Answers
The equation of the second line is written in standard form. To know the slope of this line, we can rewrite its equation in slope-intercept form by solving for y.
[tex]\begin{gathered} ax+by=c\Rightarrow\text{ Standard form} \\ y=mx+b\Rightarrow\text{ Slope-intercept form} \\ \text{ Where m is the slope and b is the y-intercept} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 4x-5y=-10 \\ \text{ Subtract 4x from both sides of the equation} \\ 4x-5y-4x=-10-4x \\ -5y=-10-4x \\ \text{Divide by -5 from both sides of the equation} \\ \frac{-5y}{-5}=\frac{-10-4x}{-5} \\ y=\frac{-10}{-5}-\frac{4x}{-5} \\ y=2+\frac{4}{5}x \\ \text{ Reorganize} \\ y=\frac{4}{5}x+2 \\ \text{ Then} \\ $$\boldsymbol{m=\frac{4}{5}}$$ \end{gathered}[/tex]Now, two lines are perpendicular if their slopes satisfy the following equation:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \text{ Where }m_1\text{ is the slope of the first equation and} \\ m_2\text{ is the slope of the second equation} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} m_2=\frac{4}{5} \\ m_1=-\frac{1}{\frac{4}{5}_{}} \\ m_1=-\frac{\frac{1}{1}}{\frac{4}{5}_{}} \\ m_1=-\frac{1\cdot5}{1\cdot4} \\ $$\boldsymbol{m}_{\boldsymbol{1}}\boldsymbol{=-\frac{5}{4}}$$ \end{gathered}[/tex]Step 2Since we already have a point on the line and its slope, then we can use the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula} \\ \text{ Where } \\ m\text{ is the slope and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} (x_1,y_1)=(6,3) \\ m=-\frac{5}{4} \\ y-3=-\frac{5}{4}(x-6) \\ \text{ Apply the distributive property} \\ y-3=-\frac{5}{4}\cdot x-\frac{5}{4}\cdot-6 \\ y-3=-\frac{5}{4}x+\frac{5}{4}\cdot6 \\ y-3=-\frac{5}{4}x+\frac{30}{4} \\ \text{ Add 3 from both sides of the equation} \\ y-3+3=-\frac{5}{4}x+\frac{30}{4}+3 \\ y=-\frac{5}{4}x+\frac{30}{4}+\frac{12}{4} \\ y=-\frac{5}{4}x+\frac{30+12}{4} \\ y=-\frac{5}{4}x+\frac{42}{4} \\ \text{ Simplify} \\ y=-\frac{5}{4}x+\frac{21\cdot2}{2\cdot2} \\ y=-\frac{5}{4}x+\frac{21}{2} \end{gathered}[/tex]Step 3Therefore, the equation of the line that passes through the point (6,3) that is perpendicular to the line 4x - 5y = -10 is
[tex]$$\boldsymbol{y=-\frac{5}{4}x+\frac{21}{2}}$$[/tex]Related Questions
Question 1 4 pts Match each quadratic expression that is written as a product with an equivalent expression that is expanded. A. (x + 2)(x + 6) [Choose ] [Choose ] B. (2x + 3)(x + 2) 2x^2 + 10x + 12 X^2 + 12x + 32 C. (X + 8)(x + 4) x^2 + 8x + 12 2x^2 + 12x + 16 D. (x + + 2)(2x + 6) [Choose ]
Answers
(x +2) (x +6) ------> x^2 +8X + 12
(2x + 8) (x +2) -------> 2x^2 +12x + 16
(x +8) (x+4) ------------> x^2 +12x +32
(x + 2) (2x+6) ----------> 2x^2 +10x +12
a portion of the graph of f(x) = -x^2 - 2x +8 is shown. which of the following describes all solutions for f(x)?
Answers
Given the function:
[tex]f(x)=-x^2-2x+8[/tex]Let's determine the expression which describes the solution for f(x).
From the graph, we can see the x-values go from -5 to 3.
The expression which describes the solution will be:
[tex](x,-x^2-2x+8),where-5\leq x\leq3[/tex]ANSWER:
[tex](x,-x^{2}-2x+8), where-5\leqslant x\leqslant3[/tex]Necesito saber si los ejercicios están correctos o no y la explicación
Answers
None of the operations with radicals are correct, as two radical terms can only be added or subtracted if they have the same radical and the same exponent.
Addition and subtraction with radicalsTerms with radicals can only be added or subtracted if they have the same radical and same exponent, for example:
[tex]3\sqrt{2} + 2\sqrt{2} = 5\sqrt{2}[/tex]
In the above example, they have the same radical, of 2, and same exponent, also of 2.
The first example is given by:
[tex]7\sqrt{3} + 4\sqrt{2} = 11\sqrt{5}[/tex]
The mistake is that the two terms cannot be added, as they have different radicals, of 3 and 2.
The second example is given as follows:
[tex]3\sqrt[3]{k} - 6\sqrt{k} = -3\sqrt{k}[/tex]
The terms have the same radical, of k, but they have different exponents, of 3 and 2, hence they cannot be subtracted.
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Anna's goal is to raise more than $200 for a
charity. Three of her neighbors donated $15 each, and one of her
friends donated $5. Write an inequality to show how much more
money Anna needs to raise. Explain how you found the answer.
Tell why you chose the inequality symbol that you used.
Answers
Answer: 200 < 50 + x
Step-by-step explanation:
Since three of her neighbors donated 15 dollars each, we can find how much she earned from them by doing 3 x 15 = 45.
Including the 5 dollars earned by her friend, we get 50 dollars by doing 45+5 = 50.
Anna needs more than 200 dollars so 200 has to be less than Anna's total earnings. (x) is how much more Anna will need to earn to make the inequality true.
Match each expression with its translation.1. 3 na number increased by three2. a +3the quotient of three and a number3. Y-3three times a number4. 3 = xthree subtracted from a number
Answers
A number increased by three:
Every time we read a number, it's an unknown value represented with a letter (x,y, a,n)
increased by three means t
Nikolas bought a Falcon's ticket for $80. The sales tax on the ticket is 7%. How much was the tax?
Answers
ok
100% ---------------------------- $80
7% ---------------------------- x
x = (80 x 7)/100
x = 560/100
x = 5.6
The tax was of $5.6
The schedule for summer classes is available and Calculus and Introduction to Psychology are scheduled at the same time, so it is impossible for a student to schedule for both courses. The probability a student registers for Calculus is 0.05 and the probability a student registers for psychology is 0.62. What is the probability a student registers for Calculus or psychology?
Answers
Explanation
The given is that the probability a student registers for Calculus is 0.05 and the probability a student registers for psychology is 0.62. Since it impossible for a student to schedule for both courses, we will have
[tex]\begin{gathered} Pr(Psychology\text{ or calculus\rparen=Pr\lparen P\rparen+Pr\lparen C\rparen-Pr\lparen P}\cap C) \\ =0.05+0.62-0 \\ =0.67 \end{gathered}[/tex]Answer: 0.67
Solye for x.7(x - 3) + 3(4 - x) = -8
Answers
Explanation
Step 1
apply the distributive property to eliminate the parenthesis
[tex]\begin{gathered} 7(x-3)+3(4-x)=-8 \\ 7x-21+12-3x=-8 \end{gathered}[/tex]Step 2
add similar terms
[tex]\begin{gathered} 7x-21+12-3x=-8 \\ 4x-9=-8 \end{gathered}[/tex]Step 3
add 9 in both sides
[tex]\begin{gathered} 4x-9=-8 \\ 4x-9+9=-8+9 \\ 4x=1 \end{gathered}[/tex]Step 4
divide each side by 4
[tex]\begin{gathered} 4x=1 \\ \frac{4x}{4}=\frac{1}{4} \\ x=\frac{1}{4} \end{gathered}[/tex]Simplify the expression leave expression in exact form with coefficient a and b so we have a✔️b.
Answers
coefficient of a = 2x
Explanation:[tex]\text{The expression: 2}\sqrt[]{x^2y}[/tex]Simplifying:
[tex]\begin{gathered} \sqrt[]{x^2}\text{ = x} \\ 2\sqrt[]{x^2\times y}\text{ = 2x}\sqrt[]{y} \end{gathered}[/tex]Since we are told the coefficient of a can be the product of a number and variable:
[tex]\begin{gathered} 2x\sqrt[]{y}\text{ is in the form a}\sqrt[]{b} \\ a\text{ = 2x},\text{ b = y} \\ 2\text{ = number, x = variable} \\ 2x\text{ = product of number and variable} \\ \text{coefficient of }a\text{ = 2x} \end{gathered}[/tex]You pick a card at random.
1 2 3 4
What is P(factor of 24)?
Write your answer as a percentage rounded to the nearest tenth
Answers
Answer:
100%
Step-by-step explanation:
All of the numbers are factors of 24. So, picking a factor of 24 is guaranteed, so the probability is 1.
This is equal to 100%.
FIND THE INDICATED PROBABILITY A magazine did a survey to determine its readers favorite types of shoesFavorite types of shoes worn Sneaker boot Sandal other 54% 16% 20% 10% What is the probability that the sneakers Will NOT be the favorite shoe of the next reader?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
table:
favorite types of shoes
Step 02:
probability:
probability (not sneakers) = 100% - 54% = 46%
The answer is:
probability (not sneakers) = 46%
Which expression is equivalent to a + 0.2c?O 1.23O 0.22O 0.2x01.023
Answers
If we have the expression:
This is the same to write:
So the answer is 1.2x.
What percent of 60 is 39?
Answers
Answer:
To find the percent of 60 is 39
Let x be the percent of 60 is 39,
we get,
[tex]\frac{x}{100}\times60=39[/tex]Solving this, we get
[tex]x=\frac{39\times10}{6}[/tex][tex]x=65[/tex]Hence 65 percent of 60 is 39.
Answer is: 65%
9. Madison needs $10 000.00 in 16 years at an interest rate of 3 %/a compounded monthly. How much should she invest?
Answers
SOLUTION:
Case: Compound interest
Method:
The formula is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]P =?
A= $10 000.00
n = 12
r = 3% or 0.03
t = 16 years
[tex]\begin{gathered} 10000=P(1+\frac{0.03}{12})^{12\times16} \\ 10000=P(1.0025)^{192} \\ 10000=P\times1.6151 \\ P=\frac{10000}{1.6151} \\ P=6191.54 \end{gathered}[/tex]Final answer: To the nearest cent
She should invest $6191.54
Find the length of the rectangle pictured above, if the perimeter is 82 units.
Answers
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
From the information given,
width = 16
Perimeter = 82
Thus, we have
82 = 2(length + 16)
By dividing both sides of the equation by 2, we have
82/2 = 2(length + 16)/2
2 cancels out on the right side of the equation. We have
41 = length + 16
length = 41 - 16
length = 25
After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests you start by jogging for 14 minutes each day. Each week after, he suggests that you increase your daily jogging time by 7 minutes. How many weeks before you are up to jogging 70 minutes?
Answers
Given that initial time for jogging is,
[tex]a_{_1}=14[/tex]After each week the time is increased by
[tex]d=7[/tex]This gives an arithmetic sequence.
To find n such that,
[tex]a_n=70[/tex]Therefore,
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ n=\frac{a_n-a_1}{d}+1 \end{gathered}[/tex]So,
[tex]\begin{gathered} n=\frac{70-14}{7}+1 \\ =\frac{56}{7}+1 \\ =8+1 \\ =9 \end{gathered}[/tex]Therefore, 9 weeks before you are up to jogging 70 minutes.
Divide. −3.52−2.2 What is the quotient
Answers
The quotient of - 3.32 / - 2.2 is 8 ÷5.
What is the quotient?Given fraction:
-3.32 / -2.2
First step is to re-write the given fraction which is - 3.52 / - 2.2
3.52 / 2.2
Second step is to convert the decimal to fraction
352 ÷ 100 / 22 ÷10
Third step is to reduce the fraction
reducing 352/100
=(2^5 × 11)/(2^2 × 5^2)
= [(2^5 × 11) ÷ 2^2] / [(2^2 × 5^2) ÷ 2^2]
= (2^3 × 11)/5²
= 88/25
Reducing 22/10
Divide the numerator and denominator by the greatest common divisor
= 22 ÷ 2 / 10 ÷ 2
= 11 /5
Now let determine or find the quotient
88 ÷ 25 × 11 ÷ 5
= 8 ÷ 5
Therefore we can conclude that 8 ÷ 5 is the quotient.
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See attachment for problem
Answers
The liters in the tank when it is filled to a height of 3.70 is 5,580 liters
The liters that needs to be added to 100% capacity is 480 liters
What is the volume?A right circular cone is a three dimensional object has a flat circular base that tapers to a vertex. The volume of a right circular cone is the amount of space in the right circular cone.
Volume of a cone = 1/3(πr²h)
Where:
π = pi = 3.14r = radius h = heightVolume of the right circular cone when its filled to a height of 3.70 = 1/3 x 3.14 x 3.70 x 1.20² = 5.58 m³
5.58 x 1000 = 5,580 liters
Volume of the right circular cone when it is full = 1/3 x 3.14 x 4 x 1.20² = 6.03 m³
6.03 x 1000 = 6030 liters
Liters that needs to be added to 100% capacity = 6030 liters - 5,580 liters = 480 liters
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a. During a basketball practice, Mai attempted 40 free throws and was successful on
25% of them. How many successful free throws did she make?
410
0
free throws
25%
Unit 3, Lesson 11
50%
75% 100% 125% 150%
Answers
Answer: 10
1/4 (25%) of 40 is 10, meaning Mai made 10 successful free throws.
. Math and Science During winter months, freshwater fish sense the water getting colder and swim to the bottoms of lakes and rivers to find warmer water. If a fish 7 swims of the depth of a 32-foot deep lake, how many feet down did the fish swim?[tex]51[/tex]
Answers
The total depth of the lake is:
[tex]32\text{ ft}[/tex]And we need to find how many feet are 7/8 of the depth.
To find how much is 7/8 out of 32 ft what we do is multiply 32 by 7/8:
[tex]32\times\frac{7}{8}[/tex]This multiplication can also be represented as follows:
[tex]\frac{32}{8}\times7[/tex]We start by solving the division:
[tex]4\times7[/tex]and finally, we solve the multiplication:
[tex]4\times7=28[/tex]-->the fish swam 28 ft.
Answer: 28 ft
37)You need at least 15 pencils or markers. You want to spend at most $14 onpencils and markers. Pencils p are $0.85 each and markers m are $1.45each. Which system of inequalities models the situation?A) p+m>150.85p+1.45m<14B) p+m>140.85p+1.45m>15C) p+m≥150.85p+1.45m≤14D) p+m≥140.85p+1.45m≤15
Answers
Given:
Minimum number of pencils or markers = 15
Maximum amount to spend on pencils and markers = $14
Cost of a pencil = $0.85
Cost of a marker = $1.45
Required: System of inequalities models the situation
Explanation:
Let p denote the number of pencil and m be the number of markers
Since the minimum number of pencils or markers is 15, it gives the inequality
[tex]p+m\geq15[/tex]Since the maximum amount to spend on pencils and markers is $14, it gives the inequality
[tex]0.85p+1.45m\leq14[/tex]Final Answer:
[tex]\begin{gathered} p+m\ge15 \\ 0.85p+1.45m\leqslant14 \end{gathered}[/tex]
all you need is in the photo please answer fast please helpppppp DON'T DO STEP BY STEP PUT ONLY THE ANSWER PLEASEEEEEEEEEEEEEEEEEEEEE
Answers
Notice that since the residuals are varying from -1 to 1 without a pattern, we have that the line is not a good fit for the data.
Also, some residuals (for 0, 2, 4 and 6) are relatively large compared to the actual data values.
If an item is discounted 30% then what percent of the original price is the sale price? if the organal price of the item is $500 what is the dollar amount of the discount?how much is the sale price ?
Answers
a.) Discount = 30%
Percent of the original price on sale = 100% - 30% = 70%
b.) Original price = $500
Discount = 30%
Dollar amount of the discount = $500 x (30% / 100%) = $500 x 0.30 = $150
c.) The sale price = $500 - (Discount Amount) = $500 - $150 = $350
Colin just travelled across Ontario on a road trip. He bought some skis in Blue Mountain for $879.95 plus tax, a boombox in Muskoka for $145.58 including taxes, a souvenir in Niagara Falls for $99.97 plus tax, and some maple syrup in Toronto for $45.14 including tax. Overall, how much HST did Colin pay on his trip? Answer should be rounded off to whole number.
Answers
The Harmonized Sales Tax that Colin paid on this trip was of $152.18.
What is the Harmonized Sales Tax?The Harmonized Sales Tax is a rate that a person pays over the values of their purchases.
In the context of this problem, the person traveled on Ontario, where the HST rate is of 13%.
The purchases of the person are given as follows:
Skis in Blue Mountain for $879.95.Boombox in Muskoka for $145.58.Souvenir in Niagara Falls for $99.97.Maple syrup in Toronto for $45.14.The total value of these purchases is given by:
Total value = 879.95 + 145.58 + 99.97 + 45.14 = $1,170.64.
The HST paid is 13% of this amount, hence it is calculated as follows:
HST = 0.13 x 1170.64 = $152.18.
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Which of the following statements is not true based on the given graph?abd0OlbicasbCO
Answers
The Solution.
From the given number line graph, we can see clearly that the following option are true.
[tex]undefined[/tex]The only option that is not true is
[tex]undefined[/tex]Function Notation - TransformationIll send a picture of the question
Answers
Given the vertices of the original quadilateral:
(3, 4), (5, 6), (7, 4), and (5, 3)
Vertices of the transformed quadilateral:
(-5, -6), (-3, -4), (-1, -6), and (-3, -7)
Let's describe the transformation rule used for this transformation.
To find the transformation rule, let's find the number of movements in the x-direction and y-direction that would map the original quadilateral to the transformed quadilateral by subtracting the x and y coordinates of the coresponding sides.
We have:
(x, y) ==> (-5 -3, -6 -4) ==> (-8, -10)
(x, y) ==> (-3 -5, -4, -6) ==> (-8, -10)
(x, y) ==> (-1 -7, -6 -4) ==> (-8, -10)
(x, y) ==> (-3 -5, -7 -3) ==> (-8, -10)
For all corresponding sides, we have: (x, y) ==> (-8, -10)
This means there was a shift 8 units to the left, and 10 units downwards.
Therefore, the rule for the transformation shown here is:
(x, y) ==> (x - 8, y - 10)
ANSWER:
B. f(x, y) = (x - 8, x- 10)
what is 1 5/8 + 2 1/3=
Answers
1 5/8 + 2 1/3
= 3 23/24
Explanation:1 5/8 + 2 1/3
= 1 + 2 + 5/8 + 1/3
= 3 + 23/24
= 3 23/24
Identify the coffecient of x in the expression below.-5x-4y^2
Answers
A coeffecient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression,
So in the given expression, the value "-5" is placed before x and hence is the coffecient of x .
Answer:
Step-by-step explanation:
3
-Jun 18 of
Find the domain and the range of the given relation.
{(6,8), (-3,4), (-1,-6), (-6, -1)}
Answers
Range: [-6, -1, 4, 8]
A right triangle is shown in the graph.
right triangle on coordinate plane with hypotenuse labeled t and one endpoint of hypotenuse at r comma s and the other endpoint at x comma y, vertical line from point x comma y and horizontal line from r comma s that meet at right angle of triangle, horizontal dotted line from point r comma s to point s on y axis, horizontal dotted line from point x comma y to point y on y axis, vertical dotted line from point r comma s to point r on x axis, and vertical dotted line from right angle to point x on x axis
Part A: Use the Pythagorean Theorem to derive the standard equation of the circle with center at (r, s) and a point on the circle at (x, y). Show all necessary math work. (3 points)
Part B: If (r, s) = (7, –4) and t = 10, determine the domain and range of the circle. (4 points)
Part C: Is the point (9, 1) inside the border of the circle if (r, s) = (7, –4) and t = 10? Explain using mathematical evidence. (3 points
Answers
Part a: The standard equation of circle: (x - r)² + (y - s)² = t².
Part b: Domain = {17, -3} and Range = {-14, 6}.
Part c: Point (9, 1) lies inside the circle.
What is termed as the Pythagorean Theorem?The Pythagorean theorem, or Pythagorean theorem, explains the relation between the three sides of such a right-angled triangle. The the hypotenuse's square is equal to the total of the squares of the remaining two sides of a triangle, according to Pythagoras' theorem.For the given question,
The right triangle are given with two of ts vertices as (r, s) and (x, y).
The distance between these two points is 't'.
Part a: The standard equation of the circle.
Centre of circle = (r,s) and
Point on the circle = (x, y)
Using Pythagorean Theorem,
(x - r)² + (y - s)² = t²
Thus, the standard equation of the circle is (x - r)² + (y - s)² = t²
Where, t is the radius of the circle.
Part b: Domain and range.
(r, s) = (7, –4) and t = 10,
For x values in the domain r ± t and y values in the range s ± t, the circle would be defined.
Domain = 7 ± 10 = {17, -3}
Range = -4 ± 10 = {-14, 6}
Part c: Point (9, 1) lies inside or not.
(r, s) = (7, –4) and t = 10
Point (9, 1) = (x, y)
Put the values;
(x - r)² + (y - s)² ≤ t²
(9 - 7)² + (1 + 4)² ≤ 10²
2² + 5² ≤ 10²
4 + 25 ≤ 100
29 ≤ 100
Thus, the points (9, 1) lies inside the circle.
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