point slope form: y-y1=m(x-x1)
coordinate (1,-7):
point y1--7
point x1=1
slope (m)=-23
input into equation:
y-(-7)=-23(x-1)
convert to slope intercept form:
-*-=+ so 7 becomes +7
y+7
distribute -23 in -23(x-1) using the rule: a(b+c)=ab+ac
-23x+23
refine
y+7=-23x+23
perform some inverse operations:
y+7=-23x+23
y+7=-23x+23-7
y=-23x+16
therefore, D. y+7=−23(x−1) equals y=-23x+16 in slope-intercept form
Required equation of the line is y+7 = −23(x−1).
So, Option four is the correct answer.
What is slope?
In mathematics, the slope of a line is the change in the y-coordinate relative to the change in the x-coordinate.
The net change in the y-coordinate is denoted by Δy and the net change in the x-coordinate by Δx.
Thus, the change in the y-coordinate with respect to the change in the x-coordinate is obtained as follows:
m = change in y/change in x = Δy/Δx
Where "m" is the slope of the line.
You can also specify the slope of the line
tan θ = Δy/Δx
So, tan θ is the slope of the line.
In general, the slope of a line gives its steepness and direction. The slope of a line between two points (x1,y1) and (x2,y2) is easily determined by finding the difference in the coordinates of the points. The slope is usually denoted by the letter "m".
Here given,a line, in point-slope form, that passes through (1, −7) and has a slope of −23.
We want to find what is an equation of a line which passes through (1, −7) and has a slope of −23 ?
We know, if a line passes through the point (a,b) and has slope m then equation of the line,
[tex](y - b) = m(x - a)[/tex]
Here,
[tex]a = 1 \\ b = - 7 \\ m = - 23[/tex]
So, required equation is
[tex](y -( - 7)) = ( - 23)(x - 1) \\ (y + 7) = ( - 23)(x - 1)[/tex]
Therefore,required equation of the line is y+7 = −23(x−1).
Line related one more question:
https://brainly.com/question/17188072
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Find the Slope and Y-Intercer
1) y = x+3
slope =
y-intercept =
What’s the slope
Answer:
slope is 1 and y-intercept is 3
Step-by-step explanation:
equation is in the format y=mx+c
c = y-intercept
m = slope
if there is no number in front of x it is assumed that 1 is in front of x
Answer:
The slope is 1 and the y-intercept is 3
Step-by-step explanation:
y = x+3 has the form y = mx + b. If we compare these two equations, it becomes readily apparent that m = 1 and b = 3.
The slope is 1 and the y-intercept is 3 (or (0, 3) )
What should the following rate be divided by to convert it to a unit rate?
6 inches
12 hours
Answer:
so if all of the awnsers are whole numbers it is going to be 12/12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Unit rate is a rate that has 1 as denominator.
Given the rate: 6 inches / 12 hours, we have to divide numerator and denominator by 12 to transform the denominator in 1, as follows:
[tex]\frac{6}{12} = \frac{6/12}{12/12} =[/tex] 0.5 inches/hour
How can I factor 24 + 32x
Answer:
8(3+4x)
Step-by-step explanation:
it it can be pulled out of both 24 and 32.
What is the quotient of the complex numbers below?
(5-5i) = (3-i)
Answer:
A. 2- i
Step-by-step explanation:
Answer:
2 + i
Step-by-step explanation:
Food bill before tax: $40
Sales Tax: 8% Tip: 17%
Answer: $50.00
Step-by-step explanation:
Org. Price- $40.00
10% - $4.00
1% - $0.40
8% - $3.20
Tax - $3.20
10% + 8% - 1% = 17%
4.00 + 3.20 - 0.40 = 6.80
Tip - $6.80
$40.00 + $3.20 + $6.80 = $50.00
A local hamburger shop sold a combined total of 500 hamburgers and cheeseburgers on Tuesday. There were 50 fewer cheeseburgers sold than hamburgers.
How many hamburgers were sold on Tuesday?
Answer: 275
Step-by-step explanation:
Let the total number of hamburger be x and the total number of cheeseburgers be y. That is
x + y = 500 ................... equation 1
Since there were 50 fewer cheeseburgers sold than hamburgers, this means that the number of hamburgers sold is more than cheeseburgers by 50 , that is
x - y = 50 ............. equation 2
solving the resulting linear equation by substitution method;
From equation 2 , make x the subject of the formula , that is
x = 50 + y ................ equation 3
substitute equation 3 into equation 1 , we have
50 + y + y = 500
50 + 2y = 500
2y = 500 - 50
2y = 450
y = 450/2
y = 225
substitute y = 225 into equation 3 to find the value of x. we have
x = 50 + y
x = 50 + 225
x = 275
Therefore 275 hamburgers were sold
In which quadrant is the number -14-5i located on the complex plane?
Answer:lll(3) Quadrant lll
Step-by-step explanation:Quadrant 3 is the quadrant where the imaginary part of a number and the real part of a number are both negative and in this number they both are.
Grant has 2/3
of ice cream in a bowl. He then removes two 1/6
cups of ice cream to share with his little br
amount of ice cream left in Grant's bowl?
Answer: 2/6 or 1/3
Step-by-step explanation:
2/3 = 4/6. 1 /6 Two times is 2/6 so by subtracting you should get 2/6 or 1/3
Need help with this math problem
Answer:
[tex]x=16[/tex]
Lenght of the equal sides: [tex]71\ units[/tex]
Step-by-step explanation:
You can observe in the picture that the triangle have two angles that have equal measure; therefore, it is an Isosceles triangle.
By definition, Isosceles triangles have two equal angles and two equal sides.
Based on this, you can write the following equation:
[tex]9x-73=3x+23[/tex]
Solving for "x", you get this value:
[tex]9x-3x=23+73\\\\6x=96\\\\x=\frac{96}{6}\\\\x=16[/tex]
Finally, you can subsitute the value of "x" into any expression to find the lenght of the equal sides:
[tex]3(16)+23=71\ units[/tex]
is y=5-2x and 4x+2y=10 a single solution
Answer:
X= 0
Step-by-step explanation:
Maura runs 5 miles in 1.25 hours. Ava runs 3 miles in 0.83 hours. Who runs faster?
Answer:
Maura runs faster
Step-by-step explanation:
To avoid decimals ,multiply all by 100
Maura 500 mi/125h = 4 mi/h
Ava 300 mi /83 h =3.61445.....mi/h
Answer:
still from 2019
wsp my dude
Step-by-step explanation:
[tex]3x - 7 = 3x + 1[/tex]
solve for x
Answer:
No Solution.
Step-by-step explanation:
3x-7=3x+1
3x-3x-7=1
0-7=1
-7=1
no solution
Solve linear equations :
Solve step by step for each one
7. 10n - 11 = 3 + 4n + 6n
8. -8(k + 4) = -96
9. -6(2k + 5) + 7k = -6 + 7k
Answer: 7.) Wrong Question
8.) 8
(9.) - 2
Step-by-step explanation:
7.) 10n - 11 = 3 + 4n + 6n
Collect like terms
10n - 4n - 6n = 3 + 11
10n - 10n = 14
It's not possible to have zero n = 14
8.) -8(k + 4) = - 96
Exland the bracket
-8k - 32 = - 96
Collect like terms
-8k = - 96 + 32
-8k = - 64
Divide through by -8
-8k/-8 = - 64/-8
k = 8
9.) -6(2k + 5) + 7k = -6 + 7k
Open the bracket
-12k - 30 +7k = -6 + 7k
Collect like terms
-12k + 7k - 7k = - 6 + 30
-12k = 24
Divide both sides by -12
-12k/-12 = 24/-12
k = -2
There are 70 students attending summer camp, 21 girls and 49 boys. What is
the ratio of girls to boys at summer camp?
O A. 7:3
O B. 3:7
O 6. 2:1
SUBMIT
how do you write six times the quantity two x plus three y with numbers??
Answer:
12x + 18y
Step-by-step explanation:
Lets first write the quantity "two x plus three y", this means, that we have x and y as unknowns. x is 2 times, so we have 2x; and y is 3 times, so he have 3y:
2x + 3y
Additionally we have that this quantity is six times, what means that it is multiplied by a number 6:
6(2x +3y)
If you like, we can apply the distributive property that means that given any three numbers a, b, c we have that a(b+c)=ab + ac. In our case a is 6, b is 2x and c is 3y. Thus, operating:
6(2x +3y) = 6*2x + 6*3y = 12x + 18y
So, "six times the quantity two x plus three y" is 12x + 18y
Marie will earn $15 per hour at a new job. During training, she will earn $10 per hour. What percent of Marie's regular rate will she earn during training?
Answer:
66.67%
Step-by-step explanation:
Marie's earnings at a new job : $15 per hour
Her earnings during training : $10 per hour
percentage of Marie's regular rate earned by her during training
= [tex]\frac{Her\ earnings\ during\ training}{Her earning\ at\ a\ new\ job}[/tex]×100
= [tex]\frac{10}{15}[/tex]×100
= [tex]\frac{200}{3}[/tex]
= 66.67%
∴percentage of Marie's regular rate earned by her during training = 66.67%
Final answer:
To find what percentage of Marie's regular rate she will earn during training, divide her training rate by her regular rate and multiply by 100%.
Explanation:
Marie will earn $10 per hour during training. Her regular rate is $15 per hour. To calculate what percentage of her regular rate she will earn during training, we use the formula: percentage = (training rate / regular rate) * 100%. Plugging in the values, we get (10 / 15) * 100% = 66.67%. Therefore, Marie will earn 66.67% of her regular rate during training.
The sum of 3 consecutive odd numbers is 183
Answer:
Step-by-step explanation:The sum of three consecutive odd numbers is 183. Find the numbers. 57; 59; 67 59; 61; 63 60; 61; 62 65; 67; 69.
The cost of having one pizza delivered is $14. Each additional pizza cost $9 more. Write the explicit and recursive formula to represent the situation.
Answer:
14 +(9×x) = y x being the number of pizzas that are not the first one and y is the amount it all cost
Answer:
See explanation below:
Step-by-step explanation:
Here we want to express the number of pizza delivered. Lets try to understand the case.
If we buy one pizza (p1) the cost is 14 because of the delivery plus 9 for the cost of the pizza. So:
p1 = 14 + 9 = 23
If we buy 2 pizzas (p2) we have to pay 14 for the delivery and 9 for each pizza:
p2 = 14 + 9 + 9 = 14 + 2*9 = 32
If 3 pizzas are bought (p3) the reasoning is the same, 14 for the delivery and 9 for each pizza:
p3 = 14 + 9 + 9 + 9 = 14 + 3*9 = 41
Here we can see a pattern: for any amount of pizzas n the cost will be 14 plus n-times 9, the price of a pizza. It is:
pn = 14 + 9*n
But we can separate the last equation in such a way:
pn = 14 + 9*(n-1) + 9 , as 9*(n-1) + 9 = 9*n
But if our general formula it true, the first to terms on the right are the vost of buying n-1 pizzas, so:
pn = pn-1 + 9
We can keep on separating terms as we did to arrive to this form, this is, separating the 9n in 9*(n-2) + 9*2, 9*(n-3) + 9*3, ..., 9*(n-m) + 9*m for any m < n . Here I will keep pn = pn-1 + 9 as the Recursive Formula, but you could use other formulation with, e.g., pn-2, pn-3, etc, using the above recursion.
Now, the explicit formula is such that gives as the value of any amount, finding all the terms of the sequence with those not depending on previous terms (contrary to the recursive). This formula was showed above and is: pn = 14 + 9*n. This is, given any number of pizzas we can find the cost without knowing the cost of previous values.
So, we have:
Recursive: pn = pn-1 + 9
Explicit: pn = 14 + 9*n
Find the area of a circle with a circumference of 18.84 units
welp
Answer:
A=28.25 is the rounded form of the answer.
A = 28.245673384359 in^2
Answer:
Area: 28.25
Step-by-step explanation:
Area = Circumference^2
4 (pi)
18.84^2 = 354.9456
4(pi) = 12.5663706144
354.9456 ÷ 12.5663706144 = 28.2456733843
Rounded to the nearest hundreth, the 5 in the thousandths place converts the 4 in the hundreths place into 5.
Find the exact volume of a cone 6yd height 5yd base
Answer:
The exact volume of a cone is 10 yd³.
Step-by-step explanation:
Given:
Height of cone (h) is 6 yd and base (b) is 5 yd.
Now, to get the volume we need to find the radius.
So, to find radius we put the formula of base:
Let the radius be [tex]r[/tex]
Base=[tex]\pi r^2[/tex]
[tex]b=\pi\times r^{2}[/tex]
[tex]5=\pi\times r^{2}[/tex]
Dividing both sides by π and using square root on both the sides:
[tex]5\div \pi=(\pi \times r^{2}) \div \pi[/tex]
[tex]\frac{5}{\pi}=r^{2}[/tex]
[tex]\frac{5}{\pi}=r^{2}[/tex]
[tex]r^{2}=\frac{5}{\pi}-----1[/tex]
Now, putting the formula for getting the volume (v) of cone:
Volume = [tex]\pi r^2\frac{h}{3}[/tex]
[tex]v=\pi\times r^{2}\times \frac{6}{3}[/tex]
[tex]v=\pi\times r^{2}\times 2[/tex]
Substituting the value of [tex]r^2[/tex] from equation (1), we get:
[tex]v=\pi\times \frac{5}{\pi}\times 2[/tex]
[tex]v=10[/tex] yd³
Volume of cone is 10 yd³
Therefore, the exact volume of a cone is 10 yd³.
Graph a line with a slope of 2/5 that contains the point (-2,4)
A graph of the line with slope 2/5 and passing through the point (-2, 4) is shown on the coordinate plane in the image below.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
x and y represent the data points.m represent the slope.At data point (-2, 4) and a slope of 2/5, an equation for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = m(x - x_1)[/tex]
y - 4 = 2/5(x - (-2))
y - 4 = 2/5(x + 2)
y = 2/5(x) + 4/5 + 4
y = 2/5(x) + 24/5
Read more on point-slope here: brainly.com/question/24907633
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24:8,39:13 equvilent
Answer:
24 : 8 ≡ 39 : 13
Step-by-step explanation:
We are given two proportion relation and we have to determine whether they are equivalent or not.
Now, the first proportion is 24 : 8
So, the simplified proportion will be 24 : 8 = 8 × 3 : 8 = 3 : 1
Again the second proportion is 39 : 13
So, the simplified proportion is 39 : 13 = 13 × 3 : 13 = 3 : 1
Therefore, the two given proportions are equivalent i.e. 24 : 8 ≡ 39 : 13. (Answer)
Are coplanar points in the same line?
Answer:
I am not sure what you mean by same line but a CO planar point have to both share the same plane so not necessarily the same ray or line segment but it has to be on the same plane
Step-by-step explanation:
h/2 + 3 = 3(h/4 - 1)
Answer:
h=24
Step-by-step explanation:
h/2+3=3(h/4-1)
h/2+3=3h/4-3
h/2-3h/4=-3-3
2h/4-3h/4=-6
-h/4=-6
-h=-6*4
-h=-24
h=24
Work out the size of angle X.
Answer:
x = 70°
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
120° is an external angle of the triangle, thus
x + 50 = 120 ( subtract 50 from both sides )
x = 70
Solve the system by graphing. Write the solution as an ordered pair.
y = –3x + 3
y = 12x – 4
The solution on the graph is the coordinate of the point where both lines intersect
Given the equation of two lines expessed as;
y = -3x + 3 and y = 12 x - 4
Since both expressions ara y values, equating both will give;
-3x + 3 = 12x - 4
-3x - 12x = -4 - 3
-15x = -7
x = 7/15
Substitute x = 7/15 into any of the equatons;
y = -3x + 3
y = -3(7/15) + 3
y = -7/5 + 3
y = 8/5
Hence the solution as an ordered pair is (7/15, 8/15)
The solution on the graph is the coordinate of the point where both lines intersect as shown in the graph below;
Learn more on graphs here: https://brainly.com/question/18872003
Bills annual salary is 2/3 of Jen's annual salary.if bills salary is$64,000, what is Jen's salary?
Answer:
$96,000
Step-by-step explanation:
To find Jen's annual salary, divide Bill's annual salary of $64,000 by 2/3, resulting in Jen's salary being $96,000.
Explanation:To calculate Jen's annual salary based on the information that Bill's annual salary is 2/3 of Jen's, first express Bill's salary as a fraction of Jen's:
Let J represent Jen's annual salary.According to the problem, we have that Bill's salary equals 2/3 of Jen's, so (2/3)*J = $64,000.To find Jen's salary J, divide Bill's salary by 2/3, so J = $64,000 / (2/3).After calculation, J = $64,000 * (3/2), which simplifies to J = $96,000.Therefore, Jen's annual salary is $96,000.
You want to work out the distance you have travelled on your bike so far. In total, you have travelled 600 km. You believe that for every 5 km travelled, 2 km of that was on your bike. How far have you travelled on your bike?
Answer:240 km
Step-by-step explanation: 600 ÷5 = 120, 120 × 2 = 240 km
I think that's the answer I'm not sure but hope this helps ;)
How do u do this I’m lost
Answer:
A = 1/3b
Step-by-step explanation:
Divide each side by 12b to isolate the variable "a". This leaves a = 4/12b. This can be simplified to 1/3b.
Steps to solve:
12ab/12b = 4/12b (Divide 12/b to both sides)
a = 4/12b
a = 1/3b (Answer)
______
Best Regards,
Wolfyy :)
Solve for y. Then find the values of y that correspond
to the given values of x for the linear function.
7. y + 8x = -2 for x = 0, 1,2-2,
8. 12x + 3y = 15 for x = -1, 0, 1
y - 3x = 9 for x = -2,0, 2
10. 0.4y + 2x = 1.2 for x = -3,0,
7.
y + 8x = -2
f(x) = y = -8x - 2
f(0)=-2, f(1)=-10, f(2)=-18, f(-2)=14
8.
12x + 3y = 15
3y = -12x + 15
f(x) = y = -4x + 5
f(-1)=9, f(0)=5, f(1)=1
9.
y - 3x = 9
f(x) = y = 3x + 9
f(-2)=3, f(0)=9, f(2)=15
10.
0.4y + 2x = 1.2
4y + 20x = 12
4y = -20x + 12
f(x) = y = -5x + 3
f(-3) = 18, f(0)=3