Answer:
A) (1/9)^8
Step-by-step explanation:
9^-5 × 9^-3 =
Rule: a^m * a^n = a^(m + n)
= 9^-8
Rule: (a^m)^n = a^(mn)
= (9^-1)^8
Rule: a^-m = 1/a^m
= (1/9)^8
Answer: A) (1/9)^8
Need help please , Find FE if TE=8
one evening 1500 concert tickets were sold for the Jazz Fest. Tickets cost $30 for covered pavillion seats and $10 for lawn seat. Total reciepts were $32,000. How many tickets of each type were sold?
14) write the equation to the line parallel to y=3x-5 that goes through the point (-2,-7) using any form
Answer:
The equation of this line would be y = 3x - 1
Step-by-step explanation:
In order to find this equation we must first find the slope of the original line. The original slope (the coefficient of x) is 3, which means the new slope will also be 3 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line.
y - y1 = m(x - x1)
y + 7 = 3(x + 2)
y + 7 = 3x + 6
y = 3x - 1
The cost to rent a lodge for a family reunion is $975 if 65 people attend and pay the same price how much does each person pay?
Answer:
15
Step-by-step explanation:
you have to divide 975/65=$15 per person
A square has a perimeter of 76 inches. Complete parts (a)-(c) (a) what is the length of each side? Each side has length of?
a - side of the square
4a - the perimeter of a square
76 in - the perimeter of a square
The equation:
4a = 76 divide both sides by 4
a = 19 in.
Answer: Each side has length 19 inches.(a) The length of each side is equal to 19 inches.
How to calculate the perimeter of a square?In Mathematics and Geometry, the perimeter of a square can be calculated by using the following formula;
P = 4s
Where:
P is the perimeter of a square.s is the side length of a square.By substituting the given parameters into the formula for the perimeter of a square, we have the following;
Perimeter of a square, P = 4s
76 = 4s
s = 76/4
s = 19 inches.
Therefore, each side has a length 19 inches.
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PLEAS HELP ME ASAP (5 points)
Answer:
m<1=134
m<2=46
x=13
Step-by-step explanation:
Angle 2 can be set equal to 180 since the angle is supplementary after transferring angle 2 to its alternate interior.
4x-6+10x+4=180
Combine like terms
14x-2=180
Solve for x
14x=182
x=13
Now plug x in for the two angles
10(13)+4
130+4
m<1=134
4(13)-6
52-6
m<2=46
134+46=180, verified
A ball is thrown vertically upward from the top of a
building 96 feet tall with an initial velocity of 80 feet
per second. The distance, s (in feet), of the ball from
the ground after t seconds is given by the function:
() = 96 + 80 − 16
2
a. How long does it take for the ball to reach its
highest point?
b. What is the maximum height the ball reaches?
Answer:
It takes 2.5 seconds for the ball to reach its highest point
Maximum height is 196 feet
Step-by-step explanation:
h(t) = -16t^2+80t +96
a=-16, b= 80, c=96
To find the maximum height , we need to find vertex
Let find x coordinate of vertex
[tex]t=\frac{-b}{2a}[/tex]
Plug in the values
[tex]t=\frac{-80}{2(-16)}= 2.5[/tex]
It takes 2.5 seconds for the ball to reach its highest point
Now plug in 2.5 for t to find maximum height
[tex]h(t) = -16t^2+80t +96[/tex]
[tex]h(2.5) = -16(2.5)^2+80(2.5) +96=196[/tex]
Maximum height is 196 feet
The circumference of my circle is 45 inches. What is the diameter
Answer:
14.32 inches to nearest thousandth.
Step-by-step explanation:
Circumference = π * d where d = the diameter.
So 45 = π * d
d = 45 / π
= 14.32 inches
The diameter of the circle is 14.33 inches.
What is the area and circumference of a circle?The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.
Given here: The circumference of the circle as 45 inches
We know that Circumference is give by 45=2×3.14×r
2r=14.33 inches
Hence, The diameter of the circle is 14.33 inches.
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Rewrite this polynomial in terms of its simplest factors using the appropriate method: x2 − 3x − 18.
Answer:
(x - 6)(x + 3)
Step-by-step explanation:
Consider the product of the factors of the constant term which sum to give the coefficient of the x-term
product = - 18 and sum = - 3
The factors are - 6 and + 3, hence
x² - 3x - 18 = (x - 6)(x + 3)
If the area of a rectangle is 100, then the length is 25 and the width is 4. The counterexample is length = ____ width =______
Answer:
length =25 and width =4
Step-by-step explanation:
If the area of a rectangle is 100, then the length is 25 and the width is 4. The counterexample is length = 20, width = 5.
Explanation:If the area of a rectangle is 100, and the length is 25, we can find the width by dividing the area by the length: 100 ÷ 25 = 4. So the width is 4. To find the counterexample, we need to find another pair of length and width that give a different area.
Let's try length = 20 and width = 5. The area of this rectangle would be 20 × 5 = 100, which is the same as the original rectangle.
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solve for 3x+4=9x+3
A. 1/3
B. 1/6
C. -1/3
D. None of the above.
50 POINTS PLEASE ANSWER QUICK Which function has the greatest value when x is equal to 0? A. x y 3 3 4 6 5 9 B. y = 4x – 7 C. 12x + 6y = 30 D. A linear function that goes through point 1, negative 1 and point 0, 4
Answer:
C. 12x + 6y = 30
Step-by-step explanation:
A. x 3 4 5
y 3 6 9
We need to make and equation
slope = (y2-y1)/(x2-x1)
= (9-3)/(5-3)
6/2
3
The slope is 3
Using point slope form
y-y1 = m(x-x1)
y-3 = 3(x-3)
Distribute
y-3 = 3x-9
Add 3 to each side
y = 3x-9+3
y = 3x-6
Let x=0
y = 0-6
y = -6
B. y = 4x – 7
Let x = 0
y = 0-7
y = -7
C. 12x + 6y = 30
Let x = 0
12(0) + 6 y = 30
6y = 30
Divide by 6
6y/6 = 30/6
y =5
D. A linear function that goes through point 1, negative 1 and point 0, 4
The point ((0,4) says when x=0 y=4
y =4
y=5 is the max so the answer is C
fred buys a video game disk for $8 after a 20% discount. what is the original price?
Find the average rate of change for f(x)=x^2-3x-10 from x=-5 to x=-10
Answer:
-18
Step-by-step explanation:
f(x) = x² - 3x -10
f(-10) = (-10)² – 3(-10) – 10
f(-10) = 100 + 30 - 10
f(-10) = 120
f(-5) = (-5)² – 3(-5) – 10
f(-5) = 25 + 15 - 10
f(-5) = 30
=====
The average rate of change is the slope m of the straight line joining the two points.
m = (y₂ - y₁)/(x₂ - x₁)
m = (30 - 120)/(-5 – (-10))
m = -90/(-5+10)
m = -90/5
m = -18
Gustave measured his pace and determined that for him, s steps make up one mile. One day Gustave walked 6300 steps, which was 3 miles. Write an equation to describe this situation.
Answer:
6300 = s * 3
s=2100
Step-by-step explanation:
s =steps per mile
steps = steps per miles * miles
6300 = s * 3
This is the equation.
Divide each side by 3.
6300/3 = s3/3
2100 /s
Answer:
6300/3=s
s=2100
Step-by-step explanation:
six thousand three hundred over 3 equals s
s equals two thousand one hundred
Two factors are multiplied and their product is 34.44 one factor is a whole number what is the least number of decimal places in the other factors explain
Answer:
2 decimal places
Step-by-step explanation:
When you multiply two decimals, the largest possible number of decimal places in the product is the sum of the number of the decimal places of the factors. Here, the product has 2 decimal places. One factor is an integer, so it has no decimal places. The other factor must have at least 2 decimal places.
4^x+2=1/2 solve for x (log equation)
[tex]\log_ab=c\iff a^c=b\\\\4^{x+2}=\dfrac{1}{2}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\(2^2)^{x+2}=2^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(x+2)}=2^{-1}\iff2(x+2)=-1\qquad\text{use distributive property}\\\\(2)(x)+(2)(2)=-1\\\\2x+4=-1\qquad\text{subtract 4 from both sides}\\\\2x=-3\qquad\text{divide both sides by 2}\\\\\boxed{x=-1.5}[/tex]
how do u graph x>-6 on a line graph?
<, > - opened circle
≤, ≥ - closed circle
<, ≤ - draw line to left
>, ≥ - draw line to right
Answer in the attachment.
<,> - dotted line
≤, ≥ - solid line
<, ≤ - shadow to left
>, ≥ - shadow to right
x = -6 - its a vertical line
a triangular prism has a volume of 240 cubic meters which of the measurements below are not possible dimensions for the area of the base and the height of the prism
Answer:
I) B = 20 m², h = 4 m are NOT possible dimensions for the area of the base and the height of the prism.
Step-by-step explanation:
Given that the triangular prism has a volume = 240 m³, we can use the formula for the volume of a triangular prism to check the given answers for possible dimensions. V = Bh, where B = the area of the base and h = height of the prism. In this case, we simply need to multiply each of the given dimensions together to see if they equal 240 m³:
F) B = 48 m², h = 5 m: v = 48 x 5 = 240 m³ (possible)
G) B = 24 m², h = 10 m; v = 24 x 10 = 240 m³ (possible)
H) B = 12 m², h = 20 m: v = 12 x 24 = 240 m³ (possible)
I) B = 20 m², h = 4 m: v = 20 x 4 = 80 m³ (NOT possible)
Which is 14% of 50 0.70,7,57,64,or70
Answer:7
Step-by-step explanation: 14%=14/100. (14/100)*50=7
Answer:
7
Step-by-step explanation:
to find your answer multiply .14 (14 as a fraction) by 50 to get 7
A group of scientists are studying a new species of insects. They observe the patterns of 6 insects. The scientists find that the insect population, x, is growing exponentiall 20% per month. Which equation can be used to find how many months, t, will it take for there to be a population of 477 insects?
Answer:
(B) [tex]477=6(1+0.20)^t[/tex]
Step-by-step explanation:
we can use formula
[tex]P(t)=P_0(1+r)^t[/tex]
where
Po is the initial population
r is the growth rate
t is the time in months
We are given
initial population of insects
so, Po=6
The scientists find that the insect population, x, is growing exponentially 20% per month
so, r=0.20
now, we can plug these values
[tex]P(t)=6(1+0.20)^t[/tex]
there to be a population of 477 insects
so, P(t)=477
now, we plug it
and we get
[tex]477=6(1+0.20)^t[/tex]
Please help; I don't understand how to solve these inequality problems.
For each problem:
Solve the combined inequality.
Explain step by step how you solved it.
State whether the combined inequality is a conjunction or disjunction and explain.
Determine which letter is in the solution.
1. -4≤x+2<1
2. 5x-4>46" or " 4x≤3x+6
3. 10≤2x-4≤20
4. 6-2x≤12" or " 7+2x<-11
5. 5≤2x+1≤11
6. 2/3 x-20≤16" or " x/3+10≥32
7. 10<1/4 (x+1)≤11
Answer:
1. -6 ≤ x < -1, conjunction
2. x > 10 or x ≤ 6, disjunction
3. 7 ≤ x ≤ 12, conjunction
4. x ≥ -3 or x < -9, disjunction
Step-by-step explanation:
These inequalities are called "compound inequalities." Each compound inequality is made up of two simple inequalities.
A compound inequality of the type 5 < x < 8 means x > 5 and x < 8. Since the word between the simple inequalities is "and", it is a conjunction.
A compound inequality of the type "x < 3 or x > 12" uses the word "or" between the simple inequalities. It is called a disjunction.
1.
-4 ≤ x + 2 < 1
Conjunction
For this type of inequality, do what you need to do to get x alone in the middle section. Do the same to all three "sides" of the inequality.
The middle section has x + 2. We want x alone,s o w must subtract 2. We subtract 2 from all three sides.
-4 - 2 ≤ x + 2 - 2 < 1 - 2
-6 ≤ x < -1
2. 5x - 4 > 46 or 4x ≤ 3x + 6
Disjunction
In this type of compound inequality, solve each inequality by itself, and always keep the word "or" between the inequalities.
5x - 4 > 46 or 4x ≤ 3x + 6
5x - 4 + 4 > 46 + 4 or 4x - 3x ≤ 3x - 3x + 6
5x > 50 or x ≤ 6
x > 10 or x ≤ 6
3. Similar to problem 1.
Conjunction
10 ≤ 2x - 4 ≤ 20
Add 4 to all sections.
14 ≤ 2x ≤ 24
Divide all sections by 2.
7 ≤ x ≤ 12
4.
6 - 2x ≤ 12 or 7 + 2x < -11
Disjunction
-2x ≤ 6 or 2x < -18
x ≥ -3 or x < -9
Answer:
1. -6≤x<-1
conjunction
2.x>10 or x≤6
Disjunction
3.7≤x≤12
Conjunction
4.x ≥-6 or x < -6
Disjunction
5.2≤x≤5
Conjunction
6. x ≤ 54 or x≥66
Disjunction
7. 39< x≤43
Conjunction
Step-by-step explanation:
conjunction is "and" like a sandwich between 2 points
disjunction is " or" like boat oars with a gap for the boat in the middle
1. -4≤x+2<1
Subtract 2 from all sides
-4-2≤x+2-2<1 -2
-6≤x<-1
conjunction
2. 5x-4>46" or " 4x≤3x+6
Add 4 to each side Subtract 3x from each side
5x-4+4 > 46+4 4x-3x≤3x-3x+6
5x >50 x≤6
Divide by 5
5x/5 >50/5
x>10 or x≤6
Disjunction
3. 10≤2x-4≤20
Add 4 to all sides
10≤2x-4≤20
10+4 ≤2x-4+4≤20+4
14≤2x≤24
Divide by 2 on all sides
14/2≤2x/2≤24/2
7≤x≤12
Conjunction
4. 6-2x≤12" or " 7+2x<-11
Subtract 6 from each side Subtract 7 from each side
6-6-2x≤12 or " 7-7+2x<-11-7
-2x≤12 2x<-18
Divide by -2 Divide by 2
Flips the inequality
-2x/-2≥12/-2 2x/2 <-18/2
x ≥-6 or x < -6
Disjunction
5. 5≤2x+1≤11
Subtract 1 from all sides
5-1≤2x+1-1≤11-1
4≤2x≤10
Divide all sides by 2
4/2≤2x/2≤10/2
2≤x≤5
Conjunction
6. 2/3 x-20≤16" or " x/3+10≥32
Add 20 from each side Subtract 10 from each side
2/3 x-20+20 ≤16+20 x/3 +10-10 ≥32 -10
2/3 x ≤36 x/3≥22
Multiply by 3/2 on each side Multiply by 3 on each side
3/2 * 2/3x ≤ 36*3/2 x/3*3 ≥22 *3
x ≤ 54 or x≥66
Disjunction
7. 10<1/4 (x+1)≤11
Multiply all sides by 4
4*10<1/4*4 (x+1)≤11*4
40< (x+1)≤44
Subtract 1 from all sides
40-1< (x+1-1)≤44-1
39< x≤43
Conjunction
How to write z times 5 as an algebraic expression
Answer:
z5
Step-by-step explanation:
Answer:
z is your answer! :)
What is the completely factored form of x4 + 8x2 – 9? (x + 1)(x – 1)(x + 3)(x + 3) (x+1)(x+1)(x+3){x^2+9} (x2 – 1)(x + 3)(x – 3) (x + 1)(x + 1)(x + 3)(x + 3)
The complete factor of the expression x⁴ + 8x² – 9 will be (x² + 9), (x - 1), and (x + 1). Then the correct option is B.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The expression is given as,
⇒ x⁴ + 8x² – 9
Factorize the expression, then we have
⇒ x⁴ + 8x² - 9
⇒ x⁴ + 9x² - x² - 9
⇒ x²(x² + 9) - 1(x² + 9)
⇒ (x² + 9)(x² - 1)
⇒ (x² + 9)(x - 1)(x + 1)
The complete factor of the expression x⁴ + 8x² – 9 will be (x² + 9), (x - 1), and (x + 1). Then the correct option is B.
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The complete question is attached below.
What is the volume of the rectangular prism? The height is 12 1/2 and the width is 8 and the length is 2
Answer:
200
Step-by-step explanation:
8x2=16
12 1/2x16=200
Let f(x) = x2 + 3x − 4 and g(x) = x + 5. Find f(x) ⋅ g(x).
A) x3 + 3x2 + 16x − 20
B) x3 + 5x2 + 14x − 20
C) x3 + 8x2 + 11x − 20
D) x3 + 9x2 + 19x − 20
Answer:
[tex]x^3 + 8x^2 + 11x-20[/tex]
Step-by-step explanation:
f(x) = x^2 + 3x − 4
g(x) = x + 5
To find f(x) * g(x) we multiply f(x) with g(x)
[tex]f(x) * g(x) = (x^2 + 3x -4) * (x+5)[/tex]
First multiply each term in f(x) and multiply with x+5
x^2 times x+5 becomes [tex]x^3+5x^2[/tex]
3x times x+5 becomes [tex]3x^2 + 15x[/tex]
-4 times x+ 5 becomes -4x -20
so f(x) * g(x) = [tex]x^3 + 5x^2 +3x^2 + 15x -4x -20[/tex]
Combine like terms
f(x) * g(x) = [tex]x^3 + 8x^2 + 11x-20[/tex]
Answer: [C]: " x³ + 8x² + 11x − 20 " .
______________________________________________________
Step-by-step explanation:
______________________________________________________
Given: " f(x) = x² + 3x − 4 " ; and
" g(x) = x + 5 " ;
Find: " f(x) ⋅ g(x) " :
______________________________________________________
f(x) ⋅ g(x) =
" (x² + 3x − 4) (x + 5) " ;
↔ " (x + 5) (x² + 3x − 4) " ;
______________________________________________________
Note: " (a + b) (c + d + e) = ac + ad + ae + bc + bd + ae " ;
______________________________________________________
→ " (x + 5) (x² + 3x − 4)
= (x * x²) + (x * 3x) + (x*-4) + (5*x²) + (5*3x) + (5*-4) " ;
= (x³) + (3x²) + (-4x) + (5x²) + (15x) + (-20) ;
= x³ + 3x² − 4x + 5x² + 15x − 20 ;
→ Combine the "like terms" :
+ 3x² + 5x² = + 8x² ;
− 4x + 15x = + 11 x ;
______________________________________________________
→ And rewrite:
______________________________________________________
→ " x³ + 8x² + 11x − 20 " ;
______________________________________________________
→ which is: Answer choice: [C]: " x³ + 8x² + 11x − 20 " .
______________________________________________________
Hope this helps!
Best wishes!
______________________________________________________
victor is building a square patio in his backyard. the area of the patio is 150 square feet. What is the length of each side rounded to the neareth tenth?
Answer:
The length of each side is 12.2 ft
what is ten times twelve
Answer:
120
Step-by-step explanation:
A 12 foot basketball hoop has a shadow 9.6ft long. How long is the shadow of a 6ft adult standing next to the basketball hoop?
Answer:
The adults shadow is 4.8 ft
Step-by-step explanation:
We can use ratio's to solve this problem
12 ft hoop 6ft adult
-------------- = -----------------
9.6 ft shadow x ft shadow
Using cross products
12 * x = 9.6 * 6
12x = 57.6
Divide each side by 12
12x/12 = 57.6 /12
x = 4.8 ft
why should the remainder be less than the divisor
Answer:
or else we can divide again