Answer:
z = -0.5
Step-by-step explanation:
Using exponent rule:
[tex]x^a = x^b[/tex] then a = b
Given the equation:
[tex]25^{z+2} = 125[/tex]
We can write 25 and 125 as:
[tex]25 = 5 \cdot 5 = 5^2[/tex]
[tex]125 = 5 \cdot 5 \cdot 5 = 5^3[/tex]
then;
[tex]5^{2(z+2)}= 5^3[/tex]
Apply the rule:
[tex]2(z+2) = 3[/tex]
using distributive property [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex]2z+4 = 3[/tex]
Subtract 4 from both sides we have;
[tex]2z = -1[/tex]
Divide both sides by 2 we have;
z = -0.5
Therefore, the solution for the given equation is, z = -0.5
a triangular plot of land has boundary lines 45 meters, 60 meters, and 70 meters long. the 60 meter boundary line runs north-south. Is there a property for the boundary line that runs east-west
No, there is no property for the boundary line that runs east-west.
Explanation:No, there is no property for the boundary line that runs east-west. This is because if we have a triangle with side lengths 45 meters, 60 meters, and 70 meters, and the 60 meter side runs north-south, then the other two sides must be at an angle to the north-south line. It is not possible for one of the sides to be parallel to the north-south line (east-west) because that would create a rectangle rather than a triangle.
The windows of a downtown office building are arranged so that each floor has six fewer windows than the floor below it. If the ground floor has 52 windows, how many total windows are on the first eight floors?
Answer:
There are 248 windows on the first eight floors.
Step-by-step explanation:
As given:
The ground floor has 52 windows.
This question is based on arithmetic sequence:
a1 = 52
d = - 6 (each floor has six fewer windows than the floor below it)
[tex]a_n=a1+(n-1)d[/tex]
[tex]a_8 =a1+7d[/tex]
=> [tex]52+[7 \times (-6)][/tex]
=> [tex]52-42 =10[/tex]
We know:
[tex]S_n= n/2 \times (a1 +a _n)[/tex]
[tex]S_8 =8/2 \times(52+10)[/tex]
= 248
Therefore, there are 248 windows on the first eight floors.
which method is most efficient in solving a system of linear equations when the two equation have x-values with opposite coefficient values
A. GUESS AND CHECK
B. GRAPHING
C. SUBSTITUTION
D. ELIMINATION
the number of squares in 15 quilts if 6 quilts have 288 squares
A jug of juice has 7 cups of pineapple juice and 3 cups of orange juice. write the ratio of number of cups of pineapple juice to total number of cups of juice *
A transformation T: (x, y) (x - 5, y + 3).
The image of A(2, -1) is
(3, 2)
(-3, 2)
(-3, -2)
Answer:
i can confirm the above awnser is correct
How do you represent 4/7 + 3/14 on a number line?
Please Help Asap!!
A mother has 5 liters of cream to make ice cream for a party.suger comes in 1kg bags how many suger will be needed
helppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
3, 12, 48, 192, 768, . . .
This sequence has a
A.] common difference of 4
B.] common ratio of 4
C.] common difference of [tex] \frac{1}{4}[/tex]
D.] common ratio of [tex] \frac{1}{4}[/tex]
Need the answer fast, anyone know?
What is the slope of a line perpendicular to the line y=3/4x+1
Mary leaves her house to take a walk. The graph shows the distance, d, in feet from her house that Mary is at any given time, t, in minutes. How many minutes has Mary walked when she reaches the farthest point from her house
A basketball player scored 2222 times during one game. hehe scored a total of 3030 points, two for each two-point shot and one for each free throw. how many two-point shots did hehe make
Use the quadratic function to predict f(x) if x equals 2. f(x) = −3x2 + 180x − 285
The next term of the arithmetic sequence 39,60,81,102,123.....is
need help ive always had trouble with writing functions.
Candy is on sale for $0.75 each. you have a coupon for $0.25 off your total purchase. write a function rule for the cost of n pieces of candy.
A. C(n)0.25n-0.75
B. C(n)=0.75n-0.25
C. C(n)=1.0n
D. C(n)=0.75n
the gray is a sidewalk and the turquoise is grass. Both are squares. What is the area of the sidewalk?
A) 4 ft2
B) 36 ft2
C) 44 ft2
D) 48 ft2
Answer:
C 44 ft2 i just took the test .
Step-by-step explanation:
Determine if each set of ordered pairs represents a function
Answer:
Function:(7,-4), (0,9), (2,-2)
(-6,5),(-5,6), (8,2)
(2,3),(6,-5),(-1,3)
Not a function:(0,3),(0,7),(4,0)
(1,9),(-3,-2),(1,-4)
Step-by-step explanation:
edge
Each summer Primo Pizza and Pizza Supreme compete to see who has the larger summer profit. Let f ( x ) f(x) represent Primo Pizza's profit x x days after June 1. Let g ( x ) g(x) represent Pizza Supreme's profit x x days after June 1. Suppose Primo Pizza's profit each day is two times as large as the profit of Pizza Supreme. Express the function f f in terms of the function g
g.
The profit of Primo Pizza is twice the profit of Pizza Supreme each day. Therefore, if g(x) represents the profit of Pizza Supreme x days after June 1, then f(x), representing Primo Pizza's profit, is given by f(x) = 2g(x). This means if Pizza Supreme's profit on a particular day is $500, Primo Pizza's profit on the same day is $1000.
Explanation:In this problem, we are given that the profit of Primo Pizza (represented by the function f(x)) is two times larger than the profit of Pizza Supreme (represented by the function g(x)). This relationship between the two profits can be expressed as f(x) = 2 * g(x). So, if you know the profit of Pizza Supreme on a particular day (g(x)), you can determine the profit of Primo Pizza on that day by doubling the profit of Pizza Supreme.
For instance, if Pizza Supreme's profit 10 days after June 1st is $500 (so, g(10) = $500), then Primo Pizza's profit on the same day would be f(10) = 2 * g(10) = 2 * $500 = $1000. Thus, Primo Pizza is making twice the profit of Pizza Supreme each day.
Learn more about Functions here:https://brainly.com/question/30721594
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A restaurant purchased 160 boxes of mustard packets. Each box contained 103 packets of mustard. How many mustard packets in total did the restaurant purchase?
Answer:
Total number of mustard packets = 16,480
Explanation:
A restaurant buy mustard box = 160
Each mustard box contain packet = 103 packet
In order to find the total number of packets
Total number of packet = (number of mustard boxes)*(number of packets in a box)
Now put the values in given formula
Total number of packet = 160 * 103
Total number of packet = 16,480
final answer, I hope it helps
Orlando bought a new couch for 2,736, using the furniture store's finance plan. He will pay $114 a month for 24 months. Which equation can Orlando use to find out how much money he still owes after each month of the plan?
Answer:
[tex]y = 2736 - 114x[/tex]
Step-by-step explanation:
It is given that the cost of the couch was $2,736. Orlando bought that couch using furniture store's finance plan. The plan says that he is supposed to pay $114 per month for a period of 24 months.
we are asked to determine the equation which can determine the total amount still due on orlando after x number of months.
Let the total number of month we are calculating = x
Payment per month = $114
Hence payment made in x months = $114x
Hence payment still owned by Orlando = $2736-$114x
Above equation gives us the dues on Orlando
Josie had a choice of 3 breads, 4 choices of meat, and 4 choices of cheeses to make a sandwich.
How many different sandwiches can she make?
24
36
48
60
Answer:
The answer is 48
Step-by-step explanation:
For every different sandwich, she needs to choose one breat, one meat and one cheese.
For each choice of bread, there are 4 choices of meat and 4 choices of cheese. Also, for each meat, there are four choices of cheese. It means that for each bread there are 4(choices of meat)*4(choices of cheeses) = 16 possible combinations.
There are also 3 choices of breads. For each bread, there are 16 possible combinations. So, in all, there are 3*16 = 48 possible combinations.
Suppose that x and y vary inversely and x = 1 when y = 12. Write a function that models the inverse variation. Graph the function and find y when x = 20.
Write a function that models the inverse variation.
Which of the following is not a method used to prove triangles congruent?
A) AAS Theorem
B) SSA Postulate
C) SAS Postulate
D) ASA Postulate
Answer:
B) SSA Postulate
Step-by-step explanation:
Two triangles are congruent if they are of the same shape and size.
Two triangles can be proved congruent by AAS ,SAS ,ASA ,SSS ,HL postulates.
Two triangles are congruent if two angles and one side of both the triangles are congruent that is AAS and ASA postulates.(option A and D)
The triangles can be congruent by SAS that is if two sides and included angle of two triangles are congruent then the triangles are congruent .(Optionc)
Option B that is SSA is not a congruence postulate.
Samantha has 3 times as many baseball cards as mark. mark has 12 baseball cards. write an equation that shows how many cards samantha has.
The area of a parallelogram is 400m2 the base is 25m find the length of the height
The radius of a circle is 10 feet. What is the angle measure of an arc 4 feet long?
I WILL GIVE 40 POINTS FOR EACH QUESTION REALLY NEED HELP THERE ANOTHER POST FOR THE OTHER QUESTION IT WILL BE ANOTHER 40 AS WELL AND MARKED AS BRAIN~LEST AND STAR RATEING
Answer:The first page is S^2
The fourth page is The last option
The fifth page maybe the last one
Step-by-step explanation:
How many solutions does the following equation have?
4(y - 30) = 4y + 12
a. No solutions
b. Exactly one solution
c. Infinitely many solutions