The equation 154 = -4(8+6r) + 24r has no solution because the variable becomes 0.
How to solve equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
We have to find the variable r of the equation to solve the equation.
A variable is a number represented with letters in an equation.
Therefore, let's find the variable r in the equation.
154 = -4(8+6r) + 24r
open the brackets on the right side of the equation
154 = - 32 - 24r + 24r
154 = -32 + 0
Therefore, the equation cannot be solved.
learn more on equation here: brainly.com/question/29021902
#SPJ1
What are the all the expressions that are equivalent to 3 3/4
Jan takes her three children and two neighbor's childrento a matinee. All of the children are under age 13. Writan expression for the total cost of admission. Howmuch in all did Jan pay for admission?(Matinee: 3$)
There are 6 people going to the movie
Jan, her 3 children, 2 neighbor children
(1+3+2)
Each costs 3 dollars to get in
Total cost = number of people * cost
Total cost = (1+3+2) * 3
= 6*3
= 18
-3, -6, -12, -24,.... Next 3 2, 4, 8-12, -6, -3-48, -96, -192 -36, -48, -60
We can see that the ratio between consecutive numbers is
[tex]\frac{-6}{-3}=\frac{-12}{-6}=\frac{-24}{-12}=2[/tex]this means that, the nex number is
[tex]\begin{gathered} -24\cdot2=-48 \\ \text{and next} \\ -48\cdot2=-96 \\ \text{and finally} \\ -96\cdot2=-192 \end{gathered}[/tex]Hence, the answer is -48, -96, -192
the lenght, l , of a rectangle is twice its width, w and the premiter is p
which mathematical relationship(s) this senerio
select all that apply
A L=W-P
B2L=W
C 2W=L
D 2(L+2W)=P
E 2(L+W)=P
F p=6W
The perimeter for the length L and width W that is 2L will be 2W=L as the definition of perimeter says, "The total length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges".
What is perimeter?The total length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The perimeter of a shape is the space surrounding its edge. A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. We must add up the lengths of the rectangle's four sides in order to determine its perimeter. Since there are two of each side length, it is easy to accomplish this by simply adding the length and width and multiplying the result by two. The perimeter formula is defined as perimeter=2(length + width).
Here,
Perimeter=2(length + width)
Length=L
Width=W=2L
2(L+W)=P
In accordance with the definition of perimeter, the perimeter for a length L and a width W that is equal to 2L will be 2W=L "In geometry, a shape's perimeter is referred to as its overall length. The perimeter of a shape is determined by adding all of its sides' and edges' lengths ".
To know more about perimeter,
https://brainly.com/question/6465134?referrer=searchResults
#SPJ1
12. What is the slope using the following points?
(12, 4) and (14, 6)
m= 1
m= 2
m=-1
m= -1
m= 10/26
Answer:
hope it helps
Step-by-step explanation:
Which of the following notations correctly describe the end behavior of the polynomial graph below?
The end behaviour of the polynomial graph is (b) x ⇒ +∝, f(x) ⇒ -∝ and x ⇒ -∝, f(x) ⇒ -∝
How to determine the end behaviour of the polynomial graph?The polynomial graph represents the given parameter
This polynomial graph is a quadratic function opened downwards
Polynomial function of this form have the following end behaviour:
As x increases, f(x) decreasesAs x decreases, f(x) decreasesThis is represented as
x ⇒ +∝, f(x) ⇒ -∝ and x ⇒ -∝, f(x) ⇒ -∝
Hence, the end behaviour is (b)
Read more about end behaviour at
https://brainly.com/question/1365136
#SPJ1
TIME REMAINING56:5412.Which points are reflections of each other across both axes?Ty24-2(-2.8) and (2. -8)(-7 -1) and (-7. 1)(5.-6) and (-5, -6)NelSubSave and ExitMark this and return
a point is reflected against both axes when the two signs of the point are opposite
for example the reflexion against both axes for the point(-2,8) is (2,-8)
among the options there is none that meets this condition
Find the equation of the perpendicular bisector of the line AB with A(-2,7) and B(5,2)
Solution
Since it is a perpendicular bisector, hence point M is the midpoint
[tex]\begin{gathered} \therefore Mid\text{ point AB}=(\frac{-2+5}{2},\frac{7+2}{2}) \\ mid\text{ point=(}\frac{3}{2},\frac{9}{2}) \end{gathered}[/tex]Slope
[tex]\text{Slope (m)=}\frac{2-7}{5--2}=-\frac{5}{7}[/tex]Since they are perpendicular
[tex]\begin{gathered} m_1\times m_2=-1 \\ -\frac{5}{7}\times m_2=-1 \\ m_2=\frac{7}{5} \end{gathered}[/tex]The equation of the perpendicular bisector of the line AB with A(-2,7) and B(5,2)
[tex]\begin{gathered} y-y_1=m(x_{}-x_1) \\ y-5=\frac{7}{5}(x-2) \\ y-5=\frac{7}{5}x-\frac{14}{5} \\ y=\frac{7}{5}x-\frac{14}{5}+5 \\ y=\frac{7}{5}x+\frac{11}{5} \end{gathered}[/tex]The final answer
[tex]y=\frac{7}{5}x+\frac{11}{5}[/tex]the basketball game had 600 people in attendance if the ratio of hawk fans to cyclone fans is 2:10 how many more cyclone fans were there
Variables:
x: hawk fans
y: cyclone fans
The basketball game had 600 people in attendance means:
x + y = 600
The ratio of hawk fans to cyclone fans is 2:10 means
[tex]\begin{gathered} \frac{x}{y}=\frac{2}{10} \\ 10x=2y \\ \frac{10x}{2}=y \\ 5x=y \end{gathered}[/tex]Substituting the last equation into the first equation, we get:
x + 5x = 600
6x = 600
x = 600/6
x = 100
And the value of y is:
y = 5*100
y = 500
There were 500 - 100 = 400 more cyclone fans
graph the function, not by plotting points, but by starting from the graph of y=e^x in the figure below.
the function is: y= e^-x -1
?? I need help finding the asymptote??
The given function has a horizontal asymptote and the equation of the horizontal asymptote is y = -1.
What is an asymptote of a function?
An asymptote is a line that a function's graph approaches as x or y approaches positive or negative infinity. Asymptotes are classified into three types: vertical, horizontal, and oblique. That is, the function approaches positive or negative infinity as approached from either the positive or negative side.
The given function is [tex]y=e^{-x}-1[/tex]
Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y = -1
Horizontal Asymptote: y = -1.
The graph of the function [tex]y=e^{-x}-1[/tex] can be drawn as
Hence, the given function has a horizontal asymptote and the equation of the horizontal asymptote is y = -1.
To learn more about Asymptotes of a function, visit:
https://brainly.com/question/4138300
#SPJ1
Ruben bought 6 comic books for $21 Each comic book was the same price.
What was the cost for 1 comic book?
26,862 divided by 407
Answer:
66
Step-by-step explanation:
it is 66
can someone help me with this assignment
Answer:
6
Step-by-step explanation:
On the coordinate plane, it shows that the y axis is 6. Therefore, (16, 6)
Answer:
5
Step-by-step explanation:
I need help with this check the picture
The numbers 7 in the domain and 10 in the range don't belong there.
Describe the domain and range of a function.The domain is the set of values over which the provided function is defined. The range is the set of all values that the function that is provided can return.
How are intervals in numbers understood?[a,b] refers to all values between a and b as well as a and b themselves.
With the exception of b, all values between a and b are referred to as (a,b).
We cannot write about them since we cannot include infinity or negative infinity since they are symbols for arbitrary enormous or tiny numbers, respectively.
Another thing to keep in mind is that when we plot functions, the inputs are typically on the x-axis and the outputs are typically on the vertical axis (y-axis).
Given : (2,7). (8, 12). (5,9). (10.15)
Domain: The initial value of numbers will always apply; 2, 8, 5, 10
Range: Numbers will always have a second value; 7, 12, 9, 15.
What you have here is :
Domain: (2,5, 7, 8, 10)
Range: (7.9. 10. 12. 15)
The problem is that 10 is in the range but 7 is in the domain. They shouldn't be there, those two. There is also an additional number there that you have. Only 4 digits should be in the Domain and Range. Given that there are four sets or pairs of values.
To know more about the domain and range, visit:
https://brainly.com/question/10197594
#SPJ1
Find the measure of the angle between the two vectors.
7) u = (6,-2)
v = (8,-8)
9) u =(2, 6)
v = (-5, -8)
8) u = (-2, 3)
v = (4, -6)
10) u = (-9, 4)
v = (-7, -1)
Answer:
780
Step-by-step explanation:
Solve the system of linear equations using matrices.4y-z=-5X+ 5y +z=-32x-y + 3z =13
The given system expressed as a matrix would be
0 4 -1 -5
1 5 1 -3
2 -1 3 13
To solve this, first, we have to change the first row for the second
1 5 1 -3
0 4 -1 -5
2 -1 3 13
Now, we multiply the first row by 2, then subtract it from the third row.
1 5 1 -3
0 4 -1 -5
0 -11 1 19
Then, we multiple the second row with -11/4 to subtract it from the third row.
1 5 1 -3
0 4 -1 -5
0 0 -7/4 21/4
The resulting system would be
[tex]\mleft\{\begin{aligned}x+5y+z=-3 \\ 4y-z=-5 \\ -\frac{7}{4}z=\frac{21}{4}\end{aligned}\mright.[/tex]We solve for z
[tex]\begin{gathered} \frac{-7}{4}z=\frac{21}{4} \\ z=\frac{21}{-7}=-3 \end{gathered}[/tex]Therefore, z is equal to -3.
We use z to find y in the second equation.
[tex]\begin{gathered} 4y-(-3)=-5 \\ 4y+3=-5 \\ 4y=-5-3 \\ 4y=-8 \\ y=\frac{-8}{4}=-2 \end{gathered}[/tex]Therefore, y is equal to -2.
We use y and z to find x in the first equation.
[tex]\begin{gathered} x+5(-2)+(-3)=-3 \\ x-10-3=-3 \\ x=-3+10+3=10 \end{gathered}[/tex]Therefore, x is equal to 10.
Find the distance between the two points.|(1,4)✓ [?](-2,-3)Enter the number thatgoes beneath theradical symbol.Enter
The distance between two points is given as;
[tex]D=\sqrt[]{(y_2-y_{1_{}})^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} \text{Where x}_1=-2 \\ y_1=-3 \\ x_2=1 \\ y_2=4 \end{gathered}[/tex][tex]\begin{gathered} D=\sqrt[]{(4-(-3)^2+(1-(-2)^2} \\ D=\sqrt[]{7^2+3^2} \\ D=\sqrt[]{49+9} \\ D=\sqrt[]{58} \end{gathered}[/tex]The number beneath the radical symbol is 58.
The rectangle below has an perimeter of 50 units.2x - 2What is the length, in units, of the shorter side?
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
From the diagram,
length = 2x - 2
width = x
Perimeter = 50
Thus,
50 = 2(2x - 2 + x)
Dividing both sides of the equation by 2, it becomes
50/2 = 2x + x - 2
25 = 3x - 2
3x = 25 + 2 = 27
x = 27/3
x = 9
The length of the shorter side is 9
Which number lines have a point that is equal to point
P? Check all that apply.
←
H
-
-60
-60
-60
-60
0
0
0
0
0
Answer:
Step-by-step explanation:
-60 -60 -60 0 0
Toby buys a new iPhone for a price of $599. What is the total amount his credit card is charged if the sales tax is 7%?
Answer:
$640.93
Step-by-step explanation:
Convert 7% into a decimal
7% = 0.07
Multiply that by $599 to get the sales tax
599(0.07) = $41.93
Add that with the $599
599 + 41.93
= $640.93Toby's credit card will get charged $640.93.
There are 348 identical plastic chips numbered 1 through 348 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 213? Express your answer as a simplified fraction or a decimal rounded to four decimal places
We have to find the probability of randomly drawing a chip number that is smaller than 213.
As the chips are numbered from 1 to 348,this probability will be equal to the proportion of chips that have a number that is less than 213.
We have 212 chips in the bag that have a number less than 213, so we can calculate the probability P as:
[tex]P=\frac{X}{N}=\frac{212}{348}=\frac{53}{87}\approx0.6092[/tex]Answer: the probability is 53/87 or approximately 0.6092.
3. (02.02 MC)
The beginning mean bi-weekly wage in a certain industry is $2,498.00. If the mean bi-weekly wage grows by 3.25%, what is the new mean annual wage? (4 points)
$62,903.63
$64,948.00
$67,058.81
$69,079.13
If the mean bi-weekly wage grows by 3.25%, the new mean annual wage is: C. $67,058.81.
What is annual wage?Annual wage can simply be defined as the amount a person is paid annually as wages . Wages can be paid daily or weekly.
Using this formula to find the new mean annual wage
New mean annual wage = [Beginning mean bi-weekly wage × ( 1+ mean bi-weekly wage ) ]× Number of weeks per year /2
Let plug in the formula
New mean annual wage = [$2,498.00 × (1+ 0.0325)] × 52 weeks /2
New mean annual wage = [$2,498.00 × (1.0325)] × 26 weeks
New mean annual wage = $2,579.185 × 26 weeks
New mean annual wage = $67,058.81
Therefore the correct option is C.
Learn more about New mean annual wage here:https://brainly.com/question/16823998
#SPJ1
7/10 3/10 solve complex fraction
The value of the complex fraction 7/10/3/10 is
2 1/3
What is a complex fraction?A fraction is made up of two parts, a numerator and a denominator; the number above the line is the numerator and the number below the line is the denominator. The line or slash in that separates the numerator and the denominator in a fraction represents division.
A complex fraction can be defined as a fraction in which the denominator and numerator or both contain fractions. For example( 5/2)/(6/4).
Therefore the fraction (7/10)/(3/10) can be simplified as 7/10÷3/10= 7/10×10/3 = 7/3= 2 1/3
Therefore the simplified value of the complex fraction is 2 1/3.
learn more about complex fraction from
https://brainly.com/question/28702241
#SPJ1
The circumference of a circle is 24π in. What is the area, in square inches? Express your answer in terms of π.
Given
[tex]circumference\text{ of circle = 24}\pi\text{ in}[/tex]Recall that the formula for the circumference of a circle C is:
[tex]C\text{ = 2}\pi r[/tex]Using the formula, we can find the radius of the circle as shown:
[tex]\begin{gathered} 2\pi r\text{ = 24}\pi \\ Divide\text{ both sides by 2}\pi \\ r\text{ = }\frac{24\pi}{2\pi} \\ r\text{ = 12 in} \end{gathered}[/tex]The area A of a circle can be found using the formula:
[tex]A\text{ = }\pi r^2[/tex]Substituting the value obtained:
[tex]\begin{gathered} A\text{ = }\pi\text{ }\times\text{ 12}^2 \\ =\text{ 144}\pi\text{ in}^2 \end{gathered}[/tex]The area is 144π square in
probe algebraically that. (2n+1)^2-(2n+1) is an even number.
(2n + 1)² - (2n + 1) is an even number for all positive integral values of n.
How to simplify an expression?
Expressions are simplified when they are rewritten in a concise manner and without any similar phrases. When we combine like terms in an expression and, if necessary, solve all of the specified brackets, we are only left with unlike terms in the simplified expression that cannot be further reduced.
What is an even number?
An even number is any number that can be divided by 2 precisely. The last digit of an even number is always one of the following: 0, 2, 4, 6, or 8. Even numbers can include 2, 4, 6, 8, 10, 12, and 14. These are even numbers because they are simple to divide by two. It is important to remember that 2 is the smallest positive even natural number.
Given, the equation under consideration is y = (2n + 1)² - (2n + 1)
Upon simplifying and solving for y, we have:
y = (2n + 1)² - (2n + 1) = 4n² + 4n + 1 - 2n - 1 ⇒ y = 4n² + (4n - 2n) + (1 - 1)
⇒ y = 4n² + 2n + 0 ⇒ y = 2 (2n² + n) --(i)
On carefully analyzing (i), we can affirm that y is divisible by 2, thus confirming that (2n + 1)² - (2n + 1) is an even number for all positive integral values of n.
Therefore, (2n + 1)² - (2n + 1) is an even number for all positive integral values of n.
To learn more about this, tap on the link below:
https://brainly.com/question/24672369
#SPJ13
find the product(x+2)(y^2+2y-12)
Answer::
[tex]=xy^2+2xy-12x+2y^2+4y-24[/tex]Explanation:
Given the expression:
[tex]\mleft(x+2\mright)\mleft(y^2+2y-12\mright)[/tex]First, distribute the left bracket:
[tex]=x\mleft(y^2+2y-12\mright)+2\mleft(y^2+2y-12\mright)[/tex]Next, open the bracket:
[tex]=xy^2+2xy-12x+2y^2+4y-24[/tex]i need help on this answer
The correlation coefficient "r" can take values from -1 to 1
If the correlation coefficient is less than zero, r < 0, the correlation will be considered negative.
If the correlation coefficient is greater than zero, r > 0. the correlation will be considered positive.
A correlation coefficient equal to zero, r = 0, then there is no correlation between both variables.
If the absolute value of the coefficient is less than 0.35: 0 < | r | < 0.35 → you can say that the correlation between the variables is weak or low.
If the absolute value of the coefficient is between 0.35 and 0.38: 0.35 < | r | 0.65 → you can say that the correlation between both variables is moderate.
If the absolute value of the coefficients is greater than 0.66: | r | > 0.66 → you can say that there is a strong/ high correlation between the variables.
If the absolute value of the coefficient is greater than 0.90: | r |>0.90 → You can conclude that the correlation between both variables is very high or marked.
To be able to classify the type of correlation, the first step is to calculate the correlation coefficient between both variables. You can do that manually using the formula:
[tex]r=\frac{\Sigma x_1x_2-\frac{(\Sigma x_1)(\Sigma x_2)}{n}}{\sqrt[]{\lbrack\Sigma x^2_1-\frac{(\Sigma x_1)^2}{n}\rbrack\lbrack\Sigma x^2_2-\frac{(\Sigma x_2)^2}{n}\rbrack}}[/tex]First, let's determine the sums
X₁: Height (in)
[tex]\begin{gathered} \Sigma x_1=20+30+40+40+70+90 \\ \Sigma x_1=290 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2_1=20^2+30^2+40^2+40^2+70^2+90^2 \\ \Sigma x^2_1=17500 \end{gathered}[/tex]X₂: Length (in)
[tex]\begin{gathered} \Sigma x_2=18+16+15+16+9+4 \\ \Sigma x_2=78 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2_2=18^2+16^2+15^2+16^2+9^2+4^2 \\ \Sigma x^2_2=1158 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x_1x_2=(20\cdot18)+(30\cdot16)+(40\cdot15)+(40\cdot16)+(70\cdot9)+(90\cdot4) \\ \Sigma x_1x_2=3070 \end{gathered}[/tex]There are 5 ordered pairs, so the sample size is n=6
Replace every value on the formula:
[tex]\begin{gathered} r=\frac{3070-\frac{290\cdot78}{6}}{\sqrt[]{\lbrack17500-\frac{290^2}{6}\rbrack\lbrack1158-\frac{78^2}{6}\rbrack}} \\ r=\frac{3070-3861}{\sqrt[]{3483.33\cdot144}} \\ r=-0.99 \\ \end{gathered}[/tex]The correlation coefficient is r= -0.99
→ r is a negative value, which means that the correlation between the height and length of the rectangles is negative
→ the absolute value of the coefficient is greater than 0.90; | r | =0.99, so the correlation between both variables can be considered as a strong correlation
You can say the there is a strong negative correlation between both variables (option F)
Can someone help me on this I’m confused
Step-by-step explanation:
if the goal is to have both numbers with denominator 6, then the first one is totally simple :
3 1/6 = 3 1/6
what else could it be ... ?
and the second, well, how many thirds are in a whole ?
right, 3, that's why we call them "thirds".
how many 6ths are in a whole ?
right, 6.
do you notice something ? it is easy to get from 3 to 6 by multiplying 3 by 2.
in order to keep the overall value of a fraction unchanged, when we multiply one part of the fraction by something we need to multiply the other part by the same number too.
so,
5 2/3 = 5 2/2×2/3 = 5 4/6
in short : yes, every third contains 2 6ths.
therefore, 2/3 = 4/6
If cos B = 7/8, then what is the positive value of tan 1/2 B, in simplest radical formwith a rational denominator?
Let us use the rule of the double of the angle
Since
[tex]\cos B=2\cos ^2\frac{B}{2}-1[/tex]Substitute cos B by 7/8
[tex]\frac{7}{8}=2\cos ^2\frac{B}{2}-1[/tex]Add 1 to both sides
[tex]\begin{gathered} \frac{7}{8}+1=2\cos ^2\frac{B}{2}-1+1 \\ \frac{15}{8}=2\cos ^2\frac{B}{2} \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{\frac{15}{8}}{2}=\frac{2\cos ^2\frac{B}{2}}{2} \\ \frac{15}{16}=\cos ^2\frac{B}{2} \end{gathered}[/tex]Take a square root for both sides
[tex]\begin{gathered} \sqrt[]{\frac{15}{16}}=\cos \frac{B}{2} \\ \cos \frac{B}{2}=\frac{\sqrt[]{15}}{4} \end{gathered}[/tex]let us find sin B
Since
[tex]\sin ^2\frac{B}{2}+\cos ^2\frac{B}{2}=1[/tex]Then
[tex]\sin ^2\frac{B}{2}+\frac{15}{16}=1[/tex]Subtract 15/16 from both sides
[tex]\begin{gathered} \sin ^2\frac{B}{2}+\frac{15}{16}-\frac{15}{16}=1-\frac{15}{16} \\ \sin ^2\frac{B}{2}=\frac{1}{16} \end{gathered}[/tex]Take a square root for both sides
[tex]\begin{gathered} \sin \frac{B}{2}=\sqrt[]{\frac{1}{16}} \\ \sin \frac{B}{2}=\frac{1}{4} \end{gathered}[/tex]Since
[tex]\tan \frac{B}{2}=\frac{\sin \frac{B}{2}}{\cos \frac{B}{2}}[/tex]Then
[tex]\begin{gathered} \tan \frac{B}{2}=\frac{\frac{1}{4}}{\frac{\sqrt[]{15}}{4}} \\ \tan \frac{B}{2}=\frac{1}{\sqrt[]{15}} \end{gathered}[/tex]The value of tan(1/2 B) is
[tex]\frac{1}{\sqrt[]{15}}\times\frac{\sqrt[]{15}}{\sqrt[]{15}}=\frac{\sqrt[]{15}}{15}[/tex]
A science teacher prepares an activity for her class. She cuts 3/4 yard of ribbon into 6 pieces of equal size. Write and solve an equation to find the length of each piece of ribbon.
The equation that represents the given situation will be (x=3/4÷6) and the length of each piece of ribbon will be 1/8 yards.
What is an equation?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions. An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, the equation that recipients the given situation:
The ribbon is 3/4 yards.Cuts into 6 equal pieces.Then, the equation will be:
x = 3/4 ÷ 6Now, calculate the equation for x as follows:
x = 3/4 ÷ 6x = 3/4 × 1/6x = 1/4 × 1/2x = 1/8
Therefore, the equation that represents the given situation will be (x=3/4÷6) and the length of each piece of ribbon will be 1/8 yard.
Know more about equations here:
https://brainly.com/question/28937794
#SPJ1