The acute angle between the two lines is approximately 24 degrees.
How find the acute angle between two lines?To find the acute angle between two lines, we need to determine the slopes of the lines and then apply the formula:
angle = arctan(|(m1 - m2) / (1 + m1 × m2)|)
Let's start by putting the given equations into slope-intercept form (y = mx + b):
Equation 1: 4x - y = 5
Rearranging, we get: y = 4x - 5
The slope of this line is m1 = 4.
Equation 2: 6x + y = 8
Rearranging, we get: y = -6x + 8
The slope of this line is m2 = -6.
Now, we can substitute the slope values into the formula to calculate the angle:
angle = arctan(|(4 - (-6)) / (1 + 4 × (-6))|)
angle = arctan(|(4 + 6) / (1 - 24)|)
angle = arctan(|10 / (-23)|)
Using a calculator or a trigonometric table, we find:
angle ≈ 24.4 degrees (rounded to the nearest degree)
Therefore, the acute angle between the two lines is approximately 24 degrees.
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What are the 6 steps to solving equations?
Answer:
The six steps to solving equations are:
Simplify both sides of the equation, if necessary, by combining like terms.
Isolate the variable on one side of the equation.
Use inverse operations to solve for the variable.
Check your solution by substituting it back into the original equation.
Write the solution in interval notation.
Graph the solution on the number line.
Note that steps 5 and 6 are only applicable when solving inequalities, not equations.
Step-by-step explanation:
CALC HELP SO PHOTO PLEASE
Answer:
Step-by-step explanation:
Add me
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What are the four types of triangles according to angle measure?
The 4 types of triangle are
Acute triangle
Obtuse Triangle
Right triangle
Equivalent triangle
What are the four types of triangles by angle measurement ?A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
A triangle having three acute angles is known as an acute triangle. A triangle having one obtuse angle and two acute angles is known as an obtuse triangle. No Euclidean triangle may contain more than one obtuse angle because in Euclidean geometry, a triangle's angles must add up to 180°.
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or more than 90°. Only 180° is equivalent to the internal angles of an acute triangle.
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PLEASE HELP
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer in the box.
The constant of proportionality of the graph is 12.
How to find the constant of proportionality?Proportional relationships are relationships between two variables where their ratios are equivalent. In other words, a proportional relationship is one in which two quantities vary directly with each other.
Proportional relationship can be represented mathematically as follows:
y = kx
where
k = constant of proportionalityTherefore, let's use (3, 36) to find the constant of proportionality.
Hence,
y = kx
36 = 3k
divide both sides by 3
3k / 3 = 36 / 3
k = 12
Therefore, the constant of proportionality is 12.
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How do you find the endpoint of a titration?
The endpoint of a titration can be found by various methods like visual indicators, conductometric titration, volumetric titration, etc.
The endpoint of a titration is the point at which the reaction between the acid and base is complete. In other words, it is the point at which the acid and base have been neutralized, and the solution reaches a neutral pH of 7.0. There are several ways to determine the endpoint of a titration, including:
Visual indicators: Certain indicators, such as phenolphthalein or methyl orange, change color at a specific pH, indicating the endpoint of the titration.Potentiometric titration: A pH sensor or electrode is used to measure the pH of the solution during the titration. The endpoint is determined when the pH reaches a specific value, such as 7.0 for a neutralization reaction.Conductometric titration: A conductivity sensor is used to measure the conductivity of the solution during the titration. The endpoint is determined when the conductivity reaches a maximum or minimum value.Amperometric titration: An electrode is used to measure the current during the titration. The endpoint is determined when the current reaches a maximum or minimum value.Volumetric titration: The endpoint is determined by measuring the volume of the titrant required to neutralize the acid or base.To find the endpoint, it is important to use a suitable indicator that changes color in the range of pH close to the endpoint of the titration. It's also important to use a burette to measure the volume of the titrant added and use it to plot the titration curve.
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9 + m / 3 = 2 PLEASEEEEE HELPPPPP
Answer: M= -3
Solve for m by simplifying both sides of the equation, then isolating the variable.
What is the value of K if X 1 is the factor of 4x³ 3x² 4x K?
The value of k is -3, if x - 1 is a factor of 4x³ + 3x² − 4x + k.
A polynomial factor is a polynomial that divides another polynomial exactly, with no remainder.
For example, if we have a polynomial P(x) = 4x³ + 3x² − 4x + k, and we have a polynomial factor F(x) = x - 1, we can say that P(x) is divisible by F(x) with no remainder.
In general, a polynomial of degree n has n roots (or zeroes) and the factorization of polynomial can be expressed as a product of its roots and its corresponding multiplicity.
To find the value of k, set x = 1 in the equation 4x³ + 3x² − 4x + k and solve for k that will make the equation equal to zero..
So when x = 1, we have:
4x³ + 3x² − 4x + k = 0
4(1)³ + 3(1)² − 4(1) + k = 0
4 + 3 - 4 + k = 0
k = -3
Hence, if x - 1 is a factor of 4x³ + 3x² − 4x + k, then k is equal to -3.
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answer PLEASE????? thanks
Answer:
2 4/5
Step-by-step explanation:
2/5 x 2 = 4/5 + 2 = 2 4/5
_______________
Hope this helps :)
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A right rectangular prism measures 12 cm tall, 8 cm long, and 5 cm wide.
A manufacturer would like to double the surface area of this prism. What should be the height of the new prism so that its surface area is doubled?
Enter your answer, to the nearest tenth, in the box.
Answer: 392
Surface area of a prism formula: A= 2(l*w*h)
2*(5*8*12*5*8*12) =392
Step-by-step explanation:
Hope this helps :))))
if you can solve this that would be great
Answer:
x<30
Step-by-step explanation:
3/6x-1/6x<10
1/3x<10
x<30
How do you dilate a triangle with a scale factor of 1 2?
If the scale factor is 1/2, then every coordinate point of the original triangle is multiplied by the scale factor 1/2. Dilation with scale factor 1/2, then multiply by 1/2.
How do construct a dilation of 1 2?To dilate the figure by a factor of 2, I will multiply the x-value of each point by 2. I plotted all the new points to find the new triangle. To dilate the figure by a factor of 2, I will multiply the x and y-value of each point by 2.If the scale factor is a fraction, the shape will be smaller. This is called reduction. Therefore, a 1/2 scaling factor means that the new shape is half of the original shapeThe scale factor = Smaller figure dimensions ÷ Larger figure dimensions = 20/40 = 1/2. Therefore, the scale factor used to create the smaller polygon is 1/2. Example 3. A triangle was increased by a scale factor of 2 resulting in the new dimensions as 6 units by 10 units by 12 units.To learn more about construct a dilation refers to:
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Which pair of angles are alternate interior angles?
- Angle 1 and 8
- Angle 1 and 7
- Angle 2 and 7
- Angle 3 and 6
In this case, the pair of alternate interior angles would be angle 2 and 7.
What is angle?Angle is a geometric object which is defined by two rays with a common endpoint. It is typically measured in degrees or radians and is used to measure the size of an angle. Angles play a key role in mathematics, being used in trigonometry, calculus, and geometry. Angles are also used in engineering and construction to ensure that components are built properly. In addition, angles are used to measure the direction of objects in the sky, such as stars and planets.
Alternate interior angles are two angles located on opposite sides of a transversal line, but within the same parallel lines. In this case, the pair of alternate interior angles would be angle 2 and 7. These two angles are located on opposite sides of the transversal line, between the two parallel lines.
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Given the figure at right.
Find the sum of angles
1, 2, and 3.
A local car dealership has 250 cars on the lot. 30% of the cars are SUVs. How many of the cars are not SUVs?
Answer:175 are not suvs
Step-by-step explanation:
Answer: 175
Step-by-step explanation:
At an animal shelter, there are 15 dogs and 5 cats what percent of the animal are cats
Answer:
25%
Step-by-step explanation:
5 out of (15+5 ) are cats
5/20 = .25 = 25 %
Answer:
25%
5 out of (15+5 ) are cats
5/20 = .25 = 25 %
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PLEASE HELP On a map, the distance from Happy Hill park to Rainbow Valley park is 4 1/2 inches. The scale is 1/2 = 3 miles. What is the actual distance between the two parks in miles?
The actual distance between Happy Hill park to Rainbow Valley park is calculated to be 27 miles
How to calculate the actual distanceScale factors are used to increase or decrease image. The situation of increment is usually called magnifying.
If on the map the distance between Happy Hill park to Rainbow Valley park is 4 1/2 inches, and the scale factor is 1/2 = 3 miles. The calculation is done as follows
1/2 = 3miles
4 1/2 miles = ?
cross multiplying
4 1/2 * 3 = 1/2 * ?
? = 4 1/2 * 3 / 1/2
? = 27 miles
the actual distance is 27 miles
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2
A math teacher observed that as the number of hours students studied their multiplication facts increased, the
number of errors the students made on their multiplication tests decreased. Which scatterplot could support this
teacher's observation?
F
G
Number of Errors
Number of Errors
10
0
y
10
0
Multiplication Tests
12 3 4
Study Time (hours)
Multiplication Tests
1 2 3 4
Study Time (hours)
5
H
J
Number of Errors
Number of Errors
10
2
10
Multiplication Tests
2
●
0 1 2 3 4
Study Time (hours)
Multiplication Tests
●
0 1 2 3 4
Study Time (hours)
5
A scatterplot that shows the number of hours studied on the x-axis and the number of errors on the y-axis would best support the teacher's observation.
What is error in math?Error in math is an incorrect answer to a mathematical equation or problem. It can be caused by a variety of factors, such as inaccurate calculations, misreading instructions, or not understanding the problem. Error in math can be frustrating and can lead to poor grades, but it can also be an opportunity for learning and growth. With the proper guidance and understanding, students can learn from their mistakes and become better mathematicians.
The scatterplot would likely show a negative correlation, with the number of errors decreasing as the number of hours studied increases. This indicates that as students study more, their performance on multiplication tests improves. It could also show an outlier or two, which could indicate that some students are able to learn multiplication facts more quickly than others.
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Match each system on the left with all words that describe the system on the right. Choices on the right can be used more than
once.
y = 3x - 1
2y - 6x = 4
2y = -x + 6
4y + 2x = 12
y = 2x + 3
x+y=-9
inconsistent
consistent
independent
dependent
So on solving the provided question we cans say that in the following linear equation values are y = -1, -3 , 3
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here ,
as we know that x = 0
so, y = 3x - 1 = -1
2y - 6x = 4 => y = 2
2y = -x + 6 = y = 3
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What are the 3 types of image?
There are the Following three types of images they are written as follows:
1. Image of an element: If x is a member of X, then the image of x under, f, denoted, f(x), is the value of f when applied to x. f(x) is alternatively known as the output of f for argument x.
2. Image of a subset: Throughout, let: f: X→Y be a function. The image under f of a subset A of X is the set of all f(a) for a ∈ A.
It is denoted by f[A],} or by f(A) when there is no risk of confusion.
3. Image of a function: The image of a function is the image of its entire or full domain, also called as the range of the function. This last usage should be evaded because the word "range" is also commonly used to mean the codomain off.
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An item is regularly priced at $93. Kira bought it at a discount of 45% off the regular price.
(50 points, thanks, 5 stars, brainliest, all that jazz, IF correct!)
If Kira had not have any discount, she would have bought the product at the normal selling price.
$ [tex]93[/tex]But that product was given a [tex]45[/tex]% discount on its regular price.
[tex]45[/tex]% [tex]=\frac{45}{100}=\frac{9}{20}[/tex]If the product had cost $[tex]100[/tex], the discount would have been $[tex]45[/tex].
So how many dollars would the discount be if it was $[tex]93[/tex]? We can determine this using a proportion.
[tex]93\frac{9}{20}=41.85[/tex]Kira will therefore be able to buy this product at a [tex]45[/tex]% discount for only;
[tex]93-(41.85)=51.15[/tex] dollars.In the accompanying figure, angle 1 measures 28o and angle 2 measures 11o. What is the measure of angle 3
The measure of angle 3 in the given triangle is 141 degrees.
Angle 1 + Angle 2 + Angle 3 = 180°
So, Angle 3 = 180° - (Angle 1 + Angle 2)
Angle 3 = 180° - (28° + 11°)
Angle 3 = 141°
The sum of the three angles in a triangle is 180 degrees, so to calculate the measure of angle 3, we can subtract the measures of angles 1 and 2 from 180 degrees. In this case, angle 1 measures 28 degrees and angle 2 measures 11 degrees, so the measure of angle 3 is 180 degrees minus (28 degrees + 11 degrees), or 141 degrees.
The measure of angle 3 in the given triangle is 141 degrees.
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Is 3x2 a exponential function?
No, 3x2 is not an exponential function. An exponential function is a function in which the variable (x) is in the exponent.
The general form of an exponential function is f(x) = a^x, where a is the base and x is the exponent.
In the case of 3x2, the variable (x) is not in the exponent, it's being multiplied by the coefficient 3. This is a linear function, not an exponential function. The general form of a linear function is f(x) = mx+c, where m is the coefficient and c is the y-intercept.
In summary, 3x2 is not an exponential function. An exponential function is a function in which the variable (x) is in the exponent. The general form of an exponential function is f(x) = a^x, where a is the base and x is the exponent. In the case of 3x2, the variable x is not in the exponent, it's being multiplied by the coefficient 3. This is a linear function, not an exponential function.
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A coach gives down and Anya a jug containing one and 5/8 gallons of water they will pour the water into three bottles Dan says he can pour 5/8 of a gallon into the first bottle one eighth of a gallon into the second bottle and 7/8 of a gallon into the third bottle Anja says she can pour 6/8 of a gallon into the first bottle 2/8 of a gallon into the second bottle and 5/8 of a gallon into the third bottle who is correct use the drop-down menus to explain
Answer:
Dan and Anja are both correct.
Step-by-step explanation:
Base on the given;
Total: [tex]1 \frac{5}{8}[/tex]
Dan:
1st Bottle: [tex]\frac{5}{8}[/tex]
2nd Bottle: [tex]\frac{1}{8}[/tex]
3rd Bottle: [tex]\frac{7}{8}[/tex]
Anja:
1st Bottle: [tex]\frac{6}{8}[/tex]
2nd Bottle: [tex]\frac{2}{8}[/tex]
3rd Bottle: [tex]\frac{5}{8}[/tex]
Since we know all the info now. Let's first add up all the bottles.
Dan:
[tex]\frac{5}{8}+\frac{1}{8}+\frac{7}{8}=[?][/tex] ⇒ Only add the numerator.
[tex]\frac{5}{8}+\frac{1}{8}+\frac{7}{8}=\frac{13}{8}[/tex] ⇒ Simplify
[tex]\frac{13}{8}=1\frac{5}{8}[/tex]
Anja:
[tex]\frac{6}{8}+\frac{2}{8}+\frac{5}{8}=[?][/tex] ⇒ Only add the numerator.
[tex]\frac{6}{8}+\frac{2}{8}+\frac{5}{8}=\frac{13}{8}[/tex]⇒ Simplify
[tex]\frac{13}{8}=1\frac{5}{8}[/tex]
Base on the given;
Total = [tex]1\frac{5}{8}[/tex]
From what we solve:
Dan and Anja are both correct.
Since the drop-down menus wasn't given. I can not farther given more info. Please have a link to the image if help is needed.
RevyBreeze
Write the rule to describe the transformation.
Answer:
Dilation of 3
Step-by-step explanation:
Note [tex]DE=2[/tex] and [tex]D'E'=6[/tex].
The scale factor is defined as the ratio of the length of the side of the image to the length of the corresponding side of the preimage.
So, the scale factor is [tex]\frac{6}{2}=3[/tex].
The dilation shown in the image is a dilation with a scale factor of 3
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (3x, 3y)
What is dilation?Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
Generally, transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
Examining the figure, Using side DE as reference we can see that DE is 1 unit
After dilation side D' E' transformed to 3 units, showing an increment of 3.
The dilation is an enlargement and the scale factor is 3
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Need help on this questuon
Answer:
2x⁷
Step-by-step explanation:
Same bases, when multiplying each other, we add the exponents.
Hence:
[tex] \displaystyle{2 {x}^{4} \times {x}^{3} = 2 {x}^{4 + 3} = 2 {x}^{7} }[/tex]
Reference to the laws of exponent here
[tex] \displaystyle{ {a}^{m} \times {a}^{n} = {a}^{m + n} }[/tex]
Which is the longest side in ∆ XYZ right angled at X?
The longest side in a right triangle is the hypotenuse, which is the side opposite the right angle.
In ∆ XYZ, if X is the right angle, then the hypotenuse would be the side connecting points Y and Z. This is because in a right triangle, the hypotenuse is always the side opposite the right angle and is also the longest side in the triangle. This can be proven using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
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Page 7:
You're helping a farmer determine the probability that certain vegetables will be
purchased. You know the following about the 100 customers the farmer provides
fruits to:
70 purchase carrots.
50 purchase cucumbers.
60 purchase lettuce.
20 purchase carrots and lettuce.
30 purchase cucumbers and carrots.
a. The probability that a randomly selected customer purchases lettuce is ___.
The probability that a randomly selected customer purchases lettuce is 3/5.
What is Probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given that there are 100 customers the farmer provides.
The number of customers purchasing lettuce is 60.
The probability that a randomly selected customer purchases lettuce,
P(L) = Number of customers purchasing lettuce ÷ Total number of customers
[tex]\implies P(L) = \frac{60}{100} \\\implies P(L) = \frac{3}{5}[/tex]
Therefore, the probability that a randomly selected customer purchases lettuce is 3/5.
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Challenge You have 2 different savings accounts. For Account A, the simple interest earned after 6 months is $4.88. For Account B, the simple interest earned after 27 months is $24.75. If the interest rate is 3.9% for Account A and 2.2% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
The principal of account A is $250.26
The principal of account B is $500
The account that would earn you more interest in the first month is account B
What are the principals?
Simple interest is the interest earned on an amount of money in a savings account.
Simple interest = principal x time x interest rate
Principal is the amount deposited
Principal = simple interest / ( time x interest rate)
Principal of account A = 4.88 / (6/12 x 0.039) = $250.26
Principal of account B = 24.75 / (27/12 xx 0.022) =$500
Interest earned in the first month:
Account A = (1/12) x 250.26 x 0.039 = .81
Account B = (1/12) x 500 x 0.022 =0.92
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Is 16 a factor of 8?
No, number 16 is not representing as a factor of 8. The given statement is false as it is a multiple of 8.
As given in the question,
Given number is equal to 8,
Given factor is equal to 16:
Factors are those numbers which divides the given numbers without leaving any remainder. It exactly divides the given original number.
Here given factor 16 does not divides the given number 8.
Instead 8 divides the the number 16.
here '8' is the factor of the number 16.
And 16 represents as a multiple of 8.
Therefore, the given statement is false and 16 is not considered as a factor of 8 instead it is a multiple of 8.
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If B is the midpoint of AC and AB = 5 Find BC and AC.
The length of BC is 5
The length of AC is 10
Midpoint of a line: Calculating length of a lineFrom the given information, we are to calculate the length of the given parts of line AC
From the given information,
B is the midpoint of AC
Thus,
We can write that
AB + BC = AC
and
AB = BC
Also, from the given information,
AB = 5
Therefore,
BC = 5
From the equation,
AB + BC = AC
Substitute the values of AB and BC
5 + 5 = AC
10 = AC
AC = 10
Hence, BC = 5 and AC = 10
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