Answer:
(6, 2)
Step-by-step explanation:
Step 1: Use substitution
x - 4 = 1/3x
Step 2: Isolate x
2/3x = 4
x = 6
Step 3: Plug back into original equation(s)
y = 6 - 4
y = 2
Answer:
(6,2)
Step-by-step explanation:
Let's use the substitution method.
x-4=1/3x
3x-12=x
3x=x+12
2x=12
x=6
y=6-4
y=2
Alex drives at an average speed that is 3/4 of the average speed that Roy's train travels. Alex takes 40 minutes to travel 65 km in her car. Roy travels for 1 hour and 15 minutes on his train. How far does Roy travel to 2 dp?
Answer:
Distance = 162.5 to 2dp.
Step-by-step explanation:
Alex car drives 65km = 40mins we round up to 1hr
= 1/2 x 65 + 65 = 32.5 +65 = 97.5 km p/h
Roy is 1/4 faster (As Alex speed is 3/4 of Roy)
To find 3/4 we divide by 3 then, add the 97.5 km etc..
97.5/3 = + 32.5km = 130 km/ph
To check we only have to divide by 4
130 / 4 = 32.5
We know 32.5 is 1/4 we can add this on as 15minutes.
130 km = 1hr +
32.5 km = 15 mins
Distance = 162.5 km
Answer:
162.50 km
Step-by-step explanation:
Alex: 40 minutes for 65 km
speed = distance/time = (65 km)/(40 min) * (60 min)/(1 hr) = 97.5 km/h
Alex's speed = 3/4 of Roy's speed
Roy's speed = (Alex's speed)/(3/4) = (97.5 km/h)/(0.75) = 130 km/h
speed = distance/time
distance = speed * time
time = 1 hour + 15 minutes = 1 hour + 15/60 hour = 1.25 hour
distance = 130 km/h * 1.25 hour = 162.50 km
Find the sum of the first 16 terms in an arithmetic series where a1 = 2, and the common difference is d=2. Question 4 options: A) 272 B) 240 C) 360 D) 306
Answer:
A) 272
Step-by-step explanation:
[tex]S_{n}=\frac{n}{2}*[2a + (n-1)d]\\\\s_{16}=\frac{16}{2}[2*2+15*2]\\\\ =8*[4+30]\\\\=8*34\\=272[/tex]
Answer:
272
Step-by-step explanation:
Select the correct shapes.
Select the shapes that are similar to shaoe A
Answer:
A , B and C are similar to each other
Step-by-step explanation:
Please give me branlest
ΔABC has been translated right to create triangle ΔXYZ. Based on this information, which of the following is a true statement? answers: A) ≅ B) ≅ C) ∠A ≅ ∠C D) ∠B ≅ ∠X
Answer:
None. (or B)
Step-by-step explanation:
A) AC≅ZY
B) AZ≅
C) ∠A ≅ ∠C
D) ∠B ≅ ∠X
Options C and D are not true and Options A is wrong and B is incomplete but using process of elimination, the answer is probably B.
The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ
What is translation transformation?A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
Given that, Δ ABC has been translated right to create triangle Δ XYZ
We know that in translation transformation, in translation, only the position of the object changes, its size remains the same.
That means Δ ABC ≅ Δ XYZ Therefore, we get,
Congruent parts are;
Angles:-
∠ A ≅ ∠ X,
∠ B ≅ ∠ Y and
∠ C ≅ ∠ Z
Side:-
AB ≅ XY,
BC ≅ YZ and
AC ≅ XZ
Hence, The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ
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Use the interactive to graph a line with the given points: (–1,7) and (1,–1) The coordinates of the y-intercept of the line are.
Answer:
The y-intercept would be 6.25
Step-by-step explanation:
I found this by taking the two points and making it into a y = mx + b line.
Answer:
(0,3)
Step-by-step explanation:
We can use the slope-intercept form to find the y-intercept.
First, we need to find the slope of the line.
We are given the points (-1,7) and (1,-1).
[tex]m=\frac{rise}{run}=\frac{-1-7}{1+1}=\frac{-8}{2}=-4[/tex]
The slope is -4.
Slope-intercept is [tex]y=mx+b[/tex].
We can replace 'y' and 'x' with one of the points given, 'm' with the slope, and solve for 'b'. "B" would be the y-intercept.
I will use (-1,7):
[tex]7=-4(-1)+b\\\\7=4+b\\\\7-4=4-4+b\\\\\boxed{3=b}[/tex]
The line's equation is [tex]y=-4x+3[/tex].
Therefore, the y-intercept is '3'. The coordinates of the y-intercept is (0,3).
Alex and Thomas share 30 sweets. They divide them in the ratio 3:2.How many sweets does Alex and Thomas receive?
Answer:
Alex: 18
Thomas: 12
Step-by-step explanation:
A : T : TOTAL
3 : 2 : 3 + 2 = 5
total number of units : 5
total number of sweets : 30
1u = 30 ÷ 5 = 6
Alex = 3u = 3 × 6 = 18
Thomas = 2u = 2 × 6 = 12
given
[tex] log(x) = 2 \: and \: log(y) = - 1[/tex]
prove that
[tex]xy - 100y {}^{2} = 9[/tex]
Step-by-step explanation:
[tex] log(x) = 2 \\ {10}^{2} = x \\ x = 100[/tex]
then for y:
[tex] log( y) = - 1 \\ {10}^{ - 1} = y \\ y = 0.1[/tex]
so:
[tex]xy - 100 {y}^{2} \\ = 100 \times 0.1 - 100 \times {(0.1)}^{2} \\ = 10 - 100 \times 0.01 \\ = 10 - 1 \\ = 9[/tex]
The ratio of the angle measures of a triangle is 1:2:2. What is the value of the smallest angle? 180° 90° 72° 36°
Answer:
36 degrees.
Step-by-step explanation:
All the angles in a triangle add up to be 180 degrees. Since the ratio is 1:2:2, you can say that the angles are x, 2x, and 2x.
x + 2x + 2x = 180
5x = 180
x = 180 / 5
x = 36
Since the smallest part of the ratio is 1, the smallest angle is 36 degrees.
Hope this helps!
Use the zero product property to find the solutions to the equation x2 - X-6 = 0.
x= -3 or x = -2
x= -3 or x = 2
Ox= -2 or x= 3
O x= 2 or x = 3
Answer:
third option
Step-by-step explanation:
Given
x² - x - 6 = 0 ← in standard form
(x - 3)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x + 2 = 0 ⇒ x = - 2
Answer:
x = -2 or x = 3
Step-by-step explanation:
The answer to your question is C.
Help please!!! A.) C and B B.) C and D C.) L and W D.) A and B
Line j is a straight line. Line j is a straight line. 2 lines come out of the line to form 4 angles. From top left, clockwise, the angles are: x, y, z, w. Which equation represents the relationship between the measures of Angle w and Angle z? Measure of angle w = measure of angle z Measure of angle w + measure of angle z = 90 degrees Measure of angle w + measure of angle z = 100 degrees Measure of angle w + measure of angle z = 180 degrees
Answer:
c
Step-by-step explanation:
In the given line the relationship between angle w and z is Measure of angle w + measure of angle z = 180 degrees.
What is a supplementary angle?This is the type of angle that when measured, two of the angles would sum up to 180 degrees.
The supplementary angle is the sum of angle w + angle z = 180 degrees. Hence c is correct.
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Help please and thank you
Answer:
73.72 ft Squared
Step-by-step explanation:
First you need to find the area of the rectangle the area of rectangle is 8x10=80. Then You take that 80=3.14x2. then you find the area by dividing it. so...
1.) 80=3.14x2
3.14x2=6.28 80=6.28 (Then you divide 6.28 by 80)
80 80
whats the difference between a sequence and a series?
Answer:
A sequence is defined as an arrangement of numbers in a particular order. On the other hand a series is defiend as the sum of the elements of a sequence!
Math help asap!
[Function Inverses]
Answer:
It's (B) [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Hope this helped you!
Answer:
f^-1(8) = 3/2
Step-by-step explanation:
f(x) = 2x + 5
y = 2x + 5
x = 2y + 5
2y = x - 5
y = (x - 5)/2
f^-1(x) = (x - 5)/2
f^-1(8) = (8 - 5)/2
f^-1(8) = 3/2
Pls help summer homework :D C:
Answer:
C) None of the above
Step-by-step explanation:
Reason is V is a shorter distance and q is longer they need to be subtraction but the other way round to enable the correct subtraction we can show (q-V) which means the longer distance minus the shorter distance.
What are the coordinates of the image of R for a dilation with center (0,0) and scale factor 3?
Answer:
(3, -3)
Step-by-step explanation:
If a point is dilated about the origin rule to be followed,
(x, y) → (kx, ky)
where k is a scale factor by which the point is being dilated.
If a point R having coordinates (1, -1) is dilated by scale factor of 3, coordinates of the image will be [3×1, 3(-1)]
Therefore, coordinates of the image R' will be (3, -3)
PLEASE HELP!!!!!!! i will give brainliest
Yes they are independent because P(California) = 0.55 approximately and P(California | Brand B) = 0.55 approximately as well
===================================================
Explanation:
P(California) is notation that means "probability the person is from California". There are 150 people from California out of 275 total. Therefore, the probability is 150/275 = 0.5454 approximately which rounds to 0.55
Now if I told you "this person prefers brand B", then you would focus your attention solely on the brand B column. The other columns are ignored because you know they don't prefer anything else. With this narrower view, we see that 54 Californians prefer this brand out of 99 total. The probability becomes 54/99 = 0.5454 which rounds to 0.55. We get the same as before.
The notation P(California | Brand B) means "the probability they are from California given they prefer brand B". The vertical line is not the uppercase letter i or lowercase letter L. It is simply a vertical line. In probability notation that vertical line means "given".
We've shown that P(California | Brand B) = 0.55 approximately. The fact that they prefer brand B does not change the original probability. So the two events are independent. If liking brand B did change the probability, then the events would be dependent.
15. Solve for x in the diagram.
Х
9
12
A. 15
B. 25
C. 14
O D. 37
Answer:
15Solution,
Hypotenuse(h)=X
Perpendicular (p)=9
Base(b)=12
Now,
Using Pythagoras theorem,
[tex] {h}^{2} = {p}^{2} + {b}^{2} \\ or \: {x}^{2} = {(9)}^{2} + {(12)}^{2} \\ or \: {x}^{2} = 81 + 144 \\ or \: {x}^{2} = 225 \\ or \: x = \sqrt{225} \\ or \: x = \sqrt{ {(15)}^{2} } \\ x = 15[/tex]
hope this helps...
Good luck on your assignment...
The length of the hypotenuse in the given triangle is A. 15 units.
This type of question makes a right-angled triangle that can be solved by Pythagoras's theorem.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, the base of the triangle is 12 units and the height is 9 units.
∴ x² = 9² + 12².
x² = 144 + 81.
x² = 225.
x = + 15 units.
So, the length of the hypotenuse is 15 units.
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The number is even. It is more than 1 but less than 100. Is it greater than 20. It is less than 5×7. The sum of the digits is 6. Is it evenly divisible by 4
Answer:
24
Step-by-step explanation:
Alright so the number has to be above 20 and below 35.
It has to be even, so our options are 22, 24, 26, 28, 30, 32, 34
Since the sum of the digits has to be 6, the only number from that list that it can be is 24.
This works because 24 is also evenly divisible by 4 (6x4=24) so it fits all of the criteria.
Hope this helps!
Answer:
24
Step-by-step explanation:
This works because 24 is also evenly divisible by 4 (6x4=24) so it fits all of the criteria.
Hope this helps!
|7t|=35 solve the equation
Answer:
t = 5,-5
Step-by-step explanation:
35/7 = 5
because it is an absolute value, it will always be positive:
-35/7 = -5
Answer:
T = 5,
Step-by-step explanation:
7T = 35
divide 7 by both
T = 5
hope this helps
Change the percent to a decimal equivalent.
9 7/10
Answer:
0.97
Step-by-step explanation:
97 /100
You can round once from behind to convert 97% to 0.97
9 7/10 equals 9.7
sorry if the answer is wrong
a ferris wheel goes around once every 20 seconds . How many times will a rider be ag thetop during an 8-minuteride?
A.23
B.24
C.25
D.160
Answer:
The answer is B.
Step-by-step explanation:
There are three 20 second time periods in 1 minute. Three times eight is equal to 24.
find the axis of symmetry of this parabola y=-x^2-2x-5 write your answer as an equation
Answer:
axis of symmetry: x=-1
Step-by-step explanation:
Samantha can write 1 1⁄2 pages in 3 minutes. How many pages could she write in 12 minutes?
Answer:
[tex]6\:\mathrm{pages}[/tex]
Step-by-step explanation:
[tex]3 \times 4 = 12[/tex]
[tex]1\frac{1}{2} \times 4=6[/tex]
Answer:
6 pages
Step-by-step explanation:
1.5 pages x pages
--------------- = ------------
3 minutes 12 minutes
Using cross products
1.5 * 12 = 3x
Divide each side by 3
18 /3 = 3x/3
6 =x
6 pages
What is the area of the shaded part of the circle that has a diameter of 8 mm? Use 3.14 for
4 mm
8 mm
O 16mm?
O 32mm?
O 34 24 mm
50.24 mm?
Answer: 34.27 sq. mm.
Step-by-step explanation:
Area of a triangle = hb / 2
= 8 x 4 / 2
= 32 / 2 = 16 mm
Area of the circle = πr^2
= π x 4^2
= 50 27 sq. mm.
Area of the shaded part
= 50.27 - 16
= 34.27 sq. mm
Answer: the answer is c, 34.24 mm
Step-by-step explanation: I just did the test
HELP AM BEING TIMED!!!!!!!!!!
Answer: A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
just got it right EDG 2021
Solve px + 12 = 17 for x.
A. x =5/p
B. X =29/p
C. X= 5-p
D. x = p + 5
Answer:
A. [tex] x = \frac{5}{p} [/tex]
Step-by-step explanation:
[tex]px + 12 = 17 \\ px = 17 - 12 \\ px = 5 \\ x = \frac{5}{p} [/tex]
Help will give brainliest
Answer:
70
Step-by-step explanation:
Answer:
70 fewer refrigerators than television
Step-by-step explanation:
What are the coordinates of M' after triangle MNO is reflected over the y-axis, and rotated 90 degrees clockwise with
the origin as the center of rotation?
Answer:
I'm not sure, but I think it is (0, -6).
If ∠ABC and ∠CBD are supplementary angles, then m∠ABC + m∠CBD = 180° represents the definition of Question 2 options: A) complementary angles. B) supplementary angles. C) triangle sum. D) congruence.
Answer:
I would think it is supplementary.
Step-by-step explanation:
If 2 angles equal 180 degrees, then they are supplementary.