Answer:
x = ± 3
Step-by-step explanation:
given y varies as [tex]\frac{1}{x^2}[/tex] , then
y = k × [tex]\frac{1}{x^2}[/tex] = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k use the condition x = 2 , y = 1
1 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
4 = k
y = [tex]\frac{4}{x^2}[/tex] ← equation of variation
when y = [tex]\frac{4}{9}[/tex] , then
[tex]\frac{4}{9}[/tex] = [tex]\frac{4}{x^2}[/tex] ( cross- multiply )
4x² = 36 ( divide both sides by 4 )
x² = 9 ( take square root of both sides )
x = ± [tex]\sqrt{9}[/tex] = ± 3
Five boxes of crackers cost 9 at this rate how much do 20 boxes cost
Answer:
36
Step-by-step explanation:
Unit price: 9 / 5 = 1.8
20 box price: 1.8 * 20 = 36
A bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).
The ball would bounce to a height of 0.92 feet at the 7th bounce
How to determine the height of the 7th bounce of the ballThe given parameters are
Initial height = 3.75 feet
Rate of bounce = 79%
The height of the ball after n-th bounce is represented as
H(n) = A * rⁿ⁻¹
Where
A = Initial height = 3.75 feetr = Rate of bounce = 79%n = Number of bounceIn this case, we have
n = 7
So, we have
H(7) = 3.75 * (79%)⁷⁻¹
Evaluate the difference
H(7) = 3.75 * (79%)⁶
Evaluate the product
H(7) = 0.92
Hence, the height of the 7th bounce of the ball is 0.92 feet
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Determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths.
The solution of x in the mathematical statement is 11.73
How to determine the value of x?From the question, the mathematical statement is given as
x over 5 and 7 tenths equals 2 and 3 tenths.
When represented as an algebraic equation, we have
x/5.10 = 2.30
To start with, we multiply both sides of the equation by 5.10
This is represented as
5.10 * x/5.10 = 2.30 * 5.10
Evaluate the product on the left-hand side
So, we have
x = 2.30 * 5.10
Evaluate the product on the right-hand side
So, we have
x = 11.73
Hence, the value of x is 11.73
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The required simplified value of the given numeral is given as 13.11.
As given in the question, to determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
The statment given in the word string, first transform the equation in the mathematical inscription,
So,
x / 5.7 = 2.3
Simplifying,
x = 5.7 × 2.3
x = 13.11
Thus, the required simplified value of the given numeral is given as 13.11.
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Funds are distributed to five families affected by floods in the ratio 5:12:2:15:29. The total amount that the five families received was $630.
a) The first family received _____
b) The difference between the amount of money the first and last family received was _____
c) A sixth family joins. They receive n amount of money and the average amount of money donated to all six families becomes 140. How much money does the sixth family receive?
Step-by-step explanation:
We must first add up the ratios:5+12+2+15+29 = 63, this will be the total ratio the money was shared Then we pick out the ratio for each family accordingly:For the first family, 5 out of the total ratio = 5/63
For the second family, 12 out of the total ratio = 12/63
For the third family, 2 out of the total ratio = 15/63
For the fifth family, 29 out of the total ratio = 29/63
a) The first family = 5/63 of the money, $630
we can therefore say the money they received is
= 5/63 ×630
= $50
b) The last family = fifth family = 29/63 of the money, 630
= 29/63 × 630
= $290
recall that the first family received $50 , the positive difference between the money received by both the first and last family
= $290 - $50
= $240
c) Since another family joins in, the total number of families become 6
the money the received is nwe can't find the average without knowing what the second, third, and fourth family received out of that money
we apply the same stepthe second family = 12/63 ×630
= $120
the third family = 2/63 × 630
= $20
the fourth family = 15/63 × 630
= $150
Average generally is = total sum/ frequency or number of occurrences or peoplein this case, we were told the average became $140
which means that
sum of money received by the families/ the number of families involved in the sharing = $140
( $50+$120+$20+$150+$290+n)/6 = $140($630+n)/6= $140
now the plan would be to make n subject of formula
multiply both sides of the equation by 6, the equation will become$630+n = $840
take $630 to the other side, it becomes -$630
n = $840-$630
n = $210
therefore the newly added family received $210
I honestly hope I explained it properly...thank you
The length of a car is 4.2m,correct to 1 decimal place. Write down the upper bond and the lower bond of the length of this car.
Answer:
The upper pound is 4.25 m and the lower bound is 4.15 m
4.15 m ≤ 4.2 m < 4.25 m
Step-by-step explanation:
Let us solve the question
∵ The length of the car corrected to 1 decimal place
→ 1 decimal place means tenth
∴ It corrected to the tenths place which is 0.1
→ Divide it by 2
∵ 0.1 ÷ 2 = 0.05
∴ The limit is 0.05 m
→ To get the lower bound subtract 0.05 from the length of the car
∵ The length of the care is 4.2 m
∴ The lower bound = 4.2 - 0.05
∴ The lower bound = 4.15 m
→ To get the upper bound add 0.05 to the length of the car
∵ The length of the care is 4.2 m
∴ The upper bound = 4.2 + 0.05
∴ The upper bound = 4.25 m
∴ 4.15 m ≤ 4.2 m < 4.25 m
∴ The upper pound is 4.25 m and the lower bound is 4.15 m
P.s hopes this helps
kayla has a deck that measures 4 feet by 21 feet. she wants to increase each dimension by equal lengths so that the area is doubled. how much should she increase each dimension?
Answer:
Increase by 3.
Step-by-step explanation:
4 x 21 = 84
84 x 2 = 168
Begin to try numbers.
5 x 22 = 110
6 x 23 = 138
7 x 24 = 168
7 - 4 = 3
24 - 21 = 3
Increase each side by 3 ft. for a total dimension of 7 ft. x 24 ft.
I will give brainlist ! very fast.. Hello its a math question is the last option the correct answer i am not sure please help
Hello!
Let's take this step-by-step:
The formula for the Area of the Triangle:
[tex]Area = \dfrac{1}{2} *\text{Base} *\text{Height}[/tex]
In this case:
Height: x + 3Base: 2x + 4Let's plug in those value's into the equation:
[tex]\text{Area}=\dfrac{1}{2} *(2x +4)*(x+3)\\\\\\\text{Let's first multiple '2x + 4' and 'x+3'}\\\text{Area}=\dfrac{1}{2} *(2x^2+6x + 4x + 12)=\dfrac{1}{2} *(2x^2+10x + 12)\\\\\\\\\\\textNow multiple 1/2 in the function in the parentheses}\\\text{Area}=\dfrac{1}{2} *2x^2 + \dfrac{1}{2}*10x +\dfrac{1}{2} *12\\\\\text{Area}=x^2+5x + 6[/tex]
Answer: [tex]x^2 + 5x +6[/tex]
Hope that helps!
Find the zeros of f(x)=x(x+2)^3
List them in order of least to greatest, separated by commas. If the multiplicity is more than one, only list the zero once.
All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.
We will also observe that they have a direct connection to the polynomial's factors.
What are polynomial zeros with an example?
Real number k is referred to as the zero of a polynomial P(x) if P(k) = 0. As a result, the polynomial x2 - 3x + 2 has a zero at 1 and a zero at 2.
The equation p(x)=(x-1) (x-3)
Although it is a polynomial of third degree, 2, only has two different zeros. This is due to the zero x=3 having a connection to the factor.
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Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces. how many pieces of fish would there be if jorge divided each fish into tenths.
The number of pieces of fish that would be there if Jorge divided each fish into tenths is 1730.
It is given that Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces.
We need to calculate the number of pieces of fish that would be there if Jorge divided each fish into tenths.
We know that each of the fish is divided into 10 parts.
The total number of fish available for the dog is 173.
The total number of pieces of fish is equal to the product of the number of available fish and the number of parts each fish is divided into.
The total number of pieces of fish is equal to 173*10.
The total number of pieces of fish is equal to 1730.
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A rectangular garden has a length that is 3 feet longer than its width. Let represent the width of the garden, in feet. The entire garden is surrounded by a 2-foot wide cement walkway. What does the algebraic expression ( w + 4) (w + 7) represent in this context?
HIghschool Alegbra 1
Expression ( w+4)(w + 7) represent the total area of the garden and walkway.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that the width of the garden, in feet be w.
The length is 3 feet longer than its width, hence: w + 3
The entire garden is surrounded by a 2-foot-wide cement walkway. Therefore:
garden and walkaway length= (w + 3) + 2 + 2 = w + 7
garden and walkaway width = w + 2 + 2 = w + 4
The area of garden and walkaway
= length times of width
=Length × Width
= (w + 7)(w + 4)
Hence expression ( w+4)(w + 7) represent the total area of the garden and walkway
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Find the two square roots of 1/16
Answer:
1/4
Step-by-step explanation:
The square root of 1/16 = 1/4
they probably
Elias has a collection of 1,200 baseball trading cards. Of these cards, 35% are from the American League, 45% are from the National League, the rest are international players. How many trading cards are of international players?
Answer:
240 trading cards
Step-by-step explanation:
20% of 1200 = .2 × 1200 = 240
In *triangle* HIJ, i = 890 inches, h = 740 inches and H=127°. Find all possible values of angle I, to the nearest degree.
The given conditions cannot form a triangle. A triangle cannot be formed if the sum of three angle measurements does not equal 180°.
How to calculate angle of Triangle ?A triangle is a three-sided polygon with three edges and three vertices in geometry. The sum of a triangle's internal angles equals 180 degrees, which is its most important property. This is known as the angle sum property of a triangle.
A triangle's interior angles always add up to 180°, whereas its exterior angles are equal to the sum of the two interior angles that are not adjacent to it. Another method for calculating a triangle's exterior angle is to subtract the angle of the vertex of interest from 180°.
A protractor is the most convenient tool for measuring angles. If you don't have a protractor, you can use the basic geometric principles of triangles to determine the size of an angle. To solve the equations, you'll need a scientific calculator.
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What is the effect on the graph of f (x) = |x| when the function is changed to g(x) =-2|x|
Here the graph shows reflection across x - axis by 2 units.
f(x) = |x| => g(x) = -2|x|.
Solution:Graph transformation is the process of modifying an existing graph or graphed equation to produce a variation of the following graph.The modification of algebraic equations is a common type of problem in algebra.Here given the parent function, f(x)=|x|
The translation is , g(x)= -2|x|
Which is an absolute function.
Here the transformation is .
f(x)=|x| => g(x)= -2|x|
The value of f(x) is reflecting over x- axis and value of y changes by 2 units.
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I also need help with this question
Answer: (-3, 3)
Step-by-step explanation:
See the attached image for my work. First, you need to know the quadrants. In order from the top right counter-clockwise, it goes I (1), II (2), III (3), and IV (4).
Next, we will count up five units since Quadrant II is above the point, in Quadrant III.
ASAP PLEASEEE HELPPP PLEASEEEE
1.If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, what transformation occurs from f(x) to h(x)?
A.Shift left 3 units
B.Shift right 3 units
C.Shift up 3 units
D.Shift down 3 units
2. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the vertex affected? Select all that apply.
A.The vertex will not change.
B.The vertex will shift right 3 units.
C.The vertex will shift left 3 units.
D.The vertex will shift up 3 units.
E.The vertex will shift down 3 units.
F.The vertex will not move up or down.
G.The vertex will not move right or left.
3. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the range affected?
A.The range will not change.
B.The range will be all real numbers.
C.The range will change from y ≥ 0 to y ≥ -3.
D.The range will change from x ≥ 0 to x ≥ -3.
1) A translation of 3 units down, option D.
2) The vertex moves 3 units down.
3) The new range is y ≥ -3, correct option is C.
Which transformation is applied?For a function f(x) a vertical shift of N units is written as:
g(x) = f(x) + N
In this case, we have:
f(x) = |x|
h(x) = |x| - 3
Then h(x) = f(x) - 3
This is a shift of 3 units down, the correct option is D.
How is the vertex affected?
The vertex is translated 3 units down, like the whole graph of the function.
How is the range affected?
The vertex defines the minimum of the range, so if the vertex goes 3 units down, then the range also does, the new range will be:
y ≥ -3.
So the correct option is C.
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Jill earns $264.50 a week. She is married and claims 3 allowances. What amount is withheld weekly for federal income tax?
As Jill claims 3 allowances then the amount which is withheld weekly for federal income tax is $11.
Given, Jill earns $264.50 a week.
She is married and claims 3 allowances.
From the table if the wage of a married person is at least $260 but less than $270 and has 3 allowances then weekly income tax is $11.
Individual federal income tax rates in the US are progressive, which means that they rise in proportion to taxable income. Federal income tax rates range from 10% to 37%, and they become effective at a certain level of income. Tax brackets are the ranges of income that the rates apply to. Each tax bracket has a different rate of taxation that applies to certain types of income.
Hence the amount is $11 for federal tax.
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What is two divided by three I’ve two
Answer:
2 divided by 3 is 0.6 or 2/3
Step-by-step explanation:
Answer:
2/3 or 0.66666666667...
Would you use circumference
or area to solve the following problem?
Your math teacher bakes a round pizza with a 4 foot
diameter to share with the class. You need to tell your teacher how many square feet?
are available to enjoy the Pizza Pi.
Answer: You always use circumference if you are talking about a round object.
Question 3 (5 points)
Find the equation of a parabola with a focus at (-2,-3) and a directrix at y = -5
The equation of a parabola with a focus at (-2,-3) and a directrix at y = -5 is y = 1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)
What is Parabola?
A parabola is the location of a moving point whose distance from a given focus point and directrix line, respectively, is always constant.
let's keep it simple: (x, y). Focus is on (7,5)
When the separation from focus is
[tex]\sqrt{(x - (-2)^{2}) + (y - (-3)^{2} ) }[/tex] . Its distance from directrix y = -5 i.e.
y + 5 = |y + 5|^2
Hence, equation of parabola:
(x - (-2))^2 + (y - (-3))^2 = |y + 5|^2
or, (x + 2)^2 + (y + 3)^2 = |y + 5|^2
x^2 + 4x + 4 + y^2 + 3y + 9 = y^2 + 10y + 25
or, x^2 + 4x + 13 + y^2 + 3y = y^2 + 10y + 25
x^2 + 4x - 12 = 7y
y = (x^2 + 4x - 12)/7
y = 1/7(x^2 + 4x +4 - 4) - 12/7
y = 1/7(x + 2)^2 - 12-4/7
y = 1/7(x + 2)^2 - 8/7
Hence, parabola's equation is y = 1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)
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The foot of a ladder is 1.5 m from a vertical wall. The ladder makes an angle of 68° with the horizontal. How far up the wall does the ladder reach? Draw a picture and show work!
The length of the wall for the ladder reach will be 3.4 meter.
What is mean by Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The foot of a ladder is 1.5 m from a vertical wall.
And, The ladder makes an angle of 68° with the horizontal.
Now,
By the figure,
The length of BC = 1.5 m
The measure of ∠ACB = 68°
So, Find the length of AC as;
cos 68° = 1.5 / AC
AC = 1.5 / 0.44
AC = 3.4 m
Therefore,
The length of the wall for the ladder reach will be 3.4 meter.
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Oct 24, 6:34:22 PM
Write two numbers that multiply to the value on top and add to the value on botton
42
-17
14 and 3 are two numbers for multiplication and addition.
What is multiplication ?
The four fundamental operations in mathematics are addition, subtraction, division, and multiplication. In mathematics, multiply refers to the repetitive addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two groups of this nature, and each group has ice cream.Multiplying in math is equivalent to adding like groups. The number of items in the group grows as we multiply. An example of a multiplication problem would be the product and the two factors. The factors and the product in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, respectively.The two numbers are 14 and 3.
14 + 3 = 17
14 * 3 = 42
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I’m not english person. I cannot understand those. Can someone explain some of them please? I’m trying to pass an english math exam..
Step-by-step explanation:
lo siento, no tengo idea de cómo explicarte esto. Ummm, hay una aplicación que puedes descargar en tu teléfono para tomar una foto de la hoja de trabajo o el papel y luego la traducirá para ti. Se llama buena traducción o algo en. buena suer
Determine which integer in the solution set will make the equation true.
6x − 6 = 2(2x + 5)
S: {−2, 0, 8, 11}
Answer:
8
Step-by-step explanation:
[tex]6x-6=2(2x+5) \\ \\ 6x-6=4x+10 \\ \\ 2x-6=10 \\ \\ 2x=16 \\ \\ x=8[/tex]
A student performed the following steps to find the solution to the equation
x² + 4x-12-0. Where did the student go wrong?
Step 1. Factor the polynomial into (x + 6) and (x-2)
Step 2. x-6= 0 and x + 2 = 0
Step 3. x = 6 and x = -2
O A. in Step 3
B. The student did not make any mistakes, the solution is correct
O C. in Step 1
OD. in Step 2
The student got the solution to the quadratic equation wrong at step 2
What are quadratic equations?A quadratic equation is a mathematical equation in which it's higher power of unknown is 2.
A quadratic equation can be solved by using 4 different method of choice which are formula method, factorization method , completing the square and graphical method.
x^2+4x-12=0 is an example of quadratic equation.
using factorization method to solve the value of x
x^2+6x-2x-12=0
grouping the equation
(x^2+6x)(-2x-12)=0
x(x+6)-2(x+6)=0
(x+6)(x-2)=0
for the equation to be satisfied
(x+6)=0
or
(x-2)=0
Therefore x= -6 or+2
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solve and show working:- log(x^2 + 7) base 4 = 2
The value of x for the given logarithm equation log(x^2 + 7) base 4 = 2 is x = ± 3.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
It is known that [tex]log_{a}b[/tex] = c can be written as [tex]a^{c}[/tex] = b.
Given that, log(x^2 + 7) base 4 = 2
Therefore, x² + 7 = 4²
x² + 7 = 16
x² = 16 - 7 = 9
x² = 9
x = ±3
Hence "The value of x for the given logarithm equation log(x^2 + 7) base 4 = 2 is x = ± 3".
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you are driving a 30 foot bus on a highway at 45 mph. the road is dry and visibility is good. a safe distance between you and the vehicle ahead of you should be at least:
HELP PSLSPSLAPSLSPSLSPSLSPSLSPSL
Answer: D) 40
Step-by-step explanation:
mph (miles per hour)
60 minutes is an hour, so the number of miles above 60 minutes (which is 40) is the answer.
Hope this helps!
How far does a rider travel in one complete rotation around the Ferris wheel?
Use 3.14 as an approximation for Pi and round the second answer below to the nearest whole number.
If the diameter of the Ferris wheel is 80 meters, then a rider will travel 251.2 meters in one complete rotation around the Ferris wheel.
The diameter of the Ferris wheel = 80 meters
The radius of the Ferris wheel = Diameter / 2
= 80/2
= 40 meters
The Total distance travelled by the rider in one revolution = The circumference of the wheel
The circumference of the wheel = 2πr
Where r is the radius of the wheel
Substitute the values in the equation
The circumference of the wheel = 2×3.14×40
= 251.2 meters
Hence, if the diameter of the Ferris wheel is 80 meters, then a rider will travel 251.2 meters in one complete rotation around the Ferris wheel
The complete question is :
If the diameter of the Ferris wheel is 80 meters, how far does a rider travel in one complete rotation around the Ferris wheel?
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if the flow rate in an artery has been reduced to 8.5% of its normal value by a blood clot and the average pressure difference has increased by 20.5%, what percent of the original is the radius of the reduced artery?
Percent of the original is the radius of the reduced artery is 0.070 times the original radius.
Given that,
A blood clot has lowered the flow rate in an artery to 8.5% of its usual value, and the average pressure difference has increased by 20.5%.
p1 = 8.5 % ,
p2 = 20.5 %
The equation is using here is From Poiseuille's equation
Q = \Delta p \pi r4 / 8 \eta L
now
Q1 = \Delta p1\pi r14 / 8 \eta L
and
Q2 = \Delta p2\pi r24 / 8 \eta L
Q1 = \Delta p1\pi r14 / 8 \eta L / Q2 = \Delta p2\pi r24 / 8 \eta L
Q1 / Q2 = \Delta p1 ro4 / \Delta p2 r24
r24 = ( 0.085 Q1 / Q1 ) ( \Delta p1 / \Delta p1 + 0.20 \Delta p1 ) ro4
r24 = 0.085 X ( 1 / ( 1 + 0.20 ) ro4
r2 = 0.070 ro
As a result, the shortened artery's radius is 0.070 times its original radius, or percent of the original.
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