Answer:
137
Step-by-step explanation:
Since angle Z and the angle of 43° are supplementary, the sum of them must equal 180. Therefore,
∠Z + 43 =180
∠Z = 137°
Answer:
137 degrees
Step-by-step explanation:
First thing, we know y is 43 because 43 degrees and y are vertical angles meaning they are congruent. (This is just a small part doesn't really do much though.)
Straight lines add up to 180 so simply just subtract 43 from 180.
180 - 43 = 137.
Therefore,
z = 137 degrees
What is the solution for this inequality? -10x ≤ 40 A. x ≤ -4 B. x ≤ 4 C. x ≥ -4 D. x ≥ 4
Answer:
C. x ≥ -4
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
-10x ≤ 40
Step 2: Solve for x
[Division Property of Equality] Divide -10 on both sides: x ≥ -4Answer:
C. x ≥ -4
Step-by-step explanation:
To solve this inequality isolate the variable. Do this by using the properties of equality, specifically the division property. So, divide both sides by -10. This equals, x ≤ -4. However, whenever an inequality is divided or multiplied by a negative number the sign must be flipped. Therefore, the final answer is x ≥ -4.
Using interval notation, identify the domain for the function:
Answer:
d)
Step-by-step explanation:
>The domain are all the values of x , so you can graph on the calculator that on the x-axis the graph starts at 9 and keeps going to the right so the domain is x≥9 or [9,∞)
or
>Solve for x in the given equation when f(x) =y = 0 to find the roots
√(x-9) = 0 , square both sides
x-9 = 0 , add 9 to both sides
x= 9
from this root the graph moves to the right to ∞
the domain is [9, ∞)
685 gym members were asked if they use the elliptical machine or treadmill as their primary cardiovascular exercise. 257 said they use the treadmill, 157 said they use the elliptical, and 85 said they use both.
a.) Organize this using a venn diagram (2 marks)
b.) A gym member is chosen from this group. What is the probability that this member uses the treadmill only? (1 mark)
Given:
Total number of gym members = 685
257 said they use the treadmill, 157 said they use the elliptical, and 85 said they use both.
To find:
a. The venn diagram.
b. The probability that a member uses the treadmill only?
Solution:
(a)
We have,
Total number of gym members = 685
Treadmill user = 257
Elliptical user = 157
Who use both = 85
Only treadmill user is:
[tex]257-85=172[/tex]
Only Elliptical used
[tex]157-85=72[/tex]
Therefore, the venn diagram for the given situation is shown below.
(b)
The member who use treadmill only = 172
Total user = 685
The probability that a member uses the treadmill only is:
[tex]P(\text{Only treadmill})=\dfrac{\text{Only treadmill users}}{\text{Total users}}[/tex]
[tex]P(\text{Only treadmill})=\dfrac{172}{685}[/tex]
Therefore, the probability that a member uses the treadmill only is [tex]\dfrac{172}{685}[/tex].
please help ,,
supply the missing reason in statement 4 of the proof of the isosceles triangle theorem.
Answer:
h
Step-by-step explanation:
You received your first credit card with a spending limit of $2,000 at 18.9% interest. You decide you need to upgrade your sound system in your car, so you are going to buy this great deal. The next month you receive your credit card statement and you now owe $2,000. You are able to pay the minimum payment of $100 each month. If you continue paying only $100 each month, how long will it take you to pay off your credit card debt?
Answer:
It will take approximately 25 months
Step-by-step explanation:
The amount owed on the credit card statement, P = $2,000
The interest rate of the credit on the credit card, r = 18.9%
The minimum monthly payment made, M = $100
The equal monthly installment formula is given as follows;
[tex]M = \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}[/tex]
Therefore, we get;
[tex]100 = \dfrac{2,000 \cdot \left(\dfrac{0.189}{12} \right) \cdot \left(1+\dfrac{0.189}{12} \right)^n }{\left(1+\dfrac{0.189}{12} \right)^n - 1} = \dfrac{2,000 \times\left(0.01575 \right) \cdot \left(1.01575 \right)^n }{\left(1.01575\right)^n - 1}[/tex]
100×1.01575ⁿ - 100 = 31.50×1.01575ⁿ
100×1.01575ⁿ - 31.50×1.01575ⁿ = 100
68.5×1.01575ⁿ = 100
1.01575ⁿ = 100/68.5
n = ln(100/68.5)/ln(1.01575) ≈ 24.21 (which is approximately 25 months, by rounding up to the nearest whole number)
Therefore, it will take approximately 25 months to pay off the credit card debt
Sales of a certain product are declining at a rate proportional to the amount of sales. If at the end of the first year the sales have declined by 22%, then how many years will have passed (since the beginning of the first year) when sales become only 31% of their original value? Express your answer as a decimal, correct to within 0.001 years.
Answer:
The answer is "6.093 years".
Step-by-step explanation:
The rate of decline in sales in [tex]22\%[/tex] per year.
The starting sales is 100 units:
Using compounding formula:
[tex]\to 100 \times (1-\frac{22}{100})^t=22\% \ of \ 100\\\\\to 100 \times (\frac{100-22}{100})^t=\frac{22}{100} \times \ 100\\\\\to (\frac{78}{100})^t=\frac{22}{100}\\\\\to 0.78^t=0.22\\\\\text{taking \log on both the sides}\\\\[/tex]
taking log on both sides
[tex]\to \log_e \ 0.78^t= \log_e\ 0.22\\\\\to t \log_e \ 0.78= \log_e\ 0.22\\\\\to t = \frac{\log_e 0.22}{\log_e 0.78}\\\\[/tex]
[tex]= \frac{-0.6575}{-0.1079}\\\\= \frac{0.6575}{0.1079}\\\\=6.093[/tex]
which of the following give the highest future value is 6000000 is invested at 6% for 3 years
Answer:
$5084745.76271
Step-by-step explanation:
Given data
Final amount= $6000000
Rate=6%
Time= 3 years
Now let us find the initial amount which is the principal
using the simple interest formula we have
6000000 = P(1+0.06*3)
6000000 =P(1+0.18)
6000000 =P*1.18
P= 6000000 /1.18
P=$5084745.76271
Hence the initial deposite is $5084745.76271
Mark and John share the cost of a birthday gift. The cost of the gift is $20.48. Mark pays for 2/3 of the gift and John pays for the remaining 1/3. How much did each boy pay?
Given:
Cost of gift = $20.48
Mark pays for [tex]\dfrac{2}{3}[/tex] of the gift and John pays for the remaining [tex]\dfrac{1}{3}[/tex].
To find:
The amount paid by each boy.
Solution:
We have,
Cost of gift = $20.48
Mark pays for [tex]\dfrac{2}{3}[/tex] of the gift. So, the amount paid by Mark is:
[tex]20.48\times \dfrac{2}{3}\approx 13.653[/tex]
John pays for the remaining [tex]\dfrac{1}{3}[/tex]. So, the amount paid by John is:
[tex]20.48\times \dfrac{1}{3}\approx 6.827[/tex]
Therefore, the amount paid by Mark and John are $13.653 and $6.827 respectively.
These tables of values represent continuous functions. In which table do the values represent an exponential function?
Answer:
c
Step-by-step explanation:
An exponential function is a function where the number is raised to a constant power
exponential function is usually in the form : f(x) = [tex]a^{x}[/tex]
a is positive and not equal to 1
x is a real number
to determine which option is an exponential function, determine which of the options have a common ratio
Option A :
28/7 = 4
49 / 28 = 1.75
option C
12 / 4 = 3
36 /12 = 3
the correct answer is C
find missing side of triangle. help
Answer:
x² + 2² =(√15)²
x²+ 4. =15
x² =15-4
x² =11
x. =√11 mi
so the answer is 4th option
In the graph increasing, decreasing, or constant?
Answer:
Step-by-step explanation:
slope>0 so graph is increasing.
Could someone please help me with this question? Thanks.
Answer:
Step-by-step explanation:
MM oute le iloa
can someone give me the answer for this? __ (5 + 4) = 2 * 5 + 2 * 4
Answer:
The answer is 2_____________________________
2 x 5 = 10
2 x 4 = 8
10 + 8 = 18
______________________________
5 + 4 = 9
_______________________________
_ 9 = 18
18 : 9 = 2
3/x + 4/5 = 11/10
For what value of x is the equation above true?
A) 3
B) 5
C) 7
D) 10
Answer:
The answer is
[tex] \frac{3}{x} = \frac{11}{10} - \frac{4}{5} \\ \frac{3}{x} = \frac{55 - 40}{50} \\ \frac{3}{x} = \frac{15}{50} \\ \frac{3}{x} = \frac{3}{10} \\ x = 10[/tex]
Determine the x-intercepts of the function. Check all that apply.
(–2, 0)
(–1, –2)
(0, 0)
(1, 0)
(2, 0)
Answer:
-2,-1,0,1,2
Step-by-step explanation:
Answer:
-2.0
0,0
Step-by-step explanation:
i just did the test
Someone please help me with this math problem?
Зу = х - 9
y = -x + 1
Using the graphing method, which of the following choices is the solution of the system?
A=(-3 ,-2)
B=(3 ,-2)
C= Infinite solutions
D= No solutions
Answer:
did i got it correct if yes follow plz
used a graphing tool to, well, graph it
see the solution in the screenshot, it's the point where the two lines intersect
Find an equation for the perpendicular bisector of the line segment
whose endpoints are (9, -3) and (-5, –7).
Step-by-step explanation:
So here is my attempt. And i guess its correct
If f(x) = 7x - 3 and g(x) = x^2, what is (g° 0(1)?
( f ∘ g ) ( x ) is equivalent to f ( g ( x ) ) . We solve this problem just as we solve f ( x ) . But since it asks us to find out f ( g ( x ) ) , in f ( x ) , each time we encounter x, we replace it with g ( x ) . In the above problem, f ( x ) = x + 3 . Therefore, f ( g ( x ) ) = g ( x ) + 3 . ⇒ ( f ∘ g ) ( x ) = 2 x − 7 + 3 ⇒ ( f ∘ g ) ( x ) = 2 x − 4 Basically, write the g ( x ) equation where you see the x in the f ( x ) equation. f ∘ g ( x ) = ( g ( x ) ) + 3 Replace g ( x ) with the equation f ∘ g ( x ) = ( 2 x − 7 ) + 3 f ∘ g ( x ) = 2 x − 7 + 3 we just took away the parentheses f ∘ g ( x ) = 2 x − 4 Because the − 7 + 3 = 4 This is it g ∘ f ( x ) would be the other way around g ∘ f ( x ) = 2 ( x + 3 ) − 7 now you have to multiply what is inside parentheses by 2 because thats whats directly in front of them. g ∘ f ( x ) = 2 x + 6 − 7 Next, + 6 − 7 = − 1 g ∘ f ( x ) = 2 x − 1
Hello,
[tex]f(x)=7x-3\\g(x)=x^2\\\\(fog)(x)=g(f(x))=g(7x-3)=(7x-3)^2=49x^2-42x+9\\\\(gof)(x)=f(g(x))=f(x^2)=7x^2-3\\\\(fog)(0)=g(f(0))=49*0^2-42*0+9=9\\\\(gof)(0)=f(g(0))=7*0^2-3=-3\\[/tex]
Since i don't know what is (g°O(1) and you haven't correct your question ,
i has put the 2 possibles answsers.
ℎ = 6 + 11 − 22
calculation path
Answer:
[tex]h = 6 + 11 - 22 \\ h = 17 - 22 \\ h = - 5[/tex]
Answer:
-5
Step-by-step explanation:
6+11 = 17↓
17-22 = -5
or
11-22 = -11↓
-11+6 = -5
Here are the first five terms of a sequence. 4, 11, 22, 37, 56 Find an expression, in terms of , for the th term of this sequence.
Answer:
[tex] a_n = 2n^2 + n + 1 [/tex]
Step-by-step explanation:
4, 11, 22, 37, 56
11 - 4 = 7
22 - 11 = 11
37 - 22 = 15
56 - 37 = 19
After the first difference, 11 - 4 = 7, each difference is 4 more than the previous difference.
Difference of differences:
11 - 7 = 4
15 - 11 = 4
19 - 15 = 4
Since we need the difference of differences to find a constant, this must be a second degree function.
[tex] a_1 = 4 = 2^2 + 1(0)[/tex]
[tex] a_2 = 11 = 3^2 + 2 = 3^2 + 2(1) [/tex]
[tex] a_3 = 22 = 4^2 + 6 = 4^2 + 3(2) [/tex]
[tex] a_4 = 37 = 5^2 + 12 = 5^2 + 4(3) [/tex]
[tex]a_5 = 56 = 6^2 + 20 = 6^2 + 5(4)[/tex]
[tex] a_n = (n + 1)^2 + (n)(n - 1) [/tex]
[tex] a_n = (n + 1)^2 + (n)(n - 1) [/tex]
[tex] a_n = n^2 + 2n + 1 + n^2 - n [/tex]
[tex] a_n = 2n^2 + n + 1 [/tex]
Solve the equation and enter the value of x below. 3(x + 4) = 123
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex]3(x + 4) = 123 \\ 3x + 12 = 123 \\ 3x = 123 - 12 \\ 3x = 111 \\ x = \frac{111}{3} \\ x = 37[/tex]
=> The answer is 37.
Answer:
X=37
Step-by-step explanation:
3(x+4)=123
3x+12=123
3x=123-12
3x=111
3x/3 =111/3
x=37
let f(x)=7x-4
what is f(6)?
Answer:
38
Step-by-step explanation:
To find the value of f(6), we substitute the value 6 where x is into the function. You would get:
7(6) - 4
42 - 4
f(6) = 38
Answer:
See my writting here have answer
Find the TWO integers whos product is -12 and whose sum is 1
Answer:
[tex] \rm Numbers = 4 \ and \ -3.[/tex]
Step-by-step explanation:
Given :-
The sum of two numbers is 1 .
The product of the nos . is 12 .
And we need to find out the numbers. So let us take ,
First number be x
Second number be 1-x .
According to first condition :-
[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]
Hence the numbers are 4 and -3
Step-by-step explanation:
[tex]numbers \: = x \: and \: y \\ x \times y = - 12......(1) \\ x + y = 1..... ..(2) \\y = 1 - x \\ put \: this \: in \: (1) \\ x(1 - x) = - 12 \\ x - {x}^{2} = - 12 \\ - x + {x}^{2} - 12 = 0 \\ factorise \\ {x}^{2} - 4x + 3x - 12 = 0 \\ x(x - 4) + 3(x - 4) = 0 \\ (x - 4)(x + 3) = 0 \\ x = + 4 \: or \: - 3 \\ thank \: you[/tex]
Which of the following is a composite number?
A. 1
B. 63
C.O
D. 19
B. 63
some simple googling would've been able to help you with this. but 0 isn't prime or composite, not sure about 1, 19 is prime, 63 is a definite composite
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities.
The batting order for nine players on a team with 11 people.
Given:
The batting order for nine players on a team with 11 people.
To find:
The number of possibilities for the given scenario.
Solution:
First, we need to select 9 players from 11 people, it involves combination, i.e. [tex]^{11}C_9[/tex].
Second, we need to arrange the order of 9 selected players, it involves permutation, i.e., [tex]^9P_9[/tex].
The number of possibilities for the given scenario is:
[tex]\text{Possibilities}=^{11}C_9\times ^9P_9[/tex]
[tex]\text{Possibilities}=\dfrac{11!}{(11-9)!9!}\times \dfrac{9!}{(9-9)!}[/tex]
[tex]\text{Possibilities}=\dfrac{11\times 10\times 9!}{2!9!}\times \dfrac{9!}{0!}[/tex]
[tex]\text{Possibilities}=\dfrac{110}{2\times 1}\times \dfrac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{1}[/tex]
[tex]\text{Possibilities}=55\times 362880[/tex]
[tex]\text{Possibilities}=19958400[/tex]
Therefore, the following scenario involves both permutation and combination, and the number of possibilities is 19958400.
If a > b and b > a, then ?
That's impossible. There are no solutions.
Translate the sentence into an equation.
Nine times the sum of a number and 4 is 3.
William used 15 cm of tape to wrap 3 presents. Find the length of tape to wrap for 1 present?
Answer:
The length of tape to wrap = 5 cm
Step-by-step explanation:
Let the length of tape used to wrap 1 present be = x
Tape length Number of presents
15 cm 3
x 1
[tex]\frac{15}{x} = \frac{3}{1} \\\\x \times 3 = 1 \times 15\\\\x = \frac{15}{3} = 5 \ cm[/tex]
Solve this equation : 12p-5=25
write step by step.
Answer:
P=2.5
Step-by-step explanation:
12p = 25+5
12p = 30
P =30/12
Simplification:
P= 15/6
= 5/2 = 2.5