Answer:
r = 3
Step-by-step explanation:
[tex]\dfrac{r}{2} - 3 = 3(4 - \dfrac{3r}{2} )[/tex]
The first step to solve for "r" is to simplify the distributive property on the RHS. To simplify the distributive property, we need to multiply the term outside the parenthesis with the terms inside the parenthesis.
[tex]\rightarrow \dfrac{r}{2} - 3 = 12 - \dfrac{9r}{2}[/tex]
Now, add 9r/2 and 3 both sides to isolate the constants and variables.
[tex]\rightarrow \dfrac{r}{2} + \dfrac{9r}{2} = 12 + 3[/tex]
Simplify both sides.
[tex]\rightarrow \dfrac{10r}{2}= 12 + 3[/tex]
[tex]\rightarrow 5r = 15[/tex]
Divide 5 both sides.
[tex]\rightarrow \boxed{r = \frac{15}{5} = 3}[/tex]
At Gulfport Electronics, Randy earns a monthly salary of $1500 plus a 5% commission of x, his total monthly sales. If his March earnings total $2500, write and solve an equation that could be used to determine his total monthly sales for the month of March
Answer:
His March Earnings is $20000
Step-by-step explanation:
Given
[tex]Salary = \$1500[/tex]
[tex]Commission = 5\%\ of\ sales[/tex]
[tex]March\ Earnings = \$2500[/tex]
Required
Determine the monthly sales
Represent the monthly sales with x
The march earnings can be determined using:
[tex]March\ Earnings = Salary + Commission[/tex]
[tex]March\ Earnings = Salary + 5\%\ of\ x[/tex]
Substitute values of March Earnings and Salary
[tex]2500 = 1500 + 5\% * x[/tex]
[tex]2500 = 1500 + 0.05 * x[/tex]
[tex]2500 = 1500 + 0.05x[/tex]
Solve for 0.05x
[tex]0.05x = 2500 - 1500[/tex]
[tex]0.05x = 1000[/tex]
Solve for x
[tex]x = 1000/0.05[/tex]
[tex]x = 20000[/tex]
Hence:
His March Earnings is $20000
Which of the following is NOT a linear function?
Answer:
x^2 + 8 = 64 is not a linear function
Step-by-step explanation:
using the process of elimination and a graphing calculator, you can see that the rest of the functions give you a linear function. therefore, the answer is x^2 + 8 = 64 is not a linear function!! i hope this helps you!! <3
The [tex]x^2 + 8 = 64[/tex] is not the liner function.
The following information regarding the linear function is:
It is the function where the graph is in the straight line. The form in the linear function should be y = a + bx.In this, there is one dependent and one independent variable.Therefore we can conclude that the [tex]x^2 + 8 = 64[/tex] is not the liner function.
Learn more about the linear function here: brainly.com/question/20286983
Distribute to create an equivalent expression with the fewest symbols possible.
1/2(10x+20y+10z) =
[tex]\\ \rm\longmapsto 1/2(10x+20y+10z)[/tex]
a(b+c)=ab+ac[tex]\\ \rm\longmapsto 10x/2+20y/2+10z/2[/tex]
[tex]\\ \rm\longmapsto 5x+10y+5z[/tex]
Answer:
5x+10y+5z
Step-by-step explanation: it was on khan academy and it was right
Question is in the picture:
Answer:
here
Step-by-step explanation:
For the first one shade 38 squares
For the second one shade 65 of the squares
#1 is 38%
#2 is 65%
Answer:shade 19 out of 50 bloxks
Step-by-step explanation:
it shows on page
Lola bought 6 bracelets for $7.50 and 10 rings for $13.00. At the same time, Bella bought 8 bracelets and 7 rings. What is the total price for the items Bella bought?
Answer:$51.5
Step-by-step explanation:
round these amounts to the nearest whole dollar.3.87cedis.9.28 cedis.11.05 cedis.4.39cedis
Answer: 4.00, 9.00, 11.00, 4.00
Step-by-step explanation:
When we round, we round from the digit one smaller than the one we're rounding to. In this case, since we're rounding to the dollar, we round from the 10th place. To round, we need to know whether the number we're rounding from is smaller than, equal to, or larger than 5. If the number is smaller than 5, we round down. Larger, and we round up. If the number is equal to 5, we also round up.
If a number is divisible by 10, then its ones digit is 0
TRUE OR FALSE
Answer:
its true, depending on the times table.
Answer:
True
Step-by-step explanation:
This statement is always true.
Find the area of each shaded sector. Round to the hundredths place
10. SR = 26m
Check the picture below.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\pi \theta r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=26\\ \theta =\stackrel{180+34}{214} \end{cases}\implies \begin{array}{llll} A=\cfrac{\pi (214)(26)^2}{360}\implies A=\cfrac{18083\pi }{45} \\\\\\ A \approx 1262.43 \end{array}[/tex]
Need help asap pleaseeeeee
Help me pleaseeee
I need to fund the point in the line using this equation
Answer:(1,2)
Step-by-step explanation: The signs may not be right(positive, negative) Sorry it’s been a long time since I did this
Use the figure below to find angle PNO
Answer:
31 degrees
Step-by-step explanation:
A line has angle of 180 degrees.
So
[tex](2z+17)+(4z-23)=180\\6z-6=180\\6z=186\\z=31[/tex]
Please ANSWER NOW, PLEASE HELP , for math 50 points!!!
An object is thrown in the air with an initial velocity of 5 m/sec from a height of 9 m. The following equation models the height of the object in meters after t seconds. How many seconds does it take for the object to hit the ground?
Check the picture below.
[tex]~~~~~~\textit{initial velocity in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&5\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&9\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-4.9t^2+5t+9\implies \stackrel{h(t)}{0}=-4.9t^2+5t+9 \implies 4.9t^2-5t-9=0[/tex]
since we don't get any neat integer values from it hmmm let's plug that in the quadratic formula to see what we get as h(t) = 0.
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{-5}t\stackrel{\stackrel{c}{\downarrow }}{-9}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ t= \cfrac{ - (-5) \pm \sqrt { (-5)^2 -4(4.9)(-9)}}{2(4.9)}\implies t=\cfrac{5\pm\sqrt{25+176.4}}{9.8} \\\\\\ t=\cfrac{5\pm \sqrt{201.4}}{9.8}\implies t\approx \begin{cases} 1.96~~\checkmark\\ -0.94 \end{cases}[/tex]
notice, we do not use the negative value for "t", since the seconds cannot be less than 0.
what is the solution of the following equation? 2x-5+3x=35
2x - 5 + 3x = 35
simplify
5x - 5 = 35
add 5 to both sides
5x - 5 + 5 = 35 + 5
simplify
5x = 40
divide both sides by 5
5x/5 = 40/5
simplify
x = 8
Write and equation to represent the function.
Input(x). 1. 2. 3. 4
Output(y). 8. 19. 30. 41
Answer:
[tex]y=11x-3[/tex]
Step-by-step explanation:
Given ordered pairs:
(1, 8) (2, 19) (3, 30) (4, 41)
As the y is directly proportional to x (y values increase +11 for every +1 increase for the x-values) then the equation will be linear.
Point-slope form of a linear equation: [tex]y-y_1=m(x-x_1)[/tex]
(where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line)
[tex]\textsf{slope }m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Let:
[tex](x_1,y_1)=(1,8)[/tex][tex](x_1,y_2)=(2,19)[/tex][tex]\implies \textsf{slope }m=\dfrac{19-8}{2-1}=11[/tex]
Using point-slope equation with m = 11 and point (1, 8):
[tex]y-y_1=m(x-x_1)[/tex]
[tex]\implies y-8=11(x-1)[/tex]
[tex]\implies y=11x-3[/tex]
4. If m 1 = (10x + 42)° and m 7 = (2x + 6)º,
what is the value of x, m 1?
Answer:
Value of x = 8
(3x - 7) = (5x - 23)
-2x = -16
x = 8
Value of m 8 = 17 degrees
5(8) - 23
40 - 23 = 17
Which graph correctly solves the system of equations below? y = x2 + 3x + 4 y = x2 + 2x + 1 (1 point) Select one: a. two quadratic graphs opening up. They intersect at negative 3, 4. b. two quadratic graphs opening up. They intersect at 0, 3. c. two quadratic graphs opening down. They intersect at 0, 3. d. quadratic graph opening up and quadratic graph opening down. They intersect at 1, 4 and 0, 3. Clear my choice
Answer:
the answer is b b is the answer I did this before
Solving a Two-Step Matrix Equation
Solve the equation:
Answer:
[tex]\boxed {x_{1} = 3}[/tex]
[tex]\boxed {x_{2} = -4}[/tex]
Step-by-step explanation:
Solve the following equation:
[tex]\left[\begin{array}{ccc}3&2\\5&5\\\end{array}\right] \left[\begin{array}{ccc}x_{1}\\x_{2}\\\end{array}\right] + \left[\begin{array}{ccc}1\\2\\\end{array}\right] = \left[\begin{array}{ccc}2\\-3\\\end{array}\right][/tex]
-In order to solve a pair of equations by using substitution, you first need to solve one of the equations for one of variables and then you would substitute the result for that variable in the other equation:
-First equation:
[tex]3x_{1} + 2x_{2} + 1 = 2[/tex]
-Second equation:
[tex]5x_{1} + 5x_{2} + 2 = -3[/tex]
-Choose one of the two following equations, which I choose the first one, then you solve for [tex]x_{1}[/tex] by isolating
[tex]3x_{1} + 2x_{2} + 1 = 2[/tex]
-Subtract [tex]1[/tex] to both sides:
[tex]3x_{1} + 2x_{2} + 1 - 1 = 2 - 1[/tex]
[tex]3x_{1} + 2x_{2} = 1[/tex]
-Subtract [tex]2x_{2}[/tex] to both sides:
[tex]3x_{1} + 2x_{2} - 2x_{2} = -2x_{2} + 1[/tex]
[tex]3x_{1} = -2x_{2} + 1[/tex]
-Divide both sides by [tex]3[/tex]:
[tex]3x_{1} = -2x_{2} + 1[/tex]
[tex]x_{1} = \frac{1}{3} (-2x_{2} + 1)[/tex]
-Multiply [tex]-2x_{2} + 1[/tex] by [tex]\frac{1}{3}[/tex]:
[tex]x_{1} = \frac{1}{3} (-2x_{2} + 1)[/tex]
[tex]x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}[/tex]
-Substitute [tex]-\frac{2x_{2} + 1}{3}[/tex] for [tex]x_{1}[/tex] in the second equation, which is [tex]5x_{1} + 5x_{2} + 2 = -3[/tex]:
[tex]5x_{1} + 5x_{2} + 2 = -3[/tex]
[tex]5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3[/tex]
Multiply [tex]-\frac{2x_{2} + 1}{3}[/tex] by [tex]5[/tex]:
[tex]5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3[/tex]
[tex]-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3[/tex]
-Combine like terms:
[tex]-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3[/tex]
[tex]\frac{5}{3}x_{2} + \frac{11}{3} = -3[/tex]
-Subtract [tex]\frac{11}{3}[/tex] to both sides:
[tex]\frac{5}{3}x_{2} + \frac{11}{3} - \frac{11}{3} = -3 - \frac{11}{3}[/tex]
[tex]\frac{5}{3}x_{2} = -\frac{20}{3}[/tex]
-Multiply both sides by [tex]\frac{5}{3}[/tex]:
[tex]\frac{\frac{5}{3}x_{2}}{\frac{5}{3}} = \frac{-\frac{20}{3}}{\frac{5}{3}}[/tex]
[tex]\boxed {x_{2} = -4}[/tex]
-After you have the value of [tex]x_2[/tex], substitute for [tex]x_{2}[/tex] onto this equation, which is [tex]x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}[/tex]:
[tex]x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}[/tex]
[tex]x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}[/tex]
-Multiply [tex]-\frac{2}{3}[/tex] and [tex]-4[/tex]:
[tex]x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}[/tex]
[tex]x_{1} = \frac{8 + 1}{3}[/tex]
-Since both [tex]\frac{1}{3}[/tex] and [tex]\frac{8}{3}[/tex] have the same denominator, then add the numerators together. Also, after you have added both numerators together, reduce the fraction to the lowest term:
[tex]x_{1} = \frac{8 + 1}{3}[/tex]
[tex]x_{1} = \frac{9}{3}[/tex]
[tex]\boxed {x_{1} = 3}[/tex]
what is the complement of 37 degrees without using a protractor, sketch the two angles so that they are adjacent
Answer:
the complement of 37 degrees is 53 degrees.
Step-by-step explanation:
90-37=53
36 (highest)POINTS PLS ANSWER ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Calculate the surface are of each of the following. Show your work.
Hey there!
[tex]⇢ \: A = 2wl + 2lh + 2hw[/tex]
L = 17 inW = 8 inH = 12Substitute
[tex]⇢ \: = 2(8)(17) + 2(17)(12) + 2(12)(8)[/tex]
[tex]⇒872[/tex]
Surface area = 872 square inches
Help
This is really confusing
Step-by-step explanation:
The 53rd ball will be blue. I don't really know how to explain but I'll try.
So there are black, white and blue balls. If you look closer you'll see that the words 'black,white,blue,black, blue were repeated twice. So let's say that the first 5 letters are a set. To get the 50th color, all you have to do is 5 × 10 which is 50 and the 50th term is blue. Just add black(51st), white(52nd) and you'll get the 53rd color to be Blue.
I don't know how to do <2>.
Hope this helps!
Please mark me brainliest :)
Simplify the following expression.
(8x + 4) - (2x2 + 4x - 7)
Answer:
-2x^2 + 4x + 11
Step-by-step explanation:
whats 2x2 ? do you mean 2x^2 ? if so then...
8x + 4 - 2x^2 - 4x + 7
4x + 11 - 2x^2
-2x^2 + 4x + 11
Answer:
this is the answers 2x^2+4x+11
Ingnd mxes 3 6 pounds of almonds with some raisins to make a trail mix She divides the trail mix into 12 equal portions Each portion weighs 0.7 of a pound How many pounds of raisins did she use to make the trail mix? Express the answer to the nearest tenth 2.9 4.8 5.1 7.2
Answer:
The 12 portions weigh a total of 12*0.7 = 8.4 lbs
So, the almonds weigh 8.4 - 3.6 = 4.8 lbs
Answer:
4.8 poundsStep-by-step explanation:
Let raisins weight be x
Then we get equation
(3.6 + x)/12 = 0.7Solving for x
3.6 + x = 12*0.7x + 3.6 = 8.4x = 8.4 - 3.6x = 4.8 poundsOption B is correct one
Find the average distance in Thursday is round your answer to the nearest 10 if necessary 7,20,9,35,12,15,7,10,20,25
= (7+20+9+35+12+15+7+10+20+25) : 10
with 10 = number of values
average distance = 160 : 10 = 16
1.2y+4.5-3.4y-6.3 pls help me
Answer:
-2.2y-1.8
Step-byStep-byStep-byStep-byStep-byStep-byStep-byStep-byStep-by
1.2y-3.4y=-2.2y
4.5-6.3=-1.8
ssoso:-2.2y-1.8
What critical value of t* should be used for a 98% confidence interval for the population mean based on a random sample of 25 observations?
A. t* = 2.485
B. t* = 2.492
C. t* = 2.787
D. t* = 2.797
Using a t-distribution calculator, it is found that the critical value of t* for a 98% confidence interval with 25 observations is given by:
B. t* = 2.492
How to find the critical value of the t-distribution?It is found using a calculator, with two inputs, which are given by:
The confidence level.The number of degrees of freedom, which is one less than the sample size.In this problem, we have a confidence level of 98% and 25 - 1 = 24 df, hence the critical value is of t* = 2.492, which means that option B is correct.
More can be learned about the t-distribution at https://brainly.com/question/16162795
#SPJ2
what are the missing numbers?
Answer:
5, 30, and 70
Step-by-step explanation:
Multiply by number of quarters by 5 to get the number of nickels.
Lucien can buy 1 lb of Colombian coffee beans for $4.25 you can buy one pound of French roast coffee beans for $3.75 if he buys one pound mixture of the two kinds of beans for $4 how much of each kind of coffee bean does he buy
Answer:
Colombian coffee bought = 0.5 lbs
French roast coffee beans bought = 0.5 lbs
Step-by-step explanation:
Let Colombian coffee bought = [tex]x[/tex] lbs
Total weight of mixture bought = 1 lbs
Therefore, French roast coffee beans bought = (1 - [tex]x[/tex]) lbs
Price of 1 lb Colombian coffee = $4.25
Price of [tex]x[/tex] lbs of Colombian coffee = $[tex]4.25x[/tex]
Price of 1 lb French roast coffee beans = $3.75
Price of (1 - [tex]x[/tex]) lbs French roast coffee beans = $3.75(1 - [tex]x[/tex])
It is given that total money spent is $4.
As per given statement:
[tex]4.25x+3.75(1-x)=4\\\Rightarrow 0.50x=0.25\\\Rightarrow x=\bold{0.5\ lbs}[/tex]
Colombian coffee bought = 0.5 lbs
French roast coffee beans bought = 0.5 lbs
1. Brother has 12 red blocks, 10 blue blocks, and 8 yellow blocks. What is the ratio of red blocks to yellow blocks?
[tex]ratio-of-red-blocks-to-yellow-blocks = \frac{number-of-red-blocks}{number-of-yellow-blocks} =\frac{12}{8} =\frac{3}{2}[/tex]
Answer: [tex]\frac{3}{2}[/tex] or 3 : 2
Hope it helps!
Answer:
3 : 2
Step-by-step explanation: