Using the Pythagorean Theorem, it is found that:
A. The straight line distance between the school and the fire station is of 4.62 miles.
B. The distance between the school and the hospital is of 2.08 miles.
Pythagorean TheoremThe Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, the distance between the school and the fire station is the hypotenuse of a right triangle with sides 4.3 and 1.7, hence:
d² = 4.3² + 1.7²
d = sqrt(4.3² + 1.7²)
d = 4.62 miles.
The hospital is 3.1 miles west of the fire station, hence the distance between the school and the hospital is the hypotenuse of a right triangle of sides 1.7 and 4.3 - 3.1 = 1.2, hence:
d² = 1.2² + 1.7²
d = sqrt(1.2² + 1.7²)
d = 2.08 miles.
Missing informationThe complete problem is given by the image at the end of the answer.
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A hot air balloon is cruising at an altitude of 150 meters above the ground when it begins its descent. The balloon descends at a rate of 5.5 meters per minute. Write an equation to model when the balloon will reach an altitude of 95 meters above the ground. Use n to represent the unknown
150 - 5.5n= 95 equation to model when the balloon will reach an altitude of 95 meters above the ground.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that,
A hot air balloon is cruising at an altitude of 150 meters above the ground when it begins its descent.
The balloon descends at a rate of 5.5 meters per minute.
We need to write an equation to model when the balloon will reach an altitude of 95 meters above the ground.
The equation is 150 - 5.5n= 95
Hence 150 - 5.5n= 95 equation to model when the balloon will reach an altitude of 95 meters above the ground.
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Please see the picture below. I need parts A B and C
We are given a graph and we are asked to determine if it is a function or not. To do that we will use the vertical line test. We will draw a vertical line and if the line touches the graph in more than two places in any given value of "x" then it is not a function. Therefore, the vertical line we get is:
Since the vertical line touches the graph in two axes this means that the given graph is not a function.
30 POINTS!!!!! NEEDS HELP ASAP!!!!
The associative property of addition says you can change the______. of addends without affecting the sum.
A. grouping
B. operation
C. order
Answer:
C. order
Step-by-step explanation:
The associative property of addition allows you to change the of numbers without affecting the sum.
Answer: Grouping
Step-by-step explanation:
Changing the grouping of addends does not change the sum. For example, ( 2 + 3 ) + 4 = 2 + ( 3 + 4 ) (2 + 3) + 4 = 2 + (3 + 4) (2+3)+4=2+(3+4)left parenthesis, 2, plus, 3, right parenthesis, plus, 4, equals, 2, plus, left parenthesis, 3, plus, 4, right parenthesis.
Hello may you please help me
The value of x for the given triangle is 30°.
According to the question,
We have the following information:
We have a triangle.
Three angles of the triangle are x°, 65° and (x+55)°.
We know that the sum of all the three angles of a triangle is 180°.
So, the sum of these angles will be 180°.
Now, adding three angles:
x° + 65° + (x+55)° = 180°
(2x+120)° = 180°
2x = 180-120
2x = 60
x = 60/2 (2 was in the multiplication on the left hand side. So, it is in the division on the left hand side.)
x = 30°
Hence, the value of x in the angles of the given triangle is 30°.
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how to find n(A-B)
q no 9 ii
sure branliest
Answer: 11
Step-by-step explanation:
[tex]A-B=\{2\}[/tex].
Since there is 1 element in this set, the answer is 1.
PLEASEE HELPPP!!! 30 POINTSSS
Create a system of equations and use algebra
To write a quadratic equation for each set of three points that lie on a parabola.
(5-6), (-2,8), (3,4)
(1,17), (-1,-9), (2,105)

The system of quadratic equations obtained on solving general equation of parabola are
a. 5=36a - 6b +c
-2=64a+8b+c
3=16a+4b+c
b. 1=289a+17b+c
-1=81a-9b+c
2=11025a+105b+c
the equation parabola
the general equation of Parabloa is written as-
y=a[tex]x^{2}[/tex]+bx+c
if the parabola passes through the point. then this point must satisfy the equation of the parabola. so, by putting the value of points we get a set equations-
5=a[tex]6^{2}[/tex]+b(-6)+c
5=36a - 6b +c
and for other two points we get equations
-2=64a+8b+c
and 3=16a+4b+c
and for other three points we get the equations
1=289a+17b+c
-1=81a-9b+c
2=11025a+105b+c
so on solving we get these three set of quadratic equations.
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Solve for d.
4d - 5 = 11
Answer:
d = 4
Step-by-step explanation:
4d - 5 = 11
a) Subtract 5 from both sides.
-5 + 5 = 11 + 5
4d = 16
b) Divide both sides by 4.
4d/4 = 16/4
16/4 = 4
Therefore, you're answer will be 4.
the variance inflation factor (vif) is another measure that can detect a high correlation between three or more predictor variables even if no pair of predictor variables has a particularly high correlation. what is the smallest possible value of vif? (absence of multicollinearity).
Variance inflation factor can have a value as low as one (absence of multicollinearity). A VIF number greater than 5 or 10 generally denotes collinearity that is problematic.
The variance of bj is not inflated at all if the VIF is 1, which indicates that there is no association between the jth predictor and the other predictor variables.
VIF equal to 1 signifies that there is no correlation between the variables. A VIF of 1 to 5 indicates a moderate correlation between the variables. Variables are highly linked when the VIF is greater than correlated2.
VIF = 1.0 if all independent variables are orthogonal to one another. VIF = infinity if there is perfect correlation.
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a researcher uses an established behavioral observation measure to collect antisocial behavior scores for a group of elementary school children. the sample mean is 20 and the standard deviation is 3. on the z-score metric, what is the standard deviation of the behavior scores?
On the z-score metric, the standard deviation of the behaviour scores is 3.
It is given that a researcher uses an established behavioral observation measure to collect antisocial behavior scores for a group of elementary school children.The sample mean is given to be equal to 20.A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is sometimes referred to as the "average."The standard deviation is given to be equal to 3.The standard deviation is a statistical metric that determines how much a bunch of values deviate from the mean.To learn more about standard deviation, visit :
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Britany is bringing birthday cake and cookies to her office. She has already spent $10.00 on the cake. Cookies cost $0.70 each, and she does not wish to spend more than $34.50 for all desserts. If x represents the number of cookies she can buy, which of the following inequalities symbolizes this situation?
A.
$10.00x + $0.70 < $34.50
B.
$0.70x + $10.00 < $34.50
C.
$0.70x + $10.00 < $34.50
D.
$10.00x + $0.70 < $34.50
Considering the definition of an inequality, the correct answer is option C. the inequiality $0.70x + $10.00 < $34.50 symbolize this situation
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.The solution of an inequality is the set of numbers that make the inequality true.
Inequality in this caseIn this case, you know that:
Britany has already spent $10.00 on the cake. Cookies cost $0.70 each. She does not wish to spend more than $34.50 for all desserts.Being "x" the number of cookies Britany can buy, the inequality that expresses the previous relationship is
10 + 0.70x <34.50
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in the diagram measure angle ACB=61 find measure angle ACEMeasure of angle ACE=...°
From the figure, angle ACB anf angle BCD are complementary, that is,
∠ACB + ∠BCD = 90°
Replacing with data
61° + ∠BCD = 90°
∠BCD = 90° - 61°
∠BCD = 29°
From the picture, angle BCD and angle FCE are vertical angles, then they are congruent, which means that:
∠FCE = ∠BCD = 29°
Angle FCA is a right angle, that is, ∠FCA = 90°. Therefore:
∠FCE + ∠FCA = ∠ACE
29° + 90° = ∠ACE
119° = ∠ACE
Triangle EFG is dilated by a scale factor of 2 centered at (0, 2) to create triangle E′F′G′. Which statement is true about the dilation?
Answer:Triangle EFG is dilated by a scale factor of 2 centered at (0, 2) to create triangle E'F'G'. Which statement is true about the dilation? segment EG ≅ segment E prime G prime. The slope of segment EF is the same as the slope of segment E prime H prime.
Step-by-step explanation:
Twenty years ago a small town in texas had a population of 10,000. the population has increased 8% each year since then. what equation would be used to solve this population growth problem? a. p = 20 (10,000) superscript .08 b. p = 10,000 (8) superscript 20 c. p = 10,000 (20) superscript 1.08 d. p = 10,000 (1.08) superscript 20
The correct answer for the given problem is option (D) .
growth rate in the initial population of 1.08.. So, the equation for solving this population growth problem is 10,000(1.08) ²⁰
Before twenty years, the actual population was 10,000.
Population growth per year = 8% = ((100+8)10,000)/100=10,800.
So, there will be an addition of 800 people to the population every year.
After a period of twenty years, the total population was 10,000 + 19×(800) = 25,200.
Population for t years = (Initial Population)× (Growth or Decay Rate)×time
Using the above population increment formula,
Time( in years) ----->Population
0------>10000
1------->10000 (1.08)
2------->10000(1.08)(1.08)
3------->10000(1.08)(1.08)(1.08)
------------------
n ----->10000(1.08)
Here, we are required to have a population after 20 years, i.e., n= 20. The required equation, which is used for solving population growth problem, is 10000(1.08)²⁰
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3. Use the following map to calculate distance between the cities. Calculate the distance between Brookline and Charleston.
Each exterior angle measure is one eighth the measure of each interior angle??
Answer:
Exterior angle = 20 degrees
Interior angle = 160 degrees
================================================
Explanation:
The phrasing "Each exterior angle measure is one eighth the measure of each interior angle" means,
exterior = (1/8)*(interior)
That rearranges to
interior = 8*(exterior)
Let's say x is the measure of the unknown exterior angle. That makes 8x the measure of the interior angle
The two must add to 180 to form a straight line.
interior + exterior = 180
8x + x = 180
9x = 180
x = 180/9
x = 20 is the measure of the exterior angle
8x = 8*20 = 160 is the measure of the interior angle
Note how 160+20 = 180 to verify our answers.
need help on this, thanks
For the given parallel lines with transversal ,and the pair of interior angles 72° and (7x +24)°, the value of x = 12°.
As given in the question,
Two parallel lines with transversal are given.
72° and (7x +24)°are pair of interior angles
Simplify the given relation to get the value of x we have,
72° + (7x +24)° =180°
⇒ 7x + (72 +24)° =180°
⇒ 7x + 96° = 180°
⇒ 7x = 180° - 96°
⇒ 7x = 84°
⇒ x = 84° /7
⇒ x = 12°
Therefore, for the given parallel lines with transversal ,and the pair of interior angles 72° and (7x +24)°, the value of x = 12°.
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Christel House DORS is taking a field trip. Some students will travel in cars, which can carry 5 students, and others will travel in vans, which can carry 15 students. The equation 5(2)+15v=100 describes the relationship between the number of vans needed, v, and the number of students going on the trip. Which statement below is true?
Given,
5(2)+15v=00
where v is the number of vans.
Solving,
15v=90
v=6
Thus the correct answer is 6 vans are needed to transport students.
Write the linear equation in standard form.
y - 2 = 1/3(x + 6)
Answer: y=x/3 + 4
Step-by-step explanation:
distribute 1/3 to the (x+6): x/3 + 2add two to both sides: y=x/3 + 4
write the following number in standard form: nine hundred twenty-eight
In this kind of problem is better to work backwards. We have the number nine hundred twenty-eigh.
This means that the two last digits are a 2 and a 8, becasue we have a "twenty-eight" = 28
And then, we have "nine hundred" = 900
The number whole, then, is:
[tex]928[/tex]8y+9>1 need help soon
Answer:
y > -1
Step-by-step explanation:
8y+9 > 1
-9 -9
8y > -8
/8 /8
y > -1
Find the m
bisector.
Answer: [tex]50^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle FDE=25^{\circ}+25^{\circ}=50^{\circ}[/tex]
I WILL GIVE YOU BRAINLIST Show your work
11/2 divide by 3/4
∠A and \angle B∠B are complementary angles. If \text{m}\angle A=(6x+2)^{\circ}m∠A=(6x+2)
∘
and \text{m}\angle B=(4x+18)^{\circ}m∠B=(4x+18)
∘
, then find the measure of \angle A∠A.
The measure of ∠ A is 44 degrees.
Given that:-
∠ A and ∠ B are complementary angles.
∠ A = (6x +2) degrees
∠ B = (4x + 18) degrees
We have to find the measure of ∠ A.
We know that the sum of two complementary angles is 90 degrees.
Hence, we can write,
(6x + 2) + (4x + 18) = 90
(6x + 4x) + (2 + 18) = 90
10x + 20 = 90
10x = 90 - 20
10x = 70
x = 70/10
x = 7 degrees
Hence,
∠ A = 6*7 + 2 = 42 +2 = 44 degrees.
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What is the equation of the line in slope-intercept form? 1,6 and 2,-6
The equation of the line in slope-intercept form would be; y = -12x + 18
How to get the slope-intercept form of a straight-line equation?If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:
y = MX +c
To find the slope of a line, we the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.
We have been given the point (1,6) and (2,-6)
y-y₁ = m(x-x₁)
m = (-6-6)/(2 -1)
m = -12/1
Now substitute;
y-y₁ = m(x-x₁)
y- 6 = -12(x- 1)
y- 6 = -12x + 12
y = -12x + 18
Hence, the equation of the line in slope-intercept form would be; y = -12x + 18
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Jan uses 78 yard of fabric for one quilt square and 17 yard in another. how much fabric has jan used? responses 914 of a yard 9 over 14 of a yard 618 yards 6 and 1 eighth yards 756 of a yard 7 over 56 of a yard 1156 yards
Based on the yards of fabric used by Jan for the quilt squares, the total fabrics used by Jan was 1 ¹ / ₅₆ yards
How to find the number of yards used?The yards of fabric used by Jan were 7 / 8 of a yard and 1 / 7 of another yard.
The total yards used by Jan can be found by adding these fractions up. To add both fractions, you first need to find the common denominator of 8 and 7 which is 56.
Then the numerators can be found by dividing 56 by the denominator and then multiplying the numerator by the result.
Fraction 7 / 8 yards:
= 56 / 8 x 7
= 49 / 56
Fraction 1 / 7:
= 56 / 7 x 1
= 8 / 56
The total number of yards used is:
= 49 / 56 + 8 / 56
= 57 / 56
= 1 ¹ / ₅₆ yards
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what is the size of the angle between north west and south east?
180°
Step-by-step explanation:Size of the angle between:North and South: 180°East and West: 180°North East and South West: 180°North West and South East: 180°North West and North East: 90°South West and South East: 90°P(3,-3) Q(8,7) R(5,-2)
Given S(11,1) is a point which lies on the extended line PR where QS is a perpendicular line to PRS. Find the area of triangle PQR.
Answer: the area of triangle PQR is 7.5 square units
Step-by-step explanation:
[tex]\displaystyle\\A_{PQR}=\frac{PR*QS}{2} \\\\1.\ (3,-3)\ \ \ \ \ (5,-2)\\\\PR=\sqrt{(5-3)^2+(-2-(-3))^2}\\\\PR=\sqrt{2^2+(-2+3)^2} \\\\PR=\sqrt{4+1^2} \\\\PR=\sqrt{4+1}\\\\ PR=\sqrt{5} \ units[/tex]
[tex]\diplaystyle\\2.\ (8,7)\ \ \ \ \ (11,1)\\\\QS=\sqrt{(11-8)^2+(1-7)^2} \\\\QS=\sqrt{3^2+(-6)^2} \\\\QS=\sqrt{9+36} \\\\QS=\sqrt{45}\\\\QS=\sqrt{9*5} \\\\QS=\sqrt{3^2*5} \\\\QS=3\sqrt{5}[/tex]
[tex]\displaystyle\\Hence,\\A_{PQR}=\frac{\sqrt{5}*3\sqrt{5} }{2} \\\\A_{PQR}=\frac{(\sqrt{5}*\sqrt{5}) *3 }{2} \\\\A_{PQR}= \frac{5*3}{2}\\\\A_{PQR}=\frac{15}{2}\\\\A_{PQR}=7.5 \ units^2[/tex]
A dozen ears of corn for $5. find the unit rate
answer please and look at the pic
Answer: slope = [tex]\frac{y}{x}[/tex]
Step-by-step explanation:
Slope means gradient which is given by change in y
change in x
on the graph, change in y = 100-0 = 100
change in x = 95-45 = 50
so, gradient is 100/50
= 2
Mrs. Frank asks four of her students to measure four different objects. Here are the results.
Which student had the greatest percent error?
The student that has the greatest percent error is Ebony.
How to calculate the percentage error?The percentage error will be calculated as:
= Change in value / Initial values × 100
From the table, we can see that Ebony had the greater difference in values. This will be illustrated as:
= (Measured length - Actual length) / Actual length × 100
= (2.1 - 1.6)/1.6 × 100
= 0.5 / 1.6 × 100
= 31.25%
Ebony had the higher percentage error.
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