Answer:
d (last choice)
Step-by-step explanation:
The explicit form of a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term while [tex]r[/tex] is the common ratio.
We are given the first term [tex]a_1=47[/tex].
We are given the sixth term [tex]a_6=-789929[/tex].
If we divide 6th term by 1st term this is the result:
[tex]\frac{a_1 \cdot r^5}{a_1 }=\frac{-789929}{47}[/tex]
Simplify both sides:
[tex]r^5=-16807[/tex]
Take the fifth root of both sides:
[tex]r=-7[/tex]
The common ratio is -7.
So all we have to do is start with the first term and keep multiplying by -7 to get the other terms.
[tex]a_1=47[/tex]
[tex]a_2=47(-7)=-329[/tex]
[tex]a_3=47(-7)^2=2303[/tex]
[tex]a_4=47(-7)^3=-16121[/tex]
[tex]a_5=47(-7)^4=112847[/tex]
[tex]a_6=47(-7)^5=-789929[/tex]
The terms -329,2303,-16121,112847 are what we are looking for in our choices.
That's the last choice.
ANSWER ASAP PLEASE!!
Clayton needs to reflect the triangle below across the line y=x
Which statements about the reflection are true? Check all that apply.
Clayton could use the relationship (x,y)→ (y,x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will remain in the same location as C because it is on the line of reflection.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.
Answer:
Clayton could use the relationship (x,y)→ (y,x) to find the points of the image
C’ will remain in the same location as C because it is on the line of reflection
The image and the pre-image will be congruent triangles
The image and pre-image will not have the same orientation because reflections flip figures
Step-by-step explanation:
Verify each statement
case A) Clayton could use the relationship (x,y)→ (y,x) to find the points of the image
The statement is true
we know that
The rule of the reflection of a point across the line y=x is equal to
(x,y)→ (y,x)
case B) Clayton could negate both the x and y values in the points to find the points of the image
The statement is false
case C) C’ will remain in the same location as C because it is on the line of reflection
The statement is true
If a point is on the line of reflection (y=x), then the point remain in the same location because the x and y coordinates are equal
case D) C’ will move because all points move in a reflection
The statement is false
Because C' is on the line of reflection (y=x), then the point remain in the same location
case E) The image and the pre-image will be congruent triangles
The statement is true
Because the reflection not change the length sides of the triangle or the measure of its internal angles. Reflection changes only the orientation of the figure
case F) The image and pre-image will not have the same orientation because reflections flip figures
The statement is true
Because in a reflection across the line y=x, the x coordinate of the pre-image becomes the y-coordinate of the image and the y-coordinate of the pre-image becomes the x-coordinate of the image
if angle a is 50° and angle b is 75° what is the measurement of angle c
Answer:
m∠C = 55°
Step-by-step explanation:
A triangle's sum of all angles = 180°
Set the equation: m∠A + m∠B + m∠C = 180°
m∠A = 50° ; m∠B = 75°
Plug in the corresponding numbers to the corresponding variables:
50 + 75 + m∠C = 180
Simplify. Combine like terms:
(50 + 75) + m∠C = 180
125 + m∠C = 180
Isolate the variable. Note the equal sign, what you do to one side, you do to the other. Subtract 125 from both sides:
m∠C + 125 (-125) = 180 (-125)
m∠C = 180 - 125
m∠C = 55
m∠C = 55°
Check: All the angles added together must equal 180°:
50 + 75 + 55 = 180
125 + 55 = 180
180 = 180 (True)
~
Tom drank 1 1/4 quarts of water and his sister Jane drank 1.75 quarts of water. Write the amount that Jane drank using a
fraction. Who drank more water?
(Doesn’t have choices)
Answer:
Jane drank 1 3/4 quarts of water.
Jane drank more water than Tom
Step-by-step explanation:
Tom drank = 1 1/4 quarts of water
Jane drank = 1.75 quarts of water
We have to write the amount of water Jane drank in fraction.
There are some steps to convert decimal into fraction.
Step 1:
Value is 1.75:
Put the 1 aside and just work on 0.75
Write down the decimal value divided by 1
Like, 0.75/1
Step 2:
Now multiply both the numerator and denominator by 100.
We will multiply the numerator and denominator by 100 because 1.75 has two values after the decimal.
0.75 *100/1*100
75/100
Step 3:
Simplify the fraction.
divide the fraction by 5.
=15/20
=3/4
Now bring back the 1: and the fraction will become.
1 3/4
Jane drank 1 3/4 quarts of water.
Now who drank more water?
Jane drank more water than Tom
Reason:
Tom drank 1 1/4 = 5/4
Jane drank 1 3/4 = 7/4
Both the fractions have same denominator, so the value with the greater numerator drank more water than the other.
Therefore Jane drank more water than Tom....
Find m(arc) IJ of circle H.
If:
m(arc) KJ=110 degrees
a=100,b=150,c=110,d=250
Answer:
100 degrees (first choice)
Step-by-step explanation:
So we can actually find the degree measure of arc KI because there is a theorem that says this twice the angle IJK.
75(2)=150 is the degree measure of arc KI.
So a full rotation around a circle is 360 degrees.
This means the following equation should hold:
m(arc)KJ+m(arc)IJ+m(arc)IK=360
Inserting the values given for the arc measures we know:
110 +m(arc)IJ+ 150 =360
Add 110 and 150:
260 +m(arc)IJ =360
Subtract 260 on both sides:
m(arc)IJ =100
So m(arc)IJ is 100 degrees.
Which function in vertex form is equivalent to fx = 4+x2-2x
Answer:
f(x) = (x-1)² + 3
Step-by-step explanation:
f(x) = 4+x²-2x or f(x) = x²- 2x + 4 -----> eq 1
consider the top-most choice
f(x) = (x-1)² + 3 = x² + 2·x·(-1) + 1² + 3
f(x) = x² - 2x+ 1 + 3
f(x) = x² - 2x+ 4 -----> compare this with eq 1 above (they match!)
hence f(x) = (x-1)² + 3 is the answer
Which input value produces the same output value for the two functions on the graph
Answer:
The input value is x=1
Step-by-step explanation:
we know that
The intersection point both graphs is the point that produces the same output value for the two functions
Observing the graph
The intersection point is (1,1)
therefore
For x=1 (input value)
The output value for the two functions is equal to 1
Answer:
ITS X=1
Step-by-step explanation:
please help me wiht this question
Check the picture below.
Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. The system of equations models the total costs for each.
y = 7.5x
y = 5.5x + 10
1. Substitute: 7.5x = 5.5x + 10
How many classes could Anna take so that the total cost for the month would be the same?
Answer:
y = 7.5x and y = 5.5x + 10
Step-by-step explanation:
this is for if you get the graph or not!
Answer:
5 classes
37.50 monthly cost for both gyms
Step-by-step explanation:
2022 edge
Please help me with this problem. Urgent
Answer:
[tex]\frac{x-1}{x^{2} +2x-3}[/tex]
[tex]\frac{1}{x+3}[/tex]
Step-by-step explanation:
first, subtract the two fractions
You will have
[tex]\frac{x-1}{x^{2} +2x-3}[/tex] the un-simplified difference of those expressions
Lets try to simplify that
Lets find the roots of the polynomial from the bottom using the formula for quadratic equation, (-b +/- sqrt( b2-4*a*c)) /(2*a)
Which are x=-3, and x=1
Thus, you have (x+3)*(x-1)
So
[tex]\frac{x-1}{x^{2} +2x-3} = \frac{x-1}{(x+3) (x-1)}= \frac{1}{x+3}[/tex]
Give the equation of the line passing through the point (3,−21) that is parallel to
y= −5x+9.
Answer:
y=-5x-6
Step-by-step explanation:
Parallel means you are looking for an equation that has the same slope as the one given.
The slope of y=-5x+9 is -5.
All I did was compare it to y=mx+b where m is slope and b is y-intercept.
So our equation is in the form y=-5x+b.
We want to find b such that y=-5x+b goes through (3,-21).
So we can plug in our point that is on this line so that that happens.
-21=-5(3)+b
-21=-15+b
Add 15 on both sides
-6=b
b=-6
So the line that is parallel to y=-5x+9 while going through (3,-21) is y=-5x-6.
If u(x)=-2x^2+3 and (x)=1/x, what is the range of (u°v)(x)
Answer:
The range is all real number y<3.
Step-by-step explanation:
[tex](u \circ v)(x)=u(v(x))[/tex]
So we have to have v(x) exist for input x.
Let's think about that. v(x)=1/x so the domain is all real numbers except 0 since you cannot divide by 0. v(x)=1/x will also never output 0 because the numerator of 1/x is never 0. So the range of v(x)=1/x is also all real numbers except y=0.
Now let's plug v into u:
[tex]u(x)=-2x^2+3[/tex]
[tex]u(v(x))=u(\frac{1}{x}[/tex]
[tex]u(v(x))=-2(\frac{1}{x})^2+3[/tex]
The domain of will still have the restrictions of v; let's see if we see any others here.
Nope, there are no, others, the only thing that is bothering this function is still the division by x (which means we can't plug in 0).
[tex]u(v(x))=\frac{-2}{x^2}+3[/tex]
Let's thing about what are y's value will not ever get to be.
Let's start with that fraction. -2/x^2 will never be 0 because -2 will never be 0.
So we will never have y=0+3 which means y will never be 3.
There is one more thing to notice -2/x^2 will never be positive because x^2 is always positive and as we know a negative divided by a positive is negative.
So we have (a always negative number) + 3 this means the range will only go as high as 3 without including 3.
The range is all real number y<3.
Write an equation: Phil’s age increased by 9 years is 18 years
Let P = Phil's age
P + 9 = 18
The correct equation representation for 'Phil's age increased by 9 years is 18 years' would be 'p + 9 = 18', which indicates that when you add 9 years to Phil's age, it equals 18. Hence, option D is the correct answer.
Explanation:The student is seeking to translate a sentence into a mathematical equation. The sentence states: 'Phil's age increased by 9 years is 18 years.' Considering 'Phil's age' as 'p', the correct translation of the sentence into a mathematical equation would be 'p + 9 = 18' since this indicates that when we add 9 years to Phil's age, we get 18 years. Therefore, the correct answer among the provided choices is option D: p + 9 = 18.
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The complete question is here:
Write as an equation: Phil's age increased by 9 years is 18 years.
A. p+18=9
B. p-9=18
C. p=18+9
D. p+9=18
helppp it's timed
Study the equations:
f(x)=11x-5
g(x)=-2x-4
What is h(x)= f(x) g(x)?
A) h(x)=-22x^2+34x+20
B) h(x)=-22x^2+10x-24
C) h(x)=22x^2-54x+20
D) h(x)=-22x^2-34x+20
Answer:
D.
Step-by-step explanation:
h(x)=f(x)g(x) means multiply the expression for f to the expression for g.
That is the problem is just asking you to do (11x-5)(-2x-4).
Let's use foil.
First: 11x(-2x)=-22x^2
Outer: 11x(-4)=-44x
Inner: -5(-2x)=10x
Last: -5(-4)=20
------------------------Add together!
-22x^2-34x+20
D.
h(x) = [tex]-22x^{2} -34x+20[/tex]
Option D is correct.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Given equations
f(x) = 11x - 5
g(x) = - 2x - 4
h(x) = f(x) g(x)
h(x) = [tex](11x -5) \times (-2x-4)[/tex]
h(x) = [tex]11x \times (-2x) +11x \times (-4) -5 \times (-2x) -5 \times (-4)[/tex]
h(x) = [tex]-22x^{2} -44x+10x+20[/tex]
h(x) = [tex]-22x^{2} -34x+20[/tex]
Option D is correct.
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I need help plz. Show your work! 23 + 5 x 3 - 100 + 19 in PEMDAS!
Answer:
-43
Step-by-step explanation:
Follow PEMDAS as well as the left -> right rule.
Note that: PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
First, solve the multiplication:
23 + (5 * 3) - 100 + 19
23 + (15) - 100 + 19
Simplify. Follow the left-> right rule:
(23 + 15) - 100 + 19
38 - 100 + 19
(38 - 100) + 19
-62 + 19 = -43
-43 is your answer.
~
Answer:
-43
Step-by-step explanation:
Steps to PEMDAS:
P: parenthesis - There are no parenthesis in this equation.
E: exponents - There are no exponents in this equation.
M: multiplication 5 x 3 = 15
D: division There is no division in this equation.
A: addition 23 + previous 15 + 19 = 57
S: subtraction Previous answer 57 - 100 = -43
Therefore, the answer is -43.
Which is the inverse of the function f(x)=1/3x+5
Answer:
f-¹(x) =(1-5x) /3x.
Step-by-step explanation:
f(x)=1/(3x+5)
Let y=1/(3x+5)
Exchanging x and y,
x=1/(3y+5)
3y+1=1/x
3y=1/x-5
3y=(1-5x) /x
y=(1-5x)/3x
f-¹(x) =(1-5x) /3x.
Answer:
y=3(x-5)
Step-by-step explanation:
Which expression is equivalent to!!!!!
Answer:
A
Step-by-step explanation:
Use the property
[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]
The numerator can be simplified as
[tex]\sqrt[7]{x^2}=x^{\frac{2}{7}}[/tex]
The denominator can be simplified as
[tex]\sqrt[5]{y^3}=y^{\frac{3}{5}}[/tex]
Also remindr property
[tex]\dfrac{1}{a^n}=a^{-n}[/tex]
Thus, the expression is equivalent to
[tex]\dfrac{\sqrt[7]{x^2} }{\sqrt[5]{y^3} }=\dfrac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}=\left(x^{\frac{2}{7}}\right)\cdot \left(y^{-\frac{3}{5}}\right)[/tex]
Given p(x)=3x^5+2x^2-5, what is the value of the function at -5/3
Answer:
[tex]-\frac{3080}{81}[/tex]
Step-by-step explanation:
The given function is:
[tex]p(x)=3x^{5}+2x^{2}-5[/tex]
We have to find the value of the function at x = -5/3
In order to do this we need to replace every occurrence of x in the given function by -5/3. i.e.
[tex]p(-\frac{5}{3})=3(-\frac{5}{3})^{5}+2(-\frac{5}{3} )^{2}-5\\\\ p(-\frac{5}{3})=3(-\frac{3125}{243} )+2(\frac{25}{9} )-5\\\\p(-\frac{5}{3})=-\frac{3125}{81}+\frac{50}{9}-5\\\\ p(-\frac{5}{3})=-\frac{3080}{81}[/tex]
Thus, the value of the function at x =-5/3 is [tex]-\frac{3080}{81}[/tex]
helpppp! The population of a town is 20,000 people in the year 2000. How many people with live in the town in 2016 if the population increases at a rate of 6% every 2 years? Round your answer to the nearest whole number.
Answer:
31877 people with live in the town in 2016 if the population increases at a rate of 6% every 2 years
Step-by-step explanation:
The formula used will be
A(t) = P(1+r)^t
A(t) = Future value
P = population
r = rate
t = time
P= 20,000
r =6% or 0.06
t = 16
Since population is increased every 2 years, so t = 16/2 = 8
Putting value:
A(16) = 20,000(1+0.06)^8
A(16)= 20,000(1.06)^8
A(16) = 31876.9 ≈ 31877
So, 31877 people with live in the town in 2016 if the population increases at a rate of 6% every 2 years
Is f(x)=e^2 an exponential function? If so what is its base? If not, why?
Answer:
No. It is a constant function.
Step-by-step explanation:
The function f(x) = e^2 is not an exponential functional. Rather, it is a constant function. The reason for this is that in f(x) = e^2, there is no x involved on the right hand side of the equation. The approximate value of e is 2.718281, and the approximate value of 2.718281^2 is 7.389051. This means that f(x) = e^2 = 7.389051. It is important to note that for any value of x, the value of the function remains fixed. This is because the function does not involve the variable x in it. The graph of the function will be a line parallel to the x-axis, and the y-intercept will be 7.389051. For all the lines parallel to x-axis, the value of the function remains the same irrespective of the value of x. Also, the derivative of the function with respect to x is 0, which means that the value of the function is unaffected by the change in the value of x!!!
which function has a vertex at the origin
In Mathematics, quadratic functions such as y=ax^2 and cubic functions such as y=ax^3, will have their vertex at the origin, represented by (0,0). These functions show this characteristic because there are no shifts involved in the equation.
Explanation:In Mathematics, there are different functions that can have their vertex at the origin (0,0). For instance, when we speak of quadratic functions, a function in the form of y = ax^2 will have its vertex at the origin as it's a parabola that opens upward or downward.
Similarly, for the case of cubic functions, a function in the form of y = ax^3 will have the vertex at the origin.
Important to note is that, for all these cases, the vertex is at the origin because there are no horizontal or vertical shifts involved in the equation. That is, the h & k in (x-h)^2+k and (x-h)^3+k are both zero.
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The sides of a rectangle have length x+ 2 and width x -5. Which equation describes the area, A, of the rectangle in terms of x?
Answer:
The area in factored form is [tex]A=(x+2)(x-5)[/tex].
The area in standard form is [tex]A=x^2-3x-10[/tex].
Step-by-step explanation:
The area of a rectangle is length times width.
So the area here is (x+2)(x-5).
They are probably not looking for A=(x+2)(x-5) because it requires too little work.
They probably want A in standard form instead of factored form.
Let's use foil:
First x(x)=x^2
Outer: x(-5)=-5x
Inner: 2(x)=2x
Last: 2(-5)=-10
---------------------Adding together: [tex]x^2-3x-10[/tex].
The area in factored form is [tex]A=(x+2)(x-5)[/tex].
The area in standard form is [tex]A=x^2-3x-10[/tex].
Final answer:
The equation describing the area of the rectangle in terms of x, given the sides x + 2 and x - 5, is A = x² - 3x - 10.
Explanation:
To find the equation that describes the area, A, of a rectangle in terms of x, we use the formula for the area of a rectangle, which is length times width. Given that the length is x + 2 and the width is x - 5, the equation for the area A in terms of x is A = (x + 2)(x - 5).
To express A as a polynomial, we can expand this equation:
A = x(x - 5) + 2(x - 5)
A = x² - 5x + 2x - 10
A = x² - 3x - 10
Therefore, the equation that describes the area of the rectangle in terms of x is A = x² - 3x - 10.
distribute and simplify (√12 + 6)(- √8 - √2)
Answer
-18√2-6√6
Step-by-step explanation:
(√12 +6) (-√8-√2)
=√12(-√8-√2)+6(-√8-√2)
= -√96-√24-6√8-6√2
= -4√6-2√6-12√2-6√2
= -6√6-18√2
= -18√2- 6√6
The table represents the multiplication of two binomials.
What is the value of A?
A: -3x
B: -3x^2
C: -5x
D: -5x^2
Answer:
B
Step-by-step explanation:
The entry A is the result of multiplying - x and 3x, that is
- x × 3x = - 3x² → B
Answer:
-3x^2
Step-by-step explanation:
A 3x * -x = -3x^2 so A = -3x^2
We can also find the value of B
B -x *5 = -5x
and C
C = 3x*2 = 6x
A card is drawn from a standard deck of 52 cards. What is the theoretical probability, as a decimal, of drawing an ace? Round the decimal to the nearest hundredth. (Hint: A standard deck of 52 cards contains 4 aces.)
P(ace) =
Answer:
0.08
Step-by-step explanation:
A standard deck of 52 cards has four aces.
The sample space is:
n(S) = 52
Let A be the event that an ace is drawn from the deck.
Then,
n(A) = 4
So,
[tex]P(A) = \frac{n(A)}{n(S)}\\ =\frac{4}{52} \\=0.0769[/tex]
Rounding off to the nearest hundredth will give us:
0.08 ..
The theoretical probability of drawing an ace from a standard deck of 52 cards is 0.08. The calculation is based on dividing the number of aces (4) by the total number of cards (52).
Explanation:The theoretical probability of an event occurring is calculated by dividing the number of ways an event can occur by the total number of possible outcomes. In this scenario, the question is asking about the theoretical probability of drawing an ace from a standard deck of 52 cards.
In a standard deck of cards, there are 4 aces. So, the number of ways the event 'drawing an ace' can occur is 4. The total number of possible outcomes, which is the total number of cards in the deck, is 52. Therefore, the probability of drawing an ace, P(Ace), is calculated as follows:
P(ace) = Number of aces in the deck / Total number of cards
P(ace) = 4 / 52
When you simplify this fraction or convert it into decimal form (rounded to the nearest hundredths), it gives:
P(ace) = 0.08
So, the theoretical probability of drawing an ace from a deck of 52 cards is 0.08.
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julio has found that his new car gets 36 miles to the gallon on the highway and 31 miles per gallon in the city. he recently drove 397 miles on 12 gallons of gasoline. how many miles did he drive on the highway? How many miles did he drive in the city?
Answer:
Miles he drove on highway = 180 miles
Miles he drove in the city = 217 miles
Step-by-step explanation:
Lets assume that gallon used on highway = x
Miles driven on highway = y
(I) 36 miles per gallon on the highway.
36x = y equation 1
(II) 31 miles per gallon in the city.He recently drove 397 miles on 12 gallons of gasoline
31(12-x)= 397-y equation 2
372-31x= 397-y
Combine the constants:
-31x= 397-372-y
y-31x = 25
Now substitute the value of equation 1 in equation 2
y-31x=25
36x-31x=25
5x=25
Now divide both sides by 5
5x/5=25/5
x=5
Now substitute the value x=5 in equation 1
36x=y
36(5)=y
180= y
Now subtract the miles driven on highway from recently drove miles to get the miles driven in the city.
397-y = 389 - 180
= 217
Therefore,
Miles he drove on highway = 180 miles
Miles he drove in the city = 217 miles ....
Julio drove 0 miles on the highway and 2856 miles in the city.
Explanation:To find out how many miles Julio drove on the highway and in the city, we can set up a system of equations. Let x represent the number of miles driven on the highway and y represent the number of miles driven in the city. We know that the total distance driven is 397 miles and the total amount of gas used is 12 gallons. Using the given miles per gallon ratings, we can set up the following equations:
x + y = 397
36x + 31y = 12
From the first equation, we can isolate x:
x = 397 - y
Substituting this value of x into the second equation, we can solve for y:
36(397 - y) + 31y = 12
14292 - 36y + 31y = 12
-5y = -14280
y = 2856
Now we can substitute the value of y back into the first equation to find x:
x + 2856 = 397
x = 397 - 2856
x = -2459
However, since we cannot have negative miles, we know that Julio did not drive any miles on the highway.
Therefore, Julio drove 0 miles on the highway and 2856 miles in the city.
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The ratio of boys to girls in a school is 5:8. If the number
of girls exceeds the number of boys by 144, calculate the
total number of students in the school.
What is m∠AKE? 120 60 70 110
Check the picture below.
We are asked to find m ∠AKE, which is the measure of angle MAK. Therefore, MAK = 70 degrees. So, m∠AKE = 70 degrees.
To find m∠AKE, we need to use the properties of angles in a triangle. First, let's identify the triangle we are dealing with. Based on the information provided, we have the following triangle:
A
/ \
/ \
/_____\
K E
Given that MAB = 110 and MDE = 130, we can use the fact that the sum of angles in a triangle is 180 degrees.
Since A is a common vertex to both angles MAB and MAE, we can write:
MAB + MAE + MAK = 180
Substitute the given values:
110 + MAE + MAK = 180
Now, we need to find MAE + MAK:
MAE + MAK = 180 - 110
MAE + MAK = 70
We are asked to find m∠AKE, which is the measure of angle MAK. Therefore, MAK = 70 degrees.
So, m∠AKE = 70 degrees.
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Is (0,0) a solution to this system y>=x^2+x-4; y<=x^2+2x+1
Answer:
yes it is a solution
Step-by-step explanation:
o>-4
0<1
yes both work out to be equal
Answer:
It is a solution
Step-by-step explanation:
Check and see if (0,0) satisfies both inequalities.
The first inequality is:
[tex]y \geqslant {x}^{2} + x - 4 [/tex]
When we put x=0, and y=0, we get:
[tex]0\geqslant {0}^{2} + 0 - 4[/tex]
[tex] \implies0\geqslant- 4[/tex]
This part is true.
The second inequality is:
[tex]y \leqslant {x}^{2} + 2 x + 1[/tex]
We put x=0 and y=0 to get:
[tex]0 \leqslant {0}^{2} + 2 (0) + 1[/tex]
[tex]0 \leqslant 1[/tex]
This part is also true.
Since the (0,0) not satisfy both, inequalities, it is a solution.
What is the length of one leg of the triangle?
Answer:
The correct answer is third option. 22 units
Step-by-step explanation:
Points to remember
If a right angled triangle with angles are 45°, 45° and 90° then the sides are in the ratio 1 : 1 : √2
To find the length of one leg of the triangle
From the figure we can see a right angled triangle with hypotenuse = 22√2 units
The other two legs are equal. Therefore the right angled triangle with angles 45°, 45° and 90°
Therefore the given triangle sides are in the ratio,
1 : 1 : √2 = x : x : 22√2
Therefore x = 22 units
The correct answer is third option. 22 units
How to work out 161 as a percentage of 3500
Answer:
161 is 4.6% of 3500
Step-by-step explanation:
Divide:
161
-------- = 0.046
3500
Now multiply this result by 100%: 4.6%.
161 is 4.6% of 3500.
Answer:
4.6%
Step-by-step explanation:
To find what percent number A is of number B, divide A by B and multiply by 100.
To find what percent 161 is of 3500, divide 161 by 3500 and multiply by 100.
percent = 161/3500 * 100 = 0.046 * 100 = 4.6%
161 is 4.6% of 3500