Answer:
p > 4 if thats what ur asking.
Step-by-step explanation:
p-1>3
Add 1 to each side, it cancels out the -1
p > 4
Answer:
p>4
Step-by-step explanation:
p-1>3 given
p>4 addition property of equality
Evaluate the following without using the calculator
[tex] \cos(30) \sin( \frac{\pi}{4} ) + \frac{ \sec(60) }{3} [/tex]
[tex]\sec x=\dfrac{1}{\cos x}\to \sec60^o=\dfrac{1}{\cos60^o}\\\\\text{Use the table of values of a trigonometric functions}\\\\\cos30^o=\dfrac{\sqrt3}{2}\\\\\sin\dfrac{\pi}{4}=\dfrac{\sqrt2}{2}\\\\\cos60^o=\dfrac{1}{2}\to\sec60^o=\dfrac{1}{\frac{1}{2}}=2\\\\\text{Substitute:}\\\\\cos30^o\sin\dfrac{\pi}{4}+\dfrac{\sec60^o}{3}=\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}+\dfrac{2}{3}=\dfrac{\sqrt6}{4}+\dfrac{2}{3}\\\\=\dfrac{3\sqrt6}{3\cdot4}+\dfrac{4\cdot2}{4\cdot3}=\dfrac{3\sqrt6}{12}+\dfrac{8}{12}\\\\=\boxed{\dfrac{8+3\sqrt6}{12}}[/tex]
Provide an example of an integer that is not a whole number
Answer:
-5
Step-by-step explanation:
The integers are ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... -- all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero). Fractions and decimals are not integers. All whole numbers are integers (and all natural numbers are integers), but not all integers are whole numbers or natural numbers. For example, -5 is an integer but not a whole number or a natural number.
An example of an integer that is not a whole number is -1, as whole numbers are non-negative and -1 is negative.
The set of integers includes all the positive whole numbers, zero, and their opposites, which are the negative whole numbers. Whole numbers are defined as non-negative integers (0, 1, 2, 3, ...). Therefore, any negative integer like -1, -2, -3, and so forth, while being an integer, is not considered a whole number.
the table shows the favorite subjects of students in a recent survey?which subject did most students choose?
Answer:
Most students chose math.
Step-by-step explanation:
art 4/25,
english 13%,
math .28,
other 7%,
science 21/100,
social studies .15
1. convert all values to the same unit (I used decimal)
Art: 4/25= 0.16
English 0.13
Math: 0.28
Other: 0.07
Science: 0.21
Social studies: 0.15
2. find the highest decimal point to determine most chosen subject.
Math is highest at 0.28
The value of y is directly proportional to the value of x. If y = 288 when x = 32. What is the value of y when x = 25?
Algebra 1
Answer:
y = 225
Step-by-step explanation:
since y and x are directly proportional the equation relating them is
y = kx ← k is the constant of proportionality
to find k use the given condition y = 288 when x = 32
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{288}{32}[/tex] = 9
y = 9x ← is the equation of proportionality
when x = 25, then
y = 9 × 25 = 225
Consider the steps to simplify the expression. Which property is used to reach Step 3? Expression: -4 3/7 + 7 + (-3 4/7 )
Step 1: = -4 3/7+(-3 4/7) + 7
Step 2: = -4 + (-3/7) + (-3) + (-4/7) + 7
Step 3: = -4 + (-3/7) + (-4/7) + (-3) + 7
Step 4: = -4 + (-1) + (-3) + 7
Step 5: = -8 + 7
Step 6: = -1
A) The associate property of addition.
B) The commutative property of addition.
C) The opposite of a sum is the sum of its opposites.
D) Subtracting a number is the same as adding its inverse.
Answer:
B) The commutative property of addition.Step-by-step explanation:
Given expression :
Step 1: = -4 3/7+(-3 4/7) + 7
Step 2: = -4 + (-3/7) + (-3) + (-4/7) + 7
Step 3: = -4 + (-3/7) + (-4/7) + (-3) + 7
Step 4: = -4 + (-1) + (-3) + 7
Step 5: = -8 + 7
Step 6: = -1
In 3rd step they just swap the positions of (-4/7) and (-3) to bring the like fractions with common denominator together.
Swapping the numbers is the Commutative Property of Addition.
Therefore, correct option is B) The commutative property of addition.Why did Vanderbilt close the Albany bridge
The closing of the Albany bridge by Commodore Cornelius Vanderbilt was likely a strategic decision to protect and enhance his railroad enterprise, demonstrating the importance of controlling transportation infrastructure in the 19th century.
Explanation:Commodore Cornelius Vanderbilt, known for his vast railroad empire, consolidated several smaller railroad lines to form the powerful New York Central Railroad Company. This consolidation allowed for more efficient connections from Midwestern suppliers to eastern markets, which was of great economic importance. The closing of the Albany bridge by Vanderbilt would have been one such strategic decision to enhance his railroad network and protect the interests of his enterprise.
The incident at Ebenezer Creek, where Union General Jefferson C. Davis ordered the cutting of the pontoon bridge to strand fleeing slaves and prevent them from crossing, shows the harsh decisions made during the Civil War. While this event does not directly relate to Vanderbilt closing the Albany bridge, it demonstrates the kind of pivotal and often harsh decisions made regarding bridges and the movement of people during that era for military or strategic reasons.
If lines joined each given point on the graph to the origin, which points would be on lines that represent a unit rate greater than the one represented in the table?
Answer:
The first three, (2, 8), (3, 9) and (4, 10).
Step-by-step explanation:
The unit rate, or rate of change, is another term for the slope.
The formula for slope is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
The slope in the table would be given by
m = (22-11)/(10-5) = 11/5 = 2.2.
For the slope of the line that goes through (2, 8) and (0, 0), we have
m = (8-0)/(2-0) = 8/2 = 4. This is greater than 2.2.
For the slope of the line that goes through (3, 9) and (0, 0), we have
m = (9-0)/(3-0) = 9/3 = 3. This is greater than 2.2.
For the slope of the line that goes through (4, 10) and (0, 0), we have
m = (10-0)/(4-0)/ = 10/4 = 2.5. This is greater than 2.2.
For the slope of the line that goes through (5, 8) and (0, 0), we have
m = (8-0)/(5-0) = 8/5 = 1.6. This is not greater than 2.2.
For the slope of the line that goes through (6, 7) and (0, 0), we have
m = (7-0)/(6-0) = 7/6 = 1.16. this is not greater than 2.2.
For the slope of the line that goes through (7, 6) and (0, 0), we have
m = (6-0)/(7-0) = 6/7 = 0.86. This is not greater than 2.2.
Please help im on the verge of tears.
Set up a right triangle model for this problem and solve by using the reference table trigonometric ratio that applies.
Who gains altitude more quickly, a pilot traveling 400 mph and rising at an angle of 30 degrees, or a pilot traveling 300 mph and rising at an angle of 40 degrees?
Answer: The pilot traveling 400 mph rising at an angle 30 degrees is going to gain more altitude faster
======================================================
Explanation:
Draw out the triangles as you see in the attached image below. We'll use the sine rule because we want to tie together the unknown height (h) which is the opposite side of the reference angle, to the known hypotenuse (the speed of the aircraft)
For the first plane,
sin(angle) = opposite/hypotenuse
sin(30) = h/400
h = 400*sin(30)
h = 200
so the first plane is gaining altitude at 200 mph (each hour, the plane is 200 miles higher up)
For the second plane
sin(angle) = opposite/hypotenuse
sin(40) = h/300
h = 300*sin(40)
h = 192.836282905961
h = 192.84
which is smaller than the previous result (200)
So we see that the first plane is rising faster
Answer:
a pilot traveling 400 mph and rising at an angle of 30 degrees
Step-by-step explanation:
Marco wants to save his money to buy a new computer for school. He has $300 in his bank account. Marco has a part-time job that pays $75 per week. He plans to put all the money he earns each week into his bank account. Which of the following functions accurately models the amount of money Marco will have saved after x weeks?
Is this relation a function?why or why not?[(-5,7),(-2,1),(0,3),(4,7)]
Answer:
No, every relation is not a function.
Step-by-step explanation:
Every function is a relation because there are two points (x,y) somehow related to each other.
But every relation is not a function
The given ordered pairs are the function
Since, we are getting different value of y for ecah x.
The condition for function is we should get different value of y for each x.
Write an exponential function to model the situation.A population of 300 animals decreased at an annual rate of 22%
Answer:
[tex] y = 300(0.78)^x [/tex]
Step-by-step explanation:
x is the number of years. y is the population after x years.
Each year, the population decreases by 22%, since 100% - 22% = 78%, and 78% = 0.78, each year, the population is 0.78 of the previous year's population.
year zero: y = 300
year 1: y = 300 * 0.78 = 300 * (0.78)^1
year 2: y = (300 * 0.78) * 0.78 = 300 * (0.78)^2
year 3: y = ((300 * 0.78) * 0.78) * 0.78 = 300 * (0.78)^3
year x: y = 300(0.78)^x
what is the area if a regular hexagon if the distance from a midpoint of a side to the midpoint of the opposite side is 10
Answer:
50√3 or 86.6
Step-by-step explanation:
Divide the hexagon into six equilateral triangles as in Figure 1 below.
Then draw a line from the midpoint of one side to the midpoint of the opposite side.
The height (h) of each triangle will be 5.
To find the area of the whole triangle, we first need to find the length of the base (see Figure 2).
If the base length (b) is 2s, we have the relation
5/s = tan60°
5/s = √3 Multiply each side by s
5 = s√3 Divide each side by √3
s = 5/√3 Rationalize
s = (5√3)/3
b = 2s
b = (10√3)/3
The area (A) of the triangle is
A = ½bh
A = ½ × (10√3)/3 × 5
A = (25√3)/3
There are six equilateral triangles in the hexagon, so
Total area = 6A
Total area = 6 × (25√3)/3
Total area = 50√3
Total area ≈ 86.6
Please factorise these using identies
7. (x-7)(x-7)
8. (3x-5y)(3x-5y)
9. (x-15)(x+3)
10.(7m+6n)(7m+6n)
11. (2x+1)(2x+1)
12. (7x+2)(7x+2)
13. (p-18)(p+4)
Notice how 7,8,10,11, and 12 are all perfect squares. A good way to tell if a trinomial can be factored into a perfect square is if the square root of the coefficient of your variable multiplied by the square root of the constant (number with no variable) multiplied by 2 equals the middle term's coefficient.
For example, take 4x^2+16x+16. Taking the square root of 4 gives us 2. Taking the square root of 16 gives us 4. So, 2*2*4=16, which is our middle term, thus proving that this trinomial is indeed a perfect square.
Kendra lost one half of her allowance but her mother gave her four more dollars now she has $9 how much was her allowance
Final answer:
Kendra's original allowance was $10.
Explanation:
To find out how much Kendra's allowance was, we can use algebraic equations. Let 'x' represent Kendra's original allowance.
Kendra lost half of her allowance, which means she had x/2 left.
Then her mother gave her four more dollars, so now she has x/2 + 4.
Given that Kendra has $9, we can set up the equation x/2 + 4 = 9 and solve for x.
x/2 + 4 = 9
x/2 = 9 - 4
x/2 = 5
Multiplying both sides of the equation by 2, we get x = 10.
Therefore, Kendra's allowance was $10.
without plotting find a point on the graph of x+y=21 whose y coordinate is three more than the x coordinate
y-coordinate is 3 more than x-coordinate: y = x + 3.
Substitute to the equation x + y = 21:
x + x + 3 = 21 subtract 3 from both sides
2x = 18 divide both sides by 2
x = 9
y = 9 + 3
y = 12
Answer: (9, 12).A 5 gallon bucket of paint costs $97.45. What is the price per gallon?
Answer:
19.49 per gallon
hope it helps
Step-by-step explanation:
total pay ÷ number of gallon = the cost of each gallon
97.45 / 5 = 19.49 per gallon
-11 , -15, -19 is an arithmetic sequence
Find the nth term of the sequence
Answer:-47
Step-by-step explanation:
1# 11+4=15
2# 15+4=19
3# 19+4=23
4# 23+4=27
5# 27+4=31
6# 31+4=35
7# 35+4=39
8# 39+4=43
9# 43+4=47
REMEBER its negative not positive.
Probability On a nearby pond, black and white ducks are swimming in groups of three. Use the table to find the experimental probability of two white ducks and one black duck swimming together. Tails up represents white ducks and heads up represents black ducks.
Answer:
There are only two choices, a black or white duck, so a coin is the best choice. To represent a set of possible outcomes, toss the coin three times. Repeat the experiment multiple times. To find the probability, divide the observed desired outcomes by the total number of trial
Step-by-step explanation:
Answer:
7/20
Step-by-step explanation:
I came across the question
which ecpression is equivalent to sqrt 8x^7y^8?
[tex]Domain:\ x\geq0\ \wedge\ y\in\mathbb{R}[/tex]
[tex]\sqrt{8x^7y^8}=\sqrt8\cdot\sqrt{x^7}\cdot\sqrt{y^8}=\sqrt{4\cdot2}\cdot\sqrt{x^6\cdot x}\cdot\sqrt{y^{4\cdot2}}\\\\=\sqrt4\cdot\sqrt2\cdot\sqrt{x^6}\cdot\sqrt{x}\cdot\sqrt{(y^4)^2}=2\sqrt2\cdot\sqrt{x^{3\cdot2}}\cdot\sqrt{x}\cdot y^4\\\\=2y^4\sqrt2\cdot\sqrt{(x^3)^2}\cdot\sqrt{x}=2y^4\sqrt{2x}\cdot x^3\\\\=\boxed{2x^3y^4\sqrt{2x}}[/tex]
[tex]Used:\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a\ for\ a\geq0[/tex]
Answer:
c is correct
Step-by-step explanation:
edge 2020
I’m supposed to find the slope intercept form. The x intercept is (2,0) and the y intercept is (0,6). I keep getting 6/2. But, the graph goes down?
[tex]\bf \stackrel{x-intercept}{(\stackrel{x_1}{2}~,~\stackrel{y_1}{0})}\qquad \stackrel{y-intercept}{(\stackrel{x_2}{0}~,~\stackrel{y_2}{6})} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-0}{0-2}\implies \cfrac{6}{-2}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=-3(x-2)\implies y=-3x+6[/tex]
As an estimation we are told 5 miles is 8 km.
Convert 13.5 miles to km
Answer:
Step-by-step explanation:
5/13.5 x 8/x (cross multiple) 108/5 (divide) = 21.6
Question
As an estimation we are told 5 miles is 8 km.
Convert 13.5 miles to km
Answer:
21.6 KmStep-by-step explanation:
you can solve with an equation
5 : 8 = 13.5 : x
x = 8 * 13.5 : 5
x = 21.6
What Is the solution to the system 5X plus 7Y equals 32 and 8X plus 6Y equals 46
[tex]\bf \begin{cases} 5x+7y=32\\ 8x+6y=46 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 5x+7y=32\implies 7y=32-5x\implies \boxed{y}=\cfrac{32-5x}{7} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting \underline{y} in the 2nd equation}}{8x+6\left(\boxed{ \cfrac{32-5x}{7}} \right)}=46\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{7}}{7\left( 8x+6\left( \cfrac{32-5x}{7} \right) \right)=7(46)} \\\\\\ 56x+6(32-5x)=322\implies 56x+192-30x=322[/tex]
[tex]\bf 26x+192=322\implies 26x=130\implies x=\cfrac{130}{26}\implies \blacktriangleright x=5 \blacktriangleleft \\\\\\ \stackrel{\textit{subsituting \underline{x} in the 1st equation}}{5(5)+7y=32}\implies 25+7y=32\implies 7y=7 \\\\\\ y=\cfrac{7}{7}\implies \blacktriangleright y=1 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (5,1)~\hfill[/tex]
Which number can be used to fill in the blanks to make both statements true? 144÷12=____ and 12 x ____ = 144
Answer:
12
Step-by-step explanation:
144/12 = 12
12 x 12 = 144
Answer:
12
Step-by-step explanation:
divide 12 by 144
Evaluate 3/2+(-k)+(-2) where k is -5/2
Answer:
2
Step-by-step explanation:
3/2 + (-k) + (-2) =
= 3/2 + [-(-5/2)] - 2
= 3/2 + 5/2 - 2
= 8/2 - 2
= 4 - 2
= 2
A sprinter can run 120 meters in 10 seconds. what is his average speed
Answer:
12 Meters Per Second
Step-by-step explanation:
Average Speed = Distance divided by time
Average Speed = 120 Meters / 10 Seconds
Average Speed = 12 Meters Per Second
if sprinter can run 120 meters in 10 seconds then 12 meters per second is the average speed.
What is Speed?Speed is defined as the rate of change of position of an object in any direction
Given that A sprinter can run 120 meters in 10 seconds.
Average Speed = Distance divided by time
Speed = Distance/ Time
The distance is 120 meters and times is 10 seconds.
Speed=120/10
=12 meters per second
Hence, if sprinter can run 120 meters in 10 seconds then 12 meters per second is the average speed.
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A school district transported a total of 409 students and teachers to a zoo in buses and vans.
-Each bus transported a total of 55 students and teachers.
-Each van transported a total of 12 students and teachers.
-There were 5 more buses than vans.
What is the total number of students and teachers who rode to the zoo in buses? What is the total number of students and teachers who rode to the zoo in vans?
Answer:
Step-by-step explanation:
Let x be the number of buses and y be the number of vans.
We know that there are 5 more buses than vans, therefore, we can set up:
[tex]x=y+5[/tex]
Since a bus transports 55 people and a van transports 12 people, therefore, we can set up:
[tex]55x+12y = 409\\[/tex]
Now lets solve the above two equations together by substitution
[tex]55(y+5)+12y = 409\\\\55y+275+12y=409\\\\67y+275=409\\\\67y=409-275\\\\67y=134\\\\y=2,x=2+5=7[/tex]
Total number of students and teachers who rode to the zoo in buses[tex]=55*7=385[/tex]
Total number of students and teachers who rode to the zoo in vans[tex]=12*2=24[/tex]
What is the best estimate for 5.07 x 0.81 ?
A. 0.4
B. 4
C. 4.5
D. 5
Please help and if so correct and answered then I’ll mark you as Brainiest Answered.
Thank you.
Answer: 5
Step-by-step explanation: 5.07 rounds to 5
0.81 rounds to 1
so the best estimate for 5.07 x 0.81 = 5(1) = 5.......ANS
Answer:
4.05
Step-by-step explanation:
5 X 0.81 = 4.05 so I say C
a bookstore has 780,000 and sales revenue in 2005 $190,000 2011 assuming a constant annual rate of decrease what is the predicted sales revenue for 2017
Answer5,90,000
Step-by-step explanation:
780,000 subtract 190,000 = 590,000
after every 6 years
i'm not sure if its correct. please let me know
102 - 42 , 33y-11y can I get four equivalent expressions plzzz
Final answer:
The equivalent expressions for 102 - 42 are 60, -42, 60 - 42, and 102 - 42. The equivalent expressions for 33y - 11y are 22y, 22y - 11y, 33y - 11y, and 11y.
Explanation:
Equivalent expressions for 102 - 42:
60-4260 - 42102 - 42Equivalent expressions for 33y - 11y:
22y22y - 11y33y - 11y11ywhich expressions are listed in the simplest form ? Check all that apply
[tex]5 \sqrt{3b} [/tex]
[tex]2 \sqrt{21} [/tex]
[tex]x \sqrt{8} [/tex]
[tex]2 \sqrt{36} [/tex]
[tex] \sqrt{5} [/tex]
[tex]c \sqrt{12 {c2}^{?} } [/tex]
[tex]5\sqrt{3b}\qquad\boxed{YES}\\\\2\sqrt{21}\qquad\boxed{YES}\\\\x\sqrt8=x\sqrt{4\cdot2}=x\sqrt4\cdot\sqrt2=2x\sqrt2\qquad\boxed{NOT}\\\\2\sqrt{36}=2\cdot6=12\qquad\boxed{NOT}\\\\\sqrt5\qquad\boxed{YES}\\\\c\sqrt{12c^2}=c\sqrt{4\cdot3\cdot c^2}=c\sqrt4\cdot\sqrt3\cdot\sqrt{c^2}=c\cdot2\cdot\sqrt3\cdot|c|=2c|c|\sqrt3\qquad\boxed{NOT}[/tex]
Here, you are required to check if each expression can be simplified further
Expression 1, 2 and 5 are in the simplest form already
5√3b
Can not be simplified further
2√21 = 2√7 × 3
aCan not be simplified further
x√8
= x × √4 × 2
= x × √4 × √2
= x × 2 × √2
= 2x√2
Can be simplified further
2√36
= 2 × √36
= 2 × 6
= 12
Can be simplified further
√5
Can not be simplified further
c√12c²
= c × √4×3×c²
= c × √4 × √3 × √c²
= c × 2 × √3 × c
= 2c²√3
Can be simplified further
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