We know that
- the Tigers scored 8 points.
- this is twice as the score of the Buzzers.
Since
2 x 4 = 8
then, 8 is twice as 4.
Then the Buzzers scored 4.
Answer: 4
Question 5 of 10 If f(x) = 2x +4, which of the following is the inverse of f(x)? , x) 7 7 O A. F-1(x) = 2(x-4) 22x O B. f-1(x) = 2(x+4) 7 O C. f-'(x) = 7(x+4) (4 2 O D. f-'(x) = 7(x-4) 2 SUBMIT 1
y = 2x/7 +4
To find the inverse, exchange x and y and solve for t
x = 2y/7 +4
Subtract 4 from each side
x-4 = 2y/7 +4 -4
x-4 = 2y/7
Multiply each side by 7
7(x-4) = 2y/7 *7
7(x-4) = 2y
Divide each side by 2
7/2 (x-4) = 2y/2
7(x-4) /2 = y
The inverse
f^-1 (x) = 7( x-4)
---------
2
Kinsey has a plan to save $60 a month for 16 months so that she can purchase a new television. After 11 monthsKinsey has saved $600. If the most that Kinsey can possibly save is $80 per month, which of the following statementsis true?a Kinsey will meet her goal and does not need to adjust her planb. Kinsey must save $72 per month to achieve her goalKinsey must save $75 per month to achieve her goalKinsey will not be able to achieve her goal.cd
The total amount she has to save can be calculated as:
[tex]60\frac{\$}{\text{month}}\cdot16\text{ months}=\$960[/tex]After 11 months, she has saved $600.
So she has 16-11=5 months to save and needs to save 960-600=$ 360 to achieve her goal.
Then, we know that she has to save an average of 360/5=72 dollars
Consider the circle below what is the length of the radius
Given:
Here AE=4 and AM=9 is given and angle A is right angle means 90
Required:
We have to find the value of r means radius
Explanation:
If the radius is r than AG=r-4
now use the Pythagoras theorem for A is right angle
[tex]r^2=9^2+(r-4)^2[/tex][tex]r^2=81+r^2-8r+16[/tex][tex]8r=97[/tex][tex]r=12.125[/tex]Final answer:
The length of radius is 12.1 as option a
1-37. On many graphing calculators, equations must be entered in y=form. Rewrite eachequation in y= form. Then use the Desmos tool to confirm that your equations are correct.1-37 HW e Tool (Desmos). Homework HelpIa. x=3y+6b. x=5y-10C. x=y2d. x=2y2-4e. x=(y-5)2
Answer:
a) y = (x-6)/3
b) y = (x + 10)/5
c)
[tex]y=\sqrt{x}[/tex]d)
[tex]y=\sqrt{\frac{x+4}{2}}[/tex]e)
[tex]y=\sqrt{x}+5[/tex]Step-by-step explanation:
In each case, first we place everything with y on the left side and everything without y on the right side. Then we apply the operation needed to isolate y.
a. x=3y+6
3y + 6 = x
3y = x - 6
y = (x-6)/3
b. x=5y-10
5y - 10 = x
5y = x + 10
y = (x + 10)/5
C. x=y2
y² = x
To simplify the square, we apply the square root to both sides. So
[tex]\sqrt{y^2}=\sqrt{x}[/tex][tex]y=\sqrt{x}[/tex]d. x=2y2-4
2y2-4 = x
2y² = x + 4
y² = (x+4)/2
Again, to simplify the square, we apply the root to both sides.
[tex]\sqrt{y^2}=\sqrt{\frac{x+4}{2}}[/tex][tex]y=\sqrt{\frac{x+4}{2}}[/tex]e. x=(y-5)2
(y-5)² = x
[tex]\sqrt{(y-5)^2}=\sqrt{x}[/tex][tex]y-5=\sqrt{x}[/tex][tex]y=\sqrt{x}+5[/tex]
Find a real number, k, such that the line 12x + ky + 20 = 0 has y-intercept -9. K = ______
Okay, here we have this:
Considering the provided information, we are going to find the requested number "k", so we obtain the following:
Since the y-intercept is the value of y when x equals zero then we get:
12x + ky + 20 = 0
12(0)+k(-9)+20=0
-9k+20=0
-9k=-20
k=-20/-9
k=20/9
Finally we obtain that k is equal to 20/9.
Simplify the expression. Write your answer as a power. 1 5 T 1 3 The expression is
explain how you can use proportional reasoning to determine the whole if you know what 21 is 60% of the whole
The whole of the number is 35.
It is given in the question that 21 is 60 % of the whole of the number.
We have to find the whole of the number.
Let the whole of the number be x.
Hence, according to the data given in the question, we can write,
60 % of x = 21
Here, we can use the unitary method to find the whole of the number.
(60/100)*x = 21
(3/5)*x = 21
Dividing the equation by (3/5), we get,
x = 21/(3/5)
x = 21*(5/3)
x = 105/3
x = 35.
Hence, the whole of the number is 35.
To learn more about unitary method, here:-
https://brainly.com/question/22056199
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Question 410What is the length of line segment DK to the nearest tenth of an inch?
The Solution:
Given the figure below:
We are required to find the length of DK to the nearest tenth of an inch.
By the Trigonometrical Ratio, we have that:
[tex]\sin 43^o=\frac{\text{opp}}{\text{hyp}}=\frac{16}{DK}[/tex][tex]\sin 43^o=\frac{16}{DK}[/tex]Cross multiplying, we get
[tex]DK\sin 43^o=16[/tex]Dividing both sides by sin43, we get
[tex]DK=\frac{16}{\sin 43^o}=23.4605\approx23.5^o[/tex]Therefore, the correct answer is 23.5 degrees.
A number squared subtracted from 3 times the number is equal to negative 70. Set up and solve a quadratic equation, then solve by factoring.
We will have the following:
From the problem we construct the expression:
[tex]3x-x^2=-70[/tex]Now, we solve for x:
[tex]\begin{gathered} \Rightarrow-x^2+3x+70=0\Rightarrow-(x^2-3x-70)=0 \\ \\ \Rightarrow-(x+7)(x-10)=0 \\ \\ x=-7 \\ x=10 \end{gathered}[/tex]The number can be either -7 or 10.
How many solutions does the equation 2(2x – 10) - 8 = -2014 - 3x) have?
Given the equation :
[tex]undefined[/tex]Find the slop and the y-intercept of line there are 2 correct answer for this question
Let's begin by listing out the information given to us:
[tex]\begin{gathered} (x_1,y_1)=(-3,4) \\ (x_2,y_2)=(0,2) \end{gathered}[/tex]The slope is calculated thus:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-4}{0--3}=\frac{-2}{3}=-\frac{2}{3} \\ m=-\frac{2}{3} \end{gathered}[/tex]The y-intercept of the graph is given by the point where the straight line touches the y-axis which is 2.
[tex]b=2[/tex]The first and second options are the correct answer
How do I divide complex numbers?[tex] \frac{(6 - i)}{(5 + 4i)} [/tex]
Convert 3 1/3 miles to feet?
1 mile = 5280 ft
So:
3 1/3 x 5280 = 17,600 ft
write the equation of a line with the slope, -1/4 which passes through the point (-4,1).Write the answer In slope-intercept form.
Given:
The slope is, m = - 1/4.
The points are, (x, y) = (-4, 1)
The general slope intercept form is given by,
[tex]y=mx+b[/tex]Here, b is the y intercept. b can be calculated by substituting the values of x and y in the slope intercept form,
[tex]\begin{gathered} 1=-\frac{1}{4}\times-4+b \\ 1=1+b \\ b=0 \end{gathered}[/tex]Thus, the equation is,
[tex]y=-\frac{1}{4}x[/tex]Complete this table so it shows a relation that is not a function
For this question, we just need to know that for a function, each x-value has just one single y corresponding value. That means we just need to complete the missing value of the table repeating one of the x values because, if there is more the one y corresponding value for the same x value, it means the table does not represent a function So a final answer can be:
NOTE: that is important to remember f(x) represent the y values.
Tom needs to rent tables for his family reunion. There will be 105 people attending. Each table seats 8 people. how many tables does Tom need to rent?
Tom needs to rent 14 tables
Explanation:Number of people attending the reunion = 105
Number of people on a single table = 8
Number of tables that Tom needs to rent =
(Number of people attending the reunion)/(Number of people on a table)
Number of tables that Tom needs to rent = 105/8
Number of tables that Tom needs to rent = 13.125
Since the number of tables has to be a whole number. If he rents 13 tables, it will not be eniugh for the people attending the reunion. Therefore, Tom needs to rent 14 tables
What is the slope of the line whose equation is x + 2y = 6?
Answer:
-1/2
Explanation:
The standard form of writng the equation of a line is expressed as y = mx+b
m is the slope
Given the equation x + 2y = 6
First we need to rewrite in standard form by making y the subject of the formula;
x + 2y = 6
2y = -x+6
y = -1/2 x + 6/2
y = -1/2 x + 3
Compare with y = mx+b
mx = -1/2 x
cancel out x from both sides to have;
m = -1/2
Hence the slope of the line whose equation is x+2y = 6 is -1/2
I need this problem from my prep guide answered, it has four answer options and I will provide another picture with the rest of the answer optionsThe subject is pre-Calc
Given,
The equation of circle is,
[tex](x+1)^2+(y+3)^2=16[/tex]The standard equation of cicle is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where, (h,k) is the center of the circle and r is the radius of the circle.
On compring the standard equation of circle with given equation then,
[tex](h,k)=(-1,-3)[/tex]Both the coordinates of the center of the circle is negative. Thus, lies in the third quadrant.
Here, the circle of option A has its center at third quadrant.
Hence, option A is correct.
Math Question 11 Assignment from math book If a seed is planted, it has a 80% chance of growing into a healthy plant.If 10 seeds are planted, what is the probability that exactly 3 don't grow? Round your answer to three decimal places.A good calculator is found at: Stattrek Binomial Calculator ________.
Given:
If a seed is planted, it has a 80% chance of growing into a healthy plant.
10 seeds are planted.
Required:
To find the probability that exactly 3 don't grow.
Explanation:
[tex]\begin{gathered} p=80\% \\ \\ =0.8 \\ \\ 1-p=1-0.8 \\ \\ =0.2 \end{gathered}[/tex][tex]\begin{gathered} N=10 \\ k=3 \end{gathered}[/tex]Seven success in 10 trails, therefore
[tex]\begin{gathered} =(10\text{ choose 7\rparen}\times(0.8)^7\times(0.2)^3 \\ \\ =\frac{(10\times9\times8)}{(3\times2)}\times(0.8)^7\times(0.2)^3 \\ \\ =(5\times3\times8)\times0.2097\times0.008 \end{gathered}[/tex][tex]=0.2013[/tex]Therefore 20% that exactly 3 don't grow.
Final Answer:
[tex]20\%[/tex]Midpoint is (-19,-19), endpoint (-18,-11) what is the other endpoint?!
Given: Midpoint is (-19,-19), endpoint (-18,-11)
so, as shown C is the midpoint of AB
C = ( -19 , -19)
Let one of the endpoint like B = (-18 , -11)
So, it is required to find A
We should know that:
[tex]\begin{gathered} C=\frac{A+B}{2} \\ A+B=2C \\ A=2C-B \\ A=2\cdot(-19,-19)-(-18,-11) \\ A=(-38,-38)-(-18,-11) \\ A=(-38,-38)+(18,11) \\ A=(-20,-27) \end{gathered}[/tex]so, the other end point is (-20, -27)
please explain to me how to get the answer as well as the answer.
Solution
Step 1
The y-intercept is the point where the line crosses the y-axis.
Final answer
y-int = 2
which method should I use to find the missing angle in the triangle? the following methods to choose from can include Law of Sines, Law of Cosine, SOH-COH-TOA, and inverse tangent. after picking a method that applicable to solving the missing angle round to the nearest whole degree!
From the given figure
The opposite side to x is AB
The adjacent side to x is BC
To find x we will use TOA
[tex]\tan x=\frac{AB}{BC}[/tex]AB = 3 cm
BC = 4 cm
[tex]\tan x=\frac{3}{4}[/tex]To find x we will use the inverse of tan
[tex]x=\tan ^{-1}(\frac{3}{4})[/tex]By using the calculator
x = 36.86989765
Round it to the nearest degree
x = 37 degrees
Find the sales tax on an appliance costing $272.26 if the tax rate is 5.2%.The sales tax is $_(Round to the nearest cent.)
To determine the sales tax, we have to compute the 5.2% of 272.26. To determine the x% of y, we use the following expression:
[tex]y*\frac{x}{100}.[/tex]Therefore, the 5.2% of 272.26 is:
[tex]272.26*\frac{5.2}{100}.[/tex]Simplifying the above result, we get:
[tex]sales\text{ tax}\approx14.16.[/tex]Answer: $14.16The playing surfaces of two foosball tables are similar. The ratio of the corresponding sidelengths is 10:7. If the perimeter of the smaller is 42, what is the perimeter of the larger table?
Given:
Ratio of corresponding sides = 10 : 7
Perimeter of smaller table = 42
Total ratio = 10 + 7 = 17
Let's find the perimeter of the larger table.
Given that both tables are similar, it means the corresponding sides are proportional.
To find the ratio of the larger table, let's first find the total perimeter of the both tables:
[tex]\frac{\text{smaller ratio}}{total\text{ ratio}}\times T=perimeter\text{ of smaller table}[/tex]Where T represents the total ratio.
Thus, we have:
[tex]\begin{gathered} \frac{7}{17}\times T=42 \\ \\ \text{Multiply both sides by 17:} \\ \frac{7}{17}\times17\times T=42\times17 \\ \\ 7T=714 \end{gathered}[/tex]Divide both sides by 7:
[tex]\begin{gathered} \frac{7T}{7}=\frac{714}{7} \\ \\ T=102 \end{gathered}[/tex]The total perimeter is 102.
To find the permeter of the larger table, we have:
Perimeter of larger table = Total perimeter - perimeter of smaller table.
Perimeter of larger table = 102 - 42
Perimeter of larger table = 60
Therefore, the perimeter of the larger table is 60.
ANSWER:
60
Find the missing angle m21 m/2=m23=3287157°12
To find angle 2 we need to remember that the addition of the interior angles of any triangle is equal to 180°, then we have:
[tex]\begin{gathered} m\angle2+71+57=180 \\ m\angle2=180-71-57 \\ m\angle2=52 \end{gathered}[/tex]Then m<2=52°.
Now, to find the angle 1 we need to notice that this is the supplementary angle of the 57° shown, then:
[tex]\begin{gathered} m\angle1+57=180 \\ m\angle1=180-57 \\ m\angle1=123 \end{gathered}[/tex]Then m<1=123°.
Finally to find angle 3 we use the same approach as we did for angle 2, in this case we have:
[tex]\begin{gathered} m\angle3+28+123=180 \\ m\angle3=180-123-28 \\ m\angle3=29 \end{gathered}[/tex]Then m<3=29°.
I need help solving this math problem Find the equation of the line in its form y = mx + b
ANSWER:
[tex]y=2[/tex]STEP-BY-STEP EXPLANATION:
The equation must be in its slope-intercept form, which is as follows:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is the y-intercept} \end{gathered}[/tex]We calculate the slope as follows:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{ Replacing the points:} \\ m=\frac{2-2}{7-(-1)}=\frac{0}{7+1}=\frac{0}{8}=0 \end{gathered}[/tex]Now, we calculate the value of b, like this:
[tex]\begin{gathered} 2=0\cdot7+b \\ b=2 \end{gathered}[/tex]Therefore, the equation is the following:
[tex]\begin{gathered} y=0x+2 \\ y=2 \end{gathered}[/tex]Use the information given to find the equation of the line using the point-slope formula (y-y_1)=m(x-x_1)). Then convert your answer to slope-intercept form (y=mx+b).Parallel to y=2x+5 and passes through the point (4,3)The point slope form is (y-Answer)=Answer(x-Answer)Converting it to slope intercept form gives us: y=Answerx+Answer
point-slopeWe are required to get the equation of the line in the point-slope and slope-intercept forms.
A line given in the form: y = mx + b is given in the slope-intercept form where m and b are the slope and intercept on the vertical axis respectively.
A pair of parallel lines have the same gradient and we will leverage this fact to get the equation of the line that passes through the point (4,3).
The point-slope slope form of a line is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where:} \\ x_1,y_1\text{ are the coordinates of the point} \end{gathered}[/tex]We therefore have:
[tex]\begin{gathered} y-3=2(x-4) \\ as\text{ our }point\text{ slope form} \end{gathered}[/tex]Converting to slope-intercept form:
[tex]\begin{gathered} y-3=2(x-4) \\ \text{Add 3 to both sides to get:} \\ y=2(x-4)+3 \\ y=2x-8+3 \\ y=2x-5 \end{gathered}[/tex]Lasso SelectInsert SpaceEditUnit 1 - Part 1 - Test ReviewWriting and Modeling with Equations1) A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50cents per ounce of toppings.a) Write an equation the represent the total cost (C) of an ice cream base on the ounce oftoppings (t).......b) Use the equation to determine how much Evan's ice cream would cost with 3 ouncesof toppings.
1
(a) The total cost, C, is given by:
[tex]C(t)=3+0.5t[/tex]b) With 3 ounces of toppings, we have
[tex]t=3[/tex][tex]C(3)=3+0.5(3)=3+1.5=4.5[/tex]Hence Evan's ice cream would cost $4.50
The equation y=x relates proportional quantities x and y. What is the value of y when x is 36? Enter your answer in the box.
Direct variation:
We are given that x and y are directly proportional.
[tex]y=x[/tex]Recall that the standard form of the directly proportional relationship is given by
[tex]y=kx[/tex]Where k is the constant of proportionality.
Comparing the standard form with the given equation we see that k is equal to 1.
[tex]y=1\cdot x[/tex]Let us substitute the value of x into the above equation
[tex]y=1\cdot36=36[/tex]Therefore, the value of y is 36.
(when the constant of proportionality (k) is 1 then the x and y values are equal)
Devon is trying to find the unit price of a6-drink package on sale for $ 2.99. His sister saysthat at that price, each drink would cost just over $ 2.00.Is he right and how do you know? If not, how would Devon's sister find the right price?
Devon is trying to find the unit price of a
6-drink package on sale for $ 2.99. His sister says
that at that price, each drink would cost just over $ 2.00.
Is he right and how do you know? If not, how would Devon's sister find the right price?
To find the unit price, divide the total cost by the number of drinks
so
2.99/6=$0.50 per drink
therefore
He is not right