Standard form of quadratic function with leading coefficient 1,
x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
As given in the question,
Given :
y is the dependent variable of the required quadratic function.
x is the independent variable of the required quadratic function.
Leading coefficient of quadratic function is 1
X-intercept of the required function is 7 and 10
Standard form of required quadratic function is equal to
y = k (x-a)(x -b)
Here k=1 , a=7 , b=10
y = 1 (x -7)(x - 10)
⇒ y = x² -7x -10x +70
⇒ y= x² -17x +70
Therefore, standard form of quadratic function with leading coefficient 1, x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
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Draw triangle QRS with altitude RT. If m/RSQ = 43°, then find the m/TRS.
Do not include a degrees symbol on your answer.
The measure of angle TRS would be of 37º.
What is the measure of angle TRS?The vertices of the triangle can be attributed freely, hence we attribute as is in the drawing.
The altitude RT bisects the triangle forming a right angle, with R and T, hence the internal angles of the triangle TRS are as follows:
43º -> as given in the problem.90º -> due to the bisection.x. -> Angle TSR, which is the missing measure that we need to find to solve this problem.The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of the missing angle TSR can be found as follows:
43 + 90 + x = 180
133 + x = 180
x = 180 - 133
x = 47º -> m<TSR = 47º.
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Please help solve!!
A football player kicks a football downfield. The height of the football increases until it reaches a maximum
height of 20 yards, 35 yards away from the player. A second kick is modeled by f(x) = -0.051x(x - 50),
where f is the height (in yards) and x is the horizontal distance (in yards). Compare the distances that the
footballs travel before hitting the ground.
The 1 first
The kick travels 1
Correct answers:
1
20
kick travels farther before hitting the ground.
10 X yards farther.
X
The distances that the footballs travel before hitting the ground is 50 yards.
What is defined as the quadratic function?A quadratic function has been one of the following: f(x) = ax² + bx + c, for which a, b, and c are positive integers and an is not equal to zero. A parabola is a curve that represents the graph of the a quadratic function. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all share a basic "U" shape.For the given question;
The football is kicked by the player.
The second kick is modeled by f(x) = -0.051x(x - 50).
Where, f is the height (in yards) and x is the horizontal distance (in yards).
For calculating the distances that the footballs travel before hitting the ground, Put f(x) = 0.
As, the ball will reach the ground the height of ball above ground will be zero, thus f(x) = 0.
f(x) = -0.051x(x - 50) = 0
Simplifying;
-0.051x² + 2.25x = 0
Or, divide wole equation by x.
0.051x = 2.25
x = 50 yards.
Thus, the distances that the footballs travel before hitting the ground is 50 yards.
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find the endpoint S given R(5,1) and midpoint M(1,4)
Given:
Point R: (5, 1)
Midpoint M: (1, 4)
Since it's been mentioned that point M is a midpoint. Finding S, the graph should look like this:
Let's determine the translation from point M to R, because the opposite of it will be the translation to get point S.
From Point M to R:
[tex]\text{ }\Delta x\text{ = 5 - 1 = 4 (4 units to the right)}[/tex][tex]\Delta y\text{ = 1 - 4 = -3 (3 units downward)}[/tex]Therefore, getting to the endpoint S, it will have 4 units to the left and 3 units upward.
We get,
[tex]x_S\text{ = 1 - 4 = -3}[/tex][tex]y_S\text{ = 4 + 3 = 7}[/tex]Therefore, the missing endpoint is: -3, 7
Given f(x)=x^2 -3x +4
Find
f(2+h)
Find
f(2+h)-f(2)/h
Answer:
h² + h + 2h + 1====================
Given Function f(x) = x² - 3x + 4To findf(2 + h),[f(2 + h) - f(2)]/h.SolutionSolve by substitution
Find f(2 + h)f(x) = x² - 3x + 4f(2 + h) = (2 + h)² - 3(2 + h) = 4 = h² + 4h + 4 - 6 - 3h + 4 = h² + h + 2Find f(2)f(2) = 2² - 2*3 + 4 = 4 - 6 + 4 = 2Find [f(2 + h) - f(2)]/h(h² + h + 2 - 2)/h = (h² + h)/h = h + 1In a photograph, a skyscraper measures 5.8 in, tall. The scale of the photo to the actual skyscraper is 1:245. How tall is the actual skyscraper to the nearest foot?○ 118 ft ○ 183 ft○ 237 ft○204 ft
SOLUTION
In a photograph, a skyscraper measures 5.8 in, tall
The scale of the photo to the actual skyscraper is 1 : 245
That is 1 : 245 = 1 / 245 = 5. 8 / x
Cross- multiply we have:
1 X x = 5 . 8 X 245
x = 1421 inches in feet = 118.4167 feet
Slope =
y-intercept = (0,
Answer:
Solutions below.
Step-by-step explanation:
This question tests on the concept of graph reading.
To find the slope of a line, we have to use the following formula:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Now, we can pick 2 random points on the line to substitute the values in to find the slope.
We will pick
(0, 3) as (x1, y1)
and
(2,0) as (x2, y2)
Therefore the slope will be:
[tex] \frac{0 - 3}{2 - 0} \\ = \frac{ - 3}{2} \\ = - \frac{3}{2} [/tex]
Now to find the y-intercept, as the name suggests, it is the point where the line intercepts the y-axis (vertical axis) , in this case, it is 3.
The point of this intercept is (0,3).
Answer:
slope = -5/3y-intercept = 3Step-by-step explanation:
You want the slope and the y-intercept of the line shown in the graph.
SlopeThe slope is the ratio of "rise" to "run". It is best found by identifying points on the graph where the line crosses grid intersections. The attachment shows two of those: (0, 3), (3, -2).
You can count grid squares or use the slope formula to find the slope.
slope = rise/run = (y2 -y1)/(x2 -x1)
slope = (-2 -3)/(3 -0)
slope = -5/3
Y-interceptThe y-intercept is the y-value of the point where the line crosses the y-axis. We have already found that to be 3, at one of the points used to find the slope.
y-intercept = 3 . . . . point (0, 3)
__
Additional comment
The slope-intercept form equation for the line would be ...
y = -5/3x +3
The standard-form equation would be ...
5x +3y = 9
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f(x) = 4x and g (x) = 4x -3. find the product of ( f . g ) (x)
Here, I hope it's helpful.
Answer:
16x² - 12x
Step-by-step explanation:
(f • g )(x)
= f(x) × g(x)
= 4x(4x - 3) ← multiply each term in the parenthesis by 4x
= 16x² - 12x
4592 round to the nearest ten
Answer:
4590
Step-by-step explanation:
less the 5 round down
Answer:
4590
Step-by-step explanation:
When rounding to the nearest ten we use these following rules.
We round the number up to the nearest ten if the last digit in the number is 5,6,7,8 or 9.
We round the number down to the nearest ten if the last digit in the number is 1,2,3, or 4.
If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.
Which linear inequality is represented by the graph?
The linear inequality that is represented by the graph is y ≤ x/3 - 4. The correct option is the second option y ≤ x/3 - 4
Graph of Linear inequalitiesFrom the question, we are to determine the linear inequality that is represented by the graph
First, we will determine two points on the line
The line in the graph passes through (0, -4) and (3, -3)
Using the equation,
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
(y - -4)/(x - 0) = (-3 - (-4))/(3 - 0)
(y + 4)/x = (-3 + 4)/3
(y + 4)/x = 1/3
y + 4 = 1/3x
y = 1/3x - 4
y = x/3 - 4
This is the equation of the line
In the given graph, the line is a solid line and the solution of the inequality is below the line
Thus,
The inequality becomes y ≤ x/3 - 4
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Answer the questions before. Show your work or explain your answers,1. A principal would like to estimate the percentage of students in the school whoplay video games. Which method should the teacher use to select the sample? Write the letter of your choice here:A. Use a computer to randomly select 30 students from all students.B. Use a computer to randomly select 30 students from all students who takecoding classes. C.select every other student from the classrooms close to her office. D. Select all students who are in the video game club. Explain. Your answer.
Given the following question:
The principal wants to estimate the percentage of students in the school who play video games, which is a good number of students. Selecting 30 random students and asking them if they play video games can represent the entire school. Asking 30 random students keeps it from being biased for example option B, asking 30 students who take coding classes is biased because they are in one specific class, they do not represent the majority of the school unless the school is a coding school.
The answer is the first option because it is a random sample of people to represent a population of people. This keeps the results from being biased so asking 30 random students is the way to go.
graph the image of the figure given in the translation
You have a figure (black lines) with the following points:
C(-4,0)
G(-5,-2)
Q(-2,-5)
I(-1,0)
After a translation, the figure becomes the red one, with the following points:
C'(1,2)
G'(0,-1)
Q'(3,-4)
I'(4,1)
You can notice that each x' coordinate of the new figure is respecto the previous figure:
x' = x + 5
Furthermore, for y':
y' = y +1
That is, the transformation applied to the figure (black lines), is:
T<5,1>
In fact, for each point you have:
T<5,1>C(-4,0) => C'(-4+5 , 0 + 1) = C'(1 , 1)
T<5,1>G(-5,-2) => G'(-5 + 5 , -2 + 1) = G'(0 , -1)
T<5,1>Q(-2,-5) => Q'(-2 +5 , -5 + 1) = Q'(3 , -4)
T<5,1>I(-1,0) => I'(-1 + 5 , 0 + 1) = I'(4 , 1)
Given the information marked on the figures below, classify each quadrilateral as a "Parallelogram" or "Not necessarily a parallelogram."
Note that each figure is drawn like a parallelogram, but you should not rely on how the figure is drawn in determining your answers.
If necessary, you may learn what the markings on a figure indicate.
Noted that the Diagonals of a parallelogram bisect each other. Here in PQSR, it does bisect PT =ST and QT = TR). Hence, PQSR is a parallelogram.
Note that IGHJ is a parallelogram. This is because the opposite sides of a parallelogram are congruent. Here, H = I and G = J. Hence, IGHJ is a parallelogram.
It is correct to state that CABD is a parallelogram because of the alternative interior angles ACB = CBD and ABC = BCD.
VWYX is NOT a parallelogram. The rule states that if opposites sides are congruent then the quadrilateral is a parallelogram. In this case, clearly, line VW ≠ XY and VX ≠ WY.
What is a parallelogram?A parallelogram (which could be a rhombus, rectangle, or square) is a quadrilateral with congruent and parallel opposing sides.
There are six critical parallelogram characteristics to note. They are:
The opposite sides are equal (AB = DC).Angles that are perpendicular to one other are congruent (D = B).(A + D = 180°) Consecutive angles are additive.All angles are proper if one is correct.The diagonals of a parallelogram intersect.The diagonals of a parallelogram divide it into two congruent triangles.Learn more about parallelograms:
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which graph of the following is yhe wquation of a line that is perpendicular to the graph of y=2/5×-1
hello
to solve this question, we need to plot the graph of this equation
1. Which of the following expressions can you factor using the reverse FOIL method? Select all that apply. (A) x²+x-6 (B) x^3 + 3x²+x-2 (C)4x^2 – 2x + 1 (D) x² + 8x + 12
We need to examine each expression at a time.
(A) x^2 + x - 6
notice the -6 has factors 3 and -2 which could be used to reverse the FOIL method:
x^2 + x - 6 = x^2 + 3 x - 2 x - 6 = x( x + 3) - 2 (x + 3) = (x+ 3) (x - 2)
(B) In this cubic expression we cannot use the reverse FOIL to extract factors.
(C) 4 x^2 - 2 x + 1 We cannot reverse the FOIL property either.
(D) x^2 + 8 x + 12
We notice that 12 has factors 2 and 6 which can be used to factor out this expression as shown below:
x^2 + 2 x + 6 x + 12 = x (x + 2) + 6 (x + 2) = (x + 2) (x + 6)
Therefore we were able to use the reverse of the FOIL property in expressions (A) and (D).
Find the x- and y-intercepts for the following equation. Then use the intercepts to graph the equation.y = −2x +1x-intercept: ( ?,0)y-intercept: (0,?)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given function
[tex]y=-2x+1[/tex]STEP 2: Determine the x-intercept for the given function.
To determine the x intercept, we set y equals zero and solve for x. Therefore, we have:
[tex]\begin{gathered} y=-2x+1 \\ y=0 \\ \therefore\Rightarrow0=-2x+1 \\ Collect\text{ like terms,} \\ 0-1=-2x \\ -1=-2x \\ Divide\text{ both sides by -2} \\ -\frac{1}{-2}=\frac{-2x}{-2} \\ \frac{1}{2}=x \\ x=0.5 \\ \\ \therefore x-intercepts\Rightarrow(0.5,0) \end{gathered}[/tex]STEP 3: Get the y-intercept
We can get the y-intercept by setting x towards zero and solve for y
[tex]\begin{gathered} y=-2x+1 \\ x=0 \\ y=-2(0)+1 \\ y=0+1 \\ y=1 \\ \\ \therefore y-intercept\Rightarrow(0,1) \end{gathered}[/tex]STEP 4: Plot the graph of the given function
What’s the correct answer answer asap for brainlist
f(x)=−x 2 −8 \text{Find }f(4) Find f(4)
IN THE PLACE OF x PLYG IN 4 AND SOLVE.
[tex]f(4) = - (4)^{2} - 8 \\ f(4) = - (16) - 8 \\ f(4) = - 16 - 8 \\ f(4) = - 24[/tex]
HOPE THIS HELPS
117 divided by 18. Show the answer as a fraction in lowest terms
Answer:
Im unsure what your asking but the answer is 6 1/2 in fraction form and 6.5 in decimal form :/
Step-by-step explanation:
math
When 117 is divided by 18 we get 117/18 in fraction form.
To divide 117 by 18, we perform long division.
We start with the first digit of the dividend (1) and divide it by the divisor (18).
Since 18 is larger than 1, the quotient for this step is 0.
We then bring down the next digit (1) and place it next to the previous result.
Again, since 18 is larger than 11, the quotient for this step is 0.
Therefore, the result of dividing 117 by 18 is 0 with a remainder of 117.
In fraction form, this can be expressed as 117/18.
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how do i find the final areahint: i have to square my units
Given:
A figure is given.
Required:
To find the area of the given figure.
Explanation:
The given figure is made up of three figures. So we will find the area of the three figures.
Area of square
[tex]\begin{gathered} A_1=(side)^2 \\ A_1=(3)^2 \\ A_1=9 \end{gathered}[/tex]Area of the triangle
[tex]undefined[/tex]each side of a square is increasing at a rate of 4cm/s. At what rate is the area of the square increasing when the area of the square is 9 cm
The rate at which the area of this square increases when the area of the square is 9 cm is 24 cm²/s.
What is rate of change?The rate of change is a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.
How to calculate the area of a square?Mathematically, the area of a square can be calculated by using this formula;
A = s²
Where:
A represents the area of a square.s represents the side length of a square.Next, we would determine the side length of a square by making s the subject of formula as follows:
A = s²
s = √A
s = √9
s = 3 cm.
By applying chain rule of differentiation, the rate of change (da/dt) in area of this square with respect to time is given by:
dA/dt = 2 × s(t) × ds/dt
dA/dt = 2 × 3 × 4
dA/dt = 24 cm²/s.
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help 1,3,7,13,21_ _ next please I don't know the answer
I need help with this problem
Answer:
what is the problem text me
I can probably
Step-by-step explanation:
find the measure of the missing angles
The most appropriate choice for Vertically opposite angle will be given by-
b = 126°, c = 54°
What is Vertically opposite angle?
At first we need to understood what is angle
Angle
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Vertically opposite angle
The angle formed by two intersecting straight lines and are opposite to one another at a specific vertex is called vertically opposite angle.
Vertically opposite angles are equal.
Here,
∠b = 126° [Vertically Opposite Angle]
∠c = 180° - 126° [Angle on a straight line]
= 54°
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Which of the following equations represents a line that passes through thepoints (-3, -14) and (0, –2)?Alg 1
Problem
Which of the following equations represents a line that passes through the
points (-3, -14) and (0, –2)?
Solution
For this case we want to create an equation with this general form:
y= mx+b
We can calculate the slope with this operation:
[tex]m=\frac{-2+14}{0+3}=4[/tex]And the intercept can be founded with the second point:
-2= 4(0)+b
b= -2
And the equation would be:
y= 4x -2
If we analyze the second option given we can see that we can write like this:
y-6 = 4(x-2)
y-6= 4x-8
y-6+8 =4x
y+2= 4x
y= 4x-2
So then the best option would be:
II. y-6 = 4(x-2)
What is the value of 2,783 +4,936?
Answer:7719
Step-by-step explanation:
Find B – C, if B={2, 4, 6, 8} and C={3, 4, 5, 6}
Answer:
Solution
verified
Verified by Toppr
Given, A={1,2,3,4}, B={2,4,6,8} and C={3,4,5,7}.
Now, B∩C={4}.
The A−(B∩C)={1,2,3}.
Answer:
B-C=(2,4,6,8)-(3,4,5,6)
=(2,8)
because we have to remove only maching number from B or any other.
4+3(x+23)=5x-2 write the answer without varible
Answer:
4+3(×+23)=5×-2
Step-by-step explanation:
4+3×+69=3×from here you will group like terms 4+69=3×-3×
=73=×
this implies that ×=73
An influencer is planning a lunch banquet. The equation C 410 + 22g models the relation between the
cost in dollars, C, of the lunch banquet and the number of
guests, g.
Find the cost if the number of guests is 50.
The cost is blank
dollars
The cost, if the number of guests is 50, will be $22500.
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation.So, the relationship between the dollar cost of the dinner, C, and the number of guests, g, is represented by the equation C = 410 + 22g.
We can see that the equation we have been given is in the form of a slope-intercept equation, y = MX + b, where m denotes the slope of the line and b denotes the y-intercept or beginning value.We can observe that the slope and C-intercept of the following equation are 22 and 410, respectively.The C-intercept tells us that when there are 0 guests in the banquet, the cost would be $450.When we have 50 guests at the banquet the cost would be:
50 x 450= $22500Hence, the cost, if the number of guests is 50, will be $22500.
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PLS HELP WILL GIVE 50 POINTS+ BRAINLIEST
Answer:
Please see the enclosed screenshot.
Step-by-step explanation:
Please see the enclosed screenshot.
21 -6 - NO a) D : {all real numbers}, R: {all real numbers Ob) D: {all real numbers), R; {y >0} O c) D: all real numbers), R: {y < 0} O d) D: {x>0}, R: {all real numbers
The domain is
[tex]D\colon\mleft\lbrace x\ge0\mright\rbrace[/tex]and the range
[tex]R=\text{all real numbers}[/tex]Then, the answer is d)