Answer:
y = (-3/5)x - 6
Step-by-step explanation:
m = slope: (-3/5); (-5, -3)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - (-3) = (-3/5)(x - (-5)
y + 3 = (-3/5)(x + 5)
y + 3 = (-3/5)x - 3
-3 -3
-------------------------
y = (-3/5)x - 6
I hope this helps!
A book sold 33,400 coples in its first month of release. Suppose this represents 7.6% of the number of coples sold to date. How many coples have been sold todate?Round your answer to the nearest whole number.
The number sold in the first month is given as 33,400.
This number is 7.6 percent of the total copies sold till date. This means x copies have been sold till date, and x copies represents 100 percent.
Therefore, you would have the following proportion;
[tex]\begin{gathered} \frac{33400}{x}=\frac{7.6}{100} \\ \text{Cross multiply and you'll have;} \\ \frac{33400\times100}{7.6}=x \\ 439473.684210\ldots=x \\ x\approx439474\text{ (rounded to the nearest whole number)} \end{gathered}[/tex]The number of copies sold till date is 439,474 (rounded to the nearest whole number)
What is the volume of this sphere?
Use a ~ 3.14 and round your answer to the nearest hundredth.
Radius =3 m
cubic meters
Explanation
We are asked to get the volume of the sphere
The volume of a sphere is given by
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \\ where\text{ r = radius =3m} \\ \pi=3.14 \end{gathered}[/tex]The volume of the sphere will be
[tex]V=\frac{4}{3}\times3.14\times3^3=113.04m^3[/tex]Therefore, the volume of the sphere will be 113.04m³
through: (5, 5), slope = 10
Answer: The correct answer is y = 10x – 45
Step-by-step explanation:
When graphing a line with a slope of 10 from point (5,5), we find that the y-intercept (where the line crosses the y-axis) is -45
Use the slope-intercept form (y=mx+b), where m=slope (10) and b=the y-intercept (-45)
y = 10x - 45
Would you Please Solve it and explain little[tex]14(.5 + k) = - 14[/tex]
To solve the given equation, we first apply the distributive property on the left side.
So, we have:
[tex]\begin{gathered} 14(0.5+k)=-14 \\ 14\cdot0.5+14\cdot k=-14 \\ 7+14k=-14 \\ \text{ Subtract 7 from both sides of the equation} \\ 7-7+14k=-14-7 \\ 14k=-21 \\ \text{ Divide by 14 from both sides} \\ \frac{14k}{14}=-\frac{21}{14} \\ k=-\frac{21}{14} \end{gathered}[/tex]Finally, we simplify.
[tex]\begin{gathered} k=-\frac{3\cdot7}{2\cdot7} \\ $$\boldsymbol{k=-\frac{3}{2}}$$ \end{gathered}[/tex]Therefore, the solution of the given equation is -3/2.
2x-5y= -19
-3x+y=9
solve by substitution
Answer: (-2,3)
Step-by-step explanation:
2x-5y=-19 (1)
-3x+y=9 (2)
2x-5y=-19 (3)
y=3x+9 (4)
2x-5(3x+9)=-19
2x-15x-45=-19
-13x=-19+45
-13x=26
Divide both parts of the equation by -13:
x=-2
Substitute the value of x=-2 into equation (4):
y=3(-2)+9
y=-6+9
y=3
Thus, (-2,3)
find a slope of the line that passes through (8,2) and (6,3)
EXPLANATION
Given the dots:
(x1,y1)=(8,2) and (x2,y2)=(6,3)
The slope equation is:
[tex]\text{Slope = }\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Replacing the ordered pairs in the slope equation will give us:
[tex]\text{Slope = }\frac{(3-2)}{(6-8)}=\frac{1}{-2}=-\frac{1}{2}[/tex]The slope of the line is -1/2.
Algebraic models grade 12 math please write the answers without explaining thank you.
Explanation
let's remember this property of the exponent number
[tex]a^m\cdot a^n=a^{m+n}[/tex]Step 1
solve by applying the property. ( let the same base and add the exponents)
[tex]\begin{gathered} 6^4\cdot6^{-5} \\ 6^4\cdot6^{-5}=6^{4+(-5)} \\ 6^4\cdot6^{-5}=6^{-1} \\ \end{gathered}[/tex]hence, the answer is
[tex]d)6^{-1}[/tex]I hope this helps you
What is the end behavior of f(x) =2^–x− 5 as x goes to infinity?
Given the function:
[tex]f(x)=2^{-x}-5[/tex]As x goes to infinity, the term (2^-x) will go to zero
And the overall value of the function will be -5
So, the end behavior of f(x) as x goes to infinity = -5
A local little league has a total of 70 players, of whom 80% are right-handed. How many right-handed players are there? There are right-handed players.
there are (0,80)(70)=56 right handed players
On which number line the location of point P represent the probability of an event that is likely, but not certain?
The straight line that best represents something probable but not certain is option D.
It shows a probability of approximately 80%.
Select ALL the pairs of points so that the line between these points has a slope of 2/3?(0,0) and (3, 2)(1,5) and (4,7)(-2,-2) and (4,2)0 (0,0) and (2,3)(20, 30) and (-20, -30)
Answer:
• (0,0) and (3, 2)
,• (1,5) and (4,7)
,• (-2,-2) and (4,2)
Explanation:
Points (0,0) and (3, 2)
[tex]m=\frac{2-0}{3-0}=\frac{2}{3}[/tex]Points (1,5) and (4,7)
[tex]m=\frac{7-5}{4-1}=\frac{2}{3}[/tex]Points (-2,-2) and (4,2)
[tex]m=\frac{2-(-2)}{4-(-2)}=\frac{2+2}{4+2}=\frac{4}{6}=\frac{2}{3}[/tex]Points (0,0) and (2,3)
[tex]m=\frac{3-0}{2-0}=\frac{3}{2}[/tex]Points (20, 30) and (-20, -30)
[tex]m=\frac{30-(-30)}{20-(-20)}=\frac{60}{40}=\frac{3}{2}[/tex]The first three options are correct.
what is the size of rectungle 2x2x2
Perimeter: 8 u
Area: 4 u^2
Volume: 8 u^3
Explanation:
u = unit (cm / m etc...)
side = 2 u
Formula for a rectangle:
Perimiter : 2*(side + side)
=> 2 * ( 2 + 2) = 8 u
Area: side * side
=> 2 * 2 = 4 u^2
Volume: Area * Height
=> 2 * 4 u^2 = 8 u^2
A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.
Part A: Find the constant of proportionality. Show every step of your work. (4 points)
Part B: Write an equation that represents the relationship. Show every step of your work. (2 points)
Part C: Describe how you would graph the relationship. Use complete sentences. (4 points)
Part D: How many gallons of water are needed for 10 scoops of drink mix? (2 points)
please help asap its almost to late
All the answers to the given parts are mentioned below -
What is the general equation of a Straight line? How it represents a proportional relationship?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have a cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.
We can write the proportional relationship as -
y = kx
Now, from the given information, we can write -
2 scoops need 0.5 gallon of water
6 scoops need 1.5 gallon of water
So -
k = 2/0.5
k = 2/(1/2)
k = 2 x 2 = 4
Equations that represents the relationship can be written as -
y = 4x + c
Now, 2 scoops need 0.5 gallon of water.
2 = 4 x 1/2 + c
2 = 2 + c
c = 0
So, the equation will be y = 4x.
Graph of y = 4x is attached at the end.
For 10 scoops of water -
10 = 4x
x = 2.5 gallons of water is needed.
Therefore, all the answers to the given parts are mentioned above.
To solve more questions on proportional relationship, visit the link below-
brainly.com/question/12917806
#SPJ1
Determine if the side lengths could form a triangle. Use an inequality to justify your answer.16 m, 21 m, 39 m
We can draw the following triangle
the triangle inequality state that
[tex]|a-b|where | | is the absolute value. In our case, if we apply this inequality we obtain[tex]|21-39|which gives[tex]\begin{gathered} |-18|since 21m is between 18m and 60m, the values 16m, 21mn and 39m can form a triangle.I am doing a homework assignment but i don’t quite understand this one may it be explained step by step?
Part A: Use the graph to identify the zeros of the polynomial.
As it is said in the introduction the graph crosses 3 times the x -axis and touched it at (2,0).
Values of x for which the function is zero can be identified by knowing the x-coordinate of these points:
[tex]x=-4[/tex][tex]x=2[/tex]And the following two that are approximate values taken from the graph:
[tex]x\approx-1.6[/tex][tex]x\approx3.6[/tex]Part B: Use the behaivor of the graph to explain whether the dregree of the polinomial is even or odd.
The graph the graph corresponds to an odd function because has no symmetry abopur the y-axis and when the value of x get smaller the values of y also. To the left from a certain point lower values are always obtained and to the right from a certain point higher values are always obtained.
Emmet opened a savings account and deposited 1,000.00 as principal the account earns 8%interest compounded monthly what is the balance after 9 years
We have to use the compound interest formula to solve this problem.
The compound interest formula:
[tex]F=P(1+r)^n[/tex]Where
F is the future value [what we are solving for]
P is the principal, or initial, amount [It is $1000]
r is the rate of interest per period [It is given 8% annual interest, so 8/12 = 0.66% per month, in decimal that is r = 0.0066]
n is the time period [monthly compounding for 9 years is n = 12 * 9 = 108]
Now, we can substitute all the known information and solve for F:
[tex]\begin{gathered} F=P(1+r)^n^{} \\ F=1000(1+0.0066)^{108} \\ F=2048.06 \end{gathered}[/tex]After 9 years, the balance is:
$2048.06answer.The number of cities in a region over time is represented by the function C(=) = 2.9(1.05). The approximate number of people per city isrepresented by the function P(t) = (1.05)35 +5.Which function best describes T(*), the approximate population in the region?OA T(I) = (3.045)* + (1.05)35 +5OB. T(1) = (6.09)45+5OC. T() = 2.9(1.05)45+5OD. Т(1) = 2.9(1.05)352 +55
Given:
[tex]\begin{gathered} \text{Number of cities: }C(x)=2.9(1.05)^x \\ \\ \text{Number of people per city: P}(x)=(1.05)^{3x+5} \end{gathered}[/tex]Let's solve for T(x) which represents the approximate population in the region.
To find the approximate population in the region, apply the formula:
[tex]T(x)=C(x)\ast P(x)[/tex]Thus, we have:
[tex]T(x)=2.9(1.05)^x\ast(1.05)^{3x+5}^{}[/tex]Let's solve the equation for T(x).
Thus, we have:
[tex]\begin{gathered} T(x)=2.9((1.05)^{3x+5}(1.05)^x) \\ \\ Apply\text{ power rule:} \\ T(x)=2.9(1.05)^{3x+5+x^{}_{}} \\ \\ T(x)=2.9(1.05)^{3x+x+5} \\ \\ T(x)=2.9(1.05)^{4x+5} \end{gathered}[/tex]Therefore, the function that best describes the approximate population in the region is:
[tex]T(x)=2.9(1.05)^{4x+5}[/tex]ANSWER:
C
[tex]T(x)=2.9(1.05)^{4x+5}[/tex]A rectangular pyramid has a volume of 90 cubic feet. What is the volume of a rectangular prism with the same size base and same height?choice;45 cubic feet90 cubic feet270 cubic feet30 cubic feet
Solution
Step-by-step explanation:
Here we are given the volume of rectangular pyramid as 90 cubic feet as we are required to find the volume of rectangular prism.
For that we need to use the theorem which says that
the volume prism is always one third of the volume of the pyramid . Whether it is rectangular of triangular base. Hence in this case also the volume of the rectangular prism will be one third of the volume of the rectangular pyramid.
Volume of Rectangular prism = 1/3 x Volume of rectangular pyramid
[tex]\begin{gathered} \frac{1}{3}\times90 \\ =30\text{ cubic feet} \end{gathered}[/tex]Therefore the volume of the rectangular pyramid = 30 cubic feet
I dont really get it or what it is asking
ANSWER
• A vertical plane that cuts through the top vertex, perpendicular to the base,: ,triangle
,• A horizontal plane, that cuts through the pyramid, parallel to the base:, ,square
,• A vertical plane that cuts through the base and two opposite lateral faces:, ,trapezoid
EXPLANATION
• A vertical plane that cuts through the top vertex, perpendicular to the base,: if we draw a rectangle perpendicular to the base that passes through the vertex,
Hence, the cross-sectional shape is a triangle.
• A horizontal plane, that cuts through the pyramid, parallel to the base:, if it is a plane parallel to the base, then it should have the same shape as the base,
Hence, the cross-sectional shape is a square.
• A vertical plane that cuts through the base and two opposite lateral faces:, again, we can draw this plane. The cross-sectional shape will have one pair of parallel sides and one pair of non-parallel sides,
Hence, the cross-sectional shape is a trapezoid.
F(x)=2|x-1| Graph using transformations and describe the transformations of the parent function y =x^2.
[Please see that in the question should be a mistake regarding the parent function. It should be written y = |x| instead of y = x².]
To answer this question, we need to know that the below function is a transformation of the parent function, f(x) = |x|:
[tex]f(x)=2|x-1|[/tex]Describing the transformationsTo end up with the above function from the parent function, we need to follow the next steps:
1. Translate the function, y = |x| one unit to right. We can do this by subtracting one unit to the parent function as follows:
[tex]f(x)=|x-1|[/tex]We can see this graphically as follows:
The blue function is the first transformation of the parent function, f(x) = |x|.
2. The function has been dilated by a factor of 2 from the x-axis. That is, the function has been dilated by a factor of 2 vertically. Then, we have:
[tex]f(x)=2|x-1|[/tex]And now, we can see the transformation graphically as follows:
Therefore, the blue line is the graph representation of the function:
[tex]f(x)=2|x-1|[/tex]determine if each graph compares the diameter and the circle with the circle's radius area or circumference
The radius of the circle is half of the diameter. Therefore, if the diameter is 2 units, then the radius is 1 unit. If the diameter is 6 units, the radius will be 3 units. The graph that represents the relationship between radius and diameter is Graph B.
The circumference of the circle can be solved by multiplying the diameter and the value of pi. Therefore, this is a linear function. If the diameter is 4 units, the circumference is approximately 12.57 units. If the diameter is 6 units, the circumference is approximately 18.85 units. The graph that best represents the relationship between diameter and circumference is Graph C.
Lastly, the area of the circle with respect to the diameter is a quadratic function due to the nature of the formula that is A = πr². The graph of a quadratic function is parabolic in nature. Therefore, the graph that best represents the relationship between diameter and area is Graph A.
To summarize, the vertical axis for each graph is:
Graph A → Area
Graph B → Radius
Graph C → Circumference
A wildlife park manager is working on a request to expand the park. In a random selection during one week, 3 of every 5 cars have more than 3 people insideIf about 5,000 cars come to the park in a month, estimate how many cars that month would have more than 3 people inside.
Determine the ratio of cars that have more than 3 people.
[tex]\frac{3}{5}[/tex]Since in a month 5000 cars comes to park. Then cars with more than 3 people are,
[tex]\begin{gathered} \frac{3}{5}\cdot5000=3\cdot1000 \\ =3000 \end{gathered}[/tex]Answer: 3000
factor they expression completely 9x−21
Answer:
3(3x - 7)
Step-by-step explanation:
9x - 21
GCF of 9 and 21 is 3
3(3x - 7)
I hope this helps!
A cookie recipe called for 3 ¼ cups of sugar for every 2 ⅓ cups of flour. If you made a batch of cookies using 4 cups of flour, how many cups of sugar would you need?
1) Gathering the data
3 ¼ cups of sugar------------------ 2 ⅓ cups of flour
x 4
2) Let's set a proportion, and then cross multiply those ratios but before that
let's convert those mixed numbers:
[tex]\begin{gathered} 3\frac{1}{4}=\frac{4\times3+1}{4}=\frac{13}{4} \\ 2\frac{1}{3}=\frac{3\times2+1}{3}=\frac{7}{3} \end{gathered}[/tex][tex]\begin{gathered} \frac{13}{4}-----\frac{7}{3} \\ x\text{ -------4} \\ \frac{7}{3}x=4\times\frac{13}{4} \\ \frac{7}{3}x=13 \\ 7x=39 \\ x=\frac{39}{7} \end{gathered}[/tex]So rewriting it above, we have. 39/7 as 39/7 is >1 then we can rewrite it into a Mixed Number:
3) Hence, I'll need 5 4/7 cups of sugar
Which of the following sets number could not represent the three sides of a right triangle
Given 4 sets of three sides of a triangle
We will find Which of the following sets of numbers could not represent the three sides of a right triangle
First, for any right triangle, the sum of the square of the legs is equal to the square of the hypotenuse
The hypotenuse is the longest side of the triangle
We will check the options:
a) { 11, 60, 61}
[tex]11^2+60^2=121+3600=3721=61^2[/tex]So, option a represent a right triangle
b) {46, 60, 75 }
[tex]46^2+60^2=2116+3600=5716\ne75^2[/tex]So, option (b) does not represent a right triangle
No need to check the other options
So, the answer will be {46, 60, 75}
Jessica is deciding on her schedule for next semester. She must take each of the following classes: English 101, Spanish 102, Biology 102, andCollege Algebra. If there are 15 sections of English 101,9 sections of Spanish 102, 13 sections of Biology 102, and 15 sections of College Algebra,how many different possible schedules arethere for Jessica to choose from? Assume there are no time conflicts between the different classes.Keypad
Jessica must take four classes: English, Spanish, Biology, and College Algebra.
There are:
15 sections of English
9 sections of Spanish
13 sections of Biology
15 sections of College Algebra.
She has 15 possible choices for English class. Once selected, she has 9 choices for Spanish class.
There is a total of 15*9 = 135 possible schedules for both subjects.
When we combine this with the rest of the classes, we find a total of:
15*9*13*15 = 26,325 possible schedules, assuming there are no time conflicts between them.
Answer: 26,325
All questions relate to the equation y=9 x^2-36 x+37Got it.1. Which way does the parabola open? Your answerYour answerYour answer2. What is the minimum value of y?Your answer3. What is the maximum value of y?Your answer5. What is the axis of symmetry?7. What is the y-intercept?Your answer8. Rewrite the equation in vertex form.
Given the parabola:
[tex]y=9x^2-36x+37[/tex]Part 1
To determine the way the parabola opens, we consider the coefficient of x².
• If the coefficient is positive, it opens downwards.
,• If the coefficient is negative, it opens upwards.
In this case, the coefficient of x²=9 (Positive).
The parabola opens downwards.
Part 2
The minimum value of the parabola occurs at the line of symmetry.
First, we find the equation of the line of symmetry.
[tex]\begin{gathered} x=-\frac{b}{2a};a=9,b=-36,c=37 \\ \therefore x=-\frac{(-36)}{2\times9} \\ x=2 \end{gathered}[/tex]Find the value of y when x=2.
[tex]\begin{gathered} y=9x^2-36x+37 \\ y=9(2)^2-36(2)+37 \\ =36-72+37 \\ Min\text{imum value of y=1} \end{gathered}[/tex]Part 3
Since the graph has a minimum value, the maximum value of y will be ∞.
Part 5
As obtained in part 2 above, the axis of symmetry is:
[tex]x=2[/tex]Part 6
The vertex is the coordinate of the minimum point.
At the minimum point, when x=2, y=1.
Therefore, the vertex is (2,1).
Part 7
The y-intercept is the value of y when x=0.
[tex]\begin{gathered} y=9x^2-36x+37 \\ y=9(0)^2-36(0)+37 \\ y=37 \end{gathered}[/tex]The y-intercept is 37.
Part 8
We rewrite the equation in Vertex form below:
[tex]\begin{gathered} y=9x^2-36x+37 \\ y-37=9x^2-36x \\ y-37+36=9(x^2-4x+4) \\ y-1=9(x-2)^2 \\ y=9(x-2)^2+1 \end{gathered}[/tex]Note: Figure is not drawn to scale.If h= 13 units and r= 4 units, then what is the approximate volume of the cone shown above?OA. 52 cubic unitsOB. 69.337 cubic unitsOC. 2087 cubic unitsOD. 225.337 cubic units
The volume of a right circular cone is computed as follows:
[tex]V=\pi r^2\frac{h}{3}[/tex]where r is the radius and h is the height of the cone.
Substituting with r = 4 units and h = 13 units, we get:
[tex]\begin{gathered} V=\pi4^2\frac{13}{3} \\ V=\pi16\frac{13}{3} \\ V=\frac{208}{3}\pi\approx69.33\pi \end{gathered}[/tex]nWhich graph shows the solution set of the compound inequality 1.5x-1 > 6.5 or 7X+3 <-25?-1010O-1050510-10-5510+-105010Mark this and returnSave and ExitNextSubmit
Solving the first inequality >>>
[tex]\begin{gathered} 1.5x-1>6.5 \\ 1.5x>6.5+1 \\ 1.5x>7.5 \\ x>5 \end{gathered}[/tex]Solving the second inequality >>>>
[tex]\begin{gathered} 7x+3<-25 \\ 7x<-25-3 \\ 7x<-28 \\ x<-\frac{28}{7} \\ x<-4 \end{gathered}[/tex]So, the solution set will be all numbers less than -4 and all numbers greater than 5.
We will have open circle at -4 and 5 and arrows to both sides.
From answer choices, second option is the right graph.
a school ordered three large boxes of board markers after giving 15 markers to each of three teachers there were ninety X the diagram represents the situation how many markers were original in the
Determine the value of x.
[tex]\begin{gathered} x-15+x-15+x-15=90 \\ 3x=90+45 \\ x=\frac{135}{3} \\ =45 \end{gathered}[/tex]So there are 45 markers originally in each box.