POWER TO A POWER
(ax) y =
When raising a base with an exponent to
another exponent, keep the
and
the exponents.
A number raised to a power represents a product where the same number is used as a repeated factor. The number is called the base and the power is given by the exponent. The base is the repeated factor and the exponent counts the number of factors. An exponent is that we are dealing with products and multiplication.
In the expression bn, b is the base and n is the exponent.
The Power Rule for Exponents: (am)n = am*n.
To raise a number with an exponent to a power, multiply the exponent times the power.
Negative Exponent Rule: x–n = 1/xn.
Invert the base to change a negative exponent into a positive.
Zero Exponent Rule: x0 = 1, for .
Any non-zero number raised to the zeroth power is 1.
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Children shorter than 48 inches get into the water park free. Howard is currently 32 inches tall. He grows approximately 3 inches per year. Write an inequality to represent the number of years, y, that he can get in free.
Answer:
5 year
3 inches every year 48 minus 32 equals 16 3 Inches divided into 16 equal 5.333333 round it equals 5 years y = 5 years
which point is the solution-2x +3y>1 -5x+6y..
A point is the solution of the inequality expression given as: -2x + 3y > 1 - 5x + 6y is (0, -2/3)
How to determine the point is the solution?The inequality expression is given as:
-2x + 3y > 1 - 5x + 6y
Collect the like terms in the above expression
So, we have:
3y - 6y > 1 + 2x - 5x
Evaluate the like terms in the above expression
So, we have:
-3y > 1 - 3x
Divide both sides by -3
y < -1/3 + x
Let x = 0
So, we have
y < -1/3
This means that a point in the solution is
(x, y) = (0, < -1/3)
-2/3 < -1/3
So, we have
(x, y) = (0, -2/3)
Hence, a point is the solution of the inequality expression given as: -2x + 3y > 1 - 5x + 6y is (0, -2/3)
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4. The
sum of a number z and 16.2 is at most 30.
z + 16.2 ≤ 30
z ≤ 13.8
1. The total length of the stage is 76 feet.
If the trap doors are centered across the
stage, what is the distance from the left
side of the stage to the first trap door?
3. Anna is 26 feet high on a rock-climbing
wall. She descends to the 15-foot mark,
rests, and then climbs down until she
reaches her friend, who is 8 feet from
the ground. How many feet has Anna
descended?
2. An actor starts at point A, walks across
the stage, and then stops at point B
before disappearing through the trap door.
How far does he walk across the stage?
Choose the best answer.
5. Jordan wants to adjust the shelves in his bookcase so that
there is twice as much space on the bottom shelf as on the
top shelf, and one and a half times more space on the
middle shelf as on the top shelf. If the total height of
the bookcase is 0.9 meter, how much space is the
middle shelf on?
A 0.2 m
B 0.3 m
C 0.4 m.
D 0.5 m
6. In a rowing race, the distance between
the teams in first and second place is 5.7
meters. The distance between the teams
in second and third place is one-third that
distance. How much farther ahead is the
team in first place than the team in third?
F 7.6 m
H 2.5 m
G 5.7 m
J 1.9 m
4. Jamilla has a piece of ribbon that is
48.5 centimeters long. For her scrapbook,
she cuts it into two pieces so that one
piece is 4 times as long as the other.
What are the lengths of the pieces?
7. On a subway route, station C is located
at the midpoint between stations A and D. Station B is located at the
midpoint between stations A and C. If the distance between stations A and D
is 2.4 kilometers, what is the distance
between stations B and D?
A 0.3 km
C 1.2 km
B 0.6 km
D 1.8 km
The distance from the left side of the stage to the first trap door is 24 3/4.
given;
total lenght of the stage is 76 feet.
Anna is 26 feet high on a rock-climbing.
here we have to substract 76-26 1/2.
=76-26 1/2
=49 1/2/2
=24 3/4
Distance is a scalar quantity. The distance of an object can be defined as the complete path travelled by an object. For example. if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km.the space between the two points are called distance
Distance is a scalar quantity. The distance of an object can be defined as the complete path travelled by an object. For example. if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km..
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i need help with this please
Answer:212
Step-by-step explanation: 36 plus 36 40 plus 40 29 plus 29 19 plus ten then add the sums then u get 212
11 = −5+y
Solve for Y
Answer:
y=16
Step-by-step explanation:
11 = −5+y
Solve for Y
Add 5 to each side
11+5 = -5+y+5
16 = y
y=16
Need help badly, I also need to know how you got the answer.
Answer:
-1/5
y=-1/5 x-8
-1/5 is the slope
Step-by-step explanation:
-1/5
Formula- y=mx+b
The slope-intercept form is
y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Rewrite in slope-intercept form.
Simplify the left side
Simplify each term.
Combine 1/8 and x.
x/9+5y/8=-5
Subtract x/8 from both sides of the equation.
5y/8=-5-x/8
Multiply both sides of the equation by8/5.
8/5.5y/8=8/5(-5-x/8)
Simplify both sides of the equation.
Simplify the left side.
Simplify 8/5.5y/8
y=-x/5-8
y=-1/5 x-8
Step-by-step explanation:
Given equation:
1/8x + 5/8y =-5
Now write it in standard form like ax+by+c=0
1/8x + 5/8y + 5= 0
Now,slope of line (m) = -a/b
here value of a is 1/8 and value of b is 5/8
now by formula..
-(1/8)÷(5/8) = m(slope)
-1/8 × 8/5 = m
-1/5 = m
here ia your answer
the sum of two numbers is 51, five times the larger number decreased by 7 equals one, more than 8 times the smaller number. find the numbers
Answer: A=32 B=19
Step-by-step explanation:
A rectangular box with a square base has a total surface area of 100cm^2. if x is the length of a side of the base, what is the volume of the box in terms if x?
The volume of the box in terms of x will be : [tex]\frac{50x-x^{3} }{2} cm^{3}[/tex]
We know, Total surface area of a cuboid is: 2(l*b + b*h + h*l)
and it is given that TSA is 100cm^2, the length of the base which is in a square shape is x. So, length l = breadth b = x, and taking height h = y
We need to find out the value of y for finding out the volume of the box.
Putting these values in the formula for TSA,
=> 2(x*x + x*y + x*y) = 100
=> 2(x^2 + 2xy) = 100 => y = (50-x^2)/2x
Put this value of y in the formula for volume.
The volume of Cuboid is : l*b*h
=> x*x*{(50-x^2)/2} => x^2{(50-x^2)/2x}
=> (50x - x^3)/2
Hence, the volume for the box is [tex]\frac{50x-x^{3} }{2} cm^{3}[/tex]
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An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, P, who contracted the flu t days after it broke out is given by the model P = -2²+ 17t + 180, where 1 st≤ 6. Find the day that 210 students had the flu. Recall that the restriction on this at most 6.
Submit Answer
Answer:
At the 3rd day 160 students caught flu.
Step-by-step explanation:
Consider the provided model P = − t ² + 13t + 130 where 1 ≤ t ≤ 6
The total number of students is represents by P.
We need to find the day that 160 students had the flu.
Substitute the value of P=160 in above formula.
Hence the value of t=10 or t=3
But it is given that 1 ≤ t ≤ 6, Therefore select t=3
Hence, at the 3rd day 160 students caught flu.
The pie chart represents the proportions of how Henry spent the £720 he took on holiday.
What fraction of his money did he spend on drink?
Give your answer in its simplest form.
Answer:
£124
Step-by-step explanation:
first of all, you're meant to add all the figures given on the pie chart, which is 29+137+58+62+74 and that will give you a total of 360 degrees
so, you say 360 degrees is equal to the total amount of money he spent, which is £720, what about 62 degrees
therefore, you just do (62×720)÷360
that will give you £124
What is the solution (x,y) to the system of equations above?
Answer:
B
Step-by-step explanation:
Evaluate the function.
f(x) = x² + 2x + 6
Find f(-7)
Answer: f(-7)=41
Step-by-step explanation:
f(x) = x² + 2x + 6
f(-7)=(-7)² + 2(-7) + 6
f(-7)=49-14 + 6
f(-7)=35 + 6
f(-7)=41
Answer:
f(-7) = 41
Step-by-step explanation:
f(x) = x² + 2x + 6
In order to find f(-7) ,we just need to substitute x in the expression of the function f by -7.
Then
f(-7) = (-7)² + 2(-7) + 6
= 49 - 14 + 6
= 35 + 6
= 41
If the polynomial function f(x)=(x+1)(x+3)9x-4) is rewritten in standard form, the degree would be ______ and the constant term would be _______.
.
If the polynomial function f(x)=(x+1)(x+3)9x-4) is rewritten in standard form, the degree would be 3 and the constant term would be 12 .
What is polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions. We can define a polynomial's degree and provide a generic definition for it.f(x)=(x+1)(x+3)9x-4)
f(x ) = 3x³ + 36x² + 27x - 4x² - 16x - 12
f(x) = 3x³ + 32 x² + 11x - 12
in above function highest degree would be 3 and constant -12 .
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.
Try It
Which are solutions of the equation 4x² - 7x= 3x + 24? Check all that apply.
We get that the solution for the equation 4 x² - 7 x = 3 x + 24 as 4 or 3 / 2.
We are given an equation:
4 x² - 7 x = 3 x + 24
We need to solve it for x.
4 x² - 7 x - 3 x = 24
4 x ² - 10 x = 24
4 x ² - 10 x - 24 = 0
4 x² - 16 x + 6 x - 24 = 0
4 x( x - 4) + 6( x - 4) = 0
(x - 4)(4 x + 6) = 0
Solving for x, we get that:
x = 4 or x = 6 / 4 = 3 / 2.
Therefore, we get that the solution for the equation 4 x² - 7 x = 3 x + 24 as 4 or 3 / 2.
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Find the value of x in the given diagram.
Answer:
The value of x is 125°.==================================
We see the exterior angle measures given with one unknown.
Recall the sum all exterior angles of a polygon is 360°.
Set up equation and find the unknown value:
70 + 65 + 60 + 40 + x = 360235 + x = 360x = 360 - 235x = 125a small furniture factory makes three types of tables coffee tables dining tables and end tables. The factory needs to make 54 tables each day. The number of dining tables made per day should equal the number of coffee tables and end tables combine. The number of coffee tables maybe she should be three more than the number of end tables. write and solve a system equation to find the numbers of table of each type of factory should make each day.
Using a system of equations, the numbers of each machine made are given as follows:
Dining: 19Coffee: 19End: 16.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the variables are given as follows, considering the situation described:
Variable x: Number of dining tables made.Variable y: Number of coffee tables made.Variable z: Number of end tables made.The factory needs to make 54 tables each day, hence:
x + y + z = 54.
The number of dining tables made per day should equal the number of coffee tables, hence:
x = y.
Then, on the first equation:
2y + z = 54.
The number of coffee tables should be three more than the number of end tables, hence:
y = z + 3.
Replacing in the equation 2y + z = 54:
2(z + 3) + z = 54
3z = 48
z = 16.
Then:
y = z + 3 = 19.x = y = 19.The numbers of each machine made are given as follows:
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I need help please!!
Answer:
9.6*10^-12
Step-by-step explanation:
To calculate this, you will do the mass of 2 times 10^(-12) gram. So, 2*(10)^-12. Then we know 30 hours = 480,000,000 bacteria.
So now now you calculate the mass, 480,000,000 * 2(10)^-12 which gives you 9.6*10^-4.
Sorry if it sounds confusing! I hope this helps, have a good day! :D
Solve the quadratic equation by completing the square.
x²+18x+79=0
Step-by-step explanation:
completing the square means finding an expression
(x + a)² = b²
or
(x - a)² = b²
(x + a)² = x² + 2ax + a²
(x - a)² = x² - 2ax + a²
because of the "+ 18x" in the original equation we know that we are looking for (x + a)².
now, let's compare the different terms :
x² = x²
18x = 2ax
18 = 2a
a = 9
so, the complete square would look like
(x + 9)² = x² + 18x + 81
but we have only "+ 79" in the original equation.
so, we add the missing 2 (to both sides to keep the equation true)
x² + 18x + 79 + 2 = 0 + 2
x² + 18x + 81 = 2
(x + 9)² = 2
x + 9 = ±sqrt(2)
x1 = sqrt(2) - 9
x2 = -sqrt(2) - 9
x = sqrt(2) - 9, -sqrt(2) - 9
yes, every quadratic equation has 2 solutions.
as every cubic equation has 3 solutions.
and so on.
Can someone explain why this is a false equation
Step-by-step explanation:
I think the answer is just no solution to begin with since the value of an absolute value will never be a negative number or in this case less than -2. therefore the equation is false
The graph of y=
-2x²5x+2 is drawn below
Draw a suitable line to solve -2x² - 5x + 2 = -5
Answer:
x = 1 and x = -3.5
Step-by-step explanation:
y = -2x² -5x + 2
-2x² -5x + 2 = -5
which means y = -5
Draw the line on y = -5 like the green line in the attached file
and see where this line intersects with the graph
the values are:
x = 1 and x = -3.5
Answer:
Draw a line at y = -5.
x ≈ -3.5
x ≈ 1
Step-by-step explanation:
Given equation:
[tex]y = -2x^2 - 5x + 2[/tex]
This is the equation of the graphed parabola.
To solve the equation [tex]-2x^2 - 5x + 2 = -5[/tex] draw a line at y = -5 and find the points of intersection of the two graphed equations.
From inspection of the graph, the x-values of the points of intersection are:
x ≈ -3.5x ≈ 1Solving algebraically
Add 5 to both sides of the equation:
[tex]\implies -2x^2-5x+2+5=-5+5[/tex]
[tex]\implies -2x^2-5x+7=0[/tex]
Factor out -1 from the left side:
[tex]\implies -1(2x^2+5x-7)=0[/tex]
Divide both sides by -1:
[tex]\implies 2x^2+5x-7=0[/tex]
Find two numbers that multiply to -14 and sum to 5: 7 and -2
Rewrite b as the sum of these two numbers:
[tex]\implies 2x^2+7x-2x-7=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(2x+7)-1(2x+7)=0[/tex]
Factor out the common term (2x + 7):
[tex]\implies (x-1)(2x+7)=0[/tex]
Apply the zero-product property:
[tex](x-1)=0 \implies x=1[/tex]
[tex](2x+7)=0 \implies x=-\dfrac{7}{2}=-3.5[/tex]
Deb wants to organize a group of friends to go to a karaoke studio Friday night. She must pay $30 to reserve a private karaoke room plus $5 for each person in the group. She also wants to have snacks for the group at a cost of $2 per person. How many people can Deb invite in order to spend a total of $65?
Fill in the blanks to create an equation to represent the situation.
blank x + 2x + blank = 65
Based on the solution below, the number of people Deb can invite in order to spend a total of $65 is 5 people.
How do we use an equation to find a number?Given:
blank x + 2x + blank = 65 ............................... (1)
Where:
x = Number of people Deb can invite
First blank with x variable = 5; since Deb must pay an additional $5 for each person in the group
Second blank without x variable = 30; since Deb $30 to reserve a private karaoke room
Substituting the relevant values into equation (1) and solving for x, we have:
5x + 2x + 30 = 65
7x = 65 - 30
7x = 35
x = 35 / 7
x = 5
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Sasha has c green notebooks. she has 6 fewer red notebooks then green notebooks. how many notebooks does sasha have in all.
The total number of notebooks on Sasha's notebook is 2c - 6.
Unitary method:
The unitary method is used to solve problems by first determining the value of a single unit and then multiplying that value by the required value.
So, this method is basically used to find the value of a unit and then the value of a required number of units.
Given,
Sasha has c green notebooks.
She has 6 fewer red notebooks then green notebooks.
So, here we need to find how many notebooks does Sasha have in all.
We know that.
Sasha has c green notebooks.
The number of red notebooks on her is
=> c − 6.
Here Sasha has either green or red notebooks.
The total number of notebooks on Sasha's notebook is
=> c + c − 6
=> 2c - 6
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find the length of each segment with the given endpoints
(3, -2) and (-4, 7)
Exact Distance: [tex]\sqrt{130}[/tex] units
Approximate Distance: 11.4018 units
===================================================
Explanation:
Use the distance formula to have the following steps
[tex](x_1,y_1) = (3,-2) \text{ and } (x_2, y_2) = (-4,7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-4))^2 + (-2-7)^2}\\\\d = \sqrt{(3+4)^2 + (-2-7)^2}\\\\d = \sqrt{(7)^2 + (-9)^2}\\\\d = \sqrt{49 + 81}\\\\d = \sqrt{130}\\\\d \approx 11.4018\\\\[/tex]
The exact distance is [tex]\sqrt{130}[/tex] units
This approximates to about 11.4018 units.
Iron has a density of 7.9 g/cm³. Gold has a density of 19.3 g/cm³.
I have a piece of metal that has a volume of 200 cm³ and a mass of 3.86 kg. Is it gold or iron?
graph the equation
picture below
please help 100 points and brainlest
Please find the value of each variable
Step-by-step explanation:
I assume these are all angles.
4x is the arc angle (at the center of the circle) between the 2 endpoints of the short triangle side (baseline).
the trials itself is isoceles, so both legs have the same length, bedclothes the arc angles between their endpoints are equal.
now, when we move the reference point of an arc angle back, back, back to the circle arc, the angle is cut in half.
so, the inner top angle of the triangle is therefore 4x/2 = 2x.
because of the isoceles nature, the second triangle inner angle at the baseline is also x.
the sum of the triangle angles is therefore
2x + x + x = 4x
and we know the sum of all angles in a triangle is always 180°.
so,
4x = 180
x = 180/4 = 45°
4x is then again 180°, and 2× 8y are then the remaining 180° of the full circle 360°.
2× 8y = 180
8y = 90
y = 90/8 = 11.25
x = 45
y = 11.25
darcy has a summer job painting houses. he is asked to paint the wooden siding on a house that is 28 feet wide and 35 feet long. the siding extends 6 feet up the side of the house. a) what is the total surface are he must paint? b) a one gallon can of the stain that darcy is using covers approximately 225 ft squared. if darcy applies 2 coats of stain, how many cabs of stain should he buy?
Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².
Length of the house = 35 feet
width of the house = 28 feet
Height of the house = 6 feet
Total surface area = 2 l b + 2 b h + 2 h l
A = 2 (35) (28) + 2 (28) (6) + 2 (6) (35)
A = 1960 + 336 + 420
A = 2716 feet²
If he uses 2 coats of stain, the area he need to cover = 2 (2716) = 5432 feet²
Gallon of paint required = 5432 / 225 = 24.14 gallons.
Therefore, Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².
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what is this i need help ASAP
Answer:
The first and fourth statement.
Step-by-step explanation:
1. - 3 - 12/3 + 5
= - 3 - 4 + 5
= - 7 + 5
= - 2
- 2 < 0
4. 4 - 2 - 3/2
= 2 - 3 / 2
= 1 / 2
1 / 2 > 0
Hope this helped! ^^
Sidenote: If you need me to explain for 2, 3 and 5, comment below this and I'll explain.
