Answer:
He hiked 10 miles.
Step-by-step explanation:
rate x time = distance
The distance up and the distance down are equal
3 mi/1 hr x (h hours + 2/3 hr) = 5 mi/1 hr x h hours
3h + 2 = 5h
2 = 2h
h = 1 hour
3mi/hr x 1 2/3 hr = 5 miles
5 mi/hr x 1 hr = 5 miles
The table below lists some of the characteristics of the houses on Katrina’s street. Characteristics of Homes For Sale on Katrina’s Street Bedrooms Acres of land Sale price Appraised value Property tax 2 0.17 $230,000 $200,000 $1,220 2 0.20 $210,000 $220,000 $1,232 3 0.20 $275,000 $250,000 $1,400 4 0.24 $275,000 $275,000 $1,540 4 0.52 $360,000 $310,000 $1,736 4 0.75 $350,000 $320,000 $1,792 5 1.23 $375,000 $350,000 $1,960 Which relationship describes a function?
Answer:
your welcome and hope this helps
A square and a regular heptagon are coplanar and share a common side $\overline{AD}$, as shown. What is the degree measure of exterior angle $BAC$? Express your answer as a common fraction.
Answer:
[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]
Step-by-step explanation:
The interior angle of a regular heptagon = = 900/7° = 128.57°
Therefore, angle DAB = 128.57°
The interior angle of the square = 90°
Therefore, angle DAC = 90°
Therefore, we have
angle DAB+ angle DAC + angle BAC = 360° (sum of angles at a point (A))
Angle BAC = 360° - angle DAB - angle DAC = 360° - 900/7° - 90° = 990/7°
Angle BAC = 141.43°
Expressing 141.43° as a common fraction gives;
[tex]141.43 ^{\circ}= \dfrac{990}{7} ^{\circ}=141\frac{3}{7} ^{\circ}[/tex]
[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]
The degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex]
Given, A square and a regular heptagon are coplanar as shown in below figure attached.
We have find the exterior angle of BAC.
We know that, The formula that gives the interior angle measure for a regular polygon with any number of sides is,
[tex]\frac{180(n-2)}{n}[/tex] where n is the number of sides.
Since the heptagon has 7 no. of sides.
So regular heptagon's interior angle measures,
[tex]\frac{180(7-2)}{7}=128\frac{4}{7}[/tex]
Hence [tex]\angle A[/tex] will be[tex]128\frac{4}{7}[/tex] degrees.
We know that a square's interior angle is 90 degrees and a heptagon's interior angle is 128.57 degrees. We will subtract those from 360 degrees to find angle BAC.
[tex]\angle BAC = 360 - (\angle A + 90)\\[/tex]
[tex]\angle BAC = 360 - (128\frac{4}{7} + 90)\\\angle BAC=141\frac{3}{7} ^\circ[/tex]
Hence the degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex].
For more details on Exterior angle follow the link:
https://brainly.com/question/2125016
In the figure, m∠CED = m∠A. Complete the following proportions: ED/ A F= CE/? = CD/?
Answer:
The completed proportions are;
ED/A_F = CE/CA = CF/CD
Step-by-step explanation:
The given m∠CED = m∠A
∴ Angle ∠CDE = Angle ∠A_FC, (corresponding angles)
Angle ∠ECD = Angle ∠ACF (reflexive property)
Triangle ΔDCE is similar to triangle ΔACF (Angle Angle Angle (AAA) similarity)
In triangle ΔDCE and triangle ΔACF
m∠A is bounded by CA and A_F
m∠CED is bounded by CE and ED
∠DCE is bounded by CE and DE
∠C is bounded by CA and CF
Based on the orientation of the two triangles, we have
ED is the corresponding side to A_F, CD is the corresponding side to CF, CE is the corresponding side to CA
Therefore, we have;
ED/A_F = CE/CA = CF/CD.
You are testing the claim that the mean GPA of night students is greater than the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.36 with a standard deviation of 0.96 You sample 60 day students, and the sample mean GPA is 2.19 with a standard deviation of 0.66 Calculate the test statistic, rounded to 2 decimal places
Answer:
Z = 0.87
Explanation:
Given the following data;
Sample 1:
n1 = 30
Mean, X = 2.36
Standard deviation, Ox = 0.96
Sample 2:
n2 = 60
Mean, Y = 2.19
Standard deviation, Oy = 0.66
The formula for test statistics for two population is;
[tex]Z = \frac{X-Y}{\sqrt{(\frac{Ox^2} {n_1} } +\frac{Oy^2}{n_2} )}}[/tex]
Substituting the values, we have;
[tex]Z = \frac{2.36-2.19}{\sqrt{(\frac{0.96^2} {30} +\frac{0.66^2}{60} )}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{(\frac{0.9216} {30} +\frac{0.4356}{60} )}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{(0.03072 +0.00726)}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{0.03798}}[/tex]
[tex]Z = \frac{0.17}{0.19488}[/tex]
Z = 0.8723
The test statistics to 2 d.p is 0.87
Therefore, Z = 0.87
Simplify.
N4 x N7 over n5
Answer:
[tex]n^6[/tex].
Step-by-step explanation:
[tex]n^4 * \frac{n^7}{n^5}[/tex]
= [tex]n^4 * n^{7 - 5}[/tex]
= [tex]n^4 * n^2[/tex]
= [tex]n^{4 + 2}[/tex]
= [tex]n^6[/tex].
Hope this helps!
Please give me the correct answer her please
Answer:
9.3 inStep-by-step explanation:
m∠UTV = 112° ⇒ m∠WTV = 180° - 112° = 68°
sin(68°) ≈ 0.9272
sin(∠WTV) = WV/TV
WV/10 ≈ 0.9272
WV ≈ 9.272
WV ≈ 9.3
10. Read the following word problem, then choose which linear equation models the problem.
The length of a rectangle is six feet more than twice the width. The rectangle’s perimeter is 84 feet. Find the width and length of the rectangle.
A. 2w + 6 + w = 84
B. 2(2w + 6) + 2w = 84
C. 2(2w +6) • (2w) = 84
D. (2w + 6) • (w) = 84
Answer:
D. ( 2w+6). (w)
i tried my best
hope this is the answer
stay at home stay safe
Triangle ABC has vertices at A(2,5), B(4,11) and C(-1,6). Determine the angles in this triangle.
I need this solved using vectors please
Answer:
The angles are
∠A = 90°, ∠B = 26.56°, ∠C = 63.43°
Step-by-step explanation:
We have that the angles of a vector are given as follows;
[tex]cos\left ( \theta \right ) = \dfrac{\mathbf{a\cdot b}}{\left | \mathbf{a} \right |\left | \mathbf{b} \right |}[/tex]
Whereby the vertices are represented as
A= (2, 5, 0), B = (4, 11, 0), C = (-1, 6, 0),
AB =(4, 11, 0) - (2, 5, 0) = (2, 6, 0) , BA = (-2, -6, 0)
BC = (-1, 6, 0) - (4, 11, 0) = (-5, -5, 0), CB = (5, 5, 0)
AC = (-1, 6, 0) - (2, 5, 0) = (-3, 1, 0), CA = (3, -1, 0)
θ₁ = AB·AC
a·c = a₁c₁ + a₂c₂ + a₃c₃ = 2×(-3) + 6×1 = 0
Therefore, θ₁ = 90°
BA·BC = (-2)×(-5) + (-6)×(-5) = 40
[tex]{\left | \mathbf{}BA \right |\left | \mathbf{}BC \right |}[/tex] = (√((-2)² + (-6)²)) × (√((-5)² + (-5)²)) = 44.72
cos(θ₂) = 40/44.72 = 0.894
cos⁻¹(0.894) =θ₂= 26.56°
CA·CB = 5×3 + 5×(-1) = 10
[tex]{\left | \mathbf{}CA \right |\left | \mathbf{}CB \right |}[/tex] = (√((3)² + (-1)²)) × (√((5)² + (5)²)) = 22.36
10/22.36 = 0.447
cos(θ₃) = 0.447
θ₃ = cos⁻¹(0.447) = 63.43°.
describe the end behavior f(x)=5x^4+3x^2-1.
An annual salary is $45000. His tax free allowances total $13000. He has to pay a tax of 20% on his taxable income.
The tax payable is?
Answer:
6400
Step-by-step explanation:
Taxable amount=45000-13000=32000
tax=32000*20/100
=6400
Pls solve ASAP!! Review the attachment and solve. Pls hurry!
Answer:
A. 3
Step-by-step explanation:
ΔDEC is bigger than ΔABC by 5. For the hypotenuse, 25 is 5 times bigger than 5.
So, side DE on ΔDEC has to be 5 times bigger than side AB on ΔABC.
If side AB equals 3, side DE equals 18 - 3, which is 15.
15 is five times bigger than 3, so the answer is A. 3.
Hope that helps.
Please help! "Create a real-life scenario involving an angle of elevation or depression. Draw an appropriate diagram and explain how to solve your example."
Answer:
Height of the kite = 86.60 meter (Approx)
Step-by-step explanation:
The angle of elevation to see a kite from a stone lying to the ground is 60 degrees. If a thread is tied with a kite and a stone, then that thread is 100 meters long, find the height of the kite.
Given:
Length of thread = 100 meter
Angle of elevation = 60°
Find:
Height of the kite.
Computation:
Using trigonometry application:
Height of the kite / Length of thread = Sin 60°
Height of the kite / 100 = √3 / 2
Height of the kite = [√3 / 2]100
Height of the kite = 50√3
Height of the kite = 86.60 meter (Approx)
which equation represents the line that is perpendicular yo y=3/2x+1 and passes through (-12,6)
Answer:
y = -2/3x - 2
Step-by-step explanation:
Step 1: Find slope m of perpendicular line
Simply take the negative reciprocal of the given line
m = -2/3
y = -2/3x + b
Step 2: Find b
6 = -2/3(-12) + b
6 = 8 + b
b = -2
Step 3: Rewrite perpendicular equation
y = -2/3x - 2
help plzz ... Trigonometry
Answer:
XYZ = 21.8
Step-by-step explanation:
the missing angle is XYZ
cos XYZ = [tex]\frac{adjacent}{hypotenus}[/tex] tan XYZ = [tex]\frac{6}{15}[/tex] tan XYz = 0.4using a calculator:
tan^(-1)(0.4)= 21.8so XYZ = 21.8
Plzzzzz Help I really need help
A Line Segment has the points (1,-2), and (3,-2). What are the new points after its dilated by a scale factor of 3/2 or 1.5
Answer:
(1.5,-3) and (4.5,-3)
Step-by-step explanation:
how would you solve #81?
find the distance of the line segment joining the two points (-4 /2 - /12) and (/32, 2/3)
Answer: [tex]4\sqrt{3}[/tex] .
Step-by-step explanation:
Distance formula : Distance between points (a,b) and (c,d) is given by :-
[tex]D=\sqrt{(d-b)^2+(b-a)^2}[/tex]
Distance between points [tex](-4\sqrt{2},\sqrt{12}) \text{ and }(-\sqrt{32}, 2\sqrt{3})[/tex].
[tex]D=\sqrt{(2\sqrt{3}-(-\sqrt{12}))^2+(-\sqrt{32}-(-4\sqrt{2}))}\\\\=\sqrt{(2\sqrt{3}+\sqrt{2\times2\times3})^2+(-\sqrt{4\times4\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}-\sqrt{2^2\times3})^2+(-\sqrt{4^2\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}+2\sqrt{3})^2+(-4\sqrt{2}+4\sqrt{2})^2}\\\\=\sqrt{(4\sqrt{3})^2+0}\\\\=4\sqrt{3}\text{ units}[/tex]
Hence, the correct option is [tex]4\sqrt{3}[/tex] .
9/10 of the weight of a loaf of bread comes from the flour used in its baking. 2/9 of the weight is the protein what fraction of the weight is protein?
Answer:
1/5
Step-by-step explanation:
2/9 * 9/10 = 2/10 = 1/5
Maya is interning at a law firm over the summer and is paid by the hour. If her hourly wage is $52, which equation represents the proportional relationship between the wages she earns (w) and the number of hours (h)?
Answer: w= 52h
Step-by-step explanation:
Given: Maya is interning at a law firm over the summer and is paid by the hour.
Her hourly pay = $52
i.e. She is paid $52 per hour.
Let the wages she earns is denoted by 'w' and the number of hours is denoted by 'h'.
Now, (Total wages earned) = (hourly pay) x (Number of hours)
w = (52) (h)
⇒ w= 52h
Hence, the equation represents the proportional relationship between the wages she earns (w) and the number of hours (h): w= 52h
Answer:52h
Step-by-step explanation: tried got it right
please help!!!!!!!!!!!
Answer:
The x value of the point 1/4 the distance from point C to point D is -0.25
Step-by-step explanation:
The given information are;
The location of point C = (1, 2)
The location of point D = (-4, -2)
The point 1/4 from point C to point D is the point 3/4 from point D to point C
Which gives;
The coordinate at point D + 3/4× The difference between the coordinates of point C and point D
Which is (-4 + 3/4×(1 - (-4), - 2 + 3/4×(2 - (-2))
Which gives;
(-4 + 3.75, -2 + 3) and (-0.25, 1)
The coordinates of the point 1/4 the distance from point C to point D is (-0.25, 1)
Therefore, the x value of the point 1/4 the distance from point C to point D = -0.25.
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
9/13
Step-by-step explanation:
rise = y₂ - y₁ = -1 - (-10) = -1 + 10 = 9
run = x₂ - x₁ = 9 - (-4) = 9 + 4 = 13
Step-by-step explanation:
Jane exchanged £100 for 216 Swiss francs. After buying a meal and a present to take home,she had 70 francs left.How much is this in £?
Answer:
£32.4
Step-by-step explanation:
£100 = 216 Swiss francs
x = 70 francs
70 x 100=7000/216=32.4
n the diagram below, points $A,$ $E,$ and $F$ lie on the same line. If $ABCDE$ is a regular pentagon, and $\angle EFD=90^\circ$, then how many degrees are in the measure of $\angle FDE$?
[asy]
size(5.5cm);
pair cis(real magni, real argu) { return (magni*cos(argu*pi/180),magni*sin(argu*pi/180)); }
pair a=cis(1,144); pair b=cis(1,72); pair c=cis(1,0); pair d=cis(1,288); pair e=cis(1,216);
pair f=e-(0,2*sin(pi/5)*sin(pi/10));
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f);
label("$A$",a,WNW);
label("$B$",b,ENE);
label("$C$",c,E);
label("$D$",d,ESE);
label("$E$",e,W);
label("$F$",f,WSW);
draw(d--f--a--b--c--d--e);
draw(f+(0,0.1)--f+(0.1,0.1)--f+(0.1,0));
[/asy]
Answer:
18
Step-by-step explanation:
Each interior angle of a regular pentagon is 108 degrees. So Angle AED is 108 degrees. Since Angle AEF is a straight line (180 degrees), Angle FED is 72. This is because 180-108 = 72. Now, since a triangle has a total of 180 degrees, we add 72 and 90, because those are the 2 degrees we have calculated. This gives us a total of 162. Now, we subtract 162 from 180 to find out the degree of Angle FDE. This is 18. So our final answer is 18.
Sidenote: I hope this answer helps!
The properties of a pentagon and the given right triangle formed by
segments EF and FD give the measure of ∠FDE.
Response:
∠FDE = 18°Which properties of a pentagon can be used to find ∠FDE?The given parameters are;
A, E, F are points on the same line.
ABCDE is a regular pentagon
∠EFD = 90°
Required:
The measure of ∠FDE
Solution:
The points A and E are adjacent points in the pentagon, ABCDE
Therefore;
line AEF is an extension of line side AE to F
Which gives;
∠DEF is an exterior angle of the regular pentagon = [tex]\frac{360 ^{\circ}}{5}[/tex] = 72°∠EFD = 90°, therefore, ΔEFD is a right triangle, from which we have;
The sum of the acute angles of a right triangle = 90°
Therefore;
∠DEF + ∠FDE = 90°
Which gives;
72° + ∠FDE = 90°
∠FDE = 90° - 72° = 18°
∠FDE = 18°
Learn more about the properties of a pentagon here:
https://brainly.com/question/15392368
Find the value of x.
Answer:
8.8Option A is the correct option.
Step-by-step explanation:
As PW is the median.
PW = [tex] \frac{1}{2} [/tex] ( YZ + TM )
Plug the values
x = [tex] = \frac{1}{2} (5.5 + 12.1)[/tex]
Calculate the sum
x = [tex] = \frac{1}{2} \times 17.6[/tex]
Calculate the product
x = [tex] = 8.8[/tex]
Hope this helps...
Best regards!
What is m∠A? please help
Answer: 50 degrees
Step-by-step explanation:
180-85=95
180-145=35
interior angle sum for a triangle is 180 degrees, so 180=95+35+a
m of angle A is 50 degrees
Write an equation for the line that is parallel to the given line and that passes through the given point. y=34x−9;(−8,−18)
Answer:
Step-by-step explanation:
eq. of line parallel to y=34x-9 is y=34 x+k
∵ it passes through (-8,-18)
∴-18=34×-8+k
k=-18+272
k=254
so reqd. eq. is y=34 x+272
HELP ME PLEASSSSEE On a winter morning, the temperature before sunrise was -10℉. The temperature then rose by 1℉ each hour for 7 hours before dropping by 2℉ each hour for 3 hours. What was the temperature, in degrees Fahrenheit, after 10 hours?
Answer:
3 degrees F
Step-by-step explanation:
if the temperature rose 1* for 7 hours, times 1 by 7. which is 7 and add to -10. which is -3. then, since the temperature rose by 2* for 3 hours, times 2 by 3 which is 6 and add to -3, which is 3.
i hope this helped?
(a) Complete the statements below about the graphs of y = -x and y=x.
Compared to the graph of y=x, the graph of y=-x is Choose one
Compared to the graph of y=x, the graph of y = -x intersects the y-axis at Choose one
2
(b) Complete the statements below about the graphs of y=x+
and y=x.
3
2
Compared to the graph of y = x, the graph of y=x+ 5 is Choose one
2
Compared to the graph of y=x, the graph of y=x+
3
intersects the y-axis at Chonse one
a higher point
the same point.
a lower point
Х
?
Answer:
this. question is not clear please send clear question
We can conclude that -
Graphs pass through the origin. (y = x) has a slope of +1 while (y = - x) has a slope of -1. The y - intercept of both the graphs will be 0.What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have the following two functions -
y = -x
AND
y = x
Refer to the graphs attached for both the functions -
y = - x and y = x
The graphs as seen pass through the origin. One graph (y = x) has a slope of +1 while the other one (y = - x) has a slope of -1. The y - intercept of both the graphs will be 0.
We can conclude that -
Graphs pass through the origin. (y = x) has a slope of +1 while (y = - x) has a slope of -1. The y - intercept of both the graphs will be 0.To solve more questions on straight line, visit the link below-
https://brainly.com/question/29030795
#SPJ2
work out the shaded area.
plzzzz
Answer:
Shaded area: 70cm^2
Step-by-step explanation:
Whole=120cm^2
White Square=
10-2.5-2.5=5
12-1-1=10
5✖️10=50cm^2
Whole-white=70cm^2
1. A test-tube has a diameter of 3cm. How many turns would a piece of thread of length
90.42cm make round the test tube. (Taken= =).
(3marks)
So if we think of a test tube, it looks sort of like a cylinder. This means that its cross-section would be a circle. To find out how many turns a piece of thread would make around the test tube, we need to find the circumference of the test tube, then divide the length of the string by the circumference.
Step 1) Find the circumference
C = pi x diameter
C = 3.14 x 3
C = 9.42
Step 2) Divide the length of the string by the circumference
90.42 / 9.42 = 9.5987
The string would make approximately 9.60 turns around the test tube.
Hope this helps!! :)