The pedestrian route that runs diagonally across the park will be [tex]6\sqrt{10}[/tex] miles long.
Here, we are given that a rectangular park is 18 miles long and 6 miles wide.
As we know that the angles formed by any two adjacent sides of a rectangle are all 90°, the diagonal divides the rectangle into 2 right angled triangles.
One side of the right angled triangle will be 18 miles and another side will be 6 miles.
According to the Pythagoras theorem,
[tex]hypotenuse^{2} = base^{2} + height^{2}[/tex]
Here, the diagonal will be the hypotenuse as it is the side opposite the right angle.
Hence we get the following equation-
[tex]hypotenuse^{2} = 18^{2} + 6^{2}[/tex]
[tex]hypotenuse^{2}[/tex] = 324 + 36
[tex]hypotenuse^{2}[/tex] = 360
Hypotenuse = [tex]\sqrt{360}[/tex]
Hypotenuse = [tex]6\sqrt{10}[/tex]
Thus, the pedestrian route that runs diagonally across the park will be [tex]6\sqrt{10}[/tex] miles long.
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(−x
2
−2x−2)(x
2
+x−3)
The expression is simplified -x^4 -3x³ -x² + 4x + 6
What are algebraic expressions?
Algebraic expressions are expressions consisting of variables, constants, factors and coefficients.
They are also made up of arithmetic operations such as addition, subtraction, multiplication, division, etc
Given the expression:
(-x² - 2x - 2) (x² + x - 3)
expand the bracket
-x^4 - x³ + 3x² -2x³ - 2x² +6x - 2x² - 2x + 6
collect like terms
-x^4 - x³ - 2x³ + 3x² - 2x² - 2x² + 6x - 2x + 6
Add or subtract like terms
-x^4 -3x³ -x² + 4x + 6
The expansion of the expression is -x^4 -3x³ -x² + 4x + 6
Hence, the expression is simplified -x^4 -3x³ -x² + 4x + 6
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all combinations from 0-9 that equals 0
A traffic helicopter flew directly from Point A to Point B in 8 minutes. Did the helicopter travel faster or slower than the driver? Explain or show your reasoning.
The time it takes the driver to travel from Point A to Point B is 8 minutes, the same as the helicopter but through a more longer path, such that, we have;
The helicopter travels slower than the driverHow can the speed of the helicopter and the car be compared?Based on a similar question, the first part required to determine if a driver that drives from Point A to Point B in 8 minutes obeyed the speed limit of 55 miles per hour.
The path of the driver consists of a short path, a bend changing the direction, then a long straight path.
The path of the helicopter is directly from Point A to Point B.
Therefore;
The length of the path of the driver, d1, is longer than that the helicopter, d2, which gives;
d1 > d2
From kinematics, we have;
[tex]Speed = \frac{Distance}{Time} [/tex]
The time taken by the helicopter and the and the driver are equal to 8 minutes, therefore;
[tex] Speed \: of \: the\: driver = \frac{d_1}{8} [/tex]
[tex] Speed \: of \: the \: helicopter = \frac{d_2}{8} [/tex]
[tex] d_1 > d_2 [/tex]
According to the division property of equality, we have;
[tex] \frac{d_1}{8} > \frac{d_2}{8} [/tex]
[tex] \frac{d_2}{8} < \frac{d_1}{8} [/tex]
Therefore;
The speed of the helicopter is lesser than the speed of the driver, which gives;
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Question 1 (Multiple Choice Worth 5 points)
(01.08 MC)
When a patient with hypertension takes a particular type of blood pressure medication, the effects on the systolic
145-6t if 0≤t≤5
pressure, S(t), can be measured by the following piecewise defined function: S(t)
115 if 5
52+7t if 9≤t≤12
where t is the time, in hours, since taking the medication. Based on the graph of the piecewise function, if the patient
takes the blood pressure medication at 7 a.m., in which interval will their systolic pressure be lowest?
O1 p.m. to 3 p.m.
4 p.m. to 6 p.m.
07 a.m. to 9 a.m.
10 am to 12 p.m.
P
The interval will their systolic pressure be lowest is 4p.m. to 6p.m.
Given that
the effects on the systolic
145-6t if 0≤t≤5
function: S(t)
115 if 5 52+7t if 9≤t≤12
where t= time
the blood pressure medication takes at 7 a.m.
first of all we have to nknow about the Interval.
What is interval?
An interval is a distinct measure of time or the physical or temporal distance between two things.
From the function given above, the lowest systolic pression can be seen from 5 and 8 hours after taken the medication.
Therefore, this will fall into or between the interval of 2pm to 5pm.
And as such, looking at the question, the option that best fit into this time range is 4pm to 6pm.
Therefore, Based on the above, the interval will their systolic pressure be lowest is 4pm to 6pm.
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the cuboid below is placed on a table.it exerts a pressure f 40 N/cm2. calculate the force exerted on the table.
Answer:
40 multiply by area of the table
Step-by-step explanation:
force = pressure * area of the table
Find the least common denominator (LCD) of 5/9 and 6/5.
Please help ASAP!!
Thanks in advance
Answer:
45
Step-by-step explanation:
5/9 = 24/45
6/5 = 54/45
5/9= 5/9× 5/5 = 25/45
6/5 = 6/5 × 9/9 = 54/45
Add or subtract use place-value blocks to help $1.33 - $0.35
Answer:
$0.98
Step-by-step explanation:
$1.33-$0.35=$0.98.
Answer:
The answer is 0.98 cents
Step-by-step explanation:
Hope it helps!
need answers for each question asap
All the questions have been solved in the above pictures 7,8,9,10,11,12 & 13
What is the equation of the line?
y = 4/3x
y = 3/4x
y = - 4/3x
y = - 3/4x
Answer:
y=-4/3x
Step-by-step explanation:
ans would be c y=-4/3x
Mark all identifiers that are included when identifying significant digits:
All nonzero digits are significant
Zeros at the end of a number to the right of a decimal point are significant
Zeros at the end of a number without a decimal point are assumed to be not significant
Zeros between two other significant digits are significant
Zeros to the left of the first nonzero digits in a decimal are not significant
All zeros are significant
The markers identified when identifying significant digits include:
All nonzero digits are significant.Zeros between two other significant digits are significantZeros to the left of the first nonzero digits in a decimal are not significantWhat are significant digits?Significant digits in mathematics refers to digits that are meaningful in mathematical calculations. This implies that their position and the quantity alters the value of the number. The particular digit and the position determines whether the digit is significant or not.
Instances of digits with their locations that are significant are:
All nonzero digits are significant.Zeros between two other significant digits are significantZeros to the left of the first nonzero digits in a decimal are not significant.Zeros at the end of a number without a decimal point are assumed to be significantThese instances results to significant digits while the instances below the digits are insignificant:
Zeros at the end of a number to the right of a decimal point are not significant Zeros at the in the front of a non zero digit are not significantRead more on significant digits here: https://brainly.com/question/24491627
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Solve: 1 4/5 x 5/6 =
Group of answer choices
1 3/11
15/30
1 2/3
1 1/2
The multiplication of given fraction is 1 4/5 x 5/6 = 1 1/2
In this question, we have been given an expression 1 4/5 x 5/6
We need solve given mathematical expression.
First we write improper fraction 1 4/5 as proper fraction.
1 4/5 = 9/5
So, given expression becomes,
1 4/5 x 5/6
= 9/5 x 5/6
= 9/6
= 3/2
Now we write 3/2 as improper fraction.
If we divide the 3 by 2,then we will get 1 as quotient and 1 as remainder.
3/2 = 1 1/2
Therefore, the multiplication of given fraction is 1 4/5 x 5/6 = 1 1/2
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if i get one point each 2 minutes how long until i get 50 points?
Like how long in time.
what is the range of h(x) = |x| − 2?
Answer: 69
Step-by-step explanation: 59+10=69
Identify the location of the values square root of 10, square root of 13, and twenty two ninths on the number line.
Number line with points plotted at two and four tenths labeled point A, three and two tenths labeled point B, and three and six tenths labeled Point C.
Point A is twenty two ninths, point B is square root of 10, and point C is square root of 13.
Point A is square root of 10, point B is square root of 13, and point C is twenty two ninths.
Point A is twenty two ninths, point B is square root of 13, and point C is square root of 10.
Point A is square root of 10, point B is twenty two ninths, and point C is square root of 13.
The location of the values square root of 10, square root of 13, and twenty two ninths on the number line will be A. Point A is twenty two ninths, point B is square root of 10, and point C is square root of 13.
How to calculate the square root?The square root of 10 will be 3.16
The square root of 13 will be 3.6
Twenty two ninths will be 22/9 = 2.44
Therefore, the location of the values square root of 10, square root of 13, and twenty two ninths on the number line will be Point A is twenty two ninths, point B is square root of 10, and point C is square root of 13.
In conclusion, the correct option is A.
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What is the slope of the line that passes through the points (2, 8) and (12, 20)?
Write your answer in simplest form.
Answer:
6/5
Step-by-step explanation:
m = (y_2 - y_1)/(x_2 - x_1) = (20 - 8)/(12 - 2) = 12/10 = 6/5
Angle A and angle B are complementary.
The measure of angle A = 3x+7. The measure of angle B=6x+11. Determine the measure of each angle.
The measure of angle A and angle B are 31° and 59° respectively.
What are complementary angles?Complementary angles that sum up to 90 degrees.
Given the angles as;
angle A = 3x+7angle B =6x+11We have that;
Angle A + Angle B= 90
Substitute the values
3x + 7 + 6x + 11 = 90
collect like terms
9x = 90 - 18
9x = 72
Make 'x the subject
x = 72/ 9
x = 8
Angle A = 3x + 7 = 3(8) + 7 = 31°
Angle B = 6x +11 = 6(8) + 11 = 59°
Thus, the measure of angle A and angle B are 31° and 59° respectively.
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Given Angle A and angle B are complementary, the measure of Angle A and angle B are 31° and 59° respectively.
What is the measure of each angle?complementary angles are angles that sum up to 90 degrees.
Given the data in the question;
Angle A and angle B are complementaryMeasure of angle A = 3x + 7measure of angle B = 6x + 11Numerical measure of each angle = ?Since complementary angles sum up to 90 degrees.
Measure of angle A + Measure of angle B = 90°
Plug in the given values and solve for x.
(3x + 7) + (6x + 11) = 90
Collect like terms
3x + 6x + 11 + 7 = 90
9x + 18 = 90
Subtract 18 from both sides
9x + 18 - 18 = 90 - 18
9x = 72
x = 72/9
x = 8
Hence;
Measure of angle A = 3x + 7 = 3(8) + 7 = 24 + 7 = 31°
Measure of angle B = 6x + 11 = 6(8) + 11 = 48 + 11 = 59°
Given Angle A and angle B are complementary, the measure of Angle A and angle B are 31° and 59° respectively.
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Identify the range of the function y=-3x+6 when the domain is {-1,2,4}
A. {-6,0,9}
B. {-9}
C. {3,-12,-18}
D. {-3,12}
E. {-6,9}
Select the correct answer. Which graphs represent functions?
Answer:
Graph D
Step-by-step explanation:
Graphs that represent functions have to correlate with each other in some way so it has to be either linear or non-linear so Graphs B and C are out of the question
To find the graph that represents a function you do the vertical line test which is when you draw a line though the x-axis and as soon as two or more points are on the same line it is no longer a function so graph a is out
By proess of elimination the function is graph D
The length of a rectangular playground is 3x−2 feet while the width is 5x +12 feet. The perimeter of the playground is
The perimeter of the playground is 16x + 20
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as;
P = 2(l+w)
Given the following
l = 3x-2
w = 5x+12
Substitute to have:
P = 2(3x-2+5x+12)
P = 2(8x + 10)
p = 16x + 20
Hence the perimeter of the playground is 16x + 20
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Find the slope of the following lines
Explain how you got the answer
[tex]-\displaystyle\frac{4}{3}[/tex]
Step-by-step explanation:Slope describes the change in y divided by the change in x.
Solving Using Slope Formula
One way to find slope when you are given 2 points is the slope formula.
Slope = [tex]\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex]To solve, plug in the x and y-values and simplify. For this question, let (-2, 3) represent the (x₂, y₂) and (1, -1) represent (x₁, y₁).
[tex]\displaystyle\frac{3-(-1)}{-2-1}=-\frac{4}{3}[/tex]This shows that the slope of this line is -4/3.
Solving Through Counting
When given the graph of a function, you can also count out the slope. Starting from the left point, count the change in y-values and the change in x-values. Remember, when the y-values decrease, the change should be negative. The y-value changes by -4 and the x-value changes by +3.
Since the slope is change in y over change in x, the slope is -4/3.
Which statement does not belong with the other three?
Responses ⬇️
If today is Tuesday, then tomorrow is Wednesday.
If today is Tuesday, then tomorrow is Wednesday.
If it is Independence Day, then it is July.
If it is Independence Day, then it is July.
If an angle is acute, then its measure is less than 90°.
If an angle is acute, then its measure is less than 90°.
If you are an athlete, then you play soccer.
If you are an athlete, then you play soccer.
Question 2
Explain your reasoning.
This statement does not belong with the other three because it is ⬇️.
True
False
Conditional statement
Not a conditional statement
Answer:
If you are an athlete, then you play soccer
Step-by-step explanation:
This statement is not true as you can be an athlete and play football, run, etc. You could play soccer but this sentence is implying that you do play soccer. It is also not a conditional statement. A conditional statement is "If A then B".
You can walk 4/5 of a mile in 1/4 of an hour (15 minutes). How far can you walk in an hour?
Answer:
0.2
Step-by-step explanation:
Multiply 4/5 and 1/4: Decimal form
.8 • .25
Answer:
3.2 miles in one hour
Step-by-step explanation:
You can walk 4/5 of a mile in 1/4 of an hour (15 minutes). How far can you walk in an hour?
If you can walk 4/5 of a mile in 1/4 of an hour the equation would be:
4/5x = 1/4
multiply both sides by 4:
4(4/5x) = 4(1/4)
3.2 miles per 1 hour
The volume of dry goods, like apples or peaches, can be measured usings bushels, pecks, and quarts. A bushel contains 4 pecks, and a peck contains 8 quarts.
What is the relationship between number of bushels, b, and the number of quarts, q? If you get stuck, try creating a table.
The relationship between the number of bushels and the number of quarts is b = 32q.
What is the relationship?The mathematical operation that would be used to determine the required value is multiplication. Multiplication is the process of determining the product of a number. The sign used to represent multiplication is x.
The equation that represents the relationship between bushel and pecks is: b = 4p
The equation that represents the relationship between a peck and quarts is: p = 8q
In order to determine the relationship between bushels and quarts, substitute for p in the first equation
b = 4(8q)
Expand the bracket : b = 4 x 8q
b = 32q
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Answer all these questions, and I will give you brainly + 50 Points.
Answer: I don’t see a attachment if you edit and add one I will come back to edit.
Step-by-step explanation:
D. 153 Jenny bought 3/4 kg of margarine. She will use 2/3
of it for her hotcake recipe. How much of Margarine
did she use?
Answer:
1/2
Step-by-step explanation:
2/3 x 3/4 = 6/12 =1/2
Find the value of x in each case
Answer: x = 23
Step-by-step explanation:
Angle in a X shape, the two 'opposite' eachother must be the same so angle HGC is 14
Angle in a Z shape where the lines of the Z are parralell, the two innercorner angles of the Z must be the same os angle GCE must be 14
In triangle GEC we now know two out of the three angles 78 and 14 and we know that angles in a trianlge add up to 180 so the missing angle GEC must be 180-78-14=88
Angles on a straight line must add up to 180 so 4x+88=180
Then this can be used to figure out x
4x+88=180
4x = 92
x = 23
Write 7,250,000,000 in scientific notation.
725 × 10−7
725 × 107
7.25 × 10−9
7.25 × 109
Answer:
7.25 x 10⁹
Step-by-step explanation:
The steps are as follows:For 7,250,000,000 , you have to move 9 places to the left to get 7.25 so the number in scientific notation is 7.25 x 10⁹
What is the measurement of this angle?
Answer:
80 degrees
Step-by-step explanation:
80 degrees because part of it is on zero and the other part is on 80 so 80-0=80 degrees,
you find a treasure map Angle is 55 A to B 7 A to C 12
Answer:
55 A
Step-by-step explanation:
The perimeter of the entire garden.