Answer: The two point questions are 45, while the four point questions are 5.
Step-by-step explanation: We shall start by assigning letters to the unknown variables. Let the first type of question be called a and the second type of question be called b.
If the final exam is made up of 50 questions, that means
a + b = 50
Also if some questions are two points while others are four points and the total score for all of them is 110 points, then
2a + 4b = 110
(That is, we assume that a is the two point question and b is the four point question, so total score equals 110)
We now have a pair of simultaneous equations
a + b = 50 ————(1)
2a + 4b = 110 ——-(2)
From equation (1), we shall make a the subject of the equation,
hence let a = 50 - b
Substitute for the value of a in equation (2)
2a + 4b = 110
2(50 - b) + 4b = 110
100 - 2b + 4b = 110
By collecting like terms we now have
4b - 2b = 110 - 100
2b = 10
Divide both sides of the equation by 2
b = 5
Now substitute for the value of b into equation (1)
a + b = 50
a + 5 = 50
Subtract 5 from both sides of the equation
a = 45.
Therefore the two point questions are 45, while the four point questions are 5
**A quick check would show the following results ; 2(45) + 4(5) = 90 + 20 = 110.**
There are 45 questions worth 2 points each and 5 questions worth 4 points each on the 110-point final exam consisting of 50 questions.
Let's call the number of 2-point questions "x" and the number of 4-point questions "y." We can set up a system of equations to represent the information given:
1. The total number of questions is 50:
x + y = 50
2. The total number of points is 110:
2x + 4y = 110
Now we have a system of two equations with two variables:
1. x + y = 50
2. 2x + 4y = 110
We can solve this system of equations using either the substitution method or the elimination method. Let's use the elimination method:
First, let's multiply the first equation by 2 to make it easier to eliminate x:
1. 2(x + y) = 2(50)
2x + 2y = 100
Now we have the following system of equations:
1. 2x + 2y = 100
2. 2x + 4y = 110
Now, subtract the first equation from the second equation to eliminate x:
(2x + 4y) - (2x + 2y) = 110 - 100
This simplifies to:
2y = 10
Now, divide both sides by 2 to solve for y:
2y/2 = 10/2
y = 5
So, there are 5 questions worth 4 points each (4-point questions), and we can find the number of 2-point questions by substituting the value of y back into one of the original equations (e.g., the first equation):
x + 5 = 50
Now, subtract 5 from both sides to solve for x:
x = 50 - 5
x = 45
So, there are 45 questions worth 2 points each (2-point questions).
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If ∠P measures 27°, q equals 6.0, and r equals 7.2, then which length can be found using the Law of Cosines?
using the Law of Cosines, we can find that the length of side ( p ) is approximately 3.29 units.
We can use the Law of Cosines to find the length of side ( p ) (opposite angle[tex]\( \angle P \))[/tex] when we know the lengths of the other two sides [tex]\( q \) and \( r \)[/tex] and the angle [tex]\( \angle P \)[/tex].
The Law of Cosines formula is:
[tex]\[ c^2 = a^2 + b^2 - 2ab \cos(C) \][/tex]
In this case, we want to find the length of side \( p \), so we'll use \( p \) as the side opposite angle \[tex]( \angle P \), \( q \) as side \( q \), and \( r \) as side \( r \)[/tex].
Substitute the given values into the Law of Cosines formula:
[tex]\[ p^2 = q^2 + r^2 - 2qr \cos(\angle P) \]\[ p^2 = (6.0)^2 + (7.2)^2 - 2(6.0)(7.2) \cos(27^\circ) \]\\[/tex]
Now, calculate the value of \( p \):
[tex]\[ p^2 = 36 + 51.84 - 86.4 \cos(27^\circ) \][/tex]
Using a calculator, find \( \cos(27^\circ) \approx 0.891 \):
[tex]\[ p^2 = 36 + 51.84 - 86.4 \times 0.891 \]\[ p^2 = 36 + 51.84 - 77.02 \]\[ p^2 = 10.82 \][/tex]
Take the square root of both sides to solve for \( p \):
[tex]\[ p = \sqrt{10.82} \approx 3.29 \][/tex]
So, using the Law of Cosines, we can find that the length of side ( p ) is approximately 3.29 units.
The number 8.375 x 10^-3 is equivalent to ____
Answer:
0.008375
Step-by-step explanation:
Answer:
hey
Step-by-step explanation:
8.375 can be written as
8375/1000
8375/ 10³
put in q
8375×10 power -3 × 10 power -3
8375× 10 power -6
0.008375
Question 6
Name the image of F(-3, 1) after being translated along the vector <5. - 1>.
Answer:
F' (2, 0 )
Step-by-step explanation:
A translation < 5, - 1 > means add 5 to the x- coordinate and subtract 1 from the y- coordinate, that is
F(- 3, 1 ) → F'(- 3 + 5, 1 - 1 ) → F'(2, 0 )
The image of the point F(-3, 1) after being translated along the vector <5, -1> is (2, 0). The process involves adding the vector components to the original point's coordinates.
Explanation:The initial point on the coordinate system is F(-3, 1). A translation moves a point by a specific vector. This vector is <5, -1>, meaning we move the point 5 units to the right and 1 unit down.
To perform the translation, we add the components of the vector to the coordinates of the original point. So, we add 5 to the x-coordinate (-3) and -1 to the y coordinate (1). This gives us the following results:
x-coordinate: -3 + 5 = 2y-coordinate: 1-1 = 0So, the image of F(-3, 1) after being translated along the vector <5, - 1> is the point (2, 0).
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5y+1=1 subtract 1 from both sides
Answer:
5y
Step-by-step explanation:
All you have to do is subtract 1 from both side so subtract 1 from one side than the other. If you have to find out what y equals, then after subtracting, divide 5 from both sides and y would equal 5. Hope this helped
Answer:
1) If you want to solve the equation, x is 0/5 or 0
2) If you want to subtract 1, the answer is 5y = 0
Step-by-step explanation:
1) 5y + 1 = 1
5y = 0
2) 5y + 1 = 1 Subtract both sides by 1
5y = 0 Isolate the variable by dividing 5 on both sides
y = 0/5 or 0
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Using the three indicated points on the given line and the concept of similar triangles, show and explain why the slope of the line is the same between any two of these three points. Calculate the slope of the line.
Answer:
Slope = 3/2 or 1.5
Step-by-step explanation:
(0,1) (2,4) (6,10)
Slopes:
(4-1)/(2-0) = 3/2
(10-4)/(6-2) = 6/4 = 3/2
(10-1)/(6-0) = 9/6 = 3/2
Any two points on the line will give the same slope because a straight line has a constant slope
estimate each quotient. show your work. 165÷4
Answer: 41 1/4
Step-by-step explanation: 160/4=40
5/4= 1 1/4
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You leave a 12% tip for a $25 meal. How much is the tip, in dollars?
Answer:
3 dollars
Step-by-step explanation: divide 25 by .12=3.00
Answer:
$3
Step-by-step explanation:
25 X 1.12 = 28 $28-$25= 3 dollar difference.
(0.12 is the decimal form of 12%)
What is the diameter of a circle with an area of 100 pie square feet
Answer: diameter =20ft
Step-by-step explanation:
(-3x^2+x^4+x)+(2x^4-7+4x)
1. Remove parentheses
-3x^2 + x^4 + x + 2x^4 - 7 + 4x
2. Collect like terms
-3x^2 + (x^4 + 2x^4) + (x + 4x) - 7
3. Simplify
-3x^2 + 3x^4 + 5x - 7
Operations with rational expressions
[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}[/tex]
Solution:
Given expression:
[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}[/tex]
To solve the given expression:
First simplify: [tex]\frac{50-2 w^{2}}{3 w^{2}+9 w-30}[/tex]
[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30}=-\frac{2(w+5)(w-5)}{3(w-2)(w+5)}[/tex]
Cancel the common factor (w + 5).
[tex]$=-\frac{2(w-5)}{3(w-2)}[/tex]
Now substitute this in the given expression.
[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{2(w-5)}{3(w-2)} \cdot \frac{w^{2}+5 w-14}{6 w-30}[/tex]
Multiply the fractions [tex]\frac{a}{b} \cdot \frac{c}{d}=\frac{a \cdot c}{b \cdot d}[/tex]
[tex]$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{3(w-2)(6 w-30)}[/tex]
Factor the denominator [tex]3(w-2)(6 w-30) =18(w-2)(w-5)[/tex]
[tex]$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{18(w-2)(w-5)}[/tex]
Cancel the common factor 2(w – 5).
[tex]$=-\frac{w^{2}+5 w-14}{9(w-2)}[/tex]
Factor the numerator [tex]w^{2}+5 w-14=(w-2)(w+7)[/tex]
[tex]$=-\frac{(w-2)(w+7)}{9(w-2)}[/tex]
Cancel the common factor (w – 2).
[tex]$=-\frac{w+7}{9}[/tex]
[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}[/tex]
What solid 3D object is produced by rotating the quarter-circle about line m
Answer:
hemisphere.
Step-by-step explanation:
it is a hemisphere with radius=5 units.
or hemisphere with diameter=10 units
Answer:
A semisphere (half sphere) with diameter 10 units
Step-by-step explanation:
What is the surface area, in square inches, of the container?
Answer:
62 inches
Step-by-step explanation:
Fuel x costs $2 per gallon and fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Write a system of linear inequalities to represent this situation.
(I did not mean to select one)
Answer:
First choice A : 2x +3y is less than or equal to 18. x greater than or equal to 0. y greater than or equal to 0.
If fuel x costs $2 per gallon, but Fuel y costs $3 per gallon. You may only spend up to $18 on petrol. The system of linear inequalities representing this situation is,2x+3y≤18,x≥0, and y≥0. Option A is correct.
What is inequality?A collection of two or more inequalities in one or more variables is known as a system of inequalities. When there are multiple constraints on a problem's potential solutions and a range of potential solutions are needed, systems of inequalities are used.
Given that, fuel x costs $2 per gallon, but Fuel y costs $3 per gallon. You may only spend up to $18 on petrol.
The maximum or minimum values of a situation with multiple constraints are frequently determined using a system of linear inequalities.
Thus, if fuel x costs $2 per gallon, but Fuel y costs $3 per gallon. You may only spend up to $18 on petrol. The system of linear inequalities representing this situation is,2x+3y≤18,x≥0, and y≥0. Option A is correct.
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The floor of a rectangular room is to be tiled with 1/3 foot square tiles along a 9 3/8 foot wall. How many tiles will be needed along the wall?
Answer: Therefore, approximately 225/8 tiles will be needed along the 9 3/8 foot wall.
Step-by-step explanation:
To determine how many tiles will be needed along the 9 3/8 foot wall, we need to find the number of tiles that can fit in that space.
First, let's convert the mixed number 9 3/8 to an improper fraction. To do this, we multiply the whole number (9) by the denominator (8) and add the numerator (3):
9 * 8 + 3 = 75/8
Now, we have the length of the wall as 75/8 feet.
To find the number of tiles needed, we divide the length of the wall by the length of each tile. The length of each tile is 1/3 foot.
Dividing 75/8 by 1/3, we multiply the first fraction by the reciprocal of the second fraction:
(75/8) / (1/3) = (75/8) * (3/1)
Simplifying the calculation, we get:
(75 * 3) / (8 * 1) = 225/8
Therefore, approximately 225/8 tiles will be needed along the 9 3/8 foot wall.
To tile a 9 3/8 foot wall with 1/3 foot square tiles, 282 tiles are needed.
Explanation:The question is asking how many 1/3 foot square tiles will be needed along a 9 3/8 foot wall in your rectangular room. To find the answer, we first need to convert the length of the wall, which is given in mixed number, into an improper fraction. So, 9 3/8 is equal to 75/8 feet. Since each tile covers 1/3 foot, the number of tiles needed along the wall will be total distance divided by the length covered by each tile.
Therefore, the number of tiles = (75/8) ÷ (1/3) = (75/8) * (3/1) = 281.25
However, because we can't use a fraction of a tile, this number needs to be rounded up. Hence, you'll need 282 tiles to cover the 9 3/8 foot wall.
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Which verbal expressions represents 4x - 10?
Answer:
four x minus ten
Step-by-step explanation:
4x = four x
-10 = minus ten
Answer:
Four times a number x minus 10
Between the time Iko woke up and lunchtime, the temperature rose by 11°. Then by the time he went to bed, the temperature dropped by 14°.
Write an addition expression for the temperature relative to when Iko woke up.
Answer: -3 degrees
Step-by-step explanation:
Lets say that the original temperature was "x."
The temperature rose by 11 degrees so it is now at 11+x.
Then the temperature fell by 14 degrees so you subtract. 11+x-14
11-14= -3 so you subtract 3 degrees from the original temperature and there fore the relative temperature is -3
I hope this helps!!!
What is the slope of the line with equation y-3=-1(x-2)?
Answer:
m = -1/2
Step-by-step explanation:
It moves right 2 and down 1.
Answer: slope is -1/2
Step-by-step explanation:
Multiplying Polynomials :
(X + 4)(X - 1/2)
Answer:
2x²+7x-4
Step-by-step explanation:
(x+4)(x-1/2)
First multiply (x-1/2) by 2.
We have (2x-1)
(x+4)(2x-1)
Expanding it, we have
x(2x-1)+4(2x-1)
2x²-x+8x-4
2x²+7x-4
How many different 4-digit personal identification numbers (PINs) can be made from the digit 0 through 9 if no digits repeat?
Answer:4960
Step-by-step explanation:
Answer:
Look below
Step-by-step explanation:
Searched it up.
66
A cylindrical barrel is 8 feet tall, and 5 feet wide at the bottom. What is the volume of the barrel?
Answer:
V = 50π ft³
Step-by-step explanation:
That "5 ft wide at the bottom" translates into "radius of (5/2) ft."
Volume of a cylinder of radius R and height H is V = πR²H, so here,
V = π(5/2)^2*8 ft³ or
V = π(25/4)(8) ft³, or
V = 50π ft³
What is the relationship between
the sine and cosine of complementary angles?
Explain your reasoning and use the relationship
to find cos 50 if sin 40 0.64.
Answer:
0.64
Step-by-step explanation:
Sine and cosine of angles are complimentary
This means
Sin x = Cos (90-x)
Cos x = sin (90 - x)
Therefore sin 40 = 0.64
Sin 40 = cos (90 - 40)
Sin 40 = cos 50
Cos 50 = 0.64
I hope this was helpful, please mark as brainliest
A 32. In bat is leaning against a fence. If the bat is 15 in. Away from the base of the fence, what angle is formed between the ground and the bat?
Trigonometry
Answer:
509.8
Step-by-step explanation:
The last one on 1/23
The angle formed between the ground and the bat is 62.04 degrees
How to calculate the angle of elevation and depressionFrom the given question, we have the following parameters:
Length of the bat = 32in
Measure of the distance from the bat to the ladder = 15in
Requiredangle of elevation
Using the SOH CAH TOA identity
Cos θ = adjacent/hypotenuse
Cos θ = 15/32
θ = arccos(15/32)
θ = 62.04degrees
Hence the angle formed between the ground and the bat is 62.04 degrees
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What are the different ways you can factor a quadratic expression?
A. Greatest Common Factor
B. Perfect Square Trinomial
C. Difference of Squares
D. Factor Quadratic Trinomials with Leading coefficient of 1
E. All of the above
Answer:E
Step-by-step explanation:
All of the above
Final answer:
The correct answer is E. All of the above.
There are several different ways to factor a quadratic expression.
Explanation:
There are several different ways to factor a quadratic expression:
Greatest Common Factor: Look for a common factor that can be factored out of all terms in the expression.Perfect Square Trinomial: If the expression can be written as the square of a binomial, it can be factored using this method.Difference of Squares: If the expression is in the form of a^2 - b^2, it can be factored using this method.Factor Quadratic Trinomials with Leading coefficient of 1: For expressions in the form of ax^2 + bx + c, where a is equal to 1, it can be factored using this method.Therefore, the correct answer is E. All of the above.
what is the area of the smallest square?
The area of the smallest square is one quarter of the original square if its height and width are each half of the original.
Using geometrical shapes' proportional relationships, the area of a scaled-down square is calculated by squaring the factor by which the dimensions are reduced.
Explanation:The area of the smallest square can be determined by comparing it with the area of a larger square.
If the dimensions (height and width) of the smallest square are half that of the original square, then its area is a quarter (1/4) of the original square.
This is because area is a two-dimensional measurement, hence when both dimensions are halved, the area is reduced by a factor of 2×2, which equals 4.
For instance, if we consider a square with an area represented by T2, and we know that the smallest square has half the height and half the width, we can calculate its area as (1/2T)×(1/2T) = T2/4.
If the area of a larger square is 4 m2, halving the dimensions will lead to an area of 1 m2 for the smallest square.
This concept is applicable to any geometrical shape where the dimensions are reduced proportionally.
The scaling down of dimensions and the resulting area calculation is a key concept in understanding how areas of similar planar figures relate to each other.
Juan wants to start a lemonade stand to earn money.
He needs money to purchase the materials before he
can sell the lemonade and earn money. His mother
agrees to loan him $10. He makes a list of the items he
wants to buy.
Answer:
1. 13 2. 10
Step-by-step explanation:
A diver starts at the surface of the water and travels 8 feet to the bottom.
Graph A shows her distance from the bottom during the journey.
Graph B will show her distance from the surface during the journey.
Complete each statement about Graph B.
Answer:
On Graph B, at 0 seconds, the graph will be 0 or nothing.
Then the graph will increase until 2 seconds.
Answer:
On Graph B, at 0 seconds, the graph will be 0 or nothing.
Then the graph will increase until 2 seconds.
Step-by-step explanation:
Write an imequality” five times some number is less than 65”
Answer: 5x < 65
Step-by-step explanation: please give brainliest hope it helps and thankyou
Answer:
5x < 65
Step-by-step explanation:
Because 5*some number, you could use x. then the less than symbol means that 5x is less than 65
the solution to -2[1 - 4x] = 3x + 8 is
Answer: " 14 " .
________________________
→ " x = 14 " .
________________________
Step-by-step explanation:
________________________
First, let us simplify the expression on the "left-hand side" of the equation:
→ -2(1 −4x) ;
________________________
Note the "distributive property of multiplication" :
→ a(b + c) = ab + ac .
________________________
As such, we can rewrite:
→ -2(1 − 4x) = (-2)(1) + (-2)(-4x) ;
= - 2 + 8x ;
↔ 8x − 2 ;
________________________
Now, rewrite the entire expression:
→ 8x − 2 = 3x + 8 ;
________________________
Subtract "(3x)" from each side of the equation;
and add "2" to each side of the equation:
________________________
→ 8x − 2 − 3x + 2 = 3x + 8 − 3x + 2 ;
to get:
→ 5x = 10 ;
Now, divide each side of the equation by "5" ;
to isolate "x" on side of the equation;
& to solve for "x" ;
________________________
→ 5x/5 = 10/5 ;
to get:
________________________
→ x = 2 .
________________________
Now, let us check our work:
________________________
Plug in "2" for all "x-values" into the original equation;
to see if the equation holds true;
that is, to see if each side of the original equation given has the same value;
when "x = 2" :
________________________
Note the given equation:
________________________
→ -2[1 − 4x] = 3x + 8 ;
________________________
Start with the left-hand side:
→ -2[1 − (4*2)} = -2(1 − 8) = -2(-7) = 14 .
Now, continue with the right-hand side:
→ 3(2) + 8 = 6 + 8 = 14 .
___________________________________
→ 14 =? 14 ??? ; Yes!
___________________________________
Hope this is helpful to you!
___________________________________
Line A passes through points (10, 9) and (6, 2)
line B is parallel to line A . what is the slope of B ?
Answer:
7/4
Step-by-step explanation:
Parallel lines have the same slope, so all you have to do is find the slope of A.
The slope of A is (9-2)/(10-6) = 7/4
Answer:
7/4
Step-by-step explanation:
Have a nice day :)
HELP ASAP
1yd 1 ft=_____ya
A 1 1/2
B 1 1/12
C 1 1/3
D 1 1/6