The linear equation in one variable is used to know on e unknown quantity. The correct answer is option a.
What is a Linear equation?A linear equation is a equation that has degree as one.
To find the solution of n unknown quantities n number of equations with n number of variables are required.
Given that,
The value of p = 10.3
Substitute p = 10.3 in all the given option as,
(a)
3.4 ÷ p = 0.34
Substitute p = 10.3 in the above equation to get,
LHS = 0.33
Since LHS = RHS
The given option is true.
(b)
437 ÷ p = 0.437
Substitute p = 10.3 in the above equation to get,
LHS = 42.427
Since LHS ≠ RHS
The given option is not true.
(c)
53.45 ÷ p = 53.45
Substitute p = 10.3 in the above equation to get,
LHS = 5.18
Since LHS ≠ RHS
The given option is not true.
(d)
340 ÷ p = 6.34
Substitute p = 10.3 in the above equation to get,
LHS =33
Since LHS ≠ RHS
The given option is not true.
(e)
2458 ÷ p = 24.582
Substitute p = 10.3 in the above equation to get,
LHS =238.64
Since LHS ≠ RHS
The given option is not true
Hence, the value of p satisfies only for option a.
To know more about linear equation click on,
brainly.com/question/11897796
#SPJ1
create a trinomial with a constant of 4 and -1 coefficient of the x term. fast help!!!
A trinomial with a constant of 4 and -1 coefficient of the x term is x² - x + 4 = 0.
What is defined as the trinomial?A trinomial is a three-term algebraic expression. An algebraic expression is made up of one or more terms' variables and constants. A perfect square trinomial is an algebraic expression formed by squaring a binomial formation. It has the formula ax² + bx + c. Here, a, b, as well as c are all real numbers, and a ≠ 0.For the given question;
Trinomial have-
constant of 4 and -1 coefficient of the x termThe general equation of the trinomial is-
ax² + bx + c = 0
Where, a and b are the coefficients and c is the constant.
Thus,
Put b = -1 and c = 4
ax² - x + 4 = 0
Now, value of a can be any number but not zero.
Thus, suitable value of a is 1.
The trinomial becomes,
x² - x + 4 = 0
Thus, a trinomial with a constant of 4 and -1 coefficient of the x term is x² - x + 4 = 0.
To know more about the trinomial, here
https://brainly.com/question/21832198
#SPJ1
Select all of the following that are statistical questions A. What is the price of the orangeB. What is the weight of an orange C. What is the average price of an orange D. What is the average weight of an orange grown in the U.S.A E. What percent of oranges grocery stores were grown in the USAThere is more than one answerPlease help no wrong answers please
Take into account that a statistical question refers to situation which data set are involved. Then, you can consider as statistical questions:
What is the average price of an orange
average takes into account the price of more than one orange.
What is the average weight of an orange grown in U.S.A
What percent of oranges grocery stores were grown in the USA
What are the terms in the expression 5b + 6m + 8?O 5,6,8O 11 b + mO 5b, 6m, 8
By definition a term is a single mathematical expression; it may be a number, a variable, or a multiplication of them.
Then, the terms in the expression given are 5b, 6m and 8.
Therefore the answer is the last choice.
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a heart and a spade.The probability of being dealt a heart and a spade is __.(Type an integer or a simplified fraction.)
Okay, here we have this:
What is 132% as a decimal?
Step 1: Problem
What is 132% as a decimal?
graph the line represented by the equation 2x + 3y = 8
Given the equation
2x + 3y = 8
The given equation represents a line
It is required at minimum two points to graph the line
So, assume two value for x and find y using the given equation
When x = -2
2 * -2 + 3y = 8
-4 + 3y = 8
3y = 8 + 4
3y = 12
y = 12/3 = 4
so, the point (-2 , 4) lie on the line
And assume x = 4
so, 2 * 4 + 3y = 8
8 + 3y = 8
3y = 0
y = 0
So, the point (4 , 0) lie on the line
so, the line is passing through the points (-2 , 4) and ( 4 , 0)
By connecting the points and extending the line we will get the graph of 2x + 3y = 8
See the following image;
Suppose that the functions fand g are defined for all real numbers x as follows.f(x)=x+5g(x)=2x²Write the expressions for (g+f)(x) and (g–f)(x) and evaluate (g.f)(-3).
The expression (g+f)(x) is equal to g(x)+ f(x), (g-f)(x) is equal to g(x) f(x) and the expression (g*f)(-3) is equal to g(-3)*f(-3).
Then, we have
[tex](g+f)(x)=g(x)+f(x)=2x^2+x+5[/tex]Similarly,
[tex](g-f)(x)=g(x)f(x)=2x^2-(x+5)=2x^2-x-5[/tex]And finally,
[tex]\begin{gathered} (g\cdot f)(-3)=g(-3)\cdot f(-3)=2(-3)^2\cdot(-3+5) \\ (g\cdot f)(-3)=2(9)\cdot(2) \\ (g\cdot f)(-3)=36 \end{gathered}[/tex]In summary, the answers are:
[tex]\begin{gathered} (g+f)(x)=2x^2+x+5 \\ (g-f)(x)=2x^2-x-5 \\ (g\cdot f)(-3)=36 \end{gathered}[/tex]Circle the value that correctly converts 6.5 cm in inches.26 in0.26 in2.6 in260 in
2.6 inches (third option)
Explanation:Given:
To convert 6.5cm to another unit
To find:
The value of 6.5 cm inches
To determine the value in inches, we need to do a conversion from cm to inches
1 inch = 2.54 cm
let 6.5 cm in inches = y
6.5cm = y
2.54cm = 1 inch
crossmultiply:
[tex]\begin{gathered} 6.5(1)\text{ = y\lparen2.54\rparen} \\ 6.5\text{ = 2.54y} \\ divide\text{ both sides by 2.54y:} \\ \frac{6.5}{2.54}\text{ = y} \\ y\text{ = 2.559} \end{gathered}[/tex]To the nearest tenth, y = 2.6
Hence, the value of 6.5cm in inches is 2.6 inches (third option)
good morning I really need help with numbers 3 and 4
a) 6 x 18 = 108
b) 8 x 74 = 592
Explanations:According to the distributive property:
a (b + c) = ab + ac
Let us do each of the exercises 3 and 4 using the distributive property:
3) 6 x 18
Step 1: Write 18 as 10 + 8
18 = 10 + 8
6 x 18 = 6 ( 10 + 8)
Step 2: Apply the distributive property
6 ( 10 + 8) = (6 x 10) + (6x8)
Step 3: Multiply each of the terms
60 + 48
Step 4: Add the two together
108
Therefore, 6 x 18 = 108
4) 8 x 74
Step 1: Write 74 as 70 + 4
74 = 70 + 4
8 x 74 = 8 ( 70 + 4)
Step 2: Apply the distributive property
8 ( 70 + 4) = (8 x 70) + (8x4)
Step 3: Multiply each of the terms
560 + 32
Step 4: Add the two together
592
Therefore, 8 x 74 = 592
The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is 7 feet. Find tje length of the three sides of the triangle. Answer exactly or round to 2 decimal places. The legs of the triangle are 7_ feet and the hypotenuse is _ feet
Taking l as the length of one of the legs and using the pythagorean theorem we have that:
[tex](2l)^2=l^2+7^2[/tex]Solve the equation for l:
[tex]\begin{gathered} 4l^2=l^2+49 \\ 4l^2-l^2=49 \\ 3l^2=49 \\ l^2=\frac{49}{3} \\ l=\sqrt[]{\frac{49}{3}} \\ l=\frac{7}{\sqrt[]{3}}=\frac{7\sqrt[]{3}}{3} \end{gathered}[/tex]It means that the hypotenuse is:
[tex]\frac{14\sqrt[]{3}}{3}[/tex]And the leg is:
[tex]\frac{7\sqrt[]{3}}{3}[/tex]When the clock first starts counting down time, there are more than 300 seconds before the start of the game. Write an inequality statement that best describes t, the time in seconds, when the clock first starts counting down time.
"When the clock first starts counting down time, there are more than 300 seconds before the start of the game", that means the variable t we will use to represent when the clock first starts counting down time is greater than 300, so we can represent this sentence with the following inequality:
[tex]t>300[/tex]So the inequality statement that best describes t is t > 300.
Which number is not equal to 225%?its is exercise number 5
To do this, you can first convert the percentage form to its decimal form, like this
[tex]225\text{\%}=\frac{225}{100}=2.25[/tex]Now, you can convert the numbers that are possible answers into their decimal form, like this
Option A.
[tex]2\frac{1}{4}=\frac{2\cdot8+1}{4}=\frac{8+1}{4}=\frac{9}{4}=2.25[/tex]Option B.
[tex]\frac{9}{4}=2.25[/tex]Option C.
[tex]\frac{50}{40}=\frac{5\cdot10}{4\cdot10}=\frac{5}{4}=1.25[/tex]Option D.
[tex]\frac{45}{20}=\frac{9\cdot5}{4\cdot5}=\frac{9}{4}=2.25[/tex]Therefore, the number that is not equal to 225% is 50/40 and the correct answer is C. 50/40.
x-6y>57x+2y>4Is (10,-2) a solution of the system?
To check if (10, -2) is a solution to the system, we have to replace x with "10" and y with "-2" and see if the inequalities hold true.
If both the inequalities hold true, then definitely (10, -2) is a solution!
Let's check the first inequality:
[tex]\begin{gathered} x-6y\stackrel{?}{>}5 \\ 10-6(-2)\stackrel{?}{>}5 \\ 10+12\stackrel{?}{>}5 \\ 22>5 \\ \text{True} \end{gathered}[/tex]Now, let's check the second inequality:
[tex]\begin{gathered} 7x+2y\stackrel{?}{>}4 \\ 7(10)+2(-2)\stackrel{?}{>}4 \\ 70-4\stackrel{?}{>}4 \\ 66>4 \\ \text{True} \end{gathered}[/tex]
The number of adults living in homes on a randomly selected city block is described by the following probability distribution. Number of adults, x1 ,2,3,4 or moreProbability, P(x) 0.250.500.15??? What is the probability that 4 or more adults reside at a randomly selected home?(A) 0.10(B) 0.15 (C) 0.25(D) 0.50 (E) 0.90
The answer is letter A. 0.1
because the probability = 1
So Probability of select 4 adults = 1 - 0.25 - 0.5 - 0.15
= 0.1
Identify the domain and range for the given relation. Indicate whether the relation is a function or not andexplain
Given :
Domain is:
[tex]D\colon\mleft\lbrace0,-1,1\mright\rbrace[/tex]Range is:
[tex]R\colon\mleft\lbrace0,1,2\mright\rbrace[/tex]Here is one output for one input.
How many gallons are equivalent to 12 quarts?
Given:
The objective is to convert 12 quarts into gallons.
In general,
[tex]1\text{ gallon=4}quart[/tex]12 quarts can be converted to gallons by,
[tex]\begin{gathered} x=\frac{12}{4} \\ x=3\text{ quarts} \end{gathered}[/tex]Hence, 12 quarts is 3 gallons.
Express the function graphed on the axes below as a piecewise function.108642-10-8-6-4-22416810-4-6-8-10
Answer:
[tex]f(x)=\begin{cases}2x+3,x\le-4 \\ 2x-12,x>2\end{cases}[/tex]Explanation:
The equation of the line to the left is 2x + 3 and we see that it only exists for x <= -4.
The equation of the line to the right is 2x - 12 and we see that it only exists for x > 2.
Therefore, we can write
f(x) = 2x + 3 for x < = -4
f(x) = 2x -12 for x > 2
Or in the notation of piecewise function, the above can be written consicely as
[tex]f(x)=\begin{cases}2x+3,x\le-4 \\ 2x-12,x>2\end{cases}[/tex]
which is our answer!
find the smallest non negative value for x in degrees that makes the equation cot (x) = √3 true.
Given:
cot (x) = √3
To find the smallest non-negative value for x in degrees:
So, we get
[tex]\begin{gathered} \cot x=\sqrt{3} \\ \cot x=\cot (30^{\circ}) \\ x=30^{\circ} \end{gathered}[/tex]Hence, the answer is,
[tex]x=30^{\circ}[/tex]5Jamal's band learns lots of new songs.The band learns a new song every fourdays. At this rate, how many new songswill the band learn in four weeks?LAsongs
Given that The band learns a new song every four days.
We need to find the number of new songs for four weeks.
We know that one week= 7 days
[tex]1\text{ w}eek\text{ = 7 days }[/tex]Multiply by 4 to find the number of days in four weeks.
[tex]1\times4\text{ w}eek\text{ = 7 }\times4\text{ days }[/tex][tex]4\text{ w}eeks\text{= 28days }[/tex]We need to find the number of new songs that the band learns in 28 days.
Divide 28 by 4 to find the number of songs since the band learns one new song every 4 days.
[tex]\frac{28}{4}=7\text{ songs}[/tex]The band learns 7 songs in four weeks.
what is the equation of the line? O y=3/2x O y=2/3x O y=3x O y=2x
Explanation:
We would apply the slope formula:
slope = change in y/change in x
change in y = 4 - 0 = 4
change in x = 6 - 0 = 6
Also note on the graph, the change in y is represented by y. And the change in x is represented by x
[tex]\begin{gathered} slope=\frac{4}{6} \\ \text{slope =}\frac{y}{x} \end{gathered}[/tex]Equating both:
[tex]\begin{gathered} \frac{y}{x}=\frac{4}{6} \\ \frac{y}{x}=\frac{2}{3} \end{gathered}[/tex]Multiply both sides by x:
[tex]\begin{gathered} \frac{y}{x}\times x=\frac{2}{3}\text{ }\times\text{ x} \\ y\text{ = }\frac{2x}{3}\text{ (option B)} \end{gathered}[/tex]hi I need help ;]]] ❄️❄️❄️
The order from least to greatest is -4.7,-4,-31/8, [tex]-3\frac{1}{8}[/tex]
What is Fraction?A fraction represents a part of a whole.
The given integers are -31/8,-4.7, -4 and -3 1/8
Now let us simplify the fraction values
-31/8=-3.875
-4.7
-4 and
[tex]-3\frac{1}{8}[/tex]=-24+1/8=-23/8=-2.875
As there is a negative sign, the smallest number with negative sign will be greatest and largest number with negative sign is smaller.
So -4.7,-4, -3.875, -2.875
-4.7,-4,-31/8, [tex]-3\frac{1}{8}[/tex]
Hence the order from least to greatest is -4.7,-4,-31/8, [tex]-3\frac{1}{8}[/tex]
To learn more on Fractions click:
https://brainly.com/question/10354322
#SPJ1
An empty swimming pool needs to be filled to the top. The pool is shaped like a cylinder with a diameter of 9 m and a depth of 1.1 m. Suppose water is pumped into the pool at a rate of 13 m^3 per hour. How many hours will it take to fill the empty pool?
Use the value 3.14 for pi, and round your answer to the nearest hour. Do not round any intermediate computations.
Answer:
πr2h
volume of cylinder
3.14×3×3×1.1=31.086m^3
1hour=13m^3
31.086m^3
divide 31.086÷13=2.3912hours
find (8.4x10^11)/(5.25x10^2)(8.0x10^3), expressed in a scientific notation
The simplified form of the expression, (8.4 x 10^11)/(5.25 x 10^2)(8.0 x 10^3), in scientific notation is 2.0 × 10⁵
Evaluating an expression in scientific notationFrom he question, we are to evaluate the given expression in scientific notation.
The given expression is
(8.4 x 10^11)/(5.25 x 10^2)(8.0 x 10^3)
First, we will write this expression properly
The expression written properly is
(8.4 x 10¹¹)/(5.25 x 10²)(8.0 x 10³)
Evaluating
(8.4 x 10¹¹)/(5.25 x 8.0)(10² x 10³)
(8.4 x 10¹¹)/(5.25 x 8.0)(10² ⁺ ³)
(8.4 x 10¹¹)/(42.0)(10⁵)
(8.4 x 10¹¹)/(42.0 × 10⁵)
(8.4/42.0) × (10¹¹ / 10⁵)
(0.20) × (10¹¹ ⁻ ⁵)
(0.20) × (10⁶)
= 0.20 × 10⁶
= 2.0 × 10⁵
Hence, the expression is 2.0 × 10⁵
Learn more on Evaluating an expression here: https://brainly.com/question/27862246
#SPJ1
What is an equation of the line parallel to the line on the graph that passes through (2,25)?
y=4x+17
ExplanationStep 1
2 equations of lines are parallel if the slope is the same, so
a) find the slope of the graphed line
the slope of a line can by calculated by using
[tex]\begin{gathered} slope=\frac{change\text{ in y }}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1) \\ and \\ P2(x_2,y_2) \\ are\text{ 2 points from the line} \end{gathered}[/tex]so
pick up 2 points from the the line and let
[tex]\begin{gathered} P1(0,10) \\ P2(10,50) \end{gathered}[/tex]replace and evaluate
[tex]\begin{gathered} slope=\frac{change\text{\imaginaryI ny}}{change\text{\imaginaryI nx}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ slope=\frac{50-10}{10-0}=\frac{40}{10}=4 \end{gathered}[/tex]hence, the slope of the line is 4
Step 2
now, using the slope and a point we can find the equation of the line
use the point-slope formula, it says
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ m is the slope} \\ (x_1,y_1)\text{ is a point from the line} \end{gathered}[/tex]so
a)let
[tex]\begin{gathered} P1(2,25) \\ sloipe=4 \end{gathered}[/tex]b) now ,replace and solve for y
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-25=4(x-2) \\ y-25=4x-8 \\ add\text{ 25 in both sides} \\ y-25+25=4x-8+25 \\ y=4x+17 \end{gathered}[/tex]so, the answer is
y=4x+17
I
D.) what is the probability of selling 25 cheesecakes ?E.) what is the probability of selling at most 10 cheesecakes ?F.) give the expected number of cheesecakes sold on any given day using the discrete probability distribution
D)
To find the probability of selling 25 cheesecakes:
It is impossible to find the probability of selling 25 cheesecakes.
So,
P(x=25)=0
The probability of selling 25 cheesecakes is 0.
E)
To find the probability of selling at most 10 cheesecakes:
That is,
[tex]\begin{gathered} P(x\leq10)=P(x=0)+P(x=5)+P(x=10) \\ =0.1+0.23+0.04 \\ =0.37 \end{gathered}[/tex]Therefore, the probability of selling at most 10 cheesecakes is 0.37.
F)
To find the expected number of cheesecakes sold on any given day using the discrete probability distribution:
[tex]\begin{gathered} \sum ^5_{i\mathop=1}x_ip_i=x_1p_1+x_2p_2+x_3p_3+x_4p_4+x_5p_5 \\ =0(0.1)+5(0.23)+10(0.04)+15(0.46)+20(0.17)_{}_{}_{} \\ =0+1.15+0.4+6.9+3.4 \\ =11.85 \end{gathered}[/tex]Hence, the expected number of cheesecakes sold on any given day using the discrete probability distribution is 11.85.
8) Suppose y varies inversely as x, if y = 7 when x = 6then find y when x = -21.
Suppose y varies inversely as x, if y = 7 when x = 6
then find y when x = -21.
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
y*x=k
where
k is the constant of proportionality
step 1
Find the value of k
we have
y=7, x=6
k=7*6
k=42
the equation is
y*x=42
step 2
For x=-21
substitute
y*(-21)=42
y=42/(-21)
y=-2What system of inequalities would you use to solve the problem below?Suppose you have a job teaching swimming lessons and get paid $6 an hour. You also have a job as a cashier and get paid $8 an hour. If you cannot work more than 15 hours a week, what are the number of hours you can work at each job and still make at least $100?A.s + c 1006s + 8c 15B.s + c 156s + 8c 100C.s + c < 156s + 8c > 100D.s + c 156s + 8c 100
Answer:
s + c <= 15
6s + 8c >= 100
Explanation:
Write 1.75 % as decimal AND simplified fraction. ANS. As decimal __________. As simplified fraction. ________.
The given percentage is 1.75%.
To find the decimal expression of this percentage, we just have to divide it by 100. It's important to know that when we divide a number by 100, we just have to move the decimal point two spots to the left, as follows
[tex]\frac{1.75}{100}=0.0175[/tex]Therefore, as a decimal is 0.0175.
Now, to find the simplified fraction, we divide the number by 10000, as follows
[tex]\frac{175}{10000}[/tex]The reason for dividing by 10000 is that we need to have a whole number in the numerator, so the extra two zeros allow us to get rid of the two of the number. Now, we simplify the fraction dividing each part by 5
[tex]\frac{175\colon5}{10000\colon5}=\frac{35}{2000}=\frac{7}{400}[/tex]Once we get the simplest fraction, we can finish.
Therefore, as a simplified fraction is 7/400.
how do I solve for x and y when I have no information for these triangles?
y is equal to 140 because they are congruent
the complement of y is 40 because 180 - 140 = 40
x = 180 - 40 - 40 = 180 - 80 = 100
1. y and 140 are congruent angles, so y = 140
2. a = 180 - 140 = 40 because it is complementary with y
3. b = a = 40 because the sides of the triangle are equal, so the angles are equal
4. c = 180 - a - b = 180 - 40 - 40 = 100 because the sum of the inner angles of a triangle measure 180
5. x = c = 100 because they are opposed by the vertex
Answer:
y = 140
x = 100
(a) Does f (x) have a horizontal asymptote? If so, what is it?(b) Does f (x) have any vertical asymptotes? If so, what are they?
a) Horizontal asymptotes are horizontal lines that the graph of a function approaches but never touches. To find the horizontal asymptote, we would apply one of the rules which states that
If the degree of the of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x axis of the graph. It occurs at y = 0
The degree is the largest exponent in the function. Looking at the given function, the degree of the numerator is 2 while the degree of the denominator is 3. Thus,
there is a horizontal asymptote at y = 0
b) The vertical asymptotes are vertical lines which correspond to the zeros of the denominator of rational functions. It is equal to the values of x that make the denominator to be zero. Looking at the given function, (x + 1) cancels out in the numerator and denominator. We are left with (x - 4) and (x + 5). We would equate both terms to zero and solve for x. These values of x would make the denominator to be equal to zero. We have
x - 4 = 0
x = 4
x + 5 = 0
x = - 5
Thus,
there are vertical asymptotes at x = - 5 and x = 4