Answer:
50 – 5x = y and 46 – 4x = y, is your answer
How many x-intercepts would the function shown below have?
f(x) = 4(4x + 3)(x + 1)² (x^2– 3)
Answer:
Answer:
4Step-by-step explanation:
Given the function
f(x) = 4(4x + 3)(x + 1)² (x^2– 3)
The x-intercept occurs at a point where f(x) = 0
f(x) = 4(4x + 3)(x + 1)² (x^2– 3)
4(4x + 3)(x + 1)² (x^2– 3) = 0
4x+3 = 0
4x = -3
x = -3/4
(x + 1)² = 0
x + 1 = 0
x = 0-1
x = -1
x^2-3 = 0
x^2 = 0+3
x^2 = 3
x = ±√3
hence the x intercepts are -3/4, -1, √3 and -√3. This shows that there are 4 x intercepts
Work out the sum of 1/6 , 4/5 and 2/3 Give your answer as a mixed number in its simplest form.
Answer:
39/30= 13/10
Step-by-step explanation:
You would need to make all numbers have a common denominator. The least common denominator for them is 30. So multiply the 1/6 by 5. the 4/5 by 6 and the 2/3 by 10. And the answer will come out to be a mixed number.
A tree is growing at a constant rate. It is recorded that at the 7th year since it was planted it was at a height of 25 feet. It was recorded again at the 10th year since it was planted and it was at a height of 31 feet. How tall was the tree when it was first planted.
Answer:
Step-by-step explanation:
h₁₀ - h₇ = 31-25 = 6 ft
The tree grew 6 ft in 3 years, or 2 ft per year.
In 7 years the tree grew 14 ft. It was 25-14 = 11 ft when planted
9 (x - 2) = 7x + 5
Does x have a value hurry only 10 minutes left!!
Answer:
x = 11.5
Step-by-step explanation:
9 (x - 2) = 7x + 5
9x - 18 = 7x + 5
+18 +18
9x = 7x + 23
-7x - 7x
2x = 23
--- ---
2 2
x = 11.5
show that the ratios 14/18 and 28/36 form a proportion by finding a common multiplier.
Step-by-step explanation:
divide it by 2...............
A large block of ice is melting and losing 5 grams of mass every minute. After 11 minutes, the ice has lost 70 grams. Assume the relationship is linear.
The linear equation of line is given by y = 6.5x - 1.5 where the slope of the equation m = 6.5 , y = amount of ice lost and x = time elapsed
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the amount of ice lost = y
Let the time elapsed be = x
A large block of ice is melting and losing 5 grams of mass every minute
So , the first point be A = A ( 1 , 5 )
After 11 minutes, the ice has lost 70 grams
So , the second point is B = B ( 11 , 70 )
Now , the slope of the line is given by the formula ,
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 70 - 5 ) / ( 11 - 1 )
Slope m = 65/10
Slope m = 6.5
Now , the equation of line is given by ,
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 5 = 6.5 ( x - 1 )
y - 5 = 6.5x - 6.5
Adding 5 on both sides of the equation , we get
y = 6.5x - 1.5
Therefore , the value of A is y = 6.5x - 1.5
Substitute the value of x = 11 minutes , we get
y = 6.5 ( 11 ) - 1.5
y = 71.5 - 1.5
y = 70 grams
Hence , The linear equation of line is given by y = 6.5x - 1.5 where the slope m = 6.5
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The length of a rectangle is five times the width the area is 125 cm² what is the length
Answer:
Length: 25
Step-by-step explanation:
the ratio we use is 5:1
125÷5=25
5 is the width and 25 is the length
to check the answer find the area with those measurements
5x25=125 so its correct
ayo!! listen to me this is an easy question :)
Apples are on sale at the local fruit stand at 4 lbs. for $2.60. Which equation can be used to find the cost, c, of n pounds of apples?
c = 4
c = .65n
c = 2.60n
c = 8n
Answer:
B ) c = 0.65n
Step-by-step explanation:
To find how much a single pound costs, divide the total cost by the total weight (2.60 ÷ 4). So, the cost (c), equals $0.65 per pound.
please help me with this
Answer:
Y=MX+C is the equations of a straight line where C is the constant (y intercept)
Looking at a and b and the two graphs c and d
The function c represents the lowest value of the y intercept which is at -3
Find the slope of -1:9 0:5 1:1,
-4/1
-1/4
1/4
4/1
Answer:
1/4
Step-by-step explanation:
A P E X
Answer: I’m a goofy goober yeah your a goofy goober yeah
Step-by-step explanation:
3x-4+2x=6+2x-4
What will be the x?
Answer:
x=2
Step-by-step explanation:
To find the value of x
3x+4 = 2x+6
3x-2x = 6–4
x=2
The value of x is 2.
16/5 where is that on the number line?
What is the first step in solving this equation :
2x - 7 = 19
Options :
A - Add 7 to both sides
B - Subtract 19 from both sides
C - Subtract 7 from both sides
D - Divide both sides by 2
Please help its due in 20 minutes!!
the answer is:
2x = 19 + 7
2x= 26
x= 13
A room has a perimeter of 40 feet. The length is 4 less than 2 times the width. What are the dimensions of the room?
Answer:
First, develop an equation for this scenario. The formula to find the perimeter of a quadrilateral is 2l+2w. Because the length is 4 less than twice the width, this would be translated to (2w-4). Plug this into the variable for the length to get 2(2w-4)+2w=40. Distribute the 2 to get 4w-8+2w=40. Add the like terms to get 6w-8=40. Add 8 to both sides and get 6w=48. Divide 6 to result with w=8.
Now that we know w, we can substitute 8 into the variable to solve for the length. 2l+2(8)=40. Multiply 8 and 2 to get 2l+16=40. Subtract 16 to both sides to get 2l=24. Divide 2 to both sides to result with l=12.
Length = 12 feet
Width = 8 feet
In the year 2007, a company made $4 million in profit. For each consecutive year after that, their profit increased by 14%. How much would the company's profit be in the year 2011, to the nearest tenth of a million dollars
Answer:
$6.76 million
Step-by-step explanation:
The computation of the profit of the year in 2011 is shown below:
Given that
In year 2007, it made $4 million profits
And it would be increased by 14% till 2011
So,
= $4 million × (1 + 0.14)^4
= $4 million × 1.68896016
= $6.76 million
Jared made 12 3 fourhs cups of snack mix for a party his guests ate two thirds of the mix how much snack mix did his guests eat
Answer: Jared guests ate = 8 1/2 cups of the snack mix.
Step-by-step explanation:
Total snack mix made by Jared = 12 3/4 CUPS
Amount eaten by guests = 2/3 of Total snack mix
which means they ate = 2/ 3 x12 3/4
= 2/3 x 51/ 4
=17/2 = 8 1/2 cups of snack mix.
Jared guests ate 8 1/2 cups of the snack mix.
Whitney works at an aquarium. She uses hoses of different sizes to fill the fish tanks. Hose A takes 16 min to fill a 160-gal tank. Hose B takes 30 min to fill a 240-gal tank.
Which hose fills at a faster rate?
Choose one option from each drop-down menu to answer the question.
Hose A fills at a rate of Choose... 0.1, 10, 144, 160 gal per min.
Hose B fills at a rate of Choose... 0.125, 8, 210, 240 gal per min.
Hose Choose... A or B fills at a faster rate.
Answer:
Hose A fills at a rate of 10 gal per min
Hose B fills at a rate of 8 gal per min
Hose B fills at a faster rate
Step-by-step explanation:
Answer:
Hose A=10 gal per min
Hose B=8 gal per min
Hose A is faster
Step-by-step explanation:
A) 160 gallon/16 minutes=10 gallons per minute
B) 240 gallon/30 minutes=8 gallons per minute
The pet store has an abundance of birds and fish and is selling them at a great price there are 230 of these pets in the store the cost for a bird is $9 and the cost per fish is $4 the store sold all the pets in a weekend blow out sale and made $1060 how many of the pets were birds and how many were fish? Equation for pets? Equations for cost?
Answer:
a) How many of the pets were birds and how many were fish?
Number of birds = x = 28
Number of fish = y = 202
b) Equation for pets?
x + y = 230....... Equation 1
c) Equations for cost?
9x + 4y = 1060...... Equation 2
Step-by-step explanation:
The pet store has an abundance of birds and fish and is selling them at a great price there are 230 of these pets In the store the cost for a bird is $9 and the cost per fish is $4 the store sold all the pets in a weekend blow out sale and made $1060 how many of the pets were birds and how many were fish? Equation for pets? Equations for cost?
Let us represent:
Number of birds = x
Number of fish = y
The pet store has an abundance of birds and fish and is selling them at a great price there are 230 of these pets
x + y = 230....... Equation 1
x = 230 - y
In the store the cost for a bird is $9 and the cost per fish is $4 the store sold all the pets in a weekend blow out sale and made $1060
$9 × x + $4 × y = $1060
9x + 4y = 1060...... Equation 2
We substitute 230 - y for x
9(230 - y) + 4y = 1060
2070 - 9y + 4y = 1060
Collect like terms
- 9y + 4y = 1060 -2070
-5y = -1010
y = -1010/-5
y = 202
Solving for x
x = 230 - y
x = 230 - 202
x = 28
Therefore,
Number of birds = x = 28
Number of fish = y = 202
Suppose that y varies directly with x and inversely with z. If y = 63 when x =
27 and z = 3, find the constant of proportionality.
Answer:
constant of proportionality = 7
Step-by-step explanation:
Let k = constant of proportionality
If y varies directly with x and inversely with z, then [tex]\frac{yz}{x} = k[/tex]
Substitute the values given into the equation and you get [tex]\frac{(63)(3)}{27} = 7 = k[/tex]
The value of a car is $18,000 and depreciating at a rate of 12% per year. Use
an exponential function to find the value of the car after 10 years.
$5012.02 is the value of the car after 10 years
How to use the exponential function to find the value of the car after 10 years?Depreciation is the reduction in the value of an asset over time
Given that: the present value of a car is $18,000 and it's depreciating at a rate of 12% per year
The exponential function is given as
Y= a ( 1 - r )^t
where a = present value of a car, r = depreciation rate and t = number of years
Y = 18,000 (1-0.12)¹⁰
Y = $ 5012.02
Therefore, the value of the car after 10 years is $ 5012.02
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How might a change in the environment affect plants differently than it would animals?
Answer:
Some plants need certain things in their environment, so if their environment changes it could make the plants not grow. Animals would most likely either move to a different area or would get used to the change.
Bonjour, je bloque sur un exercice de mon DM pouvez vous m'aider s'il vous plaît ? Voici l'énoncé : Ce tremplin a la forme de la parabole de la fonction carré dans un repère orthonormé (unité : 1m). Il est haut de 0,5 m d'un côté et de 2m de l'autre. Calculer sa largeur l en m et arrondir au dixième. Merci d'avance.
Jocelyn Smith has been injured by a local driver who was not paying attention to the road while he was texting on his cellphone. Jocelyn Smith decides to sue the driver. She believes that her own pain and suffering and other damages are worth more than $100,000. In which Florida court should she file her legal action against the driver?
Answer: florida circuit court
Step-by-step explanation:
Based on the information given, the Florida court that she should file her legal action against the driver is the Florida circuit court.
The Florida Circuit Court is a state court where cases such as civil cases, felony, juvenile cases, family law and probate issues are heard. Therefore, based on the scenario given, the Florida circuit court will be applicable here.
The side lengths of a square are each 4p. By adding 3 to the length and subtracting 3 from the width, a rectangle is made. What is the area of the rectangle?
Answer: [tex]16p^{2} -9[/tex]
The area of the rectangle is [tex]16p^{2} -9[/tex].
What is a rectangle?A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.
For the given situation,
The side length of square = 4p
The length of rectangle, l = 4p+3
The width of rectangle, w = 49-3
The formula of area of rectangle is
[tex]A=lw[/tex]
⇒ [tex]A=(4p+3)(4p-3)[/tex] [∵ [tex](a+b)(a-b)=a^{2}-b^{2}[/tex] ]
⇒ [tex]A=(4p)^{2} -3^{2}[/tex]
⇒ [tex]A=16p^{2} -9[/tex]
Hence we can conclude that the area of the rectangle is [tex]16p^{2} -9[/tex].
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1. Janna works at a lab with a huge circular particle accelerator. It has a radius of 4 kilometers. What is the accelerator's diameter?
2. KC wants to know the area of the portion with a lot of cheese. The radius of the pizza is 9 inches and the intercepted arc of the pizza with lot of cheese measures 140°. What will be the area of the shaded sector?
3. From the main entrance of the park, there are two pathways where visitors can walk along going to the circular garden. The pathways are both tangent to the garden whose center is 40m away from the main entrance. If the area of the garden is about 706.5 m2, how long is each pathway?
pakisagot po ty!!
Answer:
1. diameter=8 kilometres
2. area=98.96 inches
3. 37m
Step-by-step explanation:
1. diameter= 2*radius
2. area of sector=θ out of 360*π[tex]r^{2}[/tex] where θ is the angle
3. area of garden=π[tex]r^{2}[/tex]
706.5=π[tex]r^{2}[/tex]
[tex]r^{2}[/tex]=706.5/π
= 225(nearest whole)
r=[tex]\sqrt{225}[/tex]=15m
we now use Pythagoras theorem to find length of each pathway
[tex]40^{2} =15^{2} +x^{2}[/tex]
1600=225+[tex]x^{2}[/tex]
[tex]x^{2}[/tex]=1600-225=1375
x=[tex]\sqrt{1375}[/tex]=37 m (to nearest whole)
The tangent pathways from the entrance form right triangles from which
the length of the pathway which are the sides of the triangle, can be found.
1. The diameter is 8 kilometers2. The area of the shaded sector is 98.96 square inches3. The length of each pathway from the entrance is approximately 37.1 metersReasons:
1. The radius of the particle accelerator = 4 kilometers
The diameter of the particle accelerator = 2 × The radius
Therefore;
The diameter = 2 × 4 km = 8 km
The accelerator's diameter is 8 kilometers
2. The area of a sector of a circle is A = [tex]\displaystyle \frac{\theta}{360^{\circ}} \times \pi \cdot r^2[/tex]
The angle subtended by the sector, θ = 140°
The radius of the sector, r = 9 inches
Therefore;
[tex]\displaystyle A = \frac{140^{\circ}}{360^{\circ}} \times \pi \times 9^2 = \mathbf{ 31.5 \cdot \pi}[/tex]
The area of the shaded sector, A = 31.5·π in.² ≈ 98.96 in.²
3. The distance from the center to the main entrance, d = 40 m
Area of the circular garden, A = 706.5 m²
Solution:
The radius of the garden, r = √(A ÷ (π))
Therefore;
r = √(706.5 ÷ (π)) ≈ 15
The tangent pathways are perpendicular to the radius of the circular garden.
Therefore, the pathway from the entrance, the 40 m. distance from the center to the entrance and the radius form a right triangle.
Where;
The 40 m. distance = The hypotenuse side
By Pythagorean theorem, we have;
40² = r² + (Length of the pathway)²
Which gives;
40² = 15² + (Length of the pathway)²
Length of the pathway ≈ √(40² - 15²) ≈ 37.1
The length of each pathway is approximately 37.1 m.
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k + 11 = -3k- 25 + 2k
Answer:
k = -18
Step-by-step explanation:
GRADE 7 MATHEMATICS (QUARTER 2)
SUBJECT TEACHER:
GENERAL INSTRUCTION
SCORE:
Read and analyze carefully the given questions.
IL You may refer to your module pages 22 - 27.
Directions: Choose the letter of the best answer and write in the space provided before the number,
1. In the expression x2, 2 is what we call
A Base
B. Exponent
C. Multiply
D. Divide
2. Find the product of (x) (**)
A x?
B. 22
Сх
D. X
3. What is the product if 2x is multiplied by 5x?
A 10x
B. 7x2
C. 10x
D. 3x
4. Divide 32a9bc2 by 4a-0%
A. 8a+b+c2
B. 8ac2 C. 8a 0042
D. Sa+bc
5. Multiply 2x by 13xy
A. 26xy
B. 26x3y2
C. 26x
D. 26xy
6. What is the product of 2x3 +3x2 + 4x and x + 1?
A 2 + 2x + 3x2 + 4x B. 2X* + 5x + 7x2 + 4x C. 5x + 7x3 + 4x + 2x D. 7* *4x3 + 2x + 5x
7. What polynomial is obtained if 27x*y* + 18x2y3 + 9x^y is divide by 3xy?
A 9xy + 6x2y3 + 3y B. 9xy + 6x3y C 9xy + 18xy + 6x
D. 9x+y + xy + 3x
8. What expression will satisfy the given statement: (a + 3)(_) = a + 6a + 9
A a-3
B. -3-a
C. a + 3
D. -3 + a
9. Find the product of (x-1) and (x + 1).
A x² + 1
B. X?- 1
c. x² + x + 1
D. X2 - x + 1
10. What will be the first term of the product of (2x - 1)?
A 4x2
B. 4x
C. 1
D. 2x
11. Multiply (4y - 5d) (4y + 50)
A. 16y2 + 2502
B. 4y + 50 C. 16y2 - 25d2
D. 4y - 50
12. Evaluate ( x - 3)(x2 + 3x + 9)
A. x2 - 81
B. x - 27
C. X + 9x + 27
D. X - 9x + 27
13. Solve (x-6)
A. x2 + 12x - 36
B. x2 + 36 C. X2 - 36
D. x2 - 12x + 36
14. What is the area of the square whose side is 2x + 5?
A 4x2-20%-25 B. 4x2 - 20x + 25 C. 4x2 + 20x - 25
D. 4x2 + 20x + 25
15. Evaluate (x + 4)'
A x + 12x2 + 48x + 64 B. X- 12x2 - 48x - 64 C. X - 12x2 + 48x - 64 D. x + 12x2 - 48x + 64
GRADE 7 MATHEMATICSQUARTER 2 (WEEK 7-8)
Directions: Choose the letter of the best answer and write in the space provided before the number.
Answer:
1) B? (I think that is meant to be an exponet. if it is, you would write it as x^2)
2) I do not know
3) A (it would actually be 10x^2, but 10x is the closest to it
4) A makes the most sense
5) A
6/7/8) I do not know, sorry
9) A makes the most sense
10-15) I am sorry, I cannot solve it
Step-by-step explanation:
I am sorry you have to go through this in 7th grade
r/1000=7, algebra, got confused and this one is weird to do. (personally)
Answer:
r = 7000Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
r/1000-(7)=0
Step by step solution :
STEP1:
r
Simplify ————
1000
Equation at the end of step1
r
———— - 7 = 0
1000
STEP 2
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 1000 as the denominator :
7 7 • 1000
7 = — = ————————
1 1000
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
r - (7 • 1000) r - 7000
—————————————— = ————————
1000 1000
Equation at the end of step 2
r - 7000
———————— = 0
1000
STEP 3
When a fraction equals zero :
3.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
r-7000
—————— • 1000 = 0 • 1000
1000
Now, on the left hand side, the 1000 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
r-7000 = 0
Solving a Single Variable Equation:
Solve : r-7000 = 0
Add 7000 to both sides of the equation :
r = 7000
One solution was found :
r = 7000
Step-by-step explanation:
Hope it is helpful.....
The square table top has an area of 369 square
inches. The length of one side of the table top is
between which two measurements?
Answer:
19 in. and 20 in.
Step-by-step explanation:
18^2 = 18 * 18 = 324
19^2 = 19 * 19 = 361
20^2 = 20 * 20 = 400
369 is between 361 and 400, so the side of the table is between 19 in. and 20 in.
Answer:
19 in. and 20 in.
Step-by-step explanation:
18^2 = 18 * 18 = 324
19^2 = 19 * 19 = 361
20^2 = 20 * 20 = 400
369 is between 361 and 400, so the side of the table is between 19 in. and 20 in.
what is 5/6 -3/8 ........
Answer:
11 over 24 = 0.458
Step-by-step explanation:
