Answer:
Sum is
Step-by-step explanation:
Expand (1 + root 2) (3 - root 2)
Give your answer in the form a+b root 2 where a and b are integers.
Answer:
1+2√2
a = 1 b= 2
See the attached page, I've shown the calculation over there.
Find the nth term an of the geometric sequence described below, where r is the common ratio.
a4 = -8, r= -2
Answer:
[tex]a_n=(-2)^{n-1}[/tex]
Step-by-step explanation:
So a geometric sequence can be explicitly defined as: [tex]a_n = a_1(r)^{n-1}[/tex]. IN this case we're given r, but we don't know what a_1 is. We can find this by lugging in 4 as n, and -8 as a_n, since they're given values
Plug known values in:
[tex]-8 = a_1(-2)^{4-1}[/tex]
Subtract the values in the exponent
[tex]-8 = a_1(-2)^3[/tex]
Simplify the exponent
[tex]-8 = a_1 (-8)[/tex]
Divide both sides by -8
[tex]1=a_1[/tex]
So the nth term can be defined as: [tex]a_n = 1(-2)^{n-1}[/tex], and since the 1 is redundant, the equation can simply be defined as: [tex]a_n=(-2)^{n-1}[/tex]
Corresponding Parts Of Congruent Figures Are Congruent
Please Help !!
In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
Since we know that rigid motions preserve both the side length and angle measure, this ultimately implies that congruent segments have the same (equal) length.
Thus, line segment UV ≅ line segment XY i.e UV = XY and as such the side lengths are as follows:
SU = VX = 43 feet.
For the congruent angles, we have:
<J ≅ <K i.e m<J = m<K
m<S = m<V = 38°.
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Please help! It is due right now!!!
The total bill for dinner was $33.03 (including tax and a tip). If they paid a 20.2% tip, what was their bill before adding the tip?
Using proportions, it is found that their bill before adding the tip was of $27.48.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
They paid a 20.2% tip, hence 120.2% = 1.202 of the price x is equals to $33.03, hence the bill before the tip is found as follows:
1.202x = 33.03
x = 33.03/1.202
x = $27.48.
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Please someone help me with question a) and b). I’ve been having so much trouble with these types of questions. The booklet says that the answers are a) 134degrees and b) 14.3km. I just don’t get how to get there. Thank you!
The bearing to take is 134 degrees and the shortest distance is 14.3 km
The bearing it would takeThe attached diagram represents a labelled version of the ship movement
The angle at Q is
Q = 180 - 155 + 90 + 120 - 90
This gives
Q = 145
The distance PR is calculated as:
PR^2 =PQ^2 + QR^2 - 2 * PQ * QR * cos(Q)
This gives
PR^2 = 9^2 + 6^2 - 2 * 9 * 6 * cos(145)
Evaluate
PR^2 = 205.46
Take the square root
PR = 14.3 km
The angle at P is then calculated as:
QR/sin(P) = PR/sin(Q)
This gives
6/sin(P) = 14.3/sin(145)
Evaluate the quotient
6/sin(P) = 24.93
Make sin(P) the subject
sin(P) = 6/24.93
Divide
sin(P) = 0.2407
Take the arc sin of both sides
P = 14
The bearing is then calculated as:
Bearing = P + 120
This gives
Bearing = 14 + 120
Evaluate
Bearing = 134
Hence, the bearing to take is 134 degrees
The shortest distanceIn (a), we have
PR = 14.3 km
This represents the shortest distance
Hence, the shortest distance is 14.3 km
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ordenada al origen 6 = paralela a la recta 2x+3y+4=0
La ecuación de la recta que contiene el punto (x, y) = (0, 6) y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.
¿Cómo determinar la ecuación de una recta?
En esta pregunta tenemos que derivar una ecuación de la recta a partir de una recta y un punto. Dos rectas bajo forma implícita son paralelas si y solo si comparten los mismos coeficientes dependientes, entonces tenemos que el coeficiente independiente de la recta es:
2 · 0 + 3 · 6 + k = 0
18 + k = 0
k = - 18
Por tanto, la ecuación de la recta que contiene el punto (x, y) = (0, 6) y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.
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please help me 20 points
Out of 2000 pizzas he sells next time he should expect 797 stuffed crust or pan style. This can be obtained by using formula of probability and multiplying the total number of pizzas.
Find the expected value:The formula for Expected value:
EV = P(X) × n
where EV is the expected value and P(X) is the probability of X and n is the total number.
In the question it is given that,
Thin crust ⇒ number of thin crust sold = 307 Thick crust ⇒ number of thick crust sold = 224Stuffed crust ⇒ number of stuffed crust sold = 161Pan style ⇒ number of pan style sold = 191First we have to find the probability of stuffed crust or pan style,
P( stuffed crust or pan style) = P(stuffed crust) + P(pan style)
The number of stuffed crust and pan style = 161 + 191 = 352
The total number of crusts sold are ⇒ 307 + 224 + 161 + 191 = 883
⇒ P( stuffed crust or pan style) = 161/883 + 191/883
= 352/883
The expected value of stuffed crust or pan style,
n = 2000, P(X) = 352/883
EV = P(X) × n = (352/883) × 2000 = 797.28 ≈ 797
Hence out of 2000 pizzas he sells next time he should expect 797 stuffed crust or pan style.
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The volume of a rectangular box is 1.0 ft3. what is the length if the width is 1.0 ft and the height is 1.5 ft?
The length of the rectangular box is 0.67 feet
How to determine the length of the box?The given parameters are:
Length = ??
Width = 1.0 ft
Height = 1.5 ft
Volume = 1.0 ft^3
The volume is calculated as:
Volume = Length * Width * Height
Substitute the known values in the above equation
1 = Length * 1 * 1.5
Evaluate the product
1 = Length * 1.5
Divide both sides by 1.5
Length = 0.67
Hence, the length of the rectangular box is 0.67 feet
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Andy is collecting pocket change for a fundraiser. he begins with 102 coins in the cup, and their monetary value is $17.10. if he has a mix of dimes and quarters, how many of the coins are dimes?
If Andy has 102 coins mixed with dimes and quarters and monetary value of $17.10 then he has 56 dimes and 42 quarters.
Given number of coins Andy has is 102 and montary value of all coins is $17.10.
We have to determine number of dimes and quarters.
1 dime=$0.10
1 quarter=$0.25
Suppose the number of dimes be x and number of quarters be y.
The equations are:
0.10x+0.25y=17.10------------1
x+y=102-------------2
from equation 2, y=102-x
Put the value of y=102-x in equation 1
0.10x+0.25(102-x)=17.10
0.10x+25.5-0.25x=17.10
-0.15x=17.10-25.5
-0.15x=-8.4
x=8.4/0.15
x=56
Put the value of x in y=102-x
y=102-56
y=46
Hence Andy has 56 number of dimes and 46 quarters.
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Enacting a modeled response depends on your ability to reproduce the response by converting your stored mental images into overt behavior.
Answer:
??
Step-by-step explanation:
forty-seven marbles are shared between some children. each child receives six marbles and there are five marbles left over. how many children share the marbles?
The total number of children can be calculated using linear equation in one variable. The marbles are shared among 7children.
Solution
Total number of marbles = 47
The number of marbles received by each child = 6
Let the number of children be x
Then according to the question'
Total number of marbles received by all children + 5 = Total number of marbles
6x + 5 = 47
6x = 47- 5
6x = 42
x = 7
now, the number of children is 7.
What is linear equation in one variable?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.Here, the variables x and y, the coefficients A and B, and the constant C are all present.A linear equation's graph will always be a straight line.One-variable linear equations are fairly simple to solve. To determine the value of the unknown variable, the variables are divided and placed on one side of the equation, and the constants are combined and placed on the other side.Know more about linear equation https://brainly.com/question/12974594
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Select the statement that describes the expression 5 + (3 x 6) − 4. 5 times the sum of 3 and 6, then subtract 4 Add 5 to the product of 3 and 6, then subtract 4 Add 5 to the product of 3 and 6, then add 4 Add 5 to the quotient of 3 and 6, then subtract 4
Answer: Add 5 to the product of 3 and 6, then subtract 4
Step-by-step explanation:
We will use the order of operations. Looking at 5 + (3 x 6) − 4, we would:
[1] Multiply 3 x 6
[2] Add 5 to that product
[3] Subtract 4 from that value
This means the answer to your question is:
Add 5 to the product of 3 and 6, then subtract 4
Answer: B
i DiD tHe TeSt
A sample of 66 observations will be taken from an infinite population. the population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is:_________.
Using the normal distribution, the probability that the sample proportion will be less than 0.1768 is of 0.9222 = 92.22%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].For this problem, the proportion and the sample size are given by:
p = 0.12, n = 66.
Hence the mean and the standard error are:
[tex]\mu = p = 0.12[/tex].[tex]s = \sqrt{\frac{0.12(0.88)}{66}} = 0.04[/tex]The probability that the sample proportion will be less than 0.1768 is the p-value of Z when X = 0.1768, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.1768 - 0.12}{0.04}[/tex]
Z = 1.42
Z = 1.42 has a p-value of 0.9222.
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I need help! ASAP
As shown in the figure below, a || b and c is the transversal, m∠1= 40°, m∠2= 70°.
Question: m∠3= ?
Answer:
Step-by-step explanation:
your answer will be 110degrees
ABC Corporation recently issued an IPO. Shortly thereafter it decides it wants to buy back some of its shares. What time frame restrictions would ABC face in order to buy back their own stock
The time restriction faced by ABC Corporation for it to buy back its newly issued shares is 4 weeks
What is share buyback?
Share buyback means that the company would repurchase its own shares in the stock market by paying investors holding the shares, then reduce its number of shares outstanding by the number of shares bought back.
The shares repurchased are known as Treasury stocks, which are held until the company decides to reissue them or cancel them.
The restriction placed on a company before it can repurchase its shares is that the shares must be in issue 4 weeks, in other words, the new issued shares through Initial Public Offer(IPO) must be existence for 4 weeks before being repurchased by the company after having issued an IPO.
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Helppp please and thank uuu
What transformation is used to create this frieze pattern?
vertical reflection
glide reflection
horizontal reflection
180° rotation
Answer:
Using translation concepts, it is found that the transformation used to create this frieze pattern is a 180º rotation.
Step-by-step explanation:
A hat contains slips of paper with the letters A-Z printed on them. If you draw one at random, what is the probability that you will get a vowel?
The probability of selecting a vowel from the hat that contains slips of paper with the letters A-Z printed on them is 5/26
What is probability?Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events
How to determine the probability?The given parameters are:
Letters = A - Z
Vowels = A, E, I, O and U
The above means that the number of letters and vowels are
n(Letters) = 26
n(Vowel)
The probability of selecting a vowel from the hat that contains slips of paper with the letters A-Z printed on them is
P(Vowel) = n(Vowel)/n(Letters)
Substitute the known values in the above equation
P(Vowel) = 5/26
Hence, the probability of selecting a vowel from the hat that contains slips of paper with the letters A-Z printed on them is 5/26
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Need this question's answer.
Answer:
1.2
2.4√3÷3
3. x=45, y=15
Step-by-step explanation:
OK,
1. So the first part requires the Pythagoreanism formula which is: b²=a²+c²:
AC²=AB²+BC²====> AC²=(1)²+(√3)²===> AC²=4===> AC=2
2.The second part requires the formula of tan:
tan A=BC÷AB===> tan A=√3÷1===> tan A=√3
tan C=AB÷BC===> tan C=1÷√3===> tan C=√3/3
tan A+tan C=√3+√3/3===> 4√3÷3
3.And the last part requires the equation of angles:
A+B+C=180===>
x+y+x-y+90=180===> 2x=90===> x=45, y=15
Using rigid motion, which statement is true about the triangles?
O ABC is congruent to FED
O ABC is congruent to FDE.
Ο Δ ABC is congruent to DEF.
triangles are not congruent
Answer:
ABC is congruent to DEF
Step-by-step explanation:
I think its this one cause the angles are the same
Help ASAP will give 20 points!!!!!
use six unit multipliers to convert 33 cubic feet to cubic centimeters
Converting 33 cubic feet to cubic centimeters would give 934454. 4 cubic centimeters
How to determine the conversionIt is important to note that conversion of units requires the appropriate equivalent values
For
I cubic foot is equivalent to 28316. 8 cubic centimeters
But we were given
33 cubic feet for the conversion
If 1 cubic foot = 28316. 8 cubic centimeters
Then 33 cubic feet = x
Cross multiply, we get
x = 28316. 8 × 33
x = 934454. 4 cubic centimeters
Thus, converting 33 cubic feet to cubic centimeters would give 934454. 4 cubic centimeters
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The triangles are similar. Find the value of the variable.
PQ has endpoints P(0, 0) and Q(8, 4). Find the coordinates of the midpoint of PQ
O
O
O
(4,4)
(2,4)
(4,2)
Given f(x) = x² + 3x -3 and g(z) = 2x, find f(g(x)).
Solution
First, we need to decide which function will go inside which. Since
our function reads "f of g of z", we know that we are going to
substitute the function for g(x) into every a spot in the f(x)
function.
f(g(x))=(x
)²+3(x
)-3
Next, perform normal order of operations for each term. (Hint:
(2x)² = (2x)(2x))
f(g(x)) = 4
²+3
2-3
Let's look at how this example would be different if it was
performed in the opposite order. Given f(x) = x² + 3x - 3 and
g(x)=2x, find g(f(x)).
In this case, we'll need to plug the whole function for f(x) into the
input (2) spot in the g(x) function.
g(f(x)) = 4
(x² + 3x - 3)
Then we'll distribute to each term.
g(f(x)) = 4(x²)+2(3x)-3 3
Simplify to get the final answer.
The composition of the functions f(x) and g(x) gives the equation:
[tex]f(g(x)) = 4x^2 + 6x - 3[/tex]
How to get the composition of functions?Here we want to get the composition of the two functions:
[tex]f(x) = x^2 + 3x - 3\\\\g(x) = 2x[/tex]
f(x) is a quadratic and g(x) is a linear equation.
Now we want to get the composition:
[tex]f(g(x))[/tex]
This means that we need to evaluate function f(x) in g(x), so we can replace all the "x" in the function f(x) by the notation "g(x)"
[tex]f(g(x)) = g(x)^2 + 3*g(x) - 3[/tex]
Now we replace all the "g(x)" by the actual function g(x) = 2x, we wll get:
[tex]f(g(x)) = g(x)^2 + 3*g(x) - 3 = (2x)^2 + 3*(2x) - 3[/tex]
finally, we can simplify this to get the composition, which is a quadratic function just like f(x).
[tex]f(g(x)) = 4x^2 + 6x - 3[/tex]
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the
Answer:
10 points
Step-by-step explanation:
From the passage, we know:
1. Jay earned 15 points after spending $60
2. We want to know the number of points he can earn if he spends $40
We can set this up into proportions.
60:15 = 40:x
The x is the number of points he will get after spending $40.
15(40) = 60x
600 = 60x
x = 10
Jay will earn 10 points if he uses $40.
2. 2x+6y=6
-x-3y = -3
Solution(s):
PLEASE HELP SOLVE FOR X AND Y
Answer:
x = 0, y = 1
Step-by-step explanation:
2x + 6y = 6 → (1)
x - 3y = - 3 ( add 3y to both sides )
x = 3y - 3 → (2)
substitute x = 3y - 3 into (1)
2(3y - 3) + 6y = 6 ← distribute parenthesis and simplify left side
6y - 6 + 6y = 6
12y - 6 = 6 ( add 6 to both sides )
12y = 12 ( divide both sides by 12 )
y = 1
substitute y = 1 into (2)
x = 3(1) - 3 = 3 - 3 = 0
solution is x = 0 , y = 1
Complete the following tasks for this equation: b/7.8= -2.15.
1. give an estimate for the solution. be sure to explain how you arrived at the estimate, either by showing an equation or in words.
2. solve the equation. show or explain your work.
3. compared to your estimate, is your answer reasonable? explain your answer in complete sentences.
Answer:
Step-by-step explanation:
Factors
A term in multiplication for an entire variety by which a bigger complete quantity may be dividedA divisor is an integer that evenly divides a range without leaving the restFactorization is the decomposition of an item right into a product of other objectsInteger factorization, the manner of breaking down a composite quantity into smaller non-trivial divisorsA coefficient, a multiplicative thing in an expression, usually more than a fewThe act of forming a component institution or quotient ring in summary algebraA von Neumann algebra, with a trivial centerFactor (graph principle), a spanning subgraphAny finite contiguous sub-sequence of a word in a group concept(b)/(7.8)=-2.15
Multiply each term in the equation by 7.8.
(b)/(7.8)*7.8=-2.15*7.8
Cancel the common factor of (1)/(7.8).
1b=-2.15*7.8
Multiply -2.15 by 7.8 to get -16.77.
1b=-16.77
Divide each term in the equation by 1.
(1b)/(1)=-(16.77)/(1)
Cancel the common factor of 1.
b=-(16.77)/(1)
Divide -16.77 by 1 to get -16.77.
b=-16.77
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find the area of the following
Answer:
24000 ft²
Step-by-step explanation:
Triangle PRS:b = base = PR = 240 ft
2AS = 240 ft
[tex]\sf AS = \dfrac{240}{2}\\\\ AS = 120 \ ft[/tex]
h = height = AS = 120 ft
[tex]\sf \boxed{\bf \ Area \ of \ triangle = \dfrac{1}{2}b*h}[/tex]
[tex]\sf =\dfrac{1}{2}*240*120\\\\ = 120 * 120\\\\ = 14400 \ ft^2[/tex]
Triangle PRQ:b = PR = 240 ft
3BQ = 240 ft
[tex]\sf BQ = \dfrac{240}{3}\\\\ BQ = 80 \ ft[/tex]
[tex]\sf Area \ of \ triangle \ PRQ = \dfrac{1}{2}*240*80[/tex]
= 120 * 80
= 9600 ft²
Area of the quadrilateral PQRS = area of ΔPRS + area of ΔPRQ
= 14400 + 9600
= 24000 ft²
What is the shape of the graph of the function?
h(t)=0.6\cdot 3.2^th(t)=0.6⋅3.2
t
The graph of a function f exists the set of all points in the plane of the form (x, f(x)).
What is the graph of a function?
The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could even describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists as a special case of the graph of an equation.
Given: [tex]h(t)=0.6\cdot 3.2^t[/tex]
Substitute the values in the function, we get
t = -2, h(t) = 0.05859375
t = -1, h(t) = 0.1875
t = 0, h(t) = 0.6
t = 1, h(t) = 1.92
t = 2, h(t) = 6.144
t = 3, h(t) = 19.6608
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This table shows values represented by an exponential function x= 0,1,2,3,4,5,6 y=1,3,9,27,64,125,216 what is the average rate of change for this function for the interval from x=2 to x=4?
27.5 is the answer
For this case we know that the average rate of change of a function is given by this general expression:
m = f(b) - f(a)/ b-a
For this special case from the info in the table we have:
a =2 , f(2) = 9
a =4 , f(4) = 64
And replacing the data with the average rate formula we got:
m = 64 - 9/4 - 2 = 27.5
And then the best answer for this case would be:
27.5
The exponential function is a mathematical function represented by f (x) = \ exp or e ^ {x}. Unless otherwise specified, the term generally refers to a function of a positive value of a real variable, but it can also be extended to complex numbers or generalized to other mathematical objects such as matrices and Lie algebras.
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15 POINTS!!!! PLS HELP LOOK AT PIC
Answer:
A
Step-by-step explanation:
The solutions of a quadratic function will always be the x intercepts. Thus, if there are two solutions, there are two x intercepts.