Determine the solution to the following system of equations.
y = -2x2 + 4x + 8
y = -4x + 16
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
Learn more about the mathematical expression visit:
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Lucy bought a broken toy. She repaired it and sold it to her friend. Lucy made the following list to help her calculate her profit. -Price paid for the toy: $5.25 -Cost to repair the toy: $1.33 -Selling price of the toy: $10.00 How much profit did Lucy make by selling the toy?
Answer:
6.08
Step-by-step explanation:
10.00 - 5.25 + 1.33
A professor compares the number of students at his school majoring in statistics, engineering, both, or neither. If the number of students majoring in both is 20, how large is the population?
Answer:
1,946
Step-by-step explanation:
251+175+1500+20=1,946
PLEASE HELP WILL GIVE POINTS ABD BRAINLYIST ASAP
Garnet has a container with 15 1/2
cups of flour in it. She can make one dozen muffins with 2 1/2 cups of flour.
How many dozens of
muffins can Garnet make with the flour she has?
Answer:
6
Step-by-step explanation:
2.5x6=15 and thats the closest it'll get. To be exact, it's 6.2, but i dont know if you need that.
3. Choose the equation of the line parallel to the line 5 = -10x - 5y that passes through the point (-2,5). A y=-2x + 1 C y=x-5 By=-12x + 5 D y = 5x + 11
Answer:
y = -2x + 1
Step-by-step explanation:
The equation is in standard form, first, we need to convert it to slope-intercept form.
5 = -10x - 5y
5 + 10x = -5y
Divide both sides by -5 to isolate y variable.
y = -2x - 1
If the line is parallel, the slope remains the same.
To find the y-intercept, you need to plug the values of x and y into the equation, which is y = 2x + b
5 = -2(-2) + b
5 = 4 + b
1 = b
The equation is -2x + 1
Sam is a second grader and weighs 35 kilograms. How many milligrams does Sam weigh?
Answer:
35,000,000 miligrams
Step-by-step explanation:
1 kilograms= 1,000,000
1,000,000×35=35,000,000
A number cube has 6 different faces, numbered 1 to 6. All faces have an equal probability of being rolled. What is the probability of rolling a 5?
If a person trys to say to pick a link to find the answer I will report you and email brainly!!
Answer:
its a 1/6 chance
Step-by-step explanation:
each face has a 1/6 chance of being rolled since there are 6 faces
How many times does this polynomial change signs?
f(x) = 3x5 – 2x4 – 6x3 + x2 - 4x – 9
Answer:
3 sign changes from the highest order term to lowest
Help 10 pts!
If a point is randomly selected from the rectangular area of the graph, what is the probability that it will be in the blue region?
Round answer to the nearest whole percentage?
A. 49%
B. 59%
C. 69%
D. 79%
Answer:
D. 79%
Step-by-step explanation:
Took the the on USA Test prep
If a point is randomly selected from the rectangular area of the graph, the probability that it will be in the blue region is 79%.
What is the probability?The ratio of the number of favorable outcomes to the total number of outcomes of an event is known as probability.
It is given that, the length=20, the width=10, and the radius of half circle=10.
Calculate the area of the rectangle.
Knows the area of the rectangle is the product of length and width.
So,
[tex]\Rightarrow \text{Area of rectangle}=\text{10}\times \text{20} \\ \Rightarrow \text{Area of rectangle}=200 \\[/tex]
Calculate the area of the half-circle.
Knows the area of the half-circle[tex]=\frac{\pi r^{2} }{2}[/tex].
So,
[tex]& \Rightarrow \text{Area of half circle}=\frac{3.14\times 10\times 10}{2} \\ & \Rightarrow \text{Area of half circle}=\frac{314}{2} \\ & \Rightarrow \text{Area of half circle}=157 \\[/tex]
Calculate the probability that it will be in the blue region.
Knows the formula for the probability, [tex]\text{Probability}\left( \text{Event} \right)=\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}[/tex]
So,
[tex]& \Rightarrow \text{Probability}=\frac{\text{157}}{200} \\ & \Rightarrow \text{Probability}=0.78539 \\ & \therefore \text{Probability }\%=79\% \\[/tex]
Thus, the correct answer is an option (D). i.e., 79%.
Learn more about the probability, here
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Find an equation of the line perpendicular to y=-2x +6 that passes through the point of (-2,8)
Answer:
Joe mama
Step-by-step explanation:
You need a mean of at least 90 points to advance to the next round of the touch-screen trivia. What score in the fifth game will allow you to advance
Answer:
At least 98 is needed in the 5th game
Step-by-step explanation:
The missing parameters are:
[tex]Game\ 1 = 95[/tex]
[tex]Game\ 2 = 91[/tex]
[tex]Game\ 3 = 77[/tex]
[tex]Game\ 4 =89[/tex]
[tex]Mean = 90[/tex] at least
Required
The score in game 5 to make you advance
Mean is calculated as:
[tex]Mean = \frac{\sum x}{n}[/tex]
So, we have:
[tex]Mean = \frac{95 + 91 + 77 + 89 + Game\ 5}{5}[/tex]
[tex]Mean = \frac{352 + Game\ 5}{5}[/tex]
The mean must be at least 90.
So, we have:
[tex]\frac{352 + Game\ 5}{5} \ge 90[/tex]
Multiply both sides by 5
[tex]5 * \frac{352 + Game\ 5}{5} \ge 90 * 5[/tex]
[tex]352 + Game\ 5 \ge 450[/tex]
Make Game 5 the subject
[tex]Game\ 5 \ge450 - 352[/tex]
[tex]Game\ 5 \ge 98[/tex]
At least 98 is needed in the 5th game
A metallic cuboid measuring 16cm by 8 cm by 4cm was melted.The material was used to make a cube . What is the length of the cube
Answer:
Step-by-step explanation:
The volume of the metal cuboid = length x width x height = 16 x 8 x 3 = 16 x 24 = 384 cm^3
If this same cuboid is going to be reshaped, then
The volume of the cuboid = The volume of the cube
Therefore,
l^3 = 384
l = [tex]\sqrt[3]{384}[/tex]
l = 7.268..
l = 7.27cm ( 2dp)
Hope this helps.
[tex]=59(F−32)[/tex]
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of 59
A degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
Answer:
Think of the equation as an equation for a line y = m x + b where in this case C = 5 9 ( F − 32 ) or C = 5 9 F − 5 9 ( 32 ) You can see the slope of the graph is 5 9 , which means that for an increase of 1 degree Fahrenheit, the increase is 5 9 of 1 degree Celsius. C = 5 9 ( F ) C = 5 9 ( 1 ) = 5 9 Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 9 5 degrees Fahrenheit. C = 5 9 ( F ) 1 = 5 9 ( F ) ( F ) = 9 5 Since 9 5 = 1.8, statement II is true. The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of 5 9 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true: C = 5 9 ( F ) C = 5 9 ( 5 9 ) C = 25 81 ( which is ≠ 1 ) An increase of 5 9 degree Fahrenheit leads to an increase of 25 81 , not 1 degree, Celsius, and so Statement III is not true. The final answer is D.
Ill give brainliest ------
Answer:
about 63.59 ft squared
Step-by-step explanation:
9/2 = 4.5--> Radius
Now we use the Area formula: piR^2 (Pi x radius squared)
4.5^2 = 20.25
20.25 x 3.14 = 63.59 -(rounded answer)
Pls help I have this homework !! bye I will mark you the best or brainliest!!
Answer:
90-54w
Step-by-step explanation:
18(5−3w)=
18*5=90 , 18*3w= 54w =
so simplified it would be = (90-54w)
Please mark me as brainliest :D
Please find the radius and the circumference will give brainlyest
The function f(x)= x^2 is graphed above. Which of the graphs below represents the function g(x) = x^2 -3?
Answer:
bottom left graph
Step-by-step explanation:
The function g(x) is a translation of function f(x). It is the function f(x) moved 3 units down.
The vertex of the parabola of f(x) is (0, 0).
The vertex of the parabola of g(x) is (0, -3).
Answer:
can someone find the area of this/explain how they did it?
thanks ! it means a lot. no links pls !!!
Answer: 1914 sq. ft
Step-by-step explanation:
area of circle= pi x radius squared
=3.14 x 10^2
=3.14x100
=314
area triangle= 1/2 base x height
=1/2(20x60)
= 1/2(1200)
= 600
area of rectangle= length x width
=50 x 20
= 1000
add the totals 1000 + 600 + 314=1914 sq. ft.
What is the slope in this situation: A bean plant is growing three inches every two days.
Answer:
I need a picture of the problem to be able to solve it.
Step-by-step explanation:
Please, multiply the following Algebric sum.........
3ab+2bc, 5bc
Answer: The required product of two given algebraic expressions =15abc +10b²c²
Step-by-step explanation:
Here we need to multiple two algebraic expressions: 3ab+2bc, 5bc
i.e. The required product = (3a+2bc) x (5bc)
= 3a x 5bc + 2bc x 5bc [Using right distributive property: (a+b)c= ac+bc]
= (3x 5) abc + (2 x 5) (bc)²
= 15abc +10b²c²
Therefore, the required product of two given algebraic expressions = 15abc +10b²c²
who would like some points? 23x23x23x23x23x23x23x23
first correct answer = brainliest
Answer:
78310985281
Step-by-step explanation:
The equation of the line with slope 4 and y -intercept 4 can be written in the form y = m x + b where the number m is: the number b is:
Answer: [tex]m:4; \ b=4[/tex]
Step-by-step explanation:
Given
Slope is 4
Y-intercept is 4
For the slope-intercept form of line i.e. [tex]y=mx+b[/tex]
[tex]m=\text{slope of line}\\b=\text{Y-intercept of the line}[/tex]
So, we can write
[tex]y=4x+4[/tex]
[tex]m:4; \ b=4[/tex]
Which is the greatest common factor of
84 and 60?
A 4
B 6
© 12
D
24
Answer:
12
Step-by-step explanation:
A freight elevator is holding 15,893 pounds of merchandise stored in containers. Another container weighing 3,473 pounds is placed on the elevator. Then a container weighing 5,492 pounds is taken off the elevator. Let w represent the weight that the elevator is holding. Which equation could be used to solve for the the amount of weight the freight elevator is holding after the container is taken off of it?
Answer: [tex]W=13,874\ \text{Pounds}[/tex]
Step-by-step explanation:
Given
Elevator holds [tex]15,893\ \text{Pounds}[/tex] of merchandise
Now, 3473 Pounds of the box is loaded, and then 5492 Pound of the container is taken off
Net weight held by elevator is
[tex]\Rightarrow W=15,893+3473-5492\\\\\Rightarrow W=13,874\ \text{Pounds}[/tex]
Jim wants to make a 4 letter password. He cannot repeat any letters in his password.How many combinations can he make
My previous answer was incorrect, sorry for that... the correct answer would be 358,800
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{He has 26 letters all together (A - Z)}[/tex]
[tex]\large\text{25 if he starts from his second letter (B - Z)}[/tex]
[tex]\large\text{24 if he starts from his third letter (C - Z)}[/tex]
[tex]\large\text{ 23 if he starts from his fourth letter (D - Z)}[/tex]
[tex]\mathsf{26\times25\times24\times23}[/tex]
[tex]\mathsf{26\times 25 = \bf 650}[/tex]
[tex]\mathsf{650\times24\times23}[/tex]
[tex]\mathsf{650\times24 = \bf 15,600}[/tex]
[tex]\mathsf{15,600\times 23}[/tex]
[tex]\mathsf{ =\bf 358,800}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \huge \bf 358,800}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which statement is true about rectangular prisms?
A. All rectangular prisms have five faces.
B. The bases are always congruent.
C. The lateral faces are always congruent.
D. All rectangular prisms have three lateral faces.
Answer:
it b
Step-by-step explanation:
No links man and please if you have a question about anything comment it.
Answer:
29=1/2
30=1/5
31=1/12
32=1/6
33=1/7
Step-by-step explanation:
I just counted the numbers and then put them as fraction.
Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.
6c^2+ 2c^4 - c
Answer:
Standard form: 2c^4 + 6c^2 - c
Degree: 4th
Leading coefficient: 2
Classification: Trinomial
Step-by-step explanation:
In standard form, you have to put the term with the highest exponent first.
With finding the degree, you just look at the highest exponent and that's the degree. 4 is the highest exponent, so it is to the 4th degree.
The leading coefficient is the number attached to the highest exponent. 4 is the highest and the number attached to it is 2.
Classification goes by how many terms there are. Since there are 3, it's trinomial. Tri as in three.
In a promotion at a store, each customer gets a chance to randomly draw a ticket from a box. There are 100 tickets. 20 tickets say "winner" and 80 tickets say "sorry, try again". Assume two customers play and that the ticket is not replaced after the first customer plays.
A) What is the probability that the second customer wins, given that the first customer wins?
B) What is the probability that the second customer loses, given that the first customer wins?
C) What is the probability that the second customer wins, given that the first customer loses?
Answer:
It's B
Step-by-step explanation:
Find sin x, sin z, cos x, and cos z. Write each answer as a simplified fraction
Answer:
sin x=55/73
Sinz=48/73
cosx=48/78
cosz=55/73
Step-by-step explanation:
Using SOHCAHTOA