Slope-intercept form is y = mx +b, where the variable m represents the slope of the line and the variable b represents the y-intercept of the line. Since we weren't given the y-intercept, one way to solve this problem is substitute the slope for the variable m and then the x and y values from the ordered pair to solve for b.
y = mx + b
y = 3x + b
-4 = 3(9) + b
Now, we can simplify by computing the multiplication on the right side of the equation.
-4 = 27 + b
Finally, we can find the value for b by subtracting 27 from both sides of the equation to get:
-31 = b
Now, we should substitute this value for b back into our equation with the slope.
y = 3x - 31
Therefore, your answer is y = 3x - 31.
Hope this helps!
Answer:
The correct answer would be y = 3x - 31
Step-by-step explanation:
In order to find the answer to this question, we must use point-slope from, which is listed below.
y - y1 = m(x - x1)
Now we input the ordered pair in for x1 and y1 and the slope in for m.
y - -4 = 3(x - 9)
Then we solve for y.
y + 4 = 3x - 27
y = 3x - 31
a(3x-8)=b-18x
what is a value?
what is b value?
determine the domain of the function h(x)= 9x/x(x^2-36)
Final answer:
The domain of the function h(x)=9x/x(x²-36) is all real numbers except 0, 6, and -6, because the function is undefined at these points.
In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.
Explanation:
The question asks to determine the domain of the function h(x) = 9x / x(x² - 36).
The domain of a function consists of all the real numbers x for which the function is defined. In this case, the function will be undefined when the denominator is zero because division by zero is not defined in mathematics.
To find these values, we set the denominator equal to zero and solve the resulting equation:
x(x² - 36) = 0.This can be factored further as x(x - 6)(x + 6) = 0, which gives us the zero points of x = 0, x = 6, and x = -6.
Therefore, the domain of h(x) is all real numbers except 0, 6, and -6.
In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.
A triangular traffic island has a base half as long as its height. The island has an area of 25 m2 . Find the base and the height.
Jamie mowed 7 lawns. He earned $10, $15, $12, $15, $8, And $15 for six lawns. How much did he earn the seventh time if the mean of the data is 12
Lupe can ride her bike at a rate of 20 mph when there is no wind. On one particular day, she rode 2 miles against the wind and noticed that it took her the same amount of time as it did to ride 3 miles with the wind. How fast was the wind blowing
The speed of the wind is 4 mph.
Let, the speed of the wind is W mph.
When Lupe rides with the wind, her effective speed is 20 + W mph, and when she rides against the wind, her effective speed is 20 - W mph.
We are given two pieces of information:
Lupe rode 2 miles against the wind, and it took her the same amount of time as riding 3 miles with the wind.
The time taken to cover a distance is equal to the distance divided by the speed.
Using this information, we can set up two equations:
Time taken against the wind = Time taken with the wind
2 / (20 - W) = 3 / (20 + W)
Now, let's solve for W:
2(20 + W) = 3(20 - W)
40 + 2W = 60 - 3W
5W = 20
W = 20 / 5
W = 4 mph
The speed of the wind is 4 mph.
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Help!!!!!!!!!!!!!!!!
There is 3\8 of a pizza in one box and 1/8 of a pizza in another box. How much altogether
Charles owed $390 to his friend. On the first day Charles paid his friend $12. Each following week the amount Charles paid his friend increased by the same amount. After 10 payments, Charles had paid back the full amount. By how much did each payment increase?
Please help confused
How many positive integers $N$ from 1 to 5000 satisfy both congruences, $N\equiv 5\pmod{12}$ and $N\equiv 11\pmod{13}$?
Please answer this question I need it fast:
Together, Mary Sue and Betty have 603 necklaces. Mary Sue has 115 more necklaces than Betty. How many necklaces does Betty have?
Answer:
mary sue: 359, betty; 244
Step-by-step explanation:
⇔↓⊕㏒㏑∞
which values of x are solutions of the equation x^3+ x^2-2x=0
find any points of discontinuity for each rational function. Sketch a graph. Describe any verticals or horizontal asympyoyes and any holes
(X^2-4)/(X+2)(X^2-49)
To find the points of discontinuity and sketch the graph of the rational function (x^2-4)/(x+2)(x^2-49), we need to determine the values of x that make the denominator equal to zero. We find that x = -2, x = 7, and x = -7 are the points of discontinuity. We can then sketch the graph by plotting the vertical asymptotes at x = -2, x = 7, and x = -7, and determining the behavior of the function on each side of those points.
Explanation:To find the points of discontinuity for the rational function (x^2-4)/(x+2)(x^2-49), we need to determine where the denominator is equal to zero. The denominator has two factors, (x+2) and (x^2-49). Setting each factor equal to zero, we find that x = -2, x = 7, and x = -7. These are the points where the function has vertical asymptotes or holes.
To sketch the graph, we can start by plotting the vertical asymptotes at x = -2, x = 7, and x = -7. Next, we can examine the sign of the function on each side of the vertical asymptotes to determine the behavior of the graph. Finally, we can plot any holes in the graph at the corresponding x-values.
Additionally, we should determine if there are any horizontal asymptotes. For rational functions, horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 2 and the degree of the denominator is 3, so there is no horizontal asymptote.
ABC has coordinates of A(–5, –7), B(6, –3), and C(2, 7). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 2.
The coordinates of the image after dilation with a scale factor of 2 are A'(-10, -14), B'(12, -6), C'(4, 14).
Explanation:Your question involves geometry and specifically, dilation transformations. A dilation is a transformation that moves each point along the ray from the center of dilation to the point. The number given as the scale factor tells you how much to move. In this case, we are asked to dilate the given points with a scale factor of 2 centered at the origin (0,0).
So, each coordinate of the original triangle should be multiplied by 2. Let's find each coordinate after dilation:
A: -5*2, -7*2 = A'(-10, -14)B: 6*2, -3*2 = B'(12, -6)C: 2*2, 7*2 = C'(4, 14)So, the coordinates of the image after a dilation with a scale factor of 2 are A'(-10, -14), B'(12, -6), and C'(4, 14).
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2-2*3+3. What is the correct answer
Using the law of cosines, a=2.2
Use your answer above to find m<B, to the nearest degree. m<B=__
Answer:
81
Step-by-step explanation:
Dan uses a compass to draw an arc from Q, as shown. He wants to construct a line segment through R that makes the same angle with line segment QR as line segment PQ.
first chart
Which figure shows the next step to construct a congruent angle at R?
Charts 2 3 4 & 5
Answer:
Chart 2.
Step-by-step explanation:
In the figure Dan has constructed an angle at point Q.He wants to cinstruct an angle ar point R which is congruent to angle made at point Q.To construct the angle at point R Dan needs to draw an arc at point R .He will put the compass on point R and draw an arc .This is shown in the figure 2.
The figure is added below.
Kayla bought 9/4 pounds of apples. What is that weight as a mixed number?
A church has 10 bells in its bell tower. before each church service 3 bells are rung in sequence. no bell is rung more than once. how many sequences are there?
Answer:
720
Step-by-step explanation:
Given : A church has 10 bells in its bell tower.
Before each church service 3 bells are rung in sequence.
To Find: How many sequences are there?
Solution:
Since we are given that 3 bells are rung in sequence. no bell is rung more than once.
So, we will use permutation.
Formula :[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
Since A church has 10 bells in its bell tower.
So, n =10
We are also given that Before each church service 3 bells are rung in sequence . So, r =3
So, the number of possible sequence = [tex]^{10}P_3[/tex]
= [tex]\frac{10!}{(10-3)!}[/tex]
= [tex]\frac{10!}{(7)!}[/tex]
= [tex]\frac{10 \times 9 \times 8 \times 7!}{(7)!}[/tex]
= [tex]10 \times 9 \times 8[/tex]
= [tex]720[/tex]
Hence there are 720 sequences.
There are 120 different sequences in which the 3 bells can be rung in sequence before each church service without any bell being rung more than once.
To find the number of sequences in which the 3 bells can be rung in sequence out of 10 bells without any bell being rung more than once, you can use the concept of combinations.
The number of ways to choose 3 distinct bells out of 10 is given by the binomial coefficient "10 choose 3," which is denoted as C(10, 3) and calculated as follows:
C(10, 3) = 10! / (3!(10 - 3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
So, there are 120 different sequences in which the 3 bells can be rung in sequence before each church service without any bell being rung more than once.
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When the sum of 5 and three times a positive number is subtracted from the square of the number, 0 results. Find the number.
To solve for the positive number when the sum of 5 and three times the number is subtracted from the square of the number to yield zero, set up and solve the quadratic equation x^2 - 3x - 5 = 0 using the quadratic formula.
Explanation:The student has asked for help in finding a positive number when the sum of 5 and three times the number is subtracted from the square of the number, and the result is 0. This involves setting up a quadratic equation and solving for the number.
Let's denote this positive number as 'x'. According to the problem statement, the equation can be written as:
x2 - (5 + 3x) = 0.
We can then expand and simplify this equation:
x2 - 5 - 3x = 0
And, rearrange it into standard quadratic form:
x2 - 3x - 5 = 0
Next, we can either factorize this equation, if possible, or use the quadratic formula to find the value of 'x' that satisfies the equation. Since this equation does not factor neatly, we use the quadratic formula:
x = ∛2 - 4ac) / 2a
In this case, a = 1, b = -3, and c = -5. Plugging these into the quadratic formula, we find the two possible solutions for x. Only the positive solution is relevant since the problem states that the number is positive.
Translate the given statement into an algebraic inequality or compound inequality: The IRS says you are in a certain tax bracket if your taxable income, i, is over $24,500, but not over $59,725.
Answer:
C. your welcome
Isabel created the tree diagram to represent the different ways she could order a salad at her favorite restaurant.
According to the diagram, how many combinations of lettuce type, dressing, and topping are possible?
Answer: Option B
(B) 12
Step-by-step explanation:
Kim spun the spinner 75 times and got a three 30 times. What is the experimental probability?
Express this equation in word form:
5 + ( 2 x 6 )
How many different ways are there to choose 10 donuts from 20 varieties if at most 4 chocolate donuts are chosen?
What is the domain of this function?
{x| x > }
Kendrick travel 2/3 mile to his friend’s house.He cycles 3/4 of his distance and walks the rest of the way.What fraction of a mile did he cycle?
Need help on 1-6 please I need to solve for x and I need to get this done.
Graph 12x-9y=36 please???
Answer:
The graph for 12x-9y=36 is given below
Step-by-step explanation:
The graph for 12x-9y=36 is given below.
[tex]12x-9y=36\\\frac{12x}{36}+\frac{9y}{-36}=1\\\frac{x}{3}+\frac{y}{-4}=1[/tex]
So x intercept is 3 and y intercept is -4.
The required graph is shown below which represents the equation 12x - 9y = 36.
To graph the equation 12x-9y=36, we can rearrange it to slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
First, solve for y by subtracting 12x from both sides and then dividing by -9. This gives us y=-4/3x+4.
Now we can see that the slope is -4/3 and the y-intercept is 4.
To graph this line, we can start at the y-intercept of (0,4) and then use the slope to find another point.
Since the slope is negative, we can move down 4 units (which is the denominator of the slope) and then move to the right 3 units (which is the numerator of the slope) to get another point at (3,0).
We can then draw a straight line through these two points to graph the equation.
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sandra has 5 toy cars .Each toy car has a mass of 8 grams .what is the total mass of all 5 cars?
Final answer:
The total mass of Sandra's 5 toy cars is calculated by multiplying the mass of one toy car (8 grams) by the total number of cars, resulting in a total mass of 40 grams.
Explanation:
The question requires us to calculate the total mass of Sandra's toy cars. Since each toy car has a mass of 8 grams, we can find the total mass by multiplying the mass of one car by the number of cars, which is 5 in this case. Therefore, the calculation we need to perform is 8 grams times 5, which will give us the total mass of all the toy cars combined.
To solve: 8 grams/car × 5 cars = 40 grams.
Thus, the total mass of all 5 toy cars that Sandra has would be 40 grams.