Answer:
6 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (- 7, - 5)
d = [tex]\sqrt{(-7+7)^2+(-5-1)^2}[/tex]
= [tex]\sqrt{0+(-6)^2}[/tex] = [tex]\sqrt{36}[/tex] = 6 units
Final answer:
The distance between the points (-7, 1) and (-7, -5) on the coordinate plane is 6 units, calculated by the absolute difference in their y-coordinates.
Explanation:
The distance between the points (-7, 1) and (-7, -5) on the coordinate plane can be found by calculating the difference in their y-coordinates. Since the x-coordinates are the same, the points lie on a vertical line, and the distance is simply the absolute difference in the y-coordinates.
The calculation would be: distance = |y2 - y1| = |-5 - 1| = | -6 | = 6 units
Therefore, the distance between the two points is 6 units.
Choose all the factors of 12. (Check all that apply-)
Answer:
1,2,3,4,6,12
Step-by-step explanation:
all the number which can divide 12 is factor of 12. so 1,2,3,4,6,12
Help please!!!!!!!!!!!!!
Answer:
A. Nothing, Paul is correct
Step-by-step explanation:
Tangent to a circle is a line that touches the circle at one point. At the point of contact, tangent to a circle is always perpendicular to the radius. If two tangents are drawn from a common external point to a circle, then the two tangents have equal tangent segments.Tangent segment means line joining to the external point and the point of contact to the circle.What is the value of X?
Answer:
x = 11
Step-by-step explanation:
Since they are vertical angles, the angles are equal. Set them equal and solve for x.
5x + 10 = 7x - 12 Subtract 5x from both sides
10 = 2x - 12 Add 12 to both sides
22 = 2x Divide by 2
11 = x
In how many ways committee of 8 people can be chosen out of 10 men and 6 women if there needs to be at least 5 women?
Answer:
765
Step-by-step explanation:
Given in the question,
number of people to be choose with at least 5 women in it = 8
There are 2 ways to choose 8 members
1)
5 women
(6C5)(10C3)
6x120
720
2)
6 women
(6C6)(10C2)
1x45
45
Our final answer is 720 + 45 = 765 ways
Formula to calculate
nCr = n! / r!(n-r)!
The selection of members of the committee is an illustration of combination.
The number of ways of selection is 765
The given parameters are:
[tex]\mathbf{Men = 10}[/tex]
[tex]\mathbf{Women = 6}[/tex]
At least 5 women means that:
There are 5 women and 1 man in the committee orThere are 6 women and no man in the committeeSo, the possible selection is:
[tex]\mathbf{Selection = ^6C_5 \times ^{10}C_3 + ^6C_6 \times ^{10}C_2}[/tex]
Apply combination formula
[tex]\mathbf{Selection = \frac{6!}{5!1!} \times \frac{10!}{7!3!} + \frac{6!}{6!0!} \times \frac{10!}{8!2!}}[/tex]
[tex]\mathbf{Selection = 6 \times 120 + 1 \times 45}[/tex]
[tex]\mathbf{Selection = 720 + 45}[/tex]
[tex]\mathbf{Selection = 765}[/tex]
Hence, the number of ways of selection is 765
Read more about selections and combinations at:
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What is the slant height x of this square pyramid?
The figure shows a square pyramid. The slant height is shown as a dashed line perpendicular to the base edge and is labeled as x. The length of the lateral edge is 4 meters. The lateral edge makes a 60 degree angle with the base edge.
Answer:
= 2√3 m or 3.464
Step-by-step explanation:
Using the sine,
sin(60”) = x / 4 multiply both sides by 4
4 sin (60°) = x
4 * √3 / 2 = x
x = 2√3 m
slant height =2√3 m
Answer: The slant height is 2√3 meters.
Step-by-step explanation: The side adjacent to the 60 degree angle in the right triangle consisting of x, the lateral edge, and half of the base edge is half of the base edge, 2m. The side opposite of that angle is x. So basically you have tan(60°) = x/(2m)*tan(60°) = x = 2√3m. So thus the slant height is 2√3 meters.
What is the equation for (-3,-2)
Answer:
Y = mX + b
Step-by-step explanation:
Equation for a line:
Y = mX + b
Best regards
square root of 3 multiplyed by the square root of 2
3 is not a perfect / 100 percent square.
If we simplify we get 1.73205081. That is in its simplest form.
ANSWER ASAP!!!!!
Audrey has a box that contains one caramel chocolate (C), one milk chocolate (M), one dark chocolate (D), and one white chocolate (W). She picks one chocolate and eats it. Then she picks another chocolate and eats it. What is the sample space of the event?
Answer:
{CM} {CD} {CW} {MC} {MD} {MW} {DC} {DM} {DW} {WC} {WM} {WD}
Step-by-step explanation:
The sample space is all the possible results that can be obtained from a randomized experiment.
In this case, the experiment is to select two chocolates out of 4.
If we have 4 chocolates of different types {C, M, D, W}
and we select 2, then (taking into account the order in which she eats the chocolates} the possible results are:
{CM} {CD} {CW} {MC} {MD} {MW} {DC} {DM} {DW} {WC} {WM} {WD}
There are 12 possible results for this experiment.
A cylinder has a radius of 10 M and a height of 8 AM what is the exact volume of the cylinder
[tex]\bf \textit{volume of a right-circular cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=10\\ h=8 \end{cases}\implies V=\pi (10)^2(8)\implies V=800\pi \\\\[-0.35em] ~\dotfill\\\\ ~\hfill V\approx 2513.27~\hfill[/tex]
A line joins the point
is the point of intersection of 5x - 2y + 3 = 0 and 4x - 3y + 1 = 0 to
of intersection of x = y and x = 3y + 4.find the equation of the line.
Intersection of the first two lines:
[tex]\begin{cases}5x - 2y + 3 = 0\\4x - 3y + 1 = 0\end{cases}[/tex]
Multiply the first equation by 4 and the second by 5:
[tex]\begin{cases}20x - 8y + 12 = 0\\20x - 15y + 5 = 0\end{cases}[/tex]
Subtract the two equations:
[tex](20x - 8y + 12)-(20x - 15y + 5)=0 \iff 7y+7=0 \iff y=-1[/tex]
Plug this value for y in one of the equation, for example the first:
[tex]5x - 2\cdot (-1) + 3 = 0\iff 5x+5=0 \iff x=-1[/tex]
So, the first point of intersection is [tex](-1,-1)[/tex]
We can find the intersection of the other two lines in the same way: we start with
[tex]\begin{cases}x=y\\x=3y+4\end{cases}[/tex]
Use the fact that x and y are the same to rewrite the second equation as
[tex]x=3x+4 \iff 2x=-4 \iff x=-2[/tex]
And since x and y are the same, the second point is [tex](-2, -2)[/tex]
So, we're looking for a line passing through [tex](-1,-1)[/tex] and [tex](-2, -2)[/tex]. We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be [tex]y=x[/tex]
In the attached figure, line [tex]5x - 2y + 3 = 0[/tex] is light green, line [tex]4x - 3y + 1 = 0[/tex] is dark green, and their intersection is point A.
Simiarly, line [tex]x=y[/tex] is red, line [tex]x = 3y + 4[/tex] is orange, and their intersection is B.
As you can see, the line connecting A and B is the red line itself.
To answer the student’s question, solve for points of intersection of given pairs of equations, use these points to calculate the slope, and then apply the point-slope or two-point form to determine the equation of the line.
Explanation:To find the equation of a line that passes through the points of intersection of two sets of equations, we first need to determine the coordinates of these intersection points. We have two given sets of equations: 5x - 2y + 3 = 0 and 4x - 3y + 1 = 0, as well as x = y and x = 3y + 4. To solve for the intersection points, we can use substitution or elimination method for the pairs of equations separately.
Once we have found the two points of intersection, we use these points to determine the slope of the line (using the slope formula ∆y /∆x). After that, we apply the point-slope form or the two-point form of the equation of a line to find the equation that contains both points. The final step would be to simplify the equation to its standard form.
However, the question seems to include extraneous information, as the equation provided for a specific line, y = 9 + 3x, does not directly pertain to the given task of determining the equation of the line through the points of intersection. It does illustrate that a line's equation can be represented in the form y = mx + b, where m represents the slope, and b represents the y-intercept.
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Hello! I would appreciate the help, and please write step by step solutions. Will mark brainliest. Thanks!
Answer:
15. 31.42 cm^2
16. 25.73 m^2
17. Fly A
Step-by-step explanation:
15.
The blue shaded region is a sector of a circle. The formula for area of sector = [tex]\frac{\theta}{360}*\pi r^2[/tex]
Where [tex]\theta[/tex] is the central angle and r is the radius
For the diagram, we have 80° arc and 180° arc as the "white" area. Since the whole circle is 360°, the shaded region arc is 360 - (80+180) = 100°. this is [tex]\theta[/tex] and the radius is 6.
Plugging in it in the formula we get:
Area of shaded region = [tex]\frac{\theta}{360}*\pi r^2\\=\frac{100}{360}*\pi(6)^2\\=31.42[/tex] cm^2
16.
We can say that area of shaded region = area of parallelogram - area of circle
Now,
Area of Parallelogram = b * h
where
b is the base (it is 6+3=9) and h is the height (diameter of the circle is the height = 6)
Area of Parallelogram = 9 * 6 = 54
Area of Circle = πr^2 where r is the radius, which is 6/2=3
Area of Circle = π(3)^2 = 9π
Now,
Area of Shaded Region = 54 - 9π = 25.73 m^2
17.
For the first figure (rectangle) we could let the height be h (since not given). So area of yellow region would be 4h (area of rectangle is base * height)
And area of whole ruler would be 8*h = 8h
So probability of landing in yellow region would be [tex]\frac{4h}{8h}=\frac{1}{2}=0.5[/tex]
For 2nd figure, the yellow region has area of π(2)^2 = 4π ( radius of yellow circle is 2 and area of circle is πr^2)
Area of whole circle is π(4)^2 = 16π
So probability of landing in yellow region would be [tex]\frac{4\pi}{16\pi}=\frac{1}{4}=0.25[/tex]
Hence, Fly A is more likely to land in a yellow region.
Two angles are complementary. The measure of ∠ABC is x° and the measure of ∠DBC is (3x + 10)°. What is the value of x? Enter your answer in the box.
Step-by-step explanation:
Complementary means the total is 90 degrees.
So 90=x+3x+10
90=4x+10
80=4x
x=20 degrees
Answer:
x=20 degrees
hope this helped! :)
On a map, 1 inch equals 25 miles. Two cities are 8 inches apart on the map. What is the actual distance between the cities? (In miles)
Answer:
200 miles
Step-by-step explanation:
8x25=200
The actual distance will be 200 miles
Step-by-step explanation:The question states that
1 inch = 25 milesThe distance between two cities is 8 inches
Actual distance would be
8 * 25 = 200
So the actual distance would be 200 miles
What is the area of the polygon shown below?
Answer:
The answer is D
Step-by-step explanation:
Which expression is the simplest form of (x^-5/6)^6?
Answer:
Step-by-step explanation:
sistemul digestiv
Answer x^-5
Step-by-step explanation: since (- 5/6)*6=-5
The answer is x^-5
If h = 24 units and r = 8 units, what is the volume of the cone shown above?
Use 3.14 for .
Answer: 1607.68units^3
Step-by-step explanation:
Answer:
1607.68
Step-by-step explanation:
Cathy saves 4/5 of the money she earns from her part time job. How much does she saves when she earns 140
I believe that the answer is $175
Answer:
$112
Step-by-step explanation:
140 divided by 5 is 28, which means 1/5 of 140 is 28. You take that 28 times 4 to get 4/5 of 140 which comes out to be 112. Brainliest please!
Fay is buying a new washing machine which is on sale for $1479 she can either pay the entire amount at the time of purchase or make a down payment $250 and make monthly payments of $125 for one year how much more will it cost her to choose the payment plan then to pay the full sale price?
Answer:$271
Step-by-step explanation:
$125x12= 1500+250=1750
1750-1479=271
BRAINLIEST ANSWER: Two workers finished a job in 7.5 days. How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?
Answer:
first we must times 7.5 into 8 to find out what the answer is,
the answer is 60
Solve 9x = 27 1/3 2/3 3/2
Answer:
the answer is x=3
Step-by-step explanation:
divide by 9 on each side of = sign
9/9 and 27/9=3
Answer: 3/2
Step-by-step explanation:
I just did it on oddyseyware. Trust me and believe me its 3/2.
solve the quadtdd atic function (x + 1)2 = 16
Answer:
x = 15 or x = -17
Step-by-step explanation:
It is given that,
(x + 1)² = 16
To solve the quadratic equation
The give equation is
(x + 1)² = 16 ----(1)
From equation (1) we can see that it is a quadratic equation
So we can take square root fro both sides we get
√[(x + 1)²] =√16
x + 1 = ±16
x + 1 = 16 or x + 1 = -16
x = 16 - 1 = 15 or x = -16 - 1 = -17
Therefore x = 15 or x = -17
Calculate the circumference of the following circles correct to one decimal place
Answer:
C= 2π*4
C= 4*2= 8*3.14
C= 25.12
Step-by-step explanation:
3/8 c−2= 3/2 c−12 solve for c
To solve the equation 3/8c -2 = 3/2c -12 for c, first clear the fractions by multiplying the entire equation by 8. Then, use algebraic operations to isolate and solve for c, yielding the solution c = 80/9 or about 8.89.
Explanation:The given algebraic equation is 3/8 c−2= 3/2 c−12. Our goal is to solve for c. Here's how:
First, let's multiply the whole equation by 8 to clear out the fractions: 8*(3/8c-2) = 8*(3/2c -12) which simplifies to 3c - 16 = 12c - 96. Next, subtract 3c from both sides of the equation to collect all the terms with c on one side: -16 = 9c - 96. Now, add 96 to both sides to isolate the c term: 80 = 9c. Finally, divide both sides by 9 to solve for c: c = 80/9 or approximately 8.89.
So, the solution to the equation 3/8c - 2 = 3/2c -12 is c = 80/9 or about 8.89.
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To solve the equation:3/8 c−2= 3/2 c−1. We can solve the equation by combining like terms, eliminating fraction denominators, and distributing.
After simplifying,80/9.
Let's solve the equation:3/8 c−2= 3/2 c−1.
We can solve the equation by combining like terms, eliminating fraction denominators, and distributing.
Steps to solve:
1. Combine multiplied terms into a single fraction:
3/8 c−2= 3/2 c−12
2. Find common denominator:
3/8 c + (8/8) −2= 3/2 c−12
3. Combine multiplied terms into a single fraction:
3/8 c + (8 *(−2) /8) −2= 3/2 c−12
4. Combine fractions with common denominator:
(3c + 8 *(−2) /8) = 3/2 c−12
5. Multiply the numbers:
(3c -16) /8) = 3/2 c−12
6.Combine multiplied terms into a single fraction:
(3c -16) /8) = 3/2 c−12
7. Find common denominator:
(3c -16) /8) = 3/2 c +(2/2) (-12)
8.Combine multiplied terms into a single fraction:
(3c -16) /8) = 3/2 c +(2*-12)/2
9.Multiply the numbers:
(3c -16) /8) =(3c -24) /2)
10. Eliminate fraction denominators:
8*(3c -16) /8) = 8*(3c -24) /2)
11. Cancel multiplied terms that are in the denominator:
3c−16=4(3c−24)
12. Distribute:
3c−16=12c−96
13. Add/subtract to both sides:
3c−16+16=12c−96+16
14. Simplify:
3c=12c−80
15. Add/subtract to both sides:
3c−12c=12c−80−12c
16. Simplify:
−9c=−80
17.Divide both sides of the equation by the same factor:
−9c/-9=−80/-9
18.Simplify:
c=80/9.
The function f(x)=3g(x). Which of the following shows possible graphs of f(x) and g(x)?
Answer:
The answer is the first graph in the second raw
Step-by-step explanation:
* Lets study the dilation:
- A vertical stretching is the stretching of the graph away
from the x-axis
- A vertical compression is the squeezing of the graph
toward the x-axis.
- if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically
stretched by multiplying each y-coordinates by k.
- if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed
by multiplying each y-coordinates by k.
* Notice that the "roots" on the graph stay in their same
positions on the x-axis.
* Lets check our question:
∵ f(x) = 3g(x)
∵ f(x) = k.g(x)
∴ It is a vertical stretching or vertical compression
∵ k = 3 > 1
∴ It is vertical stretching with scale factor = 3
* That means we will multiply each y-coordinates in g(x) by 3
∴ The graph of f(x) will be away from x- axis and narrow to y- axis
∴ The answer is the first graph the second raw
Example: If g(x) = x²
∴ f(x) = 3x²
* Look to the graph:
- The red is the graph of g(x)
- The blue is the graph of f(x)
- f(x) = 3g(x)
Answer: the answer is b
Step-by-step explanation:i did the test yourself on algebra nation
PLEASE HELP ME!!
Micah rolled a number cube 30 times, and displayed her results in the table below.
N F Number Frequency
1 7
2 3
3 6
4 5
5 4
6 5
Which numbers appeared LESS that the theoretical probability? ( there ie more than one answer)
¤ 1
¤ 2
¤ 3
¤ 4
¤ 5
¤ 6
Answer:
2,5 appeared LESS
Step-by-step explanation:
the theoretical probability in this case would be 5 because Micah rolled the number cube 30 times and there is 6 total outcomes of the number cube.
To figure out the theoretical probability:
30 divided by 6
= 5
So every number that appeared less than 5 is your answer
I believe the answer is 2,5
help me please asap!!!!!!!!!!!
Answer:
[tex]4q^2 + 12q + 9[/tex]
Step-by-step explanation:
To simplify the expression, use the distributive property to write the expanded form of the quadratic.
[tex](2q+3)^2\\(2q+3)(2q+3)\\4q^2 + 6q + 6q + 9\\4q^2 + 12q +9[/tex]
Determine the length of arc JL.
A)
59
12
π
B)
5
6
π
C)
13
12
π
D)
13
6
π
Answer:
c
Step-by-step explanation:
The solution is
13
12
π. To calculate the arc length use the following formula:
Arc Length=
m(ARC)
360
· 2πr
A pizza places for drivers to deliver their pizzas. The average mileage for each car is between 21 and 24 miles per gallon. Each driver travels between 79 miles and 89 miles a day. The pizza shop estimates that they will need about 10 gallons of fuel a day for all the vehicles. Is this a reasonable estimate?
A: No, the estimate should be higher.
B: Yes, the estimate is reasonable.
C: No, the estimate should be lower.
I believe the estimate should be higher
Answer:
A. No, the estimate should be higher.
Step-by-step explanation:
Given f(x) = -3x-7 and g(x) = x^4, choose the expression for (f*g)(x)
Answer:
Step-by-step explanation:
f(x) =-3x - 7
f(g(x)) = -3*g(x) - 7
f(g(x)) = -3*x^4 - 7
bottom left.
ANSWER
[tex](f\circ g)(x) = - 3 {x}^{4} - 7[/tex]
EXPLANATION
It was given that;
[tex]f(x) = - 3x - 7[/tex]
and
[tex]g(x) = {x}^{4} [/tex]
We want to find the composite function,
[tex](f\circ g)(x) = f(g(x))[/tex]
[tex](f\circ g)(x) = f( {x}^{4} )[/tex]
We plug in x⁴ into f(x)=-3x-7 to obtain:
[tex](f\circ g)(x) = - 3 {x}^{4} - 7[/tex]
You are re-tiling the entry to your home and want to create a fancy circular medallion in the center. You want to create a large circle with a smaller circle centered inside. You want to tile the large circle with blue tile and the smaller circle with yellow tile. The circumference of the large circle is 113.097 inches and the radius of the smaller circle is 7 inches. How much blue tile do you need (in square inches)?
Answer:
Are needed [tex]863.5\ in^{2}[/tex] of blue tile
Step-by-step explanation:
we know that
To find how much blue tile do you need, subtract the area of the smaller circle from the area of the large circle
step 1
Find the radius of the large circle
The circumference of the circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=113.097\ in[/tex]
substitute and solve for r
[tex]113.097=2\pi r[/tex]
[tex]r=113.097/(2\pi)[/tex]
assume
[tex]\pi=3.14[/tex]
[tex]r=113.097/(2(3.14))=18\ in[/tex]
step 2
Find the area of the large circle
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=18\ in[/tex]
substitute
[tex]A=\pi (18)^{2}=324\pi\ in^{2}[/tex]
step 3
Find the area of the smaller circle
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=7\ in[/tex]
substitute
[tex]A=\pi (7)^{2}=49\pi\ in^{2}[/tex]
step 4
Find the difference of the areas
[tex]324\pi\ in^{2}-49\pi\ in^{2}=275\pi\ in^{2}[/tex]
assume
[tex]\pi=3.14[/tex]
[tex]275(3.14)=863.5\ in^{2}[/tex]