[tex]( {t}^{9} ) {}^{ - 8} \\ = t {}^{9 \times ( - 8)} \\ = {t}^{ - 72} [/tex]
Final answer:
The expression simplifies to [tex]1/t^72[/tex] by using exponent rules to multiply the exponents and then applying the rule for negative exponents.
Explanation:
To simplify the expression [tex](t^9)^-8[/tex] , you need to use the exponent rules.
Specifically, when you have a power raised to another power, you multiply the exponents.
Here, you have the base t raised to the 9th power, and then that result is raised to the -8th power.
The rule is: [tex](a^m)^n = a^(m*n).[/tex]
Applying this rule here gives us:
[tex]= (t^9)^-8[/tex]
[tex]= t^(9*-8)[/tex]
[tex]= t^-72.[/tex]
Since we are dealing with a negative exponent, the rule for negative exponents says that [tex]a^-n = 1/a^n.[/tex]
Therefore, our final simplified expression is [tex]1/t^72.[/tex]
How do you find the slop from this?
Answer:
Look at the rise over run
itd be 10/10 or 1
Find the slope (or rate of change) from this graph. Write out an equation to find the slope
Answer:
slope = [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Calculate the slope using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 5, - 3) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line
m = [tex]\frac{-1+3}{0+5}[/tex] = [tex]\frac{2}{5}[/tex]
A carpenter needs 3 minutes to cut a board into 5 equal sections. If each cut takes the same length of time, at what rate is the carpenter cutting?
Answer:
3/180= 60 seconds = 1m/per cut or 60 sec/per cut.
Step-by-step explanation:
This is 3 cuts executed from a board to get 5 parts.
Answer:
he cuts 1.6 section of a board in one minute
Step-by-step explanation:
They're telling you that it takes 3 minutes for the carpenter to cut one board into 5 qual section. Therfore how many sections he's cutting in one minute divide the 5 by three. With that you will have the rate
does anyone know what 2/3 x= 8. So the question is what does x equal too
Answer:
x = 12
Step-by-step explanation:
⅔x = 8
x = 8 × 3/2
x = 12
Answer:
12
Step-by-step explanation:
8 divided by 2/3 = 12.01 so 12.
find the number and type of solutions then factor and solve
4b^2+8b+7=4
20 points and brainliest
Answer:
-1/2, -3/2
Step-by-step explanation:
4b² + 8b + 3 = 0
8² - 4(4)(3) = 16 > 0
Real and distinct solutions
4b² + 6b + 2b + 3 = 0
2b(2b + 3) + 1(2b + 3) = 0
(2b + 3)(2b + 1) = 0
b = -1/2, -3/2
A circle has a circumference of 18. It has an arc of 6. What is the central angle of the arc, in degrees?
Answer:
Step-by-step explanation:
C=2πr
18=2×3.14×r
18=6.28r
r=2.88
Arc of a circle
A=®/360°πr
6=®/360°×3.14×r
®=239°
6
Answer:
120
Step-by-step explanation:
Which statement about fractions that are equivalent to 1 is correct?The denominator is greater than the numerator. The denominator is equal to the numerator. The numerator is greater than the denominator. The denominator is twice the numerator.
The denominator is equal to the numerator.
Step-by-step explanation:
For a fraction to be equal to 1, the value of denominator and the value of numerator should be same.For instance, the fraction 2/2 = 1 because the number in the denominator is 2 and the numerator is also 2.Both cancel out each other that is equal to 1.4. A health club manager wants to determine
whether the members would prefer a new
sauna or a new steam room. The club surveys
50 of its 600 members. What is the population
of this study?
Answer: 600 members of the club
Step-by-step explanation:
In a statistical study , a population is a large group of observations by the researcher's point of view regarding the objective of the study.A sample is a subset of the population that represents the entire population.
Here , we are given that ,
The club surveys 50 of its 600 members.
Clearly , Population = 600 members of the club
Sample = 50 members
Hence, the population of this study is "600 members of the club " .
Triangle 1 has vertices at (A,B), (C,D), and (E,F). Triangle 2 has vertices at (A,3B), (C,3D), and (E,3F). What can you conclude about triangle 2?
(A)Triangle 2 is not congruent to triangle 1 because the transformation applied was not a rigid motion.
(B)Triangle 2 is congruent to triangle 1 because a reflection is a rigid motion.
(C)Triangle 2 is not congruent to triangle 1 because it is not a translation of triangle 1.
(D)You cannot tell because you do not know where the points are in the plane.
Answer:
Step-by-step explanation:
A
Answer:
Answer A
Step-by-step explanation:
The graph of the function passes through the point (2, 1), and y increases by 4
when x increases by 1.
Answer:
[tex]y=4x-7[/tex]
The graph in the attached figure
Step-by-step explanation:
In this problem I will assume the the function is linear
we have the point (2,1)
we know that
y increases by 4 when x increases by 1
Remember that the formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)
so
The slope of the linear function is
[tex]m=\frac{4}{1}[/tex]
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
substitute
[tex]y-1=4(x-2)[/tex]
Convert to slope intercept form
Isolate the variable y
[tex]y-1=4x-8\\y=4x-8+1\\y=4x-7[/tex]
see the attached figure to better understand the problem
The question pertains to the characteristics of a linear function whose graph passes through the point (2, 1) with a slope of +4, indicating an increase of 4 in y for every increase of 1 in x. The line's positive slope suggests the graph rises as the x-value increases. The equation of the line is y=4x-7.
Explanation:The student is asking a question about the characteristics of a linear function based on its graph. Specifically, since the graph passes through the point (2, 1) and the value of y increases by 4 when x increases by 1, we can conclude that the slope of the line is +4. This is because the slope of a line represents the change in y divided by the change in x. Given that the slope is positive, this line will show an upward trend on the graph as the x-value increases, much like other graphs with a positive slope.
To find the equation of the line, we start by using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. We use the point (2, 1) and the slope 4 to solve for b. The process is as follows:
1 = 4(2) + b
1 = 8 + b
b = -7
Therefore, the equation of the function is y = 4x - 7.
How can you determine whether a triangle is a right triangle
Answer:
if there is a right angled square shape at the angle
Answer: MARK BRAINLIEST!!!!!!!!!
Because its the only triangle that has a 90 degree angle
Step-by-step explanation:
What is the area of the trapezoid?
110 square inches
32 square inches
140 square inches
80 square inches
X^2 + 4.7^2 = 13.4^2
Answer:
[tex]x = - \: 12.55 \: or \: x = 12.55[/tex]
Step-by-step explanation:
We want to solve for x in
[tex] {x}^{2} + 4.7^{2} = 13.4^{2} [/tex]
We group constants on the right to get:
[tex]{x}^{2} = 13.4^{2} - {4.7}^{2} [/tex]
We apply difference of two squares
[tex]{x}^{2} = (13.4 - {4.7})(13.4 + 4.7)[/tex]
[tex] {x}^{2} = 157.47[/tex]
[tex]x = \pm \sqrt{157.47} [/tex]
[tex]x = \pm \: 12.55[/tex]
Write the first six terms of the sequence.
a = -n²+6
en oo
4, 2, 0, -2, -4,-6
5, 2, -3, -10, -19, -30
2, -3, -10, -19, -30, -43
6, 5, 2, -3, -10, -19
Step-by-step explanation:
1st term = -n²+6
= -(1)²+6
= -1+6
=5
2nd term = -(2)²+6
= -4+6 = 2
3rd term= -(3)²+6
=-9+6 = -3
4th term= -(4)²+6
= -16+6 = -10
5th term = -(5)²+6 = -25+6 = -19
6th term = -(6)²+6 = -36+6 = -30
5,2, -3,-10,-19, -30
optionB
You've been given a twenty dollar bill that you need to break into smaller bills and coins in order to make change. You break it into three (3) five-dollar bills, and three (3) one-dollar bills. How many quarters do you need to complete the conversion?
Answer:
8 quarters
Step-by-step explanation:
You need to break the $20 into smaller bills. The smaller bills value has to be equal to $20. So far you have three $5 bills and three 1$ bills, so the current value is 3*$5 + 3*$1= $18
The value you need to add more will be $20- $18= $2
You need to add $2 more value to the smaller bills and you want to do it using quarters($0.25). The number of the quarter you need will be: $2/ $0.25= 8 quarters
Let's start by calculating the total value of the five-dollar bills and one-dollar bills:
You have 3 five-dollar bills, and each is worth $5, so:
3 five-dollar bills × $5 per bill = $15
You also have 3 one-dollar bills, and each is worth $1, so:
3 one-dollar bills × $1 per bill = $3
Now, let's add the value of the five-dollar bills and one-dollar bills together:
$15 (from five-dollar bills) + $3 (from one-dollar bills) = $18
You started with a twenty-dollar bill, which is worth $20, so we subtract the total value of the bills you have from $20 to find out how much is left to reach $20:
$20 (initial amount) − $18 (value of bills) = $2
You need to make up this remaining $2 with quarters. Since each quarter is worth $0.25 (25 cents), we divide the remaining amount by the value of each quarter to find out how many quarters you need:
$2 ÷ $0.25 per quarter = 8 quarters
Therefore, you need 8 quarters to complete the conversion to $20.
15 arches decreased by 80%
If it decreases by 80٪, then only 20٪ remains.
15×20٪=15×20/100=15×0.2=3
Answer: 3
Answer:
3 arches
Step-by-step explanation:
Given
15 arches decreased by 80%.
First get 80% of 15 arches
That’s 80%/100% x 15
0.8 x 15
12 arches
Now subtract 12 arches from 15 arches to get the decrease
Decrease = (15 - 12) arches
= 3 arches
Therefore, 80% decrease of 15 inches is equal to 3 arches
3 fifths÷7 eighths please help
Answer:
24/35
Step-by-step explanation 3/5 times 8/7 equals 24/35
Rosario sells bicycle wheels in packages of 2. If a store order 46 wheels.How many packages will she send?
Step-by-step explanation:
i hope this helps
A band director needs to purchase new uniforms. The ratio of small to medium to large uniforms is 3:4:6. If there are a total of 260 uniforms to purchase, how many will be small?
Answer:
60
Step-by-step explanation:
3:4:6
Add:
3+4+6=13
3:4:6=13
?:?:?=260
Divide:
260/13=20
Multiply 3 and 20:
60
SO there are 60 small uniforms
What is the solution of the system of equations?
5x + 4y = -22
2x – 3y = 5
Answer:
y = 3
x =7
Step-by-step explanation:
to solve this system of equations using substitution method we say, let
5x + 4y = -22 .................... equation 1
2x – 3y = 5...................... equation 2
from equation 2
2x - 3y = 5
2x = 5 + 3y
divide both sides by 2
we have;
2x/2 = (5+3y)/2
x =(5+3y)/2................................ equation 3
put x = (5+3y)/2 in equation 1
5x + 4y = -22 .................... equation 1
5(5+3y)/2 + 4y = -22
(25 + 15y)/2 + 4y = -22
multiply through by 2
25 + 15y + 8y = -44
25 + 23y = -44
collect the like terms
23y = -44 - 25
23y = -69
divide both sides by 23
23y/23 = -69/23
y = 3
put the value of y= 3 into equation 3
x =(5+3y)/2................................ equation 3
x = (5+3(3)]/2
x = 5+9/2
x =14/2
x =7
expression related to -1/3(6x+15)-3
Answer:
x = -4 and -2x - 8
Step-by-step explanation:
Step 1: Distribute
-1/3(6x + 15) - 3
-6/3x - 15/3 - 3
-2x - 5 - 3
-2x - 8
Step 2: IF NEEDED SOLVE FOR X
-2x - 8 + 8 = 0 + 8
-2x / -2 = 8 / -2
x = -4
Answer: x = -4 and -2x - 8
Which expression is equivalent to StartRoot negative 80 EndRoot?
Answer:
[tex]4i\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{-80}[/tex]
[tex]\sqrt{80*i^2}[/tex]
i^2 is -1
[tex]i\sqrt{80}[/tex]
[tex]i\sqrt{4^2 * 5}[/tex]
[tex]4i\sqrt{5}[/tex]
Answer: [tex]4i\sqrt{5}[/tex]
Answer:
[tex]4i\sqrt{5}[/tex]
Step-by-step explanation:
£150 is divided between David, Mark & Henry so that David gets twice as much as Mark, and Mark gets three times as much as Henry. How much does David get?
Answer:
David receives £90
Step-by-step explanation:
Let David's share be D
Let Mark's share be M
Let Henry's share be H
From the question, we obtained the following data:
David gets twice as much as Mark i.e
D = 2M
M = D/2
Mark gets three times as much as Henry i.e
M = 3H
H = M/3
H = (D/2) /3
H = D/6
The sum of their shares is £150 i.e
D + M + H = 150
D + D/2 + D/6 = 150
Multiply through by 6 to clear the fraction
6D + 3D + D = 900
10D = 900
Divide both side by the coefficient of D i.e 10
D = 900/10
D = 90
Therefore, David receives £90
solve for z
-p(d+z)=-2z+59
Answer:z=(pd+59)/(2-p)
Step-by-step explanation:
-p(d+z)=-2z+59
Open bracket
-pd-pz=-2z+59
Collect like terms
2z-pz=pd+59
Factor out z
z(2-p)=pd+59
Divide both sides by (2-p)
z(2-p)/(2-p)=(pd+59)/(2-p)
z=(pd+59)/(2-p)
30 POINTS FOR ANSWER!!
2 numbers sum 120 and product 400
INSTANT ANSWER NEEDED
Answer:
2X+20 = 400
Help please! Thank you
Solve for x: 4/7 = x-1/12
To solve for x in the equation 4/7 = x-1/12, combine the fractions, cross multiply, and solve to find x=3 and x=-7.
Explanation:Solve for x: 4/7 = x-1/12
To solve for x, first combine the fractions on the right side: 4/7 = (12x - 1)/12. Then, cross multiply to get 12*4 = 7*(12x - 1). Solve for x to find x=3 and x=-7.
By substituting these values back into the original equation, which is x is equal to (12x-1)/12, you can verify these solutions.
A cereal company packages 305.50 lbs of cereal an hour. Each cereal box contains 3.25 lbs of cereal. How many boxes of cereal are packaged in an 812 -hour day?
A
A) 752 boxes
B) 757 boxes
C
C) 799 boxes
D) 858 boxes
In an 812-hour day, a cereal company that packages 305.50 lbs of cereal an hour would package approximately 76,331 boxes of cereal, given each box contains 3.25 lbs of cereal. The provided options in the question do not match this result.
The subject of this question is Mathematics, specifically division used in a real-world context regarding a cereal company's packaging process. To find the number of cereal boxes produced in an 812-hour day, we need to divide the total weight of cereal packed in a day by the weight of cereal in each box.
Firstly, we find out the total amount of cereal produced by multiplying the hourly rate by the number of hours. This will give us: 305.50 lbs/hour x 812 hours = 248,071 lbs.
Next, we divide the total amount of cereal by the weight of cereal in each box to find the number of boxes. Therefore, 248,071 lbs ÷ 3.25 lbs/box = 76,331 boxes.
None of the options (A) 752 boxes, (B) 757 boxes, (C) 799 boxes, (D) 858 boxes match our result. There might be an error in the question or the choices provided.
Learn more about Division in Real-world Context here:https://brainly.com/question/35100561
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there are 110 calories per 28.4 grams of cereal X. find how many calories are in 42.6 grams of the cereal
Answer:
165 calories
Step-by-step explanation:
110 cal/28.4 g in Cereal X
How m any cals in 42.6 g of Cereal X
110/x=28.4/42.6
28.4x=4686
x=165
Therefore, 165 calories
The number of calories in 42.6 grams of cereal X will be 165 calories.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
There are 110 calories per 28.4 grams of cereal X. Then the number of calories in each gram is calculated as,
Rate = 110 / 28.4
Rate = 275 / 71 calories per gram
Then the number of calories in 42.6 grams of the cereal X will be given as,
⇒ (275 / 71) x 42.6
⇒ 275 x 0.60
⇒ 165
The number of calories in 42.6 grams of cereal X will be 165 calories.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
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what Is x if y=2x+7?
Answer:
x = (y - 7)/2
Step-by-step explanation:
from the question given y=2x+7 , so we are to find the value of x now we first make x the subject of the formulae from y=2x+7
y=2x+7............. equation 1
y- 7 = 2x
divide both sides by 2
(y-7)/2= 2x/2
x = (y - 7)/2
to check if your answer is correct
put the value of x in to equation 1
y=2x+7............. equation 1
y = 2[ (y-7)/2] + 7
y = y - 7 + 7
y = y.......... proved