Solve the simultaneous equations 4x+8y=-4 2y-5x=23
Answer:
x = -4, y = 3/2
Step-by-step explanation:
simplify the 1st equation by dividing each term by 4 to get:
x + 2y = -1
-5x + 2y = 23
Subtract to get: 6x = -24
x = -4
find 'y': 2y - 5(-4) = 23
2y + 20 = 23
2y = 3
y = 3/2
Answer:
y is equal to 1.5, and x is equal to -4
Step-by-step explanation:
given:
[tex]4x + 8y = -4[/tex]
[tex]2y - 5x = 23[/tex]
We can start by factoring 4 out of the first equation:
[tex]x + 2y = -1[/tex]
Now let's multiply it by -5:
[tex]-5x - 10y = 5[/tex]
We'll rearrange the other equation to match that (just for clarity):
[tex]-5x + 2y = 23[/tex]
Now let's subtract the modified equation from that:
[tex]\begin{array}{c}-5x + 2y = 23\\-5x - 10y = 5\\ \ \ \ \ \ \ \ \ \ \ 12y = 18\end{array}[/tex]
So y is equal to 18/12, or 1.5
Let's plug that into one of the first equations and see what we get:
[tex]2y - 5x = 23\\2(1.5) - 5x = 23\\3 - 5x = 23\\-5x = 20\\x = -4[/tex]
Giving us an x value of negative four. Let's plug that into the other equation to confirm:
[tex]4x + 8y = -4\\4(-4) + 8y = -4\\-16 + 8y = -4\\-4 + 2y = -1\\2y = 3\\y = 1.5[/tex]
That matches up, so our answer is correct.
Miley and 4 of her friends went to buy "C" ice cream and they bought each $24 worth of toppings. Altogether their total expense was $220 How much did they spend on ice cream? Write an expression and Show your answer *
Answer: They spent $100 on ice cream.
Step-by-step explanation:
Given : Total friends = 5
They bought each $24 worth of toppings.
Total price of toppings = (Total friends ) x (Worth of each topping)
= 5 x ($24)
= $ 120
Total expense = $220
Money amount on ice cream = (Total expense) - (Total price of toppings)
= $220 - $120
= $100
Hence, they spent $100 on ice cream.
What triangle congruence theorem could you use to
prove triangle ADE is congruent to triangle CBE?
Answer:
(ASA) Angle Side Angle
Step-by-step explanation:
Both triangles shown have the congruence line on an angle and an adjacent side. ASA proves congruence because in addition to the angle and side, the triangles ADE and CBE share the same angle on point E. Because the two lines are intersecting, their opposite angles are congruent and the triangles share the opposite angles.
The triangle congruence theorem that could be used to show that triangle ADE is congruent to triangle CBE is;
ASA Congruence theorem.
Looking at the given triangles we can say that;
∠AED = ∠CEB
This is because they are both vertically opposite angles and vertically opposite angles are equal.
Now, from the triangle, we are given that;
∠DAE = ∠BCE
We are also given that;
AE = CE
This means that we have 2 corresponding angles and 1 corresponding included side that are congruent.
Thus, the congruence theorem that this represents is ASA Congruence theorem.
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3 lines are shown. A line with points P, R, N intersects a line with points M, R, O at point R. A line extends from point R to point L between angle P R M.
Which angles form a linear pair?
AnglePRL and AngleLRM
AngleORP and AngleMRN
AngleMRN and AngleNRO
AngleLRP and AngleORP
Answer:
The answer is C
Step-by-step explanation:
This is right because that's what I did
From the options given, the angles that form a linear pair are: c. m∠MRN and m∠NRO
What is a Linear Pair?A linear pair is a set of two adjacent angles whose sum equals 180°.Linear pair are also angles that form a straight line when combined together.The 3 lines are shown in the image attached below.
In the diagram, there are two linear pairs that are formed, they are:
m∠MRN and m∠NROm∠PRO and m∠NROTherefore, from the options given, the angles that form a linear pair are: c. m∠MRN and m∠NRO
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What is the volume of a hemisphere with a diameter of 8 inches?
Answer:
Mind if ya brainiest meh
Step-by-step explanation:
The volume of the hemisphere is 1071.78 ft^3
The sale price of an item is $160 after a 20% off discount. What was the original price of the item?
Answer:
200
Step-by-step explanation:
160/80 is 2. 2 times 100 is 200
What is the correct "Name" for the given polynomial? f(x)=3x^2
Step-by-step explanation:
The given function f(x)=3x²=f(x)=3x²+0x+0 is a quadratic function
pm - qrp = 5n; solve for p
Answer:
P=5n/m-qr
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
(25 POINTS!) Identify the like terms, explain how you know they are
like terms, and simplify the expressions:
10y + 3x + 10 + x -2y
3x – y + 4x + 6 – 2y
Factor 6a + 3
Answer:
Step-by-step explanation:
Like terms: 10y, -2y, 3x, and x
These are all like terms since they have a similar variable
Simplifying the expressions:
10y + 3x + 10 + x -2y = [(10y + -2y) + (3x + x)] + 10
= 8y + 4x + 10
Like terms: 3x, 4x, y, and -2y
Same as first explanation, terms have a similar variable
3x - y + 4x + 6 - 2y = (3x + 4x) + (-2y - y) + 6
= -3y + 7x + 6
Hope I helped :)
A jar contains 600 marbles, 240 of which are blue. If Nancy reaches in and grabs a handful of 70 marbles, estimate how many of them should be blue?
Answer:
28 blue marbles
Step-by-step explanation:
600 divided by 240 = 2.5
70 divided by 2.5 = 28
Which choice is an irrational number?
Answer:
C. [tex]\sqrt{18}[/tex]
Step-by-step explanation:
[tex]\frac{4\pi }{\pi }[/tex] = 4(whole number)
[tex]\sqrt{ 6^{2}}[/tex] = 6(whole number)
[tex]\sqrt{18}[/tex] = 4.2426406871192851464050661726291(goes on and on)
21.989(terminating number)
Irrational numbers are un-whole numbers that do not terminate and cannot be turned into a fraction.
The irrational number number in the options is C. √18.
What are Rational and Irrational Numbers?Rational numbers are numbers which can be written in the form of a/b, b ≠ 0, and a and b are integers.
Irrational numbers cannot be written in this form.
Given options are 4π/π, √(6²), √18 and 21.989.
4π/π can be written as 4, which is a whole number and thus a rational number.
So, 4π/π is a rational number.
√(6²) = 6, which is also a rational number since it is a whole number.
√18 does not have a decimal which is ending.
So it is an irrational number.
21.989 has only 3 decimal places and can be written as 21989/1000 and is thus a rational number.
Hence the correct option is C.
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Trey drove to the mountains last weekend. There was heavy traffic on the way there, and the trip 8 took hours. When Trey drove home, there was no traffic and the trip only took 6 hours. If his average rate was 16 miles per hour faster on the trip home, how far away does Trey live from the mountains?
Answer:
Trey lives 384 feet.
Step-by-step explanation:
Let the average rate be represented by s, and the distance by d.
speed = [tex]\frac{distance}{time}[/tex]
⇒ distance = speed x time
i.e d = s x t
On his first trip,
d = s x 8
d = 8s ............ 1
on his trip home, the average rate was 16 miles per hour faster, so that;
d = (s + 16) x 6
d = 6s + 96 ............ 2
Equation 1 and 2, we have;
8s = 6s + 96
8s - 6s = 96
2s = 96
s = 48
The average rate is 48 miles per hour.
Thus from equation 1 (also equation 2 can be used),
d = 48 x 8
= 384
Therefore, Trey lives 384 feet from the mountains.
The mass of the liquid below is 45.5 grams if placed in a beaker with water the liquid will....
Any help is appreciated:)
Answer:
it will float!
Step-by-step explanation:
in order to find density, you must divide the mass by the volume. the volume is 56 ml, and the mass is 45.5. (45.5 / 56 = 0.8125) because we know the density of water is 1, and the density of this liquid is less than that of water, it will float because it is "lighter". hope it helped <33
Step-by-step explanation:
answer is you're question
Enter the sum in simplest form. pls answer I give brainliest
Answer:
2/5
Step-by-step explanation:
2/10+2/10=4/10
4/10 divided by 2/2= 2/5
Hope this helps!
Answer;
2/10 + 2/10 is 4/10 and then simplified it would be 2/5 because 2 goes into both 4 and 10.
2/10 + 2/10 = 4/10
4/10 = 2/5
Hope this Helps!
96 words typed in 3 minutes; 160 words typed in 5 minutes
Answer:
32 words per minute
GIVING BRAINLY OUT FOR WHOEVER IS CORRECT AND FAST!
The length of a rectangle is twice as long as it's width. The perimeter of this rectangle is how many times longer than the shorter side?
Answer:
The formula for perimeter is the sum of
twice the width and twice the length, so
the formula would be:
Perimeter = 2W + 2L
In this problem:
Width is unknown (x)
Length is twice the width (2x)
and Perimeter = 60, so to set it up:
60 = 2x + 2(2x)
60 = 2x + 4x
60 = 6x
x = 10
Width = 10; Length = 20
So then you do 20/10
= 2
2 is the answer
Step-by-step explanation:
Hope this helps,
Please give brainliest if you like my answer.
What does x equal I this problem
Answer: The answer is X= 9 Hope this helps :) Please mark Brainliest
Step-by-step explanation:
please help me with this its due tonight
Answer:
y= -1/3x-4
y=2x+2
Step-by-step explanation:
the slope is rise over run
Alfredo gives an equal number of marbles to 6 friends. Which could be the total number of marbles he gave to his friends?
Group of answer choices
15
60
56
33
I believe it would be 60, 60 is the only multiple for 6.
Brainliest! If 2a+4b=5 and a is equal to three times b, what is 3a?
Answer:
3a = [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
Given
2a + 4b = 5 ← substitute a = 3b into the equation
2(3b) + 4b = 5
6b + 4b = 5
10b = 5 ( divide both sides by 10 )
b = [tex]\frac{5}{10}[/tex] = [tex]\frac{1}{2}[/tex]
Now
a = 3b = 3 × [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex] , thus
3a = 3 × [tex]\frac{3}{2}[/tex] = [tex]\frac{9}{2}[/tex]
Answer:
The value of 3a = 9/2
Step-by-step explanation:
Given the expression
[tex]2a+4b=5[/tex]
Given that a is equal to three times b. so,
[tex]a = 3b[/tex]
plug in a = 3b in the expression
[tex]2a+4b=5[/tex]
[tex]2(3b) + 4b = 5[/tex]
[tex]6b+4b = 5[/tex]
Adding like terms: 6b+4b = 10b
[tex]10b = 5[/tex]
Dividing both sides by 10
[tex]\frac{10b}{10}=\frac{5}{10}[/tex]
simplify
[tex]b=\frac{1}{2}[/tex]
so
a = 3b ⇒ a = 3(1/2) = 3/2
Therefore, the value of 3a can be determined by substituting a = 3/2 in 3a.
3a = 3(3/2) = 9/2
Therefore, the value of 3a = 9/2
An investor invested a total of $2100 in two mutual funds. One fund earned a 4% profit while the other earned a 2% profit. If the investor's total profit was $62, how much was invested in each mutual fund?
Answer:
x+y=2100
x(0.04) + y(0.02) = 62
(2100-y)(0.04)+ 0.02y = 62
84-0.02y = 62
22/0.02=y
y=1100
x=1000
ILL MARK AS BRAINLESS
X/5=y/3 and 12/y=4/5 what does x equal and what does y equal and how?
Final Answer: [tex]x = \frac{5y}{3}[/tex], [tex]y = 15[/tex]
Steps/Reasons/Explanation:
Question: [tex]\frac{x}{5} = \frac{y}{3}[/tex] and [tex]\frac{12}{y} = \frac{4}{5}[/tex]. What does [tex]x[/tex] equal and what does [tex]y[/tex] equal and how?
Solving for [tex]x[/tex] in the equation [tex]\frac{x}{5} = \frac{y}{3}[/tex].
Step 1: Multiply both sides by [tex]5[/tex].
[tex]x = \frac{y}{3} * 5[/tex]
Step 2: Simplify [tex]\frac{y}{3} * 5[/tex] to [tex]\frac{y * 5}{3}[/tex].
[tex]x = \frac{y * 5}{3}[/tex]
Step 3: Regroup terms.
[tex]x = \frac{5y}{3}[/tex]
Solving for [tex]y[/tex] in the equation [tex]\frac{12}{y} = \frac{4}{5}[/tex].
Step 1: Multiply both sides by [tex]y[/tex].
[tex]12 = \frac{4}{5}y[/tex]
Step 2: Simplify [tex]\frac{4}{5}y[/tex] to [tex]\frac{4y}{5}[/tex].
[tex]12 = \frac{4y}{5}[/tex]
Step 3: Multiply both sides by [tex]5[/tex].
[tex]12 * 5 = 4y[/tex]
Step 4: Simplify [tex]12 * 5[/tex] to [tex]60[/tex].
[tex]60 = 4y[/tex]
Step 5: Divide both sides by [tex]4[/tex].
[tex]\frac{60}{4} = y[/tex]
Step 6: Simplify [tex]\frac{60}{4}[/tex] to [tex]15[/tex].
[tex]15 = y[/tex]
Step 7: Switch sides.
[tex]y = 15[/tex]
~I hope I helped you :)~
3x+4 = 4x+3 how many solutions are there
The equation 3x + 4 = 4x + 3 has one solution.
To determine the number of solutions for the equation 3x + 4 = 4x + 3, we can simplify and analyze the equation.
First, we can rearrange the equation by moving all the x terms to one side and the constant terms to the other side:
3x - 4x = 3 - 4
Simplifying further:
-x = -1
Next, we can multiply both sides of the equation by -1 to eliminate the negative sign:
x = 1
Therefore, we have found a single solution for x, which is x = 1. This means that when we substitute x = 1 into the original equation, both sides will be equal.
In summary, the equation 3x + 4 = 4x + 3 has one solution, which is x = 1. This can be verified by substituting x = 1 back into the equation and confirming that both sides are equal.
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HELP ME PLEASSSSSSSSSSEEEEEEEEEEEEEEEEEEEE
Answer:
105
Step-by-step explanation:
because you multiply 5 times 3 which is 15 times 7 equals 105
8 3/5 - 2 1/3 help me please
Answer:
6.26666666667, your welcome :)
Esther deposited $5,000 into an account that grows at a rate of 8% per year. To the nearest cent, how much will be in the
account after 5 years?
Answer:
The total amount after five years = $7,000
Step-by-step explanation:
Step(i):-
Given Esther deposited $5,000 into an account
Principal amount 'P' = 5000
Given rate of interest (R) = 8%
r = R / 100 = 0.08 per year
Step(ii):-
The total amount after 5 years
[tex]A = P( 1 + r t )[/tex]
[tex]A = 5000(1+ (0.08 X 5) = 7000[/tex]
Final answer:-
The total amount after five years = $7,000
the shape alongside is one quarter of a circle with radius of 14 cm. find the length of arc AB ,perimeter of the figure , area , area of triangle AOB , area of shaded segment.
Answer:
1) The length of the arc AB is approximately 21.99 cm
2) The perimeter of the figure is approximately 49.99 cm
3) The area of the figure is approximately 153.938 cm²
4) The area of the right triangle ΔAOB is 98 cm²
5) The area of the shaded segment is approximately 55.938 cm²
Step-by-step explanation:
The given parameters are;
The radius of the circle from which we have the quarter circle, r = 14 cm
Therefore, we have;
The length of segment OA = The length of segment OB = r = 14 cm
1) The length of the arc AB = 1/4 × The circumference of the circle with radius 14 cm and center O
The length of the arc AB = 1/4 × 2 × π × r = 1/4 × 2 × π × 14 c m= 7·π cm ≈ 21.99 cm which is approximately 22 cm, to the nearest whole number
2) The perimeter of the figure = The length of the arc AB + The length of segment OA + The length of segment OB
∴ The perimeter of the figure = 7·π cm + 14 cm + 14 cm ≈ 49.99 cm which is approximately 50 cm, to the nearest whole number
3) The area of the figure (sector AOB) = The area of the quarter of a circle = π × r²/4 = π × (14 cm)²/4 = 49·π cm² ≈ 153.938 cm²
4) Whereby we have arc AB and segment OA and OB form a quarter (1/4) of a circle, we have;
∠AOB = 360°/4 = 90°
Therefore, ΔAOB is a right triangle
The base length of the right triangle ΔAOB (is taken as being) = Segment OA = 14 cm
The height of the right triangle ΔAOB (is taken as being) = Segment OA = 14 cm
The area of the right triangle ΔAOB = 1/2 × The base length × The height
∴ The area of the right triangle ΔAOB = 1/2 × 14 cm × 14 cm = 98 cm²
The area of the right triangle ΔAOB = 98 cm²
5) The area of the shaded segment = The area of the quarter of a circle (Sector OAB) - The area of the triangle ΔAOB
The area of the quarter of a circle = 49·π cm² ≈ 153.938 cm²
∴ The area of the shaded segment = 49·π cm² - 98 cm² ≈ 55.938 cm²
The area of the shaded segment ≈ 55.938 cm²
The area of the shaded segment is approximately 55.938 square centimeters.
The length of the arc AB is approximately 21.991 centimeters.
The perimeter of the figure is approximately 49.991 centimeters.
The area of triangle AOB is 98 square centimeters.
The area of the circle segment is approximately 153.938 square centimeters.
Procedure - Area of the shaded segmentThe area of the shaded segment ([tex]A[/tex]), in square centimeters, is obtained by subtracting the area of the triangle from the area of the circle quarter, that is:
Area of the shaded segment[tex]A = \frac{\pi\cdot r^{2}}{4}-\frac{1}{2}\cdot \left(\frac{\sqrt{2}}{2}\cdot r \right)\cdot \left(\sqrt{2}\cdot r\right)[/tex]
[tex]A = \frac{\pi\cdot r^{2}}{4}-\frac{1}{2}\cdot r^{2}[/tex]
[tex]A = \left(\frac{\pi}{4}-\frac{1}{2} \right)\cdot r^{2}[/tex] (1)
If we know that [tex]r = 14\,cm[/tex], then the area of the shaded segment is:
[tex]A = \left(\frac{\pi}{4}-\frac{1}{2} \right)\cdot (14\,cm)^{2}[/tex]
[tex]A \approx 55.938\,cm^{2}[/tex]
Where [tex]r[/tex] is the radius of the circle segment, in centimeters.
The area of the shaded segment is approximately 55.938 square centimeters. [tex]\blacksquare[/tex]
The length of the arc AB ([tex]s[/tex]) is determined by definition of circular arc:
Length of the arc AB[tex]s = \frac{\pi}{2} \cdot r[/tex] (2)
If we know that [tex]r = 14\,cm[/tex], then the length of the arc AB is:
[tex]s = \frac{\pi}{2} \cdot (14\,cm)[/tex]
[tex]s \approx 21.991\,cm[/tex]
The length of the arc AB is approximately 21.991 centimeters. [tex]\blacksquare[/tex]
The perimeter of the figure ([tex]p[/tex]), in centimeters, is the sum of the arc AB and the two legs of the right triangle, that is:
Perimeter of the figure[tex]p = \frac{\pi}{2}\cdot r + 2\cdot r[/tex]
[tex]p = \left(\frac{\pi}{2} + 2 \right)\cdot r[/tex] (3)
If we know that [tex]r = 14\,cm[/tex], then the perimeter of the figure is:
[tex]p = \left(\frac{\pi}{2} + 2 \right)\cdot (14\,cm)[/tex]
[tex]p \approx 49.991\,cm[/tex]
The perimeter of the figure is approximately 49.991 centimeters. [tex]\blacksquare[/tex]
The area of the triangle ([tex]A[/tex]) was used in the first part of this question and we proceed to extract it below:
Area of triangle AOB[tex]A = \frac{1}{2}\cdot r^{2}[/tex] (4)
If we know that [tex]r = 14\,cm[/tex], then the area of the triangle AOB is:
[tex]A = \frac{1}{2}\cdot (14\,cm)^{2}[/tex]
[tex]A = 98\,cm^{2}[/tex]
The area of triangle AOB is 98 square centimeters. [tex]\blacksquare[/tex]
The area of the circle segment ([tex]A[/tex]) was used in the first part of this question and we proceed to extract it below:
Area of circle segment[tex]A = \frac{\pi\cdot r^{2}}{4}[/tex] (5)
If we know that [tex]r = 14\,cm[/tex], then the area of the circle segment is:
[tex]A = \frac{\pi\cdot (14\,cm)^{2}}{4}[/tex]
[tex]A \approx 153.938\,cm^{2}[/tex]
The area of the circle segment is approximately 153.938 square centimeters. [tex]\blacksquare[/tex]
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PLEASE HELP ME ASAP!!! I WILL VOTE YOU BRAINLIEST IF YOUR ANSWER IS CORRECT!!
here is the graph:
0, 1 ,2 ,3 ,4 ,5 ,6 ,7
7, 14 ,28 ,56 ,112 ,224 ,448 ,896
here is the function:
f(x)=7(2)^x
Find the domain and range.
Answer:
14 and 5
Step-by-step explanation:
the range is 5 and the domane is 14
Easy Cooking is a cooking supply company. This year, the company sold 22,169 ovens.
According to a report prepared by the sales team, that is 30% fewer than they sold last year.
How many ovens did they sell last year?
I need it worked out please
Answer:
34 is the asnwer congruent thats why.
Step-by-step explanation: