Complete the equation of the line through (-7,-3) and (-2,4)
If one line passes through the points (x₁, y₁) and (x₂, y), the slope of the line can be calculated using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}...(1)[/tex]Additionally, the equation can be expressed in point-slope form as:
[tex]y-y_2=m(x-x_2)...(2)[/tex]From the problem, we identify:
[tex]\begin{gathered} (x_1,y_1)=(-7,-3) \\ \\ (x_2,y_2)=(-2,4) \end{gathered}[/tex]Then, we calculate the slope of the line using (1):
[tex]m=\frac{4-(-3)}{-2-(-7)}=\frac{4+3}{-2+7}=\frac{7}{5}[/tex]Finally, we find the equation of the line using (2):
[tex]\therefore y-4=\frac{7}{5}(x+2)[/tex]Stacia has 28 red and blue marbles. The ratio of red to blue marbles is 1: 6.
How many blue marbles does Stacia have?
Answer:You have 24
Step-by-step explanation:
what is the measure in radians of central angle 0 in the circle below
For this exercise you need to use the following formula:
[tex]\theta=\frac{S}{r}[/tex]Where θ is the Central angle in radians, "S" is the arc length and "r" is the radius of the circle.
In this case, you can identify that:
[tex]\begin{gathered} S=8\pi cm \\ r=8\operatorname{cm} \end{gathered}[/tex]Knowing these values, you can substitute them into the formula and then evaluate, in order to find the measure of the Central angle in radians. This is:
[tex]\begin{gathered} \theta=\frac{8\pi cm}{8\operatorname{cm}} \\ \\ \theta\approx\pi radians \end{gathered}[/tex]The answer is:
[tex]\pi radians[/tex]in the diagram of BED below, FC||ED,BF=6,FE=18, and BC=22. What is the length of BD
we know that
The side splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally
so
18/6=DC/11
solve for DC
DC=3*11
DC=33
Find the length of BD
BD=BC+DC
BD=11+33=44 units
therefore
the answer is 44 units
help i’ll greatly appreciate it :)
Answer: i think B
Step-by-step explanation:
im not that sure tho
Find the surface area of the cone. Use 3.14 for pi.The surface area is about __in.2.(I need just the answer, I don't need explanation)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
s = 50in
d = 20in
surface area of a cone = ?
Step 02:
surface area of a cone
SA = πr² + πrs
r = d/2 = 20in / 2 = 10in
SA = 3.14*(10in)² + 3.14*50in*10in
SA = 314in² + 1570in²
SA = 1884in²
The answer is:
SA = 1884in²
If AACB = ADCE, ZCAB = 63°,ZECD = 52°, and ZDEC = 5xDE(c сx = [?]
Since angles ACB and ECD are vertical angles, they are congruent, so we have
Calculating the sum of internal angles in triangle ABC, we have:
[tex]\begin{gathered} ABC+ACB+CAB=180 \\ ABC+52+63=180 \\ ABC=180-52-63 \\ ABC=65 \end{gathered}[/tex]Since triangles ACB and DCE are congruent, we have [tex]\begin{gathered} DEC=ABC \\ 5x=65 \\ x=13 \end{gathered}[/tex]
2. A grocery store is tracking how many people buy barbeque chips and jalapeno chips. The table shows how the number of barbeque chips and jalapeno chips are related. Ax + By = C y = mx + b Barbeque Jalapeno Write the standard form and slope intercept form equations for the scenario given. Chips (x) Chips (y) 200 100 160 140 120 180 80 220 Hint: use your calculator (STAT: Edit)
step 1
Find the slope m
we need two points
so
(200,100) and (80,220)
m=(220-100)/(80-200)
m=120/-20
m=-6
step 2
Find the equation of the line in point slope form
y-y1=m(x-x1)
we have
m=-6
(x1,y1)=(200,100)
substitute
y-100=-6(x-200)
Convert to slope intercept form
y-100=-6x+1200
y=-6x+1300step 3
Find the equation in standard form
Ax+By=C
where
A is a positive integer
B and C are integers
so
y=-6x+1300
6x+y=1300Find the area of the triangle. 30 cm 15 cm cm2
Area of the triangle is 225 sq. cm.
Given:
The base of the triangle is, b = 30cm.
The height of the triangle is, h = 15cm.
The objective is to find the area of the triangle.
The formula to find the area of the triangle is,
[tex]A=\frac{1}{2}\times b\times h[/tex]Now, substitute the given values in the above formula.
[tex]\begin{gathered} A=\frac{1}{2}\times30\times15 \\ A=225cm^2 \end{gathered}[/tex]Hence, the area of the triangle is 225 sq. cm.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!
Answer:
To find the perimeter of the triangle, you would add p + m + n. To find the area of the triangle you would use (p x m) /2. To find a missing side of the triangle, given that it is a right triangle, you would use p^2 + m^2 = n^2
In the diagram below of rhombus ABCD,angle C is 100,what is angle DBC
Okay, here we have this:
Considering the provided information, that in a rhombus opposite angles are equal, and that the sum of the angles of a triangle is 360 °, we obtain:
360°=100°+100°+4(m∠DBC)
Now, let's clear "m∠DBC":
360°=200°+4(m∠DBC)
4(m∠DBC)=360°-200°
4(m∠DBC)=160°
m∠DBC=160°/4
m∠DBC=40°
Finally we obtain that the correct answer is the option A.
I need to order the numbers least to greatest for the numbers: sq root of 144 234/3 and 68.12
So, the order would be 8.25, 8.832 and 12
Point L is on line segment KM. Given KL = 15 and LM = 3, determine the
length KM.
Answer: KM = 18
Step-by-step explanation:
K---------------L---M
15 + 3 = 18
The population of a country dropped from 52.5 million in 1995 to 44.2 million in 2007. Assume that P(t), the population, in millions, t years after 1995, is decreasing according to the exponential decay model.a) Find the value of k, and write the equation.b) Estimate the population of the country in 2018.c) After how many years will the population of the country be million, according to this model?
we have the exponential decay function
[tex]P(t)=52.5(e)^{-0.0143t}[/tex]Part b
Estimate the population of the country in 2018
Remember that
t=0 -----> year 1995
so
t=2018-1995=23 years
substitute in the function above
[tex]\begin{gathered} P(t)=52.5(e)^{-0.0143\cdot23} \\ P(t)=37.8\text{ million} \end{gathered}[/tex]Part c
After how many years will the population of the country be 2 million, according to this model?
For P(t)=2
substitute
[tex]2=52.5(e)^{-0.0143t}[/tex]Solve for t
[tex]\frac{2}{52.5}=(e)^{-0.0143t}[/tex]Apply ln on both sides
[tex]\begin{gathered} \ln (\frac{2}{52.5})=\ln (e)^{-0.0143t} \\ \\ \ln (\frac{2}{52.5})=(-0.0143t)\ln (e)^{} \end{gathered}[/tex][tex]\ln (\frac{2}{52.5})=(-0.0143t)[/tex]t=229 years
Leeds Company produced the following number of maps during the first five weeks of last year. Prepare a bar graph. Week Maps 1 800 2 600 3 400 4 700 5 300
The bar graph is attached below.
The heights of the rectangular bars in a bar graph, which displays complete data, are proportionate to the values they indicate. The graph's bars can be displayed either vertically or horizontally. Bar graphs, commonly referred to as bar charts, are a visual depiction of groups of data. It is one method of processing data. A bar graph is a great tool for representing data that are unrelated to one another and do not need to be displayed in any particular sequence. The bars provide a visual representation for comparing amounts in several categories. The x and y axes, commonly known as the horizontal and vertical axes, the title, labels, and a bar graph are all included.
Hence we frame the desired bar graph.
Learn more about bar graph here:
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Evaluate the following expression.
1-4x (-3) +8 x (-3)
Answer:
-11
Step-by-step explanation:
1-4x(-3)+8x(-3)=
first you multiple
-4x(-3)=12
8x(-3)= -24
bring down the 1
1+12-24=
now we add
13-24=
then subtract and we get
-11
B. Are the graphs of y = a|x| and y = |ax| the same when a is negative? Why?
The absolute value gives always a positive number.
If a is negative, then a|x| is negative and |ax| is positive.
Therefore, the graph of y=a|x| won't be the same as the graph of y=|ax|.
Another way to see it, is by using the property:
[tex]\mleft|ax\mright|=\mleft|a\mright|\cdot\mleft|x\mright|[/tex]Since a is negative, then |a| = -a. So, |ax| = -a|x|, which is clearly different from a|x|.
8ftÜ4ft7ft5ftA right angle is removed from a rectangle to create the shaded region shown below find the area of the shaded region be sure to include the correct unit in your answer
First, we need to find the sides of the triangle.
The base of the triangles is 8ft - 5ft = 3ft.
The height for the triangle is 7ft - 4ft = 3ft
Now, we need to find the area of the triangle:
[tex]A_t=\frac{base\cdot height}{2}[/tex]Replacing the values:
[tex]A_t=\frac{3ft\cdot3ft}{2}[/tex]Then
[tex]A_t=4.5ft^2^{}[/tex]Now, we need to find the area for the rectangle:
Area for a rectangle = Length * Width
In this case:
Length = 8ft
Width = 7ft
Therefore:
[tex]A_r=8ft\cdot7ft[/tex]Then
[tex]A_r=56[/tex]Finally, to find the area of the shaded region we need to subtract the triangle area from the rectangle area:
[tex]A=A_r-A_t[/tex]Therefore:
[tex]A=56ft^2-4.5ft^2[/tex][tex]A=51.5ft^2[/tex]Hence, the area for the shaded region is 51.5 ft².
The elevation of a mountain is 6510 feet above sea level.
Write a signed number to represent this elevation.
I need help with this problem. Quick answer is fine
[tex]a^{\frac{-m}{n}}=\frac{1}{a\frac{m}{n}}=\frac{1}{\sqrt[n]{a^m}}[/tex]
i need help with this pls
Mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing.
A linear pair is made up of two angles, and the sum of their measures is 180°.What is the formula for linear pairs?A two-variable linear equation of the form axe + by + c, with a, b, and c all being real numbers and not equal to zero.The Transitive Property states that if all real numbers x, y, and z are equal, then x=z. Substituting characteristics. If x=y, then x can be swapped to y in any equation or formula.Mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing. A linear pair is made up of two angles, and the sum of their measures is 180°.Line pairs can be congruent. Adjacent angles are joined by a vertex. Angles that are similar cross across. A linear pairing is unnecessary.
Therefore, mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing.
A linear pair is made up of two angles, and the sum of their measures is 180°.To learn more about the Linear pair theorem refer to:
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solve for r 2r + 7 = 4r - 13
2r + 7 = 4r - 13
subtract 4 from both-side of the equation
2r - 4r + 7 = 4r - 4r - 13
-2r + 7 = -13
subtract 7 from both-side of the equation
-2r + 7 = -13 - 7
-2r = -20
divide both-side of the equation by -2
r = 10
Solve the equation for y.1/3 x + y = 4
In order to solve the equation for y, we just need to isolate the variable y in one side of the equation. So we have:
[tex]\begin{gathered} \frac{1}{3}x+y=4 \\ y=4-\frac{1}{3}x \end{gathered}[/tex]So the answer is y = 4 - 1/3 x
Mai works as a tutor for $12 an hour and as a waitress for $7 an hour. This month,she worked a combined total of 85 hours at her two jobs. Let t be the number of hours Mai worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.total earned (in dollars) = ?
Solution:
Let t be the number of hours Mai works as a tutor.
Given that She earns $12 a hour as a tutor, this implies that for t number of hours, she will earn
[tex]\begin{gathered} \$12\times t \\ =\$\text{ 12t} \end{gathered}[/tex]For the month, she worked a combined total of 85 hours. This implies that
[tex]\begin{gathered} 85=t\text{ + (number of hours worked as a waitress) } \\ \Rightarrow nu\text{mber of hours worked as a waitress = (85-t) hours} \end{gathered}[/tex]Her total eranings for the month is expressed as
[tex]\text{Total earnings = 12(number of hours worked as a tutor)+7(number of hours worked as a waitress)}[/tex]Recall that she earnes $7 an hour while working as a waitress.
Thus, we have her combined total amount in dollars expressed as
[tex]\text{Total earned (in dollars)=12t+7(85-t)}[/tex]Hence, the expression is
[tex]\begin{gathered} \text{12t+7(85-t) } \\ \text{open parentheses} \\ \Rightarrow12t+595-7t \\ \text{collect like terms.} \\ \text{thus, the expression is simplied to be} \\ 5t+595 \end{gathered}[/tex]In one us city the taxi cost is 2$ plus .50c per mile . If you are traveling from the airport there is an additional charge of 3.50$ for tolls how far can i travel for 33$
Let the number of miles I can travel for $33 be x;
The total cost of taxi ride from the airport is;
Flat fee + Tolls fee + Charge/Mile = Total cost
Flat fee = $2.00
Toll fee = $3.50
Charge per mile = 0.50x
Total cost = $33.00
Thus, we have;
[tex]\begin{gathered} 2.00+3.50+0.50x=33.00 \\ 0.50x=33.00-5.50 \\ 0.50x=27.50 \\ x=\frac{27.50}{0.50} \\ x=55 \end{gathered}[/tex]Thus, the number of miles
The formula, = / + , converts temperatures between Celsius and Fahrenheit degrees. What is the temperature in degrees Celsius that is equivalent to 14 degrees FahrenheitA) -10B) -9 C) -8D) -7
Hello there. To answer this question, we need to plug in the value given by the question and solve for C, the temperature in Celsius.
We want to find the equivalent temperature in Celsius to 14 degrees Fahrenheit.
Knowing that F = 9/5C + 32, making F = 14 lead us to:
14 = 9/5C + 32
Subtract 32 on both sides of the equation
9/5C = -18
Multiply both sides of the equation by a factor of 5/9, in order to get:
C = 5/9 (-18) = -10.
This is the equivalent temperature we were looking for.
A) how many of these voters plan to vote for the library? B) how many voters are not planning to vote for the library?
Answer:
Explanation:
From the information given, 3
the smallest four digit number that can be formed using 5, 6, 3, 0 is
Answer:
3056 can be be formed as the smallest four digit number
What is the measure of the unknown angle? (2 points)120°2100009240
To find the angle measure "n", we proceed as follows:
Step 1: Recall that the sum of angles at a point is 360 degrees, as below:
[tex]\begin{gathered} the\text{ sum of angles at a point = 360 degrees} \\ n+120\text{ = 360} \\ n=360\text{ - 120} \\ n=240^o \\ \end{gathered}[/tex]Therefore, the meas
what is[tex](6 {x}^{2} - 13x + 5) [/tex]divided by[tex](2x - 1)[/tex]
1. Divide the first term of the dividend into the first term of the divisor:
[tex]\frac{6x^2}{2x}=3x[/tex]2. Multiply the result above by the divisor:
[tex]3x(2x+1)=6x^2+3x[/tex]3. Subtract the result above from the divident to get a new polynomial:
4. Repeat the process with the new polynomial:
[tex]\begin{gathered} -\frac{16x}{2x}=-8 \\ \\ -8(2x+1)=-16x-8 \end{gathered}[/tex]Then, the result of the division is:[tex]\frac{6x^2-13x+5}{2x+1}=3x-8+\frac{13}{2x+1}[/tex]