Which function is shown in the graph? A. f(x) = x2 – 3x – 10 B. f(x) = x2 + 3x – 10 C. f(x) = x2 + x - 12 D. f(x) = x2 – 5x – 8
Answers
The graph shown have roots of x = -2 and x = 5
We could solve for x in each of the quadratic equations or we could plot the graphs of each of the quadratic equation.Then we pick the one with the roots of -2 and 5.
Plotting the graphs:
The roots of quadratic functionis the value of x when y is equal to zero.
From the graph attached above, f(x) = x² + 3x – 10 representing the blue parabola has roots of (-5, 0) and (2, 0).
This means the roots are -5 and 2.
Hence, the function in the graph is f(x) = x² + 3x – 10
Related Questions
There are 8 students in the class in art club. If 40%of the class is in art club, how many students are in class in all?
Answers
Answer: 20 is the answer
Step-by-step explanation:
Answer: 20 students
Step-by-step explanation
40% of 20 can be written as 40% × 20.
= 40/100 × 20
= 8
Fats, sugars, and proteins are important food molecules. What do these types of molecules have in common?
Answers
The fact that Fats, sugars, and proteins molecules have in common is that all of these are macronutrients.
What are macronutrients?The many categories of macronutrients include proteins, lipids—also known as fats—carbohydrates, or sugars. These are the three primary nutrients that the body uses to function. This indicates that they are chemical substances that your cells use as a source of chemical energy and that you require in quite significant quantities. These nutrients also produce energy or calories. They are broken down into smaller components during digestion. Energy is derived from carbohydrates (glucose). After being broken down into fatty acids, fats are used for energy. Although it can be used as fuel, protein's primary function is in the synthesis of hormones, muscle, and other proteins.To know more about macronutrients visit:
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Answer:
They all have carbon atoms.
Step-by-step explanation:
The points H(3,-1), I(-6, -1), and J(3,-9) form a triangle. find the
perimeter of the triangle?
Answers
The perimeter of the given triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.
The points which form a triangle are:
H(3,-1) ; I(-6,-1) and J(3,-9)
Perimeter of the given triangle with vertices H(3,-1); I(-6,-1) and J(3,-9) is required:
To find the length we have to find the distance between the points.
Using distance formula i.e.
[tex]\sqrt{ [ (x2 - x1)^2 + (y2 - y1)^2 ][/tex]
Let the length of the sides be A1, A2 , A3
On applying the distance formula to H(3,-1) and I(-6,-1) ;
We get,
A1 = [tex]\sqrt{[ (-6-3)^2 + (-1+1)^2 ][/tex]
= [tex]\sqrt{ [ (-9)^2 + (0)^2 ][/tex]
= [tex]\sqrt[ 81 + 0 ]}[/tex][tex]\sqrt{[ 81 + 0 ][/tex]
= [tex]\sqrt{81}[/tex]
= 9
On applying the distance formula to I(-6,-1) and J(3,-9);
We get,
A2 = [tex]\sqrt{ [ (3+6)^2 + (-9+1)^2 ][/tex]
= [tex]\sqrt{[ (9)^2 + (-8)^2 ][/tex]
= [tex]\sqrt{[ 81 + 64 ][/tex]
= [tex]\sqrt{145}[/tex]
= 12.04
On applying the distance formula to J(3,-9) and H(3,-1);
We get,
A3 = [tex]\sqrt{[ (3-3)^2 + (-9+1)^2 ][/tex]
= [tex]\sqrt{[ (0)^2 + (-8)^2 ][/tex]
= [tex]\sqrt{ [ 0 + 64 ][/tex]
=[tex]\sqrt{64}[/tex]
= 8
Hence,
The perimeter is 9 + 12.04 + 8 = 29.04
The perimeter of the triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.
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a stack of 20 identical boxes. The stack is 180cm tall, Julia then removes 3 boxes from the top. How tall is the stack now
Answers
A stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.
As given in the question,
Number of identical boxes in a stack=20
Stack of 20 identical boxes are 180 cm tall
Height of 1 box=180/20
=9cm
Julia removes 3 boxes from the top
Height of 3 identical boxes=9 × 3
=27 cm
Height of stack after removing 3 boxes from the top
=Original height - height of 3 boxes
=180 -27
=153cm
Therefore, a stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.
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If this trapezoid is
translation
moved through the
(x+3, y-2), what will the
coordinates of D' be?
D' = ([?], [ ])
Answers
The coordinates of D' are (4,0)
A Trapezoid is regarded as a quadrilateral that has only one pair of opposite sides that are said to be parallel.
The coordinates of the given trapezoid are:
A = (-6,2)
B = (-5,4)
C = (-2,4)
D = (1,2)
It is given that the trapezoid is moved to the points of (x+3, y-2) on the graph.
Now, consider A = (-6,2)
A' = (-6+3, 2-2)
A' = (-3,0)
Consider B = (-5,4)
B' = (-5+3, 4-2)
B' = (-2,2)
Consider C = (-2,4)
C' = (-2+3, 4-2)
C' = (1,2)
Consider D = (1,2)
D' = (1+3, 2-2)
D' = (4,0)
Therefore, D' has the coordinates (4,0)
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Find the missing side. Round answer to the nearest tenth.46°X145.910.10 0 0 013.219.5
Answers
Given the rigth triangle, you have to determine the length of the missing side marked with an x.
To do so you have to apply the trigonometric functions, these are calculated as:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{\text{hypotenuse}} \\ \cos \theta=\frac{adjacent}{hypotenuse} \\ \tan \theta=\frac{opposite}{adjacent} \end{gathered}[/tex]Where
θ is one of the inner angles of the triangle.
"opposite" indicates the opposite side to than angle
"adjacent" is the side in contact or next to the angle
and "hypotenuse" is the longest side of the triangle.
In this exercise we know the measure of the angle and the hypotenuse, the trigonometric function you have to use to determine the length of "x" is the Sine:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \text{opposite}=\sin \theta\cdot hypotenuse \end{gathered}[/tex]Replace with:=46º
hypotenuse=14
opposite=x
[tex]\begin{gathered} x=\sin 46\cdot14 \\ x=10.07\cong10.1 \end{gathered}[/tex]Correct option is b. 10.1
The balance sheet for Tempest, Inc., is shown here in market value terms. There are 19,000 shares of stock outstanding.
Answers
Based on the number of shares outstanding and the market value, the price the stock is currently selling for is $31.40
How to find the selling price of the stock?To find the selling price of the stock the formula is:
= Equity value of stock / Number of stock outstanding
The number of stock outstanding is 19,000 shares. The equity value of the stock is $596,600.
The selling price of the stock today then is:
= Equity value of stock / Number of stock outstanding
= 569,600 / 19,000
= $31.40
Full question is:
What is the stock selling for today?
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B ВaAbСLet c=12, and a=4.020. What is tan(A) in radians? Round to 3 decimal places.
Answers
Answer
Tan (A) = 0.109 radians
Explanation:
The figure given is a right angles triangle
Given that AB = c is the hypotenus
AC = b = adjacent
BC = a = opposite
Tan A can be calculated using SOH CAH TOA
Tan A = opposite / adjacent
Tan A = BC / AC
BC = a = 4.020
We need to find b uisng pythagoras theorem
[tex]\begin{gathered} c^2=a^2+b^2 \\ 12^2=4.020^2+b^2 \\ 144=16.1604+b^2 \\ \text{Collect the like terms} \\ b^2\text{ = 144 - 16.1604} \\ b^2\text{ = 127.8396} \\ b\text{ = }\sqrt[]{127.8396} \\ b\text{ = 11.307} \end{gathered}[/tex]b = 11.307
Tan A = 4.020 / 11.307
Tan A = 0.3555
A = tan ^-1 (0.3555)
A = 19.570 degrees
Convert degrees to radian
since 1 pi = 180 degrees
x pi = 19.570
Cross multiply
19.570 * 1 = x * 180
x = 19.570 / 180
x = 0.109
Therefore, tan (A) is 0.109 radians
Which age group of this set of numbers has twice as many people as another age group?
A) 76-85
B) 15-25
C) 36-45
D) 46-55
Answers
Answer:I believe it is 15-25
Step-by-step explanation:
In order to make a specific shade of green paint, a painter mixes 1/2 of a gallon of blue paint with 4/5 of a gallon of yellow paint. How many gallons of yellow paint are needed to mix with 3 gallons of blue paint?
Answers
To make a specific shade of green paint, 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.
In the question ,
it is given that
to make a specific shade of green paint , the painter mixes 1/2 gallon of blue paint and 4/5 gallon of yellow paint .
so , the ratio of yellow paint to blue paint [tex]=\frac{\frac{4}{5} }{\frac{1}{2} }[/tex]
writing in the simplified form , we get
= 4/5 × 2/1
= 8/5
So, for the given specific shade of green , the ratio of yellow : blue paint will remain same ,
let the amount of yellow paint used to mix with 3 gallons of blue paint be x gallons .
[tex]\frac{8}{5} =\frac{x}{3}[/tex]
On simplifying
x = 24/5
x = 4.8
so yellow paint required is 4.8 gallons
Therefore , to make a specific shade of green paint , 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.
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what is 30/cos40° rounded to 1 d.p.
Answers
The value of 30/cos40° rounded to 1 d.p. (decimal point) is 39.2.
How to round off any decimal number to one decimal place?
When you round to the first decimal place, or to the nearest tenth, the number in the hundredth point place will determine whether you round up or down. If the hundredths digit is a number between 5 and 9, round up to the nearest whole number. If it's a number between 0 and 4, you would "round down" by keeping the tenths place the same.
We have 30/cos40°
Value of 30/cos40° = 30/0.766044 = 39.162241 (cos40° = 0.766044)
Since the number in the hundredths place is 6, which is between 5 and 9, we would round the tenth decimal point up to 2.
Therefore, the value of 30/cos40° rounded to 1 d.p. (decimal point) is 39.2.
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Find the value of x.
Answers
Answer:
x = 8
Step-by-step explanation:
You want to know the value of x in an expression for an angle measure at parallel lines.
Angles at a transversalWhere at transversal crosses parallel lines, all acute angles created are congruent, all obtuse angles created are congruent, and the acute angles are supplementary to the obtuse angles.
The angle marked 83° is acute. The angle marked (12x+1)° is obtuse, so these angles are supplementary:
83° +(12x +1)° = 180°
12x +84 = 180 . . . . . . . divide by ° and simplify
12x = 96 . . . . . . . . . . subtract 84
x = 8 . . . . . . . . . . . . divide by 12
The value of x is 8.
How can I solve this question
Answers
Answer:
x = 10
The interior angles measure 93°, 126°, 60°, and 81°.
Step-by-step explanation:
[tex]9x + 3 + 12x + 6 + 6x + 8x + 1 = 360[/tex]
[tex]35x + 10 = 360[/tex]
[tex]35x = 350[/tex]
[tex]x = 10[/tex]
9(10) + 3 = 90 + 3 = 93°
12(10) + 6 = 120 + 6 = 126°
6(10) = 60°
8(10) + 1 = 80 + 1 = 81°
[tex]\rm\int_0^1 \frac{( {x}^ \varphi - 1 {)}^{2} }{ log {}^{2} (x) } dx\\[/tex]
Answers
I assume the natural logarithm, and not the base-10 log. Parameterize the integral as
[tex]\displaystyle I(a) = \int_0^1 \frac{(x^a - 1)^2}{\log^2(x)} \, dx[/tex]
Differentiate twice with respect to [tex]a[/tex].
[tex]\displaystyle I'(a) = 2 \int_0^1 \frac{x^{2a} -x^a}{\log(x)} \, dx[/tex]
[tex]\displaystyle I''(a) = 2 \int_0^1 (x^{2a} - x^a) \, dx[/tex]
Evaluate the last integral, then solve for [tex]I(a)[/tex] with the fundamental theorem of calculus, noting that [tex]I(0)=I'(0)=0[/tex].
[tex]\displaystyle I''(a) = 2\left(\frac1{2a+1} - \frac1{a+1}\right)[/tex]
[tex]\displaystyle I'(a) = 2 \int_0^a \left(\frac1{2t+1} - \frac1{t+1}\right) \, dt \\\\ ~~~~ = \log(2a+1) - 2 \log(a+1)[/tex]
[tex]\displaystyle I(a) = \int_0^a (\log(2t+1) - 2\log(t+1)) \, dt \\\\ ~~~~ = (2a+1) \log(2a+1) - 2(a+1) \log(a + 1)[/tex]
Let [tex]a=\phi[/tex] to recover the original integral.
[tex]\displaystyle I(a) = (2\phi+1) \log(2\phi+1) - 2(\phi+1) \log(\phi + 1)[/tex]
Using various properties of the golden ratio [tex]\phi[/tex], namely
[tex]\phi = 1 + \dfrac1\phi \implies \phi^2 = \phi + 1 \implies \phi^3 = \phi^2 + \phi[/tex]
[tex]2\phi+1 = \phi\left(2+\dfrac1\phi\right) = \phi(1 + \phi)[/tex]
[tex]\phi=\dfrac{1+\sqrt5}2 \implies \phi^3 = 2 + \sqrt5[/tex]
we can simplify the result to
[tex]\displaystyle I(\phi) = \int_0^1 \frac{(x^\phi-1)^2}{\log^2(x)} \, dx = \boxed{\sqrt5\,\log(\phi)}[/tex]
The fraction n/12 is between 1/4 and 2/3. Write down all the possible values of n.
Answers
When the fraction n/12 is between 1/4 and 2/3, the possible values of n will be 4, 5, 6, and 7.
How to calculate the fraction?It should be noted that a fraction simply means a number that isn't whole. It can be illustrated as a/b where a is the numerator and b is the denominator.
It should be noted that 1/4 is equivalent to 3/12.
It should be noted that 2/3 is equivalent to 8/12.
Therefore, the values of n will be numbers between 3 and 8. They are 4, 5, 6, and 7.
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HELP!!
Write the slope-intercept form of the equation for each line.
Answers
The equation of the line in slope intercept form is y = -5 / 9x + 2 / 9
How to find the equation of a line in slope intercept form?The slope intercept form of the equation of a line can be represented as follows:
y = mx + b
where
m = slope of the lineb = y-interceptLet's find the slope using the points (4, -2)(-5, 3)
Hence,
m = y₂ - y₁ / x₂ - x₁
x₁ = 4
x₂ = -5
y₁ = - 2
y₂ = 3
m = 3 + 2 / -5 - 4
m = 5 / -9
m = - 5 / 9
Therefore, let's find the y-intercept using (4, -2).
-2 = - 5 / 9 (4) + b
-2 = - 20 / 9 + b
b = -2 + 20 / 9
b = -18 + 20/ 9
b = 2 / 9
Therefore, the equation is y = -5 / 9x + 2 / 9
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I need help......................................................................
Answers
Answer: The answer is D.
Step-by-step explanation: Because I use a graphing calculator
Solve ×^2-4×-5=?
Your Genius If You Answered This Correctly
Answers
Answer:
(x+1)(x-5)
Step-by-step explanation:
2. Complete the table for the equation, and graph the equation. (4pts)
2x - y = - 3
Answers
I attached a photo to answer you question. Hope this helps!
Which shows the integers in order from least to greatest?
a.20, 6, -2, -13
b. -2, 6, -13, 20
c..-13, -2, 6, 20
d.20, -13, 6, - 2
Answers
The integers that are in order from least to greatest will be C. -13, -2, 6, 20.
What is an integer?It should be noted that an integer simply means a natural number or a whole number that given. It should be noted that they can either be positive or negative.
In this case, the numbers will be illustrated as thus:
The smallest number is -13.
The biggest number is 20.
Therefore, the arrangement is -13, -2, 6, 20.
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please help! giving brainliest :)
Answers
For the rhombus below, solve for y
Answers
Notice that this set of angles is congruent
herefore,
[tex]y-60=56[/tex]Solving for y ,
[tex]\begin{gathered} y=56+60 \\ \rightarrow y=116 \end{gathered}[/tex]nswer: 116
Which of the following is an equivalent expression of 15x2 +12x + 8?
27x3 + 8
15x2(12x + 8)
12x + 15x2 + 8
8(15x2 + 12x)
Answers
The option that is an equivalent expression of 15x² +12x + 8 is C. 12x + 15x² + 8.
What is an equivalent expression?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same values for the variable, two algebraic expressions that are equivalent have the same values.
If two systems of equations have the same solution, they are equivalents. In algebra, 2(2x - 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.
In this case, it should be noted that 15x² +12x + 8 is the same as 12x + 15x² + 8. Therefore, the correct option is C.
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i need help with the 2 problems in this picture.
Answers
Answer:
5 degree Celsius
Explanation:
Using the formula for conversion included in the image attached, we have:
[tex]\begin{gathered} \frac{5(F-32)}{9}=C \\ F^{\circ}=41 \\ \frac{5(41-32)}{9}=C \\ \frac{5(9)}{9}=C \\ 5^=C^{\circ} \\ \\ \therefore41^{\circ}F=5^{\circ}C \end{gathered}[/tex]Therefore, 41 degrees Fahrenheit is equivalent to 5 degrees Celsius
Two buses are driving along parallel freeways that are 5mi apart, one heading east and the other heading west. Assuming that each bus drives a constant 55mph, find the rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other.
Answers
The rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other is 101.54 km per hour.
How to calculate the rate?Let l = distance further away at which they'll meet. This will be illustrated as:
l = ✓13² - ✓5²
= ✓169 - 25
= ✓144
= 13m
Assuming that each bus drives a constant 55mph. The passes towards each other will be:
= -(55 + 55)
= -110m/h
Therefore, h² + l² = b².
Differentiate
2hdh/dt + 2ldl/dt = 2bdb/dt
= 2 × 5 × 0+ 2 × 12 (-110)
= 3 × 13db/dt
= -101.54 m/h
The rate is 101.54 m/h.
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Solve the proportion. 7 42 = 1 w w=
Answers
When the given proportion is solved the value of w is calculated to be 6.
What is proportion?
A proportion can be commonly understood as two ratios that have been set equal to each other; a proportion is an equation that can be solved.
When it is said that proportion is two ratios that are equal to each other, it means in the sense of two fractions being equal to each other.
for example 5/10 = 1/2, 5:10 = 1: 2
7:42 = 1 : w
[tex]\frac{7}{42} = \frac{1}{w} \\[/tex]
[tex]\frac{1}6{} = \frac{1}{w}[/tex]w = 1 x 6
w = 6
When the given proportion is solved the value of w is calculated to be 6
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The graph shows your distance from home while out on a walk. The next day, you jog the same route twice at a constant speed. The entire jog takes 1 hour. Compare your walk to your jog
Answers
Using proportions, it is found that your walk and jogging rates are given as follows:
Walking: 3.75 miles per hour.Jogging: 5 miles per hour.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations.
One example of application, in the context of this problem, is for the relation between velocity, distance and time, as velocity is distance divided by time, that is:
v = d/t.
From the graph, the walk takes 40 minutes = 2/3 of an hour, and you walk 1.25 x 2 = 2.50 miles, as you walk 1.25 miles and then you come back home, hence the rate is given as follows:
v = 2.50/(2/3) = 3 x 2.50/2 = 3.75 miles per hour.
For the jog, you jog the same distance twice in one hour, hence you jog 5 miles in one hour, and the rate is given as follows:
v = 5/1 = 5 miles per hour.
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Please help I’ll mark you as brainliest if correct!
Answers
I got 1 hour 28 minutes and 15 seconds
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Triangle MNP is dilated by a factor of 2 with a center of dilation at (0,0).
What are the new coordinates of point N?
A
(1, -1)
B
(-4, 4)
C
(4, 0)
D
(4, -4)
Answers
The new coordinates of the point N after the given dilation transformation is; (-2, 6)
What is the Dilation of the triangle?
From the attached image, we see the given triangle MNP. We see that it's coordinates are;
M(-1, -2)
N(0, 2)
O(2, -2)
Now, when we talk about dilation in transformation, we are simply referring to a transformation that produces an image that is the same shape as the original, but is a different size.
Thus, triangle MNP will be dilated according to the rule (x,y), where point P is the center of dilation.
Given the coordinate N = (0, 2)
The rule of dilation with scale factor k =2 and point P is the center of dilation is given by:
(x, y) = (2x - 2), (2x + 2)
Thus;
N = (0, 2) → N'(2(0) - 2), (2(2) + 2)
= N'(-2, 6)
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Increase 270 by 20%
please help asap
Answers
Answer:
324
Step-by-step explanation:
20%-> 0.2
0.2(270)= 54
270+54=324
Answer:The answer is 324
Step-by-step explanation:20% of 270 is 54 so add 54 and 270 because you increase by 20 to get the answer