ANSWER
See below
EXPLANATION
The given functions are:
[tex]g(x) = {x}^{2} [/tex]
and
[tex]h(x) = - {x}^{2} [/tex]
The following statements are true;
h(x) is the reflection of g(x) in the x-axis.
g(x) opens upwards while h(x) opens downwards
Both functions have their vertex and intercepts at the origin.
The x-axis is a tangent to both functions at x=0.
g(x) has a minimum point
h(x) has a maximum point.
Answer:
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1. TRUE
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x). TRUE
For negative values of x, g(x) > h(x). TRUE
Step-by-step explanation:
answer on edge
Quadrilateral BIRD is inscribed in circle O.
What is the measure of angle D?
Answer:
∠D = 63°
Step-by-step explanation:
Because all four corners of the quadrilateral rest on the circumference of the circle, then BIRD is a cyclic quadrilateral (circle theorem).
According to circle theorem, opposite angles of a cyclic quadrilateral are supplementary (sum to 180°).
∴ ∠I + ∠D = 180°
⇒ ∠D = 180° - ∠I
⇒ ∠D = 180° - 117° (since ∡I = 117°)
∴ ∠D = 63°
Answer:
63
Step-by-step explanation:
Find the equation of the circle that has diameter endpoints of ( 4, 8 ) and (10, 16 )
Answer:
[tex](x-7)^2+(y-4)^2=25[/tex]
Step-by-step explanation:
The circle has diameter endpoints of ( 4, 8 ) and (10, 16 ).
The midpoint of the diameter is the center
[tex](\frac{4+10}{2},\frac{8+16}{2})[/tex]
[tex](\frac{14}{2},\frac{24}{2})[/tex]
[tex](7,12)[/tex]
The radius is the distance from the center to any point on the circumference.
[tex]r=\sqrt{(7-4)^2+(12-8)^2}[/tex]
[tex]r=\sqrt{(3)^2+(4)^2}[/tex]
[tex]r=\sqrt{9+16}[/tex]
[tex]r=\sqrt{25}=5[/tex]
The equation of the circle with center (h,k) and radius r is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We plug in the values to get:
[tex](x-7)^2+(y-4)^2=5^2[/tex]
[tex](x-7)^2+(y-4)^2=25[/tex]
Answer:
The equation of the circle is (x - 7)² + (y - 12)² = 25
Step-by-step explanation:
* Lets revise the equation of the circle
- The equation of the circle which has center (h , k) is:
(x - h)² + (y - k)² = r²
- The endpoints of a diameter re (4 , 8) and (10 , 16)
- The center of the circle is the mid-point of the diameter
* Lets revise the rule of the mid point to get the center of the circle
and revise the rule of the distance to get the length of the diameter
- The mid point (x , y) of segment has endpoints (x1 , y1) and (x2 , y2) is
x = (x1 + x2)/2 and y = (y1 + y2)/2
- The distance between the two point (x1 , y1) and (x2 , y2) is:
d = √[(x2 - x1)² + (y2 - y1)²]
* Now lets find the center of the circle
∵ (h , k) is the mid-point of the diameter
∵ (4 , 8) is (x1 , y1) and (10 , 16) is (x2 , y2)
∴ h = (4 + 10)/2 = 14/2 = 7
∴ k = (8 + 16)/2 = 24/2 = 12
∴ The center of the circle is (7 , 12)
∵ The length of the diameter = √[(10 - 4)² + (16 - 8)²
∴ d = √[6² + 8²] = √[36 + 64] = √100 = 10
∵ The radius = 1/2 the diameter
∴ r = 1/2 (10) = 5
* Lets write the equation of the circle
∵ The equation of the circle is (x - h)² + (y - k)² = r²
∵ h = 7 , k = 12 , r = 5
∴ The equation of the circle is (x - 7)² + (y - 12)² = 5²
∴ The equation of the circle is (x - 7)² + (y - 12)² = 25
Given f(x) = e^x and g(x) = x – 2, what is the range of (g*f)(x)
The range of (g * f)(x) is all real numbers (ℝ).
Explanation:Composing functions: We first need to understand that (g * f)(x) refers to the composition of g and f, where f is evaluated first and then its output is used as the input for g. So, (g * f)(x) = g(f(x)) = g(e^x).
Analyzing g(e^x): The function g(x) simply subtracts 2 from its input. Since e^x is a real number for all real values of x, g(e^x) will also be a real number for all real values of x.
Range of the composed function: Therefore, as g(e^x) can take any real value, the range of (g * f)(x) will be all possible outputs of g(e^x), which is all real numbers (ℝ).
In simpler terms, no matter what real number you input into f(x), the final output after applying g(x) will always be a real number. This is because the subtraction in g(x) doesn't restrict the output in any way.
A circle has a radius of 5ft and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which equation gives the measures of the central angle q?
Answer:
[tex]\frac{q}{360}[/tex] × π10 = 7
Explanation:
The formula to find arc length is [tex]\frac{x}{360}[/tex] × [tex]\pi r^{2}[/tex]
Simply plug in radius and arc length to get your equation.
Answer:
Central angle = 80.21°
Step-by-step explanation:
The arc length in circle is the product of radius and central angle made by the arc in radians.
That is
l = rθ
Here given the values r = 5 ft and l = 7 ft
Substituting
7 = 5 x θ
θ = 1.4 radians
[tex]\theta =1.4\times \frac{180}{\pi }=80.21^0[/tex]
Central angle = 80.21°
Please answer right away
Answer:
$29000 with a margin of error of $5000
Step-by-step explanation:
We have that the midpoint between the given values is
(X1+X2) / 2 = ($34000+$24000)/2 = $29000
We have that the midpoint between the given values would be
(X2-X1)/2=($34000-$24000)/2=$10000/2=$5000
So I can write that approach as $29000 with a margin of error of $5000
Done
A dilation produces a smaller figure. Which is a possible scale factor?
A dilation producing a smaller figure requires a scale factor less than 1. If the scale factor is 1/2, the model size is half the actual size. By setting up and solving a proportion, actual dimensions can be calculated.
Explanation:When a dilation results in a smaller figure, the scale factor used is less than 1. Think of the scale factor as a fraction where the actual size is the denominator and the model size is the numerator. For instance, a scale factor of 1/2 would mean that the model is half the size of the actual figure.
For a practical example: if we have a scale factor of 1:4 and the scale measurement is 4, the actual dimension can be found by setting up a proportion as 1/4=4/x, solving for x would give us the actual dimension, which in this case would be 16.
The table below shows the relationship between the diameter, x, in inches, and the height, y, in feet, of trees in a national park
8.3
10.5
12.9
16.3 77
17.3 81
17980
81
The two models shown were developed to represent the data
Model 1: y
= 1.04r + 61.92
Model 2: y
= 1.212 + 58.4
Create a residual plot for each model and select the true statement based on the residuals for each model
Answer:
I think the answer is A.
Step-by-step explanation:
After graphing it in Desmos, I decided model A was better, and that it was non-random.
Answer:
The correct option is A) The residual plot for model 2 has a random pattern and is a good fit for the data.
Step-by-step explanation:
Consider the provided data.
The table shows the relationship between the diameter, x, in inches, and the height, y, in feet, of trees in a national park.
The residual plot for the table is shown in figure 1:
Now, consider the model 1: y = 1.04 x + 61.92
The residual of the above model is shown in figure 2:
Consider the model 1: y = 1.21 x + 58.4
The residual of the above model is shown in figure 3:
Now observe the figure 4 which compare all the three residuals.
By comparing the residual of all the three models it can be concluded that 'Model 2 has a random pattern and is a good fit for the data.
Therefore, the correct option is A) The residual plot for model 2 has a random pattern and is a good fit for the data.
will mark brainliest!!
Solve the system of equations. x2 = y + x + 8
y = -x + 2
A) ( radical 10 , 2 - radical 10 ) and ( radical 10 , 2 + radical 10 )
B) ( radical 10 , 2 - radical 10 ) and (- radical 10 , 2 - radical 10 )
C) ( radical 10 , 2 - radical 10 ) and (- radical 10 , 2 + radical 10 )
D) ( radical 10 , -2 - radical 10 ) and (- radical 10 , 2 + radical 10 )
Answer:
the answer is A) ( radical 10 , 2 - radical 10 ) and ( radical 10 , 2 + radical 10 )
Step-by-step explanation:
The two right scalene triangles shown are similar , but not congruent. Which statement about the triangles is not true
Answer:
Third choice.
The right correspondence is [tex]\angle CDB \cong \angle ECD[/tex]
Step-by-step explanation:
The third choice is not true, that is
[tex]\angle CDB[/tex] NOT corresponds to [tex]\angle ECD[/tex]
If [tex]\triangle CBD \sim \triangle CDE[/tex], then corresponding sides are proportional, and corresponding angles are congruent. The corresponding angle of [tex]\angle CDB[/tex] is
[tex]\angle CDB \cong \angle ECD[/tex]
Therefore, the third option shows a wrong correspondence, that's the right choice in this case, because it doesn't express a valid correspondence.
A squirrel runs across a road in 3 seconds. The road was more than 34 feet wide. Which inequality can be used to determine the squirrel’s speed?
3r is greater than 34
3r is less than 34
r/3 is greater than 34
r/3 is less than 34
What is the solution to the inequality? Round to the nearest tenth, if necessary.
r less than 11.3
r greater than 11.3
r less than 102
r greater than 102
How can you interpret the solution?
The squirrel can run at least 11.3
The squirrel can run faster than 11.3
The squirrel can run no faster than 102
The squirrel can run slower than 102
Answer:
Step-by-step explanation:
squirrel speed (r) x seconds (3) has to be more than 34 feet
3r is greater than 34
r is greater than 11.3
34 / 3 = 11.333
11.3 (squirrels speed) x 3 (seconds) = 33.9 feet
the squirrel can run faster than 11.3
Answer:
A). Option A
B). Option B
C). Option B
Step-by-step explanation:
A). A squirrel runs across a road in 3 seconds.
Width of the road is more than 34 feet.
We have to calculate the squirrel speed.
Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
= [tex]\frac{34}{3}[/tex]
Since distance is more that 34 so the speed will be more than [tex]\frac{34}{3}[/tex]
This is because Speed ∝ Distance.
Let r is the speed of squirrel.
r > [tex]\frac{34}{3}[/tex]
3r > 34
Option A is the correct option.
B). Inequality is 3r > 34
r > [tex]\frac{34}{3}[/tex]
r > 11.3
Option B is the answer.
C). The squirrel can run at faster than 11.3 feet per second.
Option B.
What is the midpoint between (-2, -3) and (1, 0.5)
Answer:
(-1/2,-1.25)
Step-by-step explanation:
Once you plot the points, you should be able to find the midpoint formula.
The midpoint between the points (-2, -3) and (1, 0.5) is (-0.5, -1.25).
To find the midpoint between two points, you average the x-values and the y-values of the given points separately. The formula for the midpoint M between two points P1(x1, y1) and P2(x2, y2) is
M = ((x1 + x2) / 2, (y1 + y2) / 2)
Applying this to the given points (-2, -3) and (1, 0.5), we calculate the midpoint as follows:
Average the x-values:
(-2 + 1) / 2 = -0.5
Average the y-values:
(-3 + 0.5) / 2 = -1.25
6 = 2( x + 8) - 5 x
Answer: The answer has 3 forms!
Decimal form: 3.3Exact form: 10/3Mixed Number form: 3 1/3
I hope that this helps! :D
ANSWER
[tex]x = 3. \bar3[/tex]
EXPLANATION
The given equation is
[tex]6 = 2(x + 8) - 5x[/tex]
We expand to get,
[tex]6 = 2x + 16 - 5x[/tex]
We combine similar terms,
[tex]5x - 2x = 16 - 6[/tex]
[tex]3x = 10[/tex]
[tex]x = \frac{10}{3} [/tex]
[tex]x = 3 \frac{1}{3} [/tex]
[tex]x = 3. \bar3[/tex]
Please need help on this
Answer:
The first one is not a function
The second is a function
Third not a function
Fourth is a function
Step-by-step explanation:
Write and solve a quadratic equation for the situation below. Choose the answer that has both an equation that correctly models the situation as well as the correct solution for the situation. An isosceles right triangle has sides that are x + 2 units long and a hypotenuse that is 8 units long. What is the length of the missing sides of the triangle?
Answer:
2(x^2 + 4x - 28) = 0.
The length of the missing sides are:
4√2 units.
or 5.66 units ( to the nearest hundredth).
Step-by-step explanation:
Applying the Pythagoras Theorem:
8^2 = (x + 2)^2 + (x + 2)^2
2(x^2 + 4x + 4) = 64
2x^2 + 8x + 8 - 64 = 0
2x^2 + 8x - 56 = 0
2(x^2 + 4x - 28) = 0 models the situation.
Solving:
x = [- 4 +/- √(4^2-4*1*-28)] / 2
= (-4 +/- √128) / 2
= (-4 + 8√2) / 2 , (-4 - 8√2) / 2 (we ignore this negative root).
= -2 + 4√2.
This is 3.66 to the nearest hundredth.
So the length of the 2 equal sides is 2 + (- 2 + 4√2) = 4√2.
or 5.66 to the nearest hundredth.
Find the missing exponent. Explain 5^11/5^?=5^4
Answer:
The missing exponent is 5^7
Step-by-step explanation:
5^11/5^?=5^4
1. Subtract the exponents from each other.
11-4=7
2. Plug 7 in as the exponent.
5^11/5^7
3. 11-7=4 therefore, 5^11/5^7 equals 5^4.
Answer:
? = 7Step-by-step explanation:
[tex]\text{We know:}\ \dfrac{a^n}{a^m}=a^{n-m}.\\\\\dfrac{5^{11}}{5^{?}}=5^4\\\\5^{11-?}=5^4\to?=7\ \text{because}\ 11-7=4[/tex]
Jon drove 365 on 20 gallons of gas. How many miles did he get per gallon?
Answer:
18.25
Step-by-step explanation:
365 ÷ 20 = 18.25
Jon drove 365 miles on 20 gallons of gas, so to find out how many miles he got per gallon, you divide 365 miles by 20 gallons. The result is 18.25 miles per gallon.
Explanation:To solve this problem, you need to divide the total number of miles that Jon drove by the number of gallons of gas he used. This is because the miles per gallon is calculated by dividing the total miles driven by the amount of gas used.
So, in this case, you would do the following calculation: 365 miles ÷ 20 gallons = 18.25 miles per gallon
This means that Jon got 18.25 miles per gallon of gas.
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on Saturday morning Owen earned $29. By the end of the afternoon he had earned a total of $67. Enter an equation, using x as your variable to determine whether Owen earned $38 or $34 on Saturday afternoon
Answer:
$67 = $29 + $ x
Step-by-step explanation:
Given that on Saturday morning Owen earned= $29
End of afternoon amount total earned was= $67
Let's find the amount earned in the afternoon=?
Let's take the amount earned in the afternoon to be =$ x
Equation for total amount earned by the end of afternoon= $29 + $x
But we know total amount earned by end of afternoon was=$67 hence
the equation to determine afternoon amount will be;
$67 = $29 + $ x ----------------------------go ahead and solve for x
$67-$29 = $ x
$ 38 = x
If g(x)=3x-11, what is x is g(x)=289
Answer:x=100
Step-by-step explanation:
Since you know that g(x)=3x-11 all you have to do is substitute that into g(x)=289. So you get 3x-11=289. To get x you have to add 11 on both sides.
3x-11=289
+11 +11
----------------
3x = 300
Divide 3 on both sides to get x by itself
3x =300
---- -------
3 3
x=100
The perimeter of the following figure is 18.6 inches. What is the length of n?
13.8 in.
4.8 in.
5 in.
7.5 in.
For this case we have by definition, that the perimeter of the figure will be given by the sum of its sides, that is:
[tex]n + 3 + 6.3 + 4.5 = 18.6[/tex]
We add similar terms:
[tex]n + 13.8 = 18.6\\n = 18.6-13.8\\n = 4.8[/tex]
Thus, the correct option is option b. That is, [tex]4.8 \ in[/tex]
Answer:
[tex]4.8 \ in[/tex]
Answer: second option.
Step-by-step explanation:
The perimeter of the figure is the sum the lenghts of its sides.
You know that the perimeter of this figure is 18.6 inches.
You can observe that it has four sides and three lenghts are given.
Then, you can write this expression:
[tex]18.6in=3in+6.3in+4.5in+n[/tex]
Now you need to solve for "n" to calculate its value.
This is:
[tex]n=3in+6.3in+4.5in-18.6in[/tex]
[tex]n=18.6in-3in-6.3in-4.5in[/tex]
[tex]n=18.6in-13.8in[/tex]
[tex]n=4.8in[/tex]
an outcome or set of outcomes of an experiment or situation
Answer: Probability theory would be my best guess, but I would need more information to be able to fully answer this question.
Step-by-step explanation:
If a 4 ft stick cast a shadow of 2.8 ft. What is the height of a tree that cast a shadow of 27.44 ft?
Answer:
Height of tree = 39.2 ft
Step-by-step explanation:
The relationship between the height of an object and the length of it's shadow is directly proportional.
So:
[tex]\frac{4}{2.8} =\frac{h}{27.44}[/tex]
h = Height of tree in feet
Cross multiply
2.8h = 4 · 27.44
Simplify
2.8h = 109.76
÷2.8 both sides
h = 39.2
Height of tree = 39.2 ft
The height of a tree that cast a shadow of 27.44 ft is 39.2 ft
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that a 4 ft stick cast a shadow of 2.8 ft.
We have to find the height of a tree that cast a shadow of 27.44 ft
Let us consider x as the height of a tree that cast a shadow of 27.44 ft.
Let us form a proportional equation
4/2.8=x/27.44
Apply cross multiplication.
4×27.44=2.8x
109.76=2.8x
Divide both sides by 2.8
x=109.76/2.8
x=39.2
Hence, the height of a tree that cast a shadow of 27.44 ft is 39.2 ft.
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Kim's softball team was playing in the championship game. When there were 4 innings left, the team was losing by a score of 17 to 6 points. In the last 4 innings, her team scored the same number of points per inning, and the other team did not score any more points. Kim's team won with the most points.
Write an inequality to determine the number of points per inning, ppp, Kim's team could have scored.
Answer:
The required inequality is [tex]6+4p>17[/tex].
Step-by-step explanation:
Let p represent the number of runs per inning.
It is given that the team scores the same number of runs per inning and the other team did not score any more points. So, the total score of other team after last four inning is 17.
Kim's team total score in last four inning is 4p. So, the total score of Kim's team after last four inning is
[tex]6+4p[/tex]
Kim's team win if the total score of other team after last four inning is less than the Kim's team.
[tex]6+4p>17[/tex]
Therefore the required inequality is [tex]6+4p>17[/tex].
Answer:
6+4p>17
Step-by-step explanation:
3 per inning
PLEASE HURRY!! VW is parallel to YZ in the map below. Which proportion solves for the distance between Y and Z?
Answer:
[tex]\frac{3}{9}=\frac{4}{x}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
In this problem
Triangle XVW is similar to triangle XZY
therefore
[tex]\frac{YZ}{VW}=\frac{XZ}{XV}[/tex]
substitute the given values
[tex]\frac{x}{4}=\frac{9}{3}[/tex]
[tex]x=3*4=12\ miles[/tex]
Answer:
A
Step-by-step explanation:
What are the zeros of the function f(x) = x2 - 5x + 4?
To find the zeros set the equation equal to zero:
x^2 - 5x +4 = 0
Factor:
(x-4) (x-1) = 0
Now solve each set of parenthesis so that they equal zero:
(x-4) = 0, x =4
(x-1) = 0, x = 1
The zeros are 1,4
A rectangular block measures 3 cm x 4 cm x 3 cm how much water would it displace?
Answer:
36c^3m^3x^2
Step-by-step explanation:
you first multiply 3 cm by 4 cm by 3 cm to get 36 cm.its mass in air and its effective mass when submerged in water (density = 1 gram per cubic centimeter).1.0 g/cm3then you get the answer 36c^3m^3x^2What the equation of the quadratic function in standard form represented by the graph
Answer:
x^2 +6x +8
Step-by-step explanation:
The zeros of the graphed function appear to be (-4, 0) and (-2, 0). It appears the vertex is (-3, -1).
The standard form of the function with zeros p and q is ...
(x -p)(x -q) = x^2 -(p+q)x +pq
So, for zeros p=-4, q=-2, the standard form is ...
x^2 -(-4-2)x +(-4)(-2) = x^2 +6x +8
We can check to make sure the above vertex point satisfies this function:
(-3)^2 +6(-3) +8 = 9 -18 +8 = -1
The vertex satisfies the function we wrote, so there are no additional vertical scale factors required.
The function is ...
y = x^2 +6x +8
36+4x=x^2+15
What is x?
X = -3 or X = 7
Step 1: Simplify both sides of the equation.
Step 2: Subtract x^2+15 from both sides.
Step 3: Factor left side of equation.
Step 4: Set factors equal to 0.
Answer:
x=7 or x=-3
Step-by-step explanation:
36+4x=x^2+15
36-15+4x=x^2
21+4x=x^2
0=x^2-4x-21
0=x^2-(7-3)x-21
0= x^2-7x+3x-21
0= x(x-7)+3(x-7)
0= (x-7)(x+3)
so either
x-7=0
x=7
or x+3=0
x=-3
whats is pemdas in math
P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
What PEMDAS stands for is that in a mathematical equation, parentheses has the priority of being solved. The second priority goes to exponents, then Multiplication and Division, and then finally Addition and Subtraction.
[tex]\text{Hey there!}[/tex]
[tex]\text{The P stands for parentheses}[/tex]
[tex]\text{The E stands for exponents}[/tex]
[tex]\text{The M stands for multiplication/multiply}[/tex]
[tex]\text{The D stands for division/divide}[/tex]
[tex]\text{The A stands for Addition/Add}[/tex]
[tex]\text{The S stands for Subtraction/Subtract}[/tex]
[tex]\text{Some people refer to it as: (P)lease (E)xcuse (M)y (D)ear (A)unt (S)ally}[/tex] [tex]\text{method for the abbreviations}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
what is the range of the function on the graph
Answer:
All real numbers greater than or equal to -2.
Step-by-step explanation:
The range is the set of values of the y-coordinates of the points on the graph.
The smallest y-coordinate is -2. All real numbers greater than equal to -2 are the range.
Answer: All real numbers greater than or equal to -2.
Sam worked 26 hours so far this week. He normally works a 40 hour week What fraction and percent represents the portion of hours he has worked? Simplify the fraction
Answer:
13/20, 65%
Step-by-step explanation:
So he has worked 26 hours out of 40 so that becomes 26/40 that is equal to 13/20 so that is your fraction and to convert to a percentage times 100 go that equals 65 so 65%