Answers
the correct option is the first one (counting from the top).
The true statement is:
"The leading coefficients of f(x) and g(x) are opposites"
Which statement is true?We know that f(x) and g(x) are quadratic functions, and the sum of these two functions is shown in the graph.
We can see that the sum gives a linear graph, so the terms with the exponents of 2 are cancelled by the sum.
This only can happen if f(x) and g(x) have opposite (same absolute value but different sign) leading coefficients, so the quadratic terms are cancelled when we add the functions.
For example in f(x) = 2*x^2 + 3x + 4
g(x) = -2x + x + 13
If we add these two functions, we would end with a line.
With that in mind we can conclude that the correct option is the first one (counting from the top).
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Related Questions
Please help! thanks!
Answers
two angles are complementary. The measure of the larger angle is 6 degrees less than 3 times the measure of the smaller angle. The measure of the smaller angle is _______ degrees and the measure of the larger angle is______ degrees
Answers
Step-by-step explanation:
complementary means together they are 90°.
x = 3y - 6
x + y = 90
(3y - 6) + y = 90
4y - 6 = 90
4y = 96
y (the smaller angle) = 24°
x (the larger angle) = 3y - 6 = 3×24 - 6 = 72 - 6 = 66°
How do I figure out x and y
Answers
Answer:
x = 7, y = 45
Step-by-step explanation:
[tex]7x+13=6x+20[/tex]
[tex]x=20-13\\x=7[/tex]
Angle
[tex]7(7)+13=49+13=62^{0}[/tex]
supplementary angle
180 - 62 = 118°
[tex]3y-17=118[/tex]
[tex]y=\frac{118+17}{3} =135/3=45[/tex]
Hope this helps
A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total admission revenue, not including sales tax, and had a total of 450 guests.
The system of equations below can be used to model the number of guests that were children, x, and the number of guests that were adults, y.
First, place a point on the graph representing the solution to the system of equations. Notice that one of the equations in the system has already been graphed.
Then, determine the approximate number of guests that were children and the approximate number of guests that were adults for that day.
Answers
The approximate number of guests that were children are 172 and adults are 278
How to determine the approximate number of guests that were children and adults for that day?From the complete question, we have the following system of equations
25x + 12y = 9014
x + y = 450
Make y the subject in x + y = 450
y = 450 -x
Substitute y = 450 - x in 25x + 12y = 9014
25x + 12(450 - x) = 9014
Expand the expression
25x + 5400 - 12x = 9014
Evaluate the like terms
13x = 3614
Divide both sides by 12
x = 278
Substitute x = 278 in y = 450 -x
y = 450 - 278
Evaluate
y = 172
Hence, the approximate number of guests that were children are 172 and adults are 278
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If EF = 5x, FG = 10, and EG = 10x, what is EF?
geometry
Answers
If points E,F,G are collinear, then,
EF+FG = EG
5x+10 = 10x
10 = 10x-5x
10 = 5x
5x = 10
x = 10/5
x = 2
So,
EF = 5x = 5*2 = 10EG = 10x = 10*2 = 20As a check, EF+FG = 10+10 = 20 = EG to help confirm the answer
Final Answer: EF = 10Answer:
EF = 10
Step-by-step explanation:
EF = 5x
FG = 10
EG = 10x
Please HELP ME!!!! This is really confusing. HOW DO I DO THIS?!?!?!
Answers
Answer:
Flying Disc should be 72
Step-by-step explanation:
circumference = πd
HD Coin C = 3π
9.42477796077
Flying Disc. C = 23π
72.2566310326
Jar Lid C = 8π
25.1327412287
Flower Pot C = 15π
47.1238898038
|3x| = 11.4 absolute value of X
Answers
Step-by-step explanation:
The absolute value of x is g(x)=f(x)+k.
What is the solution of −|t+3| + 3 ≥ −4?
Answers
Answer:
[tex]-1t+31 +3 \geq -4[/tex]
[tex]-1t +34 \geq -4[/tex]
[tex]-1t \geq 30[/tex]
[tex]t \geq -30[/tex]
GUY!!! PLEASE HELP it’s due in abit and I just need this final question! I’ll mark you brainliest
(geometry)
what is the perimeter of the rectangle ABCD?
Answers
Answer:
37.9 units (nearest tenth)
Step-by-step explanation:
As ABCD is a rectangle, AD = BC and AB = DC.
Find the length of AD and AB using the distance formula.
[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}}[/tex]
From inspection of the given diagram:
A = (-5, -9)B = (7, -5)D = (-7, -3)Therefore:
[tex]\begin{aligned}AD & =\sqrt{(x_D-x_A)^2+(y_D-y_A)^2}\\& =\sqrt{(-7-(-5))^2+(-3-(-9))^2}\\& =\sqrt{(-2)^2+(6)^2}\\& =\sqrt{4+36}\\& =\sqrt{40}\end{aligned}[/tex]
[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(7-(-5))^2+(-5-(-9))^2}\\& =\sqrt{(12)^2+(4)^2}\\& =\sqrt{144+16}\\& =\sqrt{160}\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Perimeter of a rectangle} & = \sf 2(length + width)\\& = 2(AB+AD)\\& = 2(\sqrt{160}+\sqrt{40})\\& = 2(18.97366596...)\\& = 37.94733192...\\& = 37.9\: \sf units\:(nearest\:tenth)\end{aligned}[/tex]
Therefore, the perimeter of the rectangle ABCD is 37.9 units (nearest tenth).
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Please help simplify
Answers
Answer: B. 24
Step-by-step explanation:
solve for x please
4 / x • 26 / 2
Answers
Answer:
x = 3.25
Step-by-step explanation:
Use the Rule of 3 to solve this
Work in picture
a parte inferior de una escalera debe colocarse a 3 pies de una pared. La escalera mide 10 pies de largo. ¿Qué tan por encima del suelo toca la escalera la pared?
Answers
[tex]\sqrt{10^2 - 3^2}=\boxed{\sqrt{91} \text{ ft}}[/tex]
What happens to the sum of the ball’s kinetic energy and potential energy as the ball rolls from point A to point E? Assume there’s no friction between the ball and the ground. An image shows a curve that starts at point A, decreases at B, then increases at C and D, and ends at E. A. The sum decreases. B. The sum increases. C. The sum remains the same. D. The sum always equals zero
Answers
The sum of the ball's kinetic energy and potential energy remains the same. as the ball rolls from point A to E.( if there is no friction between the ball and the ground).
based on the law of mechanical energy's conservation, the sum of both kinetic and potential energies i.e. the total amount of mechanical energy remain conserved even in the absence of dissipative forces ( friction or air resistance) in a bound system.
the kinetic energy is when ball goes downward but potential energy decreases and reverse happens when ball goes up. but in these case, the sum energy would be constant one.
The ball would not change the energy.
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Solve the equation P = b + a + c for b.
b= ?
Answers
Answer:
b= p-(a+c)
Step-by-step explanation:
Solve for x
|4x + 7| + 9 = 6
Answers
Add -9 to both sides.
|4x+7|+9+−9=6+−9|4x+7|=−3Solve Absolute Value.
|4x+7|=−3No solutions. (Absolute value cannot be less than 0.)
Skandar
A 5.ft tall man casts a shadow along the ground that is 8 ft. long. At the same time a giraffe casts a shadow that is 12 ft. long. How tall is the Giraffe?
Answers
Answer : 7.5 ft
Step-by-step explanation:
when the length of the shadow is 8ft, the actual height of the man = 5ft
8:5
let the giraffe be 'x' ft tall.
if the length of the shadow is 12ft, actual height = x ft
12:x
8:5 x 12:x
[tex]\frac{8}{5}[/tex] × [tex]\frac{12}{x}[/tex]
x= [tex]\frac{15}{2}[/tex]
x=7.5 ft
Therefore, the giraffe is 7.5ft tall.
Answer:
[tex]7.5\; {\rm ft}[/tex].
Step-by-step explanation:
The height of objects nearby under the sun are approximately proportional to the length of their shadows.
In other words, if the man and the giraffe are near each other and under the sun:
[tex]\begin{aligned} \frac{\text{height of man}}{\text{length of shadow of man}} = \frac{\text{height of giraffe}}{\text{length of shadow of giraffe}}\end{aligned}[/tex].
Given that:
[tex](\text{height of man}) = 5\;{\rm ft}[/tex], [tex](\text{length of shadow of man}) = 8\;{\rm ft}[/tex], and [tex](\text{length of shadow of giraffe}) = 12\; {\rm ft}[/tex].Rearrange the equation to find [tex](\text{height of giraffe})[/tex]:
[tex]\begin{aligned} (\text{height of giraffe}) &= (\text{length of shadow of giraffe})\times \frac{\text{height of man}}{\text{length of shadow of man}} \\ &= 12\; {\rm ft} \times \frac{5\; {\rm ft}}{8\; {\rm ft}} \\ &= 7.5\; {\rm ft}\end{aligned}[/tex].
Brian is buying gifts bags for all of the students in his class. The graph shows the relationship between the number of bags and the cost of the bags. Write an equation relating the number of bags, x, and the cost, y.
Answers
An equation that relates the number of bags, x, to the cost, y is y = 5x.
What is an equation?An equation is a mathematical statement that claims that the two sides are equal.
An equation involves two or more variables that require some mathematical operations to obtain their equivalent value.
Therefore, an equation contains numbers, variables, and operators, which show a value after the mathematical operations.
Data and Calculations:Let the number of bags for the class = x (number of students)
Let the unit cost of a bag = $5
Let y = the total cost
Equation, y = 5x
Thus, an equation that relates the number of bags, x, to the cost, y is y = 5x.
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Four thousand five hundred eleven ten-thousandths in standard decimal form?
Answers
Виконайте завдання:
Запишіть речення, підкресліть граматичні основи, визначте односкладні та двоскладні речення.
Тихий прихід осені
У лісі з'явилися жовті фарби. Крони дерев ще зелені. Дивишся під ноги, помічаєш перше опале листя. Тиша. Не чути співу пташок. Пташенята давно вивелись. Гнізда порожні. Ледь чутний шум листя, хруст сухого гілля. Природа чекає на зміни.
Перепишіть прислів'я. Де потрібно, поставте тире між підметом і присудком. Підкресліть граматичні основи.
1. Вірний приятель то найбільший скарб.
2. Розум скарб людини.
3. Вовка боятися в ліс не ходити.
4. Щастя біжить, а нещастя лежить.
Перепишіть і визначте вид односкладних речень (за зразком першого речення).
1. Усі національні культури побудовано на шануванні предків (побудовано - присудок, виражений формою дієслова на -но, -то; речення розповідне, неокличне, односкладне, безособове).
2. За рідний край і життя віддай.
3. Батьків і Батьківщину не вибирають.
4. Сучасне українське мистецтво...
5. Ніколи не можна забувати про мовний етикет.
6. Усі ми не в тім'я биті.
Answers
How to I round this imperfect square √11
Answers
Answer: 3.32
Step-by-step explanation:
√11=
3.3166=
3.3166=3.32 ==>When rounding to the hundredth place, if the thousandth's digit is 5 or greater, increase the hundredth's digit by 1.
A car is traveling at a speed of 45 kilometers per hour. What is the car's speed in meters per second? How many meters will the car travel in 2 seconds?
Answers
Answer:
12.50m/s
in 2 seconds: 25
im not really good at math but i tried
Given below are descriptions of two lines.
Line 1: Goes through (1,1) and (-2,7)
Line 2: Goes through (-1,4) and (1,0)
The slope of Line 1 is m =
|
The slope of Line 2 is m =
Answers
The slope of Line 1 is m = -2
The slope of Line 2 is m = -2
For Line 1;
(x₁, y₁) = (1, 1);
(x₂, y₂) = (-2, 7);
m₁ = (7-1)/(-2-1) = -2;
For Line 2;
(x₃, y₃) = (-1, 4);
(x₄, y₄) = (1, 0);
m₂ = (4-0)/(-1-1) = -2;
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ASAP HELP PLEASE!!!!
Answers
Answer:
x^21/5
Step-by-step explanation:
To change this expression to an expression with a rational exponent, we need to change the radical to a rational (fractional) exponent. Just as square root is a one half power and cuberoot is a one-third power, a fifth root is a one-fifth power.
Once the radical is changed to a fraction, we will just use the exponent rule that says when you raise a power to a power, you multiply exponents.
see image.
Find the dimensions of a rectangle given that its perimeter is 80 cm and its length is 1 cm more than twice its width.
Set up your solution using the variables L for the length, W for the width, and P for the perimeter.
Part a: Using the definition of perimeter, write an equation for P in terms of L and W .
Part b: Using the relationship given in the problem statement, write an equation for L in terms of W .
Solve the equations from parts a and b.
Answers
Answer:
The length should equal 27.
The width should equal 13.
A: P= 2L+ 2W
B: L=2W+1
Step-by-step explanation:
Perimeter is always equal to all of the sides added up.
You can find out the width and length by subsititution.
80=2(2W+1) +2W
80=4W+2+2W
80=6W+2
78=6W
W=13
L=(13*2)+1
L=27
(x³- 3x²+2x+1)/x²-4x+4 dx (dx/dy) + (x²+4y-y²)/(²√4y+y²)
Answers
Answer:
y=1 x=1
×[[×[+[[+[+[+[+[+[+[+[+[+[[
In 2008, the number of digital cameras shipped totaled 186 million. There were 24 million shipped in 2013. Find and
interpret the average rate of change in the number of digital cameras shipped per year.
Answers
Step-by-step explanation:
the average change rate for a function g(x) is defined for an interval of x values as
(g(interval end) - g(interval begin))/(interval end - interval begin)
in our case that is
(g(2013) - g(2008))/(2013 - 2008) =
= (24 mil. - 186 mil)/5 = -162 mil./5 =
= -162,000,000 / 5 = -32,400,000
that means that as a mean value there were 32,400,000 digital cameras shipped less every year.
in other words, fewer and fewer digital cameras are sold. the demand is strongly declining.
actually, following the mean values and their trend, there should have been no new digital cameras shipped in 2014 anymore (as 24 mil. - 32.4 mil is less than 0).
a² + 6b when a = -3 and b = 2
Answers
6(2)=12
9+12=21
Answer = 21
Answer:
21
Step-by-step explanation:
Just substitute -3 in for a and 2 in for b
[tex]a^2 + 6b\\-3^2 + 6(2)\\9 + 6(2)\\9 + 12\\21[/tex]
When you square a negative number, the answer is positive. Good luck, and have a great day!
Also, Jesus loves you!!!!
Susan Marciano invested part of her $12,000 bonus in a fund that paid 8% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each investment if her overall net profit was $300 .
Answers
Answer:y=mx+b
Step-by-step explanation:
Answer:
Let x be the amount invested in funds that earned 8%.
Then the amount invested in stock that suffered 3% loss is 18,000 - x.
The profit from investment in funds is 8%x
The loss from investment in stock is 3%(18,000 - x).
The net profit is 8%x - 3%(18,000 - x).
As the net profit given in the problem is $780, we have:
8%x - 3%(18,000 - x) = 780
Step-by-step explanation:
The total payroll for a baseball team is 2.48 × 109 dollars, and the total payroll for a football team is 2.8 × 1011 dollars. How many more dollars is the football team's total payroll than the baseball team's total payroll?
0.32 × 109 dollars
2.7752 × 109 dollars
2.7752 × 1011 dollars
3.2 × 1011 dollars
Answers
Answer: its c
Step-by-step explanation:
The difference between the payroll of football and baseball is 2.7752 × 10¹¹. Hence, option C is correct.
What is an equation?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right is shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine the value of an unknown variable that represents an unknown quantity.
The payroll of the baseball team is 2.48 × 10⁹ and,
The payroll of the football team is 2.8 × 10¹¹.
So, the football team's payroll is more than the baseball team's payroll by,
(2.8 × 10¹¹) - (2.48 × 10⁹)
= 2.7752 × 10¹¹.
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The probability that a live birth requires a cesarean delivery in a certain American state is 0.248. If 8 live births occur independently in this state, compute the probability that at least one of the births requires a cesarean delivery.
i need help on this question
Answers
The probability that at least one of the births requires a cesarean delivery is 0.897.
To calculate prob(x >= 1):
prob(x>=1) = 1 - prob(x = 0)
= 1 - (1-0.248)^8
= 0.897
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