Answer:
The value of y is 5 , and The value of x is - 5
Step-by-step explanation:
Given as :
The line passes through point ( - 2, 5)
The slope of line is m = [tex]\frac{2}{3}[/tex]
Equation of line is written as
y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex])
Since line passes through line ( - 2 , 5 ) and have slope [tex]\frac{2}{3}[/tex]
So, y - 5 = [tex]\frac{2}{3}[/tex] × (x + 2)
Or, 3 × ( y - 5 ) = 2 × ( x + 2 )
Or, 3 y - 15 = 2 x + 4
Or, 3 y - 2 x - 19 = 0 is the equation of line
Now points ( x , 3 ) lies on the line 3 y - 2 x - 19 = 0
So, 3 × 3 - 2 x - 19 = 0
or, 9 - 2 x - 19 = 0
or, 2 x = - 10
∴ x = - [tex]\frac{10}{2}[/tex]
I.e x = - 5
Again points ( - 2 , y ) lies on the line 3 y - 2 x - 19 = 0
So, 3 × y + 2 × 2 - 19 = 0
Or, 3 × y + 4 -19 = 0
or, 3 y = 15
∴ y = [tex]\frac{15}{3}[/tex]
I.e y = 5
Hence The value of y is 5 , and The value of x is - 5 . Answer
Mr. Thaxton has two daughters. The sum of their ages is twenty-one. The product of their ages is one hundred ten. How old is Mr. Thaxton's youngest daughter?
A.
9
B.
10
C.
11
D.
12
Answer:
B. 10
Step-by-step explanation:
x + y = 21
xy = 110
Rewrite first equation. x + y = 21 becomes y = -x + 21
Now substitute this new equation in the second equation.
x(-x+21) = 110
-x^2 + 21x - 110
Divide by -1
x^2 - 21x + 110
(x - 10)(x - 11)
x = 10, 11
10 is less, so the youngest daughter is 10
is x^2-(x-5)^2=9y linear
Answer:
yes
Step-by-step explanation:
please help with the question below!
Answer:
C
Step-by-step explanation:
If $500 is deducted for each 1,000 miles, and 10,000 miles are being driven per year, that is -$5,000 each year. Therefore your equation would be $23,000-$5,000y.
What is equivalent to 5/9
Answer:
10/18
Step-by-step explanation:
U only asked for what is equivalent
Answer:
10/18, 15/27, 20/36, 25/45, 30/54, 35/63, 40/72, 45/81, 50/90, 55/99, 60/108.
Step-by-step explanation:
if m=5 and n=3, find the value of mn.
Answer:15
Step-by-step explanation:you multiply m=5 to n=3 so what is 5 times 3? so 5 times 3 = 15
Final answer:
When m=5 and n=3, the value of mn is found by multiplying the two numbers, resulting in mn=15.
Explanation:
To find the value of mn when m=5 and n=3, you simply need to multiply the two numbers together:
1. multiply m and n-
mn = m × n
2. m= 5 and n= 3, so the expression will be as follows-
mn = 5 × 3
3. Multiplying 5 and 3, the following is obtained-
mn = 15
Therefore, the value of mn is 15.
Can someone list the amount of numbers that have a GCF of 7 and a product of 490?
Answer:
The amount of numbers that have a G C F of 7 and a product of 490 is 2.
Step-by-step explanation:
On Prime Factorization 490 = 2 x 5 x 7 x 7
G CF = Greatest Common Factor
So, here the possible number who have products as 490 and G C F as 7 is
(a) 2 x 7 = 14 and 5 x 7 = 35
As, 14 and 35 on multiplication,gives 490 as a product.
And, G C F of 14 and 3 5 is also 7.
(b) 7 and 5 x 7 x 2 = 70
As, 7 and 70 on multiplication,gives 490 as a product.
And, G C F of 7 and 70 is also 7.
⇒ (14, 35) and (7,70) are the only such pairs.
Hence, the amount of numbers that have a G C F of 7 and a product of 490 is 2.
Final answer:
The question seeks the number of number pairs with a GCF of 7 and a product of 490. There are only two pairs that meet the criteria: (7, 70) and (10, 49). Each pair multiplies to 490 and has a GCF of 7.
Explanation:
The question asks for the number of pairs of numbers that have a Greatest Common Factor (GCF) of 7 and a product of 490. First, we must note that any pair of numbers with a GCF of 7 must be multiples of 7. So, we divide 490 by 7 to find another factor that is also a multiple of 7, which gives us 70. Now, we have two pairs of numbers that satisfy the condition: (7, 70) and (10, 49) because each pair when multiplied gives 490, and the GCF of each pair is 7. It's important to note that 490 is equal to 7^2 times 10, which means we won't find more than these two pairs without repeating the same factors in a different order.
Write the equation of the line in slope intercept form that contains the point (-2,-1) and is perpendicular to the graph of y=-2x-3
The required equation of line is:
[tex]y = \frac{1}{2}x[/tex]
Step-by-step explanation:
Given equation of line is:
y=-2x-3
The coefficient of x is the slope of line as the equation is in slope intercept form
Let m1 be the slope of given graph of line
So,
[tex]m_1=-2[/tex]
The product of slopes of perpendicular lines is -1
Let m2 be the slope of required line
Then
[tex]m_1.m_2 = -1\\-2 . m_2 = -1\\m_2 = \frac{-1}{-2}\\m_2 = \frac{1}{2}[/tex]
the slope-intercept form of line is:
[tex]y=m_2x+b[/tex]
Putting the value of slope
[tex]y=\frac{1}{2}x+b[/tex]
To find the value of b, putting the given point (-2,-1) in equation
[tex]-1=\frac{1}{2}(-2)+b\\-1 = -1 +b\\-1+1 = b\\b = 0[/tex]
Hence,
The required equation of line is:
[tex]y = \frac{1}{2}x[/tex]
Keywords: Equation of line, slope-intercept form
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Two lines a and b are intersected by a transversal c prove that a//b, if
NEED IN 15 min am giving ABOUT 50 POINTS
ANY CHEATIN ANSWERS R BANNED!!
Pls help
Answer:
Because Alternate Interior angles are equal.
Step-by-step explanation:
STEP - I:
[tex]$ m \angle {5} = 3 . m \angle {\{3}\} $[/tex]
Reason:
This is the given data.
STEP - II:
It has multiplied and the reason is mentioned as well.
STEP - III:
[tex]$ m \angle{3} + m \angle{5} $[/tex] = 45° + 135° = 180°
Reason:
It has substituted the value of [tex]$ m\angle{5} $[/tex] from the previous step. The sum of [tex]$ m\angle{3} $[/tex] and [tex]$ m \angle{5} $[/tex] is 180°.
STEP - IV:
[tex]$ a \parallel b $[/tex]
Reason:
We calculated [tex]$ m\angle{5}[/tex] to be 135°.
Note that [tex]$ \angle {5} $[/tex] and [tex]$ \angle{6} $[/tex] are on the same line. That means their sum should be 180°.
i.e., [tex]$ m\angle{5} + m\angle{6} $[/tex] = 180°.
[tex]$ \implies $[/tex] 135° + [tex]$ m\angle{6} $[/tex] = 180°.
[tex]$ \implies m\angle{6} = $[/tex] 45°.
One of the ways to prove [tex]$ a \parallel b $[/tex] is to check if alternate interior angles are equal.
Here, [tex]$ m\angle{3} $[/tex] and [tex]$ m \angle {6} $[/tex] are alternate interior angles and they are equal.
[tex]$ \implies a \parallel b $[/tex].
2 Points
Which of the items below is not an example of a fixed cost?
O
A. Packaging costs
O
B. Internet access fee
O
C. Monthly rent
O
D. Weekly fixed electricity costs
STI
Answer:
A. packaging costs
Step-by-step explanation:
Packaging costs woupd change based on how many products are being shipped. The other payments are fixed because they are the same amount paid regularly. Packaging would be considered a variable cost.
Internet access fee is not an example of a fixed cost.
What is Fixed Cost?The fixed cost definition states that businesses incur a cost that does not change positively or negatively with the number of goods sold or services given.
A fixed cost is a cost that remains constant regardless of production or sales volume.
Examples of fixed costs include monthly rent, packaging costs, and weekly fixed electricity costs.
Internet access fee is not an example of a fixed cost since it fluctuates based on usage.
The cost of internet access fee will increase or decrease depending on the amount of data used or the duration of usage.
Hence, Internet access fee is not an example of a fixed cost.
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Based on Rudy’s baseball statistics,the probability that he will pitch a curveball is 1/4.if rudy throws 20 pitches,how many pitxhes most likely will be curveballs?
Answer:
5
Step-by-step explanation:
Expected value = probability × number of trials
X = 1/4 × 20
X = 5
I need a word problem of 5 * 8 equals 40
Word problem - Jose played soccer for 5 hours every afternoon for 8 days. How many hours did Jose play soccer in all?
So this problem is about Jose and the amount of time he spends playing soccer.
Next, let's pick out what we know and what we want to find out.
We know that Jose played soccer for 5 hours every afternoon for 8 days. We want to find out how many hours of soccer he played in all so we need to multiply.
We multiply the amount of time he spent playing soccer each afternoon which is 5 hours by the number of days which is 8 days.
(8) (5) = 40
This means that Jose played 40 hours of soccer in all.
I bought three shirts that had equivalent retail values I use 15 gift certificate at the time of purchase and paid a total of 81 how much did each in dividual shirt cost
Answer:
Each shirt costed $27
each
Step-by-step explanation:
HOPE IT HELPS!!! please mark brainliest :)
if 2cm represents 9m on a scale drawing how many meters do 15 cm represent
Lobsters Each year, 183 million pounds of lobster are caught in
the United States and Canada. Twenty-five percent of this amount is
sold live. (Source: Lobster Institute at the University of Maine) How
many pounds of lobster are sold live each year in the United States and
Canada?
Firen
Source:
Answer:
The quantity of lobster which are sold live each year in the United States and Canada are 46 million pounds (approximately).
Step-by-step explanation:
Given:
Each year, 183 million pounds of lobster are caught in the United States and Canada. Twenty-five percent of this amount is sold live.
Now, to find how many pounds of lobster are sold live each year in the United States and Canada.
According to question:
25% of 183 million pounds.
[tex]\frac{25}{100}\times 183[/tex]
[tex]=0.25\times 183[/tex]
[tex]=45.75[/tex]
Each year 45.75 million pounds of lobster are sold live in the United States and Canada.
Therefore, the quantity of lobster which are sold live each year in the United States and Canada are 46 million pounds (approximately).
How many significant figures does 120 have
Answer:
two significant figures
Step-by-step explanation:
What is the value of X?
Answer:
a) x=4 b) x=17.5
Step-by-step explanation:
a)5x/2+1=11 b)2x/7-3=2
5x/2=11-1 2x/7=2+3
5x/2= 10 2x/7=5
5x= 10x2 2x=35
5x=20 x=35/2
x=20/5 x=17.5
x=4
Answer:
a) x = 4b) x = 17.5Step-by-step explanation:
[tex]a)\\\\\dfrac{5x}{2}+1=11\qquad\text{subtract 1 from both sides}\\\\\dfrac{5x}{2}+1-1=11-1\\\\\dfrac{5x}{2}=10\qquad\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup^1\cdot\dfrac{5x}{2\!\!\!\!\diagup_1}=(2)(10)\\\\5x=20\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{20}{5}\\\\\large\boxed{\boxed{x=4}}[/tex]
[tex]b)\\\\\dfrac{2x}{7}-3=2\qquad\text{add 3 to both sides}\\\\\dfrac{2x}{7}-3+3=2+3\\\\\dfrac{2x}{7}=5\\\\\dfrac{2x}{7}=\dfrac{5}{1}\qquad\text{cross multiply}\\\\(2x)(1)=(7)(5)\\\\2x=35\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{35}{2}\\\\\large\boxed{\boxed{x=17.5}}[/tex]
A woman bought some large frames for $10 each and some small frames for five dollars each add a closeout sale if she bought 17 frames for $100 find how many of each type she bought
Answer:
She bought 3 large frames and 14 small frames
Charlie’s pizza charges $12 for a medium cheese pizza plus $2 for each additional topping. The cost of a medium pizza, y, with x toppings is represented by this equation:
y = 12 + 2x
Which graph represents this equation?
Answer:
Graph A is the correct answer.
explanation of the answer:
the line starts between 10 and 15 and continues to increase to the top of the graph.
The equation y = 12 + 2x represents the cost of a pizza given the number of additional toppings. The corresponding graph would be a straight line which starts at $12 on the y-axis (no toppings) and goes up by $2 on the y-axis for each increment of 1 on the x-axis (each additional topping).
Explanation:The equation given in the problem, y = 12 + 2x, is a linear equation that represents the cost of a pizza with an increasing number of toppings.
In this equation, 'x' represents the number of additional toppings and 'y' represents the total cost of the pizza. The graph representing this equation would be a straight line that starts at $12 on the y-axis (representing the cost of a medium
pizza without any additional toppings).
Then, for each increment of 1 on the x-axis (representing adding one topping), the line goes up by $2 on the y-axis (representing the additional cost).
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Solve x in the equation x12=17.
the solution for ( x ) in the equation [tex]\( x^{12} = 17 \)[/tex] is approximately [tex]\( x \approx 1.170092 \).[/tex]
To solve ( x ) in the equation [tex]\( x^{12} = 17 \),[/tex] follow these steps:
1. Take the 12th root of both sides.
2. Simplify the expression.
Step 1: Take the 12th root of both sides:
[tex]\[ x^{12} = 17 \][/tex]
[tex]\[ x = \sqrt[12]{17} \][/tex]
Step 2: Simplify the expression:
To find the 12th root of 17, you can use a calculator or approximation methods.
[tex]\[ x \approx \sqrt[12]{17} \][/tex]
Using a calculator or approximation methods, we find:
[tex]\[ x \approx 1.170092 \][/tex]
So, the solution for ( x ) in the equation [tex]\( x^{12} = 17 \)[/tex] is approximately [tex]\( x \approx 1.170092 \).[/tex]
Use sigma notation to represent the sum of the first six terms of the following sequence: −10, −13, −16, …
Sigma notation of sequence −10, −13, −16, … is [tex]\sum_{n=1}^{6}-(3 n+7)[/tex]
Solution:Need to determine the sigma notation for the following sequence
−10, −13, −16, …
Let's try to build a generic formula for given sequence
The given sequence is in Arithmetic progression where first term = -10 and common difference = -3
The formula for arithmetic progression is given as:
[tex]a_n = a_1 + (n - 1)d[/tex]
Where,
[tex]a_n[/tex] is the nth term in the sequence
[tex]a_1[/tex] is the first term in the sequence
d is the common difference between the terms
Here in this sequence [tex]a_1[/tex] = -10 and d = -3
[tex]a_n = -10 + (n - 1)(-3)\\\\a_n = -10 - 3n + 3\\\\a_n = -3n - 7[/tex]
So generic formula for a term is – ( 3n + 7 )
[tex]\begin{array}{l}{\text { For } \mathrm{n}=1, \text { term is }-(3 \times 1+7)=-10} \\\\ {\text { For } \mathrm{n}=2, \text { term is }-(3 \times 2+7)=-13} \\\\ {\text { For } \mathrm{n}=3, \text { term is }-(3 \times 3+7)=-16}\end{array}[/tex]
And so on
Using sigma notation for arithmetic sequence:
[tex]\sum_{k=1}^{n} a_{k}[/tex]
So for first six terms value of n will vary from 1 to 6 and in sigma notation it can be represented as
[tex]\sum_{n=1}^{6}-(3 n+7)[/tex]
© MP.1 Make Sense and Persevere
Meghan's vegetable garden is pictured
below. What is its area?
Answer: Need help with this too
Step-by-step explanation:
help me out
Give the correct answer
1+2=21
2+3=36
3+4=43
4+5=?
1 + 2 = 21 (reversing numbers)
2 + 3 = 32 (reversing numbers) + 4 = 36
3 + 4 = 43 (reversing numbers)
4 + 5 = 54 (reversing numbers) + 4 =58
Answer:
58Step-by-step explanation:
This is a sequence using reversed numbers, and alternating a summing fixed amount.
In the first one you can see that it's only numbers being reversed.
The second one is also reversing numbers but adding 4 units, 32+4=36.
The third one has the same pattern in the first one, just numbers being reversed.
The fourth has the same pattern than the second one, reversed numbers and add 4 units. So, it would be 54+4=58.
Therefore, the answer is 58.
if fh is an angle bisector of triangle efg with
Answer:
Step-by-step explanation:
Simplify √5−√125+√25. Identify your result as rational or irrational.
Please list steps!
A store sells rope by the meter. The equation p=0.8L represents the price p(in dollars) of a piece of nylon rope that is L meters long.
A. How much does the nylon cost per meter?
B. How long is a piece of nylon rope that costs $1.00?
The cost of the nylon rope is $0.8 per meter. For $1, you can purchase 1.25 meters of nylon rope.
Explanation:The given equation is p=0.8L. Here, 'p' stands for the price in dollars and 'L' is the length of the nylon rope in meters.
A. To determine the cost per meter, we look at the coefficient in front of 'L' in our equation. Here, it is 0.8, signifying that the nylon rope costs $0.8 per meter.
B. To find out the length of rope that could be bought for $1, we use the equation by setting 'p' equal to 1 and solving for 'L'. Doing this gives us 'L' = 1 / 0.8 which equals to 1.25 meters.
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A pair of shoes at Nordstrom‘s costs $120. The shoes are on sale for 15% off. You have a coupon that allows you to take an additional 10% off. How much will the shoes cost?
0 = -6t + 6t How many solutions does this equation have?
Answer:
there is an infinite amount of solutions
Step-by-step explanation:
negative 6t and positive 6t cancel each other out
plug in any number for t, and you will always get 0
a direct variation function contains the points
30 POINTS!!!! HELP ME ASAP!!!!!
Answer:
18
Step-by-step explanation:
I'm 90% sure I'm right but I could be wrong
4 × 18 = 72
6 × 18 = 108
72 + 108 = 180 degrees
Which means the opposite angle diagonal from 6x would also equal 108 degrees
Same thing for 4x, 72 degrees
72° + 72 ° + 108° + 108° = 360 degrees
The graph models function R. The table of values models function S. Which statement is true about these functions?
A) The two functions have the same rate of change.
B) Both functions do not have a constant rate of change.
C) Function R has a greater rate of change than Function S.
D) Function S has a greater rate of change than Function R.
Answer: OPTION D.
Step-by-step explanation:
The rate of change of a linear function is also known as "Slope".
The slope can be calculated with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Choose two points on the function "R" graphed:
[tex](1,0)\\(0,-3)[/tex]
You can say that:
[tex]y_2=-3\\y_1=0\\\\x_2=0\\x_1=1[/tex]
Substituting values into the formula, you get:
[tex]m=\frac{-3-0}{0-1}=3[/tex]
Choose two point from the table that models the function "S":
[tex](4,21)\\(6,31)[/tex]
You can say that:
[tex]y_2=31\\y_1=21\\\\x_2=6\\x_1=4[/tex]
Substituting values into the formula, you get:
[tex]m=\frac{31-21}{6-4}=5[/tex]
Therefore, you can conclude that the function "S" has a greater rate of change than Function "R".
Answer:
D: Function S has a greater rate of change than Function R.
Step-by-step explanation:
Function S has a greater rate of change than Function R.
Function R → m =
rise
run
=
6
2
= 3. Function S → m =
change in y
change in x
=
31 − 21
6 − 4
=
10
2
= 5
Since 5 > 3, function S has a greater rate of change.