Answer:
93
Step-by-step explanation:
By the definition of a midpoint, FG=GH.
[tex]16x-19=12x+9 \\ \\ 4x-19=9 \\ \\ 4x=28 \\ \\ x=7 \\ \\ GH=16(7)-19=\boxed{93}[/tex]
The lowest form of this fraction 75/100
Using the graph, find the following values of the function.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
f(1) = 1
f(4) = -2
f(0) = 2
Step-by-step explanation:
y = f(x)
Which numbers are irrational?
A. √30
B. √16
C. √42
D. √169
Select all that apply.
If JK = 8, IL =31, and JL = 25, what is IK?
Answer: IK=14
Step-by-step explanation:
IK=IJ+JK
IL=IJ+JL
IL-JL=IJ+JL-JL
IJ=IL-JL
IK=IL-JL+JK
IK=31-25+8
IK=6+8
IK=14
8^6x8^9= ?
64^15
64^3
8^15
8^54
Answer:
[tex]8^{15[/tex]
Step-by-step explanation:
Hello!
Use exponent rule: [tex]a^b * a^c = a^{b + c}[/tex]
Use the rule to simplify the exponential expression.
Simplify[tex]8^6 * 8^9[/tex][tex]8^{6 + 9}[/tex][tex]8^{15[/tex]The simplified form is [tex]8^{15[/tex].
The position of a body moving along the x-axis is given by s = t³ - 12t2+36t, with s in meters and t in seconds.
Find the total distance traveled by the body from t = 0 tot = 4.
Total distance =
The total distance travelled by the body is 48 meters
According to the question we have been given an equation of the position of a body moving along x-axis as
s = t³ - 12t² + 36t
where, s = distance in meters
t = time in seconds
We need to find the total distance traveled by the body from t=0s to t=4s
The formula for the total distance is given as :
S = |s(1) - s(0)| + |s(2) - s(1)| + |s(3) - s(2)| + |s(4) - s(3)|
Now we will find out the distance travelled in time 0s to 4s
when t = 0s , s = (0)³ - 12(0)² + 36*0
= 0m
t = 1s , s = (1)³ - 12(1)² + 36*1
= 25m
t = 2s , s = (2)³ - 12(2)² + 36*2
= 32m
t = 3s , s = (3)³ - 12(3)² + 36*3
= 27m
t = 4s , s = (4)³ - 12(4)² + 36*4
= 16m
Putting the required values in the above formula we get ,
S = |25-0|+|32-25|+|27-32|+|16-27|
S = 25 + 7 + 5 + 11 meters
S = 48 meters
Hence the total distance travelled by the body is 48 meters
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enter the sum of numbers as a product of their GCF
15 + 90
Answer:
15+90=3×18
Step-by-step explanation:
GCF= 5
Using the pencil,plot the point (-3,-6)
Answer:
-3 will be on the -x axis n the -6 will be on the -y axis so both will meet at a point.
Step-by-step explanation:
that is all I understand am not sure if I am ryt
Christa had a music lesson every week for one year.
Each of the 52 lessons lasted for 45 minutes.
Calculate the total time that Christa spent in music lessons.
Give your time in hours.
Answer:
39 hours
Step-by-step explanation:
52 × 45 = 2340
2340 mins into hours = 39 hours
hope this helps :)
The midpoint of AB is M(-6, 4). If the coordinates of A are (-7, 2), what are the
coordinates of B?
The coordinates of B is (-5, 6).
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space
What is section formula ?
The section formula helps in determining the coordinates of a point which facilitates division of the line joining two points in a ratio. This takes place either internally or externally.
P (x, y)= (c*m + a*n)/(m + n) , (d*m + b*n)/(m + n ).
Given:
let the coordinates of B (x, y)
M is midpoint M(-6,4) and coordinates of A are (-7, 2)
Using section formula
-6 = (x -7)/2
-12 = x -7
x = -5
and, 4 = y+2/2
8 = y+2
y = 6
Hence, the coordinates of B is (-5, 6)
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Sean mixes coconut oil with several other ingredients to make homemade toothpaste for his dog Rocky. He uses 1/2 cup of coconut oil to make 2/3 cup of toothpaste.
Trey Invested his savings in two Investment funds. The $12,000 that he invested in Fund A returned a 1% profit. The amount that he invested in Fund B returned a 6% profit. How much did he invest in Fund B, if both funds together returned a 3% profit?
The amount Trey invested in Fund B is $8,000.
Profit is a residual income, It is the gain amount from any kind of business activity. In short, if the selling price (SP) of the product is more than the cost price (CP) of a product, then it is considered as a gain or profit. while return is a total revenue. Profits may be negative, whereas returns, such as wages and interest are always positive.
amount invested in Fund A = $12,000 (given)
profit returned by Fund A = 1% of $12,000 (given)
= 1/100*$12,000
= $120
Let amount invested in Fund B = x (assumption)
profit returned by Fund B = 6% of x (given)
= 6/100*x
= $ 6x/100
Given that both funds A and B together returned a 3% profit, So the equation we get is
120+6x/100 = 3% of (12,000+x)
(12,000+6x)/100 = 3/100* (12,000+x)
12,000+6x = 3(12,000+x)
12,000+6x = 36,000+3x
6x-3x = 36,000-12,000 (bringing like terms on same side)
3x = 24,000
x = 24,000/3
x = $8,000
Therefore, we can conclude that the amount Trey invested in Fund B is $8,000
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The line y = kx + 4 goes through the point (2, -2). Find the value of k.
k = -3 is the value in straight line.
What is straight line?
Simply put, a straight line is a line devoid of bends. A straight line is one that does not curve and reaches to infinity on both sides.
Different type
Horizontal Line Horizontal Lines.Crossing Lines.Lines that are parallel.On putting the values of the point in the equation of line, the value of X = 2 and Y = -8
When a line passes through a point, the point satisfies the equation of the line.
The line y = kx + 4 goes through the point (2, -2)
So, ( 2 , -2 ) must satisfy the equation of the line.
Put x = 2 y= - 2 in equation y = kx + 4
-2 = k * 2 + 4
- 2 = 2k + 4
-2 -4 = 2k
-6 =2k
k = -6/2
k = -3
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3. If m/E+mZF = 120°, which expression is equivalent to mZG?
A (7x)°
C (7x+4)°
B (8x)°
D (8x + 4)º
(7x + 2)°
(8x-2)
In a triangle of EFG we have ∠E+∠F = 120°,E=(8x-2)° and F=(7x+2)°.
Option B is true and angle of G is 60°.
Given that,
∠E+∠F = 120°
In the figure we have a triangle with EFG.
E=(8x-2)°
F=(7x+2)°
We know
∠E+∠F = 120°
8x-2+7x+2=120
15x=120
x=120/15
x=8
We got x =8
∠E=8[tex]\times[/tex]8-2=62°
∠F=7[tex]\times[/tex]8+2=58°
Now, we know in a triangle all angles are equal to 180°.
∠E+∠F+∠G=180°
62°+58°+G=180°
120°+G=180°
G=180°-120°
G=60°
We have 4 option
a) (7x)° which is false
b) (7x+4)° which is true (7[tex]\times[/tex]8+4=60°)
c)(8x)° which is false
d) (8x+4)° which is false
Therefore, option B is true and angle of G is 60°.
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Find the distance between the points. Give an exact answer and an approximation
to three decimal places.
(-1,-9) and (6, - 16)
The distance between the two points are-9.87 units.
What is referred as the distance formula?In coordinate geometry, we have a list of distance formulas that can be used to obtain the distance between two points, the distance between a point and a line, the distances between two vertical lines, this same distance between these two parallel planes, and so on.The Euclidean distance formula is another name for the distance formula used to calculate the distance between 2 points in a two-dimensional plane. Acknowledge two points in the 2D plane, A(x₁, y₁) and B, to derive the formula (x₂, y₂). Assume 'd' represents the distance from A to B.The distance formula is;
d² = (y₂ - y₁)² + (x₂ - x₁)²
Let the two given points be;
A(x₁, y₁) = (-1,-9)
B(x₂, y₂) = (6, - 16)
Put the values in the formula;
d² = (-16 + 9)² + (6 + 1)²
d² = (-7)² + (7)²
d² =2 (7)²
d = 7√2
d = 7×1.41
d = 9.87
Therefore, the distance between the two points is found as 9.87 units.
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Evaluate the expressions when x = 3; y = 4 & z = -2
(x + y) * z, 2y + 3z + 4y - xz =
comma = separate
Answer:
Sub in the numbers given to x, y, z and use calculator to solve
Can someone please break this down for me.
Answer:
length: 343 marea: 6418 m²Step-by-step explanation:
Given an oval track in the shape of a 48 m by 96 m rectangle with semicircular ends, you want the length of the track and the area enclosed.
Track LengthIf you remove the rectangle, you see that what remains is a circle of diameter 48. The length of that circular portion of the track is the circumference of the circle:
C = πd
C = π(48 m) = 48π m ≈ 151 m
Added to that length are the two 96 m sides of the rectangle. So, the total length of the track is ...
track length = curved length + straight length
track length = 151 m + 2×96 m = 343 m
The length of the track is 343 meters.
Enclosed areaThe area enclosed by the track includes the area of the circle we saw above, and the area of the rectangle.
The radius of the circular portion is half the diameter, or 24 m. Then the area is ...
A = πr²
A = π(24 m)² = 576π m² ≈ 1810 m²
The area of the rectangular portion is the product of length and width:
A = LW
A = (96 m)(48 m) = 4608 m²
The enclosed area is the sum of these areas:
enclosed area = area of circle + area of rectangle
enclosed area = 1810 m² +4608 m² = 6418 m²
The area enclosed by the track is 6418 square meters.
The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.
What is the perimeter and the area enclosed by the track?In this problem we have a composite figure generated by a rectangle and two semicircles, of which we must determine its perimeter and area. The perimeter is the sum of the contour lengths of the semicircles and the rectangle and the enclosed area is the sum of areas of the two semicircles and a rectangle.
The perimeter of the composite figure is:
p = 2π · r + 2 · l
p = 2π · (24 m) + 2 · (96 m)
p ≈ 342.796 m
A = π · r² + l · (2 · r)
A = π · (24 m)² + (96 m) · (48 m)
A ≈ 6417.557 m²
The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.
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Sara has a rectangular shaped backyard. The backyard is 22.5 feet wide and 35.75 feet long. What is the area of the rectangular backyard?
The area of the rectangular backyard is 804.37
How to calculate the area of the rectangle ?
The area of a rectangle can be calculated by multiplying the length and the width
Area= length × width
Length= 35.75 feet
Width= 22.5 feet
Area= 35.75 × 22.5
= 804.37
Hence the area of the rectangular backyard is 804.37
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-5/3,-2,-7/3,-8/3 arithmetic
Answer:
Step-by-step explanation:
comment on the comment section with a complete question I will help you there please
Melatonin is fast-acting and has a half-life of approximately 30 minutes. If you take a 10 milligram tablet, write an exponential equation to model this after t time periods.
The exponential equation to model this after t time periods is:
N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]
Given,
Melatonin is fast-acting and has a half-life of approximately 30 minutes.
10-milligram tablet is taken.
We need to write an exponential equation to model this after t time periods.
What is half-life?Half-life is the time required for a quantity to reduce to half of its initial value.
The formula is given as:
N(t) = [tex]N_{0} ~(\frac{1}{2})~^\frac{t}{t_{1/2}}[/tex]
Where
N(t) = quantity of the substance remaining
[tex]N_{0}[/tex] = initial quantity of the substance
[tex]t_{1/2}[/tex] = half-life of the substance
We have,
Half-life = 30 minutes
[tex]N_{0}[/tex] = 10 mg
The exponential equation to model this after t time periods is:
N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]
Thus the exponential equation to model this after t time periods is:
N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]
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You have four cards: Jack, Queen, King, and Ace. What is the probability of drawing a face card, not replacing it, and then choosing another face card?
Write in fraction form!
Step-by-step explanation:
if I understand you correctly, then we have the 4 described cards. 3 of these 4 cards are face cards (Jack, Queen, King).
a probability is always desired cases over totally possible cases.
so, for the first pull we have a probability of
3/4 = 0.75
we have 4 total possibilities, and 3 of them are the desired outcome.
for the second pull we have then only 3 cards left (we did not replace the first pulled card). and because the first pulled card was in this scenario a face card, 2 out of these 3 cards are face cards.
so, the probability to pull a face card here is
2/3 = 0.66666...
when we combine these 2 events into one connected event (we are creating event 1 AND event 2), we multiply the probabilities, giving us
3/4 × 2/3 = 6/12 = 1/2 = 0.5
What is the length of the line segment that joins
points (4, -1) and (7,5)?
A. 5 B. √13
C. √29 D. √45
Answer:
5 is the answer to that question
Answer:
D. √45
Step-by-step explanation:
(4, -1) (7, 5)
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(7 - 4)² + (5 - (-1))²
d = √(3)² + (6)²
d = √9 + 36
d = √45
I hope this helps!
An herbalist has 50 oz of herbs costing $4 per ounce. How many ounces of herbs costing $1 per ounce should be mixed with these 50 oz of herbs to produce a mixture costing $2.50 per ounce?
The ounces of herbs costing $1 per ounce that should be mixed with these 50 oz of herbs to produce a mixture costing $2.50 per ounce?
is 50 ounces.
How to illustrate the information?Let x = the amount of herb that costs $1 per ounce.
Based on the information,the total weight will be:
x + 50 = y.
At $2.50, the cost of the mixture will be:
1x + 4(50) = 2.50y
x + 200 = 2.50y
x + 200 = 2.50(x + 50)
x + 200 = 2.50x + 125
Collect like terms
2.5x - x = 200 - 125
1.5x = 75
Divide
x = 75/1.5
x = 5.
Therefore, the correct option is 50
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How do you write 0.00007112 in scientific notation?
Answer:
7.112 x [tex]10^{-5}[/tex]
Step-by-step explanation:
You need to re-write the number so that it is 1 or larger but less than 10. To do that, we need to move the decimal 5 spaces to the right. The actually number is smaller. The [tex]10^{-5}[/tex] is telling me how much smaller the number actually is. To get the number in standard notation I would have to take 7.112 and divide it by 100,000.
HELP!!! Describe the distribution of points per game
Definition: n math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Given,
Points scored per game by 35 NBA players during the 2017 basketball season.
Context: Points scored per game by 35 NBA players
Shape: dotted, no gaps
Outliers: none
Center: 14(Median)
Spread: Data varies from somewhere between (12-14) to somewhere between (24-26)
context is about the graph
shape is about the representation
outliers is whether any point is farther
center is the median
spread is till where the graph is extended with gaps in between
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what ratio is equivalint to 3:1
Answer:
3:1 = 6:2 = 12:4
Hope this helps :)
Answer:
3.1=12.4
Step-by-step explanation:
12.4
12/12+4=12/16=3/4.
so 3.1=12.4
Two factory plants are making TV panels. Yesterday, Plant A produced 4 times as many panels as Plant B. Three percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 980 defective panels?
Answer:
7000 panels.
Step-by-step explanation:
Let x be the number of panels produced by Plant B.
Therefore:
4x = number of panels produced by Plant A.x = number of panels produced by Plant B.Given information:
Defective panels from Plant A = 3%Defective panels from Plant B = 2%Total number of defective panels = 980Create an equation with the given information and defined variables, remembering to write the percentages in their decimal form:
[tex]\implies 0.03(4x) + 0.02x = 980[/tex]
To find the number of panels Plant B produced, solve the found equation for x:
[tex]\implies 0.03(4x) + 0.02x = 980[/tex]
[tex]\implies 0.12x + 0.02x = 980[/tex]
[tex]\implies 0.14x = 980[/tex]
[tex]\implies \dfrac{0.14x}{0.14} = \dfrac{980}{0.14}[/tex]
[tex]\implies x=7000[/tex]
Therefore, Plant B produced 7000 panels.
Bob invested his savings in two investment funds. The amount he invested in Fund A was $8000 less than the amount he invested in Fund B. Fund A
returned a 2% profit and Fund B returned a 7% profit. How much did he invest in Fund B, if the total profit from the two funds together was $1730?
a = amount invested at 2%
how much is 2% of "a"? (2/100) * "a", namely 0.02a.
b = amount invested at 7%
how much is 7% of "b"? (7/100) * "b", namely 0.07b.
We know that fund A is less than fund B by 8000, that is a = b - 8000.
we also know that the yielded amount in interest is $1730, so if we simply add their interest, that'd be 0.02a + 0.07b = 1730.
[tex]\boxed{a = b - 8000} \\\\\\ 0.02a~~ + ~~0.07b~~ = ~~1730\implies 0.02(\stackrel{a}{b-8000})~~ + ~~0.07b~~ = ~~1730 \\\\\\ 0.02b-160+0.07b=1730\implies 0.02b+0.07b=1890\implies 0.09b=1890 \\\\\\ b=\cfrac{1890}{0.09}\implies \blacksquare~~ b=21000 ~~\blacksquare[/tex]
A city places street lights at equal intervals along a city street beginning 3/8 mile from one end of the street. If the street is 7/8 mile long, how many street lights will the city use? Explain.
The number of street lights that will be needed is 3 street lights.
How to calculate the fraction?From the information, it was stated that the city places street lights at equal intervals along a city street beginning 3/8 mile from one end of the street. If the street is 7/8 mile long,
The number of street lights needed will be:
= 7/8 ÷ 3/8
= 7/8 × 8/3
= 7/3
= 3 street lights.
Therefore, the number of street lights that will be needed is 3 street lights.
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Can someone please help me. This is about indices
Answer:
x = 10/9
Step-by-step explanation:
Solve:
27^(3x-2) = 81
When solving equations in exponential form make sure the two bases on both sides are the same.
3^3(3x-2) = 3^4
Once the two bases are the same you cancel them out and used its exponent to solve the equation.
3(3x-2) = 4
9x-6 = 4
Add 6 to both sides.
9x-6+6 = 4+6
9x = 10
Divide both sides by 9.
x = 10/9
Therefore x = 10/9.
