}F & = &6N\\& = & 6 \times 1.00\\& = & \mathbf{6.00}\end{array}\\\text{The equivalent value of N1.00 is $\large \boxed{\textbf{6.00 F}}$}[/tex]
Q 32.
[tex]\begin{array}{rcl}F & = &6N\\130.5& = & 6 N\\N&=& \dfrac{130.5}{6}\\\\& = & \mathbf{21.75}\\\end{array}\\\text{The equivalent value of 130.5 F is $\large \boxed{\textbf{N21.75}}$}[/tex]
Q 33.
[tex]\begin{array}{rcl}F & = &6N\\& = & 6 \times 28.00\\& = & \mathbf{168.00}\end{array}\\\text{An amount of N28.00 is $\large \boxed{\textbf{168.00 F}}$}[/tex]
Find the measure of APBˆ. A. 130 B. 63 C. 50 D. 230
Answer:
65
Step-by-step explanation:
TAB is an isosceles triangle by the point to tangent theorem theorem.
BAT and BAT are congruent because of the isosceles triangle definition.
CAT and ABT are right angles by the tangent theorem.
Thus, CAB and CBA are both 90 - 65 = 25.
ACB is 130 because triangles' angles add up to 180.
APB is one half of ACB by the inscribed angles theorem.
The measure of the arc APB will be 230°. Then the correct option is D.
What is a circle?
It is the circle of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
We know that the tangents are equal.
Then triangle ΔATB is an isosceles triangle.
Then the angle ∠TAB and angle ∠TBA are congruent.
We know that the angle sum of a triangle is 180°.
∠TAB + ∠TBA + ∠ATB = 180°
65° + 65° + z = 180°
z = 50°
We know that the radius and tangent of circle make 90°.
And the angle sum of quadrilateral is 360°.
∠TAC + ∠TBC + ∠ATB + ∠ACB = 360°
90° + 90° + 50° + y = 180°
y = 130°
Then the measure of the arc APB will be
x = 360° – 130°
x = 230°
The measure of the arc APB will be 230°.
Then the correct option is D.
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ2
Keiko sold 3 less than three-fourths of his sister's sales. Which expression represents what Keiko sold? Three-fourths x minus 3 Three-fourths x + 3 3 x + three-fourths 3 x minus three-fourths
Answer:
Step-by-step explanation:
Given that:
Keiko sold 3 less than three-fourths of his sister's sale.
To find:
Expression that represents what Keiko sold ?
[tex]1.\ \dfrac{3}{4} x - 3 \\2.\ \dfrac{3}{4} x + 3 \\ 3.\ 3 x + \dfrac{3}{4} \\4.\ 3x - \dfrac{3}{4}[/tex]
Solution:
First of all, let the sales done by Keiko's sister = [tex]x[/tex]
Now, let us consider the Keiko's sale word by word.
3 less than three-fourths of his sister's sale.
Three fourth of his sister's sale i.e. [tex]\frac{3}{4}x[/tex] 3 lessi.e. subtract 3 from the expression obtained in 1st line.
[tex]\dfrac{3}{4}x-3[/tex]
So, sales done by Keiko = [tex]\dfrac{3}{4}x-3[/tex]
So, correct answer is:
[tex]1.\ \dfrac{3}{4}x-3[/tex]
[tex]\frac{3}{4}x-3[/tex]
An algebraic expression is one that is obtained by performing a finite number of algebraic operations on symbols that represent numbers.
Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, is a basic algebraic operation.
Let [tex]x[/tex] denotes sale of sister of Keiko.
As Keiko sold [tex]3[/tex] less than three-fourths of his sister's sales,
Sales of Keiko [tex]=\frac{3}{4}x-3[/tex]
For more information:
https://brainly.com/question/19585043?referrer=searchResults
What is the value of 9 packs of Sweets if one pack of sweet cost Rs 120.5?
Answer:
1084.5
Step-by-step explanation: 120.5*9 = 1084.5
Answer:
One pack = Rs 120.5
→ Multiply both the brackets and price by 9
9 packets = Rs 1084.5
Please help as soon possible! :'(
Answer:
BC = 1/2 AC
2m angle DBC = m angle ABC
Angle ABC is bisected by ray BD
m∠WUT = 38°
Step-by-step explanation:
For both questions, we use the Angle Bisector Theorem.
Question 1:
We know since ray DB bisects ABC, AB and BC are congruent. They are split into 2 equal parts. Therefore, we know that if we take half of mAC, we should get either mBC or mAB. Therefore, the 1st statement is correct.
Since it is ray DB bisecting ABC, it created 2 right angles. If angle DBC was bisected, it would create 2 new angles that were 45° each, so the 2nd statement is incorrect.
We know that line ABC is equal to 180°. So if we add m∠ABD and m∠DBC (they both are 90°, as denoted in the picture) together, we should get 180°. Also, since they are congruent angles, one angle multiplied twice would also be 180°. Therefore, the 3rd statement is correct.
The Angle Bisector Theorem doesn't state that the bisector and one segment would be congruent. The length of the bisector could be anything and is not marked congruent to the other segments. Therefore, the 4th statement is incorrect.
Since we see that there is a bisector DB bisecting line ABC, creating 2 congruent segments and angles, we know that the 5th statement is correct.
Question 2:
The Angle Bisector Theorem states that a bisector that bisects 2 angles will become 2 smaller but congruent angles. So,
Step 1: Find x
4x + 6 = 6x - 10
6 = 2x - 10
16 = 2x
x = 8
Step 2: Find m∠WUT
m∠WUT = 6x - 10
m∠WUT = 6(8) - 10
m∠WUT = 48 - 10
m∠WUT = 38°