Answer:
f(x) = 3x + 8 is the required linear function.
Step-by-step explanation:
We know that the slope-intercept form of linear equation is
y = mx+b
here
m is the slope of the line, and b is the y-interceptGiven initial value
f(0) = 8
Meaning at x = 0, y = 8Thus, the y-intercept = b = 8
Also given
at x = 4, f(4) = 20
Meaning at x=4, y = 20so
substituting the point (4, 20) and y-intercept b=8 in the slope-intercept form to determine the slope
y = mx+b
20 = m(4) + 8
20 = 4m + 8
4m = 20-8
4m = 12
Dividing both sides by 4
m = 3
Thus, the slope = m = 3
Now, substituting m = 3 and b = 8 in the slope-intercept of linear function
y = mx+b
y = 3x + 8
or
f(x) = 3x + 8
Thus,
f(x) = 3x + 8 is the required linear function.
VERIFICATION:
Given the linear function
f(x) = 3x + 8
plug in x = 0
f(0) = 3(0) + 8
f(0) = 8
plug in x = 4
f(x) = 3x + 8
f(4) = 3(4) + 8
f(4) = 12+8
f(4) = 20
The table below shows all of the possible outcomes for rolling two six-sided number cubes.
A table with 36 possible outcomes. There are 9 desired outcomes.
What is the probability of rolling an even number first and an odd number second?
1/9
1/6
1/4
1/2
C. 1/4
There is a table with 36 possible outcomes. 9 of them are desired outcomes because they have an even number rolled first and then an odd number rolled second (a few random examples from the table would be 2,1, 2,3, 4,1, 4,5, 6,3 etc.)
All we have to do is make a fraction of the desired outcomes over the total number of possible outcomes. 9/36. That can be simplified into 1/4 and voilà, there is your answer.
Hope this helped ッ
My Answer:
The of getting an even number in first and an odd number second is 1/4.
That would be option C.
I just took the quiz in math on edge 2020/2021
I hope this helps!
:)
Please I really need help
Answer:
it would be 1/3
Step-by-step explanation:
Answer: 1/3 chance
Step-by-step explanation:
In total there are 21 animals, 7 of which are a goat or a cow, 7/21 simplified is 1/3
If you borrow 700$ for five years at a annual interest rate of 7%, how much will you pay all together
Answer:
$2,245.
Step-by-step explanation:
Your interest will have grown to $2,245 dollars and you will have earned $1,545.
Hope this helped
i’m being timed !!!
Given the function f(x) = -x^2 + 4x + 6, determine the average rate of change of
the function over the interval -4 < x < 7.
Step-by-step explanation:
I dont know the answer but I know you should make a graph for it and it will tell u the answer I will try and take a photo
N EED ANSWER NOW ON TIMER PLASERA
Answer:
17/190
Step-by-step explanation:
Its correct
Answer:
D
Step-by-step explanation:
1 x 17 = 17
10 x 18=180
so it's 17/180
x + y = 8
Let x = -1. What is y?
Enter the correct answer
DONE
Il?
Answer:
y = 9
Step-by-step explanation:
x + y = 8
-1 + y = 8
y - 1 = 8
Add one to both sides to isolate y.
y = 9
Have a great day!
Solve. W=2, p=3 ........ 5p-2w
Answer:
11
Step-by-step explanation:
w = 2
p = 3
5p - 2w
5(3) - 2(2)
15 - 4
11
Answer:
11
Step-by-step explanation:
Substituting p and w gets 5(3)-2(2). Simplifying gets 25-4 which is 21.
find two fraction with the same
denominator that are equivalent to 7/8 and 5/12
Answer:
21/24 and 10/24
Step-by-step explanation:
7/8 is equaivalent to 7*2/8*2 = 14/16 also to 7*3/8*3=21/24
5/12 is equivalent to 5*2/12*2= 10/24
so the denominators are 16 and 24 so are not the same so keep looking
the denominators 24 and 24 are same so your answer is
7/8 and 5/12 are same and have the same denominator to 21/24 and 10/24
Which expression is equivalent to
Answer:
B
Step-by-step explanation:
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Anna drives 45 km to work each day.
One day she drives the first 25 km at an average speed of 82 km/h. She takes 36 minutes to drive the remaining distance.
Calculate her average speed, in km/h, for the whole journey.
Answer:
Anna drove at an average speed of 49.73 km/h
Step-by-step explanation:
Average Speed
If an object moves at different speeds to cover a certain total distance dt in a total time tt, the average speed is:
[tex]\displaystyle \bar v=\frac{d_t}{t_t}[/tex]
Anna drives a total distance of dt=45 km each day. One day she drives a distance of d1=25 km at v1=82 Km/h. The time taken for that distance is:
[tex]\displaystyle t_1=\frac{d_1}{v_1}=\frac{25}{82}=0.3049\ h[/tex]
She takes t2=36 minutes to drive the remaining distance. 36 minutes is 36/60=0.6 h, thus the total time is:
[tex]t_t=0.3049\ h+0.6\ h=0.9049\ h[/tex]
The average speed is:
[tex]\displaystyle \bar v=\frac{45}{0.9049}=49.73\ km/h[/tex]
Anna drove at an average speed of 49.73 km/h
Help with all questions in this pic
y = 2x - 3 and x = 7
Answer:
y = 11
Step-by-step explanation:
y = 2(7) - 3
y = 14 -3
y = 11
A company sells widgets. The amount of profit, y, made by the company, is related to
the selling price of each widget, x, by the given equation. Using this equation, find out
the maximum amount of profit the company can make, to the nearest dollar.
y = -8x2 + 242x – 1056
Answer:
774 dollars
Step-by-step explanation:
Given the amount of profit, y, made by the company, is related to
the selling price of each widget, x, by the given equation
y = -8x^2 + 242x – 1056
The company made her maximum profit when dy/dx = 0
dy/dx = -16x + 242
0 = -16x + 242
16x = 242
x = 242/16
x = 15.125
Get the maximum amount of the profit
Substituting x = 15.125 into the function we have:
y = -8(15.125)^2 + 242(15.125) – 1056
y = -8(228.77)+3,660.25-1056
y = -1,830.09+3,660.25-1056
y = 773.91
Hence the maximum amount of profit the company can make, to the nearest dollar is 774 dollars
Lana has 6 bags with 3 candy bars in each bag. Markus has 3 bags with 4 candy bars in each bag. How many more candy bars does Lana have?
Answer:
Lana has 6 more candy bars than Markus.
Step-by-step explanation:
Lana has 6 bags, each with 3 candy bars. To find the total amount you multiply 6 by 3 which is 18. Markus has 3 bags, each with 4 candy bars, to find the total amount you also multiply 3 by 4 which is 12. Now you subtract: 18-12=6. So Lana has 6 more candy bars than Markus.
Answer:
Lana has 6 candy bars more than Markus
Step-by-step explanation:
6 x 3 = 18
3 x 4 = 12
18 - 12 = 6
I WILL GIVE THE REST OF MY POINTS (100 SOMETHING) TO THE PERSON WHO ANSWERS THIS RIGHT BY CREATING A NEW QUESTION AND ALSO WILL GIVE BRANLIEST
Mr. Townsend needs to make 13 pairs of butterfly wings for costumes for a play.
Each pair of wings is made with yard of fabric. The fabric costs $8 per yard.
You'll apply properties of multiplication in the following steps to find the total cost of the fabric.
1. Use multiplication to write an expression for the amount of fabric needed to make 13 pairs of wings.
2. Multiply the amount of fabric by the price per yard to find an expression for the total cost.
3. Use the associative and commutative properties to rearrange the terms in the expression to make it easier to calculate. Explain why the rearranged expression is easier to work with.
4. Simplify your expression to find the total cost. Show your work
Step-by-step explanation to answer:
So, the unit rate is $8 per yard of fabric now we need a expression which will be 13 times 8. 8 times 10 is 80 and 8 times 3 is 24. 80+24 is 104. We did associative, now we need communative. We will still get the answer to the question as we did with associative which will be 8 times 3 is 24 and 8 times 10 is 80. add that and we will get 104.
Vera owns 17 pairs of socks how many socks does have in all
We know that 2 socks are in a pair. Hence, the rate would be like this: 2 socks/pair. We could also represent it as a ratio and fraction. I will choose the fraction form.
x 17
2 socks = 34 socks
1 pair x 17 17 pairs
Therefore, if Vera owns 17 pairs of socks, she will have 34 socks in total.
Help I will mark brainly
Answer:
Use M A T H W A Y. It helps.
Answer:
A) -9.8 × (-23.5)
Step-by-step explanation:
negative × negative = positive
negative × positive = negative
positive × positive = positive
19 dozen cookies to individual cookies
Answer:
228 individual cookies.
Step-by-step explanation:
To convert 19 dozen cookies to individual cookies, we first have to identify that:
[tex]dozen=12[/tex]
If a dozen is equal to 12, to solve, we simply must multiply the amount of dozens, which is 19, by a dozen, which is 12:
[tex]19*12=[/tex]
[tex]228[/tex]
Therefore, there are 228 individual cookies.
-
We can check our work by dividing the individual number of cookies, 228, by dividing buy the amount of dozens, 19, and a dozen, 12:
[tex]228[/tex] ÷ [tex]19=12[/tex]
[tex]228[/tex] ÷ [tex]12=19[/tex]
As you can see, our quotients are the two figures we started with, and when multiplied together, give us 228 individual cookies; therefore, our solution is correct!
PLEASE HELP ME OUT I NEED THIS BY TONIGHT!!!!
A tree is 6 feet high. Each year, x, it grows 2 feet. Write an equation to model the height, y, of the tree after x years. What is the height of the tree after 7 years?
Answer:
1) y=2x+6
Step-by-step explanation:
2) y=2×7+6=20ft
Answer:
y = 2x + 6 and the height is 20 feet after seven years.
Step-by-step explanation:
Hello we meet again.
You substitute the x with 7 and then it will be 2(7)+6. 2 times 7 is 14 plus 6 equals 20 so good luck.
Complete the description of the slope of the line that joins the points
positive
negative
0
undefined
Step-by-step explanation:
the points are undefined
yeah I gotchuuu
Option on 1 blank
(2x-1)(x+9)
3x(x-9)
X+7
(2x+1)(x-9)
2 blank
3x(2x+1)
X-7
3x(x+7)
X+7
3 blank
-7
9
0
-0.5
0.5
Answer:
0.5
Step-by-step explanation:
can anyone please help i am stuck on this question?
Answer:
8/17
General Formulas and Concepts:
Trigonometry
[Right Triangles Only] cos∅ = adjacent over hypotenuseStep-by-step explanation:
Step 1: Define
We are given a right triangle. We can use trig to find the ratio.
Step 2: Identify
POV from angle S
Adjacent = 8
Hypotenuse = 17
Step 3: Write
Substitute [cosine]: cos(s) = 8/17find tan a in a triangle
a 20/21
b 21/29
c 21/20
d 20/29
Answer:
Option C
Step-by-step explanation:
By applying tan rule in the given triangle ABC,
tan(a) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{BC}{AC}[/tex]
= [tex]\frac{21}{20}[/tex]
Therefore, Option C is the correct option.
16a² − 25?? please help
Answer:
(4a - 5)(4a + 5)
Step-by-step explanation:
Assuming you require to factor the expression
Given
16a² - 25 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
16a² - 25
= (4a)² - 5²
= (4a - 5)(4a + 5) ← in factored form
Answer100 POINTS! (50 split up) PLSSSSSTO GIVE BRAINLIEST AND FIVE STARS AND A THANKS! 6TH GRADE SCIENCE! i used all my points for this!
You measure the mass of an apple using a balance.
which expression is equivalent to the expression shown below?
-1/2(-3/2x + 6x + 1) - 3x
A) 3/2x - 1/2
B) 6 3/4x - 1/2
C) -3/4x + 1/2
D) -5 1/4x - 1/2
Answer:
vcbnvjhgbvnhtrgbhj hy6tyuk
Step-by-step explanation:
The correct answer is: [D]: " (-5 )x − " .
_________________________________________________________
Explanation:
_________________________________________________________
" -1/2(-3/2x + 6x + 1) − 3x " ;
= (-1/2 * -3/2 x) + (-1/2 * 6x) + (-1/2 * 1) − 3x ;
= [ (-1 *-3) /(2*2)] x + (-3x) + (-1/2) ] − 3x ;
= [ (3/4)x − 3x − (1/2) ] − 3x ;
= (3/4)x − 3x − (1/2) − 3x ;
= ?? ; → Combine the "like terms" ;
→ "(3/4)x − 3x − 3x " = ?? ;
→ "(3/4)x − 3x = "(-9/4)x";
→ "(-9/4)x − 3x = "(-21/4)x " = " (-5 )x " ;
→ The answer is: " (-5 )x − " ;
___________________________________________________
→ which is:
___________________________________________________
→ Answer choice: [D]: " (-5 )x − " .
___________________________________________________
The answer choices are
16/25
-4/25
-16/5
4/5
I need help-
if a ladder is to reach a height of 5.6m, the base must be at least 1.4m from the wall. How long should the ladder be in order to meet this safety regulations?
Answer:
≈ 5.72 mStep-by-step explanation:
Use Pythagorean as the ladder is going to be a hypotenuse of a formed right triangle with legs of 5.6 m and 1.4 m
Ladder length:
√5.6² + 1.4² = √32.76 ≈ 5.72 m roundedYin wants to create figure Y′ that is similar to figure Y. Yin begins by reflecting figure Y across the y-axis.
Which of the following should Yin do next to get a figure similar to figure Y?
A. Yin should rotate the figure 90°.
B. Yin should dilate the figure by a scale factor of 2.
C. Yin should reflect the figure across the x-axis.
D. Yin should translate the figure 3 units to the left.
Answer: B) Dilate by scale factor of 2
====================================================
Explanation:
Your teacher isn't saying this directly, but I'm assuming s/he wants you to find a similar figure that isn't congruent to the original. Informally, your teacher seems to want you to find a figure that is the same shape but not the same size as the original.
If so, then any dilation will shrink or enlarge the image depending on the scale factor. So the new image will not be the same as the old one. In this case, a dilation with scale factor 2 means the new figure is twice as large (each side is twice as long). But the old image is similar to the new image. The angles keep their values and therefore we get the same shape. This is why choice B is the answer. Again this is assuming what I mentioned in the first paragraph.
Choices A, C, and D are all known as rigid transformations and they preserve the same size of the figure. Applying any of those operations will lead to the same figure (just rotated, reflected or shifted somehow). In other words, applying operations A,C, or D will have us get two congruent triangles. If two triangles are congruent, then they are automatically similar, but not vice versa. This is why we can rule out A,C, and D.
Answer:
B
Step-by-step explanation:
A cuboid with a volume of 924cm^3 has dimensions 4cm, (x+1)cm and (x+11)cm.
Show clearly that x^2+12x-220=0
Solve by factorisation, making sure you show the factorisation. Find the dimensions of the cuboid.
Answer:
Dimensions = 4cm, 11cm and 21cm
OR
Dimensions = 4cm, -21cm and -11cm
Step-by-step explanation:
Solving the quadratic equation by using the factorization method;
x² + 12x - 220 = 0
Factors = 22 and -10
x² + 22x - 10x - 220 = 0
x(x + 22) - 10(x + 220) = 0
(x - 10)(x + 22) = 0
Therefore, x = 10 or x = -22
Given the following data;
Length of one side = (x + 1)cm
When x = 10
Length of one side = (10 + 1)cm
Length of one side = 11cm.
When x = -22
Length of one side = (-22 + 1)cm
Length of one side = -21cm
Length of the other side = (x + 11)cm
When x = 10
Length of the other side = (10 + 11)cm
Length of the other side = 21cm
When x = -22
Length of the other side = (-22 + 11)cm
Length of the other side = -11cm
Check;
Volume of a cuboid = L*L*L
Volume of a cuboid = 4 * 11 * 21
Volume of a cuboid = 924cm³