Answer:
f(x)=x^2+9x-10
Step-by-step explanation:
Standard Form of Quadratic Function
The standard form of a quadratic function is:
\(f(x)=ax^2+bx+c\)
where a,b, and c are constants.
The factored form of a quadratic equation is:
\(f(x)=a(x-\alpha)(x-\beta)\)
Where \(\alpha\) and \(\beta\) are the roots or zeros of f, and a is constant.
We know the zeros of the function are 1 and -10. The function is:
\(f(x)=a(x-1)(x-(-10))\)
\(f(x)=a(x-1)(x+10)\)
Operating:
\(f(x)=a(x^2+10x-x-10)\)
Joining like terms:
\(f(x)=a(x^2+9x-10)\)
Since we are not given any more restrictions, we can choose the value of a=1, thus. the required function is:
\(\boxed{f(x)=x^2+9x-10}\)
How to convert 190 lbs to kg?
Answer: 86.184 kg
Step-by-step explanation:
There is 0.4536 lb in 1 kg.
So, the answer is \((190)(0.4536)=86.184\) kg.
The value of 190 lbs in kg after unit conversion is 86.17 kg.
What are the units of measurement of mass?
A unit of measurement is a specific magnitude of a quantity that has been established and recognised by law or convention and is used as a benchmark for measuring other quantities of the same kind. A multiple of the unit of measurement can be used to express any other quantity of that type.
The matter that is present in the given object is referred to as its mass. The commonly used units of measurement of mass are grams and kilograms. Both the pound (lbs) and the kilograms (kg) are weight or mass measurement units.
The value of 1 kg = 2.205 lbs
We are asked to find convert 190 lbs to kg.
1 lbs = 1/2.205
190 lbs = 190/2.205 = 86.17 kg
Therefore the value of 190 lbs in kg after unit conversion is 86.17 kg.
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What is the area, in square meters, of the shaded part of the rectangle below?
Answer:
45.5 m²
Step-by-step explanation:
Area (Shaded) = Area (Rectangle) - Area (Trapezoid)
Area (Shaded) = lb - 1/2 x (a + b) x hArea (Shaded) = 17 × 13 - 1/2 × (10 + 17) × 13Area (Shaded) = 13 (17 - 27/2)Area (Shaded) = 13 × 7/2Area (Shaded) = 91/2Area (Shaded) = 45.5 m²Area of trapezoid:-
1/2(sum of parallel side)×Height1/2(10+17)(13)1/2(27)(13)13.5(13)175.5m²Area of triangle:-
1/2BH1/2(13)(17-10)1/2(13)(7)91/245.5m²Which part is shaded not said so both shaded regions area calculated
1 3/4 + 7/8 =
what does this equal ?
Answer:
use a mixed numbers calculator .
Step-by-step explanation:
2 5/8 is yo answer tho
Answer:
1 3/4 + 7/8 = 21/8 or 2 5/8
The gateway arch in st. Louis, mo is approximately 630 ft tall. How many u. S. Nickels would be in a stack of the same height? each nickel is 1. 95 mm thick.
The gateway arch in st. Louis, MO is approximately 630 ft tall, the same height of the Nickels would be in a stack is 98474.
Height of Gateway Arch in St. Louis, MO = 630ft tall
We are asked, how many nickels would be in a stack of the same
height when 1 nickel is 1.95 mm thick.
Convert height in ft to mm
1 ft = 304.8 mm
630ft = X
After Cross Multiply,
630ft × 304.8mm/1ft
= 192024 mm.
To find how many nickel would be in a stack of the same height
= Total thickness/ Thickness of 1 US dime
= 192024 mm/1.95mm
= 98473.8
≈98474 nickels
Therefore, the number of nickel that would be in a stack of the same height is 98474.
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½ (6x + 8) = 2x + 4 + x
Answer:
True
Step-by-step explanation:
Both sides (right side and left side) of the equation are indeed equal.
I hope this helps!
Answer:
all real numbers
Step-by-step explanation:
1/2(6x + 8) = 2x + 4 + x
1/2 * 6x + 1/2 * 8 = 2x + 4 + x
3x + 4 = 2x + 4 + x
3x + 4 = 3x + 4
4 = 4
0 = 0
the answer is all real numbers because 0 will always equal 0
A candle maker is ordering wax. Each small candle uses 12 ounces of wax. Each large candle uses 18 ounces of wax. The candle maker wants to make 42 small candles and 38 large candles.
Which answer is the most reasonable estimate of the total amount of wax needed?
Answer:
1188
Step-by-step explanation:
12x42 + 18x38 = 1188
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.25 and the cost of a large greeting card is $4.50. How much would it cost to get 5 small greeting cards and 4 large greeting cards? How much would it cost to get xx small greeting cards and yy large greeting cards?
The Total cost of x small and y large greeting cards is; 1.25x + 4.50y.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the Cost of the small greeting card = is $1.25 .
The Cost of the large greeting card =$4.50.
We need to determine the Total cost of 5 small and 4 large greeting cards and the total cost of x small and y large greeting cards.
The Cost of 5 small greeting cards = 6.25
The Cost of 4 large greeting cards = 18
Then the Total cost = $6.25+ $18 =$24.25
Therefore, the Total cost of 5 small and 4 large greeting cards is; $24.25.
Now, the total cost of x small and y large greeting cards will be;
Cost of x small greeting cards = 1.25x
Cost of y large greeting cards = 4.50y
Total cost = 1.25x + 4.50y
Therefore, the Total cost of x small and y large greeting cards is; 1.25x + 4.50y.
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What is the value of W?
5 units
7 units
14 units
15 units
Answer:
5 units!
Step-by-step explanation:
Because Rectangle Perimeter = 2(a+b)
a=2w-1, b=w
2(2w-1+w)=28
3w-1=14
3w=15
w=5
So the answer is 5! 5! 5! A!A!A!
Fighting!! o(≧o≦)o
Write an equation in slope-intercept form of a line with a slope of -2 that goels through the point (4 , 2)
Answer:
y=-2x+10
Step-by-step explanation:
Please help ASAP
A map uses a scale of 3 centimeters to represent 20 miles. The distance between Mt. Hope and
Camden is 56 miles. Which proportion can be used to find 2, the distance between Mt. Hope and
Camden on the map?
Answer:
Option B is correct
Step-by-step explanation:
Hope that helped u
If z is directly proportional to the product of x and y and if z is 10 when x is 4 and y is 5, then x, y, and z are related by the equation
The equation relating x, y, and z is:
z = 0.5 * x * y.
In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.
To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.
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Venus has 80 ounces of sports drink. If she drinks 60% of it, how much sports drink will she have left?
Answer:
32 ounces
Step-by-step explanation:
balancing equations
Na + F2 —> NaF
Answer:
2Na + F2 ---> 2NaF
Step-by-step explanation:
WILL GIVE BRAINLIEST!!!! Answer each question below.
Select the triangle that shows the median of AQRS from vertex Q.
E
Step-by-step explanation:
The line stems from the vertex Q to the middle of R and S
I would greatly appreciate if you can give the brainliest answer crown!
What is the length of the dotted line? round to the nearest hundredth. 2.50 in. 3.75 in. 5.00 in. 6.25 in.
The measure of the length of the dotted line is 3.75 inches. Then the correct option is B.
What is a hexagon?The hexagon is a 2D geometry that has a 6 number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
The perimeter of the hexagon is 7.5 inches.
Then the length of the hexagon will be
\(\rm 7.5 = 6x\\\\x \ \ = 1.25\)
The length of the hexagon is 1.25 inches.
Then the diagonal length of the hexagon will be
y = 2 × 1.25
y = 2.5
The diagonal length of the hexagon is 2.5 inches.
Then the length of the dotted line is 3.75 inches.
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true or false: if you are given a graph with two shiftable lines, the correct answer will always require you to move both lines.
False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.
In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.
When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.
In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.
However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.
Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.
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I got it partially right I think but I need help !
Answer:
U got it correct
Step-by-step explanation:
please find the value of x
Answer:
x = 5.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 26 = x /12
12 tan 26 =x
x=5.85279
Rounding to the nearest tenth
x = 5.9
Could someone please help. please help asap I need it. see picture...
find the x- and y-intercepts
and write The equation in standard form with integer coefficients
The x-intercept is 5 and the y-intercept is 2.
The standard form of the line is 2x + 5y = 10.
How to find the x-intercept, y-intercept and equation in standard form?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. In other words, the x -intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.
Hence, the x-intercept is 5 and the y-intercept is 2.
Let's find the equation in standard form.
Ax + By = C
where
A, B and C are constantUsing slope intercept form,
y = mx + b
where
m = slopeb = y-interceptHence, using (5, 0) and (0, 2)
m = 2 - 0 / 0 - 5
m = - 2 / 5
Therefore.
y = - 2 / 5x + 2
Hence, let's multiply through by 5 to eliminate the fraction
5y = -2x + 10
Therefore, the standard form is as follows:
2x + 5y = 10
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The poet Claude McKay was a native of Jamaica who
spent most of his life in the United States but writing
some of his poems in the Jamaican dialect.
(A) The poet Claude McKay was a native of Jamaica
who spent most of his life in the United States
but writing
(B) Being that he was a Jamaican who spent
most of his life in the United States, the
poet Claude McKay writing
(C) Although a native of Jamaica, the poet Claude
McKay spent most of his life in the United
States, he wrote
(D) Although the poet Claude McKay spent
most of his life in the United States, he
was a native of Jamaica and wrote
(E) Because he was a native of Jamaica who spent
most of his life in the United States, the poet
Claude McKay writing
The correct option is D) Although the poet Claude McKay spent most of his life in the United States, he was a native of Jamaica and wrote
Although the poet Claude McKay spent most of his life in the United States, he was a native of Jamaica and wrote some of his poems in the Jamaican dialect.
What does a grammatical construct mean?Grammatical construction is a matching of form and meaning in the construction grammar, regardless of the complexity of its formal or semantic structure. Therefore, it is possible to think of words and word classes as examples of constructs.
The phrase "but writing" in the highlighted section of the sentence is improper here and leads to a tense mistake. The best solution to this problem, without introducing any new errors, is Option D.
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If f(1) = 0, what are all the roots of the function ? use the remainder theorem.
By using synthetic division, we can find all the roots of the function f(x) = x³ + 3x² - x - 3 and determine that the roots are 1, -1, and -3.
A root of a function is a value for x that makes the function equal to zero.
In this case, we have a function f(x) = x³ + 3x² - x - 3 and we know that f(1) = 0. To find all the roots of this function, we can use the remainder theorem.
The remainder theorem states that if we divide a polynomial by a linear expression (such as x - a), the remainder will be equal to the value of the polynomial at that value of x (a). In other words, if we write f(x) = (x - a)q(x) + r, where r is the remainder, then f(a) = r.
So, if we divide our function f(x) by x - 1, the remainder will be equal to f(1), which we know is zero. Therefore, (x - 1) is a factor of f(x), and the function has a root at x = 1.
Next, we can divide f(x) by (x - 1) to get a quotient, q(x), and a new remainder, r. We can repeat this process, dividing q(x) by another linear expression until we have no more remainders.
The roots of f(x) will be the values of x that we used as factors in each step of the division process.
This process of dividing a polynomial by a linear expression to find its roots is called synthetic division.
Complete Question
If f(1) = 0, what are all the roots of the function f(x) = x³ + 3x² - x - 3. Use the remainder theorem.
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i need help bru dis is mh last try
What is the inverse of ƒ (x) = (2x + 1)² for x ≥ −½1⁄?
The inverse of the given function is (f^-1)(x) = (1/2)×(√x - 1) for x ≥ 0.
We are given a function f(x). The function f(x) is defined as (2x + 1)². The domain of the given function f(x) is x ≥ -1/2. We need to find the inverse of the function f(x).
Let us suppose that the function f(x) is represented by the variable "y".
y = f(x)
y = (2x + 1)²
Now we will take the square root on both sides of the equation.
√y = √[(2x + 1)²]
When we cancel out the even powers, we need to take the absolute value using modulus.
√y = |2x + 1|
We already know that x ≥ -1/2, so, modulus will open with a positive sign.
√y = +(2x + 1)
√y = 2x + 1
√y - 1 = 2x
x = (1/2)×(√y - 1)
At last, we replace the variables y and x by x and (f^-1)(x).
(f^-1)(x) = (1/2)×(√x - 1) for x ≥ 0
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50 points!!! Please help ASAP!!!
Answer:
h (x)=-16x^(2)+3x+35 =
x-intercept(s): (3+√224932,0),(3−√2249 32,0)
y-intercept(s): (0,35)
Charities can claim an extra 25% of the value of a donation back from the government. This is called gift aid. Work out how much gift aid a charity can claim on a donation of £273.50. Give your answer to the nearest penny
Answer:
Gift aid 68.38 £
Step-by-step explanation:
Proportion:
273.50 £ - 100%
X £ - 25%
Gift aid:
X = 273.50·25% / 100% = 273.50 / 4 ≈ 68.38 £
which of the following choices represents the expanded form of the number 32,9062
∵ The expanded form is the way to write a number using the values of its digits
∵ The number is 32,905
→ It is a 5-digit number
∵ 3 is in the ten thousands place
∴ Its value is 30,000
∵ 2 is in the thousands place
∴ Its value is 2,000
∵ 9 is in the hundreds place
∴ Its value is 900
∵ 5 is in the units place
∴ Its value is 5
→ Add all of this value to get the expanded form
\(32,905=30,000+2,000+900+5\)∴ The answer is C
i have a c please help it will mean alot
\(\Large\boxed{\tt Answer: 5\frac{2}{3} }\)
\(\tt Step-by-step~explanation:\)
We can solve this by dividing both numbers by four.
\(\tt 8\div4=2\\12\div4=3\\\frac{2}{3}\)
We then add that to 5 to get our answer.
Cameron is older than Hassan. Their ages are consecutive integers. Find Cameron's
age
if the sum of Cameron's age and 5 times Hassan's age is 145.
Answer:
25
Step-by-step explanation:
So consecutive integers, just means they're separated by a value of 1. This can be generally expressed as "a, a+1" where these two values would be consecutive integers assuming "a" is an integer.
So let's express Hassan's age as the variable "x", since it's unknown. Since Cameron is older, and by definition of a consecutive integer, Cameron's can be expressed as "x+1"
So the equation we need to set up is Cameron's age + 5(Hassan's age) = 145
So we can substitute the variables we defined to express Cameron and Hassan's age: \((x+1) + 5(x) = 145\)
Distribute the 5: \(x+1+5x\)
Add like terms: \(6x+1 = 145\)
Subtract 1 from both sides: \(6x=144\)
Divide both sides by 6: \(x=24\)
Since we used "x" to represent Hassan's age, Hassan's age is 24. Since we used "x+1" to represent Cameron's age, Cameron's age is "24+1" which is just 25
find an equation of the plane through the point and perpendicular to the line
To find an equation of a plane through a given point and perpendicular to a given line, you can follow these steps:
1. Find the direction vector of the given line. This can be done by subtracting the coordinates of any two points on the line. Let's denote this vector as "d".
2. Find the normal vector of the plane. Since the plane is perpendicular to the line, its normal vector will be the same as the direction vector of the line. So, the normal vector of the plane is "d".
3. Use the coordinates of the given point on the plane to find the equation of the plane. Let's denote the coordinates of the point as (x₀, y₀, z₀).
The equation of the plane can be written as:
Ax + By + Cz = D,
where A, B, C are the components of the normal vector "d", and x, y, z are the variables representing any point on the plane.
To find the values of A, B, C, and D, substitute the coordinates of the given point into the equation:
A(x₀) + B(y₀) + C(z₀) = D.
Therefore, the equation of the plane through the given point and perpendicular to the line is:
d₁(x - x₀) + d₂(y - y₀) + d₃(z - z₀) = 0,
where (d₁, d₂, d₃) are the components of the direction vector "d" of the line, and (x₀, y₀, z₀) are the coordinates of the given point.
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Find the equation of the plane passing through the point (−1,3,2) and perpendicular to each of the planes x+2y+3z=5 and 3x+3y+z=0.
Can someone help me out on this please having trouble on both and show work please !!
The difference of the expression is as follows:
(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5) = - 6y⁴ + 4y² - 12
3(x - 5) - (2x + 4) = x - 19
How to find the difference of the expression?The difference of the expression can be found when we combine the like terms.
Therefore,
(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5)
6y⁴ + 3y² - 7 - 12y⁴ + y² - 5
6y⁴ - 12y⁴ + 3y² + y² - 7 - 5
- 6y⁴ + 4y² - 12
3(x - 5) - (2x + 4)
3x - 15 - 2x - 4
3x - 2x - 15 - 4
x - 19
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Dorothy buys a leash for her cat. The leash is 4 meters and 83 centimeters long. How long, in centimeters, is the leash?