Answer: (2, 8)
Since both equations in the system are equal to y, substitute -4x + 16 for y in the quadratic equation, and then solve for x as follows.
Next, substitute x = 2 into either of the original equations to find the y-value of the solution to the system of equations.
Therefore, the solution to the given system of equations is (2,8).
The solution of the system of equations will be;
⇒ x = 2
⇒ y = 8
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equations are,
⇒ y = - 2x² + 4x + 8
⇒ y = - 4x + 16
Now,
Since, The system of equations are,
⇒ y = - 2x² + 4x + 8 ..(i)
⇒ y = - 4x + 16 ..(ii)
Substitute the value of y from (ii) in equation (i), we get;
⇒ - 4x + 16 = - 2x² + 4x + 8
⇒ - 2x² + 4x + 8 + 4x - 16 = 0
⇒ - 2x² + 8x - 8 = 0
⇒ - x² + 4x - 4 = 0
⇒ x² - 4x + 4 = 0
⇒ x = - (-4) ± √ (-4)² - 4×1×4 / 2×1
⇒ x = 4 ± √16 - 16 / 2
⇒ x = 4 / 2
⇒ x = 2
And, y = - 4x + 16
⇒ y = - 4 × 2 + 16
⇒ y = - 8 + 16
⇒ y = 8
Thus, The solution of the system of equations will be;
⇒ x = 2
⇒ y = 8
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Four students ran for the position of school president. Use the following results to figure out who won. Jenna received 22% of the votes. Jordan received of the votes. Kelsey received 6 out of every 20 votes. Nathan received of the votes. The winner was A Jenna B Jordan C Kelsey D Nathan
Answer:
A Jenna
Step-by-step explanation:
Because if Jenna received 22% votes and Jordan, Kelsey, Nathan received less 20 percentage that means Jenna won for school president.
to which sets of numbers dose-1/4 belong. select each correct answer.
A. rational numbers
B. irrational numbers
C. real numbers
D. integers
Answer:
Rational.
Step-by-step explanation:
Natural numbers are numbers 1 through infinite.
Whole numbers are numbers 0 through infinite.
Integers are negative numbers (No decimals nor fractions)
Rational numbers are fraction/decimal numbers (can be negative).
Irrational numbers are squared numbers.
Real numbers includes all of the above mentioned.
Hope this helps.
Answer:
A. rational numbers
Step-by-step explanation:
-1/4 belongs to rational number
weight of sheep,in pounds, at the Southdown sheep farm:
what is the range of weights of the sheep?
plz anwser asap I'm being timed
Answer: 170
Step-by-step explanation:
275-105
what is -2.4x + 9 + 8x + 4.2 = 58
Answer:
X=8
Step-by-step explanation:
Write the decimal as a fraction or mixed number in lowest terms.
1.01 plz no links
Answer:
1/100
Step-by-step explanation:
Hope it helps
Please brainliest
What is the area of the trapezoid below
Answer:
[tex]Area: 29 cm^{2}[/tex]
Step-by-step explanation:
[tex]Aear=(8.5+6)(\frac{4}{5} )[/tex]
[tex]Area=14.5 (2)[/tex]
[tex]Area=29[/tex]
----------------------
hope it helps...
have a great day!!
At a certain time of day, the sun shines on a large flagpole causing a shadow that is twice as long as the flagpole is tall what is the height of the flagpole to the nearest tenth of a foot?
350ft
Answer:
156.5
Step-by-step explanation:
The height of the flagpole to the nearest tenth of a foot is 156.5 ft.
Word Problems Using Pythagoras Theorem:Word Problems involving the use of the Pythagoras theorem need careful understanding to discern the complexity of the variables given, the using the Pythagoras theorem to solve the eqaution.
The Pythagoras Theorem states that the sum of the squares of the opposite side and the adjacent side is equal to the hypotenuse square.
From the information;
The large flagpole height = adjacent = xThe shadow of the flagpole = opposite = 2xThe hypotenuse = 350 ftUsing the Pythagoras theorem, we have;
hyp² = opp² + adj²
350² = (2x)² + x²
350² = 4x² + x²
122500 = 5x²
x² = 122500/5
x² = 24500
x = √24500
x = 156.5 ft
Therefore, we can conclude that the height of the flagpole is approximately 156.5 ft.
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Math question :) please help
I know i may be unwanted here but I just want you to know that you are incredible and that I love you for you! You are special to everyone you meet, and should not change who you are. I know your life may be tough, but you are strong and can get through it!
You may report me as long as you know i ook the time out of my day to type this out for you
<3
How many litres will be needed if 250 ml
Answer:
0.25 liter
Step-by-step explanation:
What is the domain in interval notation of the function graphed below? Note: As x is approaching -2, the graph is getting closer and closer to a line but not touching it.
Answer:
Step-by-step explanation:
x-values approach x = -2, but do not touch the vertical line x = -2. All other x-values are permitted. Thus, the domain is (-2, infinity).
Please answer this solve the proportion x/8 = 9/4 X=
[tex]\frac{x}{8}=\frac{9}{4} \\\\4x=72\\x=18\\[/tex]
hope this helps :)
A(n) __value is any 2-value of a function that makes the y-value undefined.
1. excluded
2. discontinuous
3. quadratic
4. rational
Answer:
rational
Step-by-step explanation:
its so because they fit equaly
PLEASE HELP!!
What is the volume of this rectangular
prism?
A. 40 2/9 in.
B. 46 2/9 in.
C. 56 8/9 in
D. 92 4/9in.
Answer:
A. 40 2/9
Step-by-step explanation:
If I first multiply the whole numbers, so 2 x 5 x 4 that would equal 40. Next you can multiply the fractions, so 2/3 x 1/3 that equals 2/9. So the answer is 40 2/9
HELP PLEASE NO LINKSSS
Answer:
Step-by-step explanation:
multiply the botom olf the pick by the side of the pink and then add all the side of the blue
If it is 78°F in Memphis and -14°F
in Junaeu, what is the temperature
difference between the two cities?
Answer:
There is a 92°F difference between the two cities.
Step-by-step explanation:
Since you are finding the difference of temperatures between the two cities, you need to subtract -14 from 78. It looks like 78-(-14). Since you are subtracting a negative number, the equation becomes 78+14. 78+14 is 92.
How many lines of symmetry does a kite have
0
1
3
2
Answer:
1 i think hope this can help you with your problem
Answer:
1
Step-by-step explanation:
PLEASE ANWSER QUICK PLS PLS
Answer:
D. m/_ 4 is 137
Step-by-step explanation:
If you add 137 and 43 you get 180 which is the line's angle.
help please don’t know how to do this
Answer:
1. C,D
2. B,C,D
3. E
4.D
5.A,B,C,D
6.D
7.C,D
8.E
Step-by-step explanation:
Hope this helps ;)
Find the area of the figure.
Answer:
89m ^2
Step-by-step explanation:
purple 8x13 = 104
triangle 1/2(5)(6) = 15
104-15 = 89
Rachel ran 3 miles when she was training for a race. How many feet did she run?
Answer:
15,840 i did this in test and got 100%
Step-by-step explanation:
The total feet ran by Rachel is given by the equation A = 15,840 feet
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the total miles ran by Rachel be A = 3 miles
Now , the value of 1 mile = 5,280 feet
Substituting the values in the equation , we get
The distance of 3 miles in feet = 3 x value of 1 mile
On simplifying the equation , we get
The distance of 3 miles in feet = 3 x 5,280
The distance of 3 miles in feet = 15,840 feet
Therefore , the distance ran by Rachel A = 15,840 feet
Hence , the equation is A = 15,840 feet
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One hundred nautical miles equals about 185 kilometers. To the nearest kilometer, how far in kilometers is 140 nautical miles?
25,900 km
185 km
76 km
259 km
Answer:
259 km
Step-by-step explanation:
Butterfly method 100/185=140/???
185*140=25900
divide by 100
=295
Write in slope-intercept form.
Select one or more expressions that together represent all solutions to the equation your answer should be in radians sin(x) = -.25
Answer:
-0.25268 rad + 2πn , 3.394273 rad + 2πn
≈ - π /12 + 2πn, π + 2πn
Step-by-step explanation:
sin( x ) = -0.25
x = sin^-1 ( -25 )
The solutions of the equation sin( x ) = -0.25 are :
X = -0.25268rad + 2πn , 3.394273rad + 2πn
≈ - π /12 + 2πn, π + 2πn
If you flip a coin 15 times and it lands on heads every time, what is the probability of the coin landing on heads on
the next flip?
Answer:
Its depends on theoretical and experimental
Step-by-step explanation:
The experimental you have flipped it 15 times and got heads every time, so you have an experimental of 15/15 of heads, but theoretical is a 1/2, or 50/50, a 50% chance of getting heads or tails.
a recipe uses 10 cups of flour. you can only measure using 2/3 cups.
How many 2/3 cups are needed for the recipe?
Ok so I am not exactly sure if you want to know how many whole cups can be added or simply how many 2/3 cups make up 10, but heres what I found.
So to find how many 2/3 is in 10 cups you simply have to divide
10/(2/3) = 15
So 10 cups of flour is 15 (2/3) cups of flour.
Hope this helps :)
Find the values of x
and y that make these triangles congruent by the HL Theorem.
X = 2, Y = 1
X = 3, y = 2
X=1, y = 2
X = 2, y = 3
9514 1404 393
Answer:
(b) x = 3, y = 2
Step-by-step explanation:
In order for the triangles to be congruent by the HL theorem, the hypotenuses must be congruent:
3y = x+3
and the corresponding legs must be congruent:
y +1 = x
__
We can solve this set of equations by substituting for x:
3y = (y +1) +3
2y = 4 . . . . . . . .subtract y
y = 2 . . . . . . . . .divide by 2
2+1 = x = 3 . . . substitute for y in the equation for x
The solution is (x, y) = (3, 2).
Q10.
ABC is a right-angled triangle.
А
11 cm
B
7 cm
C
(a) Work out the size of angle ABC.
Give your answer correct to 1 decimal place.
Answer:
[tex]B = 50.5^\circ[/tex]
Step-by-step explanation:
Given
[tex]AB = 11[/tex]
[tex]BC = 7[/tex]
See attachment
Required
Determine [tex]\angle ABC[/tex]
[tex]\angle ABC[/tex] implies that we calculate the angle at B.
Given that:
[tex]AB = 11[/tex] --- Hypotenuse
[tex]BC = 7[/tex] --- Adjacent of B
We apply cosine formula
[tex]\cos(B) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos(B) = \frac{BC}{AB}[/tex]
[tex]\cos(B) = \frac{7}{11}[/tex]
[tex]\cos(B) = 0.6364[/tex]
Take arccos of both sides
[tex]B = cos^{-1}(0.6364)[/tex]
[tex]B = 50.5^\circ[/tex]
Whoever answers correctly without adding NO FILES OR LINKS gets brainliest
Answer:
C. 6.75n = 114.75
Step-by-step explanation:
The store collects $114.75, each magazine is 6.75, the number of magazines is shown by n.
Answer: The answer is A.
It is A because you have to divide the total by the cost to find out the amount of magazines purchased.
There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
help i don't understand this!!
Answer:
30 cm
Step-by-step explanation:
