[tex]y = - 2(x - 2)(x - 10)[/tex]
[tex]0 = - 2(x - 2)(x - 10)[/tex]
[tex]x - 2 = 0 \\ x = 2[/tex]
[tex]x - 10 = 0 \\ x = 10[/tex]
Answer:
The zero's are x=2 and x=10
Step-by-step explanation:
y = -2(x-2) (x-10)
We want to find the zero's so we set y=0
0 = -2(x-2) (x-10)
Using the zero product property
x-2 = 0 and x-10 =0
x-2+2 =0+2 x-10+10 =0+10
x =2 x=10
The zero's are x=2 and x=10
50 POINTS TO THE FASTEST CORRECT ANSWER
John runs a frozen yogurt stand and a sandwich shop. Last month, John lost $195 running the frozen yogurt stand, and he lost 7 times as much running the sandwich shop. Approximately how much money did John loe running the sandwich shop last month?
A: $1,400
B: $1,300
C: $1,500
D: $1,200
Answer:
A: 1,400
Step-by-step explanation:
$196 * 7 = 1365
rounded up to 1,400
Suppose that G(x)= F(x-4) which statement best compares the graph of G(x) with the graph of F(x)
Answer:
The correct option is A. The graph of g(x) is the graph of f(x) shifted 4 units to the right
Step-by-step explanation:
The graph of g(x) is given equal to f(x - 4)
We need to give the statement that best compares the graph of g(x) with the graph of f(x)
Now, f(x - 4) states that the graph of g(x) is shifted 4 units to the right as compared to the graph of f(x)
Therefore, The statement that best compares the graph of g(x) with the graph of f(x) is : The graph of g(x) is the graph of f(x) shifted 4 units to the right
Hence, The correct option is A. The graph of g(x) is the graph of f(x) shifted 4 units to the right
Answer:
Option A.
Step-by-step explanation:
The translation is defined as
[tex]G(x)=F(x+a)+b[/tex] .... (1)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
It is given that
[tex]G(x)=F(x-4)[/tex] .... (2)
On comparing (1) and (2) we get
a=-4<0, So the graph of G(x) is the graph of F(x) shifted 4 units to the right.
Therefore, the correct option is A.
Are these all correct? Please let me know quickly.
yes!!!!!!!!!!!!!!!!!!!!!
a tree was 12 3/8 inches tall when it was first planted. three years later the tree was 21 1/8 inches tall how much did the tree grow in the 3 years?
Answer:
The tree grew 8 and 3/4 inches.
Step-by-step explanation:
To get this answer, first subtract the whole numbers.
21 - 12 = 9
Now do the same with the fractions.
1/8 - 3/8 = -2/8
Now add those two together.
9 - 2/8 = 8 6/8 = 8 3/4
What is the greatest common factor (GCF) of 80 and 100?
Answer:
20.
Step-by-step explanation:
We found the factors and prime factorization of 80 and 100. The biggest common factor number is the GCF number. So the greatest common factor 80 and 100 is 20
The greatest common factor (GCF) of 80 and 100 is 20.
How to determine the gcfTo find the greatest common factor (GCF) of 80 and 100, we can determine the common factors of both numbers and identify the largest one.
The factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The common factors of 80 and 100 are: 1, 2, 4, 5, 10, 20.
The largest common factor among these is 20.
Therefore, the greatest common factor (GCF) of 80 and 100 is 20.
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Question 1 options:
x2 +x − 4 = 0
You will solve this using the Quadratic Formula.
First, what are the values of a, b, and c?
a =
your answer will be a=1 b=1 c= -4
What is the degree measure of SRP? Please show work!
Answer:
The measure of angle SRP is 90°
Step-by-step explanation:
In this problem
RS is tangent to circle P at point R
so
PR (the radius) is perpendicular to RS
therefore
m<SRP=90°
What is the volume of a cube with an edge length of 2.5 ft?
Enter your answer in the box
hurry up plzzzz
Answer:
15.625 cubic feet
Step-by-step explanation:
2y-x=5
x2+y2-25=0
Solve the system by the substitution method
Answer:
(- 5, 0), (3, 4)
Step-by-step explanation:
Given the 2 equations
2y - x = 5 → (1)
x² + y² - 25 = 0 → (2)
Rearrange (1) expressing x in terms of y
x = 2y - 5 → (3)
Substitute x = 2y - 5 into (2)
(2y - 5)² + y² - 25 = 0 ← expand parenthesis and simplify
4y² - 20y + 25 + y² - 25 = 0
5y² - 20y = 0 ← factor out 5y from each term
5y(y - 4) = 0
Equate each factor to zero and solve for y
5y = 0 ⇒ y = 0
y - 4 = 0 ⇒ y = 4
Substitute these values into (3) for corresponding values of x
y = 0 : x = 0 - 5 = - 5 ⇒ (- 5, 0)
y = 4 : x = 8 - 5 = 3 ⇒ (3, 4)
Answer:
y=0 or 4, x=-5 or 3
Step-by-step explanation:
First make one unknown in the first equation the subject of the formula.
2y-x=5 will become:x=2y-5
Then in the second equation, wherever there is x we substitute it with 2y-5
(2y-5)²+y²-25=0 (2y-5)(2y-5)+y²-25=0
opening the brackets gives: 4y²-10y-10y+25+y²-25=0
5y²-20y=0
Factorizing the equation we get the following:
y(5y-20)=0
y=0 or
5y-20=0
5y=20
y=4
Thus y=0 or 4
Substitute 0 and 4 for y in any of the equations provided.
Picking the first equation and starting with y=0
2(0)-x=5
x=-5
Using y=4
2(4)-x=5
x=3
Guys can you plese help me?!?
For both drop down menus the choices are: "is possible" and "is not possible"
n-4-9
I really need help with this
Answer:
n - 13
Step-by-step explanation:
n-4-9
We can combine like terms.
n - (4+9)
n - 13
-42-7k=14-k What is the value of k
Answer: k= around -9.33
Step-by-step explanation:
-42-7k=14-k
Move the terms
-7k+k=14+42
collect the like terms
calculate the sum
-6k=56
divide both sides by -6
k=-28/3
alternative form
-9.33
Find the slope of the line that passes through (8, 10) and (1, 4).
Answer:
slope = [tex]\frac{6}{7}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
where (x₁, y₁ ) = (8, 10) and (x₂, y₂ ) = (1, 4)
m = [tex]\frac{4-10}{1-8}[/tex] = [tex]\frac{-6}{-7}[/tex] = [tex]\frac{6}{7}[/tex]
The slope of the line that passes through the points (8, 10) and (1, 4) is found to be 6/7.
To find the slope of a line that passes through two points, we can use the formula for slope, which is:
slope (m) = (y2 - y1) / (x2 - x1)
Applying this formula to the given points (8, 10) and (1, 4), we get:
slope (m) = (10 - 4) / (8 - 1) = 6 / 7
So, the slope of the line that passes through the points (8, 10) and (1, 4) is 6/7.
a certain isotope decays so that the amount A remaining after t years is given by: A=A0 x e^-0.03t, where A0 is the original amount of the isotope. to the nearest year, the half-life of the isotope (the amount of the time it takes to decay to half the original amount) is ____ years
Answer:
[tex]t = 23.10\ years[/tex]
Step-by-step explanation:
We have an exponential decay function:
[tex]A = A_0e ^{-0.03t}[/tex]
This function decreases as the years pass. That is, if A is the quantity for a time t and [tex]A_0[/tex] is the original quantity at time t = 0 then:
[tex]A <A_0[/tex]
We want to know for what value of t the value of A decreases by half of [tex]A_0[/tex]. That is, we want to know when [tex]A = \frac{A_0}{2}[/tex]
Then we do:
[tex]\frac{A_0}{2} = A_0e ^{-0.03t}\\\\\frac{1}{2} =e ^{-0.03t}\\\\ln(\frac{1}{2}) = -0.03t\\\\t = \frac{ln(\frac{1}{2})}{-0.03}[/tex]
[tex]t = 23.10\ years[/tex]
what are reflections
reflection is when a shape is flip on the x or y axis and changes the original points to a new point
Answer:
See below
Step-by-step explanation:
A reflection is a mirror flip of an object across a line (called a mirror line or a line of reflection).
The reflection or mirror image is the same size and shape as the object Every point in the mirror image is the same distance from the mirror line as its corresponding point in object.In the diagram, Points A, B, and C in the object are the same distance from the mirror line as Points A', B', and C' in the mirror image.
Plzz help! I don't know fraction that well.
Answer:
It's the 2nd one.
Step-by-step explanation:
-1 1/8, - 5/8, 0, 1/2, and 6.
what is 1800 to the nearest 100th
A hundredth is 0.01
A hundred is 100.
You look at the digital to the right of the 1, in the example above. If that digit is 5 or greater, round up, other round down.
In both cases, you will look at the 0, therefore you would round down.
1800 to the nearest hundredth is 1800.00.
1800 to the nearest hundred is 1800.
Ross bought a bag of candy bars he give 12 candy bars to his mom he then put the rest of the candy bars into 8 small bags each small bag head for candy bars how many candy bars did Ross buy at the store
Answer:
44
Step-by-step explanation:
first we take the number he gave to his mom and put it to the side for later then we see that 8 bags had 4 candy bars each so 8*4 is 32 then we bring the 12 bars that he gave to his mom and add that to 32 so 32+12 and the answer would be 44
Ross bought a total of 44 candy bars, considering the 12 he gave to his mom and the 32 he divided among the 8 small bags.
To determine how many candy bars Ross bought at the store, we first need to calculate the total number of candy bars in the small bags. Ross divided the remaining candy bars into 8 small bags, with each small bag containing 4 candy bars. Therefore, the total number of candy bars in the small bags is
8 bags x 4 candy bars per bag,
which equals 32 candy bars. However, we must not forget that Ross also gave 12 candy bars to his mom. Thus, the total number of candy bars Ross bought is the sum of the candy bars given to his mom and the candy bars in the small bags, which is
12 candy bars + 32 candy bars,
resulting in 44 candy bars.
Please help me with this
Answer:
option C)
3^(5)
Step-by-step explanation:
given in the question an expression
3² x 3³
We will use the exponent "product rule" which tells us that, when multiplying two powers that have the same base, you can add the exponents.
Here
the base = 3
the exponent are = 2 and 3
Simplification
3^(2+3)3^(5)
[tex]\bold{Hey\ there!} \\ \\ \bold{3^2=3\times3\rightarrow9 \ \ & \ \bold{3^3=3\times3\times3\rightarrow27}} \\ \\ \\ \bold{9\times27=243} \\ \\ \\ \bold{Options\downarrow} \\ \\ \\ \bold{3^8=6,561(not\ your\ answer)} \\ \\ \\ \bold{3=3(not\ your\ answer)} \\ \\ \bold{3^5=243(answer)} \\ \\ \bold{3^6=729(not\ your\ answer)}[/tex]
[tex]\bold{Your\ front\ number(s)\ (3) \ stays\ the\ same\ \& \ 2+3=5}[/tex]
[tex]\boxed{\boxed{\bold{Thus,\ your\ answer\ is:\ Option\ C. 3^5}}}\checkmark \\ \\ \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]
Find the volume of the triangular prism
Answer: When I tried I got 432 ft
Step-by-step explanation:
All I did was this.
2 ft x 12 ft x 18 ft = 432 ft.
Check on the calculator also and see the answer for yourself.
This prism has a surface area of 172 cm². What would the surface of the prism be if each dimension was tripled? ( Scale factor is 3 )
When the dimensions of a prism are tripled, the scale factor is 3, so the new surface area is obtained by squaring the scale factor and multiplying it by the original surface area. Therefore, the new surface area will be 1548 cm².
Explanation:The concept in question here pertains to geometric scaling and involves understanding how changes in dimensions affect the surface area of a three-dimensional shape. According to the rules of geometric scaling, when the dimensions of a shape are multiplied by a scale factor, the surface area is multiplied by the scale factor squared.
In this case, the scale factor is 3, so to determine the new surface area when the dimensions of a prism are tripled, you square the scale factor (3² = 9) and multiply it by the original surface area. So, the new surface area = 9 * 172 cm² = 1548 cm².
To find the surface area of a prism, we add up the areas of all its faces. Let's assume the original prism has side lengths x, y, and z. The surface area of the prism is 2(xy + xz + yz). If each dimension is tripled, the new dimensions of the prism would be 3x, 3y, and 3z. Therefore, the new surface area of the prism would be 2(3x3y + 3x3z + 3y3z) = 18(xy + xz + yz).
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What is the area of the smaller figure in square cm?
Answer:
(25 + 25/√2)²
= 25² + 50*25/√2 + (25/√2)²
= 625 + 1250/√2 + 625/2
≈ 625 + 883.883 + 312.5
≈ 1821 sq. cm
Step-by-step explanation:
Imagine starting by putting the diameter of the semicircle directly in the corner of a square but at a 45 degree angle. That makes a 45-45-90 triangle with the hypotenuse being 50 cm.
Now take the midpoint of this and draw your semicircle. The distance from this point up will be the radius (25 cm). And down will be the side of a triangle with hypotenuse 25. This ends up being 25/√2.
So one dimension would be 25 + 25/√2, and so would the other. Multiplying this together we get:
ANSWER
The area of the smaller rectangle is 8 cm²
EXPLANATION
Let the area of the smaller rectangle be s.
The scale factor for the enlargement is
[tex]k = 5[/tex]
The corresponding change is area is
[tex] {k}^{2} = {5}^{2} = 25[/tex]
When we multiply this by the area of the smaller rectangle we obtain the area of the bigger rectangle.
[tex]25s = 200[/tex]
[tex]s = \frac{200}{25} [/tex]
[tex]s = 8 {cm}^{2} [/tex]
What is the answer thank you
b. alternate angles are equal
hope this helps!!
b.) alternate angles are equal
If a transversal intersects two parallel lines, each pair of alternate angles are equal.
Given: Two parallel lines and a transversal.
Prove: Each pair of alternate angles are equal (same degrees).
Alternate interior angles are formed when a transversal passes through two lines. The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. The theorem says that when the lines are parallel, that the alternate interior angles are equal
Try using a protractor to measure the angles to prove that they have the same angle degrees.
what is the IQR of 62, 65, 93, 51, 55, 76, 79, 85, 55, 72, 78, 83, 91, and 82
The IQR of the given data set is 23, calculated by ordering the data, finding the first and third quartiles, and then subtracting the first quartile from the third quartile.
To find the Interquartile Range (IQR) of the given data set, you must first order the data from least to greatest, then find the median (Q2), the first quartile (Q1), and the third quartile (Q3). The IQR is the difference between Q3 and Q1.
Order the data: 51, 55, 55, 62, 65, 72, 76, 79, 82, 83, 85, 91, 93.Find the median: The median is 76, which splits the data into two halves.Find Q1 and Q3: The lower half before the median is 51, 55, 55, 62, 65, 72. The median of this half is Q1 which is 62. The upper half after 76 is 79, 82, 83, 85, 91, 93. The median of this half is Q3, which is 85.Calculate the IQR: IQR = Q3 - Q1 = 85 - 62 = 23The IQR of the data set is 23.
You have 5 bikes. Altogether it costs 789$ how much does each bike cost?
Answer:
$157.80
Step-by-step explanation:
$789 / 5 bikes
157.80 you just divide
Which of these is not included in the set of rational numbers?
A
all integers
B
all whole numbers
C
all repeating decimals
D
all non-terminating decimals
Non-terminating decimals are not included in the set of rational numbers. This is because rational numbers consist of numbersthat are integers.
Answer: D) Al non-terminating decimals
Credit to: @Jimthompson5910
--_--_--_--_--_--_--_--_--_--_--_--_--_--_--_--_--
love like Jesus, live like Jesus
Answer:
33
Step-by-step explanation:
mow
a red ribbon 11 meters long is 5 times as long as a blue ribbon. How long is the blue ribbon?
Red ribbon
=Blue ribbon ×5
=11 m
So, changes the times symbol into divide
11m ÷ 5
=2.2m
Check!
Red ribbon=Blue ribbon × 5
11m=Blue ribbon × 5
11m÷5=Blue ribbon
2.2m=Blue ribbon
Blue ribbon=2.2m
Answers
2.2m
To find the length of the blue ribbon, divide the length of the red ribbon (11 meters) by 5. This calculation reveals that the blue ribbon is 2.2 meters long.
Explanation:The question asks us to find the length of a blue ribbon when we know a red ribbon is 11 meters long and is 5 times as long as the blue ribbon. To solve this, we divide the length of the red ribbon by 5:
Identify the relationship: The red ribbon's length is 5 times the blue ribbon's length.Write the equation: Red Ribbon Length = 5 × Blue Ribbon Length.Substitute the known values into the equation: 11 meters = 5 × Blue Ribbon Length.Divide both sides of the equation by 5 to find the blue ribbon's length: Blue Ribbon Length = 11 meters / 5.Calculate: Blue Ribbon Length = 2.2 meters.Therefore, the length of the blue ribbon is 2.2 meters.
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The price of a math book is $50 but you only have $35 with you. If you get a discount of 20% how much money do you need to borrow from a friend so that you can but the book?
After applying a 20% discount to the $50 math book, the price becomes $40. Since you have $35, you need to borrow $5 to purchase the book.
To calculate the discounted price of the book, you multiply the original price by the percentage of the discount in decimal form. The discount in decimal form is 0.20 (since 20% = 0.20).
Using the formula for calculating the discounted price:
Discounted Price = Original Price × (1 - Discount Rate)
Discounted Price = $50 × (1 - 0.20) = $50 × 0.80 = $40.
You have $35, so the amount you need to borrow is:
Amount to Borrow = Discounted Price - Amount You Have
Amount to Borrow = $40 - $35 = $5.
Therefore, you need to borrow $5 from your friend to buy the math book.
What is the standard notation for a distance of 9.302 x 10^10 miles?
Answer:
the distance would be 93020000000
The standard notation for a distance of 9.302 x 10^10 miles is 930,200,000,000 miles, as scientific notation is converted into standard notation by moving the decimal point right if the exponent is positive.
Explanation:The student's question asks about converting a scientific notation into its standard notation. Scientific notation is just a way to express either extremely large or small numbers in a more concise and convenient way. In this case, the scientific notation is 9.302 x 10^10 miles.
To convert 9.302 x 10^10 from scientific notation to standard notation, you move the decimal point 10 places to the right because the exponent of 10 is positive. When you do this, you should get 930200000000.
So, the standard notation for a distance of 9.302 x 10^10 miles is 930,200,000,000 miles.
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Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water’s edge. The equation of her average change in elevation over time is e = 300 – 10t, where t is the time in minutes since she left the cabin, and e is her elevation with regard to sea level. Which values are viable points, and what are their values in the table relating t and e?
For this problem, we plug in the numbers for t and the appropriate letters for e to the equation e = 300 - 10t.
a) a = 300 - 10(-2)
simplify: a = 300 + 20
simplify: a = 320 ft.
But, this is not a viable point because when t≤0, she doesn't move anywhere, thus, should consistently be 300 ft.
b) b = 300 - 10(3.5)
simplify: b = 300 - 35
simplify: b = 265 ft.
c) c = 300 - 10(30)
simplify: c = 300 - 300
simplify: c = 0 ft.