Answer:
2. the answer is 5 because the square of 5 is 25 and 4 x 25 = 100 which is 20 x 5
Step-by-step explanation:
We are required to find the unknown number from the expression
2.
let
the number = x
four times the square of a number equals 20 times that number
4x² = 20x
Divide both sides by 4x
x = 5
The number is 5
3.
let
x = the unknown number
Twice the square of the sum of a number and 3 is 98
sum of a number and 3 = x + 3
square of the sum = (x+3)²
Twice the square = 2(x + 3)²
2(x + 3)² = 98
2(x² + 6x + 9) = 98
2x² + 12x + 18 = 98
2x² + 12x +18 - 98 = 0
2x² + 12x - 80 = 0
x² + 6x - 40 = 0
using factorization method to solve the quadratic equation
x² + 10x - 4x - 40 = 0
x(x + 10) - 4(x + 10) = 0
(x + 10) ( x - 4) = 0
x + 10 = 0 or x - 4 = 0
x = -10 or x = 4
Therefore, the unknown number is -10 or 4
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Merry is making an abstract triangular collage for the wall. She has 14 feet of edging to go around the collage. If the longest side is twice the smallest and the other side is four less than three times the smallest, find the length of each side of the triangular collage
Answer:
The length of each side of the triangular collage:
a = smallest side = 3 feet
b = other side(second side) = 5 feet
c = Longest side = 6 feet
Step-by-step explanation:
She has 14 feet of edging to go around the collage.
14 feet = Perimeter of the triangle
The Perimeter of a Triangle = a + b + c where
a = smallest side
b = other side(second side)
c = Longest side
From the question, we are told that:
If the longest side is twice the smallest
c = 2a
The other side is four less than three times the smallest,
The other side = b
b = 3 × a - 4
b = 3a - 4
Hence,
P = a + b + c
14 = a + 3a - 4 + 2a
14 = a + 3a + 2a -4
14 = 6a - 4
Collect like terms
14 + 4 = 6a
18 = 6a
a = 18/6
a = 3ft
Therefore the smallest side = 3
The Longest side(c) = 2a
c = 2 × 3
c = 6ft
The other side(b) = 3a - 4
= 3(3) - 4
= 9 - 4
= 5 feet.
Therefore, the length of each side of the triangular collage:
a = smallest side = 3 feet
b = other side(second side) = 5 feet
c = Longest side = 6 feet
Segment AB has endpoints on the coordinate grid where A is (-18,5) and B is (-4,5). Point Z is located exactly 1/8 of the distance from A to B. Determine the value of the x-coordinate of point Z.
Answer:
The coordinates of point Z is (-16.25, 5)
Step-by-step explanation:
The given information are;
The coordinates of the endpoint A on segment AB = (-18, 5)
The coordinates of the endpoint B on segment AB = (-4, 5)
Therefore, given that the endpoints A and B have the same y-coordinate value, (5), then segment AB is horizontal, and the length of segment AB = -4 - (-18) = -4 + 18 = 14
The point Z located at exactly 1/8 from A to B is given as follows;
[tex]Z = \left (-18 + (-4 - (-18)) \times \dfrac{1}{8} , \ 5 + (5 - 5)\times \dfrac{1}{8} \right ) = (-16.25, \ 5)[/tex]
The coordinates of point Z = (-16.25, 5).
find the missing value of X.
9514 1404 393
Answer:
x = 72
Step-by-step explanation:
The sum of interior angles of a pentagon is (5-2)(180°) = 3·180°. The sum of the two right angles is 180°, so we can write the equation ...
180° +2x° +x° +2x° = 3·180°
5x = 2·180 = 360 . . . . divide by °, subtract 180
x = 360/5 = 72 . . . . . . divide by 5
The value of x is 72.
the sum of two fractions is 9 1^4 their difference is 3 1^8, what are the two fractions?
Answer:
[tex]6\frac{3}{16}~,~3\frac{1}{16}[/tex]
Step-by-step explanation:
let the fractions be x and y,then
[tex]x+y=9\frac{1}{4}=\frac{37}{4}=\frac{74}{8}\\x-y=3\frac{1}{8}=\frac{25}{8}\\adding\\2x=\frac{74}{8}+\frac{25}{8}=\frac{99}{8}\\x=\frac{99}{16}=6\frac{3}{16}\\again ~subtracting\\2y=\frac{74}{8}-\frac{25}{8}=\frac{49}{8}\\y=\frac{49}{16}=3\frac{1}{16}\\[/tex]
What number is the opposite of 165
Answer:
-165
Step-by-step explanation:
Answer:
-165 I think I'm not 100%
If two numbers are multiplied in any order , product will be the same. True or False
Answer:
True
Step-by-step explanation:
PLZ RESPOND ASAP
1:The total earnings from mowing a lawn for 3 hours is $19.50. What equation can be used to model the total earnings for mowing a lawn x hours?
2:The ratio of students to adults at a school is 14 : 2. Suppose there are a total of 490 students. How many adults are at the school?
Answer:6.5x=y
Step-by-step explanation:1- divide 19.50
2- get 6.5
3- add variable
4- get 6.5x=y
Answer:
1.) 3x = 19.50 (they got 6.5 and hour)
2.) 70 adults
Step-by-step explanation:
Work for #2
[tex]\frac{14}{2}[/tex] [tex]\frac{490}{x}[/tex] then cross multiply. 14*x = 14x 490*2 = 980
So 980 = 14x (divide by 14)
x = 70
So 70 adults
Hope this helps!!!
Which scale factors produce an expansion under a dilation of the original image?
Select each correct answer.
−8
−0.7
0.8
7
Answer:
The correct answer is -8 and 7
Hope you have a wonderfull day :)
Clare is paid $90 for 5 hours of work. At this rate, how long will it take her to save $360?
Answer:
20 hours
Step-by-step explanation:
We can use a ratio to solve
90dollars 360 dollars
--------------- = -----------
5 hours x hours
Using cross products
90x = 5* 360
Divide each side by 90
90x/90 = 5 * 360/90
x = 20
20 hours
Un padre está usando una manguera de jardín para llenar una pequeña piscina inflable para su hijo pequeño. La piscina tiene una capacidad de 90 galones. Apaga el agua después de 5 minutos, pero deja la manguera en la piscina durante otros 3 minutos antes de guardarla. En esta situación, la relación entre los galones de agua en la piscina y los 8 minutos desde que el padre comenzó a llenar la piscina puede verse como una función. 1. En esa función, ¿qué variable es independiente? ¿Cuál es dependiente?
Answer:
Water is being collected at the rate of 11.25 gallon per minute.
Step-by-step explanation:
In this function the filling of water in the pool is dependent on the number of minutes. The more time the tap is opened the greater amount of water can be accumulated in the pool .
So time is independent and water is the dependent variable.
The function can be represented by
f(x)= xt where t is the time in minutes
90 gallons= x * 8 minutes
or x= 90/8 = 11.25 gallon per minute.
So water is being collected at the rate of 11.25 gallon per minute.
Spanish
En esta función, el llenado de agua de la piscina depende de la cantidad de minutos. Cuanto más tiempo se abre el grifo, mayor cantidad de agua se puede acumular en la piscina.
Entonces el tiempo es independiente y el agua es la variable dependiente.
La función se puede representar por
F (x) = xt donde t es el tiempo en minutos
90 galones = x * 8 minutos
o x = 90/8 = 11,25 galones por minuto.
Entonces, el agua se recolecta a una velocidad de 11.25 galones por minuto.
0.7 bigger than 7/9 ?
Answer: no it’s the opposite
Step-by-step explanation: 7/9is greater than 0.7
Is the relationship proportional? Explain.
Answer:
What relationship??
Step-by-step explanation:
Mental Math Situation: You exercised 24 hours each month for a year. How many hours did you exercise by the end of the year? You may be able to do the math mentally thanks to expanded notation and the Distributive Property.
Answer:
So 24 hours each month times 12 would be 288 hours of working out of one year.
Hope this helps!
Step-by-step explanation:
Answer: 288h
Step-by-step explanation:
There are 12 months in a year if you exercise 24h per month you have to multiply 12 x 24 = 288h
what is 2400000 in standard form
Answer:
24*10^5
Step-by-step explanation:
Answer:
2400000 is already in its standard form.
But its form in scientific notation is
2.4 × 10^6
Step-by-step explanation:
Count the zeros until you reach between 2 and 4 then put a decimal point there.
What is the midpoint of a line segment with the endpoints of (-4, -4) and (6, 14)
(10, 18)
(2, 10)
(-1, 4)
(1, 5)
Answer:
The midpoint is ( 1,5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2
( -4+6)/2 = 2/2 =1
To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2
( -4+14)/2 = 10/2 =5
The midpoint is ( 1,5)
Express 8.3% as a ratio. OR Find 7% of 500.
Answer:
8.3 / 1
Step-by-step explanation:
Its simple... search it up
Answer:
7% of 500=7/100*500=35
How many group's of 10 are there in 230?
Answer:
the answer is 23
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
if you do 230 divided by 10 you get 23, or you can distribute 230 in 10 groups.
What is the value of 7/3 divided by 5/6
Answer:
14/5 or 2.8
Step-by-step explanation:
Answer:
2.8 or 2 4/5
Step-by-step explanation:
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 170lb and each box of books weighs 60 lb. The maximum capacity of the elevator is 1240lb. How many boxes of books can the delivery person bring up at one time?
Answer:
17.83 boxes
Step-by-step explanation:
Lets represent the number of boxes of books that can be brought up per time = x
From the question: The delivery person weighs 170lb and each box of books weighs 60 lb. The maximum capacity of the elevator is 1240lb.
Hence we have the Algebraic Expressions
170lb + 60 × x = 1240lb
170lb + 60x = 1240lb
Collect like terms
60x = 1240lb - 170lb
60x = 1070lb
x = 1070lb/60
x = 17.833333333
x = 17.83 boxes
Therefore, the delivery person can bring up 17.83 boxes per time
HELP PLZZ ASAP WILL GIVE 50 POINTS
Adrienne said that a vertical stretch by a factor of 4, a horizontal shift to the left 1 unit, and a vertical shift down 3 units of the graph of the parent function f(x)=ex produce the graph of the function g(x)=4ex−1+3. Explain whether Adrienne is correct and, if not, determine the transformations that produce the graph of the function g(x)=4ex−1+3 from f(x)=ex.
Answer:
known facts:
The graph of y=f(x−a), a>0
y=fx-a, a>0
can be obtained by shifting graph y=f(x)
y=fx, a units right side of x-axis. The graph of y=f(x)+a, a>0 y= fx+ a,a>0
can be obtained by shifting graph y=f(x)
y=fx, a units upwards along y-axis.
Adrienne said:
a vertical stretch by a factor of 4, a horizontal shift to the left 1 unit and a vertical shift down 3 units of the graph of the parent function f(x)=ex
f(x)=e^x
produce the graph of the function g(x)=4ex−1+3
g(x)=4e^x-1+3.
by the above known facts, it can be concluded that
Adrienne is not correct
Step-by-step explanation:
i hope this helps you, i'm still doing it but i have to go for a min, one sec! <3
the correct transformations for the function g(x) = 4eˣ - 1 + 3 from the parent function f(x) = eˣ are:
- Vertical Stretch by a factor of 4.
- Horizontal Shift to the Right 1 unit.
- Vertical Shift Down 3 units.
Adrienne's statement about the transformations applied to the parent function f(x) = eˣ is not entirely correct. Let's analyze the given function g(x) = 4eˣ - 1 + 3 and determine the correct transformations.
1. Vertical Stretch by a factor of 4: This transformation is correct. Multiplying the function by 4 causes a vertical stretch, which magnifies the y-values by a factor of 4.
2. Horizontal Shift to the Left 1 unit: Adrienne incorrectly mentioned a horizontal shift to the left. In the given function, g(x), there is no explicit horizontal shift. The -1 in g(x) = 4eˣ - 1 + 3 is actually a reflection of the graph across the y-axis, causing a horizontal shift to the right by 1 unit. So, there is a horizontal shift to the right by 1 unit, not to the left.
3. Vertical Shift Down 3 units: This transformation is correct. Adding 3 to the function shifts the graph vertically downward by 3 units.
Therefore, the correct transformations for the function g(x) = 4eˣ - 1 + 3 from the parent function f(x) = eˣ are:
- Vertical Stretch by a factor of 4.
- Horizontal Shift to the Right 1 unit.
- Vertical Shift Down 3 units.
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What is the following difference? 56.4 – 27.39
Answer:
29.01
Step-by-step explanation:
You just have to do the math
The answer is
29.01
9. During training, a hurdler wants to raise the height of the hurdles from the high school standard of 39 inches to the
NCAA standard of 42 inches. His best race from last season included a clear over a 39-inch hurdle that was modeled by
h(t) = (-0.0251)(1-25), where t is time (in tenths of a second) after his lead leg left the track and h is the height (in feet).
If he runs as well as his best race last year, will this hurdler clear the new height? Why or why not
Answer:
Something doesn't make sense. The time when his height is 0 is time t=0 and t=25.
The vertex would be halfway in between at time t=(0+25)/2 = 12.5 seconds.
But plugging that in, we get a height of:
3.90625 inches
I think you must have a typo... let's try this equation instead:
h(t) = (-0.25t)(t - 25)
In that case, the maximum at h(12.5) is 39.0625 inches.
Answer:
No, the function for his height has him just barely clearing 39 inches. He can't clear 42 inches.
10
No, according to the function for his height, he only just clears 39 inches. He is unable to jump 42 inches.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Something doesn't make sense. The time when his height is 0 is time t=0 and t=25.
The vertex would be halfway in between at time t=(0+25)/2 = 12.5 seconds.
But plugging that in, we get a height of:
3.90625 inches
h(t) = (-0.25t)(t - 25)
In that case, the maximum at h(12.5) is 39.0625 inches.
Therefore, the according to the function for his height, he only just clears 39 inches. He is unable to jump 42 inches.
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what value of y will make the equation true?
What number falls between 7 and 8 on the number line.
Convert 40 g to mg
Plz help me
Answer:
40000 milligrams
Hope it helps :)
Write an explicit formula for an, the nth term of the sequence 112, -28, 7, ....
Answer:
[tex]a_n=112\left(-\frac{1}{4}\right)^{n-1}[/tex]
Step-by-step explanation:
Geometric Sequences
There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.
In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.
We are given the sequence:
112, -28, 7, ...
It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.
Let's find the common ratio by dividing each term by the previous term:
[tex]\displaystyle r=\frac{-28}{112}=-\frac{1}{4}[/tex]
Testing with the third term:
[tex]\displaystyle -28*-\frac{1}{4}=7[/tex]
Now we're sure it's a geometric sequence with r=-1/4, we use the general equation for the nth term:
[tex]a_n=a_1*r^{n-1}[/tex]
[tex]a_n=112\left(-\frac{1}{4}\right)^{n-1}[/tex]
Complete the equation describing how x and y are related. Please Help!!
Answer:
muddin
Step-by-step explanation:
ya put it in the but and pull out wit some fecal matter on it
what is the rule for the reflection ?
a. rx-axis(x, y) - (-x, y)
b. ry-axis(x, y) - (-x, y)
c. rx-axis(x, y) - (x,-y)
d. ry-axis(x, y) - (x,-y)
Answer: Choice C
We have an x axis reflection
[tex](x,y) \to (x,-y)[/tex]
The x coordinate stays the same while the y coordinate flips from positive to negative, or vice versa.
For example, point L is located at (-4,2) and it moves to L ' (-4, -2). The other points follow this same pattern.
PLEASE HELP ME this is really hard please
Answer:
1100
2200
Step-by-step explanation:
Since speed is constant, the distance is proportional to the time. We notice that the number in the second column is 1650/3 = 550 times the number in the first column, so the two missing numbers are ...
2 × 550 = 1100
4 × 550 = 2200
Which of the following functions is graphed below?
Answer:
C
Step-by-step explanation: