Answer:
-7
Step-by-step explanation:
[tex]4x-12 \leq 16+8x \\ \\ -12 \leq 16+4x \\ \\ -28 \leq 4x \\ \\ 4x \geq -28 \\ \\ x \geq -7[/tex]
What equation represents the line that passes through the point (4, -5) and is perpendicular to the line x + 2y = 5?
The line that passes through the point (4, -5) and is perpendicular to the line x + 2y = 5? is y = 2x - 13.
Calculation:-
The equation of a line is y = mx + c, m is the gradient and c is the intercept
The line passes through points 4 and -5, x is 4 and y is -5
-5 = 4m + c
When two lines are perpendicular, the products of their gradients are equal to -1, m1 * m2 = -1
x + 2y = 5
2y = -x + 5
y = (-1/2 * x) + 5
therefore m = -1/2
m1 * m2 = -1
m * -1/2 = -1
-m = -2 , therefore m = 2
-5 = 4 * 2 + c
c = -5 - 8, which is -13
Therefore the equation for the line is y = 2x - 13.
To determine if a point is on a line you can simply substitute the x and y coordinates into the equation. Another way to solve the problem would be to graph the line and see if it falls on the line. Plugging in will give which is a true statement, so it is on the line. Only one line can pass through a single point. False because we can draw an infinite number of lines through a given point as shown below.
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Question is shown in image below. Thank you in advance for your time today.
Alloy #13 contains 7% gold, if means that if we need 2.7kg of this alloy, we will have to use a certain amount of gold. Multiply the percent of gold times the mass of alloy to find how much gold we need:
[tex]2.7kg\cdot7\%=0.189kg[/tex]It means that we need 0.189kg of gold.
The alloy we have contains 21% of gold. That means that for every 100kg of alloy there are 21kg of gold, use this ratio to find the mass of alloy we need:
[tex]0.189kgGold\cdot\frac{100kgAlloy}{21kgGold}=0.9kgAlloy[/tex]It means that we need 0.9kg of that alloy.
To find how much magic steel we need, we just have to substract this mass from the mass of Alloy #13:
[tex]2.7kg-0.9kg=1.8kg[/tex]It means that we need 1.8kg of magic steel.
The answer is: The dwarves need 1.8 kg of magic steel and 0.9 kg of their alloy in order to get 2.7 kg of Dragon Alloy #13.
Can someone pleaseeee help me with this pleasee! I appreciate if u do!! thank you!!
The and following system was solved by substitution, but there is a mistake in the
process. Identify which step contains the mistake, and explain how to fix it.
28) -5x-y=23
3x-y=-17 Use subtraction
Step 1: 2x + 5(x + 7) = 21
Step 2: 2x + 5x + 7 = 21
Step 3: 7x + 7 = 21
Step 4: 7x = 14
Step 5: x =2
Step 6: y=2+7
The values of x and y are -5 and 2 respectively
What is Substitution Method to Solve Linear Equation in Two Variables?
The substitution technique is one of the algebraic methods for solving a system of linear equations in two variables. In this procedure, we get the value of any variable by isolating it on one side of the equation and taking every other term on the other side.
Solution:
The problem is in the step one,
Given: -5x - y = 23
3x - y = -17
You've done the question using substraction method while it waas asked to solve by substitution method.
from equation 1 we can write -y = 23 + 5x
substituting -y in equation 2
3x + 23 + 5x = -17
8x = -40
this implies x = -5 and thus, y = 2
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Express the following quotient in simplest form without the use of negative exponents
Given:
[tex]\frac{5x^2y^{11}}{2}\frac{.}{.}\frac{x^4y^6}{6}[/tex]We first need to change the divion to multiplication by inverting the term that comes after the division sign.
That is;
[tex]\frac{5x^2y^{11}}{2}\times\frac{6}{x^4y^6}[/tex]Apply the laws of indices;
[tex]\frac{6\times5x^2y^{11}x^{-4}y^-^6}{2}[/tex][tex]=3\times5x^{2-4}y^{11-6}[/tex][tex]=15x^{-2}y^5[/tex][tex]=\frac{15y^5}{x^2}[/tex](0,4) and (x,7); m=3/2
Step-by-step explanation:
I guess you are trying to find x value
slope equation:
slope, m = (y2-y1)/(x2-x1)
3/2 = (7-4)/(x-0)
3/2=3/x
1.5 = 3/x
1.5x = 3
x = 3/ 1.5
x = 2
The terminal side of an angle What is the cot
Using the unit circle:
[tex]\begin{gathered} cot\theta=\frac{x}{y} \\ \\ cot\theta=\text{ }\frac{\frac{33}{65}}{\frac{56}{65}} \\ \\ cot\theta=\text{ }\frac{33}{56} \\ \end{gathered}[/tex]Is (5, 8) a solution to this system of equations?
X = 5
2x + y = 18
yes
no
Need answer asap
A visitor to the Grand Canyon hiked the South Kaibab Trail and the River Trail on one day. The next day, she hiked the Bright Angel Trail. How far did she hike the first day? How much farther did she hike the first day than the second day? How much longer was her total route than if she had hiked the North Kaibab Trail?
At the first day: the visitor hiked the South Kaibab Trail and the River Trail on one day
so, the length for the first day = 10.1 + 2.7 = 10.1 + 2.7 = 12.8 km
At the second day: the visitor hiked the Bright Angel Trail
so, the length of the second day = 12.6 km
We will answer the questions:
How much farther did she hike the first day than the second day?
it will be = 12.8 - 12.6 = 0.2 kilometers
How much longer was her total route than if she had hiked the North Kaibab Trail?
The total route = 12.8 + 12.6 = 25.4
if she had hiked the North Kaibab Trail, the difference will be = 25.4 - 22.9 =
= 2.5 kilometers
as many. How many successful free throws did Priya make today?
free throws
vitamin C (mg)
25%
0
50%
0
75%
2.
A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C,
which is 250% of the daily recommended allowance of vitamin C for adults. What is
100% of the daily recommended allowance of vitamin C for adults?
10000
100%
1500
125%
150%
20006
25006
Answer:
A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. What is 100% of the daily recommended allowance of vitamin C for adults?
| n | = 3.5 what are the values for n will make the expression true?
The given expression is,
[tex]\lvert n\rvert=3.5[/tex]So we know that, the absolute value of a number is its distance from the origin, say 0. SInce the distance cannot be expressed in negative values, absolute values are always expressed as positive numbers. FOr example,
[tex]\lvert-x\rvert=\lvert x\rvert=x[/tex]Therefore, the values that make the given expression true can be,
[tex]\lvert n\rvert=3.5\Rightarrow n=-3.5\text{ or n=3.5}[/tex]The owner of Rockport Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 11 small arrangements and 1 large arrangement, which took her a total of 62 minutes. After lunch, she arranged 12 small arrangements and 1 large arrangement, which took 67 minutes. How long does it take to assemble each type?
To solve this, we need to write a system of equations.
We know that it took her 62 minutes to assemble 11 small and 1 large.
Let's call the small arrangements S, and the large L.
Then:
[tex]11S+L=62[/tex]After lunch, she did 12 small and 1 large in 67 minutes. Then:
[tex]12S+L=67[/tex]Now we have the system of equations:
[tex]\begin{cases}11S+L=62 \\ 12S+L=67\end{cases}[/tex]To solve by elimination, we need to eliminate one unknown by adding or substracting the two equations. If we rest the first equation to the second equation:
[tex](12S+L)-(11S+L)=67-62[/tex]Now we can solve:
[tex]\begin{gathered} 12S-11S+L-L=65-62 \\ S=5 \end{gathered}[/tex]To make a small arrangement takes her 5 minutes. Now we can go back to the first equation and replace S = 5:
[tex]\begin{cases}11S+L=62 \\ S=5\end{cases}\Rightarrow11\cdot5+L=62[/tex]And solve for L:
[tex]\begin{gathered} 55+L=62 \\ L=62-55 \\ L=7 \end{gathered}[/tex]Then it takes her 7 minutes to make a large arrangement.
$100 for 4 tickets. what is the cost per one ticket? Plsss help me
Answer:25. Do better bro that’s sad
Step-by-step explanation:
Answer:
One ticket is 25 dollars
Step-by-step explanation:
Let T be tickets
$100 = 4T
[tex]\frac{100}{4} = \frac{4}{4}T[/tex]
$25 = T
Therefore, one ticket is equal to 25 dollars
The answer is given but I dont understand. Please explain #7
SOLUTION:
Case: Rectilinear acceleration
Answer:
Acceleration on a straight line is defined as the rate of change of velocity during motion on the straight line.
Step 3: determine if point c represents a solution
Point C (7 , 52.5) represents a solution of the equation of line y =7.5x
A point is a solution of the equation if and only if it satisfy the line equation.
To check point C is solution o it should satisfy the equation of line y = 7.5x
In point C , x = 7 and y = 52.5
putting x in equation of line and solving for y ,
y = 7.5(7)
y = 52.5
which is true so ,
The coordinates (7 , 52.5) make the equation true
so , (7,52.5) is a solution of y = 7.5x
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Used the given information to determine the probability below round solution with 3 decimal places
The conditional probability formula is
[tex]P(B|A)=\frac{P(B\cap A)}{P(A)}[/tex]which gives
[tex]P(B\cap A)=P(A)\times P(B|A)[/tex]Then, for the first question, we get
[tex]\begin{gathered} P(A\cap B)=P(B\cap A)=P(A)\times P(B|A) \\ P(A\cap B)=0.46\times0.05 \end{gathered}[/tex]which gives
[tex]P(A\cap B)=0.023[/tex]Now, for the second question, we know that, for independent events
[tex]P(A\cap B)=P(A)\times P(B)[/tex]then, we have
[tex]P(A\cap B)=0.46\times0.28[/tex]which gives
[tex]P(A\cap B)=0.129[/tex]Now, for question 3, we know that, when the events are dependent and mutually non-exclusive
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=P(A)+P(B)-P(A)\times P(B|A) \end{gathered}[/tex]By substituting the given values, we have
[tex]\begin{gathered} P(A\cup B)=0.46+0.28-(0.46\times0.05) \\ P(A\cup B)=0.74+0.023 \\ P(A\cup B)=0.763 \end{gathered}[/tex]Finally, for the 4th question, we have
[tex]P(A\cup B)=P(A)+P(B)[/tex]which gives
[tex]\begin{gathered} P(A\cap B)=0.46+0.28 \\ P(A\cap B)=0.74 \end{gathered}[/tex]In summary, the solutions are:
Question 1:
[tex]P(A\cap B)=0.46\times0.05=0.023[/tex]Question 2:
[tex]P(A\cap B)=0.46\times0.28=0.129[/tex]Question 3:
[tex]P(A\cup B)=0.46+0.28-(0.46\times0.05)=0.763[/tex]Question 4:
[tex]P(A\cap B)=0.46+0.28=0.74[/tex]A chemist is heating water so it can dissolve a larger amount of sodium chloride. The water's temperature increases 7°C each minute from an initial temperature of 21°C. How long will it take for the water to reach 49°C?
Write and solve an equation to find the answer. how many munities?
Answer:
Step-by-step explanation:
4 minutes
please help!! will mark brainliest!!
i need questions 26,27, and 28. thanks!
Dara's kite is flying 67 feet high. Jill's is flying 40 feet high. What is the difference between the heights of these two kites?
The difference between the heights of two kites is 27 feet.
What is height difference?
Given that length and height refer to a shape's length and height, respectively, respectively, there is a very clear distinction between the two. In a plane, length is the measure that is horizontal, whereas height is the measure that is vertical. Length, breadth, and height are crucial geometrical dimensions used to describe shapes.
A person's inherited genetic makeup accounts for about 80% of the normal variation in height, with the remaining 20% of the height difference coming from environmental factors like diet and upbringing.
Let, Dara's kite is flying 67 feet high. Jill's is flying 40 feet high.
So, the difference between the height of two kites is,
67 feet - 40 feet = 27 feet.
Hence, the difference between heights of kites is, 27 feet.
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If the figure below were to be reflected across the x axis, what would be the coordinates for point D?
Reflection across the X-axis
D’ = ( , )
Answer:
If the unit for the axes is 1, point D' is on coordinate (-3, -2).
Step-by-step explanation:
To find coordinates' values when reflecting over the x-axis, multiply the y value of the original point by -1.
D (-3, 2) ---> D' (-3, -2)
The rule for a relation is y= (x+1) ^2. The domain is ( -2, -1,0,1,2,3). Is the relation a function?
No, this rule for a relation is not a function because the input variable (domain) are not uniquely mapped to an output variable (range).
What is a function?In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).
When x = -2, the range (output) of this function is given by:
y = (x + 1)²
y = (-2 + 1)²
y = (-1)²
y = 1.
When x = -1, the range (output) of this function is given by:
y = (x + 1)²
y = (-1 + 1)²
y = (0)²
y = 0.
When x = 0, the range (output) of this function is given by:
y = (x + 1)²
y = (0 + 1)²
y = (1)²
y = 1.
Based on the integers shown above, we can reasonably infer and logically deduce that this rule for a relation does not represent a function because the value of "1" is mapped to more than one domain element i.e -2 and 0.
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A rectangular ground is 30 1/4 m long and 20 1/2 m broad. Find the perimeter and area of the ground.
The perimeter and the area of the ground are 101.5 m and 620.125 m², respectively.
We have a ground. The shape of the ground is a rectangle. The length and breadth of the rectangular ground are 30.25 m and 20.5 m, respectively. We need to find the perimeter and the area of the rectangular ground.
Let the perimeter and the area of the ground be denoted by the variables "P" and "A", respectively. The formulas for the perimeter and area of a rectangle are used below.
P = 2×(L + B)
P = 2×(30.25 + 20.5)
P = 2×50.75
P = 101.5
Hence, the perimeter of the rectangular ground is 101.5 meters.
A = L×B
A = 30.25×20.5
A = 620.125
Hence, the area of the rectangular ground is 620.125 square meters.
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(I need this as an actual equation and solution not just which one it is.. also any people just trying to get credits will result in a report.) The temperature of a cooling liquid is given by the function T(m) = 38 (0.82)" +21, where T represents the temperature in degrees Celsius and m represents the number of minutes, m≥0, that the liquid has been cooling. Which of the following represents a temperature that the liquid does not reach as it cools down?
(1) 53
(2) 16
(3) 41
(4) 28
Answer:
(2) 16°C
Step-by-step explanation:
[tex]T(m)=38(0.82)^m+21[/tex]
Find the temperature at the outset ([tex]m=0[/tex]):
[tex]T(0)=38(0.82)^0+21[/tex]
[tex]T(0)=38(1)+21[/tex]
[tex]T(0)=38+21[/tex]
[tex]T(0)=59[/tex]
Since the liquid is cooling, all temperatures equal to or less than 59°C are valid possibilities. However, over time (represented as [tex]m\rightarrow\infty[/tex]), [tex](0.82)^m[/tex] is reduced towards zero and, as such, [tex]38(0.82)^m[/tex] will be reduced towards zero. All that will remain is [tex]T(m)=21[/tex], which makes it the horizontal asymptote. This is shown in the attached graph.
Therefore, since 16°C falls below the asymptote, it does not represent a temperature that the liquid reaches as it cools down.
pls tell the answer pls plsplsplsplsplspls
a) 20 people travel more than 30 miles to work.
b) Sam travels 20 miles .
Given,
In the question:
From the graph:
The histogram shows information about how 550 people travel to work.
To find the how many people travel more than 30 miles to work?
Now, According to the question:
Observe the Graph :
a) How many people travel more than 30 miles to work
5 x 4 = 20 people
b) 205 of the 550 people travel further than Sam . Estimate how far Sam travel?
Now, According to the question:
205 of the 550 people travel further than Sam,
Sam travels 20 miles .
Hence, a) 20 people travel more than 30 miles to work.
b) Sam travels 20 miles .
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-12 = 12y^97
Solve for y.
Answer:
y = -1
Step-by-step explanation:
You want the solution to -12 = 12y^97.
SolutionThe one real solution is can be found by ...
-1 = y^97 . . . . divide by 12
y = (-1)^(1/97) = -1
The value of y is -1.
__
Additional comment
There are 96 complex solutions to this equation as well.
They are y = cos(nπ/97) +i·sin(nπ/97) . . . . for integer n = 0 .. 96.
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Type the missing number to complete the proportion. 86 chairs in 2 rows = chairs in 1 row Submit
hello
from the question given, we have
[tex]\begin{gathered} 86\text{chairs}=2\text{rows} \\ x\text{ chairs= 1 row} \end{gathered}[/tex]cross multiply both sides
[tex]\begin{gathered} 86\text{chairs}=2\text{rows} \\ x=1 \\ 2\times x=86\times1 \\ 2x=86 \\ \end{gathered}[/tex]divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}=\frac{86}{2} \\ x=43 \end{gathered}[/tex]from the calculation above, we have 43 chairs in 1 row
A line passes through points at (9,5) and (4,3). What is the slope of the line perpendicular to this line?
Answer:
[tex]-5/2[/tex]
Step-by-step explanation:
The slope of the line through the given points is [tex]\frac{5-3}{9-4}=\frac{2}{5}[/tex].
Perpendicular lines have slopes that are negative reciprocals of each other, so the answer is [tex]-5/2[/tex].
Answer:
perpendicular slope = - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
calculate the slope m of the line using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 5 ) and (x₂, y₂ ) = (4, 3 )
m = [tex]\frac{3-5}{4-9}[/tex] = [tex]\frac{-2}{-5}[/tex] = [tex]\frac{2}{5}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{5} }[/tex] = - [tex]\frac{5}{2}[/tex]
Calculate b1, the balance on the loan after the first month. Give your answer in dollars to the nearest dollar. Do not include commas or the dollar sign in your answer.
Given:
Interest (I)= $716.67
Total amount = $200,000
[tex]R=\frac{716.67\times100\times12}{200000\times1}[/tex][tex]R=\frac{860004}{200000}[/tex][tex]R=4.3\text{ \%}[/tex]Monthly Payment(d) :
[tex]200000=\frac{d\lbrack1-(1+\frac{r}{12})^{-25\times12}\rbrack}{\frac{r}{12}}[/tex][tex]200000=\frac{d\lbrack1-(1+\frac{0.043}{12})^{-25\times12}\rbrack}{\frac{0.043}{12}}[/tex][tex]200000=\frac{d\lbrack1-(1+0.0036)^{-300}\rbrack}{0.0036}[/tex][tex]d=\text{ \$1089}[/tex]Balance of the loan amount after one month:
[tex]b_1=200000-1089+716.67[/tex][tex]b_1=199627.67[/tex]Balance amount after the first month is $199628
Matthew drives 54 miles per hour. Benjamin drives 47 miles per hour. They started at the same spot, and drove in opposite directions. Aftersome time, they were 1272.6 miles apart. How much time has passed?After _____ hours, Matthew and Benjamin were 1272.6 miles apart.
Solution:
Matthew and Benjamin start from the same spot and drives in opposite directions.
Given:
[tex]\begin{gathered} \text{Matthew's sp}eed=54mph \\ \text{Benjamin's sp}eed=47mph \\ \text{Distance apart after time (t)=1272.6miles} \end{gathered}[/tex]The formula for speed is given by;
[tex]\begin{gathered} \text{Speed}=\frac{dis\tan ce}{\text{time}} \\ \text{Hence, } \\ \text{distance}=\text{speed}\times time \end{gathered}[/tex]During the journey, they used the same time but moved at different speeds, hence, they will have different distances.
Let the time both used be represented by t
Let Matthew's distance be represented by m
Let Benjamin's distance be represented by b
Thus,
Matthew's distance is calculated below;
[tex]\begin{gathered} \text{distance}=\text{speed}\times time \\ m=54\times t \\ m=54t \end{gathered}[/tex]Benjamin's distance is calculated below;
[tex]\begin{gathered} \text{distance}=\text{speed}\times time \\ b=47\times t \\ b=47t \end{gathered}[/tex]The distance covered by the two of them in opposite directions is their distance apart from the starting point.
Hence,
[tex]m+b=1272.6[/tex][tex]\begin{gathered} 57t+47t=1272.6 \\ 101t=1272.6 \\ \text{Dividing both sides by 101 to get the time t,} \\ t=\frac{1272.6}{101} \\ t=12.6\text{hrs} \end{gathered}[/tex]Therefore, after 12.6hours, Matthew and Benjamin were 1272.6 miles apart.
please help will give you upvotes
Answer:
C is the correct answer.
Step-by-step explanation:
[tex]f(x) = 2x + 2[/tex]
[tex]f(2) = 2(2) + 2 = 4 + 2 = 6[/tex]
Tutorials 2 2.1 An unbiased die and a fair coin are tossed once. What is the probability of having a (a) prime number and a head? a (b) An even number and a head? (c) A score less than 3 and a tail?
Answer: The probablity of two indipendant events occuring at the same time is the producht of the two independant events, therefore the solution is as follows:
(a) Prime number and a head"