Answer:
750 miles
Step-by-step explanation:
20 gallons -------------- 300 miles
1 gallon ---------------- 300/20 = 15 miles
50 gallons -------------- 15x50 = 750 miles
Find all real numbers $x$ such that $x^2 < 4$. Give your answer in interval notation.
All the real numbers x which satisfy the given inequality x²<4 , in interval form is (-2, 2).
As given in the question,
Given inequality is given by :
x²< 4
Simplify the given inequality x² < 4 to get all the real numbers x we have,
x² < 4
⇒ x² - 4 < 0
⇒ x² - 2² < 0
Apply a² - b² = ( a - b ) ( a + b ) we get,
⇒ ( x - 2 ) ( x + 2 ) < 0
⇒ x ∈ ( -2 , 2 ) as less than symbol represent open interval.
Therefore, all the real numbers x which satisfy the given inequality x²<4 , in interval form is (-2, 2).
The complete question is :
Find all real numbers x such that x^2 < 4. Give your answer in interval notation.
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Solve each equation. Write each answer as a whole number or simplified fraction using the form a/b. a. 25=x15; x= b. 43=x7; x= c. 75=28x; x= d. 114=5x; x=
The solution for the equation are a. x = 5/3 or 2
b. x= 43/7 or 6
c. x =114/5 or 23
d. x =114/5 or 23
What is simplified fraction?
Simplified fraction are fraction in there lowest value or reduced form.
a. 25=x15
Divide both sides by 15
25/ 15 = 15x/15
X = 25/ 15 = 5/3
Therefore, the value of x is 5/3 or 2.
b. 43=x7
Divide both sides by 7
43/7 = 7x/7
x= 43/7 = 6.14
Therefore, the value of x is x= 43/7 or 6
c. 75=28x
Divide both sides by 28
75/28 =28x/28
x = 75/28 =2.67
Therefore, the value of x is x= 75/28 or 3
d. 114=5x
Divide both sides by 5
114/5 = 5x/5
x =114/5 =22.8
Therefore, the value of x is x =114/5 or 23
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s: Practice
Question 3 of 5
Type the correct answer in each box. Use numerals Instead of words. If necessary, use / for the fraction bar(s).
A group of friends are ordering food. The total amount that they can spend on their food bill is $41, including the delivery charge of $6.
The equation below represents the situation, where x is the cost of each friend's meal.
6 + az = 41
The cost of each friend's meal in terms of a is
The cost of each friend's meal when the number of friends is 5 is $
Submit
Reset
Answer:
$7
Step-by-step explanation:
You want to know the cost of each friend's meal if 5 friends spend $41 on their food, which includes a $6 delivery charge.
CostFor 'a' friends spending 'x' on each meal, the total cost is ...
6 + ax = 41
Solving for x, we have ...
ax = 41 -6 = 35
x = 35/a
5 FriendsWhen the number of friends is a = 5, the cost of a meal is ...
x = 35/5 = 7
The cost of each friend's mean when the number of friends is 5 is $7.
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What is 6,10,499,999 rounded to the nearest hundred thousand?
Answer:
6,10,500,000
Step-by-step explanation:
Answer:
610500000 is the answer! I hope this helps!
If f(x) =4x^6+ x^4+4,then what is the remainder when f(x) is divided by x-1
The remainder for the given polynomial is 9
A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division (No division operation by a variable). It is a function that only uses non-negative integer powers or positive integer exponents of a variable
Given f(x) = 4x^6+ x^4+4
Now f(x-1) = 0
X= 1
Substitute the x value in the function
f(x) = 4x^6+ x^4+4
f(x) = 4(1)^6+ (1)^4+4
f(x) = 4+ 1+ 4
f(x) = 9
Therefore the remainder for the given polynomial is 9
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graph the line that passes through the point (-1,-4) and whose slope is -2
Answer:
Step-by-step explanation:
this seems tough, but, remember the formulas , point slope and how to find M ( slope) and this gets much easier.
let's use the point-slope formula to get the slope-intercept formula
from my memory, which you can also memorize
y-y1=m(x-x1) (point-slope formula)
we are given the slope m = -2
and we're given a point P(x1,y1) as ( -1,-4)
plug this info into our plug and play formula :P
y-(-4) = (-2)(x-(-1)) : note all the careful attention to minus signs
y+4 = (-2)(x+1)
y+4 = -2x -2
y = -2x -2 -4
y =-2x-6 (slope-intercept formula y = mx +b)
y= -2x + (-6)
I'll use Desmos to quickly graph this for you, see attached graph
Help! Solve this for the points
ASAP! exponent rules.
The answer to the Exponent is [tex]w^{64}[/tex]
What does the term Exponent means?
A quantity that represents the degree of power to which a particular number or expression is to be increased, commonly displayed as a raised symbol next to the number or word is termed as exponent.
Solution:
According to the rule of Exponent
[tex](a^{b} )^{c} = a^{b*c}[/tex]
Using the same rule;
[tex](w^{8})^{8} = w^{8*8}[/tex]
[tex]w^{64}[/tex]
So, the correct answer is w^64
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Simplity (34)-1
1/34
1/3-4
-34
33
Option-A is correct, when the The exponential term is (3⁴)⁻¹ which is in the division.
Given that,
The exponential term is (3⁴)⁻¹
We have to find the the exponential term which is correct from the option.
The multiplicative inverse of the base raised to a power with the opposite sign of the given power is a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. For instance, (3/2)² can be used to represent (2/3)⁻². We are aware that an exponent indicates the degree of multiplication a number has undergone.
Take the term,
(3⁴)⁻¹
1/3⁴
Therefore, Option-A is correct, when the The exponential term is (3⁴)⁻¹ which is in the division.
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two of the squares of a $7 \times 7$ checkerboard are painted yellow, and the rest are painted green. two color schemes are equivalent if one can be obtained from the other by rotating the board. how many different (non-equivalent) color schemes are possible?
300 different (non-equivalent) color schemes are possible.
For starters, there are 49 boxes in total and there are 49[tex]c_{2}[/tex] ways of picking the two yellow boxes which are 1176 ways
clearly, there are far fewer than 1176 "magical" setups
At first, I attempted to brute force this problem but realized that it was too hard to do that
according to a source, there are (1176−24)/4+24/2 =300. This is the same numerical answer as your formula, after simplification.
the system of making something much less complicated and consequently less complicated to do or recognize, or the issue that results from this technique: The corporation advises on the simplification of change strategies. this is a gross simplification of what truly took place. one of the earliest proponents of person simplification was Lufei Kui, who proposed in 1909 that simplified characters need to be used in education.
Bracket (Brackets are solved in order of (), {} and [] respectively. Of Þ multiplication, however, it's miles to be completed earlier than division. So for simplifying expressions, we ought to observe the above collection. in the previously given instance, we first divide 8 through four and upload it to 12 as division (D) is before more than one (M) in BODMAS. Simplification of terms inside the brackets may be achieved immediately. which means we are able to carry out the operations in the bracket inside the order of division, multiplication, addition, and subtraction.
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80 POINTS!!
does anybody know how to answer this?:
Answer:
Your answer would be B!!
Step-by-step explanation:
If you need me to show how to work it let me know!!
Complete by solving the square!(need help asap!)
Explain step by step!
3x^2+x-2=0
Answer: x = -2/3 , 1
Step-by-step explanation:
step 1 (hardest step!) factor by grouping:
(3x + 2)(x-1) = 0
the rest is easy:
3x + 2 = 0 or (x-1) = 0
Solve each for x:
3x + 2 = 0
x = -2/3
x-1 = 0
x = 1
So your 2 solutions for x are -2/3 and 1
- 4x + 7y = 3
x-intercept:
y-intercept:
Answer:
X intercept: (-3/4 , 0)
Y intercept: (0 , 3/7)
Step-by-step explanation: The x intercept is a coordinate whenever y is 0. The y intercept is a coordinate whenever x is 0. So to find the x intercept you put 0 in place of Y and you solve for x. So you get x=-3/4.
You do the same thing to find Y, but you put 0 instead of x and you get y=3/7.
Calvin paints pictures and sells them at art shows. He charges $156 for a large painting.
He charges $95 for a small painting. Last month he sold six large paintings and three
small paintings. How much did he make in all?
Answer:
1221
Step-by-step explanation:
if you do 156 times 6 and add that to 95 times 3, you get 1221
Answer:
$1,221
Step-by-step explanation:
156 x 6 = 936
95 x 3 = 285
936 + 285 = $1,221
NEED THIS ASAP!! A computer is used to pick four letters, one after the other, from {P, Q}. Each letter can be picked more than once and has the same chance of being picked.
The possible outcomes for this experiment are shown in the table.
P P P P P P P Q P P Q P P Q P P
Q P P P P P Q Q Q Q P P P Q Q P
Q P P Q Q P Q P P Q P Q Q Q Q P
Q Q P Q Q P Q Q P Q Q Q Q Q Q Q
Drag and drop to match the value to the probability statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
P(all P or all Q)
The probability that the same letter is obtained in all trials is given as follows:
P(all P or all Q) = 1/8.
How to obtain a probability?The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
In this problem, the trials are given as follows:
P P P P.P P P Q.P P Q P.P Q P P.Q P P P.P P Q Q.Q Q P P.P Q Q P.Q P P Q.Q P Q P.P Q P Q.Q Q Q P.Q Q P Q.Q P Q Q.P Q Q Q.Q Q Q Q.Only two out of the 16 trials resulted in the same four letters being chosen, hence the probability is:
P(all P or all Q) = 2/16 = 1/8.
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What are the coordinates of the point on the directed line segment from (-6, 8)(−6,8) to (-2, -8)(−2,−8) that partitions the segment into a ratio of 5 to 3?
Please help im having issue with this
The coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3 are [-3.5, -2].
How to determine the coordinates of P?In this exercise, line ratio would be used to determine the coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3.
Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Given the following parameters:
Point (x, y)= (-6, 8)Point (x, y) = (-2, -8)m:n = 5:3Substituting the given parameters into the line ratio formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(5(-2) + 3(-6))/(5 + 3)], [(5(-8) + 3(8))/(5 + 3)]
P(x, y) = [(-10 + (-18))/(5 + 3)], [(-40 + 3(8))/(5 + 3)]
P(x, y) = [(-10 - 18)/(8)], [(-40 + 24)/(8)]
P(x, y) = [(-28)/(8)], [(-16)/(8)]
P(x, y) = [-3.5, -2]
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A number is increased by 13, then doubled to get 72
i need explanation on similtaneous equations!
can anyone help me please!
Answer:
Step-by-step explanation:
Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. Each of these equations on their own could have infinite possible solutions.
Houa works at an electronics store as a salesperson. Houa earns a 4% commission on the total dollar amount of all phone sales she makes, and earns a 5% commission on all computer sales. Houa had $600 more in computer sales than in phone sales and earned a total of $129 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Houa made and the dollar amount of computer sales she made. Define the variables that you use to write the system.
The system of equations for determining the dollar amount of phone and computer sales are Sc = Sp + 600 and 0.05Sc + 0.04Sp = 1200
How to write a system of equations to determine the dollar amount of phone and computer sales?
A commission is defined as the compensation paid to a person or entity based on the sale of a product. It is calculated on a percentage basis
Given:
Phone sales commission = 4%
Computer sales commission = 5%
Total commission = $129
Let Sc and Sp represent the dollar amount of phone sales and computer sales respectively
If Houa had $600 more in computer sales than in phone sales, the equation can be written as:
Sc = Sp + 600
Since Houa earns a 4% commission on phone sales and a 5% commission on computer sales, and a total commission of $129. Thus, the equation for the commission can be written as:
0.05Sc + 0.04Sp = 1200
Note: 5% = 5/100 = 0.05 and 4% = 4/100 = 0.04
Therefore, the system of equations for determining phone and computer sales are Sc = Sp + 600 and 0.05Sc + 0.04Sp = 1200
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Give an example of how u worked it out, please.
a. The value of 9.9² × 1.79 is 175.44.
b. The value of ✓97.5 + 1.96 is 11.83
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value of 9.9² × 1.79 will be:
= 9.9² × 1.79
= 98.01 × 1.79
= 175.44
The value of ✓97.5 + 1.96 will be:
= ✓97.5 + 1.96
= 9.87 + 1.96
= 11.83
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Find the dimensions of a rectangle with area 1000 m2 whose perimeter is as small as possible.
Both the length and width of the rectangle are approximately 31.62 m each.
The Area of a rectangle is calculated by multiplying the length by the width.
A = L x W
We have given that area of rectangle is 1,000 m²
1000 = W× L => W = 1000/L ---(1)
The circumference of rectangle is twice the sum of the dimensions. That is,
P = 2L + 2(1000/L)
Now, it is provided that perimeter is minimum so, we differentiate perimeter with respect to L then put first order derivative equal to zero.
dP/dL = 2 + 2000(-1/L²) = 0
=> 2-2000/L²=0
=>2000/L²=2
=> L²=2000/2
=> L²= 1000
=> L= 31.622
putting value of L in (1) we get , W= 31.622m
Therefore the length and width of the rectangle are both approximately 31.622m .
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3x - 5y = -22 (find x and y)
Answer:
x = −22/3 + 5y/3
y = 22/5 + 3x/5
Step-by-step explanation:
lx²-10 + 3x = 0
a
b
C=
La ecuación es completa o incompleta? (Quisiera que me explicaran si la ecuación tiene “x” al cuadrado osea “x2” pero con el dos chiquito y no tiene ningún numero como en esta ecuación seria completa)
At Target, shirts were on sale for $16 each. This price was 80% of their original price. What was the original price of the shirt?
Answer: 20 dollar because every 20% is 4$ therefore 100% is 20$
1). If Y Varies inversely as the square of X . If Y= 10 when X=4, Find Y when X=3
2). If Y Varies inversely as X and summing that Y=8 when X=6 find the relationship between X and Y. Also, find Y when X=3
The value of Y = 17.77 when X = 3, and the value of Y = 16 when X = 3
The equation which represents "Y varies inversely as the square of X" can be written as:
Y = k/X² where "k" is a constant.
Substitute the values of X=4 and Y= 10 in the variation equation and solve for k:
⇒ 10 = k/(4)²
⇒ 10 = k/16
⇒ k = 160
The variation equation :
⇒ Y = 160/X²
Substitute the values of X = 3 in the above equation and solve for Y:
⇒ Y = 160/(3)²
⇒ Y = 160/9
⇒ Y = 17.77
Thus, the value of Y = 17.77 when X = 3
The equation which represents "Y Varies inversely as X" can be written as:
Y = k/X where "k" is a constant.
Substitute the values of Y=8 and X=6 in the variation equation and solve for k:
⇒ 8 = k/(6)
⇒ k = 48
The variation equation :
⇒ Y = 48/X
Substitute the values of X = 3 in the above equation and solve for Y:
⇒ Y = 48/(3)
⇒ Y = 16
Thus, the value of Y = 16 when X = 3
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-0.6a^2b*(-10ab^2) PLEASE HELP!!!!!!!!
Answer: 6a^3b^3
Step-by-step explanation:
Answer:
6a³b³
Step-by-step explanation:
-0.6a^2b*(-10ab^2) =
= -0.6 × (-10) × a² × a × b × b²
= 6a³b³
A student estimated the sum 7. 95 + 8. 11 + 78. 5 + 8. 05 + 79. 4 + 0. 815 as: all the numbers begin with a 7 or 8, so use cluster estimation. 8 + 8 + 80 + 8 + 80 + 0. 8 = 184. 8 explain why this reasoning is not accurate.
Reasoning is not accurate because we cannot take 79.4 and 0.815 has cluster estimates of 8.
Given:
A student estimated the sum 7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815 as: All the numbers begin with a 7 or 8, so use cluster estimation. 8 + 8 + 80 + 8 + 80 + 0.8 = 184.8
7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815
8 + 8 + 80 + 8 + 80+ 0.8 = 184.8
Cluster estimation is used to estimate sums and products when the numbers being added or multiplied cluster near/ close in value to a single number.
Here 79.4 does not cluster around 8
And 0.815 does not cluster around 8
Therefore reasoning is not accurate because we cannot take 79.4 and 0.815 has cluster estimates of 8.
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who doesnt just use this for the awnsers
8. Consider a $2 principal investment with a 10% annual simple interest rate.
a. Write and graph the simple interest equation that represents the situation.
b. What does the y-intercept represent?
c. What does the slope of the graph represent?
d. What does the point (5, 3) represent on the graph?
9. AMORTIZATION Car loans are often spread into multiple regular payments over
in collod amortization. Each payment reduces the remaining
Answer:
Step-by-step explanation: 0.2
Can anyone solve this for me?
Answer:
8°
Step-by-step explanation:
For the acute angles in a right triangle,
[tex]sin(90-\theta)=cos\theta[/tex]
Given expression is:
[tex]cos(7x)=sin(4x+2)\\sin(90-7x)=sin(4x+2)\\90-7x=4x+2\\88=11x\\x=8^o[/tex]
To check our answer, determine the measures of the other angles in a right triangle.
[tex]A1=90^o\\A2=8^o\\A3=90-8=82^o[/tex]
The smallest angle is 8°