Answer:
Step-by-step explanation:
6x+4y=14
y=5
6x+4(5)=14
6x+20=14
6x=-6
x=-1
Step 1: Where you see a y in the equation 6x + 4y =14 replace it with 5. This will help you find x
6x + 4(5) = 14
6x + 20 = 14
Step 2: Combine like terms by subtracting 20 to both sides
6x + (20-20) = 14-20
6x = -6
Step 3: Isolate x by dividng 6 to both sides
[tex]\frac{6x}{6} = \frac{-6}{6}[/tex]
x = -1
Point of intersection of these two linse is ( -1 , 5 )
Hope this helped!
A student pulls out a marble from a pag containing blue, green, and red marbles. He records the color and places it back into the bag The table below shows the frequency of
each color after 100 marbles are pulled out
Color of Marbles Blue Green Red
Number of Draws 13 29 58
How many green draws can you expect if the marbles are pulled out 1,000 times?
Answer:
Answer is B - 290.
Step-by-step explanation:
The idea here is that we're assuming the frequency each colour is drawn is a reflection of the proportion of marbles in the bag that are that colour. The more of a particular colour you have, the more likely you are to draw it, and vice versa.
Therefore we can assume the proportion of blue, gree, and red marbles is 13%, 29%, and 58% respectively based on the first 100 draws.
These percents should stay relatively similar as more draws are done, approaching the true proportions of each colour better the higher the number of draws. That means 29%, or 290, of the 1000 draws will be green.
Answer: 290
Step-by-step explanation:
what i 36 divide by 86.4
If your asking whats 86.4 divided by 36 its 2.4
Follow the process of completing the square to solve x2 - 10x + 8 = 0. How will the left side of the equation factor in step 5?
Answer:
[tex]x=5(+/-)\sqrt{17}[/tex]
Step-by-step explanation:
we have
[tex]x^{2}-10x+8=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}-10x=-8[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]x^{2}-10x+5^{2}=-8+5^{2}[/tex]
[tex]x^{2}-10x+25=-8+25[/tex]
[tex]x^{2}-10x+25=17[/tex]
Rewrite as perfect squares
[tex](x-5)^{2}=17[/tex]
Take square root both sides
[tex](x-5)=(+/-)\sqrt{17}[/tex]
Adds 5 both sides
[tex]x=5(+/-)\sqrt{17}[/tex]
Consider the function f (x) = x2.
What effect does subtracting 2 from the input have on the graph of the function?
Answer: The graph is shifted 2 units to the right.
Step-by-step explanation:
Given a function f(x), we know that one transformation rule is:
If [tex]f(x-k)[/tex] then the function is shifted "k" units to the right.
Therefore, for the function [tex]f(x)=x^{2}[/tex], when we subtract 2 from the input, then we get the function g(x) in the form:
[tex]g(x)=(x-2)^{2}[/tex]
We can conclude that subtracting 2 from the input of the function [tex]f(x)=x^{2}[/tex], then the graph is shifted 2 units to the right.
The answer is right graph shifted 2 units to the right
A right rectangular pyramid is sliced parallel to the base as shown.
What is the area of the resulting two-dimensional cross-section?
A. 2
B. 3
C. 9
D. 12
Answer:
[tex]A=2\ m^{2}[/tex]
Step-by-step explanation:
we know that
The resulting two-dimensional cross-section is a rectangle 1 m x 2 m
so
the area of this rectangle is equal to
[tex]A=2*1=2\ m^{2}[/tex]
Solve x2 + 8x = 33 by completing the square. Which is the solution set of the equation? {–11, 3} {–3, 11} {–4, 4} {–7, 7}
Answer:
The solution of the equation are 3 , -11
Step-by-step explanation:
* Lets revise how to make the completing square
- The form of the completing square is a(x - h)² + k, where a , h , k
are constant
- The general form of the quadratic is ax² + bx + c, where a , b , c
are constant
- To change the general form to the completing square form equate
them and find the constant a , h , k
* Now lets solve the problem
∵ x² + 8x = 33 ⇒ subtract 33 from both sides
∴ x² + 8x - 33 = 0
- lets change the general form to the completing square
∴ x² + 8x - 33 = a(x - h)² + k ⇒ solve the bracket of power 2
∴ x² + 8x - 33 = a(x² - 2hx + h²) + k ⇒ multiply the bracket by a
∴ x² + 8x - 33 = ax² - 2ahx + ah² + k ⇒ compare the two sides
∵ x² = ax² ⇒ ÷ x²
∴ a = 1
∴ -2ah = 8 ⇒ substitute the value of a
∴ -2(1)h = 8 ⇒ -2h = 8 ⇒ ÷ (-2)
∴ h = -4
∵ ah² + k = -33 ⇒ substitute the value of a and h
∴ (1)(-4)² + k = -33
∴ 16 + k = -33 ⇒ subtract 16 from both sides
∴ k = -49
∴ x² + 8x - 33 = (x + 4)² - 49
* Now lets solve the completing square
∵ (x + 4)² - 49 = 0 ⇒ add 49 to both sides
∴ (x + 4)² = 49 ⇒ take square root for both sides
∴ (x + 4) = ± 7
∵ x + 4 = 7 ⇒ subtract 4 from both sides
∴ x = 3
∵ x + 4 = -7 ⇒ subtract 4 from both sides
∴ x = -11
* The solution of the equation are 3 , -11
Answer:
{-11, 3}
Step-by-step explanation:
somebody help fast??????
Answer:
Option 3 (angle WXY + angle YXZ = 180) is the answer.
Lydia bought a car for $20,000. It is expected to depreciate at a continuous rate. What will be the value of the car in 2 years? Use k = 0.105 and round to the nearest dollar.
Answer:
[tex]\$16,021[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-k)^{x}[/tex]
where
V is the depreciated value
P is the original value
k is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$20,000\\k=0.105\\x=2\ years[/tex]
[tex]V=\$20,000(1-0.105)^{2}=\$16,020.50[/tex]
round to the nearest dollar
[tex]\$16,020.50=\$16,021[/tex]
the value of the car after 2 years will be approximately $16,212.
To find the value of the car after 2 years with continuous depreciation, we will use the formula for continuous exponential decay:
[tex]V(t) = V_0 \times e^{-kt}[/tex]
Where V(t) is the value after time t V_0 is the initial value, k is the decay constant and t is time
Plugging in the values:
[tex]V(2) = 20000 \times e^{-0.105 \times 2}[/tex]
Simplifying the exponent:
[tex]V(2) = 20000 \times e^{-0.21}[/tex]
[tex]V(2) = 20000 \times 0.8106 \approx 16212[/tex]
Thus, the value of the car after 2 years will be approximately $16,212.
Which line is the line of best fit for this scatter plot?
The last one. It goes and touches the most points.
The 4th line is the line of best fit for this given scatter plot.
What is a scatter plot?"A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed."
Here, 4 different lines are drawn for a given scatter plot.
We know, a line drawn on a scatter plot fits it the best is the line that is closer to most of the points.
Here, the 4th line is closer to most of the points on the scatter plot.
Therefore, 4th line is the best fit.
Learn more about scatter plot here: https://brainly.com/question/19741330
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Determine the total annual FICA tax for an annual salary of $165,000. Use $106,800 for maximum taxable earnings.
Answer:
FICA Tax =$8170.2
Step-by-step explanation:
Given
Total income=$165000
Taxable income=$106800
FICA tax includes Social security tax and medicare tax.
Medicare tax is 1.45% of the taxable wage and social security tax is6.2% of the taxable wage.
1.45% of medicare is paid by the employer and similarly 6.2% social security tax is paid by the employer.
0.9% of medical surtax is deducted if the employee earns more than $200000
So,
Medicare Tax=Taxable income*1.45/100
=106800*0.0145
=$1548.6
Social Security Tax=Taxable Income*6.2/100
=106800*0.062
=$6621.6
As the income of the employee is less than $200000, so there will be no medical surtax.
Total FICA tax=$1548.6+$6621.6
=$8170.2
Which statement describes the speed of the remote control car over time?
Answer:
Step-by-step explanation:
D
a small box has a length of (x) a width of (x+1) and a height of (x+2). what is the volume of the box
Answer:
Step-by-step explanation:
The volume of a box with dimensions length x, width (x+1), and height (x+2), is given by the formula x^3 + 3x^2 + 2x cubic units.
Explanation:The volume of the box can be calculated by multiplying its length, width, and height together. Given that the length is x, width is (x+1), and height is (x+2), the volume would be x*(x+1)*(x+2).
To further expand this, apply the distributive law which first multiplies x*(x+1), resulting in x^2 + x. Then multiply this result by (x+2), giving the final volume V = x^3 + 3x^2 + 2x.
Therefore, the volume of the box given the stated dimensions is x^3 + 3x^2 + 2x cubic units.
Learn more about Volume Calculation here:https://brainly.com/question/33318354
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solve for K thanks!!!
4.5 + 1.5k = 18 - 3k
Bring -3k to the other side by adding 3k to both sides
4.5 + (1.5k + 3k) = 18 + (-3k + 3k)
4.5 + 4.5k = 18 + 0
4.5 + 4.5k = 18
Bring 4.5 to the other side by subtracting it to both sides
(4.5 - 4.5) + 4.5k = 18 - 4.5
0 + 4.5k = 13.5
4.5k = 13.5
Isolate k by dividing 4.5 to both sides
4.5k / 4.5 = 13.5 / 4.5
k = 3
Hope this helped!
~Just a girl in love with Shawn Mendes
The radius of a circle is three meters. What is the circle’s diameter
The diameter of a circle is the radius times 2.
Diameter = 3 x 2 = 6 meters.
Answer:
6 is the answer.
3 x 2 = 6
Step-by-step explanation:
Please help, what is x?
Answer:
x = 18
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{x+x+3}{x+3}[/tex] = [tex]\frac{14+12}{14}[/tex]
[tex]\frac{2x+3}{x+3}[/tex] = [tex]\frac{26}{14}[/tex] ( cross- multiply )
14(2x+3) = 26(x + 3) ← distribute both sides
28x + 42 = 26x + 78 ( subtract 26x from both sides )
2x + 42 = 78 ( subtract 42 from both sides )
2x = 36 ( divide both sides by 2 )
x = 18
adults have 32 teeth children have 62.5% as many teeth as adults. how many teeth do children have
The answer would be 20
You multiply 62.5% by 32
32*0.625=20
They are correct it is 20.
HELPPP IDK WUT THE HECK THIS IS
ANSWER:
The 100 one is 10 and the 1,728 one is 12!
I think this is right and I hope I helped!
Tell me if it was right!
I need answers for both please!!
1 = a
2 = h
have a good day
what is the value of x to the nearest tenth?
tan 24 = x/12
0.4452 · 12 = X
5.34 = X
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −7
0 −1
1 5
g(x)
g(x) = 5x − 4
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
(10 points)
Answer:
A.
⇒The slope of the function f(x) is greater than the slope of the function g(x).
This is so because using the slope intercept form equation, the slope of f(x) is 6 while that of g(x) is 5
B.
⇒The function f(x) has a greater y-intercept than the function g(x)
⇒The y intercept for the function f(x) is -1 where as that of the function g(x) is -4
Step-by-step explanation:
This question is on the standard equation of a linear function using the slope-intercept form
y=m x+c----------where m is the gradient/slope of the line and c is the y-intercept.
Given the values in function f(x) we can identify the points in the line as;
(-1,-7), (0,-1) , (1,5)............plot the points to obtain the graph as indicated in the attachment.
Find the gradient of the graph ;
m₁=Δy/Δx
m₁= 5--1/1-0 =6/1 =6
Equation of line will be;
y-5/x-1 = 6
y-5=6(x-1)
y-5=6x-6
y=6x-1.........................m₁=6 and c₁= -1
Given that;
g(x)=5x-4.........................m₂=5 c₂= -4
⇒The slope of slope of the function f(x) is greater than the slope of the function g(x).
This is so because using the slope intercept form equation, the slope of f(x) is 6 while that of g(x) is 5
B.
⇒The function f(x) has a greater y-intercept than the function g(x)
⇒The y intercept for the function f(x) is -1 where as that of the function g(x) is -4
In the attached graph;
Red line graph, y=5x-4
Blue line graph, y=6x-1
Answer:
g(x) = y=5x-4
f(x) =. y= 6x-1
I know the slope of f(x) is greater than the slope of g(x) since the slope of f(x)=6 and g(x)=5 and 6>5.
I also know that the y-intercept of f(x) is greater because f(x)=-1 and g(x)=-4 and -1>-4.
Step-by-step explanation:
First, I will put both functions into slope-intercept form.
Next, I will use by picking two points on the table. and
this equals or 6.
So, I know the slope is 6.
To find the y-intercept I have to do, -7=6(-1)+b
So, the y-intercept is -1.
From this, I know the slope of f(x) is greater than the slope of g(x) since the slope of f(x)=6 and g(x)=5 and 6>5.
I also know that the y-intercept of f(x) is greater because f(x)=-1 and g(x)=-4 and -1>-4.
15) f(x) = 3x + 5
g(x)=-4x + 3
Find f(x) + g(x)
17) f(x) = 2x +4
g(x)= x - 5
Find f(x) - g(x)
how do u solve these equations?
Answer:
15) f(x) + g(x) = -x + 8
17) f(x) - g(x) = x + 9
Step-by-step explanation:
15)
f(x) = 3x + 5
g(x)= - 4x + 3
Find f(x) + g(x)
f(x) + g(x) = 3x + 5 + ( - 4x + 3 )
f(x) + g(x) = 3x + 5 - 4x + 3
f(x) + g(x) = -x + 8
17)
f(x) = 2x +4
g(x)= x - 5
Find f(x) - g(x)
f(x) - g(x) = 2x +4 - (x - 5 )
f(x) - g(x) = 2x +4 - x + 5
f(x) - g(x) = x + 9
[tex]
f(x)=3x+5 \\
g(x)=-4x+3 \\
(f+g)(x)=f(x)+g(x)=(3x+5)+(-4x+3) \\
3x+5-4x+3=\boxed{-x+8} \\ \\
f(x)=2x+4 \\
g(x)=x-5 \\
(f-g)(x)=f(x)-g(x)=(2x+4)-(x-5) \\
2x+4-x+5=\boxed{x+9}
[/tex]
Hope this helps.
r3t40
The circumference of a circle is 15centimeters. What is the area of the circle in terms of?
I can’t put the sign but it’s in the picture
A 0.53
B is wrong
C 56.25
D is wrong
Answer: 56.25
Step-by-step explanation:
You just need to use common sense.
What percentage kf the rolls are greater than 3?
Add the total number of rolls that were greater than 3.
This would be the number 4, 5 and 6.
8 + 11 + 10 = 29 rolls higher than 3.
Now divide the number of rolls higher than 3 by the total number of rolls which is given as 50:
29 / 50 = 0.58
Multiply by 100 to get the percent:
0.58 x 100 = 58% of the rolls were higher than 3.
Find the volume of the figure. Round your answer to the nearest hundredth, if necessary.
Answer:
Step-by-step explanation:
3.14 x 10.6^2= 352.81 pi
Answer is...
Volume = 4988.92
See attached photo
(20 points) Please answer and explain!
multiply and simplify -3x^2y^2 * y^4x3
a. -3x^5y^6
b. -3x^6y^2
c. 9x^5y^2
d. -3x ^5y^2
Answer:
[tex]\large\boxed{a.\ -3x^5y^6}[/tex]
Step-by-step explanation:
[tex]-3x^2y^2\cdot y^4x^3=(-3)(x^2x^3)(y^2y^4)\\\\\text{use}\ a^na^m=a^{n+m}\\\\=-3x^{2+3}y^{2+4}=-3x^5y^6[/tex]
A 4-PINT carton of ice cream costs $12.04. What is the price per QUART
1 quart = 2 pints.
This means a 4 pint container is 2 quarts.
To find the price for 1 quart divide the price by 2:
12.04 / 2 = $6.02 per quart.
A total of 430 dogs and people attend a fundraising dog walk. Altogether, 1210 legs participated in the walk. How many dogs were there?
1210÷4=302.5 and u can have a half of a dog so there would be 302
For Spirit Day, each 8th-grade
homeroom designs a unique two-
color T-shirt. They get to choose from
the colors red (R), blue (B), green (G),
violet (V), and orange (O). Each T-shirt
is a solid color with a different color
used for the student's name. What is
the probability that a homeroom will
have a T-shirt with a combination of
blue and violet?
(A) P(B and V)=10%
(B) P(B and V)=20%
(C) P(B and V)=30%
(D) P(B and V)=40%
Answer: Option A
P(B and V)=10%
Step-by-step explanation:
To solve this poroblema we use the formula of combinations:
[tex]nCr =\frac{n!}{r!(n-r)!}[/tex]
Where n is the number of objects that can be chosen and you choose r from them.
There are 5 colors of shirts.
The number of shirts that can be made by combining 2 of the 5 possible colors is calculated as:
[tex]5C2[/tex]
[tex]5C2=\frac{5!}{2!(5-2)!}[/tex]
[tex]5C2=10[/tex]
The number of shirts that can be made by combining 2 of the 2 possible colors (B) and (V) is calculated as:
[tex]2C2 = 1[/tex]
Then the probability is:
[tex]P(B\ and\ V)=\frac{2C2}{5C2}\\\\P(B\ and\ V)=\frac{1}{10}\\\\P(B\ and\ V)=0.1=10\%[/tex]
Answer: the answer is D
Step-by-step explanation:
Cause you have to do 100% divided by 5 you will get 20%
So if you have two of the five colors you will have two multiple 20% times 2 and get 40%
FACTOR: 36−(5+2a)^2
QUICKLY PLS!
36-(4+2a)^2=0
36-16+4a^2=0
4a^2+20=0
a^2+5=0 <— Factored form
6. Mr Wade works for 5 straight
hours when he opens his stand
After a 1 hour break he works
6 hours and 15 minutes before
Closing at 6:10p.m. What time
does Mr Wade open his stand
5:55am
Start by finding how long the stand was open. Add 5 hours + 1 hour + 6 hours 15 minutes to get 12 hours 15 minutes.
Now, just find the time that is 12 hours and 15 minutes before 6:10pm. Start by subtracting 12 hours, which just switches the time from a.m. to p.m. This brings you to 6:10am. Finally, subtract the 15 minutes to get 5:55am.