Answer:
The distance between P and Q is 54
Step-by-step explanation:
We are given that triangle RPQ is similar to triangle RTS.
Property of similar triangle: The ratio of any pair of corresponding sides is the same.
So, by property : [tex]\frac{RP}{RT}=\frac{PQ}{ST}[/tex]
PR=42
PQ=x
ST=36
RT=28
So,[tex]\frac{42}{28}=\frac{x}{36}[/tex]
[tex]\frac{42 \times 36}{28}=x[/tex]
54=x
Hence the distance between P and Q is 54
Answer:
D) 54
Step-by-step explanation:
Completed the test earlier
based on the sequence -13, -8, -3, 2, 7, 12 what will be the 500th term?
Answer:
2482
Step-by-step explanation:
Because this sequence starts with -13 and adds 5 each time, the 500th term will be 5(499)-13=2482. Hope this helps!
Answer:
2482
Step-by-step explanation:
What is the value of y?
Answer:
C
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
114° is an external angle of the triangle , thus
y + y = 114°
2y = 114° ( divide both sides by 2 )
y = 57° → C
can anyone help? i don’t understand this !
PLZZZ HELPP 3+7 - 1/2 is an example of
A. a numerical equation
B. an algebraic equation
C. a numerical expression
D. an algebraic expression
Answer:
An algebraic equation (I think :/)
Answer:
Not really
(Algebraic expression)
What the answer to this
Given:
The value of x = 2.
Solution:
F ( x ) = 2x⁴ - x³ + 5x - 9
=> 2 ( 2 )⁴ - ( 2 )³ + 5 × 2 - 9
=> 2 × 16 - 8 + 10 - 9
=> 32 - 8 + 10 - 9
=> 24 + 1
=> 25
A. 25
determine the equation of the line that has a slope of 1/3 and goes through (7,6)
Answer: y=1/3x+11/3
Step-by-step explanation:
Since we given the slope, we can write a slope-intercept form equation.
y=1/3x+b
Since we we don't have our y-intercept, we can plug in the coordinate we are given to find the y-intercept.
6=1/3(7)+b
6=7/3+b
11/3=b
Now that we have our y-intercept, we can complete our equation.
y=1/3x+11/3
5. A company is deciding which box to use for their merchandise. The first box measures 8 inches by 6.25 inches by 10.5 inches. The second box measures 9 inches by 5.5 inches by 11.75 inches. Which box required more material to make?
6. If each box (from #5) used material that cost $0.03 per square inch to make, how much does a company save by choosing to make fifty boxes of the smaller box in comparison to fifty boxes of the larger box?
Answer: 5. The second box required more material to make.
6. A company saves about $84.94 by choosing to make fifty boxes of the smaller box in comparison to fifty boxes of the larger box.
Step-by-step explanation:
5. To solve this problem you need to find the volume of the boxes.
Volume of the first box.
v= 8 * 6.25 * 10.5
v= 525
Second box volume
9 * 5.5 * 11.75 = 581.625
Which means the second box required more material to make because it has the greatest volume.
6. To solve this you have to multiply the volume of small and large boxes by 50 the multiply it by 0.03.
525 * 50 = 26250 * 0.03 = 785.5
581.625 *50 = 29081.25 * 0.03= 872.4375
872.4375 - 785.5 = 84.9375 which is about $84.94.
4.83×10^5 as an ordinary number
Answer:
483,000
Step-by-step explanation:
10^5=100,000
4.83×100,000=483,000
please help with this for brainliest
Answer:
105cm^2
Step-by-step explanation:
5 times 6 = 30
30 div 2 = 15
6 times 15 = 90
90 + 15 = 105
Help me please!! It’s due soon!!
Answer:
13.7
Step-by-step explanation:
Using cosine formula:
AB^2 = AC^2 + BC^2 - 2*AB*BC*cosC
AB^2 = 15^2 +12^2 -2*15*12*cos60
AB = 13.7 in
Plzz Help will mark brainlest!
Answer:
Step-by-step explanation:
180 degree
A train from Philadelphia to Boston left Philadelphia at 1 pm and arrived to Boston at 4 pm. What was its average speed if the distance it covered was 270 miles?
Answer:
90 miles per hour is the average speed.
Step-by-step explanation:
The formula for Average Speed can be given as follows:
[tex]\text{Average Speed}= \dfrac{\text{Total Distance Traveled}} {\text{Total Time Taken}}[/tex]
Here time taken is from 1 PM to 4 PM i.e.
Total Time taken = (4-1) hours = 3 hours
Also, it is given that the Total distance covered = 270 miles
As per the formula above:
[tex]\text{Average Speed} = \dfrac{270}{3}\\\Rightarrow \text{Average Speed} = 90\ miles/hour[/tex]
So, answer is: 270 miles/ hour is the average speed of the train from Philadelphia to Boston.
What is the value of x in the equation x - ty = 30, when y = 15?
Answer:
t15 is equal to 30-x so therefore t= 30-x/15
You start driving north for 48 miles turn right and drive east for another 14miles at the end of driving what is your striaght line distance from your starting point
Answer: 50 miles
Step-by-step explanation:
a^2 + b^2 = c^2
48^2 = 14^2 = c^2
c^2 = 2500
c = 50
I WOULD BE SO HAPPY IF SOMEONE COULD HELP ME FILL IN THESE BOXES
Which of the following situations represents a multiplicative relationship with a unit rate of 0.5?
On her diet, Mrs. Jackson lost 5 pounds every month.
Mila eats 12 cup of yogurt every day.
Marvin spent $5 on a value meal after he earned $0.50 a day for doing chores at home.
Manuel has 5 pet turtles. He hopes to add a new turtle to his reptile habitat each month.
Answer:
Marvin spent $5 on a value meal after he earned $0.50 a day for doing chores at home
Step-by-step explanation:
The relationship between two quantities could be additive (In this case, one quantity is a result of adding a value to the other quantity) or multiplicative (In this case, one quantity is the result of multiplying the other quantity by a value).
Multiplicative Relationship is a relationship that shows two quantities expressed as multiples of each other.
It can be written as: y = nx
where y and x are multiples of each other
n is equivalent to the ratio of y to x
Let's consider the options we have:
a) On her diet, Mrs. Jackson lost 5 pounds every month.
y = x -a (a= constant)
y = x-5
There is no multiplicative relationship of a unit rate of 0.5 in the statement.
b) Mila eats 12 cup of yogurt every day.
There is no multiplicative relationship of a unit rate of 0.5 in the statement.
c) Marvin spent $5 on a value meal after he earned $0.50 a day for doing chores at home.
y = nx
n = 0.5
y is the result of multiplication of 0.5 by x
y = 0.5x
d) Manuel has 5 pet turtles. He hopes to add a new turtle to his reptile habitat each month.
y = x+a (a = constant)
y = x +1
There is no multiplicative relationship of a unit rate of 0.5 in the statement.
If there is an 8.5% tax on a $30 sweater, what is the tax amount?
Answer:
$32.55
Step-by-step explanation:
Before Tax Price: $30.00
Sale Tax: 8.50% or $2.55
After Tax Price: $32.55
Determine f(5)
f(x)=2x'2-1 if x < or equal to -1
3x+2 if x > -1
Answer:
To make it clearer, I just put every thing under the formal form
f(x) = [tex]\left \{ {{2x^2-1~~~~if~~~~ x\leq -1} \atop {3x+2~~~~~if~~~~~x>-1}} \right.[/tex]
Step-by-step explanation:
Now, you have 2 equations with 2 conditions. One is > -1, and one is < -1.
The question is about f (5). So, which equation you use to replace x = 5? The first one or the second one? and why?
Answering those questions help you understand how it works.
Write an equation to describe the relationship between x and y
Answer:
y= x2+x-3
Step-by-step explanation: i think this is the answer
A bicycle ramp used for competitions is a triangular prism. The volume of the ramp is 313.2 cubic feet. Write and solve an equation to find the width of the ramp.
Answer:
l = 626.4/bh
Step-by-step explanation:
A triangular prism have a base that is triangular in shape. The volume of a prism has the volume represented as follows.
volume = Al
where
A = Base area
l = width
Since the base is a triangle the base area will be the area of a triangle. Therefore,
volume of a triangular prism = 1/2bh l
where
b = base of triangle
h = height of triangle
volume = 313.2 ft³
313.2 = 1/2bh l
Make the width(l) subject of the formula
multiply both sides by 2
626.4 = bhl
divide both sides by bh
l = 626.4/bh
l = 626.4/bh
recall l = width
What is the rate of change of the amount earned with respect
to hours worked for this function?
hours per dollar
1/13 hours per dollar
2/5 hours per dollar
3 dollars per hour 13 dollars per hour
Option D 13 dollars per hour
Fredrick has a square with an area of 36 square inches. He decides to enlarge the square by adding 4 inches on each side. What is the area of the enlarged square?
Answer:
100
Step-by-step explanation:
6x6=36
adding 4 is equal to 10
10x10 = 100
!!PLEASE HELP!! WILL MARK BRAINIEST!!!
Find the product. write your answer in exponential form 4^7 x 4^-6
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
add the exponents
(7+(-6)
=7-6
=1
and let the same base =4^1 =4
Draw a tree digram.
What is the probability of waking up early at least one day?
Answer:
The probability of waking up early at least one day is 1.2
Step-by-step explanation:
We are given the tree diagram
We are supposed to find the probability of waking up early at least one day
So, we are supposed to find the probability of waking up early for 1 and more than 1 day
By studying the tree diagram
So the probability of waking up early for 1 and more than 1 day =[tex]\frac{2}{5}+\frac{2}{5}+\frac{2}{5}[/tex]
The probability of waking up early at least 1 day = [tex]\frac{2}{5}+\frac{2}{5}+\frac{2}{5}=1.2[/tex]
Hence the probability of waking up early at least one day is 1.2
PLEASE HELP MEEEEE!!!!
Answer:
108 is the answer
Step-by-step explanation:
Josh has a itunes gift card worth $75. After he purchases the first song on itunes, the cards value is $74.11. After he purchases the second song, its value is $73.22. After he purchases the third song, its value is $72.33. Assuming the pattern continues, write an equation to define A(n), the amount of money on the gift card after n song purchases.
How many songs can Josh purchase with this card only?
Answer:
A(n)=75.89-0.89n85 songsStep-by-step explanation:
The worth of the card =$75
The value of the card decreases after each music purchase forming a sequence:
75,74.11,73.22,72.33...
Now,
74.11-75=-0.8973.22-74.11=-0.8972.33-73.22=-0.89We see that the sequence forms an arithmetic sequence:
Where the first term, a is 75
Common difference, d=-0.89
We want to write an equation to define A(n), the amount of money on the gift card after n song purchases.
For an arithmetic sequence,the nth term A(n)=a+(n-1)d
Therefore:
The amount of money on the gift card after n song purchases.
A(n)=75-0.89(n-1)
A(n)=75+0.89-0.89n
A(n)=75.89-0.89n
To find out how many songs can Josh purchase with this card only, we take our nth term A(n) of the sequence to be 0 and solve for n.
A(n)=75.89-0.89n
0=75.89-0.89n
0.89n=75.89
Divide both sides by 0.89
n=85.3
n=85
Therefore, Josh can purchase 85 songs with this card only
perpendicular help i need help
Answer:
m₁×m₂ = -1
m₁ = 3 and m₂ = -1/3
3×-1/3 = -1
-1 = -1
Hence proved, the given two lines are perpendicular.
Step-by-step explanation:
You can prove that the two lines are perpendicular if the following condition holds true.
m₁×m₂ = -1
Where m₁ is the slope of line 1 and m₂ is slope of line 2
So first you have to find out the slope of each line.
You are given 2 equations
y = 3x + 5 eq. 1
6y + 2x = 1 eq. 2
You have to write these equations in slope-intercept form to find out their slopes.
The slope-intercept form is given by
y = mx + b
Comparing the general form with eq. 1
y = 3x + 5
We notice that the slope is m₁ = 3
Now convert the eq. 2 into slope-intercept form
6y + 2x = 1 eq. 2
6y = -2x + 1
y = (-2x + 1)/6
y = -1/3x + 1/6 eq. 2
Comparing the general form with eq. 2
y = -1/3x + 1/6
We notice that the slope is m₂ = -1/3
Now we have slopes of both lines so let us test whether they are perpendicular or not
m₁×m₂ = -1
m₁ = 3 and m₂ = -1/3
3×-1/3 = -1
-1 = -1
Hence proved, the given two lines are perpendicular.
What is happening to this graph when the x-values are between -1and 1?
Answer:
B. It is Decreasing
Step-by-step explanation:
When X = -1, Y = 7/3 putting a point at (-1, 7/3)
When X = 1, Y = -1/3 putting another point at (1, -1/3)
The Y value decreases from X = -1 to X = 1
Answer:
Step-by-step explanation:
The graph and the related function are decreasing at a steady rate on the interval (-1, 1).
YEAR 9 MATHS PLEASE HLEP A café owner records the average monthly temperature and the monthly sales of soup over a year. The average monthly temperature for the next month is predicted to be 7°C. Use the graph to estimate the sales of soup that month.
Answer:
480.
Step-by-step explanation:
We would need to draw the line of best fit through these point.
An estimate would be about 480.
Segment AB is shown on the graph. Which shows how to find the x-coordinate of the point that will divide into a 2:3 ratio using the formula ? x = (−3−2) + 2 x = (2+3) − 3 x = (−3−2) + 2 x = (2+3) − 3On a coordinate plane, a line has points (negative 2, negative 4) and (4, 2). Point P is at (0, 4). Which points lie on the line that passes through point P and is parallel to the given line? Select three options. (–4, 2) (–1, 3) (–2, 2) (4, 2) (–5, –1)
Answer:
(–1, 3), (–2, 2) and (–5, –1)
Step-by-step explanation:
On a coordinate plane, a line has points (-2, -4) and (4, 2). Its slope is:
m = [2 - (-4)]/[4 - (-2)] = 1
To be parallel, both lines have the same slope.
General equation of a line:
y = mx + b
Replacing with m = 1 and Point P (0, 4), we get:
4 = 1(0) + b
4 = b
Therefore, the equation of the line is:
y = x + 4
Replacing x = -4 into the equation:
y = -4 + 4 = 0
Replacing x = -1 into the equation:
y = -1 + 4 = 3 then (-1, 3) lies on the line
Replacing x = -2 into the equation:
y = -2 + 4 = 2 then (-2, 2) lies on the line
Replacing x = 4 into the equation:
y = 4 + 4 = 8
Replacing x = -5 into the equation:
y = -5 + 4 = -1 then (-5, 1) lies on the line
Answer:
[tex](-1,3), (-2,2), (-5,-1)[/tex]
Step-by-step explanation:
1) There's Need for the segment. Reminds me the centroid of a triangle which divides the triangle into two segments in a 2:3 ratio.
2.On a coordinate plane, a line has points (negative 2, negative 4) and (4, 2). Point P is at (0, 4). Which points lie on the line that passes through point P and is parallel to the given line? Select three options. (–4, 2) (–1, 3) (–2, 2) (4, 2) (–5, –1)
1) Let's find the slope of the line [tex]r[/tex] with points [tex]A(-2,-4) \:and\:B(4,2)[/tex]
[tex]m=\frac{2-(-4)}{4-(-2)}=\frac{6}{6}=1[/tex]
2) Now the linear coefficient,
[tex]y=mx+b\\0=1(-2)+b\\b=-2[/tex]
Then the first line [tex]r[/tex] whose points are [tex]A(-2,-4) \:and\:B(4,2)[/tex] is [tex]y=x-2[/tex]
3) From Analytical Geometry, a Parallel line must have the same slope, so that these lines may never intercept each other just like the graph below. So the slope, the angular coefficient must value the same amount.
[tex]m_1=m_{2} \therefore m_{1}=m_{2}=1[/tex]
So, the line [tex]s[/tex] is :
[tex]y=mx+b\\4=1*0+b\\\therefore b=4\\y=x+4[/tex]
4) Testing the points
[tex]2=-4+4 \:\\2\neq 0\\(-1,3)\\3=-1+4\\3=3\\(-2,2)\\2=-2+4\\2=2\\(4,2)\\2\neq 2+4\\(4,2)\\2\neq 4+2\\(-5,-1)\\-1=-5+4\\-1=-1[/tex]