Answer:
3:4
Step-by-step explanation:
We know this because the GCD of 21 and 28 is 7
so we divide both numbers by 7 and get 3 and 4
so the answer is 3:4
3. (3, 5) and (k, 9), slope = 1/2
Linear relationships unit 3 lesson 10 grade 8 openuprespurces
Answer:
k = 11, if I understand the question.
Step-by-step explanation:
Please rephrase the question if my interpretation is incorrect. (BTW, isn't (k,9) a dog?)
======================
I'll assume that we want to find the value of k as given by the equation of a line that has a slope of (1/2).
Let's determine if we can establish an equation with what we know:
1. It goes through point (3,5), and
2. It has a slope of (1/2)
We'll look for a line with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
From (2) we know y = (1/2)x + b.
We can find b by using the one known point that lies on the line (3,5). Use y = (1/2)x + b, insert the point (3,5), and solve for b:
y = (1/2)x + b
5 = (1/2)(3) + b
5 = 1.5 + b
b = 3.5
The line is y = (1/2)x + 3.5.
Now use the point (k,9):
y = (1/2)x + 3.5
9 = (1/2)k + 3.5
(1/2)k = 5.5
k = 11
The point is (11,9) so k = 9
See the attached graph.
The length of a rectangle is 3 yd longer than its width. if the perimeter of the rectangle is 58 yd, find its length and width.
Answer:
Length = 16 yds
Width = 13 yds
Step-by-step explanation:
P = 2w + 2l
l = w + 3
58 = (2w + 2(w + 3))
58 = 4w + 6
52 = 4w
w = 13
L = w + 3
= 13 + 3
= 16
The length and width of the rectangle are 16,13yd.
The Length and Width of the rectangle can be found as:
Given:The length of the rectangle is 3yds longer than the width which means length = w+3
and the perimeter is given by 58yd
Let W be the width and L be the length
We know that the perimeter of a rectangle is 2(L+w)
The perimeter of a rectangle is defined as the sum of all the sides of a rectangle
By simplifying we get2(w+w+3)=58
2(2w+3)=58
2w=29-3
w=13
then the length of the rectangle will be w+3
13+3 = 16
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Bailey and julie go running during their lunch break. bailey ran x miles while julie ran 3x miles. what information can we gather about the relationship between the number of miles bailey and julie ran?
The information we can see from the given data is that the speed of Julie is three times the speed of Bailey.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Given that:-
Bailey and Julie go running during their lunch break. bailey ran x miles while Julie ran 3x miles.The speed of Bailey = x miles
The speed of the Julie = 3x miles
The ratio of the speeds will be given as:-
J / B = 3x / x
J / B = 3
J = 3 B
Therefore information we can see from the given data is that the speed of Julie is three times the speed of Bailey.
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question below, NEED ASAP!! THANK YOU!!!
Answer:
1
Step-by-step explanation:
[tex] log_{3}(5) \times log_{25}(9) = \frac{ log(5) }{ log(3) } \times \frac{ log(9) }{ log(25) } = \frac{ log(5) }{ log(3) } \times \frac{2 log(3) }{ 2log(5) } = \frac{2}{2} = 1[/tex]
Which expression is equivalent to
Answer:
AA. [tex] \frac{(2 {g}^{5} ) {}^{3} }{(4 {h}^{2}) {}^{3} } = \frac{ {g}^{15} }{8 {h}^{6} } [/tex]
Step-by-step explanation:
HOPE IT HELPS
16. a bacteria culture starts with 10 00 bacteria and the number doubles every 40minutes.(a) find a formula for the number of bacteria at time t
The formula that can be used to find the number of bacteria is FV = 1000 x 2^t.
What is the formula that can be used to find the number of bacteria?The formula that can be used to determine the number of bacteria is an exponential function with the form:
FV = P(1 + r)^t
Where:
FV = future population P = present population r - rate of increase1000 x ( 1 + 1)^t
FV = 1000 x 2^t
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If tan 0 = 4/3 and 0 lies in the third quadrant, which is the correct ratio for cos 0?
4/5
-3/5
-4/5
3/5
[tex] \frac{ - 3}{5} \\ [/tex]
because , in the third quadrant , the value of cos is negative. Moreover , we can find the third side of the triangle using Pythagoras theorem.
then ,
[tex] \cos(\theta) = \frac{base}{hypotenuse} \\ \\ \dashrightarrow \: \cos(\theta) = \frac{ - 3}{5} [/tex]
hope helpful.
The answer is cos 0 = -3/5
To calculate the answer:Given :
tan 0 = 4/3 and is in the 3rd quadrant
this implies that both the perpendicular and base are negative.
Perpendicular = -4
Base = -3
Hypotenuse = [tex]\sqrt{(perpendicular)^{2} + (base)^{2} }[/tex]
Hypotenuse = [tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]
Hypotenuse = [tex]\sqrt{25} = 5[/tex]
cos 0 = [tex]\frac{Base}{Hypotenuse}[/tex]
cos 0 = -3/5
Therefore, cos 0 = -3/5
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I’m not sure how to do this if someone could help it would be much appreciated
Answer:
(b) y = 18/x; y = 9/4
Step-by-step explanation:
Different kinds of variation are generally described by the equation ...
y = k·( ) . . . . . . . where k is the constant of proportionality
__
kinds of variationWhat goes in parentheses depends on the kind of variation. Here is a partial list of kinds that may be seen in algebra problems.
direct: xinverse: 1/xas the square: x²as the square root: √xas the inverse of the square: 1/x²jointly as: xzThe value of k can be found by solving the variation equation with given values of the variables.
__
inverse variationThe variables x and y are said to vary inversely, so the appropriate equation is ...
y = k(1/x) = k/x
Using the given values, we can find k:
9 = k/2
9·2 = k = 18
So, the equation is ...
y = k/18
__
for x=8Using the above equation, the value of y for x=8 is ...
y = 18/8 = 9/4
Note: you can also get there by realizing that x=8 is 4 times x=2, so the new value of y will be the old value of y multiplied by the inverse of this factor. 1/4 times the old value of y: (1/4)9 = 9/4.
how do i do this? i need to factor it conpletely with any method that goes with it
For which graph is the parent function y=x^2
On a coordinate plane, a parabola opens up and has a vertex at (negative 1, negative 2).
On a coordinate plane, a straight line has a positive slope.
On a coordinate plane, a cubic root function is shown.
On a coordinate plane, an absolute value function is shown.
y = x² is the parent function of a parabola opens up and has a vertex at (negative 1, negative 2)
What is the standard equation of a parabola ?The standard equation of a parabola is given by
y =a(x-h)² +k
Vertex at h , k
It is given that It has to be chosen from the options that whose parent function is
y = x²
As the plot of the first option is done , which is shown in the figure ,
The parabola is given by
y = (x +1)² +2
and the parent function is y = x²
Therefore the Option 1 is the answer.
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Triangle XYZ, with vertices X(-2, 0), Y(-2, -1), and Z(-5, -2), undergoes a transformation to form triangle X′Y′Z′, with vertices X′(4, -2), Y′(4, -3), and Z′(1, -4). The type of transformation that triangle XYZ undergoes is a .
Triangle X′Y′Z′ then undergoes a transformation to form triangle X′′Y′′Z′′, with vertices X″(4, 2), Y″(4, 3), and Z″(1, 4). The type of transformation that triangle X′Y′Z′ undergoes is a .
Using translation concepts, it is found that the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
From triangle X′Y′Z′ to triangle X′′Y′′Z′′, the rule is given by:
(x,y) -> (x, -y)
Hence the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.
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which of the following have eight faces
The figure shows the letter M and four of its transformed images—A, B, C, and D:
A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. An image of the letter M is shown on ordered pair 1, 2 and 1, 4 and 2, 3 and 3, 12, and 3, 4. Another image of letter M is shown on ordered pair 4, negative 4 and 4, negative 2 and 5, negative 3 and 6, negative 2 and 6, negative 4. This M is labeled as B. Another image of letter M labeled C is shown on negative 4, negative 4 and negative 4, negative 2 and negative 3, negative 3 and negative 2, negative 2 and negative 2, negative 4. An image of the letter W labeled A is shown on 1, negative 2 and 1, negative 4 and 2, negative 3 and 3, negative 2 and 3, negative 4. Another image of the letter W labeled D is shown on negative 2, 4 and negative 2, 2 and negative 3, 3 and negative 4, 2 and negative 4, 4. The letters A, B, C, D are written towards the bottom left of the respective W and M.
Which of the four images was formed by a reflection of the letter M?
A
B
C
D
The image was formed by a reflection of the letter M would be image A in the second quadrant b the reflection on X-axis. The correct option is A.
Explanation of how reflection across axis works?When a graph is reflected along an axis, say x axis, then that leads the graph to go just in the opposite side of the axis as if we're seeing it in a mirror.
If you study it more, you will find that it's symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
Thus, if you're reflecting a point (x,y) along the x-axis, then its x abscissa will stay the same but y coordinates will negate.
Thus (x,y) turns to (x, -y)
Similarly, if you're reflecting a point (x,y) along the y -axis, the resultant image of the point will be (-x,y).
The image was formed by a reflection of the letter M would be image A in the second quadrant b the reflection on X-axis. The correct option is A.
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The reflection of letter M is (A)
What is reflection?A figure is said to be a reflection of the other figure, then every point in a figure is at equidistant from each corresponding point in another figure.
According to the graph the reflection of Of letter M is with same coordinates but with x as positive and y as negative.
Hence the reflection is (A).
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Last Monday the temperature changed at a rate of -3 F per hour. How long did it take for the change in temperature to be -21 F?
Answer:
7 hours
Step-by-step explanation:
just multiply 3 and 7 to get 21
Answer:
[tex]\fbox {7 hours}[/tex]
Step-by-step explanation:
⇒ Rate = -3F/hour
⇒ Starting : -21F
Solving :
⇒ -21/-3
⇒ 7 hours
x + 4y = -10
2x - y = 7
Answer:
(2, - 3 )
Step-by-step explanation:
x + 4y = - 10 → (1)
2x - y = 7 → (2)
multiplying (2) by 4 and adding to (1) will eliminate y
8x - 4y = 28 → (3)
add (1) and (3) term by term to eliminate y
9x + 0 = 18
9x = 18 ( divide both sides by 9 )
x = 2
substitute x = 2 into either of the 2 equations and solve for y
substituting into (1)
2 + 4y = - 10 ( subtract 2 from both sides )
4y = - 12 ( divide both sides by 4 )
y = - 3
solution is (2, - 3 )
From the observation deck of a skyscraper, Lavaughn measures a 42°
angle of depression to a ship in the harbor below. If the observation deck is 872 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary
By using trigonometry, we conclude that the horizontal distance is 785.15ft
How to find the horizontal distance?We can think of this as a right triangle.
Where the height of the observation deck is one cathetus and the horizontal distance is the other cathetus,
We know that the depression angle when looking from above is 42°. If we step on this angle, the adjacent cathetus is the height of the deck, then the horizontal distance is the opposite cathetus.
Then we can use the relation:
tan(a) = (opposite cathteus)/(adjacent cathetus).
Replacing what we know:
tan(42°) = (distance)/(872ft)
tan(42°)*872ft = distance = 785.15ft
The horizontal distance is 785.15ft
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Select the correct answer.
The speed of a ship is given by , where d is the distance the ship travels in 3 hours. If the ship travels 48 miles in 3 hours, what is the speed of the ship?
A.
12 miles per hour
B.
16 miles per hour
C.
45 miles per hour
D.
51 miles per hour
Which logarithmic equation is equivalent to this exponential equation?
Step-by-step explanation:
i think b is right answer
Answer:
see photo for detailed analysis
What type of triangle center is shown as point H in the figure?
Answer:
centroid
Step-by-step explanation:
medians of the triangle intersect at point H, making this point centroid.
(essentially, it's the center of the triangle)
Which expression simplifies to 5√3?
OA. √30
OB. 45
OC. √75
OD. 15
Re
Answer:
C)
Step-by-step explanation:
Prime factorize.
A) √30 is in its simplest form.
[tex]B) \sf \sqrt{45}= \sqrt{3*3*5} = 3\sqrt{5}\\[/tex]
[tex]C) \sqrt{75}=\sqrt{3*5*5}=5\sqrt{3}[/tex]
So, option C
The simplified expression of 5√3 is √75.
Hence, Option C is correct.
What is an mathematical expression?Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.
The given expression is,
5√3
So it can be written as,
⇒√5² x √3
⇒ √25 x √3
Since we know that,
Square roots are multiplied by both the whole number component and the square root component individually.
Therefore,
⇒√(25x3)
⇒√75
Thus,
5√3 = √75
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In the above diagram, the demand for pepper is an example of price __________.
A.
elasticity
B.
shifting
C.
inelasticity
D.
controlling
Please select the best answer from the choices provided
A
B
C
D
Answer:
B. shifting
Step-by-step explanation:
When the price is rising or shifting higher, the demand curve moves to the left. But, t here is a corresponding change in the demand curve in that scenario while the cost stays unchanged. Since it relies on variables other than price, the simultaneous shift might go either left or right. However, the upward-pointing line depicts a rise in price and a fall in supply.
If a = 6, then the value of c is...
Answer:
[tex]\boxed{\bf B. \: c = 4 \sqrt{3} }[/tex]
Step-by-step explanation:
Since a = 6, then, b = 3.47 ( opposite of 30°).
By applying the pythagoras theorem..
[tex] \boxed{\bf {h}^{2} = {p}^{2} + {b}^{2}} [/tex][tex]\bf {(c)}^{2} = {(a)}^{2} + {(b)}^{2} [/tex][tex] \bf {c}^{2} = {(6)}^{2} + {(3.47)}^{2} [/tex][tex] \bf {c}^{2} = 36 + 12[/tex][tex]\bf {c}^{2} = \sqrt{48} [/tex][tex]\bf c = 4 \sqrt{3} [/tex]______________________Answer:
4√3 or B
Step-by-step explanation:
find the length of AD
The length of AD is 5 units. so, option A is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
The length of DC is given as 13 units.
The length of AC is given as 12 units. We can see that angle D is a right angle, so the triangle will be a right-angle triangle.
by Pythagoras theorem;
[tex]DC ^2 = AD^2 + AC^2\\\\13^2 = AD^2 + 12^2\\\\AD^2 = 169 - 144\\\\AD^2 = 25\\\\AD = 5[/tex]
Hence, the length of AD is 5 units. so, option A is the correct answer.
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Does this graph represent a function? Why or why not?
HELP PLEASE ASAP Which choices are equivalent to the quotient below? Check all that apply.
√12/√6
A. √2
B. √4/√2
c. 2/√3
D.√6/√2
E. √6/2
F. 2
Step-by-step explanation:
[tex] = \frac{ \sqrt{12} }{ \sqrt{6} } [/tex]
[tex] = \sqrt{ \frac{12}{6} } [/tex]
[tex] = \sqrt{2} [/tex]
The answer is A.
A roof repairman charges a $60 consult fee, and then $45 per hour to complete repairs. if the homeowner pays a total of $195, how long was the repairman there? answers a: 2 hours b: 2.5 hours c:4 hours d: 3 hours
The time spent by the repairman there will be 3 hours so the correct answer is option D.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
A roof repairman charges a $60 consult fee, and then $45 per hour to complete repairs. if the homeowner pays a total of $195.
The time will be calculated as:-
Total amount = $195
Now the fixed consulting cost will be $60 and will be deducted from the
total amount.
Variable cost = 195 - 60 = 135
The $45 per hour charge so for $145 the time will be:-
Time = 135 / 45
Time = 3 Hours
Therefore the time spent by the repairman there will be 3 hours so the correct answer is option D.
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What is the measure of an angle if it is 120 less
than four times its own supplement?
Answer:
120°
Step-by-step explanation:
x = angle supplement = 180-x
x = 4(180-x) -120
x = 720 - 4x - 120
5x = 600°
x =120°
A man bought a car for Gh55,000.00 and sold it for Gh65,000.00. Find the percentage gain.
Answer:
18.18%
Step-by-step explanation:
(65000-55000)/55000×100
What is the range of the translated function? {y|y < 0} {y|y ≥ 0} {y|y is a natural number} {y|y is a real number}
The Range of the function is {y|y is a real number} , Option D is the correct answer
What is Range ?Range of a function is all the value a function can obtain.
From the figure it can be seen that the graph is moving slowly in either direction.
It extends from -∞ to +∞ ,
Therefore , {y|y is a real number} , Option D is the correct answer.
The complete question is
The graph shows a vertical translation of y = ³√x
What is the range of the translated function?
{y|y < 0}
{y|y ≥ 0}
{y|y is a natural number}
{y|y is a real number}
The image of the translated function is attached.
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Which quadrilateral has exactly one pair of parallel sides?
a) rhombus
b) kite
c) trapezoid
d) parallelogram
Answer:
trapezoid
the horizontal side lengths wont touch each other if you extend them out
