A relation is plotted as a linear function on the coordinate plane starting at point A (0, 3) and ending
at point B (2, 7)
What is the rate of change for the linear function and what is its initial value?
Answer:
initial value=2
Step-by-step explanation:
equation of line,
y-[tex]y_1[/tex]=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex][tex](x-x_1)[/tex]..............(1)
put co ordinate (0,3) and (2,7) in the equation (1)
y-3=[tex]\frac{7-3}{2-0}[/tex](x-0)
y-3=2x
y=2x+3
rate of change of linear equation=[tex]\frac{\partial (2x+3)}{\partial x}[/tex]
[tex]\frac{\partial y}{\partial x}[/tex]=2
hence, initial value=2 answer
Demuestra que al utizar agrupaciones de terminos para factorizar el polinomio 6a2,+15a-4a-10 la respuesta es( 2a+5)(3a-2)
Answer:
Step-by-step explanation:
Linda owns 4 shares of a certain stock. Yesterday the total value of her shares went down by 32 dollars. What was the change in value for each share?
Answer:
The value of each share decreased by $8.
Step-by-step explanation:
Number of shares of a certain stock Linda owned = 4
Total value of shares went down by = $32
So find the change in value of each share.
Solution:
Let the total value of each share in dollars be = [tex]x[/tex]
Value of 4 shares in dollars will be = [tex]4x[/tex]
The total value of shares went down by $32
So, new value of 4 shares = [tex]4x-32[/tex]
New value of each share = [tex]\frac{New\ value\ of\ total\ shares}{4}[/tex]
⇒ [tex]\frac{4x-32}{4}[/tex]
Splitting the denominators.
⇒ [tex]\frac{4x{{4}-\frac{32}}{4}[/tex]
⇒ [tex]x-8[/tex]
Original value of each share in dollars was = [tex]x[/tex]
New value of each share in dollars = [tex]x-8[/tex]
Thus, we can see that the value of each share decreased by $8.
1. Using n, n+1, and n+2 to represent three consecutive integers, write the statement of multiplying three consecutive integers and then adding the middle integer to the result of the multiplication as an expression.
2. Simplify the expression from problem 1 and write the answer in standard form.
3. Show that the answer from problem 2 is equivalent to the cube of the middle integer.
Answer:
1) Expression is
[tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]
2) The standard form of the expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
3) The expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
Where [tex](n+1)^3[/tex] is the cube of the middle integer
Step-by-step explanation:
1) Given three consecutive integers are n. n+1, and n+2
Now multiplying the three consecutive integers
[tex](n)(n+1)(n+2)=(n^2+n)(n+2)[/tex]
[tex]=n^3+2n^2+n^2+2n[/tex]
[tex]=n^3+3n^2+2n[/tex]
Therefore [tex](n)(n+1)(n+2)=n^3+3n^2+2n[/tex]
Now adding the middle integer to the result of the multiplication.
ie, adding (n+1) to the result of the multiplication [tex]n^3+3n^2+2n[/tex]
[tex](n+1)+(n^3+3n^2+2n)=n+1+n^3+3n^2+2n[/tex]
[tex]=3n+1+n^3+3n^2[/tex]
Therefore [tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]
2) Expression is [tex]n^3+3n^2+3n+1[/tex]
Now we simplify the above expression
[tex]n^3+3n^2+3n+1=n^3+3n^2(1)+3(n)(1)^2+1^3[/tex]
[tex]=(n+1)^3[/tex] (by using [tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex] , Here a = n and b=1)
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
3) The expression is
[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]
Where [tex](n+1)^3[/tex] is the cube of the middle integer.
ie, expression is equivalent to the cube of the middle integer
How many 3/4 cup servings are in 12 cups of cherries?
Answer:
16 serving.
Step-by-step explanation:
Given: 3/4 cup servings.
Now, computing the number of serving in 12 cups of cherries.
Using unitary method to solve.
∴ Number of serving= [tex]total\ cups \times number\ of\ serving\ per\ cup[/tex]
Number of serving in one cup is [tex]\frac{4}{3}[/tex]
Number of serving in 12 cups = [tex]12\times \frac{4}{3} = 16 \ serving[/tex]
Number of serving in 12 cups= [tex]16\ serving[/tex]
∴ There are 16 serving is possible in 12 cups of cherries.
Final answer:
To calculate the number of 3/4 cup servings in 12 cups of cherries, divide 12 by 3/4, which equals 16 servings.
Explanation:
To determine how many 3/4 cup servings are in 12 cups of cherries, we can divide the total number of cups by the size of one serving.
First, we express the serving size and the total amount in the same units: 3/4 cup and 12 cups.
Next, we divide the total amount of cherries by the serving size: 12 cups ÷ 3/4 cup.
To perform the division, we can multiply 12 by the reciprocal of 3/4, which is 4/3 (12 × 4/3 = 16).
The result is that there are 16 servings of 3/4 cup in 12 cups of cherries.
What expression will Help me find 4% of 25
Solve
2w+2(w+3.8)=58
Answer:
w=12.6
Step-by-step explanation:
2w+2(w+3.8)=58
2w+2w+7.6=58
4w+7.6=58
4w=58-7.6
4w=50.4
w=50.4/4
w=12.6
Robert has seven more than five times the number of video games that Samuel has. The total number of video games that Robert and Samuel have is 25. How many video games does Robert have?
Answer: Robert has 22 video games.
Step-by-step explanation:
Let be "r" the number of video games that Robert has and "s" the the number of video games that Samuel has.
Set up a system of equations:
[tex]\left \{ {{r=5s+7} \atop {r+s=25}} \right.[/tex]
You can use the substitution method to solve the system:
- You need to substitute the first equation into the second equation and solve for "s":
[tex](5s+7)+s=25\\\\6s=25-7\\\\s=\frac{18}{6}\\\\s=3[/tex]
- Finally you must substitute the value of "s" into the first equation and evaluate:
[tex]r=5(3)+7\\\\r=22[/tex]
Answer:3
Step-by-step explanation:
5x+7=25
So lets subtract 7 from 25 to get 5x alone...
5x=18
5x/5=x
18/5=3.3
You cant have 0.3 of a video game so the answer is 3
if g(x) = 2x - 5 and h(x) = 3x + 7, then g(h(x)) = ?
Answer:
Step-by-step explanation:
g(h(x))=g(3x + 7). Since h(x)=3x + 7
g(h(x))= 2(3x + 7) - 5
g(h(x))= 6x + 14 -5
=6x +9
Which number line best shows how to solve −8 − (−6)?
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 6.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 6. Another arrow points from negative 6 to negative 8.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 6. Another arrow points from negative 6 to 2.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
Answer:
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
Step-by-step explanation:
find the number line best shows how to solve −8 − (−6)
In the number line first we start with -8 . negative and negative becomes positive
from -8 move 6 units to the right. So it ends at -2
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
Choose the point-slope form of the line passing through (3,5) with a slope of -3.
O y -3'= -3 (ix – 5)
0 -3(y – 5) = x - 3
y - 5 = -3 (0 - 3)
O 3x - 5y = -3
O
Answer:
answer is y-5=-3(x-3)
Step-by-step explanation:
your y-coordinate is 5 s you would write y-5 and your slope is -3 with your x-coordinate as 3 so that would be written as -3(x-3). The equation put together correctly would be y-5=-3(x-3)
Answer:
y-5=-3(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-3(x-3)
what is an equation in point-slope form of the line that passes through the given point and with the given slope m (-5,1);m=4
Equation for line: y=mx+b where m is the slope and b is the y-intercept
We have the slope. We just need to find the y-intercept. Plug in the point and the slope and solve for b.
y=mx+b
1=4(-5)+b
b=21
Answer: y=4x+21
Which of the following are solutions to 2x2 – 8x - 90? Select all that apply.
Answer:
x=-5, x=9
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]2x^{2} -8x-90[/tex]
equate to zero
[tex]2x^{2} -8x-90=0[/tex]
so
[tex]2=-1\\b=-8\\c=-90[/tex]
substitute in the formula
[tex]x=\frac{-(-8)\pm\sqrt{-8^{2}-4(2)(-90)}} {2(2)}[/tex]
[tex]x=\frac{8\pm\sqrt{784}} {4}[/tex]
[tex]x=\frac{8\pm28} {4}[/tex]
[tex]x=\frac{8+28} {4}=9[/tex]
[tex]x=\frac{8-28} {4}=-5[/tex]
therefore
The solutions are x=-5, x=9
HELP PLEASE!
Compare the function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformations of the given function?
Y= |6x-2|-7
A.)(1/3,7);x=1/3; translated to the right 1/3 unit and up 7 units
B.) (1/3,7);x=1/3; translated to the left 1/3 unit and down 7 units
C.) (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units
D.) (1/3,-7);x=1/3; translated to the left 1/3 unit and up 7 units
Answer:
C. (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.
Step-by-step explanation:
The function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
The parent function is:
g(x) = IxI
And we have:
f(x) = I6x - 2I - 7
Rearranging the function:
f(x) = 6Ix - 1/3I - 7
Then, now let's define some transformations:
If we start with g(x), a translation of N units to the right is:
f(x) = g(x - N)
if we start with g(x), a translation of N units up is:
f(x) = g(x) + N
A translation down would be:
f(x) = g(x) - N
And a vertical dilation of scale factor A is written as:
f(x) = A × g(x)
Then in this case we have:
A translation to the right of 1/3 units.
A dilation of scale factor 6.
A translation down of 7 units.
And the axis of symmetry will be when the absolute value part is equal to zero, or when
6Ix - 1/3I = 0
And that is when x = 1/3.
Therefore, the function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.
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the rate of watering is Rs. 4 per ll.
6) Find the area of the cardboard required to make a closed box of length
25cm, 5m and height 15cm.
dim deep is to be made. It is open at the
Answer:
The area of cardboard required is 40750 cm².
Step-by-step explanation:
Given:
Length (L) = 25 cm
Width (W) = 5 m = 5 × 100 = 500 cm
Height (H) = 15 cm
Area of the cardboard is same as the total surface area of the closed rectangular box.
Total surface area of the rectangular box is given as:
[tex]SA=2(LW+WH+LH)\\\\SA=2(25\times 500+500\times 15+15\times 25)\\\\SA=2(12500+7500+375)\\\\SA=2\times 20375=40750\ cm^2[/tex]
So, the area of cardboard required is 40750 cm².
PLEASE HELP! 20 POINTS!
What is the apparent solution to the system of equations? y=1/2x+2y=2x−1 Graph the system of equations using the Line tool. Plot a point at the apparent solution to the system using the Point tool.
Answer:
y=x/2−1/2
Step-by-step explanation:
The base of a triangle is 10 cm greater than the height. The area is 28 cm2. Find the height and the
base.
What is the slope of the line shown below?
Answer:
B
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 8) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line
m = [tex]\frac{-4-8}{2+1}[/tex] = [tex]\frac{-12}{3}[/tex] = - 4 → B
Answer:
The slope of the given line is -4.
So, option (B) is correct.
Step-by-step explanation:
We know that, slope (m) of a line passing through points (x₁, y₁) and (x₂, y₂) is given by,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Now, the given line passes through the point (-1, 8) and (2,-4).
So, (x₁, y₁) = (-1, 8) and (x₂, y₂) = (2, -4)
So, by using the above formula, we get
Slope(m) of the given line passing through (-1, 8) and (2, -4) is given by,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-4-8}{2-(-1)}[/tex]
[tex]\implies\;m = \frac{-12}{3}=-4[/tex]
∴The slope of the given line is -4.
Hence, option (B) is correct.
Is (-5,2), (5,2), (0,-3), (3,-8), (-7,4), (-1,-1) a function
Each point listed is of the form (x,y). The x coordinate is always listed first. We dont have any repeat x values, so this is enough to conclude we have a function.
If you wanted to, you could graph each point given on the same coordinate grid. Note how none of the points stack on top of each other. Or put another way, note how it is impossible to draw a single straight line through more than one point graphed. This graph passes the vertical line test.
A function is where plugging in any x value leads to exactly one y value.
If you had two points like (5,2) and (5,7) then the input x = 5 leads to more than one output y = 2 and y = 7 at the same time, making this example not a function.
Coordinates of centroid of a triangle with vertices of (0,1) (2,6) (7,2)
Answer:
The centroid is located at (3,3)
Step-by-step explanation:
Centroid Of A Triangle
The centroid of a triangle is the point where its three medians intersect. It is also the center of gravity of the triangle. The medians are lines that go from each vertex to the midpoint of the opposite side.
Given A(ax,by), B(bx,by), C(cx,cy) the points of the vertices, then the coordinates of the centroid [tex]P(x_c,y_c)[/tex] are
[tex]\displaystyle x_c=\frac{ax+bx+cx}{3}[/tex]
[tex]\displaystyle y_c=\frac{ay+by+cy}{3}[/tex]
The vertices are (0,1) (2,6) (7,2), thus
[tex]\displaystyle x_c=\frac{0+2+7}{3}=3[/tex]
[tex]\displaystyle y_c=\frac{1+6+2}{3}=3[/tex]
The centroid is located at (3,3)
The coordinates of centroid are (3,3)
Step-by-step explanation:
The coordinates of centroid of a triangle are calculated by finding average of x-coordinates of vertices and the average of y-coordinates of vertices.
Given vertices are:
(0,1) (2,6) (7,2)
So,
x-coordinate of centroid:
[tex]x = \frac{0+2+7}{3}\\=\frac{9}{3}\\= 3[/tex]
y-coordinate of centroid:
[tex]y = \frac{1+6+2}{3}\\=\frac{9}{3}\\= 3[/tex]
Hence,
The coordinates of centroid are (3,3)
Keywords: Triangle, centroid
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solve the inequality for x: -3(2x+5) < -45
Answer:
x>5
Step-by-step explanation:
-3(2x+5)<-45
2x+5<-45/-3
2x+5<15
2x<15-5
2x<10
x<10/2
x<5
x>5
Higher Order Thinking A mother
manatee, pictured to the right, is three
times as long as her baby manatee.
a. How long is her baby manatee? Write
and solve an equation.
b. If a blue whale is 9 times as long as the
manatee shown, how much longer is
a blue whale than the manatee? Write
and solve equations.
12 feet
The equation for baby manatee is 3x = 12 and length is 4 feet and length of blue whale is 108 feet.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have given:
Length of Mother manatee = 12 feet.
Let's suppose the length of a baby manatee is 'x'.
So the equation can be framed as:
3x = 12
x = 4 feet
The length of blue whale is = 9(length of mother manatee)
The length of blue whale is = 9(12) = 108 feet
Thus, the equation for baby manatee is 3x = 12 and length is 4 feet and length of blue whale is 108 feet.
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Graph the inequality.
Match the graph to the correct inequality below.
(attatched)
x > 5
x < 5
x ≥ 5
x ≤ 5
Answer:
x<=5
Step-by-step explanation:
Two things
direction its pointing is always how the sign will look likeif the circle is shaded it will have an "or equals to" sign; if its blank, there is only the "greater/lesser" sign80 Point Offer, Help is required on these questions. Highest offer I've given.
Answer:
Answer 1.) f(x)=0x-4
Answer 2.) f(x)=2/3x+4
Answer 3.) i don't really get this one so sorry
Answer 4.) f(x)= -1/5x+2
hope this helped it took me a while to figure out this but looks like the guy ahead of me beat me to it
Step-by-step explanation:
BRAINLIEST!!
Find the probability that a point chosen at random lies in the shaded region.
Answer:
0.60
Step-by-step explanation:
Again, we have a 10x10 space, which means there are 100 squares.
In this case, there are 60 shaded squares. This gives the probability of [tex]\frac{60}{100}[/tex] which simplifies to 0.60
Answer:
0.60
Step-by-step explanation:
Because there are 100 squares and 60 out of it is shaded if you chose a random point amongst these 100 square the probability of choosing a shaded one is 60/100 which is equal to 0.60.
Rewrite the equation by completing the square. x^2-20x+100 = 0
By completing the square, the equation x²- 20x + 100 = 0, we get, (x-10)²=0
Here, we have,
To rewrite the equation x² - 20x + 100 = 0 by completing the square, we can follow these steps:
Step 1: Move the constant term to the right side of the equation:
x² - 20x = -100.
Step 2: Take half of the coefficient of the x-term (-20/2 = -10) and square it to get (-10)² = 100.
Step 3: Add the result from step 2 to both sides of the equation:
x² - 20x + 100 = -100 + 100.
Simplifying:
x² - 20x + 100 = 0.
Step 4: Factor the left side of the equation. In this case, the left side is a perfect square trinomial:
(x - 10)² = 0.
Therefore, by completing the square, the equation x²- 20x + 100 = 0,
we get, (x-10)²=0
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Final answer:
The equation [tex]x^2 - 20x + 100 = 0[/tex] is already a perfect square and does not need to be completed. However, completing the square involves moving the constant to the other side, squaring half the coefficient of x, and solving for x, which leads us back to the original equation [tex](x - 10)^2 = 0[/tex] and reveals that x = 10.
Explanation:
The equation given is [tex]x^2 - 20x + 100 = 0[/tex]. This equation appears to already be a perfect square, as the constant term (100) is the square of half the coefficient of the x term (which is 10), thus completing the square is actually not needed. However, to illustrate the method of completing the square, let's ignore for a moment that it's already a perfect square and proceed with the steps:
Move the constant term to the right side of the equation: [tex]x^2 - 20x = -100.[/tex]Take half of the coefficient of x, which is -10, and square it, giving us 100.Add this square (100) to both sides of the equation, which yields [tex]x^2 - 20x + 100 = 0[/tex], the same as we started with.Now the left side is a square of (x-10): [tex](x - 10)^2[/tex] = 0.To solve for x, take the square root of both sides, giving us x - 10 = 0, which simplifies to x = 10.We've found that x = 10 is the solution to the equation, which is the same result you would get by recognizing the equation was already a perfect square in its original form.
find the area of the shape shown below
Answer:
6
Step-by-step explanation:
all you have to do is split the shape in half to create a square and a triangle then for the triangle the equation would be 2*2=4 then divide by 2 witch is 2 the do the square witch is 2*2=4 then you add 4+2=6 and i'm only in 7th grade.
Plz help me with my math
If the area is 10 square meters than double that is area of a rectangle with height = 5m and base of 4m because height • base should produce 20m^2.
Hope this helps.
Answer: base length = 4 metres
Step-by-step explanation:
A = ½bh
10m² = ½ * b * 5m
10 = 5b/2
Cross multiply
20 = 5b
b = 4m
you want to buy a new phone. The sales prise is $149.The sign says that this is $35 less than the original cost. What is the original cost of the phone?
Answer:
$114
Step-by-step explanation:
Sales price = Original Cost - $35
Sales price - $35 = Original Cost
Substitute in known values
$149 - $35 = Original Cost
$114 = Original Cost
Hope this helps :)
Does anyone know how you work out this bearings question???
The bearing of A from B according to the diagram is 82.86°
Using trigonometric relations ;
Tan B = opposite/ AdjacentB = bearing of A from B
Now we have;
Tan B = 40 /5
Tan B = 8
Take the inverse value of the tangent ;
[tex]B = Tan^{-1} (8) [/tex]
B = 82.86°
Hence, the bearing of A from B is 82.86°