Given:
The table of values for Fallon's earnings in terms of Donald's earnings.
To find:
The equation that best represents Fallon's earnings in terms of Donald's earnings.
Solution:
In the given table the x-values are increasing by 5 units and y values increasing by 5 units. It means the rate of change of y with respect to x is constant and the table represents a linear function.
If the graph of a linear function passes through two points, then the equation of linear function is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Consider any two points from the table. Let the two points are (38,45) and (43, 50). Then, the equation is
[tex]y-45=\dfrac{50-45}{43-38}(x-38)[/tex]
[tex]y-45=\dfrac{5}{5}(x-38)[/tex]
[tex]y-45=1(x-38)[/tex]
[tex]y-45=x-38[/tex]
Adding 45 on both sides, we get
[tex]y=x-38+45[/tex]
[tex]y=x+7[/tex]
Therefore, the correct option is A.
Help with hw please I’ll give brainliest
What is 8,000,000 + 100,000 + 7,000 + 400 + 20 + 4 in standard form?
Answer:
8,107,424
Step-by-step explanation:
We have an expanded form of a number and are asked to convert it into standard form.
We always have to look at the place value when it comes to expanded form.
So follow the place values :
Million , Hundred Thousand, Ten Thousand, Thousand, Hundred, Tens, Ones.
1,000,000, 100,000, 10,000, 1,000, 100, 10, 1
Look at the values given and replace it
8,000,000, 100,000, 0, 7,000, 400, 20, 4
Now add them all :
8,107,424
Which of the following word problems can be solved using the equation 10 x - 15=60
Answer:
Kit buys
Step-by-step explanation:
im right
Find the height of a cone with a diameter of 12 m and whose volume is 133 m.
A. 2 m
B. 9 m
C. 3 m
D. 1 m
Answer:
D
Step-by-step explanation:
Here, we want to get the height of the cone
radius = diameter/2
r = 12/2 = 6 m
To get this, we use the formula for the volume
V = 1/3 * pi * r^2 * h
133 = 1/3 * 3.142 * 22/7 *6^2 * h
h = 1.12 m
Does (0, 0) make the equation y = 9x − 5 true?
Answer:
no
Step-by-step explanation:
y = 9x − 5
The point (0,0) means x=0 and y=0
Substitute this into the equation and see it is true
0 = 9*0 -5
0 = 0-5
0 = -5
This is not true so the point is not a solution.
Joe went on holiday to Spain.
His flights cost a total of £320
Joe stayed in an apartment for 3 weeks.
The apartment cost 560 euros each week.
Joe hired a car for 15 days.
The car hire cost 20.16 euros each day.
The exchange rate was £1 = 1.12 euros.
Work out the total cost, in pounds, of the flights, the apartment and the car hire.
The price of a car was decreased by 9% to £14000. What was the price before the decrease? Give your answer to the nearest penny.
Answer:
152600
Step-by-step explanation:
this is because 9% of 140000 is 1523
Pls help will give branliest
Answer:
7x² - 26x + 9
Step-by-step explanation:
(g(x)²) = (3x - 2) (3x - 2)
(g(x)²) = 9x² - 6x - 6x + 4
(g(x)²) = 9x² - 12x + 4
(9x² - 12x + 4) - (2x² + 14x - 5) = 7x² - 26x + 9
Please help will mark brainliest
Answer:
26
Step-by-step explanation:
a cylinder has height of 12 and a diameter of 10 find the volome
Answer:
942.48
Step-by-step explanation:
V=πr^2h=π·5^2·12≈942.4778
Solve
7 + X = 2x-5
3
Answer:
the exact form is 22/5
decimal form is 4.4
mixed number form is 4 2/5
Step-by-step explanation
isolate the variable by dividing each side by factors that don't contain the variable
What is the equation of the line that passes through the point ( -1, 1) and is perpendicular to 2x + 4y = 16?
A. y = −2x − 1
B. y − 3 = 2x
C. y = 6x + 7
D. Cannot be determined
Answer:
B
Step-by-step explanation:
We want the equation of the line that passes through the point (-1, 1) and is perpendicular to:
[tex]2x +4y=16[/tex]
Remember that the slopes of perpendicular lines are negative reciprocals of each other.
So, let's find the slope of the original line first. We can do so by converting it to slope-intercept form. Thus:
[tex]4y=-2x+16[/tex]
Therefore:
[tex]\displaystyle y=-\frac{1}{2}x+4[/tex]
The slope is -1/2.
The negative reciprocal of -1/2 is 2.
Thus, the slope of our new line is 2.
The slope is 2 and it passes through the point (-1, 1).
We can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute:
[tex]y-(1)=2(x-(-1))[/tex]
Distribute:
[tex]y-1=2x+2[/tex]
Subtracting 2 from both sides yields:
[tex]y-3=2x[/tex]
Therefore, our answer is B.
solve this please
log(4x+16)=2
Answer:
X = -3.5
Step-by-step explanation:
Answer:
-7/2
Step-by-step explanation:
4x+16=2
-16 -16
4x= 2-16
4x=-14
/4 /4
x= -7/2
I will mark you as the brainiest if you get this correct Thx so much xxx
Answer:
22.7
Step-by-step explanation:
9³-8*6 = 729-48= 681
(8²-4) / 2 = 30
681/30 = 22.7
Answer:
[tex] \huge \boxed{ \blue{ \text{22.7}}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:order of PEMDASgiven:[tex] \frac{ {9}^{3} - 8 \times 6 }{ ({8}^{2} - 4 ) \div 2} [/tex]let's solve:[tex]step - 1 : define[/tex]
[tex] \frac{ {9}^{3} - 8 \times 6 }{ ({8}^{2} - 4 ) \div 2} [/tex]
[tex]step - 2 : simplify[/tex]
[tex] \frac{ {9}^{3} - 8 \times 6 }{ ({8}^{2} - 4 ) \div 2} [/tex][tex] \frac{729 - 8 \times 6 }{ (64 - 4 ) \div 2} [/tex][tex] \frac{721 -48}{60 \div 2} [/tex][tex] \frac{681}{30} [/tex][tex]22.7[/tex]The "h" in the lateral area formula, L = Ph, stands for
A telephone pole is 54 feet tall. A guy wire runs 79 feet, from point A at the top of the telephone pole, to the ground at point B. The base of the telephone pole is at point C. Triangle ABC is a right triangle.
How far is it from the base of the telephone pole to point B where the guy wire is secured to the ground? Round to the nearest tenth of a foot.
ft
Answer:
57.7 ft
Step-by-step explanation:
54 squared + b squared = 79 squared
2916 + b squared = 6241
-2916 -2916
b squared = 3325
b = 57.7
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The distance that the base of the telephone pole to point B where the guy wire is secured to the ground is 57.7 feet
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
Given that triangle ABC is a right triangle.
Point A is the top of the telephone pole.
Point B is the point on the ground.
Point C is the base of the telephone pole.
Given,
AB = 79 feet
AC is the height of the telephone pole = 54 feet
Angle C is a right angle.
Using Pythagoras theorem,
(AB)² = (AC)² + (BC)²
79² = 54² + (BC)²
(BC)² = 79² - 54²
(BC)² = 3325
BC = √3325 = 57.66 ≈ 57.7 feet
Hence the length of the base of the pole form the ground where the wire is secured is approximately 57.7 feet.
Learn more about Pythagoras Theorem here :
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My mother purchased 8 Pepsi products at Bi-Lo for $14.00. What is the price per
product?
Answer:
1.75 per product
Step-by-step explanation:
Answer:
112
Step-by-step explanation:
You would multiply 8 by 14 dollars because your finding the price per product Pepsi bottle so your answer would be 112 dollars.
triangle has vertices A( 0,0 ), B(2, 0) and C(0, 4). Angle ABC is transformed to angle A"B"C" by a rotation of 180 degrees clockwise about the origin, followed by a dilation with the origin as the center of dilation and scale factor of 3. find the coordinates of the vertices of angle A"B"C" and state whether the two triangles are similar or congruent.
Step-by-step explanation:
The pre-image points are A( 0,0 ), B(2, 0) and C(0, 4). The question is asking you to rotate the traingle 180°. Each rotation has its rules. For 180° rotation our rule is (x,y) → (-x,-y). Let's apply that to our points:
A( 0,0 ), → (0,0)
B(2, 0) → (-2,0)
and C(0, 4). → (0,-4)
Now we dilate our point ( remember the order in which you do transformation is important. Since it saids the rotation is followed that means the dilation is done second)
Our scale factor is 3. Remember when our scale factor is more than one our shape gets bigger. So our rule is (x,y) → (kx,ky). Let's apply our scale factor to all our points:
(0,0) → (0,0)
(-2,0)→( -6,0)
(0,-4) → (0,-12)
The answer is
A' (0,0) B' (-6,0) C' (0,-12)
The triangles will be similar not congruent. Remember congruent triangles have the same angles and same sizes. Similar angles have the same angles BUT different sizes. Every transformation produces congruent angles except for dilations.
0.583
What is it in standard form
Answer:
It should be 583*10^-3
y= x + 1
y= -x + 5
what's the answer pls I need it asap
Answer:
X= 2 and y = 3
Step-by-step explanation:
Explain what effect an index of 0 has
Answer:
Zero-based numbering is a way of numbering in which the initial element of a sequence is assigned the index 0, rather than the index 1 as is typical in everyday non-mathematical or non-programming circumstances.
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What is 2(5 to the second power) +3(5) - 12
Answer:
53
Step-by-step explanation:
Tyler finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of the length x in inches of the square cutouts used to make it. This is the graph Tyler gets if he allows x to take on any value between -1 and 7.
What is the approximate maximum volume for his box?
Answer:
Step-by-step explanation:
Domain: 0<x<3.5
To get 3.5: 7/2=3.5
Negatives and decimals can't be used
Approximate maximum volume for this box? 55
The proper domain of Noah's graph should be 0 to 3.5 and the maximum of the graph is at y = 60.
It is required to find the approximate maximum volume for his box.
What is co-ordinate geometry?Coordinate geometry is defined as the study of geometry using the coordinate points. Coordinate geometry is required to provide a link between algebra and geometry through the use of line and curve graphs.
Given:
From the attached graph (see attachment), we have the following observations:
1.The x values starts from -1 and ends at 60
2.The domain of the graph is from 0 to 4 (i.e. x-values 0 to 4 have corresponding y-values on the graph)
3.x-values 0 to 3.5 have corresponding non-negative y-values
4.Other values of x have corresponding negative y-values
5.The maximum of the graph is at y = 60
Because the volume of a box cannot be negative, the x-values to use must correspond to non-negative y-values.
Hence, the proper domain of Noah's graph should be 0 to 3.5 and the maximum of the graph is at y = 60.
Learn more about co-ordinate geometry here:
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solve question >> ( - 3x)^2
Answer:
(-3x)^2 = (-3)^2(x^2)
=9x^2
Let me know if this helps!
Markus buys an old bike for £50. He cleans it up and sells it for £60. What is his percentage profit?
Please help! I need help
Answer:
median is 32 and the mean is 21
4. The black triangle was transformed to
make the gray triangle. Which represents
the transformation?
A (x, y) + (x + 3, y + 3)
B (x, y) → (3x, 3y)
C (x,y) → (x-2, y-2)
what is true about the line x-4y=8
A garden is going to be built in the city park in the shape of a parallelogram with a rectangular walkway through it. The garden region is shown below. Find the area of the garden region by finding the areas of the individual shapes shown in the figure. 78 ft 72 ft 30 ft 20 ft Answer:
Answer:
328
Step-by-step explanation:
30+30=60 +(78 +78) = 216 + 72= 288 + (20+20) = 328
Answer:
The answer is 328
Step-by-step explanation:
I took the test an explenation is exactly like the other comment said, you add the sides up and bam.
Also, Stay Safe, SS. ps. Dont cough or sneeze on other people, wear your mask in populated areas, and sanitize. <3A bag contains 77 coins consisting of quarters and nickels. The total value of the coins is $12.50. Write a system of equations that can be used to determine the number of quarters, x, and the number of nickels, y, in the bag. a x + y = 77 0.25x + 0.5y = 12.5 b 0.25x +0.5 y = 77 x + y = 12.5 c x + y = 77 0.25x + 0.05y = 12.5 d 0.25x + 0.05y =77 x + y = 12.5
Answer:
A
Step-by-step explanation:
because the answer needs both amounts of money and the beginning equation x + y = 77 can't have any other numbers.