The minimum of this quadratic function is -55.
How to determine the axis of symmetry and the vertex of the function?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function T = n²- 10n - 30, we have:
Axis of symmetry, Xmax = -(-10)/2(1)
Axis of symmetry, Xmax = 10/2 = 5.
For the vertex of T = n²- 10n - 30, we have:
T = n²- 10n - 30
T(5) = 5²- 10(5) - 30
T(5) = -55.
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5. Match the steps for constructing a congruent line segment to their pictures.
▼
▼
1. Step 2: Draw a second line
segment that is longer than the
first.
2. Step 4: That intersection is the
final endpoint of the copied
segment.
3. Step 1: Put the point of the
compass on one endpoint of the
segment to be copied. Change the
compass setting so that the
pencil end is just touching the
other endpoint, make a small arc
to see this.
4. Step 3: Without changing the
compass setting, put the
compass point on the new
endpoint on a new line. Make a
small arc that intersects the line.
We can see here that matching the steps for constructing a congruent line segment to their pictures, we have:
Step 1 - Picture a
Step 2 - Picture b
Step 3 - Picture c
Step 4 - Picture c.
What is a line segment?Any portion of a line with two ends and a set length is referred to as a line segment. It differs from a line that has neither a beginning nor an end and can be stretched in both directions.
The endpoints of a line segment can be used to define it. The portion of the line that begins at point A and finishes at point B, for instance, is known as the line segment AB.
A ruler or measuring tape can be used to determine the length of a line segment. The distance between two line segments' endpoints is the segment's length.
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Answer:
Step-by-step explanation:
3
f(x)=3(2¹)-1
g(x)=3(2-)-1
Which statement is TRUE?
A. The y-values of both functions decrease by a
factor of 2 for each unit increase in x.
C. The functions both have the same x-intercept.
B. The y-values of both functions increase by a factor
of 2 for each unit increase in x.
D. The functions both have the same y-intercept.
The correct statement regarding the exponential functions in this problem is given as follows:
D. The functions both have the same y-intercept.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The functions in this problem are given as follows:
[tex]f(x) = 3(2^x) - 1[/tex][tex]g(x) = 3(2^{-x}) - 1[/tex]Hence the y-intercept for each function is given as follows:
[tex]f(0) = 3(2^0) - 1 = 3 - 1 = 2[/tex][tex]g(x) = 3(2^{0}) - 1 = 3 - 1 = 2[/tex]More can be learned about exponential functions at brainly.com/question/2456547
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Which function equation is represented by the graph?
f(x)=40(2.5)x
f(x)=40(1.5)x
f(x)=40(3.25)x
f(x)=40(2.25)x
Answer:
f(x)=40(2.25)^x
Step-by-step explanation:
You want the equation of the exponential function that goes through points (0, 40) and (1, 90).
Exponential functionThe exponential function can be written ...
f(x) = a·b^x
ParametersWhen x = 0, this is ...
f(0) = a·b^0 = a·1 = a
Using the given point, we have a = 40.
When x = 1, this is ...
f(1) = 40·b^1 = 40b
Using the given point, we have ...
90 = 40b
b = 90/40 = 2.25
The function equation is ...
f(x) = 40(2.25^x)
<95141404393>
Is the relation a function?
Yes or No
!PLEASE HELP!
Answer:
Is the relation a function?
no
Step-by-step explanation:
please make brainlist
PLS HELP Polygon ABCD with vertices at A(1, −2), B(3, −2), C(3, −4), and D(1, −4) is dilated to create polygon A′B′C′D′ with vertices at A′(4, −8), B′(12, −8), C′(12, −16), and D′(4, −16). Determine the scale factor used to create the image.
one fourth
one half
2
4
The scale factor used to create the image is given as follows:
4.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
In the context of this problem, we have that each vertex of A'B'C'D' is obtained with the multiplication of each of the coordinates of ABCD by four.
For example, we have that vertex A has the coordinates A(1, -2), while the equivalent vertex A' has the coordinates of A'(4, -8).
Hence the scale factor used to create the image is given as follows:
4.
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Which equation represents a horizontal line? A.y=x+1 b. X=2 c.x=y+2 d. Y=2
Answer: d. Y=2
Step-by-step explanation:
Select the correct answer.
What is the equation of the parabola shown in the graph?
The equation for the parabola in the graph is the one in option C:
y = (-1/4)x² -2x - 7
Which is the equation of the parabola?Remember that a parabola with leading coefficient a and a vertex (h, k) can be written as:
y = a*(x - h)² + k
Here the vertx is at (-4, -3), then:
y = a*(x + 4)² - 3
And we can see that it passes through the point (0, -7), replacing that we will get:
-7 = a*(0 + 4)² - 3
-7 = a*16 - 3
-7 + 3 = a*16
-4 = a*16
-4/16 = a
-1/4 = a
The quadratic is:
y = (-1/4)*(x + 4)² - 3
Expanding that, we will get:
y = (-1/4)x² -2x - 4 - 3
y = (-1/4)x² -2x - 7
The correct option is C.
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Find the y-intercept and the slope of the line.
-8x -4y =5
Answer:
[tex]\sf m = -2\\\\y-intercept =\dfrac{-5}{4}[/tex]
Step-by-step explanation:
Slope and y-intercept of the line:
Write the equation in slope y-intercept form: y =mx +c
Here, m is the slope and c is the y-intercpet.
To isolate y, add 8x to both side,
-8x - 4y = 5
-4y = 8x + 5
Now, divide the entire equation by (-4),
[tex]\sf \dfrac{-4y}{-4}=\dfrac{8x}{-4} + \dfrac{5}{-4}\\\\\\y = -2x -\dfrac{5}{4}[/tex]
Now, compare with y = mx +c
[tex]\boxed{\sf m= -2}\\\\\\\boxed{\sf y-intercept=\dfrac{-5}{4}}[/tex]
Answer:
y-intercept = -5/4
slope = -2
Step-by-step explanation:
To quickly find the slope and y-intercept of a given linear equation, we can express it in the following form, called the slope-intercept form:
[tex]\boxed{y = mx + c}[/tex],
where:
m ⇒ slope
c ⇒ y-intercept
In order to take the given equation into the slope-intercept form, we have to make y the subject of the equation:
[tex]-8x - 4y = 5[/tex]
⇒ [tex]-4y = 8x + 5[/tex] [Adding 8x to both sides of the equation]
⇒ [tex]y = -\frac{1}{4}(8x + 5)[/tex] [Dividing both sides of the equation by -4]
⇒ [tex]y = -2 x - \frac{5}{4}[/tex]
Comparing the above equation with the slope-intercept form, we can see that m = -2 and c = -5/4.
Therefore, y-intercept = -5/4, and slope = -2.
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The following table gives the number of women age 16 years and older (in
millions) in a country's civilian workforce for selected years from 1950 and
projected to 2050.
Complete parts (a) and (b) below.
a. Use x as the number of years past January 1st, 1950 to create a cubic model, y, using these data.
y=0x³+x²+x+O
To create a cubic model, we need to find a cubic equation in the form of [tex]y = ax^3 + bx^2 + cx + d[/tex] that fits the given data. Let's use the data provided in the table and the equation [tex]y = 0x^3 + x^2 + x + 0[/tex].
Since the coefficient of [tex]x^3[/tex] is 0, the cubic term does not contribute to the equation. Therefore, the cubic model simplifies to [tex]y = x^2 + x[/tex].
The equation [tex]y = x^2 + x[/tex]represents a quadratic function rather than a cubic function.
Thus, if we assume that the cubic term is indeed meant to be 0, we can use the simplified equation [tex]y = x^2 + x[/tex] as the cubic model based on the given data.
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What measurement is equal to 1 2/3 yards
1 2/3 yards is equal to 5 1/3 feet.
How to find the measurement is equal to 1 2/3 yardsTo convert from yards to feet, we know that 1 yard is equal to 3 feet. Therefore, we can calculate:
1 2/3 yards = (1 + 2/3) yards = (3/3 + 2/3) yards = 5/3 yards
Now, to convert yards to feet, we multiply by 3:
5/3 yards * 3 feet/1 yard = 15/3 feet = 5 feet
Therefore, 1 2/3 yards is equal to 5 1/3 feet.
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Help please will Mark brainliest
Answer: B =[tex]x^{\frac{4}{5} }[/tex]
Step-by-step explanation:
Rules needed:
When you have a root, you can write it in exponented form. It becomes a fraction.
EX.
[tex]\sqrt[5]{x} =x^{\frac{1}{5} }[/tex]
When you have a number that is multiplied to another number both have exponents and same bases, you can combine the two by adding the exponents
EX.
[tex]x^{\frac{1}{5} } *x^{\frac{1}{5} } = x^{\frac{2}{5} }[/tex]
Your problem:
[tex]\sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}[/tex] >convert to exponent form
=[tex]x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} }[/tex] >add all exponents [tex](\frac{1}{5} +\frac{1}{5} +\frac{1}{5}+\frac{1}{5})[/tex]
=[tex]x^{\frac{4}{5} }[/tex]
B
pls help urgent. 25 points
They are similar because AB is four more than ED, AC is three more than DF, and BC is three more than EF.
To determine if two triangles are similar, we need to compare the ratios of the corresponding sides.
In this case, the given information allows us to compare the lengths of the corresponding sides of triangle ABC and triangle DEF.
We have:
AB = 16 and ED = 12 (AB is four more than ED)
AC = 12 and DF = 9 (AC is three more than DF)
BC = 1 and EF = 9 (BC is three more than EF)
The corresponding sides are proportional because the ratios of the lengths are consistent:
AB/ED = 16/12 = 4/3
AC/DF = 12/9 = 4/3
BC/EF = 1/9
Since the ratios of the corresponding sides are the same, we can conclude that triangle ABC and triangle DEF are similar
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The diagram shows two squares constructed on the sides of a rectangle. What is the area of square A?
The area of the square A is 19.98 square feet
Calculating the area of square A?From the question, we have the following parameters that can be used in our computation:
Two squares constructed on the sides of a rectangle.
Let the side lengths of square C be x
Let the side lengths of rectangle B be x and y
So, we have
x² = 5
xy = 10
Solving for x and y, we have
x = 2.24 and y = 4.47
The area of square A is
Area = y²
So, we have
Area = 4.47²
Evaluate
Area = 19.98
Hence, the area of the square A is 19.98 square feet
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An increase from $27 to $35.10 what percent of increase?
Answer:
30% increase
Step-by-step explanation:
percentage increase is calculated as
[tex]\frac{increase}{original}[/tex] × 100%
increase = $35.10 - $27 = $8.10 , then
percentage increase = [tex]\frac{8.10}{27}[/tex] × 100% = 0.3 × 100% = 30%
Answer:
Step-by-step explanation:
step 1: 35.10-27 =8.1
step 2: 8.1/27 x 100 = 30%
so therefore = 30% increase
A scientist has two solutions what she has labeled solution a and solution b each contains salt she knows that solution a is 60% salt and solution b is 85% salt she wants to obtain 70 ounces of a mixture that is 80% salt how many ounces of each solution should she use
Solving a system of equations we can see that:
She needs to use 56 oz of the 85% solution.She needs to use 14 oz of the 60% solution.How many ounces of each solution should she use?We can use the variables:
x = mass of the 60% solution.
y = mass of the 85% solution.
We can write a system of equations.
x + y = 70
x*0.6 + y*0.85 = 70*0.8
We can isolate x on the first equation to get:
x = 70 - y
Replace that in the other one:
(70 - y)*0.6 + y*0.85 = 70*0.8
Now we can solve this for y.
y*0.25 = 70*0.8 - 70*0.6
y = 14/0.25 = 56
Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.
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literally struggling so hard
Answer: I think question two is Adjacent angles and complimentary angles.
Step-by-step explanation: Complementary angles are two acute angles that add to form a right angle.
Adjacent angles are two angles that share a common side.
what is x, I really need help
hello
the answer to the question is:
Tan (x) = 6.7/4.9 = 1.3673 ----> x = 53.81° or 54°
please help! thank uu ~ :)
Given P(G∩N)=0.24, P(G)=0.37, and P(N)=0.41. Find P(G|N).
The probability P(G|N) value is 0.585 when P(G∩N)=0.24, P(G)=0.37, and P(N)=0.41.
To find P(G|N), which represents the probability of event G given event N, we can use the formula:
P(G|N) = P(G∩N) / P(N)
Given that P(G∩N) = 0.24 and P(N) = 0.41
we can substitute these values into the formula:
P(G|N) = 0.24 / 0.41
Calculating the division:
P(G|N) = 0.585
Therefore, the value of P(G|N) is 0.585.
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Burning Brownie has five varieties of cakes as Chocolate fudge cake (Cake 1), Nutella-filled Cake
(Cake 2), Marble Cake (Cake 3), Cheese cake (Cake 4) and Fruit Cake (Cake 5) at their store. The
selling prices of each of the cakes are $9, $12, $4, $5, $8 respectively.
a. Formulate the Revenue function
The revenue function for the cakes can be shown as: R(x1, x2, x3, x4, x5) = $9x1 + $12x2 + $4x3 + $5x4 + $8x5
What is revenue function?The revenue function is described as the total amount of money earned from selling a certain quantity of cakes.
We make the following
Cake 1 sold = x1
Cake 2 = x2
Cake 3 = x3,
Cake 4 = x4,
Cake 5= x5.
The revenue generated from selling each cake is:
Revenue1 = $9 * x1
Revenue2 = $12 * x2
Revenue3 = $4 * x3
Revenue4 = $5 * x4
Revenue5 = $8 * x5
Total revenue = Revenue1 + Revenue2 + Revenue3 + Revenue4 + Revenue5
Total revenue = $9 * x1 + $12 * x2 + $4 * x3 + $5 * x4 + $8 * x5
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landon invested 110 in an account with an interest rate of 4.1 how much would be there after 5 years
As it only told interest i asume its simple interest for compound interest the answer would be different
Evaluate the expression you got in part d for b = 8
It should be noted that when b = 8, the expression b/2 - 3 evaluates to 1.
How to calculate the expressionIn order to evaluate the expression b/2 - 3 when b = 8, we substitute the value of b into the expression and perform the calculations.
Given that b = 8, we have:
8/2 - 3
Now we simplify the expression:
8/2 is equal to 4, so we have:
4 - 3
Finally, subtracting 3 from 4 gives us the result:
4 - 3 = 1
Therefore, when b = 8, the expression b/2 - 3 evaluates to 1.
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b/2-3 Evaluate the expression you got in part d for b = 8
The family then travelled 38km from Camp Carol and reached Phoenix in 27minutes. Determine the average speed they travelling at?
The family traveled from Camp Carol to Phoenix at an average speed of approximately 84.44 kilometers per hour.
How to calculate average speed?Speed is simply referred to as distance traveled per unit time.
It is expressed mathematically as:
Speed = Distance / time
Given that the family traveled 38 km from Camp Carol to Phoenix in 27 minutes:
Distance traveled = 38 kilometers
Time taken = 27 minutes
First, convert the time from minutes to hours:
Time taken = ( 27 / 60 ) hours
Time taken = 0.45 hour
We can now calculate the average speed using the above formula as follows:
Average speed = Distance / time
Average speed = 38 km / 0.45 h
Average speed = 84.44 km/h
Therefore, the average speed is approximately 84.44 km/h.
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help? A crayon is shaped like a triangular prism. The base of the crayon is shown. If the crayon is 90 millimeters long, how many cubic millimeters of wax is used to make a box of 8 crayons?
Answer:
Unknown but formula (Check step by step solution)
Step-by-step explanation:
Without the image of the base of the crayon, I cannot determine the exact dimensions of the triangular prism or calculate the volume of a single crayon. However, I can give you a general formula for calculating the volume of a triangular prism and use it to find the total volume of wax needed to make a box of 8 crayons.
The formula for the volume of a triangular prism is:
Volume = (1/2) x base x height x length
where base is the area of the base of the triangular prism, height is the height of the triangular prism, and length is the length of the triangular prism.
Assuming all the crayons in the box have the same dimensions, let's say the base of the triangular prism has a length of L and a width of W. We can calculate the area of the base of one crayon as:
Base area = (1/2) x L x W
Since the crayon is 90 millimeters long, its height is 90 millimeters. Therefore, the volume of one crayon is:
Volume of one crayon = (1/2) x L x W x 90
To find the total volume of wax used to make a box of 8 crayons, we can multiply the volume of one crayon by the number of crayons:
Total volume of wax = Volume of one crayon x 8
Total volume of wax = (1/2) x L x W x 90 x 8
Total volume of wax = 360 x L x W
Again, without knowing the exact dimensions of the triangular prism, I cannot calculate the total volume of wax used to make a box of 8 crayons. But you can use the formula above and substitute the values of L and W based on the dimensions of the base of the crayon to find the answer.
Triangle ABC, with vertices A(-8,-7), B(-4,-8), and C(-5,-5),
What is the area, in square units, of triangle ABC?
The area of triangle ABC is given as follows:
A = 5.5 square units.
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
The base AB has the length given as follows:
[tex]AB = \sqrt{(-4 - (-8))^2 + (-7 - (-8))^2}[/tex]
b = 4.12.
The midpoint of the base AB is given by the mean of the coordinates, hence:
M = (-6, -7.5).
The height is given by the distance MC, as follows:
[tex]h = \sqrt{(-6 - (-5))^2 + (-7.5 - (-5))^2}[/tex]
h = 2.69.
Hence the area of the triangle is given as follows:
A = 0.5 x 4.12 x 2.69
A = 5.5 square units.
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Michelle orders 200 T-shirts to sell at the school carnival. She pays $6.50 per shirt, plus 5% of the total order for shipping. How much does she pay in all?
A $6.83
B $65.00
C $1,235.00
D $1,365.00
Michelle pays $1365 in total.
Option D is the correct answer.
We have,
To calculate the total amount Michelle pays for the T-shirts, we need to consider the cost per shirt and the shipping fee.
The cost per shirt is $6.50, and she ordered 200 shirts, so the cost of the shirts alone is:
= $6.50 x 200
= $1300
The shipping fee is 5% of the total order, which is:
= 5% x $1300
= $65
To find the total amount Michelle pays, we add the cost of the shirts and the shipping fee:
= $1300 + $65 = $1365
Therefore,
Michelle pays $1365 in total.
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QUESTION 23 - 1 POINT
Solve: 3|x + 1| ≥-6. Write your solution in interval notation.
(If there is no solution, enter your answer as Ø.)
Sure. Here are the steps on how to solve the equation 3|x + 1| ≥-6:
Divide both sides of the equation by 3.
Simplify both sides of the equation.
Isolate x on the left-hand side of the equation.
Test each solution in the original equation to make sure it makes the equation true.
Write the solution in interval notation.
Here are the detailed steps:
Divide both sides of the equation by 3:
3|x + 1| ≥-6
|x + 1| ≥ -2
Simplify both sides of the equation:
|x + 1| ≥ -2
x + 1 ≥ -2 or x + 1 ≤ -2
Isolate x on the left-hand side of the equation:
x + 1 ≥ -2
x ≥ -2 - 1
x ≥ -3
x + 1 ≤ -2
x ≤ -2 - 1
x ≤ -3
Test each solution in the original equation to make sure it makes the equation true.
Test x = -3 in the original equation:
3|-3 + 1| ≥-6
3|-2| ≥-6
3(2) ≥-6
6 ≥-6
True
Test x = -4 in the original equation:
In a town, 60% of the police officers have ride-alongs with teenagers who want to join the police force. 258 police officers have ride-alongs. How many police officers are there altogether?
Hello !
1. Calculate the rest100% - 60% = 40%
=> 40% of police officers have ride-alongs
2. Make a tabletotal
number of policier 258 ? ??
frequency in % 60% 40% 100%
3. Calculate the total3.1 Calculate the number of of the police officers have ride-alongs with teenagers who want to join the police force
? = 258 x 40 ÷ 60 = 172
3.2 Calculate the total
?? = 258 + 172 = 430
4. ConclusionIn total there are 430 police officers.
Have a good day !
Find a polynomial function with real coefficients that has the given zeros:
2, 5 + i
By the complex conjugate root theorem, there must also be another zero - [tex]5-i[/tex].
Therefore
[tex]f(x)=(x-2)(x-(5+i))(x-(5-i))\\f(x)=(x-2)(x-5-i)(x-5+i)\\f(x)=(x-2)((x-5)^2+1)\\f(x)=(x-2)(x^2-10x+25+1)\\f(x)=(x-2)(x^2-10x+26)\\f(x)=x^3-10x^2+26x-2x^2+20x-52\\f(x)=x^3-12x^2+46x-52[/tex]
need help can someone help me
Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;
Statement Reason
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
∠BCA ≅ ∠DCA Congruent angles of a triangle (SAS).
AC ≅ AC Reflexive property
ΔABC ≅ ΔADC AAS postulate
What is an angle bisector?In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.
By applying the angle bisector theorem to the given triangle, the variable y can be calculated by using the following mathematical equation (formula):
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can logically deduce that ∠BCA is congruent to ∠DCA
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