Answer: 29
Step-by-step explanation: 3 times 7 = 21 + 8 = 29
Answer:
7=3x+8
x=-1/3
Step-by-step explanation:
we just replace f(X) with 7
7=3x+8
-8. -8
-1=3x
/3. /3
-1/3=x
Hopes this helps please mark brainliest
Steven read a total of 21 books over 7 months. After belonging to the book club for 12 months, how many books will Steven have read in all? Solve using unit rates.
Answer:
36 books
Step-by-step explanation:
21 books / 7 months = 3 books per month
3 books per month × 12 months =
36 books
What is the solution to the system of equations y =- 5x 3 y 1?.
The solution to the system of equations y=-5x+3 and y=1 is given by coordinates (x,y)=(0.4,1)
Define the system of equations ?
System of equations, or simultaneous equations, in algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
What is a subsitution method ?
The substitution method is the algebraic method to solve simultaneous linear equations.
Given:
y=-5x+3
and
y=1
On subsituting y=1 ,we get
⇒[tex]y=-5x+3[/tex]
⇒[tex]1 = -5x+3[/tex]
⇒[tex](1-3)=(-5)x[/tex]
⇒[tex]-2=-5x[/tex]
⇒[tex]2=5x[/tex]
⇒[tex]5x=2[/tex]
⇒[tex]x=\frac{2}{5} =0.4[/tex]
Hence ,x=0.4 and y=1
So, the coordinates of (x,y) are (0.4,1)
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The line passes through the points (7, -2) and (-5, 7).
Write an equation for the line in standard form.
Answer:
Step-by-step explanation:
use the y=mx+b^2 formula
8 All 66 students in a drama group take part in at least one of the four activities given below.
acting (4) dancing (D) singing (S) stage management (M)
Of these 66 students
11 take part in acting, dancing and singing
17 take part in acting and singing
14 take part in dancing and singing
16 take part in acting and dancing
33 take part in singing
37 take part in acting
29 take part in dancing
Any student who takes part in stage management does not take part in acting, dancing
or singing.
(a) Show all this information on the Venn diagram, giving the number of students in
each subset.
The Venn diagram of the 66 students in the drama group is illustrated below.
Venn Diagram:
Basically, a diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by intersections of the circles.
Given,
All 66 students in a drama group take part in at least one of the four activities given below. acting (4) dancing (D) singing (S) stage management (M) Of these 66 students 11 take part in acting, dancing and singing 17 take part in acting and singing 14 take part in dancing and singing 16 take part in acting and dancing 33 take part in singing 37 take part in acting 29 take part in dancing Any student who takes part in stage management does not take part in acting, dancing or singing.
Here we need to show all this information on the Venn diagram, giving the number of students in each subset.
While we looking into the given information,
Total number of students = 66
Here A refers acting, D refers dancing and S refers singing
=> All three activities count = 11
=> Acting and singing = 17
=> Dancing and singing = 14
=> Acting and dancing = 16
=> Singing = 33
=> Acting = 37
=> Dancing = 29
Based on these details we have drawn the following Venn diagram.
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Consider the rational equaton [tex]\frac{5}{x-6}\ \textgreater \ \frac{3}{x+2}[/tex]. Determine if each statement is true or false. Explain your answer.
a. [tex]-2 6[/tex] is a solution to the rational inequality.
b. The excluded values of the rational inequality are [tex]x=6[/tex] and [tex]x=-2[/tex] only
a. -26 is a solution to the rational inequality false
b. The excluded values of the rational inequality are and only - true
How to determine the solution of the inequalityInformation given in the question
5 / (x - 6) > 3 / (x + 2)
a. The inequality is solved by
5(x + 2) > 3 (x - 6)
5x + 10 > 3x - 18
collecting like terms
5x - 3x > -18 - 10
2x > -28
x > -14
Hence -26 is less than -14 so it is wrong as the solution says greater than -14
b. at x = 6
5 / (x - 6) = 5 / 0 which is infinity
at x = -2
3 / (x + 2) = 3 / 0 which is infinity
These two values are the excluded values
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The function f(x) is a cubic function and a limited table of values is provided below.
Write the equation of the cubic polynomial in standard form.
The formula for a cubic polynomial function is f(x)=ax³++bx²+cx+d, where a not equal to 0.
f(x) = x³+2x²-16x-32
What is cubic function?The formula for a cubic function is f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are all real values and a 0.
A cubic polynomial function has the formula f(x)=ax3++bx2+cx+d, where an is not equal to 0. A cubic polynomial always has three zeros, which could be all the same or all different. The zeros could be real or complex, depending on the function.
If x = -4, -2, or 4 then f(x) = 0
These are the roots, then.
factors include F(x) = [(x+4)(x-4)] = (x+4)(x+2)(x+4) For example, (x+2) f(x) = (x2-16) (x+2) f(x) = x3+2x2-16x-32
A cubic equation might have three real roots, similar to how a quadratic equation could have two. However, a cubic equation always has at least one real root, unlike a quadratic equation, which may not have any real solutions.
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A store sells a certain digital camera model for $108. During a special promotion, the camera is discounted by 40 percent. What is the discounted price?( please detailed)
Answer:
$32.4
Step-by-step explanation:
2. Four out of nine dogs weigh less
than 20 pounds. What is the decimal
equivalent for the number of dogs
weighing under 20 pounds?
Repeating 0.2
0.24
Repeating 0.4
0.49
The decimal equivalent for the number of dogs weighing under 20 pounds is repeating 0.4.
Given that four out of nine dogs weigh less than 20 pounds.
We want to find the decimal equivalent for the number of dogs weighing under 20 pounds.
The total number of dogs is 9.
Number of dogs whose weight less than 20 pound is 4.
The decimal equivalent of dogs whose weight is less than 20 pound is 4/9 or 0.444
Hence, the decimal equivalent for the number of dogs weighing under 20 pounds when four out of nine dogs weigh less than 20 pounds is Repeating 0.4.
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An investor invested a total of $2900 in two mutual funds.One fund earned a 6% profit while the other earned a 4% profit.If the investors total profit was $138, how much was invested in each mutual fund?
The answer will be $1100 invested in each year.
What is simple interest?
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
The formula for simple interest is:
S = p*t*r/100
where P is the principal amount of money, R is the interest rate as a decimal, T is the time.
We'll figure out how to solve the two-equation linear system:
We'll set x equal to 8% of the investment and y equal to 5% of the investment.
Equation 1: x + y = 2900 (total invested money)
Equation 2: 0.06x + 0.04y = 138 (total interest of both investments)
25*(0.06x+0.04y = 138)
Equation 3: 1.5x + y = 3450
Eq3-Eq1
0.5x = 550
x = 550/0.5 = 1100
Hence the investment in each year will be $1100.
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The following is a list of grades that students received on a recent math exam:
77, 78, 81, 62, 63, 65, 81, 92, 93, 89, 91, 78, 66, 75, 78, 80, 91, 93, 95, 93, 91, 88, 76, 89, 91, 96.
The teacher wants to list all test scores. Which of the following displays would represent the data in this way?
Box plot
Circle graph
Histogram
Stem-and-leaf plot
Histogram is the displays would represent the given data. Therefore, option C is the correct answer.
What is range?The range is the difference between the largest and smallest numbers. The midrange is the average of the largest and smallest number.
Given that, the data is 77, 78, 81, 62, 63, 65, 81, 92, 93, 89, 91, 78, 66, 75, 78, 80, 91, 93, 95, 93, 91, 88, 76, 89, 91, 96.
The ascending order of given numbers is 62, 63, 65, 66, 75, 76, 77, 78, 78, 78, 80, 81, 81, 88, 89, 89, 91, 91, 91, 91, 92, 93, 93, 93, 95, 96.
Use the class intervals 60-70, 70-80, 80-90, 90-100, to plot the histogram for the given data set.
Hence, Histogram is the displays would represent the given data. Therefore, option C is the correct answer.
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Keith wants to have a laptop case shipped to his office. Company A charges a $12 shipping fee and $1.50 per pound. Company B charges a $15 shipping fee and $1 per pound. For how many pounds is the cost of both shipping companies the same?
Six pounds is the cost of both shipping companies the same.
An equation is a mathematical statement created by joining two numerical or variable expressions with an equal sign.
How do you find the solution of an equation?An equation is a mathematical statement created by joining two numerical or variable expressions with an equal sign, as in 3x+5=11. A number that may be entered for the variable to produce a true number statement is the answer to an equation.
company A:
shipping fee is 12 and $1.50 per pound
Let p be the variable for the pounds of the package.
Liner Equation :
shipping fee = [tex]12+ 1.5p[/tex]
For company B :
shipping fee = 15 + p
if the cost of both shipping companies the same then,
12+1.5p = 15+p
ie. P = 6.
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What ate the steps for using a compass and straightedge to construct a square?.
The steps for using a compass and straightedge to construct a square is:
Given:
Let AB the length of one side given.
Steps:
a. Using your straightedge, draw a reference line, if one is not provided.
b. Copy the side of the square onto the reference line, starting at a point labeled A'.
c. Construct a perpendicular at point B' to the line through [tex]AB[/tex].
d. Place your compass point at B', and copy the side of the square onto the perpendicular B'G. Label the end of the segment copy as point C.
e. With your compass still set at a span representing AB, place the compass point at C and swing an arc to the left.
f. Holding this same span, place the compass point at A' and swing an arc intersecting with the previous arc. Label the point of intersection as D.
g. Connect points A' to D, D to C, and C to B' to form a square.
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I need helpp!
You need to Find m < B
Answer:
mAngleB = 67°
Step-by-step explanation:
The angle marked 15x is made by extending one side of the triangle. That is an exterior angle (like, its outside the triangle)
There are two angles inside the triangle that are away from that exterior angle. They are called remote interior angles. They are marked 83° and 6x+7 in this question.
Here's the rule:
If you add up the two remote interior angles it equals the exterior angle.
83° + 6x + 7 = 15x
Subtract 6x.
83 + 7 = 9x
Simplify.
90 = 9x
Divide by 9.
10 = x
Use this to find mAngleB
mAngle B = 6x + 7
= 6(10) + 7
= 60 + 7
= 67
mAngleB = 67°
amy, beth, and jo listen to four different songs and discuss which ones they like. no song is liked by all three. furthermore, for each of the three pairs of the girls, there is at least one song liked by those girls but disliked by the third. in how many different ways is this possible?
There are 132 different ways this is possible(given situation).
What is probability ?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
Calculationlet[tex]$AB, BJ$, and $AJ$[/tex] denote a song that is liked by Amy and Beth (but not Jo), Beth and Jo (but not Amy), and Amy and Jo (but not Beth), respectively. Similarly, let[tex]$A, B, J,$ and $N$[/tex] denote a song that is liked by only Amy, only Beth, only Jo, and none of them, respectively. Since we know that there is at least[tex]$1\: AB, BJ$, and $AJ$[/tex], they must be[tex]$3$[/tex] songs out of the [tex]$4$[/tex] that Amy, Beth, and Jo listened to. The fourth song can be of any type
[tex]$N, A, B, J, AB, BJ$, and $AJ$ (there is no $ABJ$[/tex]
because no song is liked by all three, as stated in the problem.) Therefore, we must find the number of ways to rearrangeand a song [tex]$AB, BJ, AJ$,[/tex]from the se[tex]t $\{N, A, B, J, AB, BJ, AJ\}$.[/tex]
Case 1: Fourth song =[tex]$N, A, B, J$[/tex]
Note that in Case 1, all four of the choices for the fourth song are different from the first three songs.
Number of ways to rearrange =[tex]$(4!)$[/tex] rearrangements for each choice[tex]$*\: 4$ choices = $96$.[/tex]
Case 2: Fourth song =[tex]$AB, BJ, AJ$\\[/tex]
Note that in Case 2 all three of the choices for the fourth song repeat somewhere in the first three songs.
Number of ways to rearrange = [tex]$(4!/2!)$[/tex]rearrangements for each choice [tex]$*\: 3$ choices = $36$.[/tex]
[tex]$96 + 36 = \boxed{\textbf{(B)} \: 132}$.[/tex]
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Brady's father is paying $60 for a monthly gym membership. the gym is offering a special sale for 18% off the regular price. After the discount, a 10% maintence fee is charged. what does brady's father pay for the gym membership? explain.
============================================================
Explanation:
If his father saves 18%, then he pays the remaining 82% since 100-18 = 82.
The 82% then converts to 0.82 which is one of the multipliers we'll use to get the answer.
The other multiplier is 1.10 to represent an increase of 10%
The net multiplier is 0.82*1.10 = 0.902
Therefore, his father pays 0.902*60 = 54.12 dollars after the discount and maintenance fee are applied.
Write an equation in standar form for the line that passes through (5,0) and (0,6)
The an equation in standard form for the line that passes through (5,0) and (0,6) is 5y + 6x - 30 = 0
We need to write an equation in standard form for the line that passes through (5,0) and (0,6)
The formula for equation of line with two points is
y - y₁ = ((y₂ - y₁)/(x₂ - x₁))(x - x₁)
y - 0 = ((6 - 0)/(0 - 5))(x - 5)
y = 6/-5 (x - 5)
-5y = 6(x - 5)
-5y = 6x - 30
5y + 6x - 30 = 0
Therefore, the an equation in standard form for the line that passes through (5,0) and (0,6) is 5y + 6x - 30 = 0
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What value of x will make AONM similar to ASRQ by the SAS similarity theorem?.
The value of x is 25 will make ΔONM similar to ΔSRQ by the SAS similarity theorem.
Given:
∠ONM is similar to ∠SRQ
From the figure
NM = 10
SR = 20
NO = 8
QR = x
SAS Similarity Theorem:
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.
Both the triangles are similar by SAS if
NO/NM = SR/QR
substitute the values
8/10 = 20/x
cross multiplication
8x = 200
dividing both sides by 8
x = 25
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there are 120 people in a theatre 72 are female of these 41 purchase an ice cream 36 males purchase and ice cream use this information to compete the frequency tree
There are 120 people in a theatre. 72 are female and 48 are male. 12 females purchase an ice cream and 31 males purchase an ice cream.
What is Frequency Tree?
Frequency trees display the real frequency of certain events. They can display the same data as a two-way table, but frequency trees are more readable since they illustrate the frequency hierarchy. Probability trees depict the likelihood of a series of occurrences.
Solution:
From the question, we can see the there are 120 people in the theatre.
Since, there are 72 females in the theatre we can find the total number of males by 120-72 = 48
Also, the male who purchased Ice Cream were 36 therefore, the males who did not purchased Ice Cream are 48-36 = 12
And, the females who purchased Ice Cream are 41. So, the female who did not purchased Ice Cream are 72 - 41 = 31
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Is the area of a triangle always 180?.
The three interior angles of a triangle will always have a sum of 180.
What is are of triangle?The area of a triangle is defined as the total space occupied by the three sides of the triangle in a two-dimensional plane. The basic formula for the area of a triangle is half the product of the base and the height, or A = 1/2 × w × h. This formula applies to all types of triangles, including scalene, isosceles, and equilateral triangles. Recall that the base and height of a triangle are perpendicular to each other.The area of a triangle is the area enclosed by the sides of the triangle.The area of a triangle varies from triangle to triangle depending on the length of the sides and the interior angles. The area of a triangle is expressed in square units. B. m2, cm2, in2, etc.Hence, The three interior angles of a triangle will always have a sum of 180.
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Rewrite the equation in terms of x.
y =4/7(x-13)
Answer:
y=(47)xy=(47)x
Rewrite the equation as 47x=y47x=y.47x=y47x=y
Multiply both sides of the equation by 7474.74(47x)=74y74(47x)=74ySimplify both sides of the equation.Tap for more steps...x=7y4
Step-by-step explanation:
confusing bro
Answer:
x = (4/7y) + 13
Step-by-step explanation:
y = 4/7( x -13)
cross multiply
y x 7( x -3) = 4
(x - 3) = 4/7y
x = (4/7y) + 13
PLEASE HELP DUE IN 2 MINUTES I NEED UNGROUNDED
Answer: wheres the question
Step-by-step explanation:
the pressure (p) at the bottom of a swimming pool varies directly as the depth (d) of the water. If the pressure is 125 pascal when the water is 2meters deep, find the pressure when it is 4.5 deep
Step-by-step explanation:
p varies directly with d.
that means there is a constant k, so that
p = kd
to find k we use the one set of numbers we know about
125 = k×2
k = 125/2 = 62.5
now, when the water is 4.5 meters deep :
p = 62.5 × 4.5 = 281.25 pascal
What is the sum of 1 triangle?.
The sum of the triangle angles is 180°.
What is area of triangle?The area of a triangle is defined as the total space occupied by the three sides of the triangle in a two-dimensional plane.The basic formula for the area of a triangle is half the product of the base and the height, or A = 1/2 × w × h.This formula applies to all types of triangles, including scalene, isosceles, and equilateral triangles. Recall that the base and height of a triangle are perpendicular to each other.The area of a triangle is the area enclosed by the sides of the triangle.The area of a triangle varies from triangle to triangle depending on the length of the sides and the interior angles. The area of a triangle is expressed in square units. B. m2, cm2, in2, etc.Hence, The sum of the triangle angles is 180°.
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Solve for X. 5 star + heart reward for best answer!! Please give step by step explanation.
-1 - 8/3(1/4x) = 2
Hint given: Change subtraction to addition of the opposite
Answer:
[tex]\sf x=-6[/tex]Step-by-step explanation:
[tex]\sf \cfrac{-1-8}{3\left(\cfrac{1}{4}x\right)}=2[/tex]
Simplify:-
[tex]\sf -\cfrac{12}{x}=2[/tex]Multiply both sides by x:-
[tex]\sf -\cfrac{12}{x}\;x=2x[/tex]Simplify:-
[tex]\sf -12=2x[/tex]Divide both sides by 2:-
[tex]\sf \cfrac{-12}{2}=\cfrac{2x}{2}[/tex]Simplify:-
[tex]\sf x=-6[/tex]______________________
Hope this helps!
Have a great day!
Enter <,> or = to make the statement true.
.320 ? .051
0.320 > 0.051
Round it up. 4 and below doesn't round and 5 and above will.
0.320. 0.051
0.320. 0.05
Look at it as 0.32 and 0.05
these would come down to 32% or 5%
as the 3 is in the tenths and the 5 is in the hundredths.
making the 3 in the tenths larger.
Simple as 30 and 5
graph the function y=-2x-2
The graph of the function denotes a straight line which passes through the points (-1 , 0) and (0 , -2) .
The graph of the function denoted as y = -2x - 2 is in the form of a straight line as it can be written as y = mx + c the slope is -2 and y intercept is at (0,-2).
The graph of the line passes through :
At x=0 , y = -2
At x = -1 , y = 0
At x = 2 , y = -6
The line passes through (0,-2) , (-1,0) and (2,-6) .
A straight line is a line with no curves and an infinite length. Any two locations can also be connected by a straight line, but its endpoints must extend into the infinite.
A straight line results from connecting two points A (x1, y1) and B (x2, y2) along the shortest path possible and stretching the endpoints of the line to infinity.
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Which point is on the graph of the equation y = -3x + 4?
(-3, 4)
(2, 2)
(1, 1)
(0, -4)
Answer:
(1,1)
Step-by-step explanation:
we fill in the equation for these points to see if they are on the line
(-3,4)
4=-3(-3)+4
4=-9+4
4=-5
Not on line
2=-3(2)+4
2=-6+4
2=-2
Not on line
1=-3(1)+4
1=-3+4
1=1
On the line
-4=-3(0)+4
-4=4
Not on line
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10 times 10+10y=-20 what is the value of the y-coordinate
The value of the y-coordinate as calculated from the equation 10+10y=-20 is -3
The given equation is 10+10y=-20
We will solve this linear equation by taking the y coordinate of the function.
Subtracting 10 from both sides of the equation:
or ,10+10y -10 = -20 -10
or, 10y = -30
Dividing both sides by 10 we get:
or, 10y ÷10 = -30 ÷ 10
or, y = -3
In mathematical formulas, the equals sign is used to indicate that two expressions are equal. It's possible that the definitions of words like "equation" or their cognates vary slightly between languages. For instance, an equation is defined as having one or more variables, whereas an equation is any well-formed formula that consists of two expressions connected by the equals sign.
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Si hace 10 años las edades de Ana y su madre eran 15 y 40, respectivamente, ¿cuál es la razón entre las edades actuales de ambas?
Opciones:
1/2
5/30
3/8
15/40
Answer:
3:8
Step-by-step explanation:
15:40
Work out the same by simplifying which they both go in 5
then doing that you can get 3/8 Or 3:8.
Hope it helps!
Spanish:
Resuelve lo mismo simplificando lo que ambos van en 5
luego haciendo eso puedes obtener 3/8 o 3: 8.
write the expression as the logarithm of a single number or expression. assume that all variables represent positive numbers. 5log x 2logy-6logz
The expression as the logarithm of a single number or expression is log( x⁵.y/z⁶).
Define the term logarithm?A logarithm is a multiplication-based mathematics notion.
The exponent that will result in a particular value is a logarithm.
An exponent or power with which a base must be increased in order to produce a particular number.
If bˣ = n, then x is the logarithm of n here to base b, which is expressed mathematically as x = logb n. For instance, 2³ = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log₂ 8.
For the stated question;
= 5log x + 2logy - 6logz
Using the addition, division and power property.
log(m x n) = log m + log n
log(m/n) = log m - log n
= log x⁵ + logy² - logz⁶
= log( x⁵ ₓ y²) - logz⁶
= log( x⁵.y/z⁶)
Thus, the expression as the logarithm of a single number or expression is log( x⁵.y/z⁶).
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