Answer:
The slope of a line is the change in y divided by the change in x.
( y1 - y2 ) / ( x1 - x2 )
It does not matter which point you choose as (x1, y1) and (x2,y2)
( 7 - 1 ) / ( 1 - 10 )
( 6 ) / ( -9 ) This will simplify to -2/3.
Explain how you can tell if the expressions 7x – 4 and 6x – 4 – x are equivalent using the interactive tool.
Answer:
commutative property: the property stating that changing the order in which two numbers are added or multiplied does not change the value of the sum or product
equivalent: having the same amount, value, area, volume, or force
evaluate: to determine the value of
like terms: terms consisting of the same variables, raised to the same exponent
Step-by-step explanation:
TRUST me this is RIGHT
To analyze whether two algebraic expressions are equivalent, you can use an interactive tool such as an algebra solver or calculator to compare the results of the expressions for various values of x. Simplify the expressions if possible, compare the simplified expressions, and verify the results by substituting different x-values.
Explanation:To determine if the expressions 7x – 4 and 6x – 4 – x are equivalent, you can use an interactive tool like an online algebra solver or calculator. This process usually involves comparing the results of the expressions for multiple values of x.
Step 1:
Firstly, simplify the expressions if possible. For the second expression, 6x – 4 – x, you can simplify it as 5x – 4.
Step 2:
Now, compare the simplified expressions, you can see that 7x - 4 and 5x - 4 are not equivalent as the coefficients of x (7 and 5) are not equal.
Step 3:
Last, for verification, you can substitute different values of x into both equations and see if the outputs are the same. If the outputs are different then, the equations are not equivalent.
Learn more about Algebraic Expressions here:https://brainly.com/question/953809
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How far from the base of the house do you need to place a 15 foot ladder so that it exactly reaches the top of a 12 foot wall?
Answer:
9 ft
Step-by-step explanation:
The ladder is 15 foot
The height the ladder reaches from the bottom of the wall is 12 ft
The distance (x) from the bottom of the wall to the foot of the ladder is:
Applying the Pythagorean theorem;
x = [tex]\sqrt{15^2 - 12^2}[/tex] = 9 ft
A 15 foot ladder needs to be placed at a distance of 9 foot from the base of the house so that it exactly reaches the top of a 12 foot wall.
Further Explanation:Right triangle A right triangle is a triangle with one of its angles being 90 degrees or right angle.The triangle has two shorter sides making the right angle and the hypotenuse which is the longest side.Scalene triangleIt is a triangle that with sides and angles that are not equal.Pythagoras Rule According to Pythagoras rule, in a right angled triangle if the squares of the shorter sides are added then they are equivalent to the square of the hypotenuse.That is; [tex]a^{2} + b^{2} =c^{2}[/tex], where a and b are the shorter sides while c is the hypotenuse.In this case;
The ladder, the wall of the house and the ground from the base of the house makes a right angled triangle;Therefore;
Length of the ladder is the hypotenuse which is 15 ftThe wall of the house is one of the leg which is 12 ftWe are going to find the distance of the ladder from the base of the house on the ground which is the other leg.
Using Pythagoras theorem;
[tex]a^{2} + b^{2} = c^{2}[/tex]
Taking the horizontal distance of the ladder from the wall as b
Then;
[tex]b^{2} = c^{2} -a^{2}[/tex]
therefore,
[tex]b^{2} = 15^{2} -12^{2}[/tex]
[tex]b^{2} = 225 -144[/tex]
[tex]b^{2} = 81[/tex]
[tex]b = \sqrt{81} \\b= 9 ft[/tex]
Hence; the ladder needs to be placed at a distance of 9 foot from the base of the house.
Keywords: Right triangle, Pythagoras rule
Learn more about: Pythagoras theorem: brainly.com/question/13035995Right triangle: brainly.com/question/13035995Application of Pythagoras theorem: https://brainly.com/question/11638432Level; High school
Subject: Mathematics
Topic: Pythagoras theorem
Describe the translation of f(x) = |x|.
f(x) = (x + 51 - 3
5 units left, 3 units down
3 units left, 5 units down
5 units right, 3 units up
3 units right, 5 units up
5 unit to left, 3 units down is the correct answer.
If you know that two angles are supplementary angles and you know the measurement of one of the angles, describe how you would find the measurement of the unknown angle.
Since supplementary angles add up to 180°, you would subtracted the measurement that you have from 180°.
Ex.
180-x= y
X being the measurement that you have, and y being the missing measurement.
what what awdddddddddddddddddddd
8,441 ÷ 21
Answer: 401.952380952
Step-by-step explanation:
In the rhombus, m angle 1 =40. Find m angle 2
ANSWER
40°
EXPLANATION
The opposite sides of a rhombus are parallel.
This implies that, the diagonal is a transversal.
This means that,
m<1 and m<2 are alternate interior angles.
Since alternate interior angles congruent,
m<1 =m<2=40°
The correct choice is C.
Help me answer this question please
Answer:
D.
Step-by-step explanation:
For this case we have:
Let k> 0:
To graph [tex]y = f (x) + k,[/tex] the graph k units is moved up.
To graph [tex]y = f (x) -k[/tex], the graph moves k units down.
Let h> 0:
To graph[tex]y = f (x-h)[/tex], the graph moves h units to the right.
To graph [tex]y = f (x + h),[/tex] the graph moves h units to the left.
So, we have:
[tex]y = f (x) = - \sqrt [3] {x}[/tex]
Shifted 7 units up and 4 to the right means:
[tex]k = 1\\h = 4[/tex]
[tex]y = f (x) = - \sqrt [3] {x-4} +7[/tex]
Answer:
Option B
Jenna's family is going on a trip * after driving 72 miles they used 3.2 gallons of gas * After driving 72 miles, they used 3.2 gallons of gas *Her family has 850 miles remaining on their road trip *The gas tank holds 15 gallons They filled the gas tank at the start of the road trip. They plan to only stop to fill up when their gas tank nears empty. There are plenty along the route. HOW MANY ADDITIONAL STOPS FOR GAS WILL THEY NEED TO MAKE TO GET TO THEIR DESTINATION? explain your answer using numbers words and/or pictures
Answer:
2
Step-by-step explanation:
Given Data:
total distance= 850 miles
gas tank holds gas= 15 gallons
mileage = 72/3.2 miles/gallon
if
72 miles uses= 3.2 gallon
then
850 miles uses= x gallons
by cross-multiplication we get
72x=3.2(850)
x=37.778
i.e. 850 miles will use 37.7778 gallon of gas
Asgas tank holds 15 gallons
number of times gas tank is used up= 37.3/15
= 2.518
rounding off
number of times gas tank is used up=3
As they filled the gas tank at the start of the road trip, hence 3-1=2
ADDITIONAL STOPS FOR GAS WILL THEY NEED TO MAKE TO GET TO THEIR DESTINATION =2 !
What is the solution to the matrix equation [2 1 1 0]x=5/10
[2 1 | 1 0 ] • x = [5 | 10]
We multiply by the inverse of
[2 1 | 1 0 ]
det( [2 1 | 1 0] ) = -1
=> [2 1 | 1 0 ]^(-1) = (-1)•[0 -1 | -1 2 ] =
= [0 1 | 1 -2]
=> [2 1 | 1 0 ] • x = [5 | 10]
=> x = [2 1 | 1 0 ]^(-1) • [5 | 10]
=> x = [0 1 | 1 -2] • [5 | 10]
=> x = [0+10 | 5-20]
=> x = [10 | -15]
Please help :) I’m struggling
Answer:
an = -1.3n -2.4
Step-by-step explanation:
The formula for an arithmetic sequence is
an = a1 +d (n-1)
where a1 is the first term and d is the common difference
an = -3.7 - 1.3(n-1)
Distribute
an = -3.7 -1.3n +1.3
an = -2.4 - 1.3n
an = -1.3n -2.4
(HELP ASAP!)
Which postulate or theorem proves △HJZ∼△WJR ?
Answer:
SAS Similarity Theorem
Step-by-step explanation:
we know that
SAS Similarity Theorem: States that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar
In this problem
∠HJZ=∠RJW ----> by vertical angles
and
WJ/HJ=JR/JZ
substitute the values
8/4=6/3
2=2 ----> is true
so
Two sides of triangle HJZ are proportional with the two corresponding sides of triangle WJR and the included angle is congruent
therefore
Triangles are similar by SAS Similarity Theorem
Can someone help find the positive and negative coterminal for this problem please. I got either the positive or negative one wrong but I keep getting the same answer separately for both.
Check the picture below.
let's notice that 89/36 => 2 and 17/36, namely 2π or two revolutions and then a bit more, the 17/36 slack, so then -89π/36 = - 2π - 17π/36.
the positive angle will of course be 2π - 17π/36 = 55π/36.
The costs of Brand A and Brand B coffee beans are $400/kg and
$280/kg respectively. x kg of Brand A coffee beans and y kg of
Brand B coffee beans are mixed so that the cost of the mixture is
$320/kg. Find the ratio of x:y.
Answer:
The ratio of x:y is 1/2
Step-by-step explanation:
Let
x----> the number of Kg of brand A
y ---> the number of Kg of brand B
we know that
400x+280y=320(x+y)
400x+280y=320x+320y
400x-320x=320y-280y
80x=40y
x/y=40/80
x/y=1/2
Final answer:
The ratio of Brand A coffee to Brand B coffee (x to y) required to achieve a mixture cost of $320/kg is 1 : 2. This is derived using the weighted average cost formula and simplifying the resulting equation.
Explanation:
To find the ratio of x to y for the mix of Brand A and Brand B coffee beans, we can use a weighted average cost formula since the mixture's cost is given to be $320/kg. Let's assume we have x kilograms of Brand A coffee at $400/kg and y kilograms of Brand B coffee at $280/kg. The total cost for all the coffee is then $400x + $280y.
The combined weight of the coffee is x + y kilograms, and for the mixture to cost $320/kg, the total cost divided by the total weight must equal $320. Therefore, we can set up the following equation:
($400x + $280y) / (x + y) = $320
Multiplying both sides by (x + y) we get:
$400x + $280y = $320x + $320y
Now, we subtract $320y from both sides to isolate terms with x:
$400x - $320x = $320y - $280y
$80x = $40y
Dividing both sides by $40 gives us the simplified ratio:
x : y = 1 : 2
Thus, the ratio of Brand A coffee to Brand B coffee in the mixture to get a $320/kg cost is 1 : 2.
If the triangles in the figure are similar what is the length of side b?
Answer:
A 36
Step-by-step explanation:
We can determine the scale factor
From triangle ABC BC =9
DEF EF = 90
We multiply by 10
The scale factor is 10
AC ( 10) = DF
We know DF = 360
b * 10 = 360
Divide each side by 10
10b/10 = 360/10
b = 36
What is the first step to solving the division problem below
Answer:
The answer is A.
Step-by-step explanation:
I got this answer by going through the regular division system.
What is the volume, in cubic units, of a pyramid of height 8 and a square base of length 15?
Answer:
900 cuboc unit
Step-by-step explanation:
Volume of pryamid= 1/3× area× height
= 1÷3×15^15×8
= 900cubic unit
For this case we have by definition, that the area of a square base pyramid is given by:
[tex]V = \frac {L ^ 2 * h} {3}[/tex]
Where:
L: It's the side of the square base
h: It's the height of the pyramid
We have that[tex]L = 15 \ units[/tex], then [tex]L ^ 2 = 15 ^ 2 = 225 \ units ^ 2[/tex]
Substituting:
[tex]V = \frac {225 * 8} {3}\\V = 600 \ units ^ 3[/tex]
Finally, the volume of the pyramid is [tex]600 \ units ^ 3[/tex]
Answer:
[tex]600 \ units ^ 3[/tex]
Three consecutive integers whose sum is 363.
For this case we must find three consecutive whole numbers whose sum is equal to 363. These numbers should be close to 120. So, these numbers are:
120,121 and 122. If we add them together we have:
[tex]120 + 121 + 122 = 363[/tex]
Answer:
120,121 and 122
[tex]120 + 121 + 122 = 363[/tex]
Calculate the product matrix for the following matrix multiplication.
Answer:
[tex]\large\boxed{\left[\begin{array}{ccc}43&6\\-70&-33\end{array}\right] }[/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}8&3\\-7&2\end{array}\right] \cdot\left[\begin{array}{ccc}8&3\\-7&-6\end{array}\right] \\\\=\left[\begin{array}{ccc}(8)(8)+(3)(-7)&(8)(3)+(3)(-6)\\(-7)(8)+(2)(-7)&(-7)(3)+(2)(-6)\end{array}\right] \\\\=\left[\begin{array}{ccc}43&6\\-70&-33\end{array}\right][/tex]
Answer:
D
Step-by-step explanation:
43, 6
-70, -33
In a study, 1,085 out of 2,321 people did not receive a flu
vaccination. 465 people were vaccinated and tested positive
for the flu. A total of 1,371 participants tested negative.
Create a two-way table for this scenario.
Answer:
Vaccinated: 465, 771, 1236
Not Vaccinated: 485, 600, 1085
Total: 950, 1371, 2321
Step-by-step explanation:
Next Question: 465/1236
It is given that:
In a study, 1,085 out of 2,321 people did not receive a flu vaccination.This means that the total of all the entries i.e. total of each row and each column is equal to 2321
Also, the sum of the second row is equal to: 1085
This means that the sum of the first row i.e. number of people who were vaccinated is: 2321-1085=1236 465 people were vaccinated and tested positive for the flu. This means that the number of people who were tested negative but were vaccinated are: 1236-465=771 A total of 1,371 participants tested negative.This means that the sum of second column is: 1371
Hence, sum of first column will be: 2321-1371=950Also, the second entry of the first column is calculated by: 950-465=485and the second entry of second column is: 1371-771=600The table is attached to the answer.
In a survey, 300 adults and children were asked whether they preferred hamburgers or pizza. The survey data are shown in the relative frequency table.
Answer:
D. 40%
Step-by-step explanation:
You can fill in the table completely
[tex]\begin{array}{cccc}&\text{Hamburgers}&\text{Pizza}&\text{Total}\\\text{Adults}&0.24&0.36&0.6\\\text{Children}&0.11&0.29&0.4\\\text{Total}&0.35&0.65&1\end{array}[/tex]
From this table you can state that the probability that a randomly selected person is a child is 0.4 that is 40%.
The percentage of the people surveyed are children is:
40%
Step-by-step explanation:We are given a table as follows:
HAMBURGERS PIZZA TOTAL
ADULTS 0.24 0.36 0.6
CHILDREN 0.11 0.29 0.4
TOTAL 0.35 0.65 1
Now we are asked to find the percent of students that were surveyed.
From the table we may see that the probability of children who were surveyed are:
0.11+0.29=0.40
( since, the second column gives the total of the probability of children)
Hence, in percentage form it is given by:
0.40×100=40%
Hence, the answer is:
40%
Martin has 48 blue balloons and 36 orange balloons he separates the balloons into mixed groups of blue and orange there are the same number of blue balloons in each group and the same number of orange balloons I'm each group.what is the leat total number of balloons that could be in each group?
A.)4
B.)7
C.)9
D.)21
Answer: A
48+ 36 = 84
84/4 = 21 groups
there are 21 groups of 4 balloons
Tim has swimming practice at 7 o clock the swimming practice ends 30 minutes later what time does it end ?
Answer:
It ends at 7:30.
Final answer:
Tim's swimming practice starts at 7 o'clock and after adding the 30 minutes duration, it ends at 7:30.
Explanation:
The question pertains to adding time, specifically calculating the end time of an activity based on its duration. If Tim's swimming practice starts at 7 o'clock and ends 30 minutes later, the end time can be found by adding 30 minutes to the start time.
Here's how you calculate it:
Start with the initial time of the practice, which is 7:00.
Add the duration of the practice, which is 30 minutes.
Since there are 60 minutes in an hour, adding 30 minutes to 7:00 does not increase the hour value. Therefore, the practice ends at 7:30.
So, Tim's swimming practice ends at 7:30.
if 1000 pencils cost $20 how much would 10 pencils cost
Answer:
20 cents.
Step-by-step explanation:
You can drop 2 zeros from both the price and the amount of pencils. If 1000 pencils costs 20.00 dollars then 10 pencils cost .20 dollars or 20 cents.
The polygons below are similar, but not drawn to scale. find the value of x
Answer:
x=21
Step-by-step explanation:
Set the two similar sides in a fraction to be compared and set them equal to another set of similar sides whose values are already known. Solve from there. See work for more.
An office suply store sold 410,309 pencils last year. what is the expanded form of 410,309?
Answer:
400000 + 10000 + 300 + 9
Step-by-step explanation:
Just simply take each place value and turn the rest after to zeros, but DO NOT include the zeros that are within the number. Zeros are unnecessary.
I am joyous to assist you anytime.
Which expression is equivalent to
Answer:
The correct answer is last option
x¹⁶y²²
Step-by-step explanation:
Points to remember
Identities
Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾
Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾
(Xᵃ)ᵇ = Xᵃᵇ
To find the correct answer
It is given an expression {X⁶Y⁸}³/X²Y²
By using identities we can write,
{X⁶Y⁸}³/X²Y² = X⁶ˣ³ Y⁸ˣ³/X²Y²
= X¹⁸Y²⁴/X²Y²
= X⁽¹⁸ ⁻ ²⁾ * Y⁽²⁴ ⁻ ²⁾
= X¹⁶Y²²
Therefore the correct answer is last optionX¹⁶Y²²
1. what are the domain and range of the function?
[tex]f(x) = \sqrt[3]{x - 3} [/tex]
2.what are the domain and range of the function?
[tex]f(x) = - 3 \sqrt{x} [/tex]
1) domain of the first is ( R ) because of its root(3) and its range is (R) because of its root again
2)and domain of the last , is [0,+infinity)
and for its range , you can draw it such as picture and will be [0,- infinity)
Answer:
1. [tex]Dom(f)=\mathbb{R} [/tex], [tex]Ran(f)=\mathbb{R} [/tex].
2. [tex]Dom(f)=\{x\in \mathbb{R} : x\geq 0 \} [/tex], [tex]Ran(f)=\{x\in \mathbb{R} : x \leq 0 \} [/tex].
Step-by-step explanation:
1. Since the degree of the radical is an odd number, the radicand can be any real number, then [tex] x [/tex] can take any real value, so the domain of [tex] f [/tex] is the set of all real numbers, [tex] \mathbb{R} [/tex].
Now, if [tex] x\in \mathbb{R} [/tex] , then [tex] x-3 \in \mathbb{R} [/tex], so [tex] \sqrt[3]{x-3} \in \mathbb{R} [/tex], and thus [tex] f(x)\in \mathbb{R} [/tex], which leads us to affirm that the range of [tex] f [/tex] is the set of all real numbers, [tex] \mathbb{R} [/tex].
2. Since the degree of the radical is an even number, the radicand can not be a negative number, then [tex] x [/tex] can take only nonnegaive values, so the domain of [tex] f [/tex] is the set of all nonnegative numbers, [tex] \{x\in \mathbb{R} : x\geq 0 \} [/tex].
Now, if [tex] x\geq 0 [/tex] , then [tex] \sqrt{x}\geq 0 [/tex] so [tex] -3\sqrt{x}\leq 0 [/tex], and thus [tex] f(x)\in \mathbb{R} [/tex], which leads us to affirm that the range of [tex] f [/tex] is the set of all nonpositive numbers, [tex] \{x\in \mathbb{R} : x \leq 0 \} [/tex].
Find the product.
3(x + 4) (x - 5)
A.
3x2 − 20x
B.
3x2 − 11x − 20
C.
3x2 − 3x − 60
D.
3x2 − x − 20
Answer:
C. 3x2 − 3x − 60
Step-by-step explanation:
3(x + 4) (x - 5) = (3x+12) (x-5)
(3x+12) (x-5) = 3x2+12x-15x-60
3x2+12x-15x-60 = 3x2 − 3x − 60
C. 3x^2-3x-60 Hope it helps
Please answer right away
Answer:
2294 balls is the approximate number of balls
Step-by-step explanation:
Find the volume occupied a ball of radius 3inches
Volume of a sphere=4/3 [tex]\pi[/tex]×r³
where r is the radius in inches
4/3× [tex]\pi[/tex]×3³ = 36 [tex]\pi[/tex]
=113.11 in³
Find volume of a rectangle prism
v=l×w×h where l is length of prism, w is width of prism and h is height of prism
L=10ft=10×12=120 inches
w=5ft=5×12=60 inches
h=3ft= 3×12= 36 inches
v=120×60×36=259200 in³
Number of balls needed
N=volume occupied by a single ball/volume of the rectangular prism
N=259200/113.11 =2291.57⇒2292 balls
A bookstore has a sale: Jen wants to buy four books: for $10.00, for $12.00, for $15.00, and for $20.00. What is the smallest she could pay for these books during the sale? By what percent would the sale reduce the total cost of these four books?
Answer:
$47, 17.5%
Step-by-step explanation:
When she buys the $20 book, she can get 40% off either the $15, $12, or $10 book. She'll save the most by getting 40% off the $15 book.
Then, when she buys the $12 book, she'll get %40 off the $10 book.
The total she pays is:
20 + (0.60)(15) + 12 + (0.60)(10)
20 + 9 + 12 + 6
47
Without the discounts, the cost of the books would have been:
20 + 15 + 12 + 10
57
So she saves $10. 10 out of 57 is approximately 17.5%.