They plan to clean the street for 3 hours.
They plan to clean the park for 3 hours.
How many hours do they plan to clean the street and the park?The first step is to set up a set of linear equations that describe the information in the question.
3p + 6s = 27 equation 1
6p + 8s = 42 equation 2
Where:
p = number of hours spent cleaning one park
s = number of hours spent cleaning on street
In order to determine the value of s, take the following steps:
Multiply equation 1 by 2
6p + 12s = 54 equation 3
Subtract equation 2 from equation 3
4s = 12
Divide both sides of the equation by 4
s = 12 / 4
s = 3 hours
Substitute for s in equation 1:
3p + 6(3) = 27
3p + 18 = 27
3p = 27 - 18
3p = 9
p = 9/3
p = 3
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Help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee.
In the given diagram, we have a pair of parallel lines intersected by a transversal line. To determine the relationship between the angles and solve for x, we can use the properties of angles formed by parallel lines and a transversal.
From the diagram, we can observe the following angle relationships:
Angle A is alternate interior to the angle (4x - 10)°.
Therefore, we can write: A = (4x - 10)°.
Angle B is corresponding to the angle (4x - 10)°.
Therefore, we can write: B = (4x - 10)°.
Angle C is alternate interior to the angle 2x°.
Therefore, we can write: C = 2x°.
Angle D is corresponding to the angle 2x°.
Therefore, we can write: D = 2x°.
Since the sum of angles in a straight line is 180°, we can set up the equation:
A + B + C + D = 180°
Substituting the known values, we get:
(4x - 10)° + (4x - 10)° + 2x° + 2x° = 180°
Simplifying the equation, we can solve for x:
8x - 20 + 4x + 4x = 180
16x - 20 = 180
16x = 200
x = 12.5
Therefore, the value of x is 12.5.
Please note that this solution assumes the given diagram accurately represents the angle relationships.
How do I find x? Please explain the process.
X=90 ....angles in a semi-circle
Angle B=A ...Radii
Question
The histogram shows the numbers of concerts choir students at a school have performed in. How many choir students have performed in at least 3 concerts?
The number of choir students that performed in at least 3 concerts is given as follows:
16 students.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed, or the number of observations in each range of a data-set.
Hence, for this problem, the meaning of the histogram is given as follows:
8 students performed in between 0 and 2 concerts.9 students performed in between 3 and 5 concerts.4 students performed in between 6 and 8 concerts.3 students performed in between 9 and 11 concerts.Hence the number of choir students that performed in at least 3 concerts is given as follows:
9 + 4 + 3 = 16 students.
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7. Fatima plans to solve the system below using elimination. Which is a
reasonable first step Fatima could take?
-3x + 4y = -14
x + 2y = -12
A. Multiply the 2nd equation by -3
B. Multiply the 2nd equation by -2
C. Multiply the 2nd equation by 2
D. Any of the above
Answer:
Step-by-step explanation:
D is the answer. See attachment for reason.
In the pyramid and prism below, the height is the same and the sides of the pentagon bases are the same. If the volume of the pyramid is 435.7 cm3, what is the volume of the prism?
Step-by-step explanation:
volume of any type of pyramid :
1/3 × base area × height
FYI (not needed to solve the problem) :
base area is a pentagon.
the area of a pentagon is
1/2 × p × a
p is the perimeter (5 × side length) of the pentagon.
a is the apothem (the direct - right-angled- distance from the center of the pentagon to the center of a side).
volume of any type of regular prism :
base area × height
since the sides of the pentagon are the same, also their base areas are the same.
the height is the same.
so, when we compare both formulas, we see that the only difference is the factor 1/3.
the volume of the pyramid is 1/3 the volume of the prism.
therefore,
volume prism = volume pyramid × 3 = 435.7 × 3 =
= 1,307.1 cm³
Select the correct answer. Joel and Kevin are each putting money in a savings account to buy a new bicycle. The amount, in dollars, in Joel's savings account, x weeks after the start of the year, is modeled by function j. The amount of money in Kevin's account, at the same time, is modeled by function k. j(x) = 25 + 3x k(x) = 15 + 2x Which function correctly represents how much more money, in dollars, is in Joel's account than in Kevin's account x weeks after the start of the year? O A. (j − k)(x) = 40 + 5x (j − k)(x) = 40 + x (j-k)(x) = 10 + 5x (j-k)(x) = 10 + x O B. C. O D. Reset dtry Next
The correct answer is (j - k)(x) = 10 + x.
To find the difference in the amount of money between Joel's and Kevin's accounts, we subtract the value of Kevin's account (k(x)) from Joel's account (j(x)).
(j - k)(x) = (25 + 3x) - (15 + 2x)
= 25 - 15 + 3x - 2x
= 10 + x
This expression represents how much more money is in Joel's account compared to Kevin's account after x weeks.
Therefore, the correct function is (j - k)(x) = 10 + x.
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What number is halfway between
a. Three point six and nine point six
b. One point one and one point five
c. Seven point two six and seven point two eight
a. The number halfway between 3.6 and 9.6 is 6.6.
b. The number halfway between 1.1 and 1.5 is 1.3.
c. The number halfway between 7.26 and 7.28 is 7.27.
To find the number halfway between 3.6 and 9.6, we can add the two numbers and divide by 2:
(3.6 + 9.6) / 2 = 13.2 / 2 = 6.6
The number halfway between 3.6 and 9.6 is 6.6.
To find the number halfway between 1.1 and 1.5, we can use the same approach:
(1.1 + 1.5) / 2 = 2.6 / 2 = 1.3
The number halfway between 1.1 and 1.5 is 1.3.
To find the number halfway between 7.26 and 7.28, we can apply the same method:
(7.26 + 7.28) / 2 = 14.54 / 2
= 7.27
The number that is between 3.6 and 9.6:
(3.6 + 9.6) / 2 = 13.2 / 2 = 6.6
6.6 is the number that falls between 3.6 and 9.6.
We can apply the same strategy to determine the value that lies between 1.1 and 1.5:
(1.1 + 1.5) / 2 = 2.6 / 2
= 1.3
1.3 is the number that falls between 1.1 and 1.5.
We can use the same procedure to determine the number that is halfway between 7.26 and 7.28:
(7.26 + 7.28) / 2 = 14.54 / 2
= 7.27
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The names eben , evelyn , eunice, frieda and frank are to be randomly chosen, and each has the same probability of being selected. Use events E,F,G and H to determine the probabilities in part A to E .
A: Find P(e) in simple fraction form
B: find p(f) In simplest fraction form
C : find p(g) In simplest fraction form
D: find p ( E U F) simplest fraction form
A. P(E) = 1/5
B. P(F) = 1/5
C. P(G) = 1/5
D. The probability of selecting either "Eben" or "Frank" is 2/5.
A: To find the probability of selecting the name "Eben," we need to determine the fraction of the total possible outcomes that result in selecting "Eben." Since there are a total of five names to choose from, the probability of selecting "Eben" can be expressed as:
P(E) = (Number of favorable outcomes) / (Total number of possible outcomes)
In this case, there is only one favorable outcome (selecting "Eben"), and there are five possible outcomes (choosing any of the five names). Therefore:
P(E) = 1/5
B: Similarly, to find the probability of selecting the name "Frank," we can apply the same approach. The probability of selecting "Frank" can be expressed as:
P(F) = (Number of favorable outcomes) / (Total number of possible outcomes)
Again, there is only one favorable outcome (selecting "Frank"), and there are five possible outcomes (choosing any of the five names). Thus:
P(F) = 1/5
C: To find the probability of selecting the name "Evelyn," we follow the same method as above. The probability of selecting "Evelyn" is:
P(G) = (Number of favorable outcomes) / (Total number of possible outcomes)
Once again, there is only one favorable outcome (selecting "Evelyn"), and there are five possible outcomes (choosing any of the five names). Therefore:
P(G) = 1/5
D: To find the probability of selecting either event E or event F (P(E U F)), we can add their individual probabilities and subtract the probability of their intersection (P(E ∩ F)). The probability of the union can be calculated as follows:
P(E U F) = P(E) + P(F) - P(E ∩ F)
Since event E and event F are independent, the probability of their intersection is zero (no name can be both "Eben" and "Frank" simultaneously). Therefore:
P(E U F) = P(E) + P(F) - 0
= P(E) + P(F)
= 1/5 + 1/5
= 2/5
Thus, the probability of selecting either "Eben" or "Frank" is 2/5.
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determine the inclination of the following straight line
1. y=x+3 2) 3x-2y = 6
The inclination of the line represented by the equation y = x + 3 is 1, and the inclination of the line represented by the equation 3x - 2y = 6 is 3/2.
To determine the inclination (or slope) of a straight line, we can examine the coefficients of the variables x and y in the equation of the line.
The inclination represents the ratio of how much y changes with respect to x.
Equation: y = x + 3
In this equation, the coefficient of x is 1, which means that for every increase of 1 in x, y also increases by 1.
This indicates that the inclination of the line is positive, meaning it slopes upwards as x increases.
Since the coefficient of x is 1, the inclination can be expressed as 1/1 or simply 1.
Equation: 3x - 2y = 6
To determine the inclination, we need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope.
First, isolate y:
-2y = -3x + 6
Divide the entire equation by -2 to solve for y:
y = (3/2)x - 3
Now we can observe that the coefficient of x is 3/2.
This indicates that for every increase of 1 in x, y increases by 3/2. Therefore, the inclination of this line is positive, indicating an upward slope.
The inclination can be expressed as 3/2.
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please help, 6 possible outcomes
Answer: Landing on X and heads, landing on Y and heads, landing on Z and heads, landing on X and tails, landing on Y and tails, landing on Z and tails
Step-by-step explanation:
There are three possible spinner options and 2 possible coin options. 3 * 2 = 6, leading to 6 possible outcomes.
The spinner could land on X, Y, or Z.
The coin could land on heads or tails.
If we type out all of these possibilities (each spinner section and heads, each spinner section and tails) we end up with;
➜ Landing on X and heads
➜ Landing on Y and heads
➜ Landing on Z and heads
➜ Landing on X and tails
➜ Landing on Y and tails
➜ Landing on Z and tails
PUT THE NUMBERS LEAST TO GREATEST AND EXPLAIN WHY. i will mark you brainliest
Answer:
The answer is
-5.79×10²³,6.88×10‐²³,5.73×10²³,57.8×10²²,5.83×10²³
Step-by-step Explanation:
solve the equation x²+2x-3=0
Answer:
x = - 3, x = 1
Step-by-step explanation:
x² + 2x - 3 = 0
consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (+ 2)
the factors are + 3 and - 1 , since
3 × - 1 = - 3 and + 3 - 1 = + 2 , then
(x + 3)(x - 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 3 = 0 ( subtract 3 from both sides )
x = - 3
x - 1 = 0 ( add 1 to both sides )
x = 1
solutions are x = - 3 , x = 1
Divide.
(x²+10x+16)÷(x+3)
Your answer should give the quotient and the remainder.
Answer: quotient: x+7 remainder: -5
FIGURE A FIGURE B FIGURE C FIGURE D 2.1.1. Calculate the area of figure A 2.1.2. Calculate the area of figure 2.1.3. Calculate the area of figure C
D
Answer:
Step-by-step explanation:FIGURE A FIGURE B FIGURE C FIGURE D 2.1.1. Calculate the area of figure A 2.1.2. Calculate the area of figure 2.1.3. Calculate the area of figure C
Sure, here are the calculations for the area of each figure:
Figure A is a rectangle with a length of 4 cm and a width of 3 cm. The area of a rectangle is calculated by multiplying the length and the width, so the area of Figure A is 4×3=12 square centimeters.
Figure B is a triangle with a base of 4 cm and a height of 3 cm. The area of a triangle is calculated by multiplying the base and the height and dividing by 2, so the area of Figure B is (4×3)/2=6 square centimeters.
Figure C is a trapezoid with a top base of 4 cm, a bottom base of 6 cm, and a height of 3 cm. The area of a trapezoid is calculated by averaging the top and bottom bases and multiplying by the height, so the area of Figure C is (4+6)/2×3=15 square centimeters.
Figure D is a circle with a radius of 2 cm. The area of a circle is calculated by multiplying the square of the radius by π, so the area of Figure D is 2
2
π=4π square centimeters.
(Polynomials (all operations)) Find the *
area of the triangle below with base
length -6x + 3.
4(x - 2)
Please help
The area of a triangle is:
12x² -18x - 12
How to find the area of the triangle?The area of a triangle can be calculated using the formula:
A = 1/2 * b * h
where b is the base and h is the height of the triangle
We have:
b = -6x + 3
h = 4(x - 2) = 4x - 8
substituting into the formula:
A = 1/2 * (6x + 3) * (4x - 8)
A = 1/2 * (24x² -48x + 12x - 24)
A = 1/2 * (24x² -36x - 24)
A = 12x² -18x - 12
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1. Write down the next three numbers and describe each pattern: b) 1; 8; 15; 22; c) 7; 9; 8; 10; 9:0 a) 3; 6; 9; 12; d) 4; 1; 16; 1; 64; 1; e) 2; 4; 8; 16; 32; f) 3; 9; 27; 81; 2. Draw the next diagram in each pattern. Explain the rule. a) b) P 3. The diagrams below show artwork that the Nguni people paint c their houses. Describe the pattern in the sequence of artwork.
I cannot describe the pattern in the sequence of artwork without visual representation.
Let's analyze each pattern:
The pattern appears to be adding 7 to each number to get the next number.
The next three numbers would be:
29, 36, 43.
The pattern alternates between adding 2 and subtracting 1.
The next three numbers would be:
11, 10, 12.
The pattern increments by 3 each time.
The next three numbers would be:
15, 18, 21.
The pattern alternates between squaring and taking the square root of the previous number.
The next three numbers would be:
1, 8, 1.
The pattern doubles each time.
The next three numbers would be:
64, 128, 256.
The pattern multiplies each number by 3 to get the next number.
The next three numbers would be:
243, 729, 2187.
As a text-based AI model, I am unable to draw diagrams.
I can describe the next diagram in each pattern:
The next diagram would consist of three rows, each containing four dots arranged in a square.
The next diagram would consist of a single dot positioned 7 units below the bottom dot of the previous diagram.
The next diagram would consist of two vertical lines with three dots each.
The next diagram would consist of a single dot positioned 4 units above the top dot of the previous diagram.
The next diagram would consist of a row of six dots arranged in a straight line.
The next diagram would consist of four rows, each containing three dots arranged in a square.
A text-based AI model, I am unable to see or analyze images or diagrams.
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b. Express log2 24 in terms of prime factors and leave answer in the most simplified form using properties of logarithms. (2 Marks)
log₂ 24 can be expressed as 3 + log₂ 3 in terms of prime factors, using the properties of logarithms.
To express log₂ 24 in terms of prime factors, we can use the properties of logarithms and the fact that any positive integer can be expressed as a product of prime factors.
First, let's find the prime factorization of 24.
24 can be divided by 2, so we have 24 = 2 × 12.
12 can be divided by 2, so we have 12 = 2 × 6.
6 can be divided by 2, so we have 6 = 2 × 3.
Therefore, the prime factorization of 24 is 2 × 2 × 2 × 3, or 2³ × 3.
Now, using the properties of logarithms, we can express log₂ 24 as the sum of logarithms of its prime factors.
log₂ 24 = log₂ (2³ × 3)
According to the properties of logarithms, we can separate the factors inside the logarithm as individual terms:
log₂ (2³ × 3) = log₂ 2³ + log₂ 3
Since log₂ 2³ is equal to 3, we can simplify the expression further:
log₂ (2³ × 3) = 3 + log₂ 3
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A man wants to borrow $125,000 for 30 years. He will pay 8.5% interest. What will be his monthly payments?
a) $961.25
b) $1231.25
c) $1080
d) $1085
it will be A .......................................
Find a measure of angle cbd in regular octagon ABCDEFGH
The measure of angle cbd in regular octagon ABCDEFGH is 22.5°.
We are given that;
The octagon ABCDEFGH
Now,
To find the measure of angle CBD. Since ABCDEFGH is a regular octagon, triangle BCD is an isosceles triangle with BC = BD2. Therefore, the base angles of triangle BCD are congruent and have the same measure. Let x be the measure of angle CBD. Then, we have:
x + x + 135° = 180° (sum of angles in a triangle)
2x + 135° = 180°
2x = 180° - 135°
2x = 45°
x = 45°÷2
x = 22.5°
Therefore, by the angle the answer will be 22.5°.
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5. A $1,500 loan grows at 5.5% simple interest.
a) Develop a formula to calculate the amount after n months.
b) What is the amount owed after 14 months?
(a) A formula to calculate the amount after n months: 1,500(1 + nx0.0046)
(b) the amount owed after 14 months = $1596.6
Given that,
Principal amount = P = $1,500
interest of grown = R = 5.5%
Now we can write is,
5.5% = 5.5/100
= 0.055
We know that,
The simple interest formula,
A = P(1 + rt)
Where,
A represents Amount after T years
R represents rate of interest
T is time in year
Now,
Since 1 month = 1/12 years
= 0.084
Therefore amount after 1 month be
A = 1,500(1+0.055x0.084)
= 1,500(1+0.0046)
= 1506.93
Amount after 2 month be
A = 1,500(1+ 2 x 0.055x0.084)
= 1,500(1+2x0.0046)
Amount after 3 month be
A = 1,500(1+ 2 x 0.055x0.084)
= 1,500(1 + 3x0.0046)
Hence amount of n months = 1,500(1 + nx0.0046)
Hence,
The amount after 14 months,
= 1,500(1 + 14x0.0046)
= $1596.6
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which point from the equation would you use? y-7=3(x+9)
Another point on the line is (-9, 7). Ultimately, the choice of which point to use depends on the context or specific requirements of the problem you are solving.
To determine which point to use from the equation y - 7 = 3(x + 9), we need more information.
The equation provided represents a linear equation in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Without additional context or specific instructions, we can choose any point that satisfies the equation to use as a reference.
For example, if we let x = 0, we can solve the equation for y:
y - 7 = 3(0 + 9)
y - 7 = 3(9)
y - 7 = 27
y = 27 + 7
y = 34
So, one point on the line is (0, 34).
Alternatively, if we let x = -9, we can solve the equation for y:
y - 7 = 3(-9 + 9)
y - 7 = 3(0)
y - 7 = 0
y = 7
So, another point on the line is (-9, 7).
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Which statement must be true?Choose all that apply.
From the attached image, it can be seen that triangle PQR is an isosceles triangle and therefore option (A), option (B), option (C) and option (D) are all correct.
Understanding Isosceles TriangleAn isosceles triangle has 2 sides equal meaning 2 opposite angles are also equal.
Let us assume the following:
PR = 1cm
QR = 1cm
PQ = 2cm
cos P = adj/hyp
= PR/PQ = 1/2
cos Q = adj/hyp
= QR/PQ = 1/2
Therefore cos P and cos Q are equal.
sin P = opp/hyp
= QR/PQ = 1/2
sin Q = opp/hyp
= PR/PQ = 1/2
Also sin P and sin Q are equal.
From this analogy, we can deduce the following:
sin P = sin Q = 1/2
cos P = cos Q = 1/2
sin P = cos Q = 1/2
cos P = sin Q = 1/2
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A small class has 10 students, of whom are 5 girls and 5 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the teacher will choose two girls? Write your answer as a fraction in simplest form
2/9 is the probability that the teacher will choose two girls
To calculate the probability of choosing two girls from the class
we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes: Since the teacher is choosing two students from a class of 10, the total number of outcomes is given by the combination formula C(10, 2), which is calculated as:
C(10, 2) = 10! / (2!(10 - 2)!) = 10! / (2! × 8!) = (10 × 9) / (2 × 1) = 45
Number of favorable outcomes
We want to choose two girls from the 5 girls in the class.
The number of ways to choose 2 girls from 5 is given by the combination formula C(5, 2), which is calculated as:
C(5, 2) = 5! / (2! × (5 - 2)!) = 5! / (2! × 3!) = (5× 4) / (2× 1) = 10
Therefore, the number of favorable outcomes is 10.
The probability of choosing two girls is given by the number of favorable outcomes divided by the total number of outcomes:
Probability = Number of favorable outcomes / Total number of outcomes = 10 / 45 = 2 / 9
Hence, the probability that the teacher will choose two girls is 2/9.
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six ordered pairs of f(x)=-x^2+3x+2
The six ordered pairs for the function f(x) = -x^2 + 3x + 2 are:
(-2, -8), (-1, -2), (0, 2), (1, 4), (2, 4), (3, 2).
To find six ordered pairs for the function [tex]f(x) = -x^2 + 3x + 2[/tex], we can substitute different x-values into the function and evaluate the corresponding y-values.
Let's choose six x-values and calculate the corresponding y-values:
When x = -2:
[tex]f(-2) = -(-2)^2 + 3(-2) + 2 = -4 - 6 + 2 = -8[/tex]
Therefore, the ordered pair is (-2, -8).
When x = -1:
[tex]f(-1) = -(-1)^2 + 3(-1) + 2 = -1 - 3 + 2 = -2[/tex]
Therefore, the ordered pair is (-1, -2).
When x = 0:
[tex]f(0) = -(0)^2 + 3(0) + 2 = 0 + 0 + 2 = 2[/tex]
Therefore, the ordered pair is (0, 2).
When x = 1:
[tex]f(1) = -(1)^2 + 3(1) + 2 = -1 + 3 + 2 = 4[/tex]
Therefore, the ordered pair is (1, 4).
When x = 2:
[tex]f(2) = -(2)^2 + 3(2) + 2 = -4 + 6 + 2 = 4[/tex]
Therefore, the ordered pair is (2, 4).
When x = 3:
[tex]f(3) = -(3)^2 + 3(3) + 2 = -9 + 9 + 2 = 2[/tex]
Therefore, the ordered pair is (3, 2).
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Find the missing angles using trigonometry
The value of x is 24.426 degrees when the opposite side is 9 and adjacent side is 20 and value of x is 58.211 degrees degrees when the adjacent side is 17 and hypotenuse is 32
In the given triangle
We have to find the missing angle x
By tan function we know that tan is a ratio opposite side and adjacent side
tanx=9/20
tanx=0.45
x=tan⁻¹(0.45)
x=24.426 degrees
For example 2, we find x by using cosine function which is a ratio of adjacent side and hypotenuse
cosx=17/32
cosx=0.53
x=cos⁻¹(0.53)
x=58.211 degrees
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Mrs. Matthews came up with an expression. Holly and Jim wrote the expression in their notebooks in order to simplify the expression. They compared their expressions.
Holly's expression is equal to 864, and Jim's expression is equal to 36. So, Jim's expression is 828 less than the other expression.
How to simplify expressions?Holly's notebook:
6 × (24 ÷ 2)²
= 6 × (12)²
= 6 × 144
= 864
Jim's notebook:
6 × 24 ÷ 2²
= 6 × 24 ÷ 4
using PEMDAS
P = parenthesis
E = exponents
M = multiplication
D = Division
A = Addition
S = Subtraction
6 × 24 ÷ 4
= 144 ÷ 4
= 36
Therefore, Jim's expression is less than Holly's expression.
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2
2780-4
Which is more, the average of the 4 even whole numbers from 8 to
15 or the average of the 4 odd whole numbers from 8 to 15?
After calculating the average of numbers here, the average of the four odd numbers from [tex]8 \ to \ 15[/tex] is greater than the average of the four even numbers.
The step-by-step solution to this is given below:
To determine which average is greater, let's calculate the averages of the even and odd numbers separately.
The four even numbers from [tex]8 \ to \ 15 \ are \ 8, 10, 12, and \ 14[/tex]. To find their average, we sum them up and divide by [tex]4[/tex]:
[tex]\[\text{Average of even numbers} = \frac{8 + 10 + 12 + 14}{4} = \frac{44}{4} = 11\][/tex]
The four odd numbers from [tex]8 \ to \ 15 \ are \ 9, 11, 13, and \ 15.[/tex] Similarly, we calculate their average:
[tex]\[\text{Average of odd numbers} = \frac{9 + 11 + 13 + 15}{4} = \frac{48}{4} = 12\][/tex]
Now, the next step will be comparing the two averages, we find that the average of the four odd numbers, [tex]12[/tex], is greater than the average of the four even numbers, [tex]11[/tex].
Therefore, the average of the four odd numbers from [tex]8 \ to \ 15[/tex] is greater than the average of the four even numbers.
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Which expression is equivalent
Answer:
4th option
Step-by-step explanation:
using the rule of exponents
• [tex]a^{m}[/tex] ×[tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
then
[tex]x^{9}[/tex] × x = [tex]x^{9}[/tex] × [tex]x^{1}[/tex] = [tex]x^{(9+1)}[/tex] = [tex]x^{10}[/tex]
Then
[tex]\sqrt[3]{x^{10} }[/tex] ≡ [tex]\sqrt[3]{x^9 . x}[/tex]
Please help me with these geometry questions
Answer:
a. 30 b. indeterminate, unless you're given the measure of either of the other sides.
Step-by-step explanation:
a. lazy solution: it's a 3-4-5 right triangle scaled up (18 is 3*6, 24 is 4*6, last side will be 5*6= 30. Less than lazy solution: it's a right triangle, pythagorean theorem applies:
[tex]x^2= 18^2+24^2 = 324+576 = 900\\x= 30[/tex]
b.problem is indeterminate as long as you don't know the measure of any of the other sides. the 30-60 triangle is half of an equilateral triangle and x is [tex]\sqrt3[/tex] times the short side, or [tex]\frac{\sqrt3} 2[/tex] times the long side. It's easily shown by mirroring the triangle along the vertical side, and if the short leg measures k, the hypotenuse measures 2k, and the vertical side measures [tex]x^2+k^2=(2k)^2\\x^2+k^2 = 4k^2\\x^2 = 3k^2 \implies x=\sqrt3\ k[/tex]
Point P is on a bearing of 135° and 320° respectively from point Q and R.If PQ=25km and PR=40km,find
a)QR
b)bearing of Q from P
(a). The distance QR is equal to 45.3 using the cosine rule.
(b) Bearing of Q from P is 315°
What is bearing?Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.
(a). Let ∆PQR be the triangle formed with bearings so that:
angle P = 45° + 40° {alternate angles from Q and R respectively to P}
angle P = 85°
PQ = 25km
PR = 40km
The distance QR is calculated using the cosine rule as follows:
QR² = 25² + 40² - 2(25)(40)cos85° {cosine rule}
QR² = 2225 - 174.3115
QR = √2050.6885 {take square root of both sides}
QR = 45.2845
(b) Bearing of point Q from P is the angle measured from the north of P to the straight line distance between Q and P
Bearing of Q from P = 45° + 270° = 315°
Therefore, the distance QR is equal to 45.3 using the cosine rule. Bearing of Q from P is 315°
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