Answer:
Step-by-step explanation:
4/9 on the number line would be 0.44.
-7/9 on the number line would be -0.77
If f(1) = 2 and f(n) = f(n − 1)2 + 3 then find the value of f(3).
Answer:
52
Step-by-step explanation:
f(n) is purely based on the previous value of f(n), or f(n-1), so we can start with f(1) and work our way up. We know f(1) = 2, so to find f(2), we plug f(1) into
f(n-1)²+3 to get
f(1)²+3 = 2²+3 = 4+3=7
Thus, f(2) =7. Similarly,
f(3) = f(3-1)²+3 = f(2)² + 3 -= 7² + 3= 52
The product of two integers is (-112).
If one of them is (-8), find the other.
[tex]\huge\bold{Given :}[/tex]
Product of two integers = - 112
One of the integer = -8
[tex]\huge\bold{To\:find :}[/tex]
The other integer.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\sf\blue{The \:other \:integer\:is\: 14.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
Let the other integer be [tex]x[/tex].
As per the question, we have
[tex]Product \: \: of \: \: two \: \: integers = - 112[/tex]
➼ [tex] \: - 8 \times x = - 112[/tex]
➼ [tex] \: x = \frac{ - 112}{ - 8} [/tex]
➼ [tex] \: x = 14[/tex]
[tex]\sf\purple{Therefore,\:the\:other\:integer\:x\:is\:14.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex] - 8 \times 14 = - 112[/tex]
➺ [tex] \: - 112 = - 112[/tex]
➺ L. H. S. = R. H. S
Hence verified.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]
Answer:
If the product of two integers is -112 and one of them is -8, that means the value of the second integer would be 14.
Step-by-step explanation:
The product of two integers equals -112 means that there are two numbers that, when multiplied, were equivalent to -112. Since you know one of the integers is -8, you can infer that the second integer is both a positive number AND the remainder of [tex]\frac{-112}{-8}[/tex] or 14.
What is the average rate of change of f
over the interval (-5,0]?
Give an exact number.
Answer:
Average rate of change = 0.6
Step-by-step explanation:
Average rate of change of a function between x = a and x = b is given by,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
From the graph attached,
f(-5) = 0
f(0) = 3
Average rate of change of the graph between x = -5 and x = 0,
Average rate of change = [tex]\frac{3-0}{0-(-5)}[/tex]
= [tex]\frac{3}{5}[/tex]
= 0.6
Therefore, average rate of change of the given function between x = -5 and x = 0 is 0.6.
Find the solutions to 8x2 + 56x = 0. Check all that apply.
A. X = 8
B. x = 0
C. X = -7
D. X = 7
Answer:
B and C
Step-by-step explanation:
fjdjjsngbsnsjf x
Which of the following is true of the discriminant for the graph below
Answer:
Step-by-step explanation:
The discriminant is used to determine the number and nature of the zeros of a quadratic. If the discriminant is positive and a perfect square, there are 2 rational zeros; if the discriminant is positive and not a perfect square, there are 2 rational complex zeros; if the discriminant is 0, there is 1 rational root; if the discriminant is negative, there are no real roots.
The roots/solutions/zeros of a quadratic are where the graph goes through the x axis. Those are the real zeros, even if they don't fall exactly on a number like 1 or 2 or 3; they can fall on 1.32, 4.35, etc. They are still real. If the graph doesn't go through the x-axis at all, the zeros are imaginary because the discriminant was negative and you can't take the square root of a negative number. As you can see on our graph, the parabola never goes through the x-axis. Therefore, the zeros are imaginary because the discriminant was negative. Choice C. Get familiar with your discriminants and the nature of quadratic solutions. Your life will be much easier!
The average of 7 numbers is 45.If the last two numbers are 27 and 43 what is the average of the first five
Answer:
49
Step-by-step explanation:
The average is calculated as
average = [tex]\frac{sum}{count}[/tex] Given the average of 7 numbers is 45 , then
[tex]\frac{sum}{7}[/tex] = 45 ( multiply both sides by 7 )
sum of 7 numbers = 315
Subtract 27, 43 from the sum to obtain the sum of first 5 numbers
315 - (27 + 43) = 315 - 70 = 245 , then
average of first 5 numbers = [tex]\frac{245}{5}[/tex] = 49
Water is flowing into a conical drinking cup with an altitude of 8 inches and a radius of 5 inches, as shown in the figure.
Answer:
[tex]V=435.41\ \text{inches}^3[/tex]
Step-by-step explanation:
Given that,
Water is flowing into a conical drinking cup.
The radius of cup, r = 5 inches
The height of the cup, h = 8 inches
Let us assume to find the volume of water coming. The formula for the volume of a cone is given by :
[tex]V=\dfrac{1}{3}\pi r^2 h\\\\=\dfrac{1}{3}\times 3.14\times 52\times 8\\\\=435.41\ \text{inches}^3[/tex]
So, the volume of water flowing is [tex]435.41\ \text{inches}^3[/tex].
How many quarters are there in 5 3/4?
Answer:
One quarter= 1/4
5 3/4= 23/4
Number of quarters in 5 3/4= 23/4 divided by 1/4
23/4 ÷ 1/4
= 23/4 × 4
=23
I hope this helps!
Answer:
23
Step-by-step explanation:
5x4 + 3
5 x 4 = 20
20 + 3 (3 Is the fraction part)
help me with these asap
[tex]\sqrt{8}+2\sqrt{3}[/tex]
"You want to purchase a North Face jacket for $180. You have already saved $115 and can set aside $13 a week.
Write and solve an inequality to find the number of weeks, w, it will take you to save at least $180.
Answer:
115 + 13w [tex]\geq[/tex] 180
Step-by-step explanation:
Select the fraction greater than 7/9. a)4/5 b)2/3 c)13/18 d)3/5
Answer:
A)4/5
Step-by-step explanation:
7/9=0.778
so you need to convert the other fractions into decimals as well. The one that's greater than 0.778 will be your answer.
a)4/5=0.8
b)2/3=0.667
c)13/18=0.722
d)3/5=0.6
The decimal that's greater than 0.778 is A=0.8 so that's the answer.
Please help me answer 23, 24, 25 and 26!!!
Answer:
23. c
24.b
25. box 2
26. 48, 26
Step-by-step explanation:
how do u factor..
x^2 + 10× - 2400 = 0
Answer:
[tex]{ \bf{ {x}^{2} + 10x - 2400 = 0}} \\ { \bf{ \red{it \: has \: no \: rational \: factors}}} \\ x = - 54.2 \: \: and \: \: 44.2[/tex]
A truck is being filled with cube-shaped packages that have side lengths of \frac{1}{4} 4 1 foot. The part of the truck that is being filled is in the shape of a rectangular prism with dimensions 8ft\times6\frac{1}{4}ft\times7\frac{1}{2}ft8ft×6 4 1 ft×7 2 1 ft.
Complete Question
A truck is being filled with cube-shaped packages that have side lengths 1/4 foot. The part of the truck that is being filled is in the shape of a rectangular prism with dimensions 8ft × 6 1/4 ft × 7 1/2 ft. Find the number of cubes that can fill that part of the truck
Answer:
1500 cubes
Step-by-step explanation:
Step 1
Find the volume of the cube
V = side length ³
V = (1/4 ft)³
V = 1/64
Step 2
Find the volume of the rectangular prism
= Length × Width × Height
= 8ft × 6 1/4 ft × 7 1/2 ft
= 8 × 25/4 × 15/2
= 375 ft³
Step 3
Number of cubes in the truck
Volume of the Rectangular Prism ÷ Volume of the cube
= 375ft³ ÷ 1/4ft³
= 375 × 4
= 1500 cubes
Therefore, the number of cubes that can fill that part of the truck(Rectangular prism) = 1500 cubes
The graph shows the value of a certain model of car compared with its age.
Which statement is false?
Car's value ($)
Car's ago (years)
A. The correlation coefficient is close to -1,
B. The car's value is the explanatory variable.
O O Od
C. The car's age is strongly correlated to its value.
D. The data show a negative linear relationship.
Answer:
B. The car's age is the explanatory variable
Step-by-step explanation:
The graph shows a negative linear relationship between car's age and car's value because, as as one variable increases, the other decreases.
Also, data points are close to each other along the line of best fits, therefore, the correlation coefficient would be close to -1, showing a strong negative relationship.
An explanation variable is one that isn't affected or dependent on another variable. In this case, the car's age is the explanatory variable and not the car's value. The car's value is dependent on the car's age, therefore, the car's age is the explanatory variable.
The statement in option B is FALSE.
Berapakah hasil dari
=> 7³ + 8?
[tex] \: [/tex]
Answer:
[tex]351[/tex]
Step-by-step explanation:
[tex]7³ + 8[/tex]
[tex](7 \times 7 \times 7) + 8[/tex]
[tex]343 + 8[/tex]
[tex]351[/tex]
Hope it is helpful....Berapakah hasil 7^3 + 8 = ...
Mari kita coba jawab!
Langkah pertama:
= 7 × 7 × 7
= 49 × 7
= 343 .
Langkah kedua:
= 8
= 8 .
Langkah ketiga:
= 343 + 8
= 351 .
Maka, hasilnya 351 .
given that x^2+y^2=9 and xy=5, find the value of (x - y)^2.
Answer:
[tex](x -y)^2 = -1[/tex]
Step-by-step explanation:
[tex](x - y)^2 = x^2 + y^2 - 2xy[/tex]
[tex]= (x^2 + y^2 ) - 2(xy)\\\\=(9) - 2( 5)\\\\= 9 - 10 \\\\ = -1[/tex]
The binomial expansion of (x - y)² is
(x - y)² = x² - 2xy + y²
Substitute the given values to the equation
(x - y)² = x² - 2xy + y²
(x - y)² = x² + y² - 2xy
(x - y)² = 9 - 2(5)
(x - y)² = 9 - 10
(x - y)² = -1
Therefore the value of (x - y)² is -1.
#ILoveMath
#ILoveYouShaina
What they mean by 1/2? I mean I do know that 1/2 means half, but what they mean?
Step-by-step explanation:
See you know the area of rectangle that is base x perpendicular
When you cut half the area of rectangle, it becomes a triangle
That is why the formula is 1/2 x base x perpendicular
(x+1)^2 . (x^2+1) = 0
Answer:
[tex]x^4+2x^3+2x^2+2x+1[/tex]
Step-by-step explanation:
Given that,
[tex](x+1)^2 . (x^2+1) = 0[/tex]
We know that, [tex](a+b)^2=a^2+b^2+2ab[/tex]
So,
[tex](x+1)^2=x^2+1+2x[/tex]
So,
[tex](x+1)^2 . (x^2+1) = (x^2+1+2x)(x^2+1)\\\\=x^2\times x^2+x^2+2x^3+x^2+1+2x\\\\=x^4+2x^3+2x^2+2x+1[/tex]
So, the value of the given expression is equal to[tex]x^4+2x^3+2x^2+2x+1[/tex]
Suppose that F(x)= x^2 and G(x) 4/5 x^2. Which statements best compares the graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically.
b. The graph of G(x) is the graph of F(x) stretched vertically and flipped over the x-axis.
C. The graph of G(x) is the graph of F(x) compressed vertically.
d. The graph of G(x) is the graph of F(x) compressed vertically and flipped over the x-axis.
Answer:
Step-by-step explanation:
C. The graph of G(x) is the graph of F(x) compressed vertically.
If, for example, x = 1, then F(1) = 1^2 = 1, while G(1) = (4/5)(1^2) = 4/5.
Note that G(1) < F(1); we say G(x) is a vertical compression of F(x).
17. Find the area of a triangle whose base is 6 cm and height is 8 cm.
48 square cm
24 square cm
48 cm
24 cm
Answer:
24 square cm
Step-by-step explanation:
Answer:
48cm
Step-by-step explanation:
Because 6 times 8= 48cm
what is the distance from the origin to point A graphed on the complex plane below
Answer:
√13
Step-by-step explanation:
d² = (-3)² + (-2)²
d² = 9 + 4
d² = 13
d = √13
show the solution 3×(2÷3)^3+(2÷3)^2−20×2÷3+12
Answer with Step-by-step explanation:
We are given that
[tex]3\times (2\div 3)^2+(2\div 3)^2-20\times 2\div 3+12[/tex]
[tex]3\times (\frac{2}{3})^3+(\frac{2}{3})^2-20\times \frac{2}{3}+12[/tex]
[tex]3\times \frac{8}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]
[tex]\frac{24}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]
[tex]\frac{24+12}{27}-\frac{40}{3}+12[/tex]
[tex]\frac{36}{27}-\frac{40}{3}+12[/tex]
[tex]\frac{4}{3}-\frac{40}{3}+12[/tex]
[tex]\frac{4-40}{3}+12[/tex]
[tex]-\frac{36}{3}+12[/tex]
[tex]-12+12[/tex]
[tex]=0[/tex]
3
2
In the diagram above, Z3 = 40°.
Find the measure of Z2.
L2 = [?]°
MCQ type questions.
[tex]1) \sqrt{ - 1 } = [/tex]
[tex]i) \: i \\ ii) \: {i}^{2} \\ iii) {i}^{3} \\ iv) \: {i}^{4} [/tex]
Answer: Option one i.
Explanation:
Just rewrite √-1 as i.
Estimate the product of -3.33 and 0.199 using the compatible numbers -3 and 0.2. Find the exact product of -3.33(0.199).
Answer:
-0.6
-0.66267
Step-by-step explanation:
Estimating the product :
Using compatible number :
-3 * 0.2
__ 0.2
* ___-3
______
_ - 0.6
______
-3 * 0.2 = 0.6
The exact product :
-3.33(0.199).
Using calculator :
-3.33(0.199) = - 0.66267
Answer:
-0.66267
Your. Welcome
Mr. Brown has a gate that measures 65 ft by 72 ft. He needs to reinforce the gate by placing a strip of wood on the diagonal of the fence. How long will the strip of wood need to be?
I don't really understand it's due soon can someone please help me
Answer:
60
Step-by-step explanation:
Given: 1/2a + 2/3b =50
(Since b is equal to 30 we will automatically replace b with 30)
Step 1: Simplify both sides of the equation.
1/2a+20=50
Step 2: Subtract 20 from both sides.
1/2a=50-20
1/2a=30
Step 3: Multiply both sides by 2.
2(1/2a) 2(30)
a=60
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
Answer:
a = 15
Step-by-step explanation:
1/2(a) + (2/3 x 30) = 50
2/3 x 30 = 20
1/2(a) + 20 = 50
Rearrange > 20 to -20
-20 + 50 = 30
1/2(a) = 30
Rearrange 1/2 to 2
2 > 30/2
30/2 = 15
a = 15
Hope this helps, and please let me know if it is correct or isn't.
Have a nice day
6. A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again. If the ball continues to rebound and fall in this manner, find the total distance the ball has travelled after it hits the ground the 5th time. This may be answered in decimal form. Round your answer to 2 decimal places.
Answer:
The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient of consecutive terms is the same. The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term and [tex]q[/tex] is the common ratio.
A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again.
This means that:
[tex]q = 0.7, a_1 = 25*0.7 = 17.5[/tex]
Then
[tex]a_n = a_1q^{n-1}[/tex]
[tex]a_n = 17.5(0.7)^{n-1}[/tex]
First 5 terms:
[tex]a_1 = 17.5[/tex]
[tex]a_2 = 17.5(0.7)^{2-1} = 12.25[/tex]
[tex]a_3 = 17.5(0.7)^{3-1} = 8.58[/tex]
[tex]a_4 = 17.5(0.7)^{4-1} = 6[/tex]
[tex]a_5 = 17.5(0.7)^{5-1} = 4.2[/tex]
Find the total distance the ball has travelled after it hits the ground the 5th time.
[tex]T = 17.5 + 12.25 + 8.58 + 6 + 4.2 = 48.53[/tex]
The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.