Answer:
13 in
Step-by-step explanation:
Let the hypotenuse be x. Then, by the Pythagorean theorem,
[tex](x-8)^2 + 12^2=x^2 \\ \\ x^2-16x+64+144=x^2 \\ \\ 16x=64+144 \\ \\ x=4+9 \\ \\ x=13[/tex]
Use Gaussian elimination to solve.The burkes pay their babysitter $5 per hour before 11p.m. and $7.50 after 11 p.m. One evening they went out for 5 hours and paid the sitter $35.00. Whag time did they come home?
Given the information on the problem, we can write the following system of equations:
[tex]\begin{cases}x+y=5 \\ 5x+7.5y=35\end{cases}[/tex]then, we can write the following augmented matrix:
[tex]\begin{bmatrix}{1} & {1} & {5} \\ {5} & {7.5} & {35}\end{bmatrix}[/tex]now, if we multiply by 5 the first row and then substract it from the second row, we get:
[tex]\begin{bmatrix}{1} & 1{} & {5} \\ {5} & {}7.5 & 35{}{}\end{bmatrix}\rightarrow\begin{bmatrix}{1} & 1{} & 5{} \\ {0} & {2.5} & {10}{}\end{bmatrix}[/tex]notice that from the second equation, we can find the value of y:
[tex]\begin{gathered} 2.5y=10 \\ \Rightarrow y=\frac{10}{2.5}=4 \\ y=4 \end{gathered}[/tex]now that we have that y = 4, we can use this value on the first equation to find x:
[tex]\begin{gathered} x+4=5 \\ \Rightarrow x=5-4=1 \\ x=1 \end{gathered}[/tex]now, we have that the babysitter worked 1 hour before 11pm and 4 hours after 11 pm,then, the Burkes came home at 3 am
When you first looked at the image, you saw that Dina has 24 tickets for carnival rides, and she wants to use all of them. Some rides have a height requirement, and some rides do not have a height requirement.
-Dina has 24 tickets and wants to use all of them. She plans to go on a ride most once.
-Rides with no height requirement cost 3 tickets.
-Rides with a height requirement cost 4 tickets.
Let's answer the question "How many rides can Dina go on using all of her tickets?"
1. Which statements are true about the variables involved in this situation and the values for each variable? Select all that apply.
A. The variables should represent the number of tickets spent on rides with no height requirement and the number of tickets spent on rides with a height requirement.
B. The variables should represent the cost in tickets for rides with no height requirement and the cost in ticket for rides with a height requirement.
C. The values for the variables can be any real number.
D. The values for the variables can be any nonnegative integers.
2.To answer the question, think about the strategy you would use along with all the information you have. What answer do you get? Select all that apply.
Note that 3-ticket rides have no height requirement, and 4-ticket rides have a height requirement.
A. 3-ticket rides: 0; 4-ticket rides: 6
B. 3-ticket rides: 2; 4-ticket rides: 6
C. 3-ticket rides: 4; 4-ticket rides: 3
D. 3-ticket rides: 6; 4-ticket rides: 2
E. 3-ticket rides: 8; 4-ticket rides: 0
3.D. Does your answer make sense in the context of the situation? How do you know? Select the correct words to complete the answer.
The answer makes sense in the context of the situation because the numbers of rides are A._______ and the number of tickets totals B._______.
1. The statements that are true about the variables involved in this situation and the values for each variable are:
A. The variables should represent the number of tickets spent on rides with no height requirement and the number of tickets spent on rides with a height requirement2. The number of rides Dina can go on using all of her tickets are
C. 3-ticket rides: 4; 4-ticket rides: 33. Yes, The number of rides equals the total number of tickets while maintaining going for a ride most once
The answer makes sense in the context of the situation because the numbers of rides are A. 7 and the number of tickets totals B. 24
How to find how many rides can Dina go on using all of her ticketsgiven data
Dina has 24 tickets for carnival rides
She plans to go on a ride most once
Rides with no height requirement cost 3 tickets
Rides with a height requirement cost 4 tickets
1. The given statement includes: She plans to go on a ride most once. This means that Dina will not have a zero ride.
zero is a real number and a non negative integer hence option A is correct
2. Option C maintains she plans to go on a ride most once and the number of tickets used totals 24
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Use front end rounding to round each number. Then add the rounded
numbers to get an estimated answer. Finally, find the exact answer.
35.25
197.39
+ 4.835
Step-by-step explanation:
A35 (whole number )35.3 (1 decimal place)35.28 (2 decimal place)B197 (whole number )197.4 (1 decimal place)197.39 (2 decimal place)C5 (whole number )4.8 (1 decimal place)4.89 (2 decimal place)The normal cruising speed of a certain airplane is about 170 m/sec. What is this speed in miles per hour?
The speed of airplane in miles per hour (mph) is 380.2968 .
What is speed?
Speed is the time rate at which an object is moving along a path. The SI unit of speed is meter per second ( m/s ). Miles per hour ( mph ) is a British imperial and United States customary unit of speed expressing the number of miles travelled in one hour.
Given that
Speed of a certain airplane = 170 m/s or m[tex]s^{-1}[/tex]
We know that
In 1 meter = 0.0006214 miles
In 1 sec = [tex]\frac{1}{3600}[/tex] hour
but 1 [tex]sec^{-1}[/tex] = 3600 hour
Speed of this airplane in miles per hour = 170 × 0.0006214 × 3600 mph
= 0.105638 × 3600 mph
= 380.2968 mph
Hence, the speed of airplane in miles per hour (mph) is 380.2968 .
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Find the value of x:
Answer: it should be 5
we can multiply 3x4 to get twelve so it must be the same for the other one
So 5x4=20
Step-by-step explanation:
have a great day!
Answer:
5
Step-by-step explanation:
12/4 = 3. 20/4 = 5
Side 12 divided by side 3 is four. You know four is now your key. Side 12 divided by 4 is Side 3. Side 20 divided by 4 is 5. So 5 is your answer.
Hope this helps! :)
Find the z-value so that the area to the right of z (shaded in the picture) is 0.9429.
To determine the z-value so that the area to the right of z is 0.9429
[tex]\begin{gathered} Pr(0Hence the corresponding Z- score from the shaded picture of x - value 0.4429 = 1.58Wilbert bought a new dirt bike and is now $229 in debt. How much money does Wilbert have? What does $0 represent in this problem? 6.NS.5
Answer:
The money that Wilbert has is -$229 because of the debt.
$0 Represents his current, with no debts.
I need help with question 4. The model is at the very top, no need to answer the question that has been scribbled out.
Step 0 ---- 2
2+1
step 1 ------ 3
3+3
step 2 --------- 6
6+5
step 3 ----------11
11 + 7
step 4 ------------ 18
terms are 2, 3, 6,11, 18
There is an increment of odd numbers from a preceding term
2 increase to 3 by the first odd i.e 1
3 increase to 6 by the next odd i.e 3
6 increase to 11 by the next odd i.e 5
Therefore 11 will increase by the next odd, i.e 7
Thus, 11 + 7 = 18
Solve for x.
8x = 4x-32
determine whether the ordered pair is a solution of the given equation Remeber to use alphabetical order for substitution (-6,-2) a solution of the equation r-s=4 is (-6,-2) a solution of the equation r-s=4?
To check if an ordered pair is a solution to an equation, substitute the value for each coordinate into the equation.
Since the substitution has to be performed in alphabetical order, then the coordinates are given in the form:
[tex](r,s)[/tex]Substitute r=-6 and s=-2 into the given equation to check if (-6,-2) is a solution:
[tex]\begin{gathered} r-s=4 \\ \Rightarrow(-6)-(-2)=4 \\ \Rightarrow-6+2=4 \\ \Rightarrow-4=4 \end{gathered}[/tex]Since -4 is NOT equal to 4, then the point (-6,-2) is not a solution to the equation r-s=4.
across which axis was point F reflectedF(10, -5) - F'(-10, -5)
y-axis
Explanations:When a figure is reflected about any axis, the coordinate of that axis still remains the same, but the coordinate of the other axis is negated
For example:
If the point A(x, y) is reflected about the x-axis, the reflected image becomes A' (x, -y)
If the point A(x, y) is reflected about the y axis, the reflected image becomes A'(-x, y)
In this exercise, the point F(10, -5), after reflection, becomes F' (-10, -5)
Since the y-axis still remains -5 after reflection, this means that the point F was reflected across the y-axis.
Pedro has scores of 95, 84, 68, 92 after four tests. what score must he make on his fifth test to have an average of 78 or greater?
Answer:
51 or above
Step-by-step explanation:
He already averages more then 78. But he at least needs a 51 in order for him to average 78. For him to get more than that he just needs a 52 or higher.
78 x 5 = 390
95 + 92 + 84 + 68 = 339
339/ 4 = 84.75 ( just to let you know the average before #5 )
390 - 339 = 51
51 is that last score needed
Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?
2(25) + c
25c + 3
3(c) + 25
3(c + 25)
The expression which can be used to represent the total owed for 3 months given the cost per month and a one-time equipment fee is 3(c) + 25
The correct answer option is option C
The expression that represents the total owedPrice of the cable per month = cOne time equipment fee = $25Number of months = 3 monthsThe total owed = Number of months(Price of the cable per month) + One time equipment fee
The total owed = 3(c) + 25
I'm conclusion, the expression for the total owed is represented by 3(c) + 25
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Answer: option c
bc 3<c> is the fee for 25
7 * the smaller of two consecutive even integers is the same as -248 minus 6 * the larger integer. find the integers
7 * the smaller of two consecutive even integers is the same as -248 minus 6 * the larger integer. find the integers
let
x ----> the smaller of two consecutive even integers
x+2 -----> the second integer
so
7x=-248-6(x+2)
solve for x
7x=-248-6x-12
7x+6x=-248-12
13x=-260
x=-20
the second number is
-20+2=-18
the numbers are -20 and -18calculate the sum of the infinite series S ∞=5-3+9/5-…A.)not possible B.)31/8C.)25/8D.)21/8
Looking at the series, we have a geometric sequence, where the first term is a1 = 5 and the common ratio is q = -3/5.
(This ratio can be calculated by dividing one term by the term before)
To find the sum of an infinite geometric sequence, we can use the formula below:
[tex]S_{\infty}=\frac{a_1}{1-q}[/tex]Since a1 = 5 and q = -3/5, we have:
[tex]S_{\infty}=\frac{5}{1-(-\frac{3}{5})}=\frac{5}{1+\frac{3}{5}}=\frac{5}{\frac{8}{5}}=5\cdot\frac{5}{8}=\frac{25}{8}[/tex]Therefore the correct option is C.
Find the volume of each figure. Round your answers to the nearest whole, if necessary.
Given that
The figure is of a cone and we have to find the volume of the cone.
Explanation -
The diameter of the cone is 22km and the height is also 22 km.
So the radius will be
radius = r = d/2 = 22/2 km = 11 km
Hence, r = 11 km and h = 22 km
The formula for the volume of the cone will be
[tex]Volume=\frac{1}{3}\times\pi\times r^2h[/tex]On substituting the values we have
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times11^2\times22\text{ km}^2 \\ \\ V=\frac{1}{3}\times\frac{22}{7}\times11\times11\times22\text{ km}^2 \\ \\ V=\frac{58564}{21}\text{ km}^2=2788.7\text{ km}^2 \end{gathered}[/tex]So B is the correct option.
Final answer -
Hence the final answer is 2788 sq km.Calculate the distance between the points E = (-4 , 5) and L=(1 , -3) in the coordinate plane. Give an exact answer (not a decimal approximation).
The distance between the points E = (-4,5) and L = (1,-3) in the coordinate plane is [tex]\sqrt{89}[/tex]
The points are E = (-4,5) and L = (1,-3)
We know the distance between the two points d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Where d is the distance between two points
[tex](x_{1},y_{1} )[/tex] and [tex](x_{2},y_{2} )[/tex] are the coordinates of the points
Here the given points are E = (-4,5) and L = (1,-3)
To find the distance between the given points, we have to substitute the values in the equation
d = [tex]\sqrt{1-(-4))^{2}+(-3-5)^{2} }[/tex]
d = [tex]\sqrt{5^{2}+(-8)^{2} }[/tex]
d = [tex]\sqrt{25+64}[/tex]
d = [tex]\sqrt{89}[/tex]
Hence, the distance between the points E = (-4,5) and L = (1,-3) in the coordinate plane is [tex]\sqrt{89}[/tex]
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Sam's mother has entered a 10K race. Sam and his family want to show their support of their mother, but they need to
figure out where they should go along the race course. They also need to determine how long it will take her to run the
race so that they will know when to meet her at the finish line. Previously, his mother ran a SK race with a time of
hours. Assume Sam's mother ran the same rate as the previous race in order to complete the chart.
Create a table that shows how far Sam's mother has run after each half hour from the start of the race, and graph it on
the coordinate plane to the right.
Mother's 10K Race
Time
(H. in hours)
Distance Run
(D, in kilometers)
Distance (in kilometers)
12
10
0
0.5
1
1.5
Time (in hours)
3.5
The specific thing about this graph is it forms a straight line, and it extends to point of origin. The time x is on the x-axis and the distance y is on the y-axis. The coordinates on the graph are the same as the pairs in the table. (2, [tex]6\frac{2}{3}[/tex]) means Sam's mother ran [tex]6\frac{2}{3}[/tex] km in 2 hours.
What is a proportional relationship?Relationships between two variables are called as proportional when you see that their ratios are equal. One variable in a proportional connection is always a constant value multiplied by the other. "Constant of proportionality" is the name that is given to this constant.
What is a proportional relationship graph?The graph of a proportionate connection is a straight line that passes through the origin and rises steadily. The graph's unit rate can be represented by the point on this graph.
The graph depicting this proportional relationship formed in the table can be seen in the image attached.
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The complete question is:
"Sam's mother has entered a 10K race. Sam and his family want to show their support of their mother, but they need to
figure out where they should go along the race course. They also need to determine how long it will take her to run the
race so that they will know when to meet her at the finish line. Previously, his mother ran a SK race with a time of
hours. Assume Sam's mother ran the same rate as the previous race in order to complete the chart.
Create a table that shows how far Sam's mother has run after each half hour from the start of the race, and graph it on
the coordinate plane to the right.
a) What are some specific things you notice about this graph?
b) What is the connection between the table and the graph?
c) What does the ordered pair (2,6 [tex]\frac{2}{3}[/tex]) Represent in the context of this problem?"
The frequency (F) and length (L) of a wave are related by the following formula F x L = 3.0 x 10^10. Consider that wavelength of violet light is 1.3 x 10^-8. What is the frequency of violet light
Answer:
B: 2.3 x 10^18
expination:
Substitute values into the formula.
F x L = 3.0 x 10*10
F x 1.3 x 10^−8 = 3.0 x 10^10
F = 3.0 x 10^10 1.3 x 10^−8 F = 2.3 x 10^18
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Find the domain and range of the function represented by the graph.
The graph is a filled-in point at ordered pair negative 4 comma negative 1, a line segment from ordered pair negative 4 comma negative 1 to ordered pair 0 comma 3, a line segment from ordered pair 0 comma 3 to ordered pair 2 comma 3, a line segment from ordered pair 2 comma 3 to ordered pair 3 comma 4, and a filled-in point at ordered pair 3 comma 4.
The domain is
$\le x\le$
.
The range is
$\le y\le$
.
WORTH 35PTS
what is equivalent to (3^4)^6÷3^2
The required expression equivalent to the given expression is 3²² .
An expression in mathematics is said to be algebraic if it was constructed using integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
However, transcendental numbers like such and e are not algebraic because they are not created from integer constants and algebraic operations.While the definition of e necessitates an infinite number of algebraic operations, the generation of is frequently expressed as a geometric expression.If an expression can be reduced to a reasonable fraction using the features of arithmetic operations, it is said to be rational (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).Given : the expression of the form ( 3 ⁴ ) ⁶ ÷ 3²
Simplifying we get:
= ( 3 ⁴ ) ⁶ ÷ 3²
= 3⁽²⁴⁻²⁾
= 3²²
Therefore the required expression equivalent to the given expression is
3²² .
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Evalúe the limit. Show steps
After evaluating the limit we have came to find that the limit of [tex]\frac{x + 1}{x^2 -4x +4}[/tex] as x approaches 2 is ∞
What is limit?A limit in mathematics is the value that a function, sequence, or index approaches as an input, or an index, approaches a certain value. The definitions of continuity, derivatives, and integrals depend on limits, which are fundamental to calculus and mathematical analysis.
The idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network, and it is closely related to the concepts of limit and direct limit in category theory.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit we will use L'Hôpital's Rule
Find the derivative
[tex]\lim_{x \to 2} \frac{1 + 0}{2x -4 +0}[/tex]
Evalúe 2 as x
⇒ [tex]\frac{1 + 0}{2x -4 +0}[/tex]
⇒ [tex]\frac{1}{2(2) -4 +0}[/tex]
⇒ [tex]\frac{1}{0}[/tex]
⇒ ∞
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I need help with number 3
Answer: A.
Step-by-step explanation:
Answer:
the perimeter of a triangle is 84 cm and its area is 336 cm? if one of its side is 30 cm find the length of reamining two side
I NEEEED HELLPPP LIKE ASAP I ONLY GOT 5 MINS TO DO THIS AND MORE WILL GIVE BRAINLY AND A LOT OF POINTS
Answer:
I can see that (0, 2) is the solution to this equation because that is the point where the lines intersect.
Step-by-step explanation:
[tex] - 3x + 2 = \frac{1}{2} x + 2[/tex]
[tex] - 3x = \frac{1}{2} x[/tex]
[tex]x = 0[/tex]
[tex]y = 2[/tex]
I need help answering this question.
You have to determine which of the given square roots can be expressed as a fraction:
1) The square root of one is 1
[tex]\sqrt[]{1}=1[/tex]One can be expressed as a fracion:
[tex]1=\frac{1}{1}[/tex]So it is a rational number.
2) The square root of 2 is an irrational number and cannot be expressed as a fraction.
[tex]\sqrt[]{2}=1.414213562\ldots..[/tex]Its decimal expantion has no end, i.e. it has infinite decimal values.
3) Square root of three is an irrational number and cannot be expressed as a fraction.
[tex]\sqrt[]{3}=1.732050808\ldots.[/tex]4) The square root of 5 is an irrational number and cannot be expressed as a fraction.
[tex]\sqrt[]{5}=2.236067977\ldots..[/tex]In conclusion the only rational number in the given set is the square root of 1.
Calculate the future value of the $9,000 earning 9% interest compounded quarterly for 8 years round answer to two decimal places
Compound interest formula:
A = P (1 + r/n )^nt
Where:
A = future vale
P= Principal investment = 9,000
r = interest rate in decimal form = 9/100 = 0.09
n = number of compounding periods = 4
t = years = 8
Replacing:
A = 9000 ( 1 + 0.09/4)^ (4*8)
A = 9000 (1.0225)^32
A= 18,342.93
The future value is $18,342.93
1. An angle in a right triangle is identified as θ. If the tangent of θ equals one, what must be true about the triangle side lengths?
A. The side adjacent to theta is half the length of the hypotenuse.
B. The side opposite to theta is longer than the adjacent side.
C. The sides opposite and adjacent to theta are the same length.
D. The side adjacent to theta is longer than the adjacent side.
If the tangent of θ equals one (1), the true statement about the right-angled triangle side lengths is that: C. The sides opposite and adjacent to theta are the same length.
What is a tangent?In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.
Mathematically, the tangent of an angle is given by this expression:
Tanθ = Opp/Adj
Where:
Opp represents the opposite side of a right-angled triangle.Adj represents the adjacent of a right-angled triangle.θ is the angle.For this right-angled triangle, the tangent of the angle (θ) is given by:
Tanθ = Opp/Adj = 1
Opposite/Adjacent = 1
Cross-multiplying, we have:
Opposite = Adjacent
In conclusion, the opposite side length of this right-angled triangle is equal to its adjacent side length.
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Write an equation (slope-intercept form) of the line
passing through the point (-20, 4)
that is perpendicular to the line
2x + 5y = 10.
y =
Blank 1:
The equation in the slope-intercept form will be y = (-2/5)x + 4.4.
What do we mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.So, point is (-20, 4) and line is 2x + 5y = 10, then the equation will be:
m = -2/5y = (-2/5)x + bNow, solve for b as follows while inserting the values of x and y:
y = (-2/5)x + b4 = (-2/5)-20 + b4 = 40/-100 + b4 = -0.4 + b4.4 = bb = 4.4So, equation will be y = (-2/5)x + 4.4
Therefore, the equation in the slope-intercept form will be y = (-2/5)x + 4.4.
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Chris bought 18.4 gallons of gasoline. There are approximately 3.8 liters in 1 gallon.
Which measurement is closest to the number of liters of gasoline Chris bought?
14.6 L
6.21 L
69.92 L
4.84 L
yall what is 2 divided by 4/9
Answer:
4.5
Step-by-step explanation:
2/1 x 9/4 = 18/4 = 4.5
Answer:
4.5 is your answer
Step-by-step explanation:
hope it helps