Step-by-step explanation:
44r + 43g = 217
45r + 18g = 144
r = a pound of raspeberries
g = a pound of grapes
solve for x. enter the solutions from least to greatest (x+7)^2-11=0
Answer:
[tex]x=-7-\sqrt{11}, -7+\sqrt{11}[/tex]
Step-by-step explanation:
[tex](x+7)^2=11 \\ \\ (x+7)=\pm \sqrt{11} \\ \\ x=-7-\sqrt{11}, -7+\sqrt{11}[/tex]
SHOW WORK PLEASE AND THANK YOU
Find the equation of a line parallel to y = − x + 7 y=−x+7that passes through the point ( 4 , 5 )
The line parallel to line y= -x + 7 is y= -x + 9.
What is slope intercept form?
The intercept formula y = mx + b is used when you know the slope of the line you are examining, and the specified point is also the y-intercept (0, b). In this formula, b represents the y-value of the y-intercept.
Solution: We will use slope intercept formula y= mx + b
Given that the parallel line passes through (4,5), which means x=4 and y=5
Also, m = -1
Putting value of x and y in slope intercept form to find b, we get
y=mx + b
⇒ 5= (-1x4) + b
⇒ 5= -4 +b
⇒5 + 4= b
⇒b=9
Now putting value of b and m in slope intercept form, we get the parallel line
y= -x + 9
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Elizabeth is going to drive from her house to city a without stopping. Elizabeth’s house is 120 miles from Cytie and she plans to drive at a speed of 30 mph. Make a table of values and then write an equation for D in terms of t representing Elizabeth distance from city A t hours after leaving her house
A table of values that models this situation is as follows;
Distance (miles) Time (hour)
120 0
150 1
180 2
210 3
240 4
An equation for D in terms of t representing Elizabeth's distance from city A, t hours after leaving her house is d = 30t + 120.
How to write a function for the distance and time?Mathematically, a constant of proportionality (time) for Elizabeth's journey (distance) with respect to time can be represented with the following mathematical expression:
d = kt
Where:
d represents the distance.t represents the time.k represents the constant of proportionality (speed).Therefore, the required function that relates the distance (d) and speed (s) at t hours is given by;
d = 30t + 120
Next, we would develop a table of value;
At time (t) = 1 hour, we have;
Distance, d = 30(1) + 120
Distance, d = 150 miles.
At time (t) = 2 hours, we have;
Distance, d = 30(2) + 120
Distance, d = 180 miles.
At time (t) = 3 hours, we have;
Distance, d = 30(3) + 120
Distance, d = 210 miles.
At time (t) = 4 hours, we have;
Distance, d = 30(4) + 120
Distance, d = 240 miles.
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amanda wants to put some of her books on 4 shelves with 6 books on each shelf can amanda arrange her books this way explain
The number of ways the 6 books can be arranged on the 4 shelves by Amanda is 360 ways
How to determine the ways of the books can be arranged?From the question, we have the following parameters that can be used in our computation:
Total number of books, n = 6
Total number of shelves, r = 4
The number of ways the books could be arranged on the shelves is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 6 and r = 4
Substitute the known values in the above equation, so, we have the following representation
Total = ⁶P₄
Apply the permutation formula
ⁿPᵣ = n!/(n - r)!
So, we have the following representation
Total = 6!/2!
Evaluate the quotient
Total = 360
Hence, the number of ways is 360
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A number is 11 more than another number. Twice the sum of the two numbers is 50 . Find the two numbers.
The first number is -4 and the second number is 7
What is word problem?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
Let first number = n
second number = n+11
2(n+n+11)= 6
expanding the bracket
2(2n+11)=6
4n+22 =6
collecting like terms
4n = -16
n=-4
The first number = n =-4
second number = n+11=-4+11=7
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The midpoint of AB is at (-2.3). If A=(7,-6) , find B.
Answer:
Step-by-step explanation:
mid point = a+b/2
let b(x,y)
-2 = [7+x]/2 3 = [-6+y]/2
-4 = 7 + x 6 = -6 + y
-11 = x 12 = y
Hence B is at (-11,12)
find the GCF for 12 and 42
Answer:
6
Step-by-step explanation:
The temperature in Austin is 65◦F and falling at a rate of 2 ◦F per hour. The temperature in Round Rock is 72◦F and falling at a rate of 3 ◦F per hour. Write an inequality that shows when the temperature in Round Rock is colder than that in Austin.
The inequality that shows how long the temperature in Round Rock will remain colder than that in Austin is 72 - 3t > 65 - 2t and the time is less than 13 hours
How to determine the inequality and the intervalsFrom the question, we have the following parameters that can be used in our computation:
Austin
Initial temperature = 65 degrees Fahrenheit
Rate of decrement = 2 degrees Fahrenheit
Round Rock
Initial temperature = 72 degrees Fahrenheit
Rate of decrement = 3 degrees Fahrenheit
The above parameters mean that
Current temperature = Initial temperature + Rate of increment x Number of hours
So, we have
Austin: A(t) = 65 - 2t
Round Rock: B(t) = 72 - 3t
When Round Rock is colder than Austin, we have
B(t) > A(t)
Substitute the known values in the above equation, so, we have the following representation
72 - 3t > 65 - 2t
Evaluate the like terms
-t > -13
Divide both sides by -1
t < 13
Hence, the interval is less than 13 hours
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Liam works at a zoo. He was looking at some data showing the masses of their
5
55 African elephants. The mean mass of the elephants was
3
,
800
kg
3,800kg3, comma, 800, start text, k, g, end text, and the median mass was
3
,
600
kg
3,600kg3, comma, 600, start text, k, g, end text. The smallest elephant, named Lola, weighed
2
,
700
kg
2,700kg2, comma, 700, start text, k, g, end text.
Lola then got very sick and lost weight until her mass reached
1
,
800
kg
1,800kg1, comma, 800, start text, k, g, end text.
How will Lola's mass decreasing affect the mean and median?
Median won't change, however Mean will fall by 180.
What do mean and median?By summing all the numbers in a data collection and dividing by the total number of values in the set, one may get the mean (average) of the data set. When a data collection is sorted from least to largest, the median represents the midpoint value.
African elephants total 555 in number.
Elephants had a 3800 kg average mass.
Elephants had a 3600 kg median mass.
Lola, the elephant that was the smallest, weighed 2700 kg.
Later, Lola became really ill and lost a lot of weight, reaching a mass of 1800 kg.
What effect will Lola's weight loss have on the mean and median as well as Currently, the median is 3600 and the lowest is 2700.
now 2700 becomes 1800
so Median remains the same as 3600
No change in Median
The mean mass of the elephants was 3800 kg
=> total weight = 5 x 3800 = 19000 kg
2700 kg becomes 1800 kg
Hence new total mass = 19000 - 2700 + 1800 = 181000 kg
New Mean = 18100/5 = 3620 kg
Mean reduced by 3800 - 3620 = 180 kg
No change in Median weight
Mean reduced by 180 kg
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The figure of the right is the result of a translation followed by a dilation of the figure on the left.
With the help of AA similarity rule option C,D,E,F will be the answer which is C:-∠ adc is 52.8°
D:- ∠ dac is 26.7°
E:- dac/adc = 0.506
F:- cd/bc =1.8
What is AA similarity rule?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.
Similar figures are items that feature more than two figures that are the same form but different sizes.
Despite having the same form, each might have different sizes.There are no matching angles that are not equal.Similar equivalent side ratios exist.When two triangles are comparable, all of their matching angle pairs and sides are congruent and proportionate. However, you do not necessarily need to have information about all of the sides and angles of two triangles in order to be certain that they are identical.
AA similarity rule
So, ∠ adc is 52.8°
and ∠ dac is 26.7°
So, the ratio of dac/adc = 0.506
And the ratio of side will also be equal as well which is 1.8
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3. In the diagram at the right JK bisects ∠LJM ,. What is the m∠LJM ?
(1) 35
(2) 52
(3) 26
(4) 86
4. What is the area of the triangle shown on the graph below?
(1) 10
(2) 11
(3) 14
(4) 25
Answer:
3= 26
4= 11 because it is area of triangle
In an isosceles triangle, the measured of the third angle us 46. Which equation can be used to find x, the measure of each angle
Answer:
[tex]\huge{\boxed{46 \text{ or } 67 \text{ or } 88 \text{ degrees}}}[/tex]
Step-by-step explanation:
An isosceles triangle is a triangle in which two of the sides and angles are equal. Because the sum of all of the angles in a triangle is 180°, you may setup the following equation.
46 + x + z = 180°
Depending on the following scenario, your answer may be one of two options. If the "third angle" refers to the angle that is not at the base of the triangle, then your equation is as follows:
z = x
46 + x + x = 180
46 + 2x = 180
2x = 134
x = 67
If the third angle is one of the base angles and x is a base angle, then x is also 46, because base angles are equal.
If the third angle is one of the base angles and x is the third angle, then your equation is as follows:
z = 46
46 + 46 + x = 180
92 + x = 180
x = 88
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question content area top left part 1 the functions f and g are defined by the following tables. use the tables to evaluate the given composite function. f^-1
After solving, the value of f^(-1)(g(7)) is 6.
In the given question, we have to find the f^(-1)(g(7)).
The given table of functions f and g is:
x f(x) y g(x)
-3 1 -2 -5
0 4 1 -4
1 5 5 2
6 -6 7 -6
To find the value of f^(-1)(g(7)) we put the value of g(7) from the table. As we can see in the table that at the value of g(x) at point 7 is -6.
Then we find the value of from the table of f(x).
f^(-1)(g(7)) = f^(-1)(-6)
The value of f^(-1)(-6) from the table f(x) is
f^(-1)(g(7)) = 6
Hence, the value of f^(-1)(g(7)) is 6.
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Please help me the question image is attached to the question
Answer:
10-x
Step-by-step explanation:
Simplify this expression.
(4/5)² x (-25) - 4² =
Using PEMDAS, -32 is solution of (4/5)² x (-25) - 4².
Define PEMDAS.A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations. Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right). We are provided with the proper steps for solving a mathematical expression by the PEMDAS rule. Operations are carried out in parenthesis first according to the PEMDAS rule. The next step is to conduct operations on exponents or powers. Then, depending on which occurs first, the operations of multiplication and division are performed from left to right. The final step is to conduct addition or subtraction from left to right, depending on which comes first.
Given
(4/5)² x (-25) - 4²
Using PEMDAS,
Squaring the exponents,
16/25 × -25 - 16
Multiplying,
-16 - 16
Subtracting,
- 32
Using PEMDAS, -32 is solution of (4/5)² x (-25) - 4².
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-x²-22x - 121 = 0 quadratic
Answer: 11
Step-by-step explanation:
we know that : ax² + bx + c = 0
then,
a = −1
b = −22
c = −121
putting the values in the following equation:
x=−b±√b²−4ac ⁄ 2a
=−(−22)±√(−22)²−4⌈(−1)(−121)⌉ ⁄ 2(−1)
=22±√484−484 ⁄ −2
=22±√0 ⁄ −2
=22 ⁄ −2
=11 ⁄ −1
=11
Hence the answer for this equation will be 11.
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You need to be at least 39.37 inches tall (about a meter) to ride on a bumper car. Diego’s cousin is 35.75 inches tall. How many more inches will he need to grow before Diego can take him on the bumper car ride? Explain or show your reasoning.
Answer: 3.62 inches
Step-by-step explanation:
Diego's cousin is too short for this ride, we know how tall he is now and what height he needs to be.
This can be solved by subtracting his needed height from his current height.
39.37-35.75=3.62 inches
What is the common difference for the arithmetic sequence?
4.7, 6, 7.3, 8.6, 9.9, …
Answer:
1.3 is the common difference.
Step-by-step explanation:
Determine the quadratic function f whose graph is given.
The vertex is (3,-3) and the other given point is (2, -1).
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=3\\ y=-3 \end{cases}\implies y=a(x-3)^2 - 3\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=-1 \end{cases} \\\\\\ -1=a(2-3)^2 -3\implies 2=a(-1)^2\implies 2=a~\hfill \boxed{y=2(x-3)^2 -3}[/tex]
Solve for x.
18
12
6.75
85.3
Step-by-step explanation:
32^2-24^2=448
square root 448=21
the small and large parallel line is 21=21
24+9=33
33^2+21^2=1530
square root 1530=39
39-32=7
~7~=6.75
x=6.75
Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 85 miles per hour. The eastbound train travels at 95 miles per hour. How long will it take for the two trains to be 396 miles apart?
Do not do any rounding.
The time it takes the trains 2.2 hours to be 396 miles apart.
What is time?Time is the duration of an event.
How to find how long will it take for the two trains to be 396 miles apart?Since two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 85 miles per hour. The eastbound train travels at 95 miles per hour.
Let
d = distance travelled by first train = vt where v = speed of train = 85mph and t = timeAlso,
D = distance travelled by secnd train = Vt where V = speed of second train = 95 mph and t = timeSince both trains move in opposite directions and leave at the same time, their distance apart after time t is D' = d + D
= vt + Vt
= 85t + 95t
= 180t
Since D' = 396 miles, we have that
396 = 180t
t = 396 m/180 mph
t = 2.2 hours
So, it takes the trains 2.2 hours to be 396 miles apart.
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A sight-seeing boat travels at an average speed of 21 miles per hour in the calm water of a large lake. The same boat is also used for sight-seeing in a nearby river. In the river, the boat travels 2.6 miles downstream (with the current) in the same amount of time it takes to travel 2 miles upstream (against the current). Find the current of the river.
Answer:
Step-by-step explanation:
Let's call the speed of the boat in the river x miles per hour. The boat travels 2 miles downstream in the same amount of time it takes to travel 2 miles upstream, so the speed of the boat relative to the water is the same in both directions. We can set up the following equation to represent this relationship:
21 - x = x + current speed
Solving for x, we find that the speed of the boat in the river is (21 - x)/2 = 10.5 miles per hour.
We can then use this value to find the current speed of the river. The boat travels 2.6 miles downstream in the same amount of time it takes to travel 2 miles upstream, so the speed of the boat relative to the ground is the same in both directions. We can set up the following equation to represent this relationship:
10.5 + current speed = 10.5 - current speed
Solving for the current speed, we find that it is (10.5 - 10.5)/2 = 0.
Therefore, the current speed of the river is 0 miles per hour.
Use the formula A=P\left(1+r/n)^nt to solve the compound interest problem.
Find how long it takes a 1700$ investment to earn 500$ interest if it is invested at 2% interest compounded quarterly.
500$ interest will be earned in approximately years. (Round to the nearest tenth.)
The total years taken to double the money according to Compounding will be 13.75 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 2%
amount = $1700
Total amount = $2200
Compounded monthly,
so formula becomes,
Total amount = amount (1+r/400)^4t
T = A([tex](1+r/400)^{4t[/tex]
2200 = 1700(1 +2/400)^4t
22/17 = (1 +1/200)^4t
22/17 = (1.005)^4t
1.29 = (1.005)^4t
taking log on both sides
0.11/0.002 = 4t
t = 13.75 years.
Hence the time taken to double the money is 13.75 years.
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Compute GCD(1240, 6660)
The greatest common factor between the given two numbers will be 20.
What is the greatest common factor?The greatest common factor is the largest positive number which can be divided into given numbers evenly.
Given that the two numbers are 1240 and 6660. First, factorize each number and find the common multiple of both numbers.
1240 = 2 x 2 x 2 x 5 x 31
6660 = 2 x 2 x 3 x 3 x 5 x 37
The common numbers are,
2 x 2 x 5
4 x 5
20
Therefore, the greatest common factor between the given two numbers will be 20.
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How can we prove these triangles congruent?
Answer:
Angle-Side-Angle or also known as ASA
Step-by-step explanation:
The Cosmic Consoles factory makes video game consoles, packs them into boxes, and ships them by truck. In v boxes, there are 24v video game consoles. This morning, a truck carrying 100 boxes of the latest model game consoles left the factory.
How many video game consoles were on the truck?
Write your answer as a whole number or decimal.
video game consoles
Answer:
Step-by-step explanation:
2,400 consoles
Use the slope formula to find the slope of the line through the points (8,−3) and (−6,4)
Answer:
-1/2
Step-by-step explanation:
You want the slope of the line through points (8, -3) and (-6, 4) using the slope formula.
Slope formulaThe formula for the slope of the line through points (x1, y1) and (x2, y2) is ...
m = (y2 -y1)/(x2 -x1)
ApplicationFor the two given points, the slope is ...
m = (4 -(-3))/(-6 -8) = 7/-14 = -1/2
The slope of the line is -1/2.
It is given & = {x: 1 ≤ x ≤ 10, x is an integer); P= {odd numbers); Q= {prime numbers) and R= {1,2,3,4,5} List the elements of each of the following sets. (a) (PNQ)UR (b) (RMP)'UQ (c) Q'N(PUR) (d) (PUQUR)' (POR)
The elements of the required sets would be
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
What are sets?
A set is a mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Given:
Let the universal set is (S) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
P = {Odd numbers} = {1, 3, 5, 7, 9}
Q = {Prime Numbers} = {2, 3, 5, 7}
R = {1, 2, 3, 4, 5}
So by using the properties of sets we can find
P' = {2, 4, 6, 8, 10}
Q' = {1, 4, 6, 8, 9, 10}
R' = {6, 7, 8, 9, 10}
P∩Q = {3, 5, 7}
R'∪P' = {2, 4, 6, 7, 8, 9, 10}
P∪R = {1, 2, 3, 4, 5, 7, 9}
P∩R = {1, 3, 5}
P∪Q∪R = {1, 2, 3, 4, 5, 7, 9}
P'∩Q'∩R' = S - P∪Q∪R
= {6, 8, 10}
Now we can find the elements of the required sets:
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
Hence, the elements of the required sets would be
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
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ΔADE and ΔABC are similar. Which best explains why the slope of the line between points A and D is the same as the slope between points A and B ?
As ΔADE and ΔABC are similar because of their slope so correct option is A.
What are similar triangles?
Similar triangles square measure triangles that have identical form, however their sizes might vary. All equal triangles, squares of any facet lengths square measure samples of similar objects.
Main Body;
let co-ordinates of the points
A = (x₁ ,y₁ ) E =(x₂, y₂)
D =( x₃,y₃) C= (x₄ ,y₄) B =( x₅,y₅)
Now, Slope of a line = Δy/Δx
.: Slope of line AD = y₃ -y₂/x₂-x1 .
= DE/AE
... Slope of line AB = y₅-y₄/x₄-x₁ = BC/ AC
Since ΔADE ~ ΔABC
Now , Slope of AD = slope of AB
=> DE/ AE = BC /AC
In option A
By property of Similar triangle -
DE /BC = BC /АC
Hence, option A is correct answer.
All other options are incorrect
Since Sides of a similar triangle may not be equal.
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