Answer: [2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x
Step-by-step explanation:
I think of a number, represented by the variable/pronumeral x.
I add 5 to it: x + 5
then double the result: 2(x + 5)
I then subtract 10 from this answer: [2(x + 5)] - 10
I then subtract the original number I thought of: [2(x + 5)] - 10 - x
Simplifying the expression will explain why you get the original number.
[2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x.
A truck carries 4 chairs and tables. The table weighs 35 pounds. The total weight of the chairs and tables is 63 pounds. How much does each chair weigh?
The weight of each chair is 7 pounds.
What is basic arithmetic?Specific numbers and their computations employing a variety of fundamental arithmetic operations are at the center of arithmetic mathematics. Algebra, on the other hand, deals with the limitations and guidelines that apply to all other types of numbers, including whole numbers, integers, fractions, functions, and so on. Arithmetic math serves as the foundation for algebra, which always adheres to its definition. A large range of subjects fall within the broad definition of mathematics, which encompasses a very broad range of topics. Beginning with the fundamentals like addition, subtraction, and division of numbers, they then move on to more complicated topics like exponents, variations, sequence, progression, and more. This part does touch on some of the mathematical formulas and mathematical sequence. Four essential mathematical operations—addition, subtraction, multiplication, and division—are covered in basic arithmetic.
Total weight = 63 pounds
Weight of the table = 35 pounds
Weight if 4 chairs = 63 - 35
= 28 pounds
Weight of one chair = 28/4
= 7 pounds
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A 90% confidence interval for a proportion is found to be (0.52, 0.58). What isthe sample proportion?
A 90% confidence interval for a proportion is given as (0.52,0.58).
It is required to find the sample proportion.
Recall that for confidence interval (x,y), the sample proportion is the midpoint:
[tex]c=\frac{x+y}{2}[/tex]Substitute x=0.52 and y=0.58 into the equation:
[tex]c=\frac{0.52+0.58}{2}=\frac{1.1}{2}=0.55[/tex]The answer is C.
identify whether each phrase is an expression equation or quantity
the last one of the right column is a inequality, because it has the sign "<"
the second one of the right column in an expression because it doen't have the sign "="
the first one of the right column is a equation because it has the sign "=".
How do you Graph g(x)=x^5-2x^4 ?
Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values.
Oaks Hardware purchases an extension ladder list priced at $120. It is available at a 15% discount. What is the available price?
A 15% discount means that the retail price is 85% of the original price.
To calculate said retail price, we'll use a rule of three:
Thereby,
[tex]x=\frac{120\cdot85}{100}\rightarrow x=102[/tex]Therefore, we can conclude that the available price is $102
▸ Charice created a painting with an area of 63 square inches and a length of 7 inches. They create a second painting with an area of 81 square inches. It has the same width as the first painting. What is the length of the second painting?
The length of the second painting is 9 inches.
Given,
The area of the first painting = 63 square inches
Length of the first painting = 7 inches
The area of the second painting = 81 square inches
Width of the first painting = Width of the second painting = x
We have to find the length of the second painting:
Here,
We can consider the painting as a rectangle.
Area of rectangle = length × width
Now,
First painting:
Area = length × width
63 = 7 × x
x = 63/7 = 9
That is, the width of the first painting is 9 inches.
The width of the second painting also 9 inches.
Now,
Second painting:
Area = length × width
81 = length × 9
length = 81/9 = 9
Therefore, the length of the second painting is 9 inches.
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For each ordered pair, determine whether it is a solution to the system of equations. 7x - 4y=8 -2x+3y=7 Is it a solution? (x, y) Yes No (0, -2) a (-9,-6) (4,5) (7.7)
7x - 4y = 8 (eq. 1)
-2x + 3y = 7 (eq. 2)
Isolating y from equation 1:
-4y = 8 - 7x
y = 8/(-4) - 7/(-4)x
y = -2 + 7/4x
Isolating y from equation 2:
3y = 7 + 2x
y = 7/3 + 2/3x
Given that the slopes of the equations are different, then there is a solution, which can be found as follows,
[tex]\begin{gathered} -2+\frac{7}{4}x=\frac{7}{3}+\frac{2}{3}x \\ \frac{7}{4}x-\frac{2}{3}x=\frac{7}{3}+2 \\ \frac{^{}_{}7\cdot3-2\cdot4}{4\cdot3}x=\frac{7+3\cdot2}{3} \\ \frac{13}{12}x=\frac{13}{3} \\ x=\frac{13}{3}\cdot\frac{12}{13} \\ x=4 \end{gathered}[/tex]Replacing x = 4 into one of the equations, we get:
[tex]\begin{gathered} y=-2+\frac{7}{4}x \\ y=-2+\frac{7}{4}\cdot4 \\ y=-2+7 \\ y=5 \end{gathered}[/tex]The solution is (4,5)
To check if an ordered pair is a solution, we have to replace the x-coordinate and the y-coordinate of the pair into the equation, as follows:
(0, -2)
7(0) - 4(-2) = 8
8 = 8
-2(0) + 3(-2) = 7
-6 ≠ 7
Given that the second equation is not satisfied, then (0, -2) is not a solution
(-9, -6)
7(-9) - 4(-6) = 8
-81 + 24 ≠ 8
-2(-9) + 3(-6) = 7
18 - 18 ≠ 7
Given that the equations are not satisfied, then (-9, -6) is not a solution
(7,7)
7(7) - 4(7) = 8
49 - 28 ≠ 8
-2(7) + 3(7) = 7
-14 + 21 = 7
Given that the first equation is not satisfied, then (7, 7) is not a solution
6. Point A (-16,8) is one of the verticesof a rectangle. After a dilation of 1/2, arotation of 90 degrees clockwise, and areflection over the x-axis, what are thecoordinates of A"'?
Given the coordinate: A(-16, 8), let's perform the following:
First step:
A dilation with a scale factor of 1/2.
Here, we are to multiply the coordinates by 1/2.
A(-16, 8) ==> A'(-16*½, 8*½) = A'(-8, 4)
Second step:
Perform a rotation of 90 degrees clockwise.
(x, y) will change to (y, -x)
A'(-8, 4) ==> A''(4, 8)
Third step:
A reflection over the x axis.
To perform a reflection over the x axis, (x, y) becomes (x, -y)
A''(4, -8) ==> A'''(4, -8)
Therefore, the coordinates of A''' are:
A'''(4, -8)
question given below slove the following equations for r4al x and y .
S={(-24,7/3)}
1) When we're dealing with Complex Numbers we can rewrite this expression:
[tex](3+4i)^2-2(x-yi)=x+yi[/tex]Considering that their real and their imaginary parts can be taken as equal, so:
[tex]\begin{gathered} (3+4i)^2-2(x-yi)=x+yi \\ (3+4i)^2-2(x-iy) \\ 9+24i+16i^2+2x+2yi \\ \end{gathered}[/tex]2) Rewrite that into the Standard form for complex numbers y= ax +bi combining like terms:
[tex]\begin{gathered} 9+24i-16+2x+2yi \\ (-7-2x)+i(24+2y)\text{ = x+ iy} \\ \end{gathered}[/tex]Finally writing those two expressions as a System of equations we have:
[tex]\begin{gathered} \begin{cases}-7-2x=\text{ x} \\ 24+2y=y\end{cases} \\ -7-2x=x\Rightarrow-7=2x+x\Rightarrow3x=7\Rightarrow\frac{3x}{3}=\frac{7}{3} \\ 24+2y=y\Rightarrow24=-2y+y\Rightarrow-y=24\Rightarrow y=-24 \\ S=\mleft\lbrace(\frac{7}{3},-24)\mright\rbrace \end{gathered}[/tex]3) Hence, the answer is S={(-24,7/3)}
Directions: Identify the slope and y-intercept of the line on the graph. Then, write the equation of the line in slope-intercept form.
To find out the slope, we need two points
so
looking at the graph
we take
(-4,5) and (0,-3)
m=(-3-5)/(0+4)
m=-8/4
m=-2the y-intercept (value of y when the value of x is zero) is the point (0,-3)
the equation of the line in slope-intercept form is
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
so
m=-2
b=-3
substitute
y=-2x-3you are 5 feet and 4 inches tall and cast a shadow 6 feet long. At the same time , a nearby tree cast a shadow 40 feet 6 inches long. Find the heigh of the tree.
The height of the tree is such that it cast a shadow 40 feet 6 inches long and maintains the given ratio will be 36 feet.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given question,
The height of a person is 5 feet and 4 inches.
Since 1 feet = 12 inches so 4 inches = 1/3 feet
Therefore,height of a person = 5 + 1/3 = 16/3 feet
Its shadow length = 6 feet
The ratio of the height to shadow length = (16/3)/6
Now, the shadow of the tree = 40 feet and 6 inches so 40.5 feet
Let's say its length was x feet.
Then x/40.5 = (16/3)/6
x = 36 feet
Hence "The height of the tree is such that it cast a shadow 40 feet 6 inches long and maintains the given ratio will be 36 feet".
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The graph above shows the graph of the cost in blue and revenue in red function for a company that manufactures and sells small radios.ABCD
a) 500 radios
b) Going out = $5000
Coming in = $5000
c) P(x) = 6x - 3000
d) Profit of $900
Explanation:a) To get the number of radios that must be produced to break even, we will equate the cost function and the revenue function:
[tex]\begin{gathered} \cos t\text{ function:} \\ C(x)\text{ = 3000 + 4x} \\ \text{revenue function:} \\ R(x)\text{ = 10x} \\ \\ \text{Break even:} \\ C(x)\text{ = R(x) } \\ \text{3000 + 4x = 10x} \end{gathered}[/tex]collect like terms:
[tex]\begin{gathered} 3000\text{ = 10x - 4x} \\ 3000\text{ = 6x} \\ \text{divide both sides by 6:} \\ x\text{ = 3000/6} \\ x\text{ = 500} \\ \text{If x represents number of radios produced,} \\ \text{Then to break even, 500 radios will have to be produced } \end{gathered}[/tex]b) The dollar amount going in and coming out is gotten by replacing the value of x in both function with 500:
[tex]\begin{gathered} \text{when x = }500 \\ C(x)\text{ = 3000 + 4x = 3000 + 4}(500) \\ C(x)\text{ = }5000 \\ \text{Amount going out = \$5000} \\ \text{when x = 500} \\ R(x)\text{ = 10x = 10(500)} \\ R(x)\text{ = 5000} \\ \text{Amount coming in = \$5000} \end{gathered}[/tex]c) Profit = Revenue - Cost
[tex]\begin{gathered} \text{Profit function, }P(x)\text{= R(x) - C(x)} \\ P(x)\text{ = 10x - (3000 + 4x)} \\ P(x)\text{ = 10x - 3000 - 4x} \\ P(x)\text{ = 6x - 3000} \end{gathered}[/tex]d) To find the profit when the number of radios is 650
[tex]\begin{gathered} \text{Profit function: P(x) = 6x - 3000} \\ \text{for 650 radios, x = 650} \\ P(650)\text{ = 6(650) - 3000} \\ P(650)\text{ = 900} \\ \text{The company will make a profit of \$900} \end{gathered}[/tex]7, -28, 112, -448, ..... as a formula
n = number
We can see that the value of each number is multiplied by 4 at each point in time
And the initial value is 7
[tex]a_n=7(4)^{n-1}[/tex]The measure of the smallest angle in a right triangle is 45° 45 ° less than the measure of the next larger angle. Find the measures of all three angles.
Angle A or B must be 90 degrees since it is a right triangle. Given that C is more than 60 and that there are 180 degrees in a triangle, the other angle must be less than 30 degrees.
How to measure the three angles?The smallest angle in a right triangle has a measure that is 45° smaller than the next largest angle.As a result, the other two angles' measurements must sum up to 90. The only solution to this would be for both of the remaining angles to be 45 degrees if the lowest angle is 45 degrees less than the next largest angle. The correct angle would be the next biggest angle.Angle A or B must be 90 degrees since it is a right triangle. Given that C is more than 60 and that there are 180 degrees in a triangle, the other angle must be less than 30 degrees.To learn more about Right triangle refer to:
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? QuestionWhat is the equation of the quadratic function represented by this table?х5678910f(x)-4585-4-19HolaType the correct answer in each box. Use numerals instead of words.f(x) =(x -12 +
To determine the equation of the quadratic equation, which is a parabola, we substitute the coordinates of the vertex of the parabola (h,k) into the general equation.
[tex]y=a(x-h)^2+k[/tex]From the given, notice that the only value of f(x) that does not repeat is 8. This means that the vertex is at (7,8).
[tex](h,k)=(7,8)[/tex]Thus, we only need to obtain the value of a.
Substitute the coordinate of a point (x,y) into the equation and the vertex as well. In this case, let us use the first given point, (5,-4).
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ (5,-4)\rightarrow-4=a(5-7)^2+8 \end{gathered}[/tex]Simplify the obtained equation.
[tex]\begin{gathered} (5,-4) \\ -4=a\mleft(5-7\mright)^2+8 \\ -4=a\mleft(-2\mright)^2+8 \\ -4=a(4)+8 \\ -4-8=4a \\ -12=4a \\ a=\frac{-12}{4} \\ a=-3 \end{gathered}[/tex]Now that we have the value of a, substitute the coordinates of the obtained vertex and the value of a into the equation of the quadratic equation.
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=-3(x-7)^2+8 \end{gathered}[/tex]To check, the graph of the given function is as follows:
Therefore, the equation of the quadratic equation is y=-3(x-7)²+8.
What is the output value for the following function if the input value is 5?y = 4x - 34223172
Answer:
17
Explanation:
Given the function:
[tex]y=4x-3[/tex]When the input value, x = 5
[tex]\begin{gathered} y=4x-3 \\ =4(5)-3 \\ =20-3 \\ =17 \end{gathered}[/tex]The output value if the input value is 5 is 17.
Find the measure of the indicated angle to the nearest degreeQuestion 15
Question 15.
Given:
Length of side opposite the indicated angle = 12 units
Length of side adjacent the hypotenuse = 24 units
Let's find the measure of the indicated angle.
Here, we have a right triangle.
To find the measure of the indicated angle, apply the trigonometric ratio formula for sine:
[tex]sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]Where:
θ is the indicated angle.
Thus, we have:
[tex]\begin{gathered} sin\theta=\frac{12}{24} \\ \\ sin\theta=\frac{1}{2} \end{gathered}[/tex]Take the sine inverse of both sides:
[tex]\begin{gathered} \theta=sin^{-1}(\frac{1}{2}) \\ \\ \theta=30^o \end{gathered}[/tex]Therefore, the measure of the indicated angle us 30 degrees.
• ANSWER:
30°
A saw blade is rotating at 2700 revolutions per minute. Find theangular speed in radians per second.
The rule of the angular speed is
[tex]\omega=No\text{ of revolution per min }\times\frac{2\pi}{60}[/tex]Since the number of revolutions is 2700 per min, then
[tex]\begin{gathered} \omega=2700\times\frac{2\pi}{60} \\ \\ \omega=90\pi\text{ rad per sec} \end{gathered}[/tex]The answer is 90pi rad per second
The answer is the 3rd answer
Based on the diagram below, which statement is true? b a C 110° 115° d 60° e 120° Oь || с Oa || ь alle Odlle
we have that
Verify each statement
1) b parallel to c
If b is parallel to c then
115+60=180
175=180 ----> is not true
2) a parallel to b
If a is parallel to b
then
110+60=180
170=180 -----> is not true
3) a parallel to c
If a is parallel to c
then
110=115 -----> is not true
4) d parallel to e
If d is parallel to e
then
60+120=180
180=180 -----> is true
therefore
the answer is
d parallel to ePart 2
In this problem
If n and m are parallel
then
the interior angles of the triangle are
30, 80 and x degrees
so
30+80+x=180
110+x=180
x=180-110
x=70 degrees16. Four solids labelled A, B, C, and D are shown below. o A B D a. Which of the solids has a curved face? 1mk b. Which solid has 5 faces? 1mk c. Which solid has 12 edges? Imk
a. A solid has curved surface area.
b. C solid has 5 faces.
c. D solid has 12 edges.
Identify the algebraic expression for the following word phrase: 5 less than twice a number y.
Answer:
5-2y because 5 less is 5- and 2 twice a number is y number is y and twice mean 2
[tex] - \frac{5}{6} e - \frac{2}{3} e = - 24[/tex]cual es la respuesta
Resolvamos esta ecuación para la variable "e":
[tex]\begin{gathered} -\frac{5}{6}e-\frac{2}{3}e=-24 \\ \frac{5}{6}e+\frac{2}{3}e=24 \\ \frac{5}{6}e+\frac{4}{6}e=24 \\ \frac{(5+4)e}{6}=24 \\ \frac{9e}{6}=24 \\ 9e=24\cdot6 \\ 9e=144 \\ e=\frac{144}{9} \\ e=16 \end{gathered}[/tex]Entonces, el valor de "e" es 16.
use the data below make a frequency table take a picture of you frequency table and attach it to your answer marathon time
A frequency table is a table that shows how many times each number appears.
Looking at this set of numbers, we can see that each number appears only one time.
So we can create the following frequency table:
[tex]\begin{gathered} \text{value | frequency} \\ 135\text{ | 1} \\ 211\text{ | 1} \\ 220\text{ | 1} \\ 180\text{ | 1} \\ 175\text{ | 1} \\ 161\text{ | 1} \\ 246\text{ | 1} \\ 201\text{ | 1} \\ 192\text{ | 1} \\ 167\text{ | 1} \\ 235\text{ | 1} \\ 208\text{ | 1} \end{gathered}[/tex]Consider the following inequality:x < -2Step 2 of 2: What type of interval does the following inequality represent?
You have the following inequality:
x≤2
the prevous inequality can be written in interval notation as follow:
(-oo, 2]
then, you can conclude that the inequality is represented by a half-open interval (this happens when you have an open parentheses and a close parentheses)
What is 175% of 48? Show work.
Let 175% of 48 be y.
This implies that
[tex]\frac{175}{100}\times48=y[/tex]To evaluate y,
[tex]\begin{gathered} \frac{175}{100}\times48=y \\ \Rightarrow\frac{175\times48}{100}=y \\ \frac{8400}{100}=y \\ \Rightarrow y=84 \end{gathered}[/tex]Hence, 175% of 48 is 84.
the rotation are is a 60° rotation about O,the center of the regular hexagon State the image of B for the following rotation
You have the following rotation:
[tex]R^2\circ R^{-2}[/tex]The result of the previous rotation, by taking into account the rules for the exponents for the transformations is:
[tex]R^2\circ R^{-2}=R^0[/tex]The rotation R⁰ means a rotation of 0 degrees of a specific point.
Then, the given rotation appiled to point B does not move the point B from its place. The transformation makes B to go to B
answer: B
A ladder is 12 ft tall, and the base is 4 ft from the house. How high up thehouse does the ladder reach? Round to the nearest tenth of a foot.
ok
t = 12
b = 4
h = ?
[tex]\begin{gathered} \text{ 12}^2=4^2+h^2 \\ \text{ h}^2\text{ = 144 - 16} \\ \text{ h}^2\text{ = 128} \\ \text{ h = }\sqrt[]{128} \\ h\text{ = 11.3 ft} \end{gathered}[/tex]height = 11.3 ft
If a line passes thru the points (5,5) and (9,3) the slope of this line is
The initial point is (5,5)
the final point is (9, 3)
The formula for determining slope is expressed as
slope = (y2 - y1)/(x2 - x1)
y2 and y1 are the final and initial y values
x2 and x1 are the final and initial x values
From the information given,
x1 = 5, y1 = 5
x2 = 9, y2 = 3
Slope = (3 - 5)/(9 - 5) = - 2/4
Slope = - 1/2
four tenths squared minus 19 plus the quantity negative 5 divided by the absolute value of 6.7 minus 9.2 end quantity times 3.81
The expression has a value of -26.46 when evaluated
How to evaluate the expression?From the question, the expression is given as
four tenths squared minus 19 plus the quantity negative 5.......
Rewrite the expression properly as
0.4² - 19 + (-5)/|6.7 - 9.2| * 3.81
Start by evaluating the exponent
So, we have
0.16 - 19 + (-5)/|6.7 - 9.2| * 3.81
Remove the expression in the bracket
0.16 - 19 - 5/|6.7 - 9.2| * 3.81
So, we have
0.16 - 19 - 5/|-2.5| * 3.81
Remove the absolute bracket
0.16 - 19 - 5/2.5 * 3.81
Divide
0.16 - 19 - 2 * 3.81
Evaluate the products
0.16 - 19 - 7.62
So, we have
-26.46
Hence, the value of the expressions is -26.46
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The table below shows the average price of a Miami Marlins baseball ticket between 2006 and 2021.
Ticket price as a function of time. If you write the number [tex]2040[/tex] where you see [tex]x[/tex] in this function and take the value where you see [tex]y[/tex], you will reach the correct answer.
[tex]y=1.83(2040)-2225.5[/tex][tex]y=1507.7[/tex]