Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
To find the length marked x, establish the ratio 0.5 inch/20 miles = 8 inches/x miles, cross-multiply, and solve for x to get x = 320 miles, making sure to round only after the final calculation step.
Explanation:To solve for the length labeled x, you would first need to set up the correct ratio. Given that the scale length is 8 inches and the corresponding actual length is unknown, the initial ratio would be 0.5 inch/20 miles = 8 inches/x miles. You can solve this proportion by cross-multiplication.
Following these steps:
Multiply 0.5 inch by x miles to get 0.5x inch-miles.Multiply 8 inches by 20 miles to get 160 inch-miles.Now you would set the products equal to each other: 0.5x = 160.Divide both sides by 0.5 to solve for x: x = 320 miles.Therefore, the unknown length x is 320 miles. Remember to always perform rounding off at the final step of your calculation to ensure accuracy.
The length of side [tex]\( x \)[/tex] is approximately 13.9 units when rounded to the nearest tenth.
To find the length of side [tex]\( x \)[/tex], we utilize the tangent function because it relates the opposite side to the adjacent side in a right-angled triangle. The tangent of [tex]\( 41^\circ \)[/tex] equals the ratio of side [tex]\( x \)[/tex] (the side opposite to [tex]\( 41^\circ \))[/tex] to 16 (the side adjacent to [tex]\( 41^\circ \))[/tex]:
[tex]\[ \tan(41^\circ) = \frac{x}{16} \][/tex]
To solve for [tex]\( x \)[/tex], we multiply both sides by 16:
[tex]\[ x = 16 \times \tan(41^\circ) \][/tex]
[tex]x=13.9[/tex]
The length of side [tex]\( x \)[/tex] is approximately 13.9 units when rounded to the nearest tenth.
list possible rational zeros of f using the rational zero theorem. Then find all thezeros of the function.
f(x)=x^3+ 4x^2+ 9x+36
1. (4.8x + 15.5) + (2.1x - 12.2)
2. (7x + 8) - (3x + 12)
3. (0.5x + 0.74) + (0.5x - .25)
Francine solves the system of equations using the linear combination method.
4x+3y=−1
3x−5y=4
Which steps would allow her to eliminate the x terms in the system of equations?
A. Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4 . Add the resulting equations together.
B. Multiply 4x+3y=−1 by 4. Multiply 3x−5y=4 by 3. Add the resulting equations together.
C. Multiply 4x+3y=−1 by 5. Multiply 3x−5y=4 by 3. Add the resulting equations together.
D. Multiply 4x+3y=−1 by −4 . Multiply 3x−5y=4 by 3. Add the resulting equations together.
Answer:
Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4 . Add the resulting equations together.
Step-by-step explanation:
Given the simultaneous equation below:
4x+3y=−1 ...(1) × 3
3x−5y=4 ...(2) × -4
Using elimination method to solve the problem,
Before we can eliminate x, the coefficient of x in both equation must have similar whole number as coefficient.
To make the coefficient equal, we will multiply equation 1 by 3 and equation 2 by -4 as shown above
The equations will then become
12x+9y = -3
-12x+20y = -16
Then we will add the resulting simultaneous equations.
The steps that would allow her to eliminate the x terms in the system of equations is to "Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4 . Add the resulting equations together"
What's the recursive formula for this sequence
The recursive formula for a geometric sequence is a₁=-4 and [tex]a_n}=6.a_{n-1}[/tex]. Therefore, option D is the correct answer.
What is a geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.
The given geometric sequence is -4, -24, -144, -864.
A recursive formula for a geometric sequence with common ratio r is given by [tex]a_n}=ra_{n-1}[/tex] for n≥2.
Here, a=-4 and r=-24/(-4) =6
So, recursive formula is [tex]a_n}=6.a_{n-1}[/tex]
Therefore, option D is the correct answer.
To learn more about the geometric sequence visit:
https://brainly.com/question/11266123.
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Please answer this! It confuses me. 20 points for it.
PLEASE HELP!!!!!!!!!!!!!!
4.
(08.02 HC)
The function f(x) = −x2 + 44x − 384 models the daily profit, in dollars, a shop makes for selling cake ball combos, where x is the number of combos sold and f(x) is the amount of profit.
Part A: Determine if this function has a maximum or a minimum value. How did you know? (2 points)
Part B: Determine the vertex. What does this calculation mean in the context of the problem (hint: compare the profit they are making (f(x)) vs. the sales (x))? Show your work for finding the vertex. (4 points)
Part C: Determine the x-intercepts. What do these values mean in the context of the problem? Show your work for finding the x-intercepts. (4 points)
add and simplify : x+1/x+2 add 2x+15/x+2
Your friend earns $10.50 per hour this is 125% of her hourly wage last year how much did your friend make last year
Please help!!
Shiloh has to earn at least $200 to meet her fundraising goal. She has only 100 cakes that she plans to sell at 5 dollars each. Which inequality shows the number of cakes, x, Shiloh can sell to meet her goal?
20 ≤ x ≤ 200
40 ≤ x ≤ 100
100 ≤ x ≤ 200
20 ≤ x ≤ 100
Thank you in advance.
~Micah K.,
Could I get some help with this question on Trigonometric Identities?
Compare the values of the underlined digits.
6,300 and 530
the value of 3 in ______is _____times the value of 3 in _____
To solve this problem, you have to determine the value of the number 3 in both numbers:
6,300 – the number 3 is in the hundreds place so its value is 300
530 – the number 3 is in the tens place so its value is 30
To answer the question, the value of 3 in 6,300 is 10 times the value of 3 in 530.
PLEASE HELP
8.08, part 2
11. Find an equation in standard form for the hyperbola with vertices at (0, ±6) and foci at (0, ±9).
A) y squared over 45 minus x squared over 36 = 1
B) y squared over 81 minus x squared over 36 = 1
C) y squared over 36 minus x squared over 81 = 1
D) y squared over 36 minus x squared over 45 = 1
12. Find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ± 1 divided by 4. x.
A) y squared over 16 minus x squared over 64 = 1
B) y squared over 16 minus x squared over 256 = 1
C) y squared over 256 minus x squared over 16 = 1
D) y squared over 64 minus x squared over 4 = 1
13. Eliminate the parameter.
x = t - 3, y = t2 + 5
A) y = x2 + 6x + 14
B) y = x2 - 14
C) y = x2 - 6x - 14
D) y = x2 + 14
14. Find the rectangular coordinates of the point with the polar coordinates.
ordered pair 3 comma 2 pi divided by 3
A) ordered pair negative 3 divided by 2 comma 3 square root 3 divided by 2
B) ordered pair 3 square root 3 divided by 2 comma negative 3 divided by 2
C) ordered pair negative 3 divided by 2 comma 3 divided by 2
D) ordered pair 3 divided by 2 comma negative 3 divided by 2
15. Find all polar coordinates of point P where P = negative pi divided by 6 .
A) (1, negative pi divided by 6 + (2n + 1)π) or (-1, negative pi divided by 6 + 2nπ)
B) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ)
C) (1, negative pi divided by 6 + 2nπ) or (1, pi divided by 6 + (2n + 1)π)
D) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + (2n + 1)π)
16. Determine two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°.
A) (4 square root 2 , 135°), (-4 square root 2 , 315°)
B) (4 square root 2 , 45°), (-4 square root 2 , 225°)
C) (4 square root 2 , 315°), (-4 square root 2 , 135°)
D) (4 square root 2 , 225°), (-4 square root 2 , 45°)
17. The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph.
a circular graph with an inner loop on the left
[-5, 5] by [-5, 5] (5 points)
A) r = 3 + 2 cos θ
B) r = 2 + 3 cos θ
C) r = 2 + 2 cos θ
D) r = 4 + cos θ
18. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = -2 + 3 cos θ
A) No symmetry
B) y-axis only
C) x-axis only
D) Origin only
19. A railroad tunnel is shaped like a semiellipse, as shown below.
A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis.
The height of the tunnel at the center is 54 ft, and the vertical clearance must be 18 ft at a point 8 ft from the center. Find an equation for the ellipse.
20. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 2 cos 3θ
Answer:
11. Equation of hyperbola having vertices at (0, ±6) and foci at (0, ±9).
is given by [tex]\frac{y^2}{a^2}- \frac{x^2}{b^2}=1[/tex]
also b²= c²-a²
b²=81-36
b²=45
So, Equation becomes , [tex]\frac{y^2}{36}- \frac{x^2}{45}=1[/tex]
Option (D) is correct.
12.Vertices (0, ± 4), Asymptotes = ±1/4.x
equation of asymptote is given by, [tex]x = \pm y \frac{b}{a}[/tex]
[tex]\frac{4}{b}=\frac{1}{4}[/tex]
So a=4 and b=16,
So , equation becomes [tex]\frac{y^2}{16}- \frac{x^2}{256}=1[/tex]
Option (B) is correct.
13. x= t-3, and y = t²+ 5
Replace t by x+3, we get
y= (x+3)² +5
y=x²+ 6x +14
Option (A) is correct.
14. Polar coordinates is given by (r,∅)
Polar coordinates of point is (3, 2π/3)
So, r =3, ∅ =2π/3
x= r cos∅ and y = r sin∅
x=3 Cos (2π/3) and y= 3 Sin (2π/3)
x= -3/2 and y=3√3/2
Option (A) is correct.
14. Polar coordinate is given by (r,∅)
Here , r=1, and ∅ = -π/6
x= r Cos ∅ and y =r Sin∅
x= 1 Cos (-π/6) and y= 1 Sin (-π/6)
x =√3/2 and y =1/2
Option (B) which is B) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ) is correct.
16. Two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°.
is option (B) which is B) (4 square root 2 , 45°), (-4 square root 2 , 225°).
17. A circular graph with inner loop on the left of a limacon curve is given by
r = a + b Cos∅.
In this case a> b.
So , Option (D) r = 4 + cos θ as well as (A) r = 3 + 2 cos θ looks correct.
18. Equation of limacon curve is given by r = -2 + 3 cos θ, here , a<b
So it is symmetric about y-axis only.Option (B) is correct.
We toss two coins and observe the upper faces of the coins.
a.observe at least one head
b.observe at least one tail what is the probability that both a and b occur? what is the probability that a or b or both events occur?
What is the value of n?
Enter your answer in the box.
n = cm
Answer:
15cm
Step-by-step explanation:
i had the same question but difrent if you know what i mean. in mine you solved it for me in your picture of 6.
Which of the following expressions represents "twelve diminished by six times a number"?
A: 12-6n
B: 6n-12
C: 12n-6
four times the sum of g+6 is equal to thirty-six what is the value of g? huh
What ratio is equivalent to 4: 32?
1 : 8
1 : 6
3 : 16
8 : 60
Yani buys a certain brand of cereal that costs $10 per box. Yani changes to a super-saving brand of the same size. The equation shows the price, y, as a function of the number of boxes, x, for the new brand.
y = 7x
Part A: How many more $'s is the price of a box of Yani's original brand of cereal than the price of a box of the super-saving cereal? Show your work.
Part B: How much money does Yani save each month with the change in cereal brand if he buys 5 cereal boxes each month? Show your work.
How do u do this? PLz show work!!!!
Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent?
PLEASE ANSWER FAST I HAVE 5 MINUTES LEFT ON THIS TEST
SSS
AAS
SAS
HL
TIMER CAN SOMEBODY HELP ME???
Describe how the value of n affects the shape of the binomial probability histogram. choose the correct answer below.
a. as n decreases, the binomial distribution becomes skewed left.
b. as n increases, the binomial distribution becomes skewed right.
c. as n increases, the binomial distribution becomes more bell shaped.
d. as n decreases, the binomial distribution becomes more bell shaped.
e. the value of n does not affect the shape of the binomial probability histogram
Final answer:
The value of n, or the number of trials in a binomial experiment, affects the shape of the binomial probability histogram. As n increases, the histogram becomes more symmetric and bell-shaped, reflecting the Central Limit Theorem. The correct answer is (c): as n increases, the binomial distribution becomes more bell-shaped.
Explanation:
The shape of the binomial probability histogram is indeed influenced by the value of n, which stands for the number of trials in a binomial experiment. As the value of n increases, the distribution becomes more symmetrical and tends to resemble a normal distribution. Specifically, the correct statement regarding the effect of n on the shape of the histogram is: as n increases, the binomial distribution becomes more bell-shaped. Therefore, the correct answer to the student's question is (c).
When the sample size n is small, the histogram may appear skewed left or right, depending on the probability of success p. However, as n becomes larger (especially when both np and n(1-p) are greater than 5), the distribution's shape becomes more symmetric due to the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases.
Solve 3x2 − x = 10
x = 2 and x = −15
x = −5 and x = two over three
x = − five over three and x = 2
x = −3 and x = 10
The correct solution of the quadratic equation 3x^2 - x = 10 is found using the quadratic formula, giving two solutions x = -5/3 and x = 2.
Explanation:The equation given is 3x2 − x = 10, which is a quadratic equation that needs to be rearranged to the standard form ax2 + bx + c = 0.
First, we subtract 10 from both sides of the equation, resulting in 3x2 − x − 10 = 0. Now, we can use the quadratic formula:
x = −b ± √(b2 - 4ac) / (2a)
Substituting the values a = 3, b = −1, and c = −10 into the formula yields:
x = −(−1) ± √((−1)2 - 4 × 3 × (−10)) / (2 × 3)
This simplifies to:
x = 1 ± √(1 + 120) / 6
Which further simplifies to:
x = 1 ± √121 / 6
And results in:
x = 1 ± 11 / 6
Therefore, the two solutions are:
x = 2 (1 + 11 / 6)
x = − five over three (1 − 11 / 6)
Hence, the correct answer is x = − five over three and x = 2.
The quadratic equation 3x^2 - x = 10 is solved via the quadratic formula, resulting in two solutions: x = 2 and x = -5/3 (or -1.67 when expressed as a decimal).
Explanation:To solve the quadratic equation 3x2 − x = 10, we first need to set it to zero by subtracting 10 from both sides, yielding 3x2 − x − 10 = 0. This is a standard form quadratic equation, ax2 + bx + c = 0, where a = 3, b = -1, and c = -10. We can solve for x by using the quadratic formula, x = ∛ ( b2 - 4ac ) / (2a).
Plugging in our values, we get:
x = (-(-1) ± √ ( (-1)2 - 4(3)(-10) ) ) / (2(3))
x = (1 ± √ ( 1 + 120) ) / 6
x = (1 ± √ (121) ) / 6
x = (1 ± 11) / 6
Thus:
x = (1 + 11) / 6 = 12/6 = 2x = (1 - 11) / 6 = -10/6 = − five over three or approximately -1.67Therefore, the solutions are x = 2 and x = -5/3.
Y=4x^2-1 find the inverse. I cant it’s to difficult.
A lawn is in the shape of a trapezoid with a height of 7070 feet and bases of 4040 feet and 160160 feet. how many full bags of fertilizer must be purchased to cover the lawn if each full bag covers 40004000 square feet and only full bags of fertilizer can be bought?
on sunday, Antonio spent a total of 3 1/4 hours driving and 1 3/4 hours gardening. How much longer did he spend driving than gardening? write as a mix number.
Answer:
1 1/2 hours
Step-by-step explanation:
Time spent by Antonio in driving = 3 1/4 = 13/4
Time spent in gardening = 1 3/4 = 7/4
In order to find how much he spend driving than gardening, we can subtract 13/4 and 7/4.
[tex]\frac{13}{4}-\frac{7}{4}[/tex]
Te denominator is same. So, we can directly subtract the numerators.
[tex]\frac{13-7}{4}\\\\=\frac{6}{4}\\\\=\frac{3}{2}=1\frac{1}{2}[/tex]
Therefore, Antonio spent 1 1/2 hours more in driving than gardening.
PLEASE MATH HELP WILL GIVE BRAINLIEST!!!!!
In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 5 in.?
√5 in.
5√5 in.
2√5 in.
5√2 in.
You bought one skirt at $18.27, two shirts at $15.78, and a pair of shoes at $34.50. if the tax rate is 7%, what is the total cost of your purchase?
To determine the total cost including sales tax, first calculate the subtotal of the items, then apply the 7% tax rate to this subtotal. After adding the sales tax to the subtotal, the final cost comes to $90.23.
Explanation:To calculate the total cost of your purchase including sales tax, first figure out the total cost of the items before tax. You bought one skirt at $18.27, two shirts at $15.78 each, and a pair of shoes at $34.50. The cost of the shirts needs to be doubled since you bought two. Then, apply the 7% sales tax to the subtotal to find the overall total.
Skirt: $18.27Shirts: $15.78 × 2 = $31.56Shoes: $34.50Subtotal before tax: $18.27 + $31.56 + $34.50 = $84.33
To calculate the sales tax, convert the tax rate to a decimal (7% = 0.07) and multiply by the subtotal: $84.33 × 0.07 = $5.90 (rounded to the nearest cent).
Add the sales tax to the subtotal for the total cost: $84.33 + $5.90 = $90.23.
Therefore, the total cost of your purchase after including the 7% sales tax is $90.23.
Mrs. Green invested $10,000 in mutual fund for a period of 6 years. At the end of 6 years, she received a total amount of $25,000. Calculate the ROI and write the answer in the space provided.
Answer:
ROI = 150
Step-by-step explanation:
ROI = (25,000-10,000)/10,000 ×100=150