Answer:
6.50x + 5 = 21.25 is the answer
Step-by-step explanation:
x=2.5
The inequality that represents Tricia's goal to earn at least $21.25 through her $5 allowance and $6.50 per hour from babysitting is E = 5 + 6.50h ≥ 21.25, where h represents the number of hours she babysits.
The student's question asks for an inequality to represent the situation where Tricia receives a $5 weekly allowance and earns $6.50 for each hour she babysits. The goal is to earn at least $21.25 to buy a present.
Let's denote the number of hours Tricia babysits as h. The inequality representing her total earnings E from both her allowance and babysitting will be:
E = 5 + 6.50h ≥ 21.25
This inequality implies that the sum of Tricia's weekly allowance ($5) and her babysitting earnings ($6.50 per hour multiplied by the number of hours h) should be at least $21.25.
Quadrilateral PQRS has vertices P(2, 10), Q(6, 8), R(6, 3), and K(2, 3).
What are the coordinates of S’ after a dilation of quadrilateral PQRS by a factor of 2 centered at the origin?
Answer:
[tex]S'(4,6)[/tex]
Step-by-step explanation:
Dilation rules :
For a pre-image point [tex](x,y)[/tex] which is dilated by a scalar factor of [tex]k[/tex] about the origin, the corresponding point of the image can be given by [tex](kx,ky)[/tex]
Pre-image point [tex](x,y)\rightarrow (kx,ky)[/tex] Image point
Given points of quadrilateral PQRS.
P(2,10)
Q(6,8)
R(6,3)
S(2,3)
The quadrilateral is dilated about the origin by a scalar factor of 2.
The co-ordinates of point S' after dilation can be given by:
[tex]S(2,3)\rightarrow S'((2\times2),(2\times3))[/tex]
Thus [tex]S'(4,6)[/tex] (Answer)
Answer:
As jitumahi456 states B).(4, 6) is the correct answer.
Step-by-step explanation:
I took the test on edg.
Jackson has let out 50 meter of kite string when he observes that his kite is directly above a point on the ground 30 meters away from him, how high is the kite?
The height of the observer can be taken negligible in case of big measurements. The height of the kite from the ground is 40 meters approximately.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Referring to the figure attached below, we have the vertical distance of the kite from the ground as the length of the side BC.
(assume that the height of the observer flying kite is negligible and that kite's string is straight, and some more basic assumptions)
Using the Pythagoras theorem as the triangle ABC is a right angled triangle as vertical distance means line perpendicular to the ground, we get the length of the line segment BC as:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|BC|^2 = |AC|^2 - |AB|^2\\\\|BC| = \sqrt{|AC|^2 - |AB|^2}\\[/tex]
(positive root since length is a non-negative quantity).
We have |AC| = length of the kite's string = 50 meters
|AB| = distance of the observer from the point directly above which the kite is flying = 30 meters
Thus, we get the height of the kite from the ground as:
[tex]|BC| = \sqrt{|AC|^2 - |AB|^2}\\|BC| = \sqrt{50^2 - 30^2} = \sqrt{1600} = 40\: \rm \text{(in meters)}[/tex]
Thus, the height of the kite from the ground is 40 meters approximately.
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A bag contains 10 red, 9 white, 8 yellow and 2 blue marbles. How many marbles must be taken out from the bag so that there will be 4 marbles of the same colour?
Answer:25
Step-by-step explanation:
10 plus 9+4+2 will give you 21 and it will have 4 yellow ones left
The ratio of pears to green apples is 1:3 how many pears are there
Answer:
There is 1 pear for every green apple! So in this ratio there would be 1 pear!
Step-by-step explanation:
-viridiancat4, an 8th grader! :)
the sum of 2fifteens and 10 fifteens
Answer:4/5
Step-by-step explanation:
2/15 + 10/15=12/15=4/5
easy right?
Which of the following pairs are alternate interior angles?
A.6 and 7
B.2 and 7
C.5 and 2
D.5 and 4
Ashots height changed from 150 cm to 165 cm during the last year. By what percent did Ashot become taller?
150 cm ......... 100 %
165 cm ...............x %
x = 165×100/150 = 16500/150 = 110 %
Answer:
10%
Step-by-step explanation:
Subtract 150 from 165, which gives 15.
Then, do 15/150 = 0.1
Convert decimal to percent by moving the decimal point two spaces back. 0.1 becomes 10%.
please help me with these, oh sweet jesus
Answer:
77. [tex]\cot^{6} x = \cot^{4} x \csc^{2}x - \cot^{4} x[/tex]Proved
78. [tex]\sec^{4}x \tan^{2} x = \sec^{2}x [\tan^{2}x + \tan^{4}x ][/tex] Proved
79. [tex]\cos^{3} x\sin^{2} x = [\sin^{2}x - \sin^{4}x] \cos x[/tex] Proved.
80. [tex]\sin^{4}x - \cos^{4}x = 1 - 2\cos^{2}x + 2 \cos^{4} x[/tex] Proved.
Step-by-step explanation:
77. Left hand side
= [tex]\cot^{6} x[/tex]
= [tex]\cot^{4} x \times \cot^{2} x[/tex]
= [tex]\cot^{4}x [\csc^{2}x - 1][/tex]
{Since we know, [tex]\csc^{2} x - \cot^{2}x = 1[/tex]}
= [tex]\cot^{4} x \csc^{2}x - \cot^{4} x[/tex]
= Right hand side (Proved)
78. Left hand side
= [tex]\sec^{4}x \tan^{2} x[/tex]
= [tex]\sec^{2} x [1 + \tan^{2}x] \tan^{2} x[/tex]
{Since [tex]\sec^{2}x - \tan^{2}x = 1[/tex]}
= [tex]\sec^{2}x [\tan^{2}x + \tan^{4}x ][/tex]
= Right hand side (Proved)
79. Left hand side
= [tex]\cos^{3} x\sin^{2} x[/tex]
= [tex]\cos x[1 - \sin^{2} x] \sin^{2} x[/tex]
{Since [tex]\sin^{2}x + \cos^{2} x = 1[/tex]}
= [tex][\sin^{2}x - \sin^{4}x] \cos x[/tex]
= Right hand side
80. Left hand side
= [tex]\sin^{4}x - \cos^{4}x[/tex]
= [tex][\sin^{2}x + \cos^{2}x]^{2} - 2\sin^{2} x \cos^{2}x[/tex]
{Since [tex]\sin^{2}x + \cos^{2} x = 1[/tex]}
= [tex]1 - 2\cos^{2} x[1 - \cos^{2}x ][/tex]
= [tex]1 - 2\cos^{2}x + 2 \cos^{4} x[/tex]
= Right hand side. (Proved)
Find the solution for 72 < 7x − 5.
1 x < -11
2 x > 11
3 x > 21
4 x < 11
Answer:
Option 2. [tex]x > 11[/tex]
Step-by-step explanation:
we have
[tex]72 < 7x-5[/tex]
Solve the inequality for x
Adds 5 both sides
[tex]72+5 < 7x-5+5[/tex]
[tex]77 < 7x[/tex]
Divide by 7 both sides
[tex]77/7 < 7x/7[/tex]
[tex]11 < x[/tex]
Rewrite
[tex]x > 11[/tex]
if I add .002 ounces of coloring to 3 lbs of product what is the percentage of coloring I used to product. I need to increase the amount of product but maintain the correct percentage of coloring. thank you
Answer:
0.0042%
Step-by-step explanation:
We know that 1 pound is equivalent to 16 ounces.
So, 3 pounds of a product is equivalent to (16 × 3) = 48 ounces of the product.
Now, it is given that I add 0.002 ounces of coloring to 3 lbs of product.
So, the required percentage of coloring I used to product is [tex]\frac{0.002 \times 100}{48 + 0.002} = 0.0042[/tex]% (Answer)
bob bought bill an item that cost 193. bill gave him 200. bob then took 100 out of the 200 to buy bill an item for 93. how much does bill owe Bob totally?
Answer:Bob Owes $186 to the store he purchased an item at
Step-by-step explanation:
Whats the slope of (-5,9) (7,3)
Answer:
-1/2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3-9)/(7-(-5))
m=-6/(7+5)
m=-6/12
m=-1/2
linear combination
Answer:
linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants)
Step-by-step explanation:
Five times the difference of twice a number and seven is negative twenty-five. Find the number.
The number is 1
Step-by-step explanation:
Let x be the required number
Then according to given statement
Five times the difference of twice a number and seven is negative twenty-five.
[tex]5(2x-7) = -25[/tex]
Simplifying
[tex]10x-35 = -25\\[/tex]
Adding 35 on both sides
[tex]10x-35+35 = -25+35\\10x = 10[/tex]
Dividing both sides by 10
[tex]\frac{10x}{10} = \frac{10}{10}\\x = 1[/tex]
Verification:
[tex]5[2(1)-7] = -25\\5(2-7) = -25\\5(-5) = -25\\-25=-25[/tex]
Hence,
1 is the number
Keywords: Linear equation
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Eric jogged for 47 minutes, ending at 3:35 p.m. When did Eric start his jog?
A) 2:48 p.m.
B) 2:30 p.m.
C) 2:58 p.m.
D) 4:22 p.m.
plz help ASAP TwT
Answer:
im pretty sure its c
Step-by-step explanation:
Citizens less than 18 years old are not allowed to vote define a variable and write an inequality for the ages of citizens who are not allowed to vote
Answer:
[tex]x < 18[/tex]
Step-by-step explanation:
We are given the following information in the question:
"Citizens less than 18 years old are not allowed to vote"
We define a variable x such that x represents the age of citizens.
We have to write a relationship with the help of an inequality for the ages of citizens who are not allowed to vote.
Citizens less than 18 are not allowed to vote.
So x should be less than 18.
This can be written as:
[tex]x < 18[/tex]
is the required inequality for the ages of citizens who are not allowed to vote.
Four runners formed a relay team at Jan’s high school. The team completed the relay in 3.86 minutes. Each runner ran exactly the Same time. What was each runners time?
Answer: All four runners ran .96 seconds
Step-by-step explanation: The total time of the four runners, divided by the amount of runners.
3.86/4= .965
Identify the transformation on the figure shown.
A) reflection over the x-axis
B) reflection over the y-axis
C) rotation about the x-axis
D) rotation about the y-axis
The transformation on the figure is a reflection over the y-axis.
How to identify the transformation?In the image, we can see that we have an original figure in the left side of the y-axis, and then it is reflected over it.
We can see that it is a reflection and not a translation, because the orientation of the figure changes (you can see that in both figures, the 90° is in the side farthest away from the axis).
So the correct option is B, reflection over the y-axis.
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a.3/8
b.1/2
c.5/8
d.7/8
Answer:
3/8
Step-by-step explanation:
You'd first want to count all the triangles (possibilities) which is 8 total numbers
Then find the even numbers. There is 2, 2, and 4 which is a total of 3 even numbers
The fraction would be 3/8 and it can't be simplified any further
Answer:
3/8
Step-by-step explanation:
This is because, out of 8 results, only 3 of them are even numbers. That is the biggest chance you have at getting an even number.
Differentiate from first principle
1. y= x^2 + 3x
2. y= x^2 + 3x + 8
Answer:
Differentiation of both the term is [tex]2x+3[/tex]
Step-by-step explanation:
As we have to use first principle of derivatives lets recall the formula.
[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]
Solving our eqaution.
[tex]y=x^2+3x[/tex]
We will work with [tex]f(x+h)[/tex] then [tex]-f(x)[/tex] separately then put in the above formula.
1.
[tex]f(x+h)=(x+h)^2+3(x+h)[/tex]
[tex](x^2+h^2+2hx+3x+3h)[/tex]
Now [tex]-f(x)[/tex]
[tex]-f(x)=-x^2-3x[/tex]
Plugging the values of both.
[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]
[tex]f(x)= \lim_{h\to 0}\frac{(x^2+h^2+2hx+3h+3x)- x^2-3x}{h}=\frac{h^2+2hx+3h}{h}[/tex]
Taking [tex]h[/tex] as common.
[tex]f(x)= \lim_{h\to 0}\frac{h^2+2hx+3h}{h}=h+2x+3[/tex]
Putting [tex]h=0[/tex]
Then
[tex]f(x)=2x+3[/tex] is the final derivative.
This will be same for [tex]y= x^2 + 3x + 8[/tex] as we have to put [tex]8[/tex] only.
2.
[tex]f(x+h)=(x+h)^2+3(x+h)+8[/tex]
[tex](x^2+h^2+2hx+3x+3h)[/tex]
Then [tex]-f(x)=-x^2-3x-8[/tex]
Plugging the values of both.
[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]
[tex]f(x)= \lim_{h\to 0}\frac{(x^2+h^2+2hx+3h+3x+8)- x^2-3x-8}{h}=\frac{h^2+2hx+3h}{h}[/tex]
Taking [tex]h[/tex] as common.
[tex]f(x)= \lim_{h\to 0}\frac{h^2+2hx+3h}{h}=h+2x+3[/tex]
Putting [tex]h=0[/tex]
Then
[tex]f(x)=2x+3[/tex] is the final derivative.
So both the derivatives are same.
The graph of a function, f(x), is plotted on the coordinate plane. Select the function that would move the graph of the function to the right of the coordinate plane.
a.f(x+6)
b.f(x)+4
c.f(x-3)+1
d.f(x)-3
Correct option:
c.f(x-3)+1
Explanation:From the options we have either vertical or horizontal shift. So, for this type of transformation we have:
For any real positive number [tex]c[/tex], vertical and horizontal shift in the graph [tex]y=f(x)[/tex] are expressed as follows:
[tex]\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)[/tex]
From these rules, we know that:
[tex]f(x-3)+1[/tex]
would move the graph of the function to the right of the coordinate plane because of [tex]f(x-3)[/tex]. In other words, the transformation is as follows:
[tex]f(x-3)+1[/tex] shifts the graph of [tex]f(x)[/tex] three units to the right and one unit up
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A golf ball, thrown upwards, rises at a speed of v metres per second.
The ball reaches a maximum height of h metres.
h is proportional to the square of v.
When v = 20, h = 8
Work out the maximum height reached by the golf ball when v = 35
Answer:24.5
Step-by-step explanation:
Formula:
H=KV²
8=K×20²(400)
=8/400
=0.02
H=0.02×35²
=24.5
Answer:
The maximum height reached by the golf ball when v = 35 is 24.5 meters.
Step-by-step explanation:
Given : A golf ball, thrown upwards, rises at a speed of v metres per second. The ball reaches a maximum height of h metres. h is proportional to the square of v. When v = 20, h = 8.
To find : Work out the maximum height reached by the golf ball when v = 35 ?
Solution :
h is proportional to the square of v i.e. [tex]h\propto v^2[/tex]
[tex]h=kv^2[/tex]
Where, k is the constant of proportionality
When v = 20, h = 8,
[tex]8=k(20)^2[/tex]
[tex]8=400k[/tex]
[tex]k=\frac{8}{400}[/tex]
[tex]k=0.02[/tex]
The equation became [tex]h=0.02v^2[/tex].
Now, when v = 35 the value of h is
[tex]h=0.02(35)^2[/tex]
[tex]h=0.02\times 1225[/tex]
[tex]h=24.5[/tex]
Therefore, the maximum height reached by the golf ball when v = 35 is 24.5 meters.
The sum of two numbers is 89. Three times the smaller
number is 71 more than the larger. Find the numbers.
Answer:
The numbers are 40 and 49
Step-by-step explanation:
Smaller number = x
Larger number = y
Let's write our system of equations:
x + y = 89
3x = y + 71
***************************
x = 89 - y
Substituting x in the 2nd equation and solving for y:
3 (89 - y) = y + 71
267 - 3y = y + 71
-3y - y = 71 - 267 (Like terms)
-4y = - 196
y = -196/-4
y = 49
Solving for x in the 1st equation:
x + y = 89
x + 49 = 89
x = 89 - 49
x = 40
The numbers are 40 and 49
Which expression is equivalent to −13(6x+15)−3
The expression is equivalent to −78x − 198.
To simplify the expression −13(6x + 15) − 3, you can start by distributing the −13 across the terms inside the parentheses:
−13 * 6x = −78x
−13 * 15 = −195
So, the expression becomes:
−78x − 195 − 3
Next, combine the constant terms:
−195 − 3 = −198
The simplified expression is now:
−78x − 198
This expression is equivalent to the original expression −13(6x + 15) − 3. It cannot be further simplified as the terms are not like terms and cannot be combined further. So, the answer is −78x − 198.
The expression represents a linear equation where x is the variable. It can be used to find the value of the expression for specific values of x.
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Barry's house has 4 windows that he is planning to replace to improve energy efficiency. The width of each window is between 3.3 and 3.7 ft, and the length of each window is between 3.7 and 4.1 ft. Barry estimates the area of all 4 windows to be 62 sq ft. Is this a reasonable estimate?
A.
No, the estimate should be lower.
B.
No, the estimate should be higher.
C.
Yes, the estimate given is reasonable.
Answer:
B)No, the estimate should be higher
Answer:
no the estimate should be lower
What is 4 divided by 3/5
4 divided by 3/5
pretend that 4 has a denominator which is 1
4/1 divided by 3/5
when dividing always flip over the second fraction
4/1*5/3
multiply the numerators together
4*5=20
multiply the denominators together
1*3=3
answer:
20/3 or 6 2/3
A pool holds 33500 gallons of water. The pool is filled at a constant rate of 485 gallons every 6.5 minutes. Select whether each statement is true or false.
________ The unit rate for filling the pool is 74 gallons per minute
________ It will take 4 hours and 15 minutes to fill the pool to 85% of its capacity.
________ The difference between the pool being 64% full and 48% full is 3600 gallons.
________ A slow leak has left the pool with only 19800 gallons, a 12% decrease.
________ The pool can be completely filled in less than 5 hours.
1. It's True. Since it's 485 gallons every 6.5 minutes, then to find 1 minute you would do 485/6.5 which is approximately 74 gallons.
2. It's False. 85% of 33500 is 28475 gallons. If you divide that by 74, since that's the number of gallons per minute, you get approximately around 384 minutes. Since you want the time in hours, you divide 384 by 60, and you get the decimal 6.4. Since 6 hours is greater than 4 hours, it's false.
3. It's False. 64% of 33500 is 21440 gallons. 48% of 33500 is 16080 gallons. 21440-16080 is 5360 gallons, not 3360 gallons.
4. It's False. To find the percent of change, you first need to subtract 19800 from 33500, which gives you a result of 13700. Then you divide 13700/33500, which gives you a quotient of approximately 0.41. You multiply that by 100 to find the percent, which is 41%. 41% is not equal to 12%.
5. It's False. Since the unit rate is 74 gallons per minute, you divide 33500 by 74 to see how many minutes it takes. That gives you a quotient of approximately 453 minutes. You divide that by 60 since you want the time in hours, and the quotient of that is 7.55. 7 hours is greater than 5, so it's false.
I'm not too sure about some of them, so you might want to check my math. :)
Which of the following are true of linear functions? Select all that apply.
There is exactly one output for each input.
The graph of a linear function is a straight line.
Alinear function can cross the y-axis in two places
Alinear function has a constant rate of change.
Alinear function must cross the x-axis
Answer:
There is exactly one output for each input.
The graph of a linear function is a straight line.
A linear function has a constant rate of change.
Step-by-step explanation:
Answer:
A,B,D
Step-by-step explanation:
i took the assignment and quiz on ed2020
Which action describes an aspect of technological design?
O building a telescope to look deeper into space
O creating a collection of mosquitoes that cause disease
o observing Doppler radar as a storm approaches
O designing an experiment to measure the heat of a volcano
Answer: A)
Step-by-step explanation: This is correct because a telescope is a piece of technology use to look further into space
what is 2/9+1/3= i need it for for my homework
Answer:
5/9
Step-by-step explanation:
Answer:
5/9
Step-by-step explanation:
Now we need to make our denominators match.
9 goes into 3 evenly, so we only need to multiply one term to get a common denominator.
Multiply 1 by 3, and get 3, then we multiply 3 by 3 and get 9.
Since our denominators match, we can add the numerators.
2 + 3 = 5
That gives us the sum, which is
5/9
Now, do we need to simplify this fraction?
First, we attempt to divide it by 2...
Nope! So now we try the next greatest prime number, 3...
Nope! So now we try the next greatest prime number, 5...
Nope! So now we try the next greatest prime number, 7...
No good. 7 is larger than 5. So we're done reducing.
There you have it! Here's the final answer to 2/9 + 1/3