Answer:
Step-by-step explanation:
huh???????????????
find a value for c so that the polynomial y^2 + 10y + c factors to (y+5)^2
Notice that
[tex]\begin{gathered} (y+5)^2=y^2+10y+25 \\ \text{and} \\ y^2+10y+c=(y+5)^2 \\ \Rightarrow y^2+10y+c=y^2+10y+25 \\ \Rightarrow c=25 \end{gathered}[/tex]Then, the answer is c=25.
the number of women graduating from 4-yr colleges in a particular country grew from 1930, when 48780 women earned a bachelor's degree, to 2003, when approximately 756000 women received such a degree. find an exponential function that fits the data, and the exponential growth rate.
The exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).
What is defined as the Growth Function?When we need to start writing a growth function, we use three separate components. The first component is the starting population, the second is the growth rate, and also the third is the time elapsed. By combining all three, we can create a growth equation that will assist us in determining the growth rate if we are provided with the final population as well as the time elapsed.The following equation can be used to calculate an exponential function again for number of women graduating from four-year colleges in t years after 1930:
A(t) = A₀e∧(rt)
In which A₀ is the starting point and r is the exponential growth rate expressed as a decimal.
In 1930, 48780 women received a bachelor's degree.
This implies that;
A₀ = 48780
In 2004, approximately 756000 people
The year 2003 is 73 years after 1930, that also means
Using the equation as an example:
A(t) = A₀e∧(rt)
Put the values;
756000 = 48780 e∧(73r)
e∧(73r) = 756000/ 48780
e∧(73r) = 15.49
Taking log both side;
73r = ㏑ 15.49
r = 2.7/7
r = 0.037
The function becomes;
A(t) = A₀e∧(0.037t)
Thus, the exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).
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Indicate whether the line on the graph is a function
The line on the graph is a function
How to determine if the line is a function?The given parameter is the graph
From the graph, we can see that the curve or the line is a quadratic function
As a general rule, all lines represented by a quadratic function are functions
This implies that the line is a function
It should be noted that:
Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
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Given the polynomial below:
9m5 +3n³2q² + 1 +
State:
Degree:
Number of Terms:
Constant:
This polynomial have 5 degree , 4 terms and one connstant
What is polynomial ?Algebraic expressions called polynomials only have non-negative integer powers for their variables. A polynomial is, for instance, Expressions with one or more terms that have a non-zero coefficient are called polynomials. The terminology include constants, exponents, and variables. The "leading term" refers to the first term of the polynomial in standard form. A standard polynomial is one in which the first term, which has the highest degree, is followed by succeeding terms that are organized in descending order of the exponents or powers of the variables, then by constant values. A "coefficient" is a number that has been multiplied by a variable.
Given that : [tex]9m^{5}+3n^{2} +2q^{2} +1[/tex]
[tex]9m^{5}+3n^{2} +2q^{2} +1[/tex]
This polynomial have 5 degree , 4 terms and one connstant
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Triangle abc is congruent to triangle a'b'c'. Describe a sequence of rigid motions that takes a to a, b to b', and c to c'
To transform A to A', B to B' and C to C' rotate the triangle ABC clock- wise 90° about the A.
What is a Triangle ?Simple polygons with three sides and three internal angles make up triangles.
It is one of the fundamental geometric shapes in which the three vertices are connected to one another.
Triangles come in 4 different varieties.
1. Equilateral: Equilateral triangles have three equal sides and three identical 60-degree angles.
2. Isosceles: Isosceles triangles have equal sides and angles on both of their two sides.
3. Right-angled: In right-angled triangles, one of the angles is a right angle (90°).
4. Scalene: Triangles with this property do not have equal sides or angles.
To transform A to A', B to B' and C to C' rotate the Triangle ABC 90° clock- wise about the A.
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Find the value of x(Options are included in the photo)
23
Explanation
Complementary angles are pair angles with the sum of 90 degrees, so we can say that
[tex]\begin{gathered} (3x-9)\text{ and }(x+7) \\ \end{gathered}[/tex]are complementary angles, therefore
[tex](3x-9)\text{ and }(x+7)[/tex]Step 1
so,we need to equals to 90 and solve for x
[tex]\begin{gathered} (3x-9)\text{ and }(x+7) \\ (3x-9)\text{ + }(x+7)=90 \\ 3x-9+x+7=90 \\ \text{add like terms} \\ 4x-2=180 \\ \text{add 2 in both sides} \\ 4x-2+2=90+2 \\ 4x=92 \\ \text{divide both sides by 4} \\ \frac{4x}{4}=\frac{92}{4} \\ x=23 \end{gathered}[/tex]so, the answer is
23
I hope this helps you
find the next number in the sequence 128,64,32
Answer:
16!
Step-by-step explanation:
The sequence shows that from left to right, the numbers are being divided by two (or multiplied by 1/2). So, for that reason I think that the answer must be 16.
The four algebra classes at sanchez school are going on a field trip to a museum. each class contains s students. the museum charges $8 per student for admission. there is also a flat fee of $200 for the buses. a. write an expression for the total cost of the buses and the museum admission fees for all four classes. b. write a rational expression for the cost per student. simplify the expression as much as possible. c. use the expression you wrote in part (b) to find the cost per student if each class has 20 students.
a)The expression for the total cost for all four classes can be given as 32s + 200. b) the rational expression for the cost per student is 2(4s+25)/s c) if each class has 20 students then the cost per student is equal to $10.50.
a) Total cost expression can be determined as follows:
total fees of admission + fees of bus = total cost
total cost = (4s × 8) + 200
total cost = 32s + 200
b) A rational expression to determine the cost per student can be calculated as follows:
cost per student = total cost ÷ the total number of students
cost per student = 32s + 200 ÷ 4s
We now factor the numerator by using its GCF;
cost per student = 4 × 2 (4s + 25) / 4×s
cost per student =2 (4s + 25) / s
c) Now using this expression we can find the cost per student if each class has 20 students;
cost per student = 2 (4s + 25) / s
cost per student = 2 ( 4×20 + 25)/ 20
cost per student = 2 ( 80 + 25) / 20
cost per student = 2 (105) / 20
cost per student = 210 / 20 = $10.50
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Determine the total surface area of each pyramid with a regular polygon base
The total surface area of the pyramid (a) is 624.32 cm² , and of pyramid (b) is 265.6 m² .
The Total Surface Area of the Pyramid with pentagon base can be calculated using the formula
TSA = 5/2*b(a+s) ,
where b is the base length (side of pentagon)
s is the slant height ,
a is the apothem
and the Total Surface Area of the Pyramid with square base can be calculated using the formula .
TSA = b² + 2bs
where , b is the base and
s is the slant height .
Pyramid (a)
we can see from the figure that ,the pyramid has a pentagon base ,
So, the TSA will be 5/2*b(a+s) ,
in the figure , given that height =12 cm , apothem = 7.8cm
we find the slant height by Pythagoras theorem
(slant height)²=(height)²+(apothem)²
(slant height)² = 12² + 7.8²
(slant height) = √(12² + 7.8²)
(slant height) = √(144+60.84)
(slant height) = 14.3 cm
Substituting in TSA formula , TSA = 5/2*b(a+s)
we get ,
TSA = 5/2*11.3(7.8+14.3)
= 2.5*11.3(22.1)
= 28.25*22.1
=624.32 cm²
Pyramid (b)
we can see from the figure that ,the pyramid has a square base ,
So, the TSA will be b² + 2bs,
in the figure , given that height =12 m , apothem = 4 m
we find the slant height by Pythagoras theorem
(slant height)²=(height)²+(apothem)²
(slant height)² = 12² + 4²
(slant height) = √(12² + 4²)
(slant height) = √(144+16)
(slant height) = 12.6 m
Substituting in TSA formula , TSA = b² + 2bs
we get ,
TSA = 8² + 2*8*12.6
= 64 + 16*12.6
= 64 + 201.6
= 265.6 m²
Therefore , the total surface area of the pyramid (a) is 624.32 cm² , and of pyramid (b) is 265.6 m² .
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Pls Help asap for math
Answer:
A
Step-by-step explanation:
it reflects over the y axis
Joanne slices a large banana bread into pieces 16 There are 6 adults and 6 children who get a piece of banana bread. The rest of the pieces will be donated to the homeless. What fraction of the banana bread will be donated?
The most appropriate choice for fraction will be given by
Fraction of banana bread will be donated to the homeless is [tex]\frac{1}{4}[/tex]
What is a fraction?
Suppose there is a collection of objects and some part of the objects are taken from the collection. The part which has been taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.
Here,
Total number of banana breads 16
Number of adults who got banana bread = 6
Number of Children who got banana bread = 6
Total number of children and adult who got banana bread = 6 + 6 = 12
Number of banana breads given to the homeless = 16 - 12 = 4
Fraction of banana bread given to the homeless = [tex]\frac{4}{16}[/tex]
= [tex]\frac{1}{4}[/tex]
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Given a triangle with coordinates at A(2, 3), B(8, 3), and
C(5, 6) classify the triangle as obtuse/acute/right and
scalene/isosceles/equilateral.
Use the sketch to show your thinking.
(Select all that apply.
Right
Acute
Obtuse
Isoceles
Equilateral
The triangle is Isosceles and Acute.
From the given data, the coordinates of the three points of the triangle are, A(2, 3), B(8, 3), and C(5, 6).
applying the distance formula, D = √((x2-x1)²+(y2-y1)²) the distance AC and BC are obtained as 3√2 and the distance AB as 2√3.
From this, it can be concluded that AC=BC≠AB.
thus since two of the sides, AC and BC are equal and the third side AB is not equal to AC and BC hence the given triangle is an isosceles triangle.
To check whether the given triangle is right, acute.
A right triangle is a triangle with one of its angles equal to 90 degrees.
An acute triangle is a triangle with all three of its angles less than 90 degrees.
An obtuse triangle is a triangle with at least one of its angles greater than 90 degrees.
To check whether the given triangle is right, acute, or obtuse we use the law of cosines.
To find the angle of a triangle given 3 of its sides, let the angle between the sides AB and AC be A then,
cos(A) = (AC² + AB² − BC²)÷(2×AB×AC).
cos(A) = (3√2² + 2√3² - 3√2²)÷(2×2√3×3√2) =2÷√6
[tex]cos^{-1}[/tex](2÷√6) = 39.182.
Let the angle between the sides AB and BC be B then,
cos(B) = (BC² + AB² − AC²)÷(2×AB×BC).
cos(B) = (3√2² + 2√3² - 3√2²)÷(2×2√3×3√2) =2÷√6
[tex]cos^{-1}[/tex](2÷√6) = 39.182.
Let the angle between the sides AC and BC be then,
cos(C) = (AC² + BC² − AB²)÷(2×AC×BC).
cos(C) = (3√2² + 3√2² - 2√3²)÷(2×3√2×3√2) =2÷3
[tex]cos^{-1}[/tex](2÷3) = 53.544.
Since all the angles A, B, and C is less than 90 degrees the triangle is acute.
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Grace has a job power washing houses.
She needs to power wash 11 houses to
earn enough money to pay for a new robot
kit. If each house takes the same amount
of time, and she can wash 2 houses in 8
hours, how long will it take her to wash 11
houses?
Coffee with sugar and milk added to it can contain up to
how many calories.
Answer:
The total of all calories in a coffee with milk and sugar, is somewhere between 120 and 180. A couple of cups per day could easily add a lot of calories to the 2 000 calories needed per day.
Step-by-step explanation:
Answer:
A standard coffee with whole milk and sugar contains around 140 calories. This number can increase depending on the type of milk used, as well as the amount of sugar added.
2|x+3|+1>3 I need help!!
Answer:
x < -4 or x > -2
Step-by-step explanation:
[tex]2 |x + 3| + 1 > 3[/tex]
[tex]2 |x + 3| > 2[/tex]
[tex] |x + 3| > 1[/tex]
x + 3 > 1 or x + 3 < -1
x > -2 or x < -4
Answer:
Step-by-step explanation:
9. Reflect in the y-axis.
B
C
a. A'(3, 3), B'(6, 3), C'(5, 6), D'(0, 6)
b. A'(-3, 3), B'(-6, 3), C'(-5, 6), D'(0, 6)
c. A'(3,-3), B'(6, -3), C'(5, -6), D'(0, -6)
d. A'(-3, -3), B'(-6, -3), C'(-5, -6), D'(0, -6)
C
The coordinates of the vertices of triangle A'B'C' after a reflection over the y-axis to triangle ABC are: C. A' = (3, -3), B' = (6, -3), C' = (5, -6), D' = (0, -6).
What is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (x, y).
By applying a reflection over the y-axis to triangle ABC, the coordinates of the vertices of the image triangle A'B'C' include the following:
(x, y) → (x, y)
Point A = (3, -3) → Point A' = (3, -3)
Point B = (6, -3) → Point B' = (6, -3)
Point C = (5, -6) → Point C' = (5, -6)
Point D = (0, -6) → Point D' = (0, -6)
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Solve 2(1-x)>2x
X<0.5
X<2
X>2
X>0.5
Answer:
x < 0.5
Step-by-step explanation:
2(1 - x) > 2x ( divide both sides by 2 )
1 - x > x ( add x to both sides )
1 > 2x ( divide both sides by 2 )
0.5 > x , that is
x < 0.5
I don’t understand how to solve
By using a translation rule, the coordinates of C' are (- 1, - 2). (Correct choice: E)
How to translate the vertices of a triangle in a accordance to a vector
Triangles are defined by the locations of its three vertices on Cartesian plane and we must find the locations of the images of the three vertices after applying a translation rule. In this case, we must translate each vertex 2 units upward and 4 units to the right. The general translation formula is described below:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Location of the vertex.T(x, y) - Translation vector.P'(x, y) - Location of the image of the vertex.If we know that C(x, y) = (- 5, - 4) and T(x, y) = (4, 2), then the location of the image of point C is:
C'(x, y) = (- 5, - 4) + (4, 2)
C'(x, y) = (- 1, - 2)
The coordinates of C' are (- 1, 2).
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need help with this, thanks
Answer:
x = 11°
Step-by-step explanation:
Hello!
These angles are called vertical angles or angles opposite to each other during the intersection of two lines.
Vertical angles are equal to each other, so we can set the expressions equal to each other and solve for x.
Solve for x9x - 4 = 8x + 7 -> Subtract 8xx - 4 = 7 -> Add 4x = 11The value of x is 11°.
Answer:
[tex]x=\boxed{11}[/tex]
Step-by-step explanation:
Vertical Angle Theorem
The opposite vertical angles of two straight intersecting lines are congruent.
Therefore, equate the expressions and solve for x:
[tex]\boxed{\begin{aligned}(9x-4)^{\circ}&=(8x+7)^{\circ}\\9x-4&=8x+7\\9x-4-8x&=8x+7-8x\\x-4&=7\\x-4+4&=7+4\\x&=11\end{aligned}}[/tex]
Therefore:
[tex]x=\boxed{11}[/tex]
A group of friends wants to go to the amusement park. They have no more than $195 to spend on parking and admission. Parking is $9.75, and tickets cost $17.75 per person, including tax. Which inequality can be used to determine xx, the maximum number of people who can go to the amusement park?
Answer:
7
Step-by-step explanation:
assuming everyone takes their own car, 9.75+17.75 * 7 = 192 I don’t know the state tax, because each state is different but 192 gives about $3 worth of room for tax. If the tax is higher in your state maybe I’d answer with 6 people. Hope this helped!
These are radical and complex number questions, i need to simplify both WITH WORK, please help
The values of the radical expressions are [tex]\frac{5x^4z^3}{7y}[/tex] and [tex]2x^2y\sqrt{5z}[/tex]
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the radical expression?Expression 1
Here, we have
[tex]\sqrt{\frac{25x^8z^6}{49y^2}}[/tex]
Take the square roots of 25 and 49
So, we have
[tex]\frac{5}{7}\sqrt{\frac{x^8z^6}{y^2}}[/tex]
Next, we apply the law of indices in simplifying the radical expressions
This gives
[tex]\frac{5}{7}\frac{x^{(8/2)}z^{(6/2)}}{y^{(2/2)}}[/tex]
Evaluate
[tex]\frac{5}{7}\frac{x^4z^3}{y}[/tex]
Rewrite as
[tex]\frac{5x^4z^3}{7y}[/tex]
Expression 2
Here, we have
[tex]\frac{\sqrt{100x^4y^2z}}{\sqrt 5}}[/tex]
Take the square roots of 100
So, we have
[tex]10\frac{\sqrt{x^4y^2z}}{\sqrt 5}}[/tex]
Rationalize
[tex]10\frac{\sqrt{5x^4y^2z}}{5}[/tex]
Next, we apply the law of indices in simplifying the radical expressions
This gives
[tex]10\frac{\sqrt{5z}x^{4/2}y^{2/2}}{5}[/tex]
Evaluate
[tex]2\sqrt{5z}x^2y[/tex]
Rewrite as
[tex]2x^2y\sqrt{5z}[/tex]
Hence, the solution is [tex]2x^2y\sqrt{5z}[/tex]
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Determine whether the ratios are equivalent.
1 : 4 and 2 : 6
Responses
The ratios, 1 : 4 and 2 :6 are not equivalent.
Are the ratios equivalent?
Ratio shows the relationship that exist between two or more numbers. Ratio is used to compare two or more numbers. It shows the number of times that one value is contained within other value(s).
In order to determine if the ratios are equivalent, express 2 : 6 in its simplest form. To do this, divide 2 and 6 by 2, a common multiple of both numbers.
2 :6 in its simplest form is 1 : 3
Since, 1 : 3 is different from 1 : 4, the ratios are not equivalent.
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What numbers are missing from the pattern below? Enter your answer, using
a comma to separate each number.
72, 3, 28, 42, ?, ?, ?, ?, 72, 3, 28, 42
Answer:
78, 3, 28, 42
Step-by-step explanation:
This appears to be a repeating sequence of four numbers:
72, 3, 28, 42
so the missing 4 numbers must be as above
Out of 120 students, 80 passed in Science, 70 in Nepali, 10 failed in both subjects and 7 did not appear in an examination. Find the number of students who passed in both subjects by representing the above information in a Venn-diagram.
Step-by-step explanation:
we can find the number of students passed in both subject by following method.
Solution;
Of which type of equation are there the greatest number:
A )Equations with no solutions
B) Equations with infinitely many solutions
C) Equations with exacly one solution
EXPLAIN YOUR REASONING
The greatest number of equations are available in all the types specified in option A), option B) and option C). So 'all of the above' is the correct choice.
As given in the question,
Let us discuss
option A) Equations with no solutions
examples are:
x+ y = 0
x+ y = 1
Many such pairs of simultaneous linear equations can be formulated and number of such equations possible is infinite.
Let us discuss
option B) Equations with infinitely many solutions
example:
x+ y = 0
Number of such equations possible is infinite.
Let us discuss
option C) Equations with exactly one solution
example:
x=4
Number of such equations possible is infinite.
Therefore, the greatest number of equations are available in all the types specified in option A), option B) and option C). So 'all of the above' is the correct choice.
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what is 23/10 times 16/3
Given that n is an integer and that n>1
Prove algebraically that n²-(n-2)²-2 is always an even number.
The expression can be rewritten as:
2*(n - 3)
This is twice an integer number, so this is an even number
How to prove that the expression gives an even number?Here we know that n is an integer larger than 1, and we have the expression:
n² - (n - 2)² - 2
Now, remember that for any integer m, 2m is always an even number.
Expanding the term in the middle of the expression we get:
n² - (n - 2)² - 2
n² - (n² - 4n + 4) - 2
4n - 4 - 2 = 4n - 6 = 2*(n - 3)
Integer numbers are closed under addition, then n - 3 is an integer, so we have:
2*(n - 3)
This is twice an integer, so this is an even number.
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Help pls with number 7
Answer:
-1.5 goes in between -2 and -1
3/2 goes in between 2 and 1 but closer to 1
-2/3 goes in between 0 and -1 but closer to 0
I’m not very sure about -4/3 but I think it goes in between -2 and -1 but closer to -1 than 3/2
Step-by-step explanation:
the following data represent the number of grams of fat in breakfast meals offered at a local fast food restaurant. (a) construct an ordered stem-and-leaf plot and (b) describe the shape of the distribution.
An ordered stem-and-leaf plot has the following results:
0=4 counts
1=7 counts
2=6 counts
3=4 counts
4=1 count
The shape of the distribution is skewed to the right
Part 1
An ordered stem-and-leaf plot:
Total Counts
0 | 3 4 5 7 | 4
1 | 2 2 4 4 5 7 7 | 7
2 | 0 3 4 4 5 8 | 6
3 | 3 4 7 9 | 4
4 | 1 | 1
Part 2
Shape of distribution
When the data in the stem-and-leaf plot given above is plotted in graph, the tail of the plot will be on the right. Hence, the shape of the distribution is skewed to the right
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The temperature of a place was 6°F in the morning. At noon, the
temperature rose by 13°F and dropped by 4°F at night. What was the
temperature recorded at the end of the day?