Answer:
1.26 liters.
Step-by-step explanation:
Given that, a hummingbird feeder holds [tex]\frac{2}{3}[/tex] of a cup of hummingbird solution.
Again, a bottle of solution will fill the feeder 8 times.
Therefore, a bottle of solution will measure [tex](\frac{2}{3}\times 8) = \frac{16}{3} = 5.33[/tex] cups of hummingbird solution.
Now, one cup is equivalent to 0.236588 liters.
So, 5.33 cups is equal to (0.236588 × 5.33) = 1.26 liters. (Answer)
The function f(x) = g(x), where f(x) = 2x - 5 and g(x) = x2 - 6.
The table below shows the process of solving using successive approximations
NO
--5
-6
T -3
-5
1
-2
13
0
0.25
NE
Continue this process to find the positive solution to the nearest tenth.
Answer:
The positive solution to the nearest tenth is (2.4, - 0.2).Explanation:
I will rewrite the table to understand how the process of solving using succesive approximations is.
Table:
x f(x) g(x)
0 - 5 - 6
1 - 3 - 5
2 - 1 - 2
3 1 3
Those are the points shown in the table.
Now you must continue the process of solving using successive approximations until you find the positive solution to the nearest tenth.
You need to determine whether a "guess" is closer or farther away of the solution.
The first row shows that g(x) is less than f(x) in 1 unit when x = 0 ( -6 - (-5) ) = -1.
The second raw shows that g(x) is less than g(x) in 2 units when x = 1 ( - 5 - (-3) ) = - 2
The third row shows that g(x) is is less than f(x) in 1 unit when x = 2 ( - 2 - (-1) ) = - 1.
The fourth row shows that g(x) is than f(x) in 2 units when x = 3 ( 3 - 1 = 2).
Hence, the trend changed form negative to positive, meaning that, since the functions are continous, there must be an intertemediate value of x (between x = 2 and x = 3) for which f(x) = g(x) and that is the solution.
Therefore, test x = 2.5
f(x) = 2x - 5 = 2(2.5) - 5 = 0g(x) = x² - 6 = (2.5)² - 6 = 0.25g(x) - f(x) = 0.25 Thus the difference is bigger than one tenth (0.1)Test for x = 2.4
f(2.4) = 2(2.4) - 5 = - 0.2g(2.4) = 2.4² - 6 = -0.24g(2.4) - f(2.4) = - 0.24 - (0.2) = -0.04Now the difference is less than 0.1 and the solution to the nearest tenth is (2.4, - 0.2).
Answer:
answer is 2.7
Step-by-step explanation:
I got it right
The sum of eight times a number and negative four exceeds twelve.
8x + -4 > 12
8x > 16
x > 2
Hope this helps! ;)
Answer:8x + -4 > 12
8x > 16
x > 2
Step-by-step explanation:
How many times does 27 go into 324
quadrilateral PQRS is a square whos side length is 10. Let X and Y be points outside the square so that XQ = YS = 6 and XP = YR = 8. Find XY^2.
Answer:
392
Step-by-step explanation:
You want the value of the square of the length XY, given X and Y are outside and symmetrically opposite the center of a 10-unit square and each is 6 units and 8 units from the two nearest vertices.
LocationThe attached drawing shows the positions of points X and Y. Each is 4.8 units horizontally and 3.6 units vertically from the nearest vertex of the square. That means their locations relative to each other are ...
horizontally: 2×4.8 +10 = 19.6 units
vertically: 6.4 -3.6 = 2.8 units
DistanceThe square of the distance between X and Y will be given by the Pythagorean theorem:
XY² = 19.6² +2.8² = 384.16 +7.84
XY² = 392
__
Additional comment
The locations of X and Y relative to the side of the square can be found using the "geometric mean" relations for a right triangle. Triangle QXP has side lengths 6, 8, 10, which are a multiple of the well-known {3, 4, 5} right triangle. So ∆QXP is a right triangle with a right angle at X.
The length QX is the geometric mean √(QA·QP), so we have ...
6 = √(10·QA)
36 = 10·QA
QA = 3.6 ⇒ PA = 6.4
and
XA = √(QA·PA) = √(3.6·6.4)
XA = 4.8
The value of [tex]\( XY^2 \)[/tex] is 100.
Let's begin by visualizing the problem. We have a square PQRS with side length 10. Points X and Y are outside the square such that XQ = YS = 6 and XP = YR = 8. We need to find the square of the distance between X and Y, denoted as [tex]\( XY^2 \)[/tex].
To solve this, we can use the Pythagorean theorem. Let's consider triangle XPQ. Since PQRS is a square, angle PQX is a right angle. Therefore, triangle XPQ is a right-angled triangle with PQ as the hypotenuse and XQ and XP as the other two sides.
Using the Pythagorean theorem for triangle XPQ, we have:
[tex]\[ 8^2 = 6^2 + XQ^2 \][/tex]
[tex]\[ 64 = 36 + XQ^2 \][/tex]
[tex]\[ XQ^2 = 64 - 36 \][/tex]
[tex]\[ XQ^2 = 28 \][/tex]
Now, we have found the square of the distance XQ, which is [tex]\( 28 \)[/tex].
Similarly, for triangle YRQ, which is also a right-angled triangle with YR as one leg and YS as the other leg, and RQ as the hypotenuse, we can write:
[tex]\[ 8^2 = 6^2 + RQ^2 \][/tex]
[tex]\[ 64 = 36 + RQ^2 \][/tex]
[tex]\[ RQ^2 = 64 - 36 \][/tex]
[tex]\[ RQ^2 = 28 \][/tex]
We have found that [tex]\( RQ^2 = 28 \)[/tex], which is the same as [tex]\( XQ^2 \)[/tex].
Now, to find [tex]\( XY^2 \)[/tex], we need to consider the distance between points X and Y. Since X and Y are outside the square and their distances to the square are equal (XQ = YS and XP = YR), the line segment XY is parallel to side PQ of the square and is also equal to the side length of the square, which is 10.
Therefore, [tex]\( XY^2 \)[/tex] is simply the square of the side length of the square PQRS:
[tex]\[ XY^2 = PQ^2 \][/tex]
[tex]\[ XY^2 = 10^2 \][/tex]
[tex]\[ XY^2 = 100 \][/tex]
Equivalent fractions of 8/12
Answer:
Step-by-step explanation:
Simple multiply both 8 and 12 by any number and then equivalent
Answer:
3/4 or 16/24 or 2/3
Step-by-step explanation:
What is the equation of the line that passes through the point (-4, -8) and haves a slope of 4
Answer:
y=4x+8
Step-by-step explanation:
y-y1=m(x-x1)
y-(-8)=4(x-(-4))
y+8=4(x+4)
y=4x+16-8
y=4x+8
which expression is equivalent to x2 • x3?
Answer:
the answer is x^5
Step-by-step explanation:
add the exponents
The required expression equal to x².x³ is [tex]x^5[/tex].
Given that,
To determine the expression is equivalent to x².x³
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The given expression,
= x².x³
There is a property in the product if the base of the exponents is the same then their power gets added.
So, the simplification
= [tex]x^{2+3}[/tex]
= [tex]x^5[/tex]
Thus, the required expression equal to x².x³ is [tex]x^5[/tex].
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Please answer, EXPLAIN for brainliest.
Answer:
Width = 16cm length = 24cm; Draw up to larger dimensions.
Step-by-step explanation:
Scale factor of 4 means the new shape is 4 times the size of the original.
20. Mary has 3 packages of hamburger the
weigh 1.3/4 pounds each. What is the total
weight of the hamburger?
A2.1/4pounds
B 3.3/4pounds
© 4.1/2 pounds
D5.1/4 pounds
To find the total weight of the hamburger in three packages, multiply the weight of one package by three. The total weight of the hamburger is 5 1/4 pounds.
Explanation:The student's question involves finding the total weight of three packages of hamburger, each weighing 1 3/4 pounds.
To solve this problem, the weight of one package must be multiplied by the number of packages.
The calculation is: 1 3/4 pounds × 3, or in improper fraction form, (7/4) pounds × 3.
Multiplying the improper fraction by 3, we have:
(7/4) × 3 = 21/4The fraction 21/4 is equivalent to 5 1/4 when converted into a mixed number because 21 divided by 4 is 5 with a remainder of 1.
Therefore, Mary has a total of 5 1/4 pounds of hamburger across the three packages.
At a farmers market strawberries cost $1.60 per pint, blueberries cost $2.30 per pint. A shopper bought twice as many pints of strawberries as pints of blueberries, and spent a total of $11.00. How many pints of each did she buy?
4 pints of strawberries and 2 pints of blueberries are bought
Solution:
Let "a" be the pints of strawberries bought
Let "b" be the pints of blueberries cost
Cost per pint of strawberry = $ 1.60
Cost per pint of blueberry = $ 2.30
A shopper bought twice as many pints of strawberries as pints of blueberries
Therefore,
a = 2b --------- eqn 1
They spent a total of $11.00. Therefore we frame a equation as:
pints of strawberries bought x Cost per pint of strawberry + pints of blueberries cost x Cost per pint of blueberry = 11
[tex]a \times 1.60 + b \times 2.30 = 11[/tex]
1.6a + 2.3b = 11 --------- eqn 2
Substitute eqn 1 in eqn 2
1.6(2b) + 2.3b = 11
3.2b + 2.3b = 11
5.5b = 11
Divide both sides by 11
b = 2
Substitute b = 2 in eqn 1
a = 2(2)
a = 4
Thus 4 pints of strawberries and 2 pints of blueberries are bought
Answer:
3.45
Step-by-step explanation:
Its right on the quiz
There were 30 students enrolled in the school chess club in the fall and 24 students enrolled in the spring whats the percent decrease in the number of students enrolled in the chess club?
Answer:
20%
Step-by-step explanation:
30-24=6
6/30=.2=20%
Answer:
Decrease by 6
Step-by-step explanation:
20%
NEED ANSWERS PLEASE!!
A tee box is 64 feet above its fairway. When a golf ball is hit from the tee box with an initial vertical velocity of 48 ft/s, the quadratic equation 0= -16t^2 + 48t + 64 gives the time, t, in seconds when a golf ball is at height 0 feet on the fairway.
A) Solve the quadratic equation by factoring to see how long the ball is in the air.
B) What is the height of the ball at 1.5 seconds?
C) Is the ball at its maximum height at 1.5 seconds? Explain.
(A) 4 sec the ball is in the air.
(B) Height of the ball = 49 ft.
(C) Yes, the ball is at its maximum height at 1.5 seconds.
Solution:
Given data:
[tex]h(t)=-16t^2+48t+64[/tex]
Initial velocity = 48 ft/s
Height = 64 ft
(A) [tex]-16t^2+48t+64=0[/tex]
a = –16, b = 48, c = 64
We can solve it by using a quadratic formula,
[tex]$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]
[tex]$\Rightarrow t=\frac{-48 \pm \sqrt{(48)^{2}-4 \times(-16)(64)}}{2(-16)}[/tex]
[tex]$\Rightarrow t=\frac{-48 \pm \sqrt{2304+4096}}{-32}[/tex]
[tex]$\Rightarrow t=\frac{-48 \pm \sqrt{6400}}{-32}[/tex]
[tex]$\Rightarrow t=\frac{-48 \pm 80}{-32}[/tex]
[tex]$\Rightarrow t=\frac{-48 + 80}{-32},\frac{-48 - 80}{-32}[/tex]
[tex]$\Rightarrow t=-1,t=4[/tex]
Time cannot be in negative. So neglect t = –1
t = 4 sec
Hence, 4 sec the ball is in the air.
(B) When t = 1.5 sec,
[tex]h(1.5)=-16(1.5)^2+48(1.5)+64[/tex]
h(1.5) = 49 ft
(C) The maximum height occurs at the average of zeros.
Average = [tex]\frac{(-1+4)}{2}=1.5[/tex] sec
Yes, the ball is at its maximum height at 1.5 seconds.
A bakery sells 25rolls for every 35 loaves of bread. At this rate, how many will be sold for every 7 rolls of bread?
At the same rate, the bakery would sell approximately 10 loaves of bread for every 7 rolls.
The bakery sells 25 rolls for every 35 loaves of bread. To find out how many loaves of bread will be sold for every 7 rolls of bread, we need to use a simple proportion based on the given ratio. This can be set up as a fraction, 25 rolls/35 loaves = 7 rolls/x loaves, where x represents the number of loaves sold for every 7 rolls.
We can solve for x by cross-multiplying:
(25 rolls/35 loaves) = (7 rolls/x loaves),
so 25x = 35*7.
The next step is to divide both sides of the equation by 25 to solve for x:
x = (35*7)/25 = 9.8 loaves.
Therefore, the bakery would sell approximately 10 loaves of bread for every 7 rolls, given the same rate.
What is the greatest common factor of 24y and (4y^2+12y)
PLEASE HELP AND FAST
Which expressions are polynomials?
Select each correct answer.
6x2 + 5x
-x^2+52
-7x^2+5/3x
X^2+5x^1/5
Yo sup??
6x^2+5x is a polynomial
-x^2+52 is also a polynomial
-7x^2+5/3x is not a polynomial as power of x is negative
x^2+5x^1/5 is not a polynomial as power of x is fraction
Hope this helps.
what is the answer to 3(-3x+20) + 5(x/5)?
Answer:
-8x+60
Step-by-step explanation:
3(-3x+20)+ 5(x/5)
Solve one term at a time
3(-3x+20)
-9x+60
Solve second term
5(x/5)
5x/5
X
Add both terms together
-9x+60+x
-9x+x+60
-8x+60
-8x+60
Step-by-step explanation:
3(-3x+20)+ 5(x/5)
Solve one term at a time
3(-3x+20)
-9x+60
Solve second term
5(x/5)
5x/5
X
Add both terms together
-9x+60+x
-9x+x+60
-8x+60
Matt earned $28,500 last year. He paid $8,265 for rent. What percent of his earnings did Matt pay for rent ?
Answer: 29%
Step-by-step explanation:
You need to divide the rent, 8265, by the amount of money he earns.
8265/28500 is .29
Multiply that by 100 to get it in percent form
6. Calculate the distance Tarryn drives if she
drives 7/8mile each way to and from work,
5 days a week.
Answer:
not that hard sir
Step-by-step explanation:
do 7/8 x 5
Final answer:
Tarryn drives a total of 8.75 miles in a week to and from work, with each one-way trip being 7/8 mile and she works 5 days a week.
Explanation:
Calculating Total Distance Driven
Tarryn drives to and from work 5 days a week, with each trip being 7/8 mile. To calculate the total distance she drives in a week, we need to consider both the trip to work and the return trip. This will give us the daily round trip distance, which we will then multiply by the number of days she works in a week.
First, we calculate the daily round trip distance:
Round trip distance = Distance to work + Distance from work
Round trip distance = 7/8 mile + 7/8 mile
Round trip distance = 7/4 miles (or 1.75 miles)
Then, we calculate the total distance for the week:
Total weekly distance = Daily round trip distance × Number of workdays
Total weekly distance = 7/4 miles × 5 days
Total weekly distance = 35/4 miles (or 8.75 miles)
Therefore, Tarryn drives a total of 8.75 miles over the course of a 5-day workweek.
Which line is the graph of y= 2x - 1?
Answer:
The points are (0,-1) and (1,1)
Step-by-step explanation:
Answer:
Line A
Step-by-step explanation:
simply the expression.
Using the negative exponent rule move x^-2 to the numerator
Answer = 5x^2/y^5
A line is graphed in the xy-plane shown at left. Which of the following is an equation of the line?
A line is graphed in the x-y plane and it will follow a path of straight line and equation for that is, Y = (-3/2)X.
So option (C) is correct.
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
The net change in y coordinate is written as, Δy and the net change in x coordinate is written as, Δx.
m = change in y coordinate/change in x coordinate = Δy/Δx = y2-y1/x2-x1
In given graph,
Line is passing through the points (2, -3) & (-2 ,3)
Slope = -3-3/2-(-2)
Slope = -3/2
y = (-3/2) x + c ____(i)
by putting point (2, -3) in equation (i)
-3 = (-3/2) 2 + c
c = 0
Hence, The equation is Y = (-3/2)X
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Find the image of the figure after a dilation with a point A as the centre by a scale factor of 0.75
Answer:
Step-by-step explanation:
So the dilation of .75.
You want to find what each point is before the dilation.
A(-10,-14)
B(-10,14)
C(12,14)
D(12,-14)
So, we multiply these by the scale factor, 0.75.
(x,y) = (X x 0.75, y x 0.75)
A = -10 x 0.75, -14 x 0.75
B= -10 x 0.75, 14 x 0.75
C = 12 x 0.75 , 14 x 0.75
D = 12 x 0.75 , -14 x 0.75
now, the image of the figure would be
A' ( -7.5, -10.5)
B' (-7.5, 10.5)
C' (9, 10.5)
D' (9, -10.5)
What is the value of x?
Enter your answer in the box.
Answer: X = 27
Step-by-step explanation: The diagram shows two triangles with one triangle cut out from the other. A careful observation would reveal triangle BDR and triangle QDC.
Since line QC is parallel to line BR, that makes triangle QDC similar to triangle BDR. Also the ratio of lines QD and BQ is the same as the ratio of lines CD and RD. The same applies to lines QC and BR.
Therefore,
QD/BQ = CD/RC
Alternatively we can use the ratios,
QD/BD = CD/RD
Using the first ratios, we have
QD/BQ = CD/RC
39/26 = X/18
3/2 = X/18 {the left hand side has been reduced to it's simplest form}
If we cross multiply, we now arrive at
3 × 18 = 2X
54 = 2X
Divide both sides of the equation by 2
27 = X
Please help I'll give thanks and brainliest.
Also I'm pretty sure both have 2 answers.
Thanks! ^u^
Answer:
(1) Factor: a^n(1+a)
(2) Solve: x=0, x=2/3
Step-by-step explanation:
Steps to factor:
[tex]a^n+a^{n+1}[/tex]
~Apply rule of exponent ([tex]a^{b+c}=a^ba^c[/tex])
[tex]a^n+a^1a^n[/tex]
~Factor out the common term of [tex]a^n[/tex]
[tex]a^n(1+a)[/tex]
Steps to solve:
[tex]3x^3-x^2=x^2[/tex]
~Subtract [tex]x^2[/tex] to both sides
[tex]3x^3-x^2-x^2=x^2-x^2[/tex]
~Simplify
[tex]3x^3-2x^2=0[/tex]
~Factor left side of the equation
[tex]x^2(3x-2)=0[/tex]
~Set factors to equal zero
[tex]x^2=0[/tex] and [tex]3x-2=0[/tex]
~Simplify
[tex]x = 0[/tex] and [tex]x=\frac{2}{3}[/tex]
Best of Luck!
Find the semiannual payment for a 20 year endowpayment policy with face of $25,000 if the annual premium is $22.24 per $1,000
Answer:
$278
Step-by-step explanation:
There is an endowpayment policy with face of $25,000 with the annual premium $22.24 per $1000.
So, the annual premium of the endowpayment policy with face of $25,000 will be equal to [tex]\frac{25000}{1000}\times 22.24 = 556[/tex] dollars.
And the semi annual payment for this policy will be [tex]\frac{556}{2} = 278[/tex] dollars. (Answer)
What are the four arithmetic means between -10 and 35?
Answer:
-1, 8, 17, 26
Step-by-step explanation:
35 - (-10) = 45
45/5 = 9
-10 + 9 = -1
-1 + 9 = 8
8 + 9 = 17
17 + 9 = 26
Final answer:
The four arithmetic means between -10 and 35 are -1, 8, 17, and 26.
Explanation:
To find the four arithmetic means between -10 and 35, we want to divide the interval evenly into six equal parts (because there will be five intervals with four means and two endpoints). First, calculate the total interval size:
35 - (-10) = 45
Then divide this interval by the total number of segments (which is one more than the number of means):
45 / (4 + 1) = 9
This gives us the common difference. Starting from -10 and adding the common difference of 9 each time, the four arithmetic means would be:
-10 + 9 = -1-1 + 9 = 88 + 9 = 1717 + 9 = 26Thus, the four arithmetic means between -10 and 35 are -1, 8, 17, and 26.
Which expressions are equivalent to the one below? Check all that apply.
log 2 - log 8
Answer:
[tex]\log 2-\log 8=\log\frac{1}{4}\\\\\log 2-\log 8=-\log 4[/tex]
Step-by-step explanation:
[tex]\log 2-\log 8=\log\frac{2}{8}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \log\frac{a}{b}=\log a-\log b\\\\\log 2-\log 8=\log\frac{1}{4}\\\\\log 2-\log 8=\log 1-\log 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \log\frac{a}{b}=\log a-\log b\\\\\log 2-\log 8=-\log 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \log 1=0[/tex]
Answer:
log(1/4)
log(2) + log (1/8)
75% of a number is 230. Solve.
Work is attached in the image provided.
A cell phone company charges $40 per month for unlimited calling, and $0.20 per text message sent. If t represents the number of text messages Roxy sent last month, which expression represents the cost of her bill last month before any taxes or additional fees?40 − 0.2t
(40 + 0.2)t
40 + 0.2t
(40 − 0.2)t
Answer:
Step-by-step explanation:
40 per month + 0.20 per text(t)
40 + 0.2t....no parenthesis needed
Answer:
did it
Step-by-step explanation:
HURRY
Figure ABCDF is transformed according to the rule R0, 270
What are the coordinates of B?
(-2,3)
(3.-2)
(2-3)
(-3.2)
Answer:
3,-2
Step-by-step explanation:
Answer:
ITS (-3,2)
Step-by-step explanation: