Step-by-step explanation:
a) Let 'm' represents score in a Mathematics test. The variable has a fixed value because the marks Sarah obtained in her test will not change
b) Let 'd' represent the distance between the Zen house and the school. The variable has a fixed value because by using the same route, the distance will always remain constant.
c) Let 't' represent the temperature on the summit of Mount Everest. The variable has a changed value because the temperature may alter depending on the time of day and also climatic conditions which will affect the temperature.
The angle \theta_1θ
1
theta, start subscript, 1, end subscript is located in Quadrant \text{II}IIstart text, I, I, end text, and \cos(\theta_1)=-\dfrac{12}{19}cos(θ
1
)=−
19
12
cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, minus, start fraction, 12, divided by, 19, end fraction .
What is the value of \sin(\theta_1)sin(θ
1
)sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Answer:
[tex]sin\theta_1 = \dfrac{\sqrt{217}}{19}[/tex]
Step-by-step explanation:
It is given that:
[tex]cos\theta_1 = -\dfrac{12}{19}[/tex]
And we have to find the value of [tex]sin\theta_1 = ?[/tex]
As per trigonometric identities, the relation between [tex]sin\theta\ and \ cos\theta[/tex] can represented as:
[tex]sin^2\theta + cos^2\theta = 1[/tex]
Putting [tex]\theta_1[/tex] in place of [tex]\theta[/tex] Because we are given
[tex]sin^2\theta_1 + cos^2\theta_1 = 1[/tex]
Putting value of cosine:
[tex]cos\theta_1 = -\dfrac{12}{19}[/tex]
[tex]sin^2\theta_1 + (\dfrac{12}{19})^2 = 1\\\Rightarrow sin^2\theta_1 + \dfrac{144}{361} = 1\\\Rightarrow sin^2\theta_1 = 1-\dfrac{144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{217}{361}\\\Rightarrow sin\theta_1 = +\sqrt{\dfrac{217}{361}}, -\sqrt{\dfrac{217}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{\sqrt{217}}{19}, -\dfrac{\sqrt{217}}{19}[/tex]
It is given that [tex]\theta_1[/tex] is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.
[tex]\Rightarrow sin\theta_1 = \dfrac{\sqrt{217}}{19}[/tex]
Answer:
− square root 15/4
Step-by-step explanation:
A rectangle or prism with a volume of three cubic units is filled with Cubes with side length of one for a few how many 1/4 unit does it take to fill the prism
Answer:
192 cubes.
Step-by-step explanation:
The volume of each cube = (side)³ = (1/4)³ = 1/64 units ³
Next is to find how many cubes are needed to fill the prism.
The number of cubes that will fill the prism :
Vol. of prism / Vol. of cube = 3 / [tex]\frac{1}{64}[/tex]
=192 cubes.
Therefore, it takes 192 cubes to fill the prism.
There are 300 boys in a mixed school. If the ratio of the boys to the girls is 4:5 what is the total number of students in the school?
｡☆✼★ ━━━━━━━━━━━━━━ ☾
4 : 5
300 : ?
Divide 300 by 4 to find out what '1 part' would count as:
300/4 = 75
Multiply this by 5
75 x 5 = 375
Add the two values together
375 + 300 = 675
There are 675 students
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Step-by-step explanation:
Number of boys=300
Ratio of boys to girls=4:5
let the number of girls=y
300/y=4/5
Cross multiply
300×5=4×y
1500=4y
Divide through both sides by 4
1500/4=4y/4
374=y
Number of girls is 375
Total number of students=Number of boys+Number of girls
Total number of students=300+375
Total number of students=375
A concrete driveway is 5 feet longer than twice its width. It has a brick walkway 3 feet wide on the front and side of the driveway. The area of the brick walkway is 213
square feet. Find the dimensions of the driveway.
Answer:
The dimensions of the driveway are 21 ft x 47 ft, which is option "D" in your list of possible answers
Step-by-step explanation:
Notice that the length "L" of the driveway can be written in terms of its width as:
L = 2 w + 5
based on the given information.
Please see the attached diagram to understand the geometry of the problem, and what the area of the brick walkway involves (depicted in brick color) as the addition of the area of two rectangles:
1) one of length L= 2 w + 5 (w being the width of the driveway - depicted in grey) times 3 feet (the width of the brick walkway
and the other one:
2) w + 3 times 3
Therefore the total area of the brick walkway is given by the formula:
(2 w + 5) * 3 +(w + 3) * 3 = 213 square feet
Now we can solve for "w" in the above equation:
6 w + 15 + 3 w + 9 = 213
9 w + 24 = 213
9 w = 213 - 24
9 w = 189
w = 189/9
w = 21 feet
We can now solve for the L of the driveway, using the first formula we created:
L = 2 w + 5
L = 2 (21) + 5
L = 42 + 5
L = 47 feet
Therefore the driveway's width is w = 21 feet
and its length is L = 47 feet
(8 + 2 x 6)2 =
the two at the end before the equals is a squared number is a small 2
The expression [tex](8 + 2 \times 6)^2[/tex], following PEMDAS, simplifies to 400.
Let's break down the steps in solving the expression [tex](8 + 2 \times 6)^2[/tex] in more detail (Follow PEMDAS).
Step 1: MultiplicationWe start by evaluating the multiplication operation, which is 2 x 6. The result of this operation is 12.
Step 2: AdditionNext, we evaluate the addition operation, which is 8 + 12. The sum of 8 and 12 is 20.
Step 3: SquaringFinally, we square the result of the addition, which is 20. Squaring a number means multiplying it by itself. In this case, [tex]20^2[/tex] means 20 multiplied by 20, which equals 400.
Therefore, the expression [tex](8 + 2 \times 6)^2[/tex] simplifies to 400.
Learn more about PEMDAS here:
https://brainly.com/question/36185
#SPJ4
Please answer correctly !!!!!!!!! Will mark brianliest !!!!!!!!!!!!
Answer:
g(x) has a greater y intercept than f(x)
Step-by-step explanation:
f(x) = 6x^2 + 18x +3
f(0) = 0+0+3
The y intercept is 3
g(x) crosses the y axis at 6
The y intercept is 6
g(x) has a greater y intercept than f(x)
Answer:
g(x) has a greater y intercept than f(x)
Step-by-step explanation:
f(x) = 6x^2 + 18x +3
f(0) = 0+0+3
The y intercept is 3
g(x) crosses the y axis at 6
The y intercept is 6
g(x) has a greater y intercept than f(x)
hope I could help
Match the parabolas represented by the equations with their foci.
Answer:
Step-by-step explanation:
Before we begin this, there are a few things that need to be said and a few formulas you need to know. First is that we need to use the work form of a parabola, which is
[tex]y=a(x-h)^2+k[/tex]
All of the parabolas listed in blue highlight open either up or down, and this work form represents those 2 options. The only thing we need to know is that if there is a negative sign in front of the a, the parabola opens upside down like a mountain instead of up like a cup.
Another thing we need to know is how to find the focus of the parabola. The formula to find the focus for an "up" parabola is (h, k + p) and the formula to find the focus for an upside down parabola is (h, k - p). Then of course is the issue on how to find the p. p is found from the a in the above work form parabola, where
[tex]p=\frac{1}{4|a|}[/tex] .
In order to accomplish what we need to accomplish, we need to put each of those parabolas into work form (as previously stated) by completing the square. I'm hoping that since you are in pre-calculus you have already learned how to complete the square on a polynomial in order to factor it. Starting with the first one, we will complete the square. I'll go through each step one at a time, but will provide no explanation as to how I got there (again, assuming you know how to complete the square).
[tex]y=-x^2+4x+8[/tex] and, completing the square one step at a time:
[tex]-x^2+4x=-8[/tex] and
[tex]-(x^2-4x+4)=-8-4[/tex] and
[tex]-(x-2)^2=-12[/tex] and
[tex]-(x-2)^2+12=y[/tex]
From this we can see that the h and k values for the vertex are h = 2 and k = 12. Now to find p.
[tex]|a|=1[/tex], ∴
[tex]p=\frac{1}{4(1)}=\frac{1}{4}[/tex]
Using the correct focus formula (h, k - p), we get that the focus is
[tex](2, 12-\frac{1}{4})[/tex] which simplifies to (2, 11.75) which is choice 2 in your options.
Now for the second one (yes, this takes forever...)
[tex]y=2x^2+16x+18[/tex] and completing the square one step at a time:
[tex]2x^2+16x=-18[/tex] and
[tex]2(x^2+8x+16)=-18+32[/tex] and
[tex]2(x+4)^2=14[/tex] and
[tex]2(x+4)^2-14=y[/tex]
From this we can see that the vertex is h = -4 and k = -14. Now to find p from a.
[tex]|a|=2[/tex], ∴
[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex] .
Using the correct focus formula for an upwards opening parabola (h, k + p),
[tex](-4, -14+\frac{1}{8})[/tex] which simplifies down to (-4, -13.875) which is choice 3 in your options.
Now for the third one...
[tex]y=-2x^2+5x+14[/tex] and completing the square step by step:
[tex]-2x^2+5x=-14[/tex] and
[tex]-2(x^2-\frac{5}{2}x+\frac{25}{16})=-14-\frac{50}{16}[/tex] and
[tex]-2(x-\frac{5}{4})^2=-\frac{137}{8}[/tex] and
[tex]-2(x-\frac{5}{4})^2+\frac{137}{8}=y[/tex]
From that we can see the vertex values h and k. h = 1.25 and k = 17.125. Now to find p.
[tex]|a|=2[/tex], ∴
[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]
Using the correct focus formula for an upside down parabola (h, k - p),
[tex](1.25, 17.125-\frac{1}{8})[/tex] which simplifies down to (1.25, 17) which is choice 4 in your options.
Now for the fourth one...
[tex]y=-x^2+17x+7[/tex] and completing the square step by step:
[tex]-x^2+17x=-7[/tex] and
[tex]-(x^2-17x)=-7[/tex] and
[tex]-(x^2-17x+72.25)=-7-72.25[/tex] and
[tex]-(x-8.5)^2=-79.25[/tex] and
[tex]-(x-8.5)^2+79.25=y[/tex]
From that we see that the vertex is h = 8.5 and k = 79.25. Now to find p.
[tex]|a|=1[/tex], ∴
[tex]p=\frac{1}{4(1)}=\frac{1}{4}[/tex]
Using the correct formula for an upside down parabola (h, k - p),
[tex](8.5, 79.25-\frac{1}{4})[/tex] which simplifies down to (8.5, 79) and I don't see a choice from your available options there.
On to the fifth one...
[tex]y=2x^2+11x+5[/tex] and again step by step:
[tex]2x^2+11x=-5[/tex] and
[tex]2(x^2+\frac{11}{2}x+\frac{121}{16})=-5+\frac{242}{16}[/tex] and
[tex]2(x+\frac{11}{4})^2=\frac{81}{8}[/tex] and
[tex]2(x+\frac{11}{4})^2-\frac{81}{8}=y[/tex]
from which we see that h = -2.75 and k = -10.125. Now for p.
[tex]|a|=2[/tex], ∴
[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]
Using the correct focus formula for an upwards opening parabola (h, k + p),
[tex](-2.75, -10.125+\frac{1}{8})[/tex] which simplifies down to (-2.75, -10) which is choice 1 from your options.
Now for the last one (almost there!):
[tex]y=-2x^2+6x+5[/tex] and
[tex]-2x^2+6x=-5[/tex] and
[tex]-2(x^2-3x+2.25)=-5-4.5[/tex] and
[tex]-2(x-1.5)^2=-9.5[/tex] and
[tex]-2(x-1.5)^2+9.5=y[/tex]
from which we see that h = 1.5 and k = 9.5. Now for p.
[tex]|a|=2[/tex], ∴
[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]
Using the formula for the focus of an upside down parabola (h, k - p),
[tex](1.5, 9.5-\frac{1}{8})[/tex] which simplifies down to (1.5, 9.375) which is another one I do not see in your choices.
Good luck with your conic sections!!!
a store employees 11 women and 12 men.what percentage of employees are men?
Answer:
easy just find the total of how many people work there then put that no. as a denominator and put 12 on the numerator then times it by 100 and the answer should be 52.2% or 52.17%
Answer:
52.2% or 52.17%
12 men
Total = 23
12 / 23 =
Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!
Answer:
25
Step-by-step explanation:
To find the constant
take the coefficient of x
10
divide by 2
10/2 =5
Square it
5^2 =25
Add this
x^2 +10x+25
What are the solutions of 2x²-6x+5=0?
Answer:
D
Step-by-step explanation:
a = 2 ; b = -6 ; c = 5
[-b±√b²-4ac]/2a=[-(-6)±√6²-4*2*5]/2*2
=[6±√√36-40]/4
=[6±√-4]/4
=[6±√i²*2²]/4
=[6±2i]/4
=2[3±i]/4
=3±i/2
= 3+i/2 or 3-i/2
What is the answer to this problem.
Answer:
[tex]2a^2 + 3x - 2a[/tex]
Step-by-step explanation:
[tex] (6a^2 + 3x) - (4a^2 + 2a) = [/tex]
The first set of parentheses is unnecessary and can be removed.
[tex] = 6a^2 + 3x - (4a^2 + 2a) [/tex]
To remove the second set of parentheses, you must distribute the negative sign to its left as if it were a -1 multiplying the quantity inside the parentheses.
[tex] = 6a^2 + 3x - 1(4a^2 + 2a) [/tex]
[tex] = 6a^2 + 3x - 4a^2 - 2a [/tex]
Now combine like terms. Like terms are terms with the same variable part.
[tex] = 2a^2 + 3x - 2a [/tex]
PLZ HELP! WILL GIVE BRAINIEST!!
Answer:
i think its c idk if im wrong im sorry
Step-by-step explanation:
A 20-foot ladder leans against a wall so that it is 16 feet high at the top. The ladder is moved so that the base of the ladder travels toward the
wall twice the distance that the top of the ladder moves up. How much higher is the top of the ladder now? (Hint Let 12 – 2x be the distance from
the base of the ladder to the wall.)
х
2x
The top of the ladder is
feet higher now.
Answer:
3.2 ft
Step-by-step explanation:
The initial distance from the base of the ladder to the wall is:
[tex]20^2=16^2+d^2\\d=12\ ft[/tex]
After moving the ladder, the distance from the base to the wall is 12 - 2x while the height of the ladder is 16 + x. The distance x is given by:
[tex]20^2 = (12-2x)^2+(16+x)^2\\400 = 144-48x+4x^2+256+32x+x^2\\5x^2-16x=0\\5x=16\\x=3.2\ ft[/tex]
Therefore, the top of the ladder is 3.2 ft higher now.
Answer:
3.2ft higher
Step-by-step explanation:
A contractor is building a circular swimming pool. The radius of the circle 12 feet. He needs to know the
circumference in order to buy tile to put around the edge of the pool.
What is the circumference if he uses n=2217 ?
Answer:
75.41 ftStep-by-step explanation:
This problem is on the mensuration of flat shape, a circle.
we know that the circumference of a circle is expressed as
[tex]C= 2\pi r[/tex]
Given that radius = 12 ft
The circumference can be solved for by substituting the value of r in the formula
C=2*3.142*12
C= 75.408ft
to 2 d.p the circumference is 75.41 ft
A bag contains 9 red marbles, 18 orange marbles, 2 yellow marbles, and 5 purple marbles. A marble is drawn at random from the bag. What is the probability that the marble drawn will not be orange?
Answer:
8/17
Step-by-step explanation:
total balls= 9 + 18 + 2 + 5 = 34
balls drawn should NOT be Orange.
so, 34 - 18 (as there are 18 orange balls)
16 balls
probability= 16/34 = 8/17
answer = 8/17
A boy saves up $79 for a gift for his friend. However, upon reaching the store, he realizes that he saved 257% of the actual amount he needed to buy the present. How much does the present cost? Round to the nearest cent.
Hint: This is a Part = Percent × Whole problem.
You're given the part (79) and the percent (257%, or 2.57).
Substitute these into the equation to find the whole.
Answer:
$30.74
Step-by-step explanation:
Easy points for y’all mathy people, fairly easy question. It’s in the photo!!
Answer:
W
Step-by-step explanation:
The input is the x-axis.
The output is the y-axis.
Make them coordinates. Hope this helped!
Originally the dimensions of a rectangle were 20cm by 23cm. When both dimensions were decreased by the same amount, the area of the rectangle decreases by 120. Find the dimensions of the rectangle.
^^^
Quickly answer please
Answer:
400
Step-by-step explanation:
help me help me help me asap
Answer:
9 cubic feet
Step-by-step explanation:
Assuming that the garden box is a rectangular prism, its volume is:
[tex]4\dfrac{1}{2} \cdot 4 \cdot \dfrac{1}{2}=9 \text{ ft}^3[/tex]
Hope this helps!
Solution,
Length(L)=4 1/2 ft
Breadth(b)= 4 ft
Height(H)=1/2 ft
Now,
Volume=L*B*H
= 4 1/2*4*1/2
=9/2*4*1/2
= 9 cubic feet
Hope it helps
Good luck on your assignment
Felipe is working to find the quotient of 6 and 3/4
Answer:
Felipe's answer is 8.
6 divided by 3/4
= 6 * 4/3
= 24/3
= 8
Answer:
8
Step-by-step explanation:
6÷3/4=6×4/3=8
Justin and Alexis were Dave and Busters. What you need to pay an initial fee of $ 5.00 and a price per game. Justin played 5 games and paid $ 12.50 in total. Alexis played 7 games and paid $ 15.25 in total. We can express the relationship between the number of games played and the total cost with the ordered pairs (5, 12.75) and (7, 15.25).
Find the rate of change and explain the importance of the rate of change in terms of the problem.
Answer:
The equation of the relationship is y = 1.25x + 6.5
Step-by-step explanation:
I graphed the ordered pairs on the graph below and found the slope and y-intercept of the line.
The price per game is $7.75. (If needed)
Brainliest question please help me answer my question please
Answer:
Step-by-step explanation:
The area for a trapezoid is
[tex]A=\frac{1}{2}h(b_{1}+b_{2})[/tex]
h is the length of ST, one of the bases is the length of MK, and the other base is the length of AS. First we'll find h:
The coordinates for S are (0, -2) and T are (1, 2). Using the distance formula:
[tex]d=\sqrt{(1-0)^2+(2-(-2))^2[/tex] and
[tex]d=\sqrt{17}[/tex]. So h = √17
Now for the length of MK. The coordinates for M are (-7, 4) and for K (5, 1). Using the distance formula again:
[tex]d=\sqrt{(-7-5)^2+(4-1)^2}[/tex] and
[tex]d=\sqrt{(-12)^2+(3)^2}[/tex] so
[tex]d=\sqrt{153}[/tex] which simplifies to
[tex]d=3\sqrt{17}[/tex]. So MK = 3√17.
Now for the length of AS. The coordinates for A: (-4, -1) and for S: (0, -2). Using the distance formula one more time:
[tex]d=\sqrt{(-4-0)^2+(-1-(-2))^2}[/tex] and
[tex]d=\sqrt{(-4)^2+(1)^2}[/tex] and
[tex]d=\sqrt{17}[/tex]. So AS = √17.
Now we can fill in our area formula:
[tex]A=\frac{1}{2}(\sqrt{17})(3\sqrt{17}+\sqrt{17})[/tex]
Simplifying a bit:
[tex]A=\frac{1}{2}(\sqrt{17})(4\sqrt{17})[/tex] and simplifying a bit more:
[tex]A=\frac{4*17}{2}[/tex] and
A = 34
Draw the following lines and label them with the matching letter. Then write an equation for each. Slope is 0, y-intercept is 5 Slope is 2, y-intercept is -1 Slope is -2, y-intercept is 1 Slope is -12, y-intercept is -1
Answer:
See explaination:
Graphs are on the right, equations are on the left, and they are color coded.
Step-by-step explanation:
Which equation is equivalent to the following?
4x^2 + 4y^2 +16x – 24y = 34
Please answer it:(
Answer:
The correct answer is the third expression.
Step-by-step explanation:
We have the following equation:
[tex]4*x^2 + 4*y^2 + 16*x - 24*y = 34[/tex]
Let's organize it by variables, putting together the ones that have the same letter or no letter at all. We have:
[tex]4*x^2 + 16*x + 4*y^2 - 24*y = 34[/tex]
We can extract the common factor on the left side by dividing them by 4, we have:
[tex]4*(x^2 + 4*x) + 4*(y^2 - 6*y) = 34[/tex]
We need to complete the squares on the parenthesis without changing the value of the equation, to do that we will sum the proper values inside the parenthesis and those multiplied by four on the other side of the equation, we have:
[tex]4*(x^2 + 4*x + 4) + 4*(y^2 - 6*y + 9) = 34 + 16 + 36\\4*(x + 2)^2 + 4*(y - 3)^2 = 86[/tex]
The correct answer is the third expression.
Find the circumference of the circle to the nearest hundredth. Use 3.14 for π. Radius 21 cm.
Answer:
[tex]131.95[/tex] [tex]cm[/tex]
Step-by-step explanation:
[tex]C=2 \pi r[/tex]
[tex]C=2 \pi \times 21[/tex]
[tex]C=42\pi[/tex]
[tex]C \approx 131.946891451[/tex]
Somebody, please help me!! I will mark the brainiest
Answer:
65 = <JKL
Step-by-step explanation:
There are two expressions that represent the same thing.
The diagram shows that <JKL = 45 + x
The question states that JKL = 3x + 5
The two expressions must be equal since they represent the same thing.
3x + 5 = x + 45
Subtract 5 from both sides
3x + 5 - 5 = x + 45 - 5
3x = x + 40 Subtract x from both sides
3x - x = x - x + 40
2x = 40 Divide by 2
2x/2 = 40/2
x = 20
So x + 45 = 20 + 45 = 65
or
3x + 5 = 3*20 + 5 = 60 + 5 = 65
All i have to ask is what is this polygon or figure called ???? Picture is supplied
Answer:
Step-by-step explanation:
rectangle + semicircle
= 8*6 + pi r^2/2
=48 + 22/7 * 3/2 * 3/2
then simplyn..
Answer:
The figure is a rectangle and a semicircle
Step-by-step explanation:
Which is the best description of the equivalency of the two expressions?
Expression 1
Expression 2
5 x squared minus 2 x minus 4 + 6 x + 3
6 x squared minus 6 x + 6 minus x squared + 10 x minus 7
Answer:
The answer is option D
Took the quiz
Answer: They are equivalent because when x=2, the two expressions have the same value.
Step-by-step explanation:
Question attached Simultaneous equations
Answer:
9 spoons knives =12
9 spoons cost= £ 82.80
total no of 1 knife = 12x9 = 108
1 knife = 82.80 x 108 = 8,94, 240
so, 1 knife Cost's =£ 8,94,240
