m∠ZAB + m∠CAB = 180° by the angle addition postulate
m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem
m∠ZAB = m∠ACB + m∠CBA using the subtraction property
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
m∠ZAB + m∠CAB = 180° by the angle addition postulate
m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem
m∠ZAB = m∠ACB + m∠CBA using the subtraction property
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Answer:
We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition.
We know that m∠ZAB + m∠CAB = 180° by the
✔ angle addition postulate
.
We also know m∠CAB + m∠ACB + m∠CBA = 180° because
✔ of the triangle angle sum theorem
.
Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.
Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the
✔ subtraction property
.
Step-by-step explanation:
Lilly is a pizza driver. Lilly has to make 4 deliveries.
Delivery 1: 35 Minutes
Delivery 2: 14 Minutes
Delivery 3: 18 Minutes
Delivery 4: 27 Minutes
What is the average amount of time it takes to deliver pizza?
Answer:
23 min 30 sec
Step-by-step explanation:
First, you add 35 + 14 + 18 + 27 which is 94.
Next, you divide 94 by the number of deliveries there were. Which is 4.
94/4 = 23.5.
So your answer would be 23 minutes and 30 seconds.
I Hope This Helped :D
Answer:
23.5 minutes or 23 minutes and 30 seconds
Step-by-step explanation:
1. add all the minutes
35 minutes + 14 minutes + 18 minutes+ 27 minutes = 94 minutes
2. Divide the total amount of minutes by the number of deliveries
94 minutes = 23.5 minutes or 23 minutes and 30 seconds
4 deliveries
Sylvia bought 4 bananas for 50 cents each and 1 apple for 80 cents. Write a numerical expression to represent this situation and then find the total cost.
Answer: 280
Step-by-step explanation:
50 cents for each banana so: 4* 50= 200
200+80
Answer is 280
In a school, the number of girls is 70 more than boys. the total number of students is 1280. find the number of girls and boys simple equations
Answer:
Boys = 605
Girls = 675
Step-by-step explanation:
Let x be the number of boys in school.
So, girls = (x+70)
Total no. of students = 1280
x + x + 70 = 1280
2x + 70 = 1280
2x = 1280 - 70
2x = 1210
x = 1210/2
x = 605
Hence, no. of boys = 605
no. of girls = 605 + 70 = 675
5y + 3= 14
pleaseeeee help
Answer:
5y + 3= 14
subtract 3 from each side
5y=11
divide each side by 5
5y/5=11/5
y=11/5 or 2.2 or 2 1/5
Hope This Helps!!!
Answer:
2.2
Step-by-step explanation:
Properties needed:
Subtraction Property of EqualityDivision Property of Equality
First we need to subtract 3 from both sides because of subtraction property of equality to make both sides equal.
5y + 3 = 14
-3 -3
5y = 11
Then we need to divide 5 from both sides (division property of equality) to get y.
[tex]\frac{5y}{5} = \frac{11}{5}[/tex]
And we get 2.2
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I hope this helps!
Have a great day!
Match each expression with its value -5,-3,3 or undefined
G(0)
G(0.0001)
G(2.999)
G(3)
By using the given graph, we will see that:
G(0) = -5G(0.0001) = -3G(2.999) = -3G(3) = -3How to evaluate function G?Here we have a graph of function G(x), and we want to evaluate it in different values of x.
To do that, we need to look at the interval where the lines are defined. An open dot means that the endpoint does not belong to the interval, while the closed dot means that the endpoint belongs.
First, G(0).
If you look at the graph, when x = 0 we have a closed dot on the bottom line. That is the line that we need to look to do this evaluation, there we can see that when x = 0, we have G(0) = -5.
Then we have x = 2.999.
Notice that x < 3.
And the second line (the one at y = -3) is on the interval (0, 3].
Then x = 2.999 is included on that interval, it means that:
G(2.999) = -3.
Now we have x = 0.0001
Again, notice that the second line is on the interval (0, 3]
Because 3 > 0.0001 > 0, then:
0.0001 ∈ (0, 3]
From that, we conclude that:
G(0.0001) = -3
Finally:
G(3).
Again, 3 belongs to the interval (0, 3]
Then we use the second line again.
G(3) = -3
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Answer:
G(0) = -5
G(0.0001) = -3
G(2.999) = -3
G(3) = -3
Step-by-step explanation:
3/2 x 7/2= 2^x
A. X= 1
B. X= 3
C. X= 5
D. X= 8
Out of 475 applicants for a job, 240 have 10 years experience and 83 have over 10 years experience and a graduate degree. what is the probability that a randomly chosen applicant has a graduate degree given that they have over 10 years of experience?
Answer:
1
Step-by-step explanation:
Could this be a tricky question? See the point:
240 have 10 years experience (exactly)and 83 have over 10 years experience and a graduate degreeCombining 1 and 2 the answer is 1Though it's inlikely that the first 240 people have only 10 years. Don't take this answer very seriously
Mark ran a mean distance of 13.2 km in five days. The next day, Mark ran 20 km.
Find the mean distance Mark ran in the six days.
Answer:
16.6
Step-by-step explanation:
Add the numbers together.
13.2+20=33.2
Now divide the number by 2.
33.2/2=16.6
Hope this helps!
If not, I am sorry.
Given a b and m/1 = 42°
What is m/6?
Enter your answer in the box.
Find the value of X.
Answer:
x=6
Step-by-step explanation:
check the scale factor by the fraction 10/5
after/before
it simplifies to 2 meaning that the second triangle is two times the size of the first
then take 3 fron segment AB to the similar segment DE and times it by the scale factor(2)
2×3=6
Answer:
6
Step-by-step explanation:
since AC = 5. and DF = 2(5) = 10
FW = 2(4)=8 DE= 2(3) = 6
therefore x = 6
Divya is solving the following equation for w. 3w -√20-5w = 2 Her first few steps are given below. 3w = √20-5w+2 3w-2= √/20 - 5w (3w - 2)² =(√20 – 5w) 9w² - 12w + 4 = 20 - 5w Is it necessary for Divya to check her answers for extraneous solutions?
Divya should not check her answers for extraneous solution as it's not required in this case.
What is an extraneous solution?It should be noted that an extraneous solution simply means is the transformed equation that's isn't the root of the original equation.
Based on the information given, Divya had already solved the equation and it's not necessary to check the answers for extraneous solution.
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Answer:
No, she shouldn't.
Half the product of two numbers is 36 if one number is 9 what is the other number
Answer:
x=9
y=?
36= 1/2(x*y)
36 *2 = 2* 1/2 (9*y)
72 = 9*y
72/9= 9*y/9
8=y
The other number is 8.
??????????????????????????????????????????????????
Answer:
x=20
Step-by-step explanation:
The angles are 'Co-interior Angles', they make a C shape and add up to 180 degrees
so 4x +5x =9x
9x=180
x=20
4x=80
5x=100
Solve by using Vertical Velocity model: h=-16t^2+vt+s
Where v = velocity
s = starting height
h = ending height
t = time
You can ignore the previous work, just solve B and C. Just there for context
USE VERTICAL VELOCITY MODEL FORMULA.
An equation that models the height of the ball as a function of time t is; h(t) = -16t² + 40t + 3. The maximum height that the ball will reach is 28 ft
How to Solve the Vertical velocity model?We are given the equation for the vertical velocity model as;
h = -16t² + vt + s
Where;
v = velocity
s = starting height
h = ending height
t = time
A) From the question, we have;
v = 40 ft/s
s = 3 ft
Thus, the equation is;
h = -16t² + 40t + 3
B) To find the time that the ball reaches its maximum height, we will equate the height equation to zero and find the roots. Thus;
-16t² + 40t + 3 = 0
Using an online quadratic equation calculator gives;
t = 2.573 s
C) The maximum height that the ball will reach is;
h'(t) = -32t + 40
At h'(t) = 0;
-32t + 40 = 0
32t = 40
Thus;
t = 1.25 s
Max height = -16(1.25)² + 40(1.25) + 3
Max height = 28 ft
D) The height of the ball after 2 seconds is;
h(2) = -16(2)² + 40(2) + 3
h(2) = 19 ft
E) Time for the ball to hit the ground is;
T = 2 * 2.573
T = 5.146 s
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Unit 11: volume & surface area homework 6: surface area of pyramids and cones
The answer for the following part is
What is Volume?Surface area is the amount of space covering the outside of a three-dimensional shape.
Surface Area of Cone,
= πrl + πr²
=3.14*8*15.77 + 3.14* 8*8
= 597.61804 mm²
Surface Area of triangular pyramid,
= apothem * slant height * length
= 73.6 m²
Surface Area pentagonal pyramid
= B + LA
= 247.75 + 5 ( 1/2*12*19.5)
= 247.75 + 5 ( 117)
= 832.75 in²
Surface area of square pyramid
= P*l /2
= 2400 ft²
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Determine whether the given differential equation is exact. If it is exact, solve it. (tan(x)-sin(x)sin*y))dx+cos(x)cos(y)dy=0 g
The differential equation
[tex]M(x,y) \, dx + N(x,y) \, dy = 0[/tex]
is considered exact if [tex]M_y = N_x[/tex] (where subscripts denote partial derivatives). If it is exact, then its general solution is an implicit function [tex]f(x,y)=C[/tex] such that [tex]f_x=M[/tex] and [tex]f_y=N[/tex].
We have
[tex]M = \tan(x) - \sin(x) \sin(y) \implies M_y = -\sin(x) \cos(y)[/tex]
[tex]N = \cos(x) \cos(y) \implies N_x = -\sin(x) \cos(y)[/tex]
and [tex]M_y=N_x[/tex], so the equation is indeed exact.
Now, the solution [tex]f[/tex] satisfies
[tex]f_x = \tan(x) - \sin(x) \sin(y)[/tex]
Integrating with respect to [tex]x[/tex], we get
[tex]\displaystyle \int f_x \, dx = \int (\tan(x) - \sin(x) \sin(y)) \, dx[/tex]
[tex]\implies f(x,y) = -\ln|\cos(x)| + \cos(x) \sin(y) + g(y)[/tex]
and differentiating with respect to [tex]y[/tex], we get
[tex]f_y = \cos(x) \cos(y) = \cos(x) \cos(y) + \dfrac{dg}{dy}[/tex]
[tex]\implies \dfrac{dg}{dy} = 0 \implies g(y) = C[/tex]
Then the general solution to the exact equation is
[tex]f(x,y) = \boxed{-\ln|\cos(x)| + \cos(x) \sin(y) = C}[/tex]
A,B, C and D are the four corners of a rectangular plot marked out on level ground. Given that the bearing of B from A is 40 and the bearing of C from A is 90, Find the bearing B frOm C
Answer:
given - a rectangle ABCD
AB = 40
AC. = 90
BC = ?
in triangle ABC
using Pythagoras theorem
(AB) ² + (BC) ² = (AC) ²
(40)² + (BC) ² = (90)²
(BC) ² = (90)²- (40)²
(BC) ² = 8100 - 1600
(BC) ² = 6500
BC =
[tex]20 \sqrt{10} [/tex]
5w-8x+20y+6z
Term:
Coefficient:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \sf{5w\rightarrow coefficient = 5} [/tex][tex] \sf{-8x\rightarrow coefficient = -8} [/tex][tex] \sf{20y\rightarrow coefficient = 20} [/tex][tex] \sf{6z\rightarrow coefficient = 6} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Term refers to each variable or constant separated by a mathematical operator.
Coefficient refers to the numberic part of variable or a constant number present in an expression.
[tex]\qquad \tt \rightarrow \: 12a - 10b + 6[/tex]
[tex] \large\textsf{Terms :} [/tex]
[tex] \texttt{5w } [/tex][tex] \texttt{coefficient = 5} [/tex]
[tex] \texttt{-8x} [/tex][tex] \texttt{coefficient = -8 } [/tex]
[tex] \texttt{20y} [/tex][tex] \texttt{coefficient = 20} [/tex]
[tex] \texttt{6z} [/tex][tex] \texttt{coefficient = 6} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below: Step 1: 4(2x − 4) = 8 + 2x + 8 Step 2: 6x − 8 = 16 + 2x Step 3: 6x − 2x = 16 + 8 Step 4: 4x = 24 Step 5: x = 6 In which step did the student first make an error and what is the correct step? (5 points) Step 2; 8x − 4 = 2(6 + x + 6) Step 2; 8x − 16 = 16 + 2x Step 3; 6x − 2x = 16 − 8 Step 3; 6x + 2x = 16 + 8
The entire graph of the function h is shown in the figure below.
Write the domain and range of h using interval notation.
Answer:
Step-by-step explanation:
What is the measure of the unknown angle?
straight angle divided into a one hundred thirty two degree angle and an unknown angle
48°
49°
51°
53°
f(x) = x^2 + 5x - 1 is shifted 3 units left the result is g(x). What is g(x)?
Answer:
A. g(x)=x^2+5x+2
Step-by-step explanation:
f(x) = x^2 + 5x - 1 Shift 3 units to the left. k=3
g(x)=x^2+5x-1+3=x^2+5x+2
g(x)=x^2+5x+2
Hope this helps!
If not, I am sorry.
Estimate the original volume of the pyramid in Fig. 15.28, given that its frustum has a 4 m by 4 m square top which is 12 m vertically above the square base which is 20 m by 20m.
The volume of the pyramid is 2496 cu.m.
What is a Pyramid ?A pyramid is a three dimensional structure which has a polygon base and in general triangular faces which join at the top .
It is given that
A pyramid [tex]\rm frustum[/tex] has a 4 m by 4 m square top
Height = 12 m
Base = 20 m
The volume of a square pyramid with a [tex]\rm frustum[/tex] is given by
V = (1/2) * ( Area of base + Area of [tex]\rm frustum[/tex] ) * height of the [tex]\rm frustum[/tex] from the base
V = 0.5 * ( 20 *20 + 4*4 ) * 12
V = 2496 cu.m
The volume of the pyramid is 2496 cu.m.
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Work out the values of a, b, c and d.
Step-by-step explanation:
The are two angles ie. 45 and 80 than find the third angle
80 will be vertically opposite and alternative angle to a
Peter works as a dishwasher and earns 7.30 /h. He also receives 7% of the gratuities earned by all the staff. Two weeks ago he worked 32 hours and the gratuities totalled 1587.30. What was Peter's gross pay?
Peter's gross pay will be 1820.9.He put in 32 hours of work two weeks ago, and the tip money came to $1587.30.
What is gross pay?Before taxes, benefits, and other payroll deductions are taken out of an employee's paycheck, that amount is known as their gross pay.
Given data;
Peter earn per hour = 7.30
Gratuities = 7 %
Given condition;
No of hour person work = 32
Gratitutes = 1587.30
Let the gross pay will be x;
x = gratuities + no of hoy\ur work × money earned per hour;
x = 1587.30 + 32 × 7.30
x = 1820.9
Hence,Peter's gross pay will be 1820.9.
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Raya buys a van for £9500 plus VAT at 20%
Raya pays a deposit for the van.
She then pays the rest of the cost in 12 equal payments of £665 each month.
Find the ratio of the deposit Ray pays to the total of the 12 equal payments.
Give your answer in its simplest form.
Step-by-step explanation:
yo thara bhai joginder tu he ek bndr
Type a number for the types of journals that will be available to you in the new lma
Answer:
Step-by-step explanation:
What are the 6 types of journals?
There are various types of journals including:
academic/scholarly journals.
trade journals.
current affairs/opinion magazines.
popular magazines.
newspapers.
what is 25:28 in slimpelst from
Answer:
25:28 is the simplest form
Step-by-step explanation:
This is a ratio, think of it like a fraction. You can simplfy it by dividing by common factor.
25 and 28 have no common factors except for 1.
25: 1,5,25
28: 1,2,4,7,14,28
It will stay as 25:28
Answer:
it stays the exact same or 0.893
Step-by-step explanation:
Which currency is it
Answer:
pounds (£)
Step-by-step explanation:
pounds are used in countries such as the UK and South Georgia
If the side length of a square is 4 inches, it’s area is how many square inches and it’s perimeter is how many inches
Answer:
The area is 16 inches squared and the perimeter is also 16 inches
Step-by-step explanation:
To find the area, you must multiply the length by the width. Since this is a square, you have to multiply one adjacent side by the other. For perimeter, you can either multiply one side by 4 or add all 4 sides.
