Here, we want to solve the given equation
We proceed as follows;
[tex]\begin{gathered} a^2+6^2=14^2 \\ a^2+36\text{ = 196} \\ a^2=\text{ 196-36} \\ a^2\text{ = 160} \\ a\text{ = }\sqrt[]{160} \\ a\text{ = +12.6 or -12.6} \end{gathered}[/tex]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.
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
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.
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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]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.
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]
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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
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;
What is the surface area of the regular pyramid below?A. 648 sq. unitsB. 552 sq. unitsC. 396 sq. unitsD. 522 sq. units
Step 1:
Concept: Calculate the area of each face and add all together to get the surface area of the pyramid.
The regular pyramid below have 4 triangles and a square
Step 2: Apply the area formula to find the area of the 4 triangles and a square.
[tex]\begin{gathered} \text{Area of a triangle = }\frac{Base\text{ x Height}}{2} \\ \text{Area of the square base = Length x Length} \end{gathered}[/tex]Step 3:
Given data for the triangle
Height = 21
Base = 12
[tex]\begin{gathered} Area\text{ of a triangle = }\frac{Base\text{ x Height}}{2} \\ =\text{ }\frac{21\text{ x 12}}{2} \\ =\text{ }\frac{252}{2} \\ =126\text{ sq. units} \\ \text{Area of the four triangles = 4 x 126 = 504 sq. units} \end{gathered}[/tex]Step 4: Find the area of the square
Given data for the square
Length = 12
Area = length x length = 12 x 12 = 144 sq. units
Step 5: Add the area of the four triangles and the square.
Surface area of the regular pyramid = 504 + 144
= 648 sq. units
What 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:
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
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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!
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.
What is 132% as a decimal?
Step 1: Problem
What is 132% as a decimal?
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.
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]2) Given that XY || AC, what is YC if BX = 10, BA = 15, and BY = 8?A) 4 B) 6 C)8D)12
We can see that triangles ABC and AXY are congruent
This means that
[tex]\frac{AX}{BX}=\frac{YC}{BY}[/tex]Now, we know that BX=10, BY=8 and BA=AX+BX, hence AX=BA-BX, we have
[tex]\frac{BA-BX}{10}=\frac{YC}{8}[/tex]now, since BA-BX=15-10, BA-BX=5, it yields,
[tex]\frac{5}{10}=\frac{YC}{8}[/tex]Now, we need to isolate YC, this is given by
[tex]YC=8(\frac{5}{10})[/tex]Since
[tex]\frac{5}{10}=\frac{5\cdot1}{5\cdot2}=\frac{1}{2}[/tex]we have that
[tex]\begin{gathered} YC=8(\frac{1}{2}) \\ YC=\frac{8}{2} \\ YC=4 \end{gathered}[/tex]hence, the answer is YC=4, which corresponds to A).
(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
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=-2x-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]
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
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]help me asap please!!! no explanation just the process and answer
To find out the determinant, multiply in cross
so
(3)*(-2)-(5)*(-7)=-6+35=29
therefore
the answer is 29
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
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)
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]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.
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.
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