[tex]\bf \begin{cases} 5x+7y=32\\ 8x+6y=46 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 5x+7y=32\implies 7y=32-5x\implies \boxed{y}=\cfrac{32-5x}{7} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting \underline{y} in the 2nd equation}}{8x+6\left(\boxed{ \cfrac{32-5x}{7}} \right)}=46\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{7}}{7\left( 8x+6\left( \cfrac{32-5x}{7} \right) \right)=7(46)} \\\\\\ 56x+6(32-5x)=322\implies 56x+192-30x=322[/tex]
[tex]\bf 26x+192=322\implies 26x=130\implies x=\cfrac{130}{26}\implies \blacktriangleright x=5 \blacktriangleleft \\\\\\ \stackrel{\textit{subsituting \underline{x} in the 1st equation}}{5(5)+7y=32}\implies 25+7y=32\implies 7y=7 \\\\\\ y=\cfrac{7}{7}\implies \blacktriangleright y=1 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (5,1)~\hfill[/tex]
1. What are the end points of the triangle called? How are they labeled?
2. Two triangles are congruent if:
a) each pair of corresponding sides is congruent
b) two pairs of corresponding angles are congruent and a pair of corresponding sides
are congruent
c) two pairs of corresponding sides and the angles included between them are
congruent
d) If three sides of one triangle are congruent to three sides of a second triangle,
e) If two angles and a non-included sides of each triangle are congruent
The endpoints of a triangle are called vertices and triangles are labeled by their vertices, e.g., triangle ABC. Conditions for congruent triangles include having congruent sides (SSS), congruent sides and included angle (SAS), and congruent angles with either the included or non-included side (ASA or AAS).
Endpoints of a Triangle and Conditions for Congruent Triangles
The endpoints of a triangle are called the vertices, and they are typically labeled with capital letters such as A, B, and C. When referring to a triangle by its vertices, it is commonly denoted as triangle ABC.
Two triangles are congruent if:
Each pair of corresponding sides is congruent (SSS Congruence)
The conditions (a), (c), (d), and (e) from the student's options are correct descriptions of congruent triangles according to congruence theorems and postulates such as the Second Theorem of Congruence, ASA, SAS, and AAS Congruence. However, option (b) could potentially create ambiguity since it mentions two pairs of corresponding angles and a pair of corresponding sides, but does not specify the included side which is necessary for congruence based on ASA or AAS Congruence.
what is the recursive formula for this geometric sequence? 4, -12, 36, -108, ...
Answer:
aₙ = 4(-1)ⁿ⁻¹(3)ⁿ⁻¹
Step-by-step explanation:
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
We can get the value for r by dividing aₙ by aₙ₋₁.
a₄/a₃ = -108/36
a₄/a₃ = -3
r = -3
aₙ = 4(-3)ⁿ⁻¹
aₙ = 4(-1)ⁿ⁻¹(3)ⁿ⁻¹
The (-1)ⁿ⁻¹ term makes even-numbered terms negative.
Answer:
answer is attached
Step-by-step explanation:
Write the equation of a line with the slope of 2, which contains the point (4,-8).
Answer:
y = 2x-16
Step-by-step explanation:
To find a line when we know the slope and a point, we can use the point slope formula for a line
y-y1 = m(x-x1)
where the point is (x1,y1) and the slope is m. Substituting the known information in.
y--8 = 2 (x-4)
y+8 = 2(x-4)
We can manipulate this into slope intercept form by distributing the 2
y+8 = 2x-8
and subtracting 8 from each side
y+8-8 = 2x-8-8
y = 2x-16
In math, how do you solve 2h<200?
Answer:
h < 100
Step-by-step explanation:
isolate h by dividing both sides by 2
h < 100
Someone help me with this question ASAP and show work please and thank you
Answer:
g(f(x)) = x
Step-by-step explanation:
You are given f(x) = -4x - 1 and g(x) = [tex]\frac{x+1}{-4}[/tex]. Keep in mind that f(x) or g(x) is the same as a y = equation, but two separate equations.
You are trying to find g(f(x)), which means that you will use f(x) and substitute this value into the x value in the equation of g(x).
It will look like: g(-4x - 1) = [tex]\frac{x+1}{-4}[/tex]
[tex]\frac{(-4x-1)+1}{-4}[/tex]
Now evaluate the expression to solve the problem. Start by combining like terms.
[tex]\frac{(-4x)}{-4}[/tex]
You are left with -4x/-4. We can simplify this even further by dividing both sides of the fraction by -4/-4. The -4's cancel out and become 1's, so you are left with:
[tex]x[/tex]
Answer:
Step-by-step explanation:
g(f(x)) means that wherever you see an x in g(x) you put f(x) in it's place. Read that sentence a couple of times until it makes sense.
g(x) = (x + 1)/-4
g(f(x)) = (f(x) + 1) / - 4 Now wherever you see f(x), put in -4x - 1
g(f(x)) = [(-4x - 1) + 1] / - 4 Remove ( )
g(f(x)) = [-4x - 1 + 1 ] / - 4
g(f(x)) = [-4x] / - 4 Do the division
g(f(x)) = x
Neat problem. thanks for posting.
Points A and B are 200 mi apart. A cyclist started from point A and a motorcyclist started from point B, moving towards each other.The speed of the cyclist was 17 mph, the speed of motorcyclist was 83 mph. At what distance from point A will they meet?
Answer:
D from A = 34 miles
Step-by-step explanation:
We know the total distance is 200 miles (this would be when they meet)
The rate for cyclist A is 17
The rate for cyclist B is 83
We know the time is equal
Distance = rate * time
Distance for A = 17t
Distance for B = 83 t
The total distance = distance for A + distance for B
200 = 17t + 83t
Combine like terms
200 = 100t
Divide each side by t
200/100 = 100t/100
They will meet at t =2 hours
I know you say we need the distance
Distance for A
D = 17*t
We now know t
D = 17*2
D = 34 miles
Answer:
Step-by-step explanation:
cyclist going 17 mph n motorcyclist going 83 mph opposite way
so their net closing speed=17+83=100mph
A n B 200 mi apart
so they will meet in 200/100=2hrs
at dat time, cyclist will be 2x17=34mi from pt A
What is $4.99 x 0.5lb + $6.99 x 0.25lb?
Answer:
$3.77
Step-by-step explanation:
$4.99 x 0.5lb + $6.99 x 0.25lb?
First we multiply
2.495+1.725
Then we add
3.77
We will spend $3.77
what is the simplified version of 4b-7-3b+9
Answer: b+2
Step-by-step explanation:
4b-7-3b+9
b+2
Simplifying:
3b + -9 + -8b = 11
Reorder the terms:
-9 + 3b + -8b = 11
Combine like terms: 3b + -8b = -5b
-9 + -5b = 11
Solving
-9 + -5b = 11
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + -5b = 11 + 9
Combine like terms: -9 + 9 = 0
0 + -5b = 11 + 9
-5b = 11 + 9
Combine like terms: 11 + 9 = 20
-5b = 20
Divide each side by '-5'.
b = -4
Simplifying
Answer: b = -4
help I only got till 5:00
Answer:
II think it is A
Step-by-step explanation:
Its doing a measurement which equals the same thing.
Hope that helps feel free to ask more questions
Brainliest??
What is 42% of 120ml?
Answer:
50.4
Step-by-step explanation:
What is the eighth term in the arithmetic sequence defined by the explicit formula an=2n+7?
Enter your answer in the box.
Answer:
The 8th term is 23
Step-by-step explanation:
If you are given a formula for the sequence,
an = 2n+7
then substitute n=8 to find the 8th term.
a8 = 2(8) +7
a8 = 16+7
a8 = 23
Answer:
a8 = 23
Step-by-step explanation:
if the ratio of 7 less than a number and 7 more than the number 2, what is the number?
Answer:
Step-by-step explanation:
I assume you mean "if the ratio of 7 less than a number and 7 more than the number is 2".
Let x be the number.
Ratio is division.
(x-7)/(x+7)=2
Multiply by (x+7) on each side:
x-7=2(x+7) = 2x+14
Add 7 on each side
x=2x+21
Subtract 2
-x=21
x=-21
how do i solve y=2x+5 y=3x-1 with substitutions dont know how to do this
Answer:There is an app that helps you with this stuff.
Step-by-step explanation:
Which value in the replacement set is a solution to this equation? 2n + 5 = 27 Replacement set: {11, 12, 13} Drag the solution into the box.
write 423% as a decimal
[tex]p\%=\dfrac{p}{100}\\\\423\%=\dfrac{423}{100}=4\dfrac{23}{100}=4.23\\\\\boxed{423\%=4.23}[/tex]
Answer:
4.23
Step-by-step explanation:
423%
Percent means out of 100
423/100
Pt the decimal 2 places to the left of the 3
4.23
You got 3 problems on a 25 question yest what was the percent of the questions you got right?
If you got 3 questions wrong, then you got 25-3 = 22 right. So that would be 22/25 = 0.88 = 88% questions correct
------------------------------
If you got 3 questions right out of 25, then 3/25 = 0.12 = 12% is the score you get. Note how 88% + 12% = 100%
WILL MARK BRAINLIEST! PLEASE HELP!
The formula for converting Celsius temperatures to Fahrenheit temperatures is a linear equation. Water freezes at 0 °C, or 32 °F, and it boils at 100 °C, or 212 °F. Find the slope and y-intercept for a graph that gives degrees Celsius on the horizontal axis and degrees Fahrenheit on the vertical axis. Then write an equation in slope-intercept form that converts degrees Celsius into degrees Fahrenheit.
The equation for converting a Celsius temperature into a Fahrenheit one is given by the linear equation F = 1.8C + 32. The slope of this equation is 1.8 and the y-intercept is 32.
Explanation:
The subject of this question is Mathematics, specifically the study of linear equations. To find the slope and the y-intercept of the equation that transforms a Celsius temperature into a Fahrenheit one, we can use the two points you provided: (0, 32) and (100, 212). The slope can be calculated as follow: (212 - 32) ÷ (100 - 0) = 180 ÷ 100 = 1.8. The y-intercept is the Fahrenheit temperature when the Celsius temperature is zero, so it's 32. Therefore, the equation you are looking for in slope-intercept form is: F = 1.8C + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius.
Learn more about Linear Equations here:https://brainly.com/question/32634451
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A juicer holds 43 3/4 pints of juice. How many 2 1/2 pint bottles can be filled with that much juice?
ANSWER AS A FRACTION
A scientist builds a Mars rover that can travel 4.9 centimeters per second on flat ground. If the rover continues at the same rate, how many centimeters will it travel in 15 1/2 seconds?
Answer:
The rover would travel 75.95 centimeters in 15 1/2 seconds.
Step-by-step explanation:
Simply multiply 4.9 by 15 1/2.
Hope it helps!
Answer:
75.95 cm
Step-by-step explanation:
We know that distance = rate times time
d =rt
We know the rate = 4.9 cm/s
and time = 15 1/2 s = 15.5 s
Substituting these into d=rt
d = (4.9 cm/s) * 15.5 s = 75.95 cm
You invest 23,400 annual interest rate of 4% compounded annually for seven years what is the balance of the account at the end of that time
Answer: 30792.80
=====================================
Work Shown:
We deposit P = 23400 dollars for t = 7 years, which is compounded n = 1 times per year at an interest rate of r = 4% = 0.04 (we'll use the decimal form of the interest rate)
So this means...
A = P*(1+r/n)^(n*t)
A = 23400*(1+0.04/1)^(1*7)
A = 23400*(1+0.04)^(7)
A = 23400*(1.04)^(7)
A = 23400*1.31593177923584
A = 30792.8036341187
A = 30792.80
based on the sample results about what proportion of the population would you expect to prefer merchant D on iready lesson
Answer:
About 0.12
Step-by-step explanation:
There are 3 people who prefer merchant D out of n = 25 total
Divide: 3/25 = 0.12
Optionally, you can multiply both top and bottom of 3/25 by the value 4 and it leads to 3/25 = 12/100 = 12% = 0.12
What is the slope of the line that passes through (5,4) and (7,10)?
(10-4)/(7-5)=6/2=3.
The slope of the line that passes through those two points is 3.
The slope of the line that passes through (5,4) and (7,10) is 3.
Given that,
It passes through (5,4) and (7,10).We need to find out the slope of the line.Based on the above information, the slope of the line is:
[tex]= \frac{y_2 - y_1}{x_2 - x_1} \\\\= \frac{10-7}{5-4} \\\\= \frac{3}{1}\\[/tex]
= 3
Therefore we can conclude that the slope of the line that passes through (5,4) and (7,10) is 3.
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In the first week students at RSM solved 25 percent of their monthly quota of problems. In the second week, they solved 110 percent of the number of problems solved in the first week. In the third week they solved 60 percent of the number of problems they had solved in the first two weeks and, in the fourth week, they solved the remaining 320 problems. How many problems did students solve in the four-week month?
Answer:
The number of problems solved = 2000
Step-by-step explanation:
Let us assume the monthly quota of problems be x
number of problem solved in first week = 25 % of x =[tex]0.25x[/tex]
number of problems solved in 2nd week = 110% of (problems solved in 1st week)
= [tex]1.10 (0.25x)[/tex]
=[tex]0.275x[/tex]
number of problem solved 3rd week= 60% of ( problems solved in 1st and 2nd week)
= [tex]0.60(0.25x+0.275x)[/tex]
=[tex]0.60(0.525x)[/tex]
=[tex]0.315x[/tex]
number of problem solved in 4th week = [tex]320[/tex]
now we have
number of problems solved in ll 4 weeks = x
[tex]0.25x +0.275x+0.315x+320=x[/tex]
[tex]0.84x+320=x[/tex]
[tex]320=x-0.84x[/tex]
[tex]320=0.16 x[/tex]
[tex]x=\frac{320}{0.16}[/tex]
[tex]x=2000[/tex]
Hence the number of problems solved = 2000
Final answer:
In the third week they solved 60% of the number of problems they had solved in the first two weeks and, in the fourth week, they solved the remaining 320 problems. The total number of problems solved in the four-week month is 492.
Explanation:
To solve this problem, we need to find the number of problems solved in each week and then add them together to get the total number of problems solved in the four-week month.
In the first week, the students solved 25% of their monthly quota of problems. Let's say their monthly quota is 'x'. So, they solved 0.25x problems in the first week.
In the second week, they solved 110% of the number of problems solved in the first week. That means they solved 1.1 * 0.25x = 0.275x problems in the second week.
In the third week, they solved 60% of the number of problems they had solved in the first two weeks. So, they solved 0.6 * (0.25x + 0.275x) = 0.345x problems in the third week.
In the fourth week, they solved the remaining 320 problems. This means the total number of problems solved in the first three weeks is 0.345x, and we can set up the following equation to find x: 0.345x + 320 = x.
Solving this equation, we get x = 491.429. Since we can't have a fractional number of problems, we can round x up to 492. Therefore, the students solved a total of 492 problems in the four-week month.
A petri dish has 246 bacteria. It grows at a rate of 7% per month. How many bacteria will there be in 5 months? Round your answer to the nearest whole number. Question 20 options:
A.253
B.345
C. 171
D.281
Answer:
B 345
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
95% of 7-year-old children are between_________inches and________ inches tall.
Answer: The answer is 46.5 inches to 49.5 inches.
Step-by-step explanation: We are to tell the height limits of a 7-year old child.
Various scientific experiment shows that the height of maximum 7-year old girl child lies between 46.5 inches and 49.4 inches and the height of maximum 7-year old boy child lies between 46.6 inches and 49.5 inches.
So, combining the height limits of girls and boys, we can say that the height limit of 95% 7-year old child lies between 46.5 inches and 49.5 inches.
Thus, the answer is 46.5 inches and 49.5 inches.
Answer:
45 and 53 are the answer
Step-by-step explanation:
answered on edu
DONT KEEP SCROLLING PLEASE
Please I don’t understand 50 POINTS BRAINLIEST
Answer:why didn’t you want me to scroll down ? Can you answer my question
Step-by-step explanation:
1)Not necessarily a parallelogram
2)parallelogram
3)parallelogram
4)parallelogram
How determine if a quadrilateral is a parallelogramTo classify a shape as a parallelogram, the following four conditions must be satisfied
1. Opposite sides are equal in length.
2. Opposite angles are equal.
3. Consecutive angles are supplementary
4. Diagonals bisect each other.
Each of these conditions contributes to the definition of a parallelogram, and all of them must be satisfied for a shape to be considered a parallelogram.
From the figures
1) Not necessarily a parallelogram
The opposite sides are not equal.
GH is congruent to Gl and HJ is congruent to IJ. These are adjacent sides instead of opposite sides equality.
2) Given
RS is parallel to TU
SU is parallel to R(Converse of the Opposite Sides Are Congruent (OSAC) Theorem)
Since the both pairs of opposite sides of the quadrilateral are congruent, then the quadrilateral is a parallelogram.
3) Given PQRS
PQ||RS(given)
PR||QS(Converse of the Opposite Sides Are Congruent (OSAC) Theorem)
Since the both pairs of opposite sides of the quadrilateral are congruent, then the quadrilateral is a parallelogram.
4) <ABC ≅ DCB(alternate angles, AB||CD BC is transversal)
<ACB ≅ DBC(alternate angles,AC||BD,BC is transversal)
Therefore
Opposite angles are equal.
Pairs of opposite sides are parallel.
Adjacent angles are supplementary.
so, the quadrilateral is a parallelogram.
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In a shipment if 1,000 bulbs 1/40 of bulbs were defective.How many bulbs were Not defective
Answer:
975 bulbs
Step-by-step explanation:
1/40 bulbs were defective
That means 1-1/40 were not defective
40/40 - 1/40 = 39/40 were not defective
We have 1000 bulbs
Multiply the number of bulbs by the fraction that is not defective to get the number of bulbs that should not be defective.
1000 * 39/40 = 975 bulbs
Coach Miller bought 5.15 pounds of ground beef to make burgers. The cost of ground beef is $3.40 for each pound. What was the total cost for all the ground beef?
Answer:
$17.51
Step-by-step explanation:
3.40(1) = 3.40 - the (1) represents how many pounds you are buying.
3.40 (5.15) = 17.51
problem 1: two numbers add together equals 47. their difference is 13. write and solve a system to find the two numbers
problem 2: the sum of two numbers is 54 and their difference is 12. write and solve a system to find the two numbers
Answer:
34+13= 47
Step-by-step explanation:
47-34=13
The bank charged Travis a $20 fee because his balance dropped below $0. He knows that he currently had an outstanding charge for $7.85 that he had not recorded yet. How much money will Travis have to deposit into his account so that the outstanding charge does not create another bank fee
Final answer:
Travis must deposit $27.85 to cover the $7.85 outstanding charge and the previous $20 overdraft fee, to avoid further overdraft fees and bring his account balance back to at least $0.
Explanation:
Travis needs to not only cover the outstanding charge to avoid further overdraft fees but also bring his account balance back to at least $0. If Travis currently has an outstanding charge of $7.85, and overdraft fees are typically $35 or higher, it's clear that merely covering the charge won't be enough; he must also compensate for any negative balance incurred from previous overdraft fees.
Assuming the $20 fee has already been applied to his account and his balance is now at -$20 (not considering any other transactions that have taken place), Travis would need to deposit enough money to cover both the fee and the outstanding charge. Therefore, he would need to deposit a total of $20 (to bring his balance to $0) plus the $7.85 outstanding charge, which sums up to $27.85. By depositing this amount, Travis would avoid a second overdraft fee and any additional monetary penalties.
It is worth noting that financial literacy is essential to manage personal finances effectively and avoid potential overdraft situations which could lead to a cycle of fees and negative balances.