Answer:
Angles 1 & 4 are alternate interior angles.
The correct name for the relationship between angles 1 and 4 in the given scenario is that they are corresponding angles.
When two parallel lines are cut by a transversal, the following relationships exist between the angles formed:
1. Corresponding angles are equal. These are the angles that are in the same relative position at each intersection where a straight line crosses two others. In this case, angle 1 corresponds to angle 4 because they are both above the parallel lines and on the same side of the transversal.
2. Alternate interior angles are equal. These are the angles that are inside the parallel lines and on opposite sides of the transversal. Angle 3 would be the alternate interior angle to angle 1, not angle 4.
3. Alternate exterior angles are equal. These are the angles that are outside the parallel lines and on opposite sides of the transversal.
4. Consecutive interior angles (also known as same-side interior angles) are supplementary. These are the angles that are on the same side of the transversal and inside the parallel lines.
Since angle 1 and angle 4 are in the same relative position at each intersection (both are above the parallel lines and on the same side of the transversal), they are corresponding angles. Therefore, if the lines are parallel, angle 1 is equal to angle 4.
y=−7x+8 y=−7x−8 Choose 1 answer: Choose 1 answer: (Choice A) A Exactly one solution (Choice B) B No solutions (Choice C) C Infinitely many solutions
Answer:
I THINK ITS A ;-;
Step-by-step explanation:
Answer:
no solution
Step-by-step explanation:
the ordered pair is not a solution to the equation
A landscaper planted 10 cattails by a new pond. The number of cattails double each month over a period of time. Write a function f(x) to model the number of cattails in the pond after x months. f(x)=?
Answer:
[tex]\large \boxed{f(x) = 10(2)^{ x}}[/tex]
Step-by-step explanation:
Write a table giving the number of cattails for the first few months
[tex]\begin{array}{lr}\mathbf{x} & \mathbf{f(x)}\qquad \qquad\quad \\0 & 10 = 2^{0}(10) = 10(2)^{0}\\1 & 2(10) = 2^{1}(10)= 10(2)^{1} \\2 & 2\times2(10) = 2^{2}(10)= 10(2)^{2} \\3 & 2\times 2^{2}(10) = 2^{3}(10)= 10(2)^{3}\\4 & 2\times 2^{3}(10) = 2^{4}(10)= 10(2)^{4}\\\end{array}\\\text{The pattern appears to be $\large \boxed{\mathbf{f(x) = 10(2)^{\mathbf{x}}}}$}[/tex]
find the product d^j•d^k
Answer:
d^(j+k)
Step-by-step explanation:
d^j * d^k
We know that a^b * a^c = a^(b+c)
d^(j+k)
What is the gradient of the line 12x=15-3y
Answer:
-4
Step-by-step explanation:
12x=15-3y
+3y
12x+3y=15
-12x
3y=-12x+15
/3
y=-4x+15
Gradient= -4 as in the equation y=mx+c
, m=the gradient therefore the gradient is -4
Answer:
-4
Step-by-step explanation:
12x=15-3y +3y
12x+3y=15 -12x
3y=-12x+15 /3
y=-4x+15
Factor and solve: -3p^2 - p - 2 = 0
Please show step by step and how to factor trinomials when the leading coefficient is a negative number.
Answer:
Step-by-step explanation:
-3p² - p - 2 = 0
a = -3; b = -1 c = -2
[-b ±√(b² - 4ac)]/2a = [1 ± √(1-4*-3*-2) ] /2*-3
=[1 ± √(1-48) ]/-6
= - [1 ±√-47]/6
= - [1 ±√47i]/6
The volume of a cylinder can be found using the formula V = pi r squared h.
Which is the correct first step in finding the height of a cylinder with a volume of 192 pi cubic inches and a radius of 5 inches?
5 = pi (192) squared h
V = pi + (5) squared + 192 pi
V = pi (5) squared (192)
192 pi = pi (5) squared h
Answer:
The answer is D
192 pi = pi (5) squared h
Step-by-step explanation:
Answer:
The answer is D
Step-by-step explanation:
It points out to find the height and it already gives you the volume and radius so all you have to do is plug in those to #'s.
So the "V" is always going to go first then the equal sign the the pi sign then a number followed by squared.
Right after that you should have an "H" which is the height you have to use to multiply.
What is the m in 45m - 900 = 90m
Step-by-step explanation:
[tex]45m - 900 = 90m \: [/tex]
[tex]45m - 90m = 900[/tex]
[tex] - 45m = 900[/tex]
[tex]m = \frac{900}{ - 45} = - 20[/tex]
Answer:
m=-20
Step-by-step explanation:
45m -900=90m
-900=45m
-900/45=45m/45
m=-20
Please help me with the following question.
I am pretty sure x is 9 because if you divide 14 by 2 you get 7. 18 divided by 2 is 9.
Answer:
x=9
Step-by-step explanation:
the word similar means the same shape but different sizes. That means that you can think of this problem as ratios. The ratio for the first triangle would be 14:14:18. Since the second ones ratio is 7:7:x we know that the seven was found by dividing 14 by two so we do that with the rest of the of the number to find x you divide 18 by two and get 9. So x=9.
If m = 35 cm and n = 37 cm, what is the length of l?
A. 15 cm
B. 13 cm
C. 12 cm
D. 2 cm
So the right answer is 12cm.
Look at the attached picture ⤴
Hope it will help u..
Answer:
12
Step-by-step explanation:
The length of a rectangle is 1 meter less than its
width. The area of the rectangle is 42 square
meters. Find the dimensions of the rectangle.
If the length of the rectangle is x, then we know the width is x + 1.
The area of a rectangle is length · width, so we can substitute as x · (x + 1)
Now, we now x · (x + 1) = 42
Expand
x² + x = 42
Solve
x² + x - 42 = 0
(x + 7)(x - 6) = 0
So, x = 6
That means the length is 6 meters and the width is 7 meters.
The dimensions of the rectangle are:
Width, W = 7 meters
Length, L = 6 meters
Let's denote:
L = the length of the rectangle
W = the width of the rectangle
Given that the length of the rectangle is 1 meter less than its width, we can write the equation:
L = W - 1
We're also given that the area of the rectangle is 42 square meters. The formula for the area A of a rectangle is:
A = length × width
Substituting the given values, we have:
42 = (W - 1) × W
Now, let's solve this equation for W to find the width of the rectangle.
42 = [tex]W^2[/tex] - W
Rearranging terms, we get a quadratic equation:
[tex]W^2[/tex] - W - 42 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula. Factoring seems simpler in this case:
Product = 1 × -42 = -42
Sum = -1
Required numbers: 6 × -7
[tex]W^2[/tex] - W - 42 = 0
[tex]W^2[/tex] + 6W - 7W - 42 = 0
W (W + 6) - 7 (W + 6) = 0
(W - 7) (W + 6) = 0
Setting each factor equal to zero gives us two possible values for W:
W - 7 = 0 or W + 6 = 0
Solving each equation:
W - 7 = 0W = 7
W + 6 = 0W = -6
Since the width of the rectangle cannot be negative, we discard W = -6.
So, the width of the rectangle is W = 7 meters.
Now, to find the length L, we can use the equation L = W - 1:
L = 7 - 1
L = 6
The question is:
The length of a rectangle is 1 meter less than its width. The area of the rectangle is 42 square meters. Find the dimensions of the rectangle.
Find the circumference of the circle.r=9in
56.52 inches
14.13 inches
63.59 inches
254.34 inches
28.26 inches
Answer:56.52
Step-by-step explanation: I just did it
(a) Find the GCF of 18 and 8
(b) use the GCF to factor 18-8
18 - 8 = blank x (blank - blank)
The Greatest Common Factor (GCF) of 18 and 8 is 2. Using this GCF, 18 - 8 can be factored as 2 × (9 - 4).
(a) To find the GCF (Greatest Common Factor), we need to determine the largest number that divides both 18 and 8 without leaving a remainder.
Prime factors of 18: 2 × 3 × 3
Prime factors of 8: 2 × 2 × 2
The only common prime factor is 2.
So, the GCF of 18 and 8 is 2.
(b) We know that 18 - 8 = 10. To factor this expression using the GCF, we rewrite 10 as a product involving the GCF.
Factor out the GCF (2) from 18 - 8:
10 = 2 × (9 - 4)
So, 18 - 8 = 2 × (9 - 4).
Mai's water bottle had 24 ounces in it. After she drank x ounces of water, there were 10 ounces left. Select all the equations that represent this situation.
Answer:
x+10=24
Step-by-step explanation:
the actual equation would give you 14
To represent the situation, you can use the equation x = 24 - 10 or the proportion x/24 = 10/24.
Explanation:To represent the situation, we can use the equation: x = 24 - 10, where x represents the amount of water Mai drank. This equation represents the fact that the initial amount of water in the bottle (24 ounces) minus the amount of water that Mai drank (x ounces) equals the remaining amount of water (10 ounces).
Alternatively, we can also use the proportion x/24 = 10/24 to represent the situation. This proportion shows that the ratio of the amount of water Mai drank to the initial amount of water in the bottle is equal to the ratio of the remaining amount of water to the initial amount of water.
In a scale drawing, the height of a tree is 3 inches. In real life, the height of the tree is 6 feet. What is the scale factor?
A. 1/24
B. 24
C. 3 in : 6 ft
D. 6 in : 3 ft
Answer:
The answer is A 1/24
Mark sold 445 tickets for the school play. Student tickets cost $3 and adult tickets
cost $5. Mark's total income for the event was $1871. How any adult tickets did he
sell?
Answer:
Mark sold 268 adult tickets.
Step-by-step explanation:
We are given the following in the question.
Let x be the number of students ticket sold and y be the number of adult tickets sold.
Total number of tickets sold = 445
Thus, we can write the equation:
[tex]x + y = 445[/tex]
Cost of student ticket = $3
Cost of an adult ticket = $5
Total income = $1871
Thus, we can write the equation:
[tex]3x + 5y = 1871[/tex]
Solving the two equations, we get,
[tex]3x + 5y - (3x+3y) = 1871 - 3(445) \\2y = 536\\\Rightarrow y = 268\\\Rightarrow x = 445 - 268 = 177[/tex]
Thus, Mark sold 268 adult tickets.
Answer:he sold 268 adult tickets at the school play
Step-by-step explanation:
What is the solution to the division problem 426 Divided By 5113 written as a mixed number
Answer:
[tex]12\frac{1}{426}[/tex]
Step-by-step explanation:
please check the attached files for more explanation
A divisor is a number that divides another number either completely or with a remainder and the divisor [tex]5113[/tex] is divided by [tex]426[/tex] is [tex]12[/tex].
What is divisor ?
The divisor is any number that divides another number. A factor, however, is a divisor that divides the number entirely and leaves no remainder. So, all factors of a number are its divisors. But not all divisors will be factors.
To know more about divisors.
The solution using the "Long Divison Method'
Now, start the divisor [tex]426[/tex] on the left side and the dividend [tex]5113[/tex] on the right side :
12
[tex]\sqrt[426]{5113} \\426\\----\\853\\852\\----\\1[/tex]
Hence, the result of the divisor [tex]5113[/tex] divided by [tex]426[/tex] is [tex]12[/tex].
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HELP ASAP !!!
Please explain why
The whale swims down 300 feet to feed. What is the whale’s elevation now?
The elevation of the whale is -300 feet.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the whale swims down 300 feet to feed. The elevation of the whale will be:-
Elevation = -300 feet
Therefore, the elevation of the whale is -300 feet.
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Air Jordan’s are manufactured in China and reportedly cost Nike a bit more then $16 a pair in 2014. The Air Jordan 10s are listed on Amazon for $240. What is the percent increase for Air Jordan’s sold in the US to the nearest tenth?
Answer: That would be a massive 1500% increase from 16 to 240
Easy 50 points, one multi choice question
Answer:
A
Step-by-step explanation:
but it prob doesnt help tho
Answer:
B is the correct answer
Step-by-step explanation:
Solve for an angle in right triangles help
Answer:
71.57
Step-by-step explanation:
Tangent = opposite over adjacent (sides)
TanA = ( 9/3 )
A = [tex]Tan^{-1}[/tex](3)
A = 71.57
Which fraction has the greatest value 1/3 2/3 2/9 2/9
Answer:
2/3
Step-by-step explanation:
What is the factor pair for the multiplication sentence below?
11 x 9 = 99
A. 9,99
B. 11.99
c. 11,9
The graph below represents the path of a grasshopper as it jumps which type of function models the data on the graph
Answer:
Quadratic
Step-by-step explanation:
Given function is a quadratic function.
There are many key features in a quadratic graph such as the zeroes (x-intercepts, also known as the roots), y-intercept, axis of symmetry, and the vertex.
The graph of a quadratic function is a parabola, which has several important properties:
Vertex: The vertex is the point where the parabola changes direction. It is the highest or lowest point on the parabola, depending on whether the parabola opens upward or downward, respectively.
Axis of symmetry: The axis of symmetry is a vertical line that divides the parabola into two symmetrical halves. It passes through the vertex and is perpendicular to the directrix.
Directrix: The directrix is a horizontal line that is located at a distance equal to the distance between the vertex and the focus. It is perpendicular to the axis of symmetry and reflects the parabola onto itself.
Focus: The focus is a point on the axis of symmetry that is located at a distance equal.
As we can see that given graph has two roots and it is symmetric to the line parallel to the y-axis.
From the graph we know this is a quadratic function { a parabola with respect to symmetry and axis symmetry}
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When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?
The faster pipe will fill the pool in 6 hours and the slower pipe will fill the pool in 12 hours.
What is time and work for commercial mathematics?Work Done = Time Taken × Rate of Work. Rate of Work = 1 / Time Taken. Time Taken = 1 / Rate of Work. If a piece of work is done in x number of days, then the work done in one day = 1/x.
Given here, two pipes fill the pool in 4 hours if they work together and If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours.
Let volume of the pool be LCM(9,4)= 36 unit³ and their efficiencies be E₁ and E₂ respectively then we have E₁+E₂ = 36/4
=9 units
Also 18/ E₁ +18/E₂ = 9
putting E₁=9-E₂ we get
18₁/ 9-E₂ +18/E₂ = 9
E²₂ -9E₂ +18 =0
(E₂ +3) (E₂ -6) =0
Therefore E₂ =6 units as efficiency cannot be negative and consequently E₁ =3 units
Hence, if they are working alone they finish the work in 36/3 =12 hours and 36/6=6 hours respectively.
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The angle of depression between a bird and its prey is 70 degrees. If the bird is 18 ft off the ground, what is the distance between the bird and its prey? Round to the nearest foot
Answer:
19 ft
Step-by-step explanation:
We are given that
[tex]\theta=70^{\circ}[/tex]
Height of bird from the ground=h=18 ft
We have to find the distance between the bird and its prey.
We know that
[tex]sin\theta=\frac{perpendicular\;side}{hypotenuse}[/tex]
Using the formula
[tex]sin70=\frac{18}{hypotenuse}[/tex]
[tex]hypotenuse=\frac{18}{sin70}=19.1 ft\approx 19ft[/tex]
Hence, the distance between the bird and its prey=19 ft
Gavin is starting a running plan to train for a race. In the first week of his running plan, Gavin will run 5 miles. The plan calls for Gavin to increase his weekly milage by 3.5 miles every week. If Gavin sticks to the plan, how many miles would he be expected to run during his 11th week of the training plan? Round to the nearest tenth (if necessary).
Step-by-step explanation:
In the first week of his running plan,the number of miles covered = 5 miles
Weekly mileage will increase by 3.5 miles every week.
At the end of second week, the number of miles covered = 5 + 3.5 = 8.5
At the end of third week, the number of miles covered = 8.5 + 3.5 = 12
The series is 5, 8.5, 12, ...
Consider this as an AP, where a = 5, d = 3.5
By formula,
[tex]a_{n} = a + (n-1)d[/tex]
Substituting the values in the above equation, we get
[tex]a_{11} = 5 + (10-1) 3.5[/tex]
= 5 +(9)3.5
= 5 + 31.5
=36.5 miles.
Gavin would be expected to run during 36.5 miles during his 11th week of the training plan
The points in the table lie on a line. What is the slope of the line?
To find the slope(m), use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] And plug in two points on the line. I will use
(-2, 1) = (x₁, y₁)
(4, -6) = (x₂, y₂)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{4-(-2)}{-6-1}[/tex] (two negative signs cancel each other out and become positive)
[tex]m=\frac{4+2}{-6-1}[/tex]
[tex]m=\frac{6}{-7}[/tex]
To calculate the slope of the line passing through the points (-8, -2) and (4, 10), use the formula m = (y2 - y1) / (x2 - x1), which gives a slope of 1.
The question pertains to finding the slope of a line that passes through certain points with given x and y coordinates. The slope of a line is the ratio of the change in y (the rise) to the change in x (the run). To calculate it, we can use any two points on the line. Let's use the points (-8, -2) and (4, 10) as an example.
We calculate the slope (m) using the formula:m = (y2 - y1) / (x2 - x1)
Substituting the values:m = (10 - (-2)) / (4 - (-8))
m = (12) / (12)
The slope m equals 1.This means for every increase of 1 on the horizontal axis, there is a rise of 1 on the vertical axis.
2) What is 8% of 24.52? Round your answer to the nearest hundredth.
What is 8% of 24.52= 1.9616
just round up
Answer:
What is 8% of 24.52= 1.9616
Step-by-step explanation:
round it
Would do anything for the answer to this question
Given:
The length of the entire rectangle is 10x + 7.
The width of the entire rectangle is 6x.
The length of the unshaded rectangle is 4x - 5.
The width of the unshaded rectangle is 2x.
We need to determine the area of the shaded region of the rectangle.
Area of the entire rectangle:
The area of the entire rectangle can be determined using the formula,
[tex]A=length \times width[/tex]
Substituting the values, we have;
[tex]A_1=(10x+7)(6x)[/tex]
[tex]A_1=60x^2+42x[/tex]
Thus, the area of the entire rectangle is 60x² + 42x
Area of the unshaded rectangle:
The area of the unshaded rectangle can be determined using the formula,
[tex]A=length \times width[/tex]
Substituting the values, we have;
[tex]A_2=(4x-5)(2x)[/tex]
[tex]A_2=8x^2-10x[/tex]
Thus, the area of the unshaded rectangle is 8x² - 10x
Area of the shaded region of the rectangle:
The area of the shaded region of the rectangle can be determined by subtracting the area of the entire rectangle by the area of the unshaded rectangle.
Thus, we have;
[tex]A=A_1-A_2[/tex]
Thus, we have;
[tex]A=60x^2+42x-(8x^2-10x)[/tex]
[tex]A=60x^2+42x-8x^2+10x[/tex]
[tex]A=52x^2+52x[/tex]
[tex]A=52x(x+1)[/tex]
Thus, the area of the shaded region of the rectangle is 52x(x + 1)