The slope of the given line that runs through the points are:
1. Defined
2. Defined
3. undefined.
What is an Undefined Slope of a Line?An undefined slope of a line can be described as the slope of a vertical line that has no run but only rise. That is, the x-coordinates do not change even though the y-coordinates of the line are changing.
Thus, the change in x-coordinates is always 0.
Slope = change in y / change in x.
a. (5 , − 4) and (0 , 1):
Slope = (-4 - 1)/(5 - 0)
Slope = -5/5 = -1 [the slope is defined]
b. (−1 , 8) and (7 , 10):
Slope = (10 - 8)/(7 -(-1))
Slope = 2/8
Slope = 1/4
c. (-4, 12) and (-4, 5)
Slope = (12 - 5)/(-4 -(-4))
Slope = 7/0 [cannot divide, therefore, the slope is undefined]
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Pls I need help ASAP!!!!!
( 5,0 ) and ( 0,4 ) are the x and y-intercept of the function 4x + 5y = 20 respectively.
How to solve for x and y-intercept?The intercept of a line on a graph is simply the point at which it intersects either the x-axis or y-axis.
Given the data in the question;
4x + 5y = 20Input value when output is 0 = ?Output value when input is 0 = ?Now, we find the intercepts of the equation of line, plug in y = 0 and solve for x
4x + 5y = 20
4x + 5(0) = 20
4x = 20
x = 20/4
x = 5
Hence, the x-intercept is ( 5,0 )
For the y-intercept, plug in x = 0 and solve for y
4(0) + 5y = 20
5y = 20
y = 20/5
y = 4
Hence, the y-intercept is ( 0,4 ).
Therefore the x and y-intercept are ( 5,0 ) and ( 0,4 ).
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Find the perimeter and the area of the figure.(assume right angles and parallel sides except we’re obviously otherwise)Simplify your answer and round to the nearest TENTH.
Given:
The length of the parallel sides,
a=17.4 m
b=44.1 m
The height, h=23.5 m
The measurements of the other two sides are,
c=27.5m and d=26.6m.
To find the area of the trapezium:
Using the formula,
[tex]\begin{gathered} A=\frac{1}{2}\times(a+b)\times h_{} \\ =\frac{1}{2}\times(17.4+44.1)\times23.5 \\ =\frac{1}{2}\times61.5\times23.5 \\ =722.625\text{ square meters} \end{gathered}[/tex]Hence, the area of the figure is 722.6 sq. m (rounded to the nearest tenth).
To find the perimeter of the trapezium:
[tex]\begin{gathered} P=a+b+c+d \\ =17.4+44.1+27.5+26.6 \\ =115.6\text{ m} \end{gathered}[/tex]Hence, the perimeter of the figure is 115.6 m.
If 10 workers take eight hours to sew a stores order of pants, then how long would 15 workers take to sew the stores order of pants? Assume all workers work at the same steady rate and all the pants are the same. Part A.) Is the proportion 8hours/10 workers = Xhours/15 workers appropriate for solving the sewing problem why or why not? Part B.) explain how to reason about multiplication and division with quantities to solve the sewing problem
According to the given data we have the following proportion:
8hours/10 workers = Xhours/15 workers
A) The above proportion is not appropiate for solving the problem.
Since, the relationship between the number of workers and the time taken for sewing is an inverse relation:
The above proportion is just a direcly proportional relation.
B). As I stated above the relationship between the number of workers and the time taken for sewing is an inverse relation, hence, if the number of workers doubles then the number of time taken reduces to half.
So, since 15=10*15/10
therefore, time taken for 15 workers to sew pants is:
8/ 15/10 = 8* 10/15
=5 1/3 hours.
The time taken for 15 workers to sew pants is 5 1/3 hours.
calcula correctamente cada una de las ecuaciones de la recta.
pasa por los puntos a(4,-6) y b(-5,3)
The equation of straight line of the points is given as y = -x - 2
Equation of Straight LineTo solve this problem, we simply need to find the equation of straight line which can be done by finding the slope of the line and then intercept of the line.
In the given points;
A = (4, -6)B = (-5, 3)The formula of slope of a line is given as
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Substituting the values into the equation;
[tex]m = \frac{3 - (-6)}{-5 - 4} \\m = \frac{9}{-9} \\m = -1[/tex]
The slope of the line is equal to 1.
Let's find the intercept of the line
[tex]y = mx + c[/tex]
Taking point A;
[tex]y = mx + c\\-6 = -1(4) + c\\-6 = -4 + c\\c = -2[/tex]
The equation of the line is y = -x - 2
Translation: Find the equation of a straight line from two point A(4, -6) and B(-5, 3).
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The two parallelograms are similar. Find the degree measure of the angle. Explain your reasoning.
Answer:
3. ∠A = 110°
4. ∠H = 70°
5. ∠D = 70°
6. ∠F = 70°
Step-by-step explanation:
In a parallelogram, adjacent angles are supplementary (sum to 180°).
⇒ ∠A + ∠B = 180°
⇒ ∠A + 70° = 180°
⇒ ∠A = 110°
In a parallelogram, opposite angles are congruent.
⇒ ∠C = ∠A = 110°
⇒ ∠D = ∠B = 70°
If two parallelograms are similar, their corresponding interior angles are congruent.
⇒ ∠A = ∠E = 110°
⇒ ∠B = ∠F = 70°
⇒ ∠C = ∠G = 110°
⇒ ∠D = ∠H = 70°
. A farmer ships oranges in wooden crates. Suppose each orange weighs the same amount. The total weight of a crate filled with g oranges is 24.5 pounds. Write an equation that represents the relationship between the weight of the crate and the number of oranges it contains.
The equation that represents the relationship between the weight and number of oranges is [tex]w[/tex]·[tex]g=24.5[/tex]
What is an equation?
An equation is a formula which represents the equality between two expression.
We are given each orange weight the same.
Let the weight of one orange be [tex]w[/tex].
Also we are given that there are [tex]g[/tex] oranges in the crate
Also the weight of the crate is 24.5 pounds
Now the equation representing the relationship between weight and number can be given by
[tex]w[/tex]·[tex]g=24.5[/tex]
Hence the equation representing the relationship between weight and number can be given by [tex]w[/tex]·[tex]g=24.5[/tex]
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In one serving of oatmeal, the ratio of the number of ounces of oats to the number of ounces of dried fruit is 4 to 7.
how many ounces of oats and dried fruit are needed for different numbers of servings.
The number of ounces of oats and dried fruit are needed for different numbers of servings are as follows:
2 servings = 8 ounces of oats and 14 ounces of dried fruit.6 servings = 24 ounces of oats and 48 ounces of dried fruit.7 servings = 28 ounces of oats and 49 ounces of dried fruit.What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
In this scenario, we know that the ratio of the number of ounces of oats (O) in one serving to the number of ounces of dried fruit (D) in one serving is equal to 4 to 7.
For 2 servings, the ratio would be given by:
O:D = 2 × 4 : 2 × 7 = 8:14
Therefore, we have 8 ounces of oats and 14 ounces of dried fruit.
For 6 servings, the ratio would be given by:
O:D = 6 × 4 : 6 × 7 = 24:48
Therefore, we have 24 ounces of oats and 48 ounces of dried fruit.
For 7 servings, the ratio would be given by:
O:D = 7 × 4 : 7 × 7 = 28:49
Therefore, we have 28 ounces of oats and 49 ounces of dried fruit.
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The annual yield per walnut tree is fairly constant at 50 pounds per tree when the number of trees per acre is 30 or fewer. For each additional tree over 30, the annual yield per tree for all trees on the acre decreases by 1.5 pounds due to overcrowding.
Express the total yield for an acre, T, in pounds as a function of the number of walnut tree per acre, x
The total yield for an acre, T, in pounds as a function of the number of walnut tree per acre, x is given by T = -1.5x² + 95x.
How to determine an equation for the total yield?In order to solve this word problem, we would assign variables to the number of walnut tree per acre and total yield for an acre, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of walnut tree per acre.Let the variable T represent the total yield for an acre.Mathematically, the total yield for an acre can be calculated by using this mathematical expression:
Total yield for an acre (T) = yield of each tree × number of trees per acre
Substituting the given parameters into the mathematical expression, we have the following;
Total yield for an acre (T) = [50 - 1.5(x - 30)] × x
Opening the bracket, we have:
Total yield for an acre (T) = [50 - 1.5x + 45] × x
Total yield for an acre (T) = 50x - 1.5x² + 45x
Next, we would rearrange the function by collecting like terms and simplifying as follows:
Total yield for an acre (T) = -1.5x² + (50x + 45x)
Total yield for an acre (T) = -1.5x² + 95x
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The slope is For 3 and 4, find the slope of the line that passes through the given points. 3. (0, 10) and (24, 6) 4. (0,6) and (20, 14)
3. The slope of the line through the points (0, 10) & (24, 6) is [tex]\frac{1}{4}[/tex]
4. The slope of the line through the points (0, 6) & (20, 14) is [tex]\frac{2}{5}[/tex]
What is meant by slope?The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope of a line, or a section of a line connecting two points, is a measure of its steepness.
Or. A line's slope is the ratio of how much y increases as x increases by some amount. The slope-intercept form of an equation is when the equation of a line is written in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b).
How are the slopes calculated?
3. We know that , slope = m
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex](x_{1}, y_{1})=(0, 10)\\\\(x_{2}, y_{2})=(24, 16)[/tex]
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m= \frac{16- 10}{24 -0}\\\\m= \frac{6}{24}\\\\m=\frac{1}{4}[/tex]
4. We know that , slope = m
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex](x_{1}, y_{1})=(0, 6)\\\\(x_{2}, y_{2})=(20, 14)[/tex]
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m= \frac{14- 6}{20 -0}\\\\m= \frac{8}{20}\\\\m=\frac{2}{5}[/tex]
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The sale price of every item in a store is 85% of its usual price. The usual price of a backpack is $30. What is its sale price? The sale price of a sweatshirt is $34. What is its original price?
The sale price of the backpack is $25.50.
The original price of the sweatshirt is $40.
How to calculate the price?From the information, the sale price of every item in a store is 85% of its usual price and the usual price of a backpack is $30.
The sale price will be:
= Percentage × Original price
= 85% × $30
= $25.50
The sale price of a sweatshirt is $34, its original price will be:
= 85% × x = $34
0.85x = $34
x = $34 / 0.85
x = $40
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30 students in Mrs. Woodward‘s class and 1/5 of the class has their own cell phone of this group of students 1/2 of them are allowed to use social media how many of the students have a cell phone and you can use social media
Answer:
6 students have their own cell phone and 3 of them can use social media.
Step-by-step explanation:
One fifth of 30 is 6. One half of six is 3.
10. Cual de los siguiente enunciados es
verdadero?
1. e
4
es irracional por que es un
decimal
2. 2.33333...... es irracional por
que este no termina.
3. 0.125 es racional por que este se
puede escribir como una
fraccion.
4. 0.28152121.... es racional por
que este no termina.
ordered pair
-5x-4y=3
3x+10y=-17
The ordered pair of the solution of the equations -5x-4y=3 and 3x+10y=-17 is (1,-2).
The provided equations are,
Equation 1,
-5x-4y=3
Equation 2,
3x+10y=-17
Both the equations are linear equations is two variables,
We can use substitution method to solve these two equations,
From equation 1 we get,
-5x-4y=3
y = (-5x-3)/4
Now, substituting the value of y in equation 2,
we get,
3x+10( (-5x-3)/4)=-17
Solving and simplifying,
12x-50x-30 = -68
-38x = -38
x = 1,
Now, substituting x = 1 in equation 2,
we get,
3(1)+10y=-17
10y = -20
y = -2.
So, the ordered pair is (1,-2).
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A financier plans to invest up to $500,000 in two projects. Project A yields a return of 10% on the investment where Project B yields a return of 15% on the investment. Because the invesemtns in project B is risker than the invesments in project A, the finaniced has decided that the invesment in projcect B should not exceed 40% of the total investment. How much should she invest in each project in order to maximize the retirn on her invesment? what is the maximum return?
She needs to invest $[tex]300,000\\[/tex] in project A and $[tex]200,000[/tex] in project B in order to maximize the return on her investment.
$[tex]500,000[/tex] is allotted for two projects Project A yields a return of [tex]10%[/tex]% and Project B yields a return of [tex]15%[/tex]% Investments in project B are riskier than investments in project A Investments in B should not exceed [tex]40%[/tex]% of the total invest How much money needs to invest in each project in order to maximize the return on the investment?What is the maximum return?Since a financier has $[tex]500,000[/tex] which she needs to invest in two projects named A and B
Out of the two projects A and B, project B is giving higher rate of return on the investment so maximum investment needs to be done on the project B
Hence in project B total percentage of investment will be [tex]40%[/tex]% which is also given it needs not to exceed more than [tex]40[/tex]%
Hence the investment amount on the project B is [tex]40[/tex]% of $[tex]500,000[/tex]
which is [tex](0.4)*$500,000[/tex] which is equal to $[tex]200,000[/tex] which is an investment in project B
Now the investment in project A will be $[tex]500,000[/tex]-$[tex]200,000[/tex]=$[tex]300,000[/tex]
Hence she needs to invest $[tex]300,000[/tex] in project A and $[tex]200,000[/tex] in project B.
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On a sunny day, a 3-foot red kangaroo casts a shadow that is 5 feet long. the shadow of a nearby eucalyptus tree is 7 feet long. find the height of the tree.
Answer: 5 feet
Step-by-step explanation:
The kangaroo added 2 feet of length to the shadow, therefore adding 2 feet of length of the 5 foot tree.
7-2=5
( sorry if it's confusing ^^ )
Solve the equation for x. 2x+y=7
Answer:
b)
Step-by-step explanation:
2x+y=7
2x=7-y
x=(7-y)/2
Answer: B
Step-by-step explanation:
n
Select the locations on the number line to plot the points -2, -11, and -17
Answer:
-17 would be three tick marks to the right of -20
-11 would be 9 tick marks to the right of -20 or 6 right of the tick mark for -17
-2 would be 18 tick marks to the right of -20 or 15 tick marks to the right of -17 or 9 tick marks to the right of -11
Step-by-step explanation:
-20, -19, -18,-17 This is what -17 is three tick marks to the right of -20
-20 -19 -18 -17 -16 -15 -14 -13 -12 -11
-20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2
Question on my test that I need to do. It's due today in 35 minutes! Please help!
The equivalent expression to 3x - [tex]\frac{1}{2}[/tex]y + 2 [tex]\frac{2}{3}[/tex]y - [tex]\frac{5}{6}[/tex]x is C. 2 [tex]\frac{1}{6}[/tex]x + 2 [tex]\frac{1}{6}[/tex]y
What is an expression?An expression is simply used to show the relationship between the variables that are given in the data.
The fractions given will be illustrated as:
3x - [tex]\frac{1}{2}[/tex]y + 2 [tex]\frac{2}{3}[/tex]y - [tex]\frac{5}{6}[/tex]x
Collect like terms
= 3x - x + 2 [tex]\frac{2}{3}[/tex]y - [tex]\frac{1}{2}[/tex]y
= 2 [tex]\frac{1}{6}[/tex]x + 2 [tex]\frac{4}{6}[/tex]y - [tex]\frac{3}{6}[/tex]y
= 2 [tex]\frac{1}{6}[/tex]x + 2 [tex]\frac{1}{6}[/tex]y
In conclusion, the correct option is C.
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help ne
-photos attached!!
Translate the triangle 4 units right and 3 units down. What are the coordinates of the image
-4-3-2
K
4
3
-2
O
2
234x
The coordinates are J'(_,_)K’(_,_)and L’(_,_)
Answer:
J': (3, 6)
K': (3, 4)
L': (0, 4)
Step-by-step explanation:
When we translate a point 4 units right, the x-coordinate of the point increases by 4 units, the y-coordinate remains the same
When a point is translated 3 units down, the y coordinate increases by 3 units, the x-coordinate remains the same
When you translate by 4 units right and 3 units down both x and y coordinates increase by 4 and 3 respectively
So when we apply this translation to the triangle, every point on that triangle, (x, y) changes to (x + 4, y + 3)
If we take the vertices of the triangle we see that the 3 vertices are
J(-1, 3) K(-1, 1) and L(-4, 1)
After applying the translation:
J(-1, 3) ==> J'(-1 + 4, 3 + 3) ==> J'(3, 6)
K(-1, 1) ==> K'(-1 + 4, 1 + 3) ==> K'(3, 4)
L(-4, 1) ==> L'(-4 + 4, 1 + 3) ==> L'(0, 4)
katlin bought 14 pencils, it costs her $3.50. how much did each pencil cost?
Answer: 0.25$ or a quarter
Step-by-step explanation:
Katlin bought 14 pencils, which cost her $3.50. So all you have to do is divide the amount ($) by the number of pencils.
3.50/14 = 0.25$
3.50 divided by 14
Each pencil cost a quarter
The distance from the earth to the sun is 1.5 extend eight KM and the distance from Mars to the sun is 2.2 8 X 10 eight KM what is the distance between earth and mars expressed in scientific notation
The distance between the Earth and the Sun is 1.5 extend eight kilometers, and the distance between Mars and the Sun is 2.2 8 X 10 eight kilometers. The scientific notation for the distance between Earth and Mars is 3.78 x 10^8 km.
How to find a distance?The length of the line connecting two points is the distance between them. If the two points are on the same horizontal or vertical line, the distance can be calculated by subtracting the non-identical coordinates.
Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point.
Given,
The distance between Earth and Sun = 1.5 x 10^8 km
The distance between Sun and Mars = 2.28 x 10^8 km
Therefore the distance between Earth and Mars =
(1.5 x 10^8 + 2.28 x 10^8) km
= (1.5 + 2.28) x 10^8 km
= 3.78 x 10^8 km (Ans)
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What is the value of g(-4)?
The value of g(-4) from the function is 1
What is a function?A function can be defined as a law, rule or theorem that asserts or explains the relationship between two variables in an equation or expression.
These variables are called;
The dependent variableThe independent variableGiven the functions as;
g(x) = [tex]\sqrt[3]{x + 5}[/tex] when x ≤ -4g(x) = - x²+ 11 when x > -4To determine g(-4), we can see that the first function of g(x) would be used.
We have;
g(-4) = [tex]\sqrt[3]{x + 5}[/tex]
Substitute the value of x as - 4, we have;
g(-4 = [tex]\sqrt[3]{-4 + 5}[/tex]
g(-4) = ∛1
Find the cube root
g(-4) = 1
Hence, the value is 1
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988 x 6.2
show your work
can someone pls give the answers to this
Answer:
(-1,2),(-1,-3),(3,-3)
Step-by-step explanation:
You times the coordinate by 1/3
which expression is equivalent to 4 sqrt 6/3 sqrt 2
12 sqrt 27/2
4 sqrt 24/2
12 sqrt 55296/2
12 sqrt 177147/3
The provided expression is equivalent to the expression mentioned in option (C) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The number expression is:
[tex]= \dfrac{\sqrt[4]{6} }{\sqrt[3]{2} }[/tex]
After applying the integer exponent property:
[tex]= \dfrac{\sqrt[4]{6} }{\sqrt[3]{2} } \times\dfrac{\sqrt[3]{2^2} }{\sqrt[3]{2^2} }[/tex] (rationalization)
[tex]= \dfrac{\sqrt[4]{6} \times\sqrt[3]{2}}{2 }[/tex]
= [tex]\rm \dfrac{\sqrt[12]{55296} }{2}[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
Thus, the provided expression is equivalent to the expression mentioned in option (C) is correct.
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Two families purchased lunch at a hotdog cart. The Cortez family paid $18.00 for 4 hot dogs and 4 drinks. The Lee famliy paid $20.00 for 5 hot dogs and 3 drinks.
What is the price, in dollars, of a hot dog?
Answer:
it would be 4.5 or 4.50 for the Cortez and the Lees payed 4 dollars
Step-by-step explanation:
what is the new side length of a in the actual figure
Answer:
Context? You need to have some information or a picture.
Step-by-step explanation:
A rectangular park is w ft wide. The park is 25 ft longer than its wide.Record your answer to each using Algebra.
What is the length of a fence (inculding the gates) that was built around the park
The length of the fence (including the gates) that was built around the park is (4w + 50) feet.
Here, we are given that a rectangular park is w ft wide and the park is 25 ft longer than its wide.
Thus, the length of the park = (w + 25) ft
Now, the park has to be fenced along all of its sides. Thus, we need to find the perimeter of the rectangular park.
The perimeter of a rectangle is given as-
2( length + breadth)
Thus, here, the perimeter will be-
2( w + 25 + w )
= 2( 2w + 25 )
= 4w + 50
Thus, the length of the fence (including the gates) that was built around the park is (4w + 50) feet.
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3ab+3c=2x solve for b
Step-by-step explanation:
ab + 3c = 2x
Subtract 3c from both sides
ab = 2x - 3c
Isolate b by dividing by a
b = (2x -3c)/a
What is prime factorization explained very simply? (Please show an example)
We got the factors which is prime numbers = 2 × 2 × 2 × 3
Define Prime Factorization ?
The technique of expressing all numbers as the product of primes is known as prime factorization. So, let's take something like the number 20 as an example. That can be divided into two components. "Well, that's 4 times 5," we can respond. Observe that 5 is a prime number.
For e.g, let's take number of 24 and factor it,
24/2 = 12
12/2 = 6
6/2 = 3
3/3 = 1
We got the factors which is prime numbers = 2 × 2 × 2 × 3
which is equal to given number i.e, 24.
See another example in image.
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