Answer:
Step 1: Set x to -1 in the first equation
[tex]f(x) = -x^2 + x[/tex]
[tex]f(-1) = -(-1)^2 + (-1)[/tex]
[tex]f(-1) = -(1) - 1[/tex]
[tex]f(-1) = -1 - 1[/tex]
[tex]f(-1) = -2[/tex]
Step 2: Set x to -1 in the second equation
[tex]f(x) = -x[/tex]
[tex]f(-1) = -(-1)[/tex]
[tex]f(-1) = 1[/tex]
Martina is currently 12 years older than her cousin Joey. In 4 years she will be 3 times as old
as Joey. Use this information to answer the following questions.
[tex]\Huge{\underline{\underline{\sf{\red{AnSwEr:}}}}}[/tex]
[tex]\boxed{\sf{Martina's \: Present \: age = 14 \: years}}[/tex]
[tex]\boxed{\sf{Her \: cousin's \: Present \: age = 2\: years}}[/tex]
[tex]\Huge{\underline{\underline{\sf{\green{ExpLaNaTion:}}}}}[/tex]
= Let Martina's cousin's age be = n
= Let her age be = n+12
After four years,
Cousin's age = n+4
Her age = n+12+4=n+16
But according to the question her age = 3(n+4) = 3n+12
Thus,
3n+12=n+16
3n-n=16-12
2n=4
n=4/2
[tex] \boxed{ \sf {n = 2}}[/tex]
Thus ,
Her cousin's present age = n = 2
Her cousin's present age = n = 2Her present age = n+12 = 2+12=14
Is 4.39463 a natural number
Answer:
i wanna say yes it is a natural number, i hope this helps
What is the measure of B, in degrees?
A square in a rectangle have the same perimeter. The length of a side of the square is 4x-1. The length of the rectangle is 2x+2 and the width is 2x
The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.
Step-by-step explanation:
The given is,
A square in a rectangle have the same perimeter
The length of a side of the square is 4x-1
The length of the rectangle is 2x+2 and width is 2x
Step:1
Let, a - Side of square
l - Length of the rectangle
w - Width of the rectangle
Step:2
Formula for perimeter of square is,
[tex]p=4a[/tex].............................(1)
Formula for perimeter of rectangle is,
[tex]p=2(l+w)[/tex]....................(2)
Step:3
From given,
Equation (1) = Equation (2)
[tex]4a = 2 (l+w)[/tex]
where,
a = 4x-1
l = 2x+2
w = 2x
Substitute the values,
4 ( 4x-1 ) = 2 ( 2x+2+2x )
16x - 4 = 2 (4x + 2)
16x - 4 = 8x + 4
16x - 8x = 8
8x = 8
x = 1
Step:4
Substitute the values of x,
a = 4(1)-1 = 3
l = 2(1)+2) = 4
w = 2(1) = 2
Perimeter of square and rectangle is 12 units
Result:
The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.
Suppose you only look at the height of the bars on the graph. Which conclusion would you MOST LIKELY reach?
A) Twice as many Democrats as Republicans agreed with the court.
B) Twice as many Republicans as Independents agreed with the court.
C) Three times as many Democrats as Republicans agreed with the court.
D) The total number of Republicans and Independents agreeing with the court is half the number of the Democrats that agreed.
Answer:c
Step-by-step explanation:
answer n.8 for me pls
Answer:
Step-by-step explanation:
(13)2−(2x+7)=0
19x2−2x−7=0
9(19x2−2x−7)=9(0)
x2−18x−63=0
(x−21)(x+3)=0
Therefore, the value of x are
x - 21 = 0 and x + 3 = 0
x = 21 x = -3
Eric is reading a book that has 144 pages. He reads 8 pages a day. How many days will it take Eric to finish reading the book?
Answer:
It will take him 18 days to finish the book.
Step-by-step explanation:
[tex]144/8=18[/tex]
Answer:
18
Step-by-step explanation:
You divide 144 by 8 and get the answer.
Help please, I’m stressing and I’m going to have a mental break down
Answer:
Step-by-step explanation:
Volume = surface area of base * height
[tex]=\frac{25}{4}*\frac{8}{5}\\\\=5*2=10\\\\=10 units^{3}[/tex]
15 Points! Can someone help me with this?
Given:
Spinning top is in the shape of a square pyramid.
Side length of the base = 32 mm
Height of the pyramid = 32 mm
To find:
Volume of the spinning top
Solution:
Volume of the square pyramid:
[tex]$V=\frac{1}{3} b^{2} h[/tex]
[tex]$V=\frac{1}{3} \times (32)^{2} \times 32[/tex]
[tex]$V=1024 \times 32[/tex]
[tex]V=10922.66[/tex] cubic millimeter
The volume of the spinning top is 10922.66 cubic millimeter.
Complete the point-slope equation of the line through (-1,6) and (1,5).
Use exact numbers.
Y= 6
Answer:
Y-6=-1/2(x-(-1) )
Step-by-step explanation:
The Equation for the point-slope of the line is y - 6 = -1/2(x + 1).
What is the slope of a line?A line's slope is defined as the ratio of the change in y coordinates to the change in x coordinates.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Given coordinates (-1,6) and (1,5).
the slope of line is given by,
m = (y₂- y₁)/(x₂ - x₁)
y₂- y₁ = 5 - 6 = -1
x₂ - x₁ = 1 - (-1) = 2
m = -1/2
to find the equation at y = 6
when y = 6, x = -1
the equation is given by
y - y₁ = m(x - x₁)
y - 6 = -1/2(x -(-1))
y - 6 = -1/2(x + 1)
Hence equation of a line is y - 6 = -1/2(x + 1).
Learn more about the slope of a line;
https://brainly.com/question/16180119
#SPJ5
Select the correct answer. If the graph of function g is 6 units below the graph of function f, which could be function g? f(x) = -2x + 7
A. g(x) = -2x − 6
B. g(x) = -2x + 20
C. g(x) = -6x + 7
D. g(x) = -2x + 1
Answer:
D
Step-by-step explanation:
NEED HELP ASAP
which set of numbers could represent the lengths of the sides of right triangle
A. 7,9,11
B. 12,18,22
C. 10,15,20
D. 8,15,17
We have to use Pythagorean Theorem to solve this. We square the two smallest sides, then add. If the sum is the square of the largest side, then it's our answer.
A. 7, 9, 11
49 + 81 = 130 ≠ 121
B. 12, 18, 22
144 + 324 = 468 ≠ 484
C. 10, 15, 20
100 + 225 = 325 ≠ 400
D. 8, 15, 17
64 + 225 = 289 = 289
So, our answer is D
Point A (-3, 5) is rotated 180º about the origin. What are the coordinates of A' after the rotation?
A point when rotated 180º about the origin flips the sign of the coordinates. Thus, point A' after rotating point A (-3,5) 180º about the origin would have coordinates (3,-5).
Explanation:A rotation of 180º about the origin essentially changes the signs of the coordinates. If we have Point A as (-3, 5), after a 180° rotation about the origin, you'll get Point A', which will be the opposite of Point A. That means it turns (-3, 5) to (3, -5).
Rotation about the origin flips the point across both axes. This is based on a rule in mathematics: When we rotate a point 180° about the origin, (x, y) becomes (-x, -y).
The coordinates of A' after the 180° rotation are (3, -5).
Learn more about Rotation here:https://brainly.com/question/34828607
#SPJ2
Lucia has $600 in her checking account. She wants to spend part of this money on a computer. She wants to have exactly $250 left in her checking account after buying the computer. The equation shown can be used to find t, the amount of money in dollars that Lucia can spend on the computer: t + 250 = 600 Which solution represents the correct answer? *
Answer:
t = 350
Step-by-step explanation:
subtract 250 from each side, and then you'll have t = 350
Answer:
350
Step-by-step explanation:
600 minus 250 =350
350 plus 250 =600
I basically did the inverse operation to solve this equation
Ju Wenjun is an ecologist who studies the change in the tiger population of Siberia over time. The relationship between the elapsed time ttt, in years, since Ju Wenjun started studying the population, and the number of tigers, N(t)N(t)N, left parenthesis, t, right parenthesis, is modeled by the following function N(t)=650⋅(1625)t
Complete the following sentence about the rate of change in the tiger population.
Round your answer to two decimal places.
The number of tigers decays by a factor of \dfrac45
5
4
start fraction, 4, divided by, 5, end fraction every
Answer:
The number of tigers decays by a factor of
[tex]\dfrac{4}{5}[/tex] every 0.50 years
Explanation:
The correctly written function is
[tex]N(t)=650\cdot \bigg(\dfrac{16}{25}\bigg)^t[/tex]
Convert 16/25 into its equivalent form (4/5)²
[tex]N(t)=650\cdot \bigg(\dfrac{4}{5}\bigg)^{2t}[/tex]
If you make t = 1/2, this is half-year, the population of tigers will decay by a factor of 4/5 in that time. Every time the half-year passes, the population is multiplied by 4/5, which means that the polulation will decay by a factor of 4/5 whenever half a year elapses.
Hence, the number of tigers decays by a factor of 4/5 every 0.50 years.
The tiger population model indicates a decay by a factor of 4/5 every year. This factor shows the yearly reduction rate for the tiger population in Siberia.
To determine the rate of change in the tiger population modeled by the function N(t) = [tex]650 \cdot \left(\frac{16}{25}\right)^t,[/tex] we look at the decay factor in the exponential function. The base of the exponent, [tex]\frac{16}{25}[/tex], indicates that the population is decaying.
This decay factor can be expressed as [tex]\frac{4}{5}[/tex], where every year, the number of tigers decays by a factor of [tex]\frac{4}{5}[/tex]. Thus, we can complete the sentence as follows:
The number of tigers decays by a factor of [tex]\frac{4}{5}[/tex] every year.
Here is a list of numbers: -10, -11, -8, 17, -17, 4, -11 ,12 ,12 ,-4 State the median.
Answer:
The answer is (-6).
Step-by-step explanation:
Order the numbers from smallest to largest.
Then start eliminiating one from left, one from right until you get the median. Since in our case the median is in between (-8) and (-4). Sum the numbers and divide them by 2.
Good luck!
What is the volume of a cylinder with base radius 3 and height 8? Either enter an exact answer in terms of \piπpi or use 3.14, for \piπpi and enter your answer as a decimal.
answer is 72 then pi symbol
C is directly proportional to the square of D and when C=32, D= 4. Find C when D= 3
Answer:C=6
Step-by-step explanation:C directly proportional to D
C=kD where k=constant
C=32, D=4×4
32=k16
K=32÷16
K=2
Now D=3 and k=2
C=kD
C=2×3
C=6
Answer: c=18
Step-by-step explanation:
C is directly proportional to square of D
C € D2
€ rep directly proportional
C=kd2
K is a constant
C=32
D=4
Substitute
32=k(4^2)
32=k(16)
32=16k
K=32/16
K=2
Since we know our constant k to be 2
Substitute
We are looking for c,when d=3
C=kd2
C=2×(3^2)
C=2×9
C=18
what’s the fraction fro 5/12+(-7/12)
Answer:
-.167= -1/6
Step-by-step explanation:
5/12+(-7/12)
=(5 × 12) + (-7 × 12)
_______________
12 × 12
=-24/144
= -24 ÷ 24
________
144 ÷ 24
= - 1
_______
6
Can someone check if this is right
PLZZ HELPPP!!! Each edge of a wooden cube is 6 centimeters long. The cube has a density of 0.71 g/cm3
.
What is the mass of the wooden cube?
Enter your answer in the box.
g
Answer:
153.36g
Step-by-step explanation:
Density is defined as the ratio of mass per unit volume of a material.
Density = Mass/Volume
Given the edge of a cube which is equivalent to its length L to be 6cm.
Density of the cube = 0.71g/cm³
Volume of the cube = L³
Volume = 6³
Volume of the cube = 216cm³
Mass = Density × Volume
Mass of the cube = 0.71×216
Mass of the cube = 153.36grams
Answer:
153.36 grams
Step-by-step explanation:
Density is mass divided by volume: d = m/v.
Here, we already know that d = 0.71 g/cm³.
We can find the volume of hte cube. The volume of a cube is denoted by:
V = s³, where s is the side length
The cube's length is 6, so plug this in:
V = s³
V = 6³ = 216 cm³
Plug these values in:
d = m/v
0.71 g/cm³ = m / 216 cm³
m = 0.71 * 216 = 153.36 grams
The answer is 153.36 grams.
Answer please?????!!!!
Answer:
x = 3
Step-by-step explanation:
4x + 3 + 7x = -2x + 42
11x + 3 = -2x + 42
13x = 39
x = 3
Answer:
x=3
Step-by-step explanation:
4x+3+7x=-2x+42
combine like terms
11x+3=-2x+42
add 2x to both sides
13x+3=42
subtract 3 from both sides
13x=39
divide both sides by 13
x=3
What’s common denominators for 2/5 and 3/5
Answer:
5
Step-by-step explanation:
The fractions already have a common denominator of 5
Find the perimeter of the figure.
square with a measure of 1x1
triangle with a measure of 5x3x3
Answer:
what does the shpe look like
Step-by-step explanation:
Answer:
perimeter=2
perimeter = 11
Step-by-step explanation:
A birthday hat is the same shape as a *
triangle
cone
ice cream scoop
What is the volume?
17 cm
13 cm
5 cm
It’s a triangular prism.
Answer:
1105 cubic centimetre
Step-by-step explanation:
volume of rectangular prism
[tex] = 17 \times 13 \times 5 \\ = 1105 \: {cm}^{3} [/tex]
Estimate by rounding each number to the nearest ten thousand and then subtract
Answer:
50,000
Step-by-step explanation
80,000 - 30,000 = 50,000
In ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45. What is the value of the cosine of ∠X to the nearest hundredth?
Answer:
Step-by-step explanation:
0.53 is the answer to the nearest hundredth.
To calculate the cosine of ∠X in the right triangle WXY, we use the ratio of the adjacent side length (YW = 45) to the hypotenuse length (XW = 53), which results in approximately 0.85 when rounded to the nearest hundredth.
In ΔWXY, we're given that ∠Y is a right angle, meaning that the triangle is a right triangle. To find the cosine of ∠X, we can use the definition of cosine in a right triangle, which is the ratio of the adjacent side to the hypotenuse in the context of the angle we're interested in. Since ∠X is across from side YW, and XW is the hypotenuse, we'll take the length of YW as the adjacent side. The formula for the cosine of angle X then becomes:
cos(∠X) = adjacent/hypotenuse = YW / XW = 45 / 53
Calculating this value, we get cos(∠X) = 0.8490566037735849, which when rounded to the nearest hundredth is 0.85.
PLZ HELP!!!!!
3x/2 − 5/12
= 1/4
Answer:
x=4/9
Step-by-step explanation:
you have to multiply both sides by 12 to get 18x-5=3 then add 5 to both sides which would get you 18x=8, then divide both sides by 18 and you will get 4/9.
Which could be the area of one face of the triangular prism? Select three options.
A triangular prism. The rectangular sides are 12 by 10, 12 by 8, and 12 by 6. The triangular sides have a base of 8 and height of 6.
[Not drawn to scale]
24 square units
48 square units
72 square units
96 square units
144 square units
Answer:
(A)24 square units
(C)72 square units
(D)96 square units
Step-by-step explanation:
Triangular face
Height of the Triangle=6 Units
Base of the Triangle=8 Units
Area of the Triangular Face
[tex]=\frac{1}{2}bh\\ =\frac{1}{2}*8*6\\=24 $ square units[/tex]
Rectangular Faces
Area of Rectangular face with dimension 12 by 10=12 x 10=120 Square Units
Area of Rectangular face with dimension 12 by 8= 12 X 8=96 Square Units
Area of Rectangular face with dimension 12 X 6=12 x 6=72 Square Units
From the options, the areas are:
24 square units 72 square units 96 square unitsAnswer:
acd
Step-by-step explanation: