Answer:
Part A) The length of a straight line between the school and the Fire Station is [tex]4.6\ miles[/tex]
Part B) The length of a straight line between the school and the hospital is [tex]2.1\ miles[/tex]
Step-by-step explanation:
The complete question in the attached figure
Let
The positive x-coordinates ----> East
The positive y-coordinates ----> North
The negative x-coordinates ----> West
The negative y-coordinates ----> South
take the point A (0,0) as the Middle School (reference point)
Part A) we have
Town Hall is located 4.3 miles directly east of the Middle School
so
The coordinates of Town Hall are B(4.3,0)
The Fire Station is located 1.7 miles directly North of Town Hall
so
The coordinates of Fire Station are C(4.3,1.7)
What is the length of a straight line between the school and the Fire Station?
Remember that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
A(0,0) and C(4.3,1.7)
substitute
[tex]d=\sqrt{(1.7-0)^{2}+(4.3-0)^{2}}[/tex]
[tex]d=\sqrt{(1.7)^{2}+(4.3)^{2}}[/tex]
[tex]d=4.6\ miles[/tex]
Part B) we have that
The hospital is 3.1 miles west of the fire station
so
The coordinates of the hospital are D(4.3-3.1,1.7)
D(1.2,1.7)
What is the length of a straight line between the school and the hospital?
Remember that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
A(0,0) and D(1.2,1.7)
substitute
[tex]d=\sqrt{(1.7-0)^{2}+(1.2-0)^{2}}[/tex]
[tex]d=\sqrt{(1.7)^{2}+(1.2)^{2}}[/tex]
[tex]d=2.1\ miles[/tex]
Using both the rotation matrices earlier in this lesson and your matrix calculator, find each determinant.
det= [ -1 0
0 -1 ]
det= [ 0 1
-1 0 ]
Answer:
both are one
Answer:
det = 1 and det = 1
Step-by-step explanation:
just took the lesson on ed-genuity, these are both right :)
When you are multiplying, does the order of the factor matters??
Answer:
no
Step-by-step explanation:
communitive propery unless there are ( )
If it is only multiplication, no it does not, but you should always go from left to right.
What is the measure of ABC?
A. 45°
O B. 60°
O c. 120
O D. 75
Answer:
It is gonna be B not very sure
Answer:
b.60
Step-by-step explanation:
tell me if there's is a outlier in these numbers please
20,24,58,59,63,63,65,66
Answer:
the outlier is 20 and 24
Step-by-step explanation: An outlier, in mathematics, statistics and information technology, is a specific data point that falls outside the range of probability for a data set. In this Case 20 and 24 are outliers because they are not in the range of 58, 59, 63, 63, 65, 66. :) your welcome.
Example 1: Find the lateral area of the regular rectangular pyramid.
5 cm
Step 1: Identify the base. Draw it to help find the perimeter of it.
2.5 cm
"regular rectangular" means
all sides are
P= 4(2.5cm) =
cm
2.5 cm
Step 2: Identify the slant height of the pyramid, height of the lateral face of the pyramid.
I=
cm
Step 3: Substitute "P" and "l' into the lateral area formula.
L=P7
Answer:
the answer should be 2.5
To find the lateral area of the given rectangular pyramid, calculate the perimeter of the base, determine the slant height using the Pythagorean theorem, and then apply the lateral area formula. The lateral area is approximately 45.4 cm².
To find the lateral area of a regular rectangular pyramid with base edge length 2.5 cm and height 9 cm, follow these steps:
Identify the base: The base is a square with each side measuring 2.5 cm. The perimeter (P) of the base can be calculated as follows:Thus, the lateral area of the pyramid is approximately 45.4 cm².
PLEASE HELP ME ASAP WILL NAME YOU BRAINIEST
Answer:
A) resturant is at (-4,5)
A)the equation is: [tex](x-0)^2+(y-0)^2=6^2[/tex]
B) Consuela can get free delivery
Step-by-step explanation:
see picture
If the discriminate is less than zero, the quadratic will have:
A) one solution
B) no real solution
C) 2 Solutions
D) infinity many solutions
If discriminate is less than zero, the quadratic will have no real solution.
Answer: B
Divide and simplify your answer
2 1/2 divided by 3 3/4
Answer:
2/3
Step-by-step explanation:
Calculators help :)
To divide 2 1/2 by 3 3/4, convert the mixed numbers to improper fractions, change division to multiplication of the inverse, multiply, and simplify the result to 2/3.
To divide and simplify the expression 2 1/2 divided by 3 3/4, we begin by converting the mixed numbers into improper fractions. The mixed number 2 1/2 becomes 5/2 (2 times 2 + 1), and 3 3/4 becomes 15/4 (3 times 4 + 3).
Next, we use the rule for dividing fractions: invert the second fraction and change the division to multiplication. Therefore, the division becomes 5/2 times 4/15. We can now multiply the numerators together and the denominators together, resulting in 20/30.
To simplify, we can reduce the fraction by dividing both the numerator and the denominator by the greatest common factor, which is 10. Simplifying gives us 2/3, the final answer.
What is X equal to in the equation
Answer:
x=10
Step-by-step explanation:
8x+30=110
8x+30-30=110-30
8x=80
8x/8=80/8
x=10
hope this helps
please mark me brainliest it would help(✿◠‿◠)
Answer:
10 =8
Step-by-step explanation:
The two angles are vertical angles and we know that vertical angles are equal
110 = 8x +30
Subtract 30 from each side
110-30 = 8x+30-30
80 = 8x
Divide each side by 8
80/8 = 8x/8
10 =8
what is a parabola in mathamatics
Answer:
a parabola is a curve often resembling a U and follows a mathematical equation
Step-by-step explanation:
for example:
Answer:
In mathematics, a parabola is a plane curve
Step-by-step explanation:
Which percent is equivalent to 2 and StartFraction 5 over 6 EndFraction?
2.56%
2.8ModifyingAbove3 with bar%
256%
283.ModifyingAbove3 with bar%
Answer:
B.
Step-by-step explanation:
Sorry I am late. Here's the answer for everybody else. :)
To convert 2 and 5/6 to a percent, convert the fraction to a decimal and add it to the whole number. Then multiply by 100 to find the percentage (approximately 283.3%).
Explanation:In mathematics, to convert a mixed number like 25/6 to a percentage, you can first convert it to a decimal and then multiply by 100. The fraction can be converted into decimal by dividing the numerator by the denominator. In this case, 5 divided by 6 is approximately 0.8333. Since we have 2 whole and 0.8333, we can add them to get approximately 2.8333. By multiplying this by 100, we get 283.33% which we can take as an approximate value of 283.3% because it's the closest listed option in the question.
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The polynomial p(x) = x3 + 3x2 - 4 has a known factor of (1 - 1).
Rewrite p(x) as a product of linear factors.
Answer:
34
Step-by-step explanation:
Factor the expression completely.
[tex] {8x}^{2} - 18[/tex]
O A. 2(2x - 3)(2x - 3)
O B. 2(42 - 9)
O C. 2(2x+3)(2x-3)
O D. 2(4x + 3)(x - 3)
Answer:
C. 2(2x + 3)(2x - 3)
Step-by-step explanation:
[tex]8 {x}^{2} - 18 \\ = 2 \times 4 {x}^{2} - 2 \times 9 \\ = 2(4 {x}^{2} - 9) \\ = 2 \{( {2x})^{2} - ( {3)}^{2} \} \\ = 2(2x + 3)(2x - 3) \\ [/tex]
Final answer:
The expression 8x² - 18 is factored by first taking out the common factor of 2, and then applying the difference of squares formula to get the fully factored form, 2(2x + 3)(2x - 3). Option C is accurate.
Explanation:
To factor the expression 8x² - 18, we need to first take out the common factor. Here, we can see that both terms are multiples of 2. Thus, we can factor out a 2, which gives us:
2(4x² - 9)
Now, we recognize that the expression inside the parentheses is a difference of squares because 4x² is (2x)² and 9 is 32. A difference of squares can be factored into:
(a² - b²) = (a + b)(a - b)
Applying this to our expression, we get:
2((2x) + 3)((2x) - 3)
Hence, the fully factored form of the expression 8x² - 18 is:
2(2x + 3)(2x - 3) (Option C)
Samuel and Christopher go to the movie theater and purchase refreshments for their friends.
Samuel spends a total of $34.00 on 6 bags of popcorn and 4 drinks.
Christopher spends a total of $66.25 on 12 bags of popcorn and 7 drinks.
Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
Using these equations, determine and state the price of a drink, to the nearest cent.
Answer:
Drink=5.75
Popcorn=1.83
Percentage for drink=75.9%
Step-by-step explanation
Let the popcorn be p
the drinks be d
6p+4d=34....(1)
12p+7d=66.25...(2)
Multiply (1) by 2
12p+8d=72....(3)
Substrate (2) from (3)
d=5.75
Substitute the value for d into (1)
6p+4(5.75)=34
6p+23=34
Substrate 23 from both sides
6p=11
Divide both sides by 6
p=1.83
So for one drink=$5.75
For one popcorn=$1.83
To determine the% for drink
5.75+1.83=7.58
5.75/7.58 ×100
575/7.58
75.858~75.9%
The percentage for drink is 75.9%
How do I Graph y= -1/4x+6.
Step-by-step explanation:
Use Desmos
EASY WAY TO GET POINTS!!!!
Answer:
Step-by-step explanation:
3ft x 5 ft x 6 ft
15 x 6 = 90 cubic feet
Step-by-step explanation:
To get the volume, you have to do LxWxH so its 3x5x6=90
so its 90 cubic feet.
Anybody know the answer??
Answer: m = 7 and b = 0
Step-by-step explanation:
y = mx + b is slope-intercept form
m = slope
b = y-intercept
You would put +0 on the end of the equation because it doesn't change anything
Helpppp y’all I need it quick ❗️
Answer:
14
Step-by-step explanation:
You fins the measure of angle C, and get 180-(118+22) = 40 degrees
You use law of sines, and get:
24/(sin40) = AC/(sin22)
Multiply both sides by sin(22)
24sin(22)/sin(40)=AC
Plug into a calculator, and get: 13.9868256738, which rounds to 14
Over 5 days 5,385 people went to Chick-Fil-A. If the same amount of people went each day, how many people went on one day?
Answer:
1077
Step-by-step explanation:
Write an equation of the line that passes through (1,2) and is perpendicular to the line y= 1/3x+4
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
For lines to be perpendicular, their slopes have to be the negative reciprocal of each other. (Basically flip the sign +/- and the fraction(switch the numerator and the denominator))
For example:
Slope = 2 or [tex]\frac{2}{1}[/tex]
Perpendicular line's slope = [tex]-\frac{1}{2}[/tex] (flip the sign from + to -, and flip the fraction)
Slope = [tex]-\frac{3}{4}[/tex]
Perpendicular line's slope = [tex]\frac{4}{3}[/tex] (flip the sign from - to +, and flip the fraction)
y = 1/3x + 4 The slope is 1/3, so the perpendicular line's slope is [tex]-\frac{3}{1}[/tex] or -3.
Now that you know the slope, substitute/plug it into the equation:
y = mx + b
y = -3x + b To find b, plug in the point (1, 2) into the equation, then isolate/get the variable "b" by itself
2= -3(1) + b Add 3 on both sides to get "b" by itself
2 + 3 = -3 + 3 + b
5 = b
y = -3x + 5
The equation of the line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4) is (y = -3x + 5) and this can be determined by using the given data.
Given :
The line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4).
The following steps can be used in order to determine the equation of the line:
Step 1 - When two lines are perpendicular to each other then their slopes are:
mm' = 1
where m and m' are the slopes of the lines.
Step 2 - So, the slope of the line which is perpendicular to the line (y = 1/3x + 4) is:
[tex]\rm \dfrac{1}{3}\times m' = -1[/tex]
m' = -3
Step 3 - Now, the equation of a line that passes through the point (1,2) and has a slope -3 is:
[tex]\rm (y -2) = -3(x-1)[/tex]
Step 4 - Simplify the above equation.
y = -3x + 5
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here are the scores that Jenna has received on her seven quizzes what is the upper quartile
Line C passes through the points (-3,-6) and (-1,-12). What is the slooe of the line perpendicular to the line C
Answer:
the answer is -1/3
Step-by-step explanation:
here is your step by step solution
Answer:
[tex]- \frac{1}{3} [/tex]
Step-by-step explanation:
The product of the gradients of perpendicular lines is -1.
Let the slope of the line perpendicular to line C be x.
(slope of Line C)(x)= -1
x= -1 ÷ (slope of Line C)
Let's find the slope of line C using the gradient formula.
[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]
Gradient of Line C
[tex] = \frac{ - 6 - ( - 12)}{ - 3 - ( - 1)} \\ = \frac{ - 6 + 12}{ - 3 + 1} \\ = \frac{-6}{ - 2} \\ = 3[/tex]
Thus substituting gradient of Line C= 3,
x= -1÷ (3)
x= [tex]- \frac{1}{3} [/tex]
The transformation T =
is applied the figure below.
What type of transformation of triangle ABC was applied by T?
rotate 180° counterclockwise about the origin
reflect across the line y = x
reflect across the line y=-x
rotate 270° counterclockwise about the origin
Answer:
See explanation
Step-by-step explanation:
You question is missing some necessary information.
However these are the mappings for the following transformation.
Rotate 180° counterclockwise about the origin. The mapping is
[tex](x,y)\to(-x,-y)[/tex]
Reflect across the line y=x.
The mapping is
[tex](x,y)\to(y,x)[/tex]
Reflect across the line y=-x
The mapping is:
[tex](x,y)\to(-y,-x)[/tex]
Rotate 270° counterclockwise about the origin. The mapping is
[tex](x,y)\to(-y,x)[/tex]
Hope this is helpful.
Please try post complete questions to get the exact answer you are looking for .
Answer:
reflect across the line y = –x (C)
Step-by-step explanation:
If you multiply the point 1,4 by the matrix you get -4, -1
it cant be 180 since that would make it -1,-4 not -4,-1.
y=x would mean its positive making it 4,1
y=-x would mean atleast -x is present and if you use other values it swaps x and y
270 would be x,-y
What is the radius of the cone?
An oblique cone has a height equal to the diameter of the
base. The volume of the cone is equal to 187 cubic units.
O
O
O
O
2 units
3 units
6 units
9 units
The radius of the oblique cone is; B: 3 units
What is the radius of the cone?
Formula for the volume of an oblique cone is;
V = ¹/₃πr²h
where;
V is volume
r is radius
h is height
We are told that diameter is equal to the height. Thus;
diameter = 2r = h
Thus;
V = ¹/₃πr²(2r)
18π = ¹/₃πr²(2r)
r = ∛(18π * 3/2π)
r = 3 units
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The radius of the cone is approximately 3 units.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is 1/3πr²h.
We have,
We know that the height of the cone is equal to the diameter of the base, which means h = 2r.
Substituting this into the formula for the volume, we get:
V = (1/3) x π x r² x (2r) = (2/3) x π x r³
We are given that the volume of the cone is 187 cubic units, so we can set up an equation:
(2/3) x π x r³ = 187
Multiplying both sides by 3/2π, we get:
r³ = (187 x 3)/(2π)
Taking the cube root of both sides, we get:
r = (187 x 3/(2π))^(1/3) ≈ 3.00
Therefore,
The radius of the cone is approximately 3 units.
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•Pls help
• 1/3cup olive oil
1/6 cup balsamic vinegar
a pinch of herbs
• a pinch of salt
Makes 6 servings
a. How many cups of salad dressing will this recipe make? Write an
equation to represent your thinking. Assume that the herbs and salt do
not change the amount of dressing.
b. If this recipe makes 6 servings, how much dressing would there be in
one serving? Write a number sentence to represent your thinking.
Answer:
The recipe makes 1/2 cup of salad dressing assuming that the salt and herbs do not make a difference. Each serving has 1/12 of a cup. I am not gifted in the number sentence and equation department
Step-by-step explanation:
1/3=2/6
+
1/6=1/6
--------------
3/6=1/2
The recipe will make 1/2 cup of salad dressing. Each serving would have 1/12 cup of dressing.
Explanation:To find out how many cups of salad dressing the recipe will make, we can add the quantities of olive oil and balsamic vinegar. We have 1/3 cup of olive oil and 1/6 cup of balsamic vinegar, so the total is 1/3 + 1/6 = 1/2 cup. Therefore, the recipe will make 1/2 cup of salad dressing.
To determine how much dressing there would be in one serving, we divide the total quantity of dressing (1/2 cup) by the number of servings (6). This can be represented as the number sentence: 1/2 ÷ 6 = 1/12 cup per serving.
Help me please with math
Let's make a table of differences
0 3 8 15 24
3 5 7 9
2 2 2
Constant second difference means a quadratic polynomial,
f(n)=an² + bn +c
f(1)=0, f(2)=3, f(3)=8
0 = a+b+c
3 = 4a + 2b + c
8 = 9a + 3b + c
Subtracting pairs
3 = 3a+b
5 = 5a + b
Subtracting,
2 = 2a
a = 1
b = 5 - 5a = 0
c = -a-b = -1
f(n)=n² -1
Duh, shoulda noticed that at the beginning.
f(17)=17²-1 = 288
a₁ =5
aₙ = aₙ₋₁ - 7
aₙ = a₁ + d(n-1)
aₙ = 5 - 7(n-1)
a₇ = 5 - 7(6) = -37
Answer: -37
45 books represent 5% of total books at library 2.
1.
Mrs. Henderson sells houses. She gets a
5% commission on all sales. How much
commission would she make on a house
that sells for $180,000?
a. $1800
b. $9000
c. $18,000
d. $90,000
Answer:
b. $9000
Step-by-step explanation:
Quick way of doing this:
10% is one-tenth. 10% of $180,000 is $18,000.
5% is half of 10%, so it's half of $18,000.
Answer: b. $9000
Conventional way of doing this:
To find a percent of a number, multiply the percent by the number. To change the percent to a decimal, move the decimal point of the percent two places left.
5% of $180,000 = 5% * $180,000 = 0.05 * $180,000 = $9,000
Answer: c. $9000
Mrs. Henderson's commission for selling a house worth $180,000 is $9000.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Mrs. Henderson sells houses. She gets a 5% commission on all sales.
∴ His commission for selling a house worth $180,000 is 5% of $180,000 which is,
=(5/100)×180000.
= $9000.
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Compare 2.95 to 2.949
Answer:
2.95 is bigger
Step-by-step explanation:
Always remember that each place after the integer in a decimal spot ends are all 0's.
This helps when we are comparing decimals.
In that case we really have:
2.9500 and 2.9490
Since 9500 is bigger than 9490, we can see that the one's digits are the same.
Since they are, 2.95 is the bigger number.
PLEASE ANSWER I NEED HELP WITH NUMBER 6 AND 7!!