We have been given that a line [tex]y=mx+b[/tex] passes through the point (10, 3) and is parallel to the line [tex]2x+5y=12[/tex]. We are asked to find the y-intercept of the line.
First of all we will rewrite our given equation in slope-intercept form as:
[tex]2x-2x+5y=12-2x[/tex]
[tex]5y=-2x+12[/tex]
[tex]\frac{5y}{5}=-\frac{2}{5}x+\frac{12}{5}[/tex]
[tex]y=-\frac{2}{5}x+\frac{12}{5}[/tex]
We know that slope of parallel lines is equal, so slope of parallel line to our given line would be [tex]-\frac{2}{5}[/tex].
Now we will use slope-intercept form of equation to find y-intercept.
[tex]y=mx+b[/tex], where,
m = Slope,
b = The y-intercept.
Let us substitute [tex]m=-\frac{2}{5}[/tex] and coordinates of point [tex](10,3)[/tex] in above equation as:
[tex]3=-\frac{2}{5}(10)+b[/tex]
[tex]3=-2(2)+b[/tex]
[tex]3=-4+b[/tex]
[tex]3+4=-4+4+b[/tex]
[tex]7=b[/tex]
Therefore, the y-intercept is 7 and our required equation would be [tex]y=-\frac{2}{5}x+7[/tex].
The price of 8 citrons and 9 fragrant wood apples is 145 units. The price of 9 citrons and 8 fragrant wood apples is 144 units. Find the price of a citron and the price of a wood apple.
Answer:
The price of a citron is 8 and the price of a wood apple is 9
Step-by-step explanation:
First of all we make two equations that represents the problem
c = citrons price
w = wood apples price
8c + 9w = 145
9c + 8w = 144
we clear c in the first equation
8c + 9f = 145
8c= 145 - 9w
c = (145 - 9w) /8
c = 145/8 - 9w/8
we replace c by (145/8 - 9w/8) in the second equation and solve
9(145/8 - 9w/8) + 8w = 144
163.125 - 10.125w + 8w = 144
163.125 - 144 = 10.125w - 8w
19.125 = 2.125w
19.125/2.125 = w
9 = f
now we replace w in the first equation
8c + 9w = 145
8c + 9(9) = 145
8c + 81 = 145
8c = 145 - 81
8c = 64
c = 64 / 8
c = 8
The price of a citron is 8 and the price of a wood apple is 9
what is the difference about the trapezoid formula from the triangle formula
Step-by-step explanation:
Do you mean area formula or the perimeter formula?
both formulas are different from the other because a triangle does not have 4 sides. A trapezoid is a quadrilateral.
and the triangle doesn't have "a base" usually
while trapezoids have two, one on the top and one on bottom
Jordan went to the store to buy a bicycle that was advertised for $50. When he arrived, he learned that the model he wanted was sold out, but there was another bicycle available that cost 15% more. How much did the available bicycle cost before taxes? $7.50 $57.50 $65.00 $15.00
Answer: 57.50
Step-by-step explanation:
50*.15=7.50
50+7.5=57.50
B - $57.50
Step-by-step explanation:
To find the cost of the available bicycle before taxes, we need to add another 15% to the original $50. To do that, all you do is multiply $50 by 15%, and then re-add the $50. Work is shown below:
First, change 15% into a decimal:
15% -> 15/100 -> 0.15
Next, lets find the cost of the available bicycle:
x = 50 (0.15)
x = 7.5
Now add the $50 back 7.5:
50 + 7.5 = 75.50
So your answer is B = $57.50
What is the slope and x-intercept of y=2x+1?
Answer:
slope: 2
x-intercept = -1/2
Step-by-step explanation:
The equation is in y = mx + b form. m = slope. The slop is equal to 2.
To find the x-intercept set y equal to 0 and solve for x.
0 = 2x + 1
-1 = 2x
x = -1/2
Answer:
slope= 2
x intercept=-0.5 or -1/2
Step-by-step explanation:
y= mx+b
m is the slope, therefore 2 is the slope of the equation.
X-intercept
substitute 0 to y
0=2x + 1
Subtract 1 from both sides
0-1=2x+1-1
-1=2x
Divide both sides by 2
-1/2=2x/2
x=-1/2 or -0.5
Look at the graph of the linear function. On a coordinate plane, a line goes through 4 points. Point A is (negative 2, negative 4), point B is (negative 1, negative 2), point C is (1, 2), and point D is (2, 4). The rate of change between point A and point B is 2. What is the rate of change between point C and point D?
Answer:
2
Step-by-step explanation:
For a linear function, the rate of change is the same everywhere. It is the same between points C and D as it is between points A and B: 2.
The rate of change between points C and D is 2.
Answer:
D
Step-by-step explanation:
how do i find the area of this shape?
Answer: 288
Parallelogram Area Using Sides
Suppose a and b are the set of parallel sides of a parallelogram and h is the height, then based on the length of sides and height of it, the formula for its area is given by: Area = Base × Height. A = b × h [sq.unit]
Answer:
288 ft
Step-by-step explanation:
The height is 16 and the base is 18.
base times height equals area in a parallelogram.
16x18=288
20. Helen and Carla live in states that have
different sales tax rates. They each bought
a new bicycle. Helen paid $14 for a 5.6%
sales tax on her bicycle. Carla paid $12 for
a 4.8% sales tax on her bicycle. Who paid
more for their bicycle, not including sales
tax?
Answer: Helen paid $250 for the bike
Carla paid $250 for the bike.
They both paid the same amount
Step-by-step explanation:
Final answer:
By calculating the pre-tax prices of the bicycles using the provided sales tax amounts and rates, we determine that both Helen and Carla's bicycles cost $250 before tax, meaning neither paid more for their bicycle excluding the sales tax.
Explanation:
To determine who paid more for their bicycle excluding the sales tax, we need to calculate the pre-tax price of each bicycle using the sales tax amounts given. This requires us to work backwards from the sales tax paid to the original cost of the item.
For Helen, we know that the sales tax was $14, and the rate was 5.6%. We find the pre-tax price by dividing the sales tax paid by the sales tax rate (converted into decimal form):
Pre-tax price for Helen = $14 / 0.056 = $250
For Carla, the sales tax was $12, and the rate was 4.8%. The pre-tax price calculation is similar:
Pre-tax price for Carla = $12 / 0.048 = $250
Since both pre-tax prices are equal, neither Helen nor Carla paid more for their bicycle when we do not include the sales tax.
Cost to store: $75
Percent of Markup:
Selling price: $112.50
Answer:
15%
Step-by-step explanation:
pretty sure thats right
Final answer:
The student's question involves a business math concept of calculating the percent markup from the cost and selling price, resulting in a 50% markup for this example.
Explanation:
The question involves calculating the percent markup based on the cost to store an item and its selling price.
To find the percent of markup, you subtract the cost to store from the selling price and then divide by the cost to store.
Finally, multiply by 100 to get the percentage.
For example, if an item costs $75 to store and sells for $112.50, the markup is ($112.50 - $75) / $75 = 0.50, or 50%.
This is an example of a basic markup calculation commonly covered in business and economics classes in high school.
2n-3/ 10n^2-17n+3 multiplied by 15n^3-3n^3/ 6n^2-6n
Show the work
Multiplying Rational Expressions
Algebra 1 honors
PLEASE HELP ILL MARK BRAINIEST
Answer:
[tex]\frac{2n^2}{5n^2-6n+1}[/tex]
Step-by-step explanation:
The problem is as follows:
[tex]\frac{2n-3}{10n^2-17n+3} *\frac{15n^3-3n^3}{6n^2-6n}[/tex]
To make this problem simpler to solve, you can simplify the fractions. The first fraction can be simplified by factoring the denominator and cancelling out like factors.
[tex]\frac{2n-3}{10n^2-17n+3} \\\frac{2n-3}{(2n-3)(5n-1)} \\\frac{1}{5n-1}[/tex]
The second fraction can be simplified by cancelling out like factors.
[tex]\frac{15n^3-3n^3}{6n^2-6n}\\\frac{12n^3}{6n^2-6n}\\\frac{2n^2}{n-1}[/tex]
Now, you can multiply the two fractions quite easily
[tex]\frac{1}{5n-1} *\frac{2n^2}{n-1}\\\frac{2n^2}{5n^2-6n+1}[/tex]
A pedestal on which a statue is raised on is a rectangular concrete solid measuring nine
feet long, nine feet wide, and six inches high. How much is the cost of the concrete in the
pedestal, if concrete costs $70 per cubic yard?
Answer:
The cost of the rectangular concrete solid is $104.87Step-by-step explanation:
If the pedestal on which a statue is raised on is a rectangular concrete solid measuring nine feet long, nine feet wide, and six inches high, the volume of the rectangular concrete solid will be expressed as shown;
Volume of the rectangular concrete solid = Length * Width * Height
Given Length = 9ft, Width = 9ft and Height = 6inches
Converting all the units to yards
Given 1ft = 0.333yard
Length = 9 * 0.333 = 2.997yards
Width = 9* 0.333 = 2.997yards
Also given 1inch = 0.0278yard
Height = 6 * 0.0278yards = 0.1668yards
Volume of rectangular concrete solid in cubic yards = 2.997*2.997*0.1668
Volume of rectangular concrete solid in cubic yards = 1.4982cubic yards
If concrete costs $70 per cubic yard, the cost of the rectangular concrete solid will be 1.4982 *$70 = $104.87
A county manager used a representative sample of two populations in the county to determine the number of pounds of trash thrown away per person per week. The results are shown in the dot plots below. Sample 1: A dot plot titled Sample 1. A number line going from 0.5 to 2.5 in increments of 0.5 is labeled Pounds of Trash. There is 1 dot above 0.5, 3 above 1, 4 above 1.5, 2 above 2, and 2 above 2.5. Sample 2: A dot plot titled Sample 2. A number line going from 0.5 to 2.5 in increments of 0.5 is labeled Pounds of Trash. There are 2 dots above 0.5, 3 above 1, 4 above 1.5, 2 above 2, and 1 above 2.5. The town manager uses the median to show that the average amount of trash thrown away per person per week in each sample is the same. What is the town manager's error?
Answer:
its B
Step-by-step explanation:
Answer:
it is b
Step-by-step explanation:
i took the test
I need help finding the area of the kite and trapezoid.
Answer:
Kite = 72cm²
Trapezoid = 144 km²
Step-by-step explanation:
Kite:
4×6 = 24cm
8×6 = 48cm
24+48 = 72cm²
Trapezoid:
9×12 = 108 km
12×6 = 72 km
72÷2 = 36 km
36+108 = 144 km²
the function g(x)= f(x+3)+2. Which of the following is true of the graph of g(x)
Answer:
You forgot to put the answer options.
Step-by-step explanation:
Answer:b. The graph of g(x) is shifted 3 units to the left and 2 units above the graph of f(x)
Step-by-step explanation:
Which number gives you an irrational product when you multiple it by 0.2
Answer:
the answer is
[tex] \sqrt{5} [/tex]
as you can see I got it right.
A jar contains 10 marbles marked with the numbers 1 through 10. You pick a marble at random. What is the probability of not picking the marble marked with the number 3? Enter you’re answer as a simplified fraction.
Answer:
1/10
Step-by-step explanation:
There's 10 marbles that you can pick, and there's only one marble with a 3 on it. So it'd be 1/10
I did the question and the correct answer was 9/10. Not 1/10 like the other answer.
7/6d+4/3=1/3 solving for d
Answer:
d = -6/7
Step-by-step explanation:
7/6d+4/3=1/3
Subtract 4/3 from each side
7/6d+4/3-4/3=1/3-4/3
7/6 d = -3/3
Simplify the right side
7/6 d = -1
Multiply each side by 6/7 to isolate d
6/7 *7/6 d = -1 *6/7
d = -6/7
Answer:
D= -3.23077
Step-by-step explanation:
7/6d+4/3=1/3
-4/3 -4/3
7/6d= -1
divide each side by 7/6
d= -3.23077
Find the equation of the hyperbola centered at the origin that satisfies the given conditions: x-intercepts = +,-4 and asymptote at y=3/4x
Answer:
The equation of the hyperbola is presented as follows;
[tex]\frac{x^2}{16} - \frac{y^2}{9} =1[/tex]
Step-by-step explanation:
Here we have the standard equation of an hyperbola given as follows;
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} =1[/tex]
Where:
a = x intercept
The asymptote is ±(b/a)x
Since the intercept, a is ± 4, the vertices are (-4, 0) and (4, 0)
We are given the asymptote as y = 3/4x, therefore, since the genral form of the asymptote is ±(b/a)x, comparing, we have;
±(b/a)x ≡ 3/4x
We have a = ±4, therefore, b = 3
Hence the equation of the hyperbola is found by putting in the values of a and b in the general form as follows;
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} =1 \Rightarrow \frac{x^2}{4^2} - \frac{y^2}{3^2} =1[/tex]
The equation of the hyperbola = x²/16 - y²/9 = 1.
Answer:
B
Step-by-step explanation:
edge
Drag the vertices of the triangle below to draw a right triangle with side lengths 5, 12, and 13.
I hope that helps, coz l've done what i know
Line segment ON is perpendicular to line segment ML.
Circle O is shown. Line segments M O, N O, and L O are radii. Lines are drawn to connects points M and N and points N and L to form chords. A line is drawn from point M to point L and intersects line O N at point P. The length of O M is 13 and the length of P N is 8. Angle O P L is a right angle.
What is the length of chord ML?
20 units
24 units
26 units
30 units
Answer:
B. 24 units
Step-by-step explanation:
Each triangle has 13 as the hypotenuse and 8 as a leg length; the lengths carry over.
The longer leg length (MP & PL) is 12 from the pythagorean theorem.
13^2 - 8^2 = 12^2.
MP + ML = PL, so 12 + 12 = 24.
Answer:
24
Step-by-step explanation:
3. Para encontrarmos o resultado de 300 – 650, podemos: a) efetuar 650 + 300 e manter o sinal do resultado b)efetuar 650 + 300 e inverter o sinal do resultado c) efetuar 650 – 300 e manter o sinal do resultado d) efetuar 650 – 300 e inverter o sinal do resultado
Answer:
To find the result of 300 - 650, we can:
a) do 650 + 300 and keep the result sign
b) do 650 + 300 and invert the result sign
c) do 650 - 300 and keep the result sign
d ) perform 650 - 300 and invert the result sign
Step-by-step explanation:
The correct answer is the letter D .
(perform 650 - 300 and invert the result sign)
300 - 650
300 is more than - 650 on the number line this is because of the negative sign of 650
so we can also write it as 650 - 300 and after getting the require result with put the negative sign to the result, so the result will be -350
Keep the sign of the number with the highest absolute value and subtract from it the lowest absolute value.
- (650 - 300)
Subtract the numbers.
- 350
therefore, the answer is d ) perform 650 - 300 and invert the result sign
Amanda has a ribbon that is 6 feet long. She wants to cut it into 12 equal pieces. How long will each piece be? Write the steps, in order, you would take to solve the problem. * 2 points Your answer
Answer:
Each of the pieces will be 0.5 feet long
Step-by-step explanation:
In this question, we are asked to calculate the individual length Anita will cut a ribbon 6 feet long into to ensure that each of the piece has the same length.
To calculate this, since we don not know what length each of the piece would be, we can say let the length of each of the pieces be x feet
Now, we know that there are 12 pieces that are equal in length. The length of all these 12 pieces would be 12 * x = 12x feet
Now what do we know again?
We also know that these 12x feet equals a total of 6 feet
mathematically therefore;
12x = 6
x = 6/12
x = 0.5 feet
Answer: Each piece will be 1/2 feet long.
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given.
We simply have to divide the length of the ribbon (6) by the number of pieces that she wants to cut (12).
Mathematically speaking:
6 /12 = 1/2
In conclusion, each piece will be 1/2 feet long.
Feel free to ask for more if needed or if you did not understand something.
PLZ HELP ASAP FIRST ANSWER GETS BRAINLEST WEN THERES TWO PPL WHO ANSWER QUESTION I CHOOSE WHO FIRST 1 WAS GETS IT N FIVE STAR N THANKS 14 POINTS
Answer:
£375
Step-by-step explanation:
Difference will be equal to the difference in VAT
(20% - 17.5%) of 15000
2.5% of 15000
2.5/100 × 15000
375
James had a peach that was 98 mm in diameter. One day he watered it with a magical solution, and it grew to 188,869 mm
in diameter.
Approximately how many times as large did the diameter of the peach become after James watered it?
To determine how many times larger the peach got, you will divide the new diameter by the original diameter length.
188869/98 = 1927.2
The new diameter is approximately 1927 times longer.
To convert this to scientific notation, move the decimal point from the end (on the right) to between the 1 and the 9 to get 1.927.
Then count the number of decimal places you moved to get there, because this represents how many groups of 10 you adjusted your place value by and then becomes your exponent in scientific notation.
1.927 x 10^3 times is the answer in scientific notation.
Answer:
2*10^3
Step-by-step explanation:
evaluate the expression
Factor the number: 64 = [tex]4^3[/tex]
Apply radical rule: [tex]\sqrt[n]{a^n}[/tex] = a
a [tex]\geq 0[/tex]
[tex]\sqrt[3]{4^3} =4[/tex]
= 4
The citizens of the Union were always happy with how the war was going.
True
Or
False
Answer:
False
Step-by-step explanation:
Lemme know if it helped
Factor out the greatest common factor of 25x^5-10x^3-15x
Answer:
5x (5x²+3) ( x-1 ) ( x+1 )
Step-by-step explanation:
hope this helps
-3x-5 less than or equal\] to -23
Answer:
Step-by-step explanation:
What's x
A number m increased by 5 is 7.
Answer:
m+5=7
"A number m" will be a unknown nmber known as a variable. So it will be m.
"Increased by 5" is addition. So you are adding 5.
"Is 7" is equal to 7. it will be =7.
So when you put this together it will give you m+5=7
You received $97 in all selling paintings. You sold one painting for $29 and the rest for $17 each. Solve the equation below to find x, the number of $17 paintings you sold.
17x + 29 = 97
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
97=29+17x
subtract 29 from both sides
68=17x
divide both sides by 17
4=x
Is the number 3 a rational number?
Answer:
Yes.
Step-by-step explanation:
The number 3 is a natural number, and all of these types of numbers are rational.
Another way to look at it is if a number can be written as a fraction, the number is rational.
Answer:
in fact yes
Step-by-step explanation:
it is since it's actually a normal number