Answer:
a) Number of laundry he can do with this box = 78 laundries.
b) Price he paying for each load = 0.256 $
Explanation:
Total scoop contained in detergent box = 195 scoops.
Scoops used by each load of laundry = [tex]2\frac{1}{2} =\frac{2*2+1}{2} =\frac{5}{2}[/tex] scoops = 2.5 scoops
Number of laundry he can do with this box = 195/2.5 = 78 laundries.
Price of detergent box = 19.99 $
Price he paying for each load = Total price/ Number of loads
= 19.99/78
= 0.256 $
Michael drove 350 miles in 7 hours at a constant speed. Is the unit rate for miles to hours 50?
Answer:
Unit rate of driving (speed) is 50 miles per hour
Step-by-step explanation:
Michael drove 350 miles in 7hrs
Speed = Distance ÷ time
Speed= 350 miles ÷ 7 hours = 50 miles per hour.
The question is in the attached below , thank you for helping me .
I' just going to type some of it so if there is someone in the future can find it
3. AB ~= CE
4. CE ~= AC
5. Definition of isosceles triangle
6. Transitive Property of Congruence
A sugar bowl holds 237 grams. You have a one kilogram bag of sugar. Estimate how many bowls of sugar you can fill from the bag.
Answer:
The required number of bowls are 5.
Step-by-step explanation:
Given : A sugar bowl holds 237 grams. You have a one kilogram bag of sugar.
To find : Estimate how many bowls of sugar you can fill from the bag?
Solution :
1 bowl can hold 237 gram of sugar.
We have, 1 kg of sugar or 1000 gram of sugar.
According to question,
237 gram of sugar can hold in 1 bowl.
So, 1 gram of sugar can hold in [tex]\frac{1}{237}[/tex] bowl.
1000 gram of sugar can hold in [tex]\frac{1000}{237}[/tex] bowl.
1000 gram of sugar can hold in [tex]4.21[/tex] bowl.
Which means, The required number of bowls are 5.
As 4 bowls have [tex]237\times 4=948[/tex] grams of sugar.
Sugar left is 1000-948=52 grams
That 52 grams is filled into 5th bowl.
Write three numbers that are greater than 12,000 but less than 13,000
The answers to your question are,
12,001, 12,562, 12,999
-Mabel <3
12,001, 12,562, 12,999 .
Is your answers, hope this helps.
~hEcKiNsHoBe
Cookies come in trays of 100 tovah needs 700 cookies she has 300 cookies
The question centers on mathematics, where we calculate the number of cookies Tovah needs and explore probability and trading scenarios related to assorted cookies and resource allocation.
Explanation:The subject of this question is Mathematics, particularly focusing on basic arithmetic, probability, and problem-solving. Tovah needs a total of 700 cookies and already has 300 cookies. To determine how many more cookies Tovah needs, we can subtract the number she already has from the total number needed: 700 - 300 = 400. Hence, she needs to obtain 400 more cookies.
Additionally, when discussing assorted cookies, we can delve into probability and combinatorics. For instance, if we consider a scenario with cookies containing chocolate, nuts, or both, we can calculate the probability that a certain combination is selected. This involves understanding percentages, probability trees, and independence of events.
Lastly, we can explore resource allocation and trading as seen in examples where individuals barter items like chocolate bars or Halloween candy. This introduces concepts like gains from trade and distribution of resources, which are essential to economic mathematics.
One month julia collected 8.4 gallons of rainwater. That month she used 5.2 gallons of rainwater to water her garden and 6.5 gallons of rainwater to water flowers.How much was the supply of rainwater increased or decreased by the end of the month
Given
One month julia collected 8.4 gallons of rainwater.
she used 5.2 gallons of rainwater to water her garden
6.5 gallons of rainwater to water flowers
Find out how much was the supply of rainwater increased or decreased by the end of the month.
To proof
As given in the question
One month julia collected 8.4 gallons of rainwater
she used 5.2 gallons of rainwater to water her garden and 6.5 gallons of rainwater to water flowers
Total water she used in the month = 5.2 gallons + 6.5gallons
= 11.7 gallons
Let the supply of rainwater increased or decreased by the end of the month
be x .
Than the equation become in the form
x + 8.4 = 11.7
x = 3.3 gallons
Therefore the supply of rainwater increased or decreased by the end of the month is 3.3 gallons.
Hence proved
Total rainwater collected by Julia = 8.4 gallons
Water used for watering garden = 5.2 gallons
Water used for watering flowers = 6.5 gallons
Hence, total water used by Julia = [tex]5.2+6.5=11.7[/tex] gallons
11.7 gallons were used and only 8.4 gallons were collected , so supply of rainwater decreased by [tex]11.7-8.4=3.3[/tex] gallons
RS=6y+5,ST=2y-3, and RT=12y-14
Find Y.
._______.___.
R S T
Note that RT is the whole line segment, and RS and ST are parts of it
RS = 6y + 5
ST = 2y - 3
RT = 12y - 14
Set the equation
RS + ST = RT
(6y + 5) + (2y - 3) = 12y - 14
Simplify. Combine like terms
6y + 2y + 5 - 3 = 12y - 14
(6y + 2y) + (5 - 3) = 12y - 14
8y + 2 = 12y - 14
Note the equal sign. What you do to one side, you do to the other. Isolate the variable (y). Subtract 12y from both sides, and 2 from both sides.
8y (-12y) + 2 (-2) = 12y (-12y) - 14 (-2)
8y - 12y = -14 - 2
Simplify. Combine like terms
(8y - 12y) = (-14 - 2)
-4y = -16
Isolate the y. Divide -4 from both sides
-4y/-4 = -16/-4
y = (-16)/-4
y = 4
--------------------------------------------------------------------------------------------------------------------------
4 is your answer for y.
--------------------------------------------------------------------------------------------------------------------------
hope this helps
The line for which equation has a negative slope?
A. y = 6
B. y = -5x
C. y = 2x + 5
What is the slope of the line represented by -14y = 7x ?
A. −2
B. 1/2 negative
C. 2
The driver of a car travels 150 miles to reach his destination. If he travels 60.0 mi/h for 100.0 miles and 55.0 mi/h for the remaining 50.0 miles, how long does it take for him to reach his destination
I think the answer is 2.7 hours
Using the formula Time = Distance ÷ Speed, we find that the driver would spend approximately 1.67 hours on the first 100 miles and 0.91 hours on the last 50 miles. Adding these two times gives a total travel time of approximately 2.58 hours.
Explanation:The first thing you need to do is calculate the time spent in each part of the trip. To calculate time, we use the formula Time = Distance ÷ Speed. For the first 100 miles at 60 mi/h, it takes: Time = 100 miles ÷ 60 mi/h = 1.67 hours. Moving on to the next 50 miles at 55 mi/h, it takes: Time = 50 miles ÷ 55 mi/h = 0.91 hours.
Adding these two times together gives us the total time for the trip: 1.67 hours + 0.91 hours = 2.58 hours. So, the driver would take approximately 2.58 hours to reach his destination if he traveled 100 miles at 60 mi/h and the remaining 50 miles at 55 mi/h.
Learn more about Speed and Time Calculations here:https://brainly.com/question/38034168
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There were 5 girls and 22 boys in math express the number of girls as a fraction of the number of boys then express the fraction as a decimal
5/22 is the fraction of girls to boys and as a decimal it is 2.3 rounded and not rounded is 2.27 repeated.
A triangle has side lengths of 6, 8, and 5. Is it a right, acute or obtuse triangle
Examine this set of Pythagorean triples. Look for a pattern that is true for each triple regarding the difference between the three values that make up the triple.
Describe this pattern. Then see if you can think of another Pythagorean triple that doesn’t follow the pattern you just described and that can’t be generated using the identity (x2 − 1)2 + (2x)2 = (x2 + 1)2. Explain your findings.
I have attached an image of the triples. If anyone could help me with this, I'd greatly appreciate it. Please respond correctly. Tysm.
A Pythagorean triplet is a set of 3 positive integer numbers which may be the sides of a right triangle, i.e. they meet the Pythagorean theorem c² = a² + b².
You can check that the numbers on your table are Pythagorean triplets by substituting them in the Pythagorean equation:
Now, lets look for the pattern:
x-value Pythagorean
triple
3 (6, 8, 10) 6/2 = 3
3² - 1 = 9 - 1 = 8
3² + 1 = 9 + 1 = 10
----------------------------------------------------------------------
4 (8, 15, 17) 8/2 = 4
4² - 1 = 16 - 1 = 15
4² + 1 = 16 + 1 = 17
---------------------------------------------------------------------
5 (10, 24, 26) 10/2 = 5
5² - 1 = 25 - 1 = 24
24² + 1 = 25 + 1 = 26
--------------------------------------------------------------------------
6 (12, 35, 37) 12/2 = 6
6² - 1 = 36 - 1 = 35
6² + 1 = 36 + 1 = 37
----------------------------------------------------------------------
From which you find the pattern: the first number is 2x, the second number is x² - 1, and the third number is x² + 1
⇒ (2x)² + (x² - 1)² = (x² + 1)², or
(x² - 1)² + (2x)² = (x² + 1)².
Other example of a Pythagorean triple is (3, 4, 5). You migth think that it does not follow the pattern, but if you do x = 2, you end with:
x = 22x = 2(2) = 4x² - 1 = 2² - 1 = 3x² + 1 = 2² + 1 = 5Hence, (3, 4, 5) also follows the pattern.
Only right triangles with non-integer sides do not form Pythagorean triples.
Of course you may proof that (x² - 1)² + (2x)² = (x² + 1)² is an identity (always true):
Left hand side: (x⁴ - 2x² + 1) + 4x² = x⁴ + 2x² + 1
Right hand side: x⁴ + 2x² + 1
∴ The equation is always true.
At the end, the pattern is true for any Pythagorean triplet, but a more formal proof is beyond the scope of this question.
Draw 3 rows with 2 counters in each row. Write a word problem to that can be acted out using these counters
What is 2+2.
15 points
Get it right
ITS 4!! THE ANSWE IS 4!!! BRAINLIEST?!?!
A car can travel 105 miles on 7 gallons of gas. How far can it travel on 9 gallons
Find how far the car can travel on one gallon of gas, by dividing total miles by number of gallons:
105 miles / 7 gallons = 15 miles per gallon.
Now multiply that by the number of gallons to find total miles:
15 miles per gallon x 9 gallons = 135 total miles.
find an equation of a line containing the points (-6,1) and (2,-5).
y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 6, 1 ) and (x₂, y₂ ) = (2, - 5 )
m = [tex]\frac{-5-1}{2+6}[/tex] = [tex]\frac{-6}{8}[/tex] = - [tex]\frac{3}{4}[/tex]
the partial equation is
y = - [tex]\frac{3}{4}[/tex] x + c
to find c substitute either of the 2 given points into the partial equation
using (- 6, 1 ), then
1 = [tex]\frac{9}{2}[/tex] + c ⇒ c = 1 - [tex]\frac{9}{2}[/tex] = - [tex]\frac{7}{2}[/tex]
y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex] ← equation of line
Naomi starts the engine on her small private airplane. The engine drives a propeller with a radius of 8 feet and its centerline 13 feet above the ground. At idle, the propeller rotates at a constant speed of approximately 700 revolutions per minute. The height of one propeller tip as a function of time is given by h = 13 + 8 sin(700t), where h is the height in feet and t is the time in minutes. Use degrees to find h when t = 4 minutes.
Answer:
5.13 feet
Step-by-step explanation:
Engine is driving the propeller with a radius of 8 feet and its centerline 13 feet above the ground.
And the speed is 700 revolutions per minute, the height of one propeller tip as a function of time is given by:
[tex]h=13+8 \sin(700t)[/tex]
We have been asked to find the value of height, 'h', when t=4 minutes.
Plugging the value of time, 't', in the equation, we already know that we need to use degrees (not radians) we get:
[tex]h=13+8 \sin (700 \times 4)[/tex]
[tex]h=13+8 \sin (2800)[/tex]
[tex]h=13+8 \times (-0.984)[/tex]
[tex]h=13+(-7.872)[/tex]
[tex]h=13-7.872[/tex]
[tex]h=5.128\approx 5.13[/tex]
So the height of one propeller tip at t=4 minutes is 5.13 feet.
which of the binomials below is a factor of this expression? 121A2-64B2
A. 121A+8B
B. 11A+32B
C. 121A +32B
D. 11A+8B
Answer: 11A + 8B
Step-by-step explanation:
Which equations are correct? Select each correct answer. −5a4(2a2+4)=−10a6−20a4 −4x2(2x2+5)=−8x4−20x2 −6y4(4y2+2)=−24y8−12y4 −4b3(5b2+3)=−20b6−12b3
1. Consider the expression [tex]-5a^4(2a^2+4)=-10a^6-20a^4.[/tex]
Start with left side and use dustributive property :
[tex]-5a^4(2a^2+4)=-5a^4\cdot 2a^2-5a^4\cdot 4=-10a^6-20a^4.[/tex]
This option is true.
2. Consider the expression [tex]-4x^2(2x^2+5)=-8x^4-20x^2.[/tex]
Start with left side and use dustributive property :
[tex]-4x^2(2x^2+5)=-4x^2\cdot 2x^2-4x^2\cdot 5=-8x^4-20x^2.[/tex]
This option is true.
3. Consider the expression [tex]-6y^4(4y^2+2)=-24y^8-12y^4.[/tex]
Start with left side and use dustributive property :
[tex]-6y^4(4y^2+2)=-6y^4\cdot 4y^2-6y^4\cdot 2=-24y^6-12y^4\neq -24y^8-12y^4.[/tex]
This option is false.
4. Consider the expression [tex]-4b^3(5b^2+3)=-20b^6-12b^3.[/tex]
Start with left side and use dustributive property :
[tex]-4b^3(5b^2+3)=-4b^3\cdot 5b^2-4b^3\cdot 3=-20b^5-12b^3\neq -20b^6-12b^3.[/tex]
This option is false.
Answer: A, B - true, C, D - false.
Answer
−5a⁴(2a²+4)=−10a⁶−20a⁴ is correct.
−4x²(2x²+5)=−8x⁴−20x² is correct.
−6y⁴(4y²+2)=−24y⁸−12y⁴ is NOT correct.
−4b³(5b²+3)=−20b⁶−12b³ is NOT correct.
Explanation
Equation 1
−5a⁴(2a²+4)=−10a⁶−20a² ⇒ −5a⁴(2a²+4) = ( −5a⁴×2a²)+ ( −5a⁴×4)
= -10a⁶ - 20a⁴
−5a⁴(2a²+4)=−10a⁶−20a² is correct
Equation 2
−4x²(2x²+5)=−8x⁴−20x² ⇒ −4x²(2x²+5) = (-4x²×2x²) + (-4x²×5)
= -8x⁴ - 20x²
−4x²(2x²+5)=−8x⁴−20x² is correct.
Equation 3
−6y⁴(4y²+2)=−24y⁸−12y⁴ ⇒ −6y⁴(4y²+2) = (−6y⁴×4y²) + (-6y⁴×2)
= -24y⁶ - 12y⁴
−6y⁴(4y²+2)=−24y⁸−12y⁴ is NOT correct.
Equation 4
−4b³(5b²+3)=−20b⁶−12b³ ⇒ −4b³(5b²+3) = (−4b³×5b²) + (-4b³×3)
= -20b⁵ - 12b³
−4b³(5b²+3)=−20b⁶−12b³ is NOT correct.
Find the slope. If you don't know the answer, don't waste my points, please.
What is 6x+2=9x-1 ahngfhwejgfjhygfweugfuweg
By simplifying both sides of the equation, then isolating the variable.
x = 1
Answer:
x=1
Step-by-step explanation:
1. Move the terms: move the variable to the left hand side and change it sign
2. Move the constant to the right hand side and change its sign
3. Collect like terms
4. Calculate the difference
5. Divide both sides of the equation by -3, therefore x = 1
please mark brainliest! :)
What is 0.79 x 3.7 with an explanation?
My answer for 0.79 x 3.7 is 2.923. It is 2.923 because when you do the problem on paper that is what you get. Also not to be rude or nothing im good at math.
[tex]Solution, 0.79\cdot \:3.7=2.923[/tex]
[tex]Steps:[/tex]
[tex]\mathrm{Multiply\:without\:the\:decimal\:points,\:then\:put\:the\:decimal\:point\:in\:the\:answer}, 79\cdot \:37=2923[/tex]
[tex]79\cdot \:37, \mathrm{Line\:up\:the\:numbers}, \begin{matrix}\space\space&7&9\\ \mathrm{x}&3&7\end{matrix}[/tex]
[tex]\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}, \begin{matrix}\space\space&\textbf{7}&\textbf{9}\\ \mathrm{x}&3&\textbf{7}\end{matrix}[/tex]
[tex]\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:9\cdot \:7=63[/tex][tex]\mathrm{Carry\:}6\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}3\mathrm{\:in\:the\:result\:line}[/tex][tex]\frac{\begin{matrix}\space\space&6&\space\space\\ \space\space&7&\textbf{9}\\ \mathrm{x}&3&\textbf{7}\end{matrix}}{\begin{matrix}\space\space&\space\space&3\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:6+7\cdot \:7=55[/tex], [tex]\mathrm{Carry\:}5\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}5\mathrm{\:in\:the\:result\:line}, \frac{\begin{matrix}\space\space&5&\textbf{6}&\space\space\\ \space\space&\space\space&\textbf{7}&9\\ \mathrm{x}&\space\space&3&\textbf{7}\end{matrix}}{\begin{matrix}\space\space&\space\space&5&3\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:carried\:digit,\:}5\mathrm{,\:to\:the\:result}, \frac{\begin{matrix}\space\space&5&6&\space\space\\ \space\space&\space\space&7&9\\ \mathrm{x}&\space\space&3&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&\textbf{7}&\textbf{9}\\ \space\space&\mathrm{x}&\textbf{3}&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&2&\space\space\\ \space\space&\space\space&7&\textbf{9}\\ \space\space&\mathrm{x}&\textbf{3}&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\\ \space\space&\space\space&7&\space\space\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&2&\textbf{2}&\space\space\\ \space\space&\space\space&\textbf{7}&9\\ \mathrm{x}&\space\space&\textbf{3}&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\\ \space\space&3&7&\space\space\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&2&2&\space\space\\ \space\space&\space\space&7&9\\ \mathrm{x}&\space\space&3&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\\ 2&3&7&\space\space\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&7&9\\ \space\space&\mathrm{x}&3&7\end{matrix}}{\begin{matrix}0&5&5&3\\ 2&3&7&0\end{matrix}}[/tex]
553+2370=2923, =2.923
May has 1,473 and kay has -44 what is the diference
The difference would be:
1,517.
Question 3
What is the approximate solution of the following system of equations?
graph of lines y equals negative x minus 5 and y equals x plus 9
(2, -7)
(-7, 2)
(7, 2)
(-7, -2)
answer is (-7,2)
y = -x -5
y= x+9
Both equations have y on the left hand side
So we equate both equations
We replace -x-5 for y in the second equation
-x -5 = x+9
Subtract x on both sides
-2x -5 = 9
Now add 5 on both sides
-2x = 14
Divide by -2 from both sides
x = -7
Now plug in -7 for x in the first equation
y = -x -5
y = -(-7) -5= 7-5 = 2
So answer is (-7,2)
1. You have the following system of equations:
[tex]\left \{ {{y=-x-5} \atop {y=x+9}} \right.[/tex]
2. Therefore, you have that [tex]y=y[/tex], then:
[tex]-x-5=x+9[/tex]
3. Solve for [tex]x[/tex]:
[tex]-5-9=x+x\\2x=-14\\x=-7[/tex]
3. Now, substitute this value into one the original equations:
[tex]y=x+9\\y=-7+9\\y=2[/tex]
The answer is: (-7,2)
What is 8+0.0+0.05+0.009+0.0006 in standard form
Please help with geometry homework!!!!!
Answer: First option 120 sq.in
Solution:
Perimeter of the base of the prism: p=20"=20 in
Height of the prism: h=6"=6 in
Lateral area of the prism: Al=?
Al=p*h
Replacing the known values in the formula above:
Al=(20 in)*(6 in)
Al=120 sq.in
The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.654
What percent of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers?
Answer:
42.7716% of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers.
Step-by-step explanation:
The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.654
For finding the percent of the variation in one variable explained by the other variable, we just need to take square of the correlation coefficient.
Here, [tex]r=0.654[/tex]
So, [tex]r^2 = (0.654)^2 = 0.427716[/tex]
Now, for converting it into percentage, we will multiply it by 100.
So, [tex]0.427716*100\% = 42.7716 \%[/tex]
Thus, 42.7716% of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers.
Final answer:
About 42.8% of the variation in the bags of trash collected can be attributed to the number of volunteers, as indicated by the squared correlation coefficient (0.654²).
Explanation:
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. When squared to calculate the coefficient of determination (r²), it represents the proportion of the variance in the dependent variable that is predictable from the independent variable. In the given scenario, with a correlation coefficient of 0.654, the coefficient of determination would be 0.654², which calculates to approximately 42.8%. This percentage indicates that about 42.8% of the variation in the number of bags of trash collected (y) can be explained by the variation in the number of volunteers (x).
Geometry help? : which triangle could NOT be similar to triangle ABC ?
I think that the answer is the 4th triangle hope this helped.
That would be triangle DEF and the last one (M - -)
The corresponding sides compared with triangle ABC are not in same ratio
Can someone Please help with this Geometry question, thanks!
The length of CD is -9 to 7 = 16 units long
CE is 1/4 of that length, so 16 x 1/4 = 4 units long.
Add 4 to C: -9 + 4 = -5
Point E would be located at -5.
Consider two functions: g(x)=x2 and the linear function f(x) with slope 1 and y-intercept of 0.
Which statements are true?
Select each correct answer.
f(−1) is equal to g(−1) .
f(1) is equal to g(1) .
f(x) is greater than g(x) on the interval (0,1) .
g(x) has a greater y-intercept than f(x) does.
ANSWER
The correct answers are option B and C
EXPLANATION
A linear function with slope [tex]m=1[/tex] and y - intercept [tex]0[/tex] has equation, [tex]f(x)=x[/tex]
Option A
[tex]f(-1)=-1[/tex]
[tex]g(-1)=(-1)^2=1[/tex]
Therefore [tex]f(-1) \ne g(-1)[/tex]
Option B
[tex]f(1)=1[/tex]
[tex]g(1)=(1)^2=1[/tex]
Therefore [tex]f(1) = g(1)[/tex]
Option C
[tex]f(0.5)=0.5[/tex]
[tex]g(0.5)=(0.5)^2=0.25[/tex]
Therefore [tex]f(x) > g(x)[/tex]
on [tex](0,1)[/tex] See graph also.
Option D
At y-intercept, [tex]x=0[/tex]
This implies that,
[tex]f(0)=0[/tex]
[tex]g(0)=(0)^2=0[/tex]
Therefore g(x) does not have a greater y-intercept.
The function f(x) with a slope of 1 and a y-intercept of 0 is compared with the quadratic function g(x)=x^2. f(1) is equal to g(1) and f(x) is greater than g(x) on the interval (0,1).
Explanation:The function g(x)=x^2 is a quadratic function, and the function f(x) with a slope of 1 and a y-intercept of 0 is a linear function. Let's evaluate the given statements:
f(-1) is equal to g(-1). To evaluate this, substitute -1 into both functions: f(-1) = -1(1) + 0 = -1, and g(-1) = (-1)^2 = 1. Since -1 is not equal to 1, this statement is false.f(1) is equal to g(1). Again, substitute 1 into both functions: f(1) = 1(1) + 0 = 1, and g(1) = 1^2 = 1. Since 1 is equal to 1, this statement is true.f(x) is greater than g(x) on the interval (0,1). To determine this, we need to compare the values of f(x) and g(x) on the interval (0,1). Evaluating both functions at x = 0.5, we get f(0.5) = 0.5(1) + 0 = 0.5 and g(0.5) = 0.5^2 = 0.25. Since 0.5 is greater than 0.25, this statement is true.g(x) has a greater y-intercept than f(x) does. The y-intercept of g(x) is 0, and the y-intercept of f(x) is also 0. Therefore, this statement is false.In summary, the true statements are: f(1) is equal to g(1), and f(x) is greater than g(x) on the interval (0,1).
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