Problem
The perimeter of a rectangle is less than 10 inches. The length is x and the width is x - 5. If the solution is x<5, ThEn the length is less than 5. Is this viable solution.
Solution
For this case the perimete rof a rectangle is given by:
P= 2x+2y
x= lenght y = width
And we also know that y= x-5
And replacing the condition given: P<10 we got:
2x +2y <10
2x +2(x-5)<10
4x -10 >10
And we can rewrite as:
4x >20
x>5
So then the best answer would be:
B. non viable
What is the sum of 1/8+5/16+3/8?
Firsr we have to make sure that all of the enominators are the same , before we can proceed with the addition. We have to convert the fraction so it willl have the same denominator. We will use the greatest denominator, 16.
[tex]\frac{1}{8}=\frac{\text{?}}{16}[/tex]We can do that by cross multiplication,
[tex]\begin{gathered} \frac{1\cdot16}{8}=\text{?} \\ \questeq2 \\ \end{gathered}[/tex]Thus,
[tex]\frac{1}{8}=\frac{2}{16}[/tex]We, will do the same for 3/8,
[tex]\begin{gathered} \frac{3}{8}=\frac{?}{16} \\ \frac{3\cdot16}{8}=\frac{48}{8}=6 \\ \end{gathered}[/tex]Thus,
[tex]\frac{3}{8}=\frac{6}{16}[/tex]Now that we have the same denominator, we can proceed with additiion.
[tex]\frac{2}{16}+\frac{5}{16}+\frac{6}{16}=\text{?}[/tex]In adding fractions , we just have to add the numerator and copy the common denominator.
[tex]\frac{2}{16}+\frac{5}{16}+\frac{6}{16}=\frac{2+5+6_{}}{16}=\frac{13}{16}[/tex]Answer:
[tex]\frac{13}{16}[/tex]Need help Which expression is equivalent to the given expression?(ab^2)^3/b^OA.a3/bOB.a3boc.a4/bOD.a3
Given the expression:
[tex]\frac{(ab^2)^3}{b^5}[/tex]We will use the following rules to modify the given expression:
[tex]\begin{gathered} (a^{m)n}=a^{mn} \\ \frac{a^m}{a^n}=a^{m-n} \end{gathered}[/tex]So, the answer will be as follows:
[tex]\frac{(ab^2)^3}{b^5}=\frac{a^3b^6}{b^5}=a^3b^{6-5}=a^3b[/tex]So, the answer will be option ⇒ B. a³b
the temperature at 3pm was 65 degrees it dropped 21 degrees by 7 pm what was the temperature at 7pm
Given:
it is given that the temperature at 3pm was 65 degrees it dropped 21 degrees by 7 pm.
Solution:
Now, the temperature at 7 pm will be
[tex]65-21=44[/tex]So, temperature at 7 pm is 44 degree.
Iif it cost 950 on my monthly cost for housing what is my yearly cost?
Firstly
cost per month = 950
12 months make a year
Yearly cost of housing = 12 x 950
= 11400
4 ). Peter went to a bookstore to buy a pen and a binder. He used three- tenths of his money to pay the pen , while the rest of his money was used to pay the binder . the binder costs P64 more than the pen , what was the total price that Peter paid in the bookstore?
The total price that Peter paid in the bookstore is P91.43.
What is the total price?The first step is to determine the fraction of the amount that Peter has that he spent on the binder.
Fraction spent on a binder = 1 - fraction spent on pen
Fraction spent on a binder = 1 - 3/10
Fraction spent on a binder = 7/10
The next step is to divide the cost of the binder by the fraction spent on the binder.
Total price that Peter paid in the bookstore = price of the binder /fraction spent on the binder
Total price that Peter paid in the bookstore = P64 ÷ 7/10
Total price that Peter paid in the bookstore = P64 X 10/7 = P91.43
To learn more about cost, please check: https://brainly.com/question/14145412
#SPJ1
3. Find the surface area of each object to the nearest tenth of a square unit. d=2.5 cm b) d=0.003 m 16cm wooden rod 16 m flag pole 62 MHD
The formula for the surface area of a cylinder is given:
[tex]A=2\cdot\pi\cdot r\cdot h+2\cdot\pi\cdot r^2[/tex]then, since the information given is a diameter, rewrite the expression using the diameter.
[tex]\begin{gathered} D=2\cdot r \\ r=\frac{D}{2} \\ \text{then, } \\ A=D\cdot\pi\cdot h+2\cdot\pi\cdot(\frac{D}{2})^2 \end{gathered}[/tex]Replace with the data given
[tex]\begin{gathered} A=(2.5)\cdot(\pi)\cdot(16)+2\cdot\pi\cdot(\frac{2.5}{2})^2 \\ A=40\pi+3.125\pi \\ A=43.125\pi \end{gathered}[/tex]Change the following expression to radical notation: 5x^1/9
To convert exponential to radical expression and vice versa, we follow the pattern below:
[tex]ab^{\frac{x}{n}}=a\sqrt[n]{b^x}^{}[/tex]In the given term in the question, a = 5, b = x, n = 9, and x = 1. Let's plug these values into the radical form shown above.
The radical form of the given term is:
[tex]5\sqrt[9]{x}[/tex]The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).202,198,194,...Find the 37th term.
The first 3 terms of the sequence are 202, 198, 194
Since 198 - 202 = -4
Since 194 - 198 = -4, then
The sequence is Arithmetic and decreases by 4
The rule of the arithmetic sequence is
[tex]a_n=a+(n-1)d[/tex]a is the first term
d is the common difference
n is the position of the term
Since the first term is 202, then
a = 202
Since the common difference is -4, then
d = -4
Since we need to find the 37th term, then
n = 37
Substitute them in the rule above
[tex]\begin{gathered} a_{37}=202+(37-1)(-4) \\ a_{37}=202+(36)(-4) \\ a_{37}=202-144 \\ a_{37}=58_{} \end{gathered}[/tex]The 37th term is 58
g(x)=4x^2+3 is the function g even odd or neither? prove it
Answer:
Even
Step-by-step explanation:
A function is called even if, for all values of x, f(-x) = f(x).
A function is called odd if, for all values of x, f(-x) = -f(x).
If none of these equalities is satisfied, the function is neither even nor odd.
In this question:
g(x) = 4x² + 3
g(-x) = 4(-x)² + 3 = 4x² + 3
Since g(-x) = g(x), the function g is even.
In IJK, the measure of K=90 degrees, JI=53, IK=45, and KJ=28, What ratio represents the sine of I?
The given triangle is a right angle triangle. The diagram is shown below.
From the triangle, considering angle I as the reference angle,
hypotenuse = JI = 53
adjacent side = IK = 45
opposite side = KJ = 28
To find Sin I, we would apply the Sine trigonometric ratio which is expressed as
Sin # = opposite side/hypotenuse
Thus,
Sin I = 28/53
Find the coordinates of the other endpoint of the segment, given its midpoint and one endmidpoint (1,-1), endpoint (3,8)
The midpoint (a, b) = (1, -1)
One endpoint, (x₁, y₁) = (3, 8)
The other endpoint, (x₂, y₂) = ?
Using the formula for midpoint and solving for the missing parameters
[tex]\begin{gathered} a=\frac{x_1+x_2}{2} \\ \\ 1=\frac{3+x_2}{2} \\ \\ 2=3+x_2 \\ \\ x_2=2-3 \\ \\ x_2=-1 \end{gathered}[/tex][tex]\begin{gathered} b=\frac{y_1+y_2}{2} \\ \\ -1=\frac{8+y_2}{2} \\ \\ -2=8+y_2 \\ \\ y_2=-2-8 \\ \\ y_2=-10 \end{gathered}[/tex]The coordinates of the other endpoint = (-1, -10)
The 8 foot diameter circular table has a 4 foot wide extension.1. What is the total area with the extension?2. How does the area compare to the area o4 ft.O8 ft. table with extension10 ft. table
1.- Area
[tex]\begin{gathered} \text{Area of the circle = 3.14 x (4)}^2 \\ \text{Area of the circle = 50.24 ft}^2 \end{gathered}[/tex]2.- Area of the extended table
Area = 50.24 + (8 x 4)
Area = 50.24 + 32
Area = 82.24 ft^2
Second question
Area = 3.14 x (5)^2
Area = 25 x 3.14
Area = 78.5 ft^2
The area of the larger circle is smaller than the area of the table with the extension.
Rectangle ABCD is shown on the grid.What is the area of rectangle ABCD in square units?O 3V17 square units6B|(313)06/17 square units2417 square unitsO 34 square units-5.53.234G21.3C (1.-5)Mark this and returnSave and ExitNextSubmit
The rectangle is:
To find the area of this rectangle, we need to find the distances of the two different sides of the rectangle. We know that the area of a rectangle is given by:
[tex]A_{\text{rectangle}}=w\cdot l_{}[/tex]Then, we need to find the distance between two points for the width, that is, it could be the distance between points C and D (segment CD) or segment AB.
To find the length, we need to find the distance of the segment AD or the distance of the segment BC.
After finding them, we need to multiply the result for w and l, and this product will be the area of the rectangle.
Finding WWe need to apply the formula for the distance between two points:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]A(-1, 4) ---> x1 = -1, y1 = 4
B(3, 3) ---> x2 = 3, y2 = 3
Then, we have:
[tex]d_{AB}=\sqrt[]{(3-(-1))^2+(3-4)^2}=\sqrt[]{(3+1)^2+(-1)^2}=\sqrt[]{(4)^2+(-1)^2}=\sqrt[]{16+1}[/tex]Therefore, this distance, which is w, is equal to:
[tex]d_{AB}=w=\sqrt[]{17}[/tex]Finding LWe can apply the same procedure to find l. We have that:
B(3,3) ---> x1 = 3, y1 = 3
C(1, -5) ---> x2 = 1, y2 = -5
Then, this distance, which is also l is:
[tex]d_{BC}=l=\sqrt[]{(1-3)^2+(-5-3)^2}=\sqrt[]{(-2)^2+(-8)^2}=\sqrt[]{4+64}=\sqrt[]{68}[/tex]Area of the Rectangle ABCDThe area is given by the product of w and l. Then, we have:
[tex]A_{\text{rectangle}}=w\cdot l=\sqrt[]{17}\cdot\sqrt[]{68}[/tex]We know that the factors of 68 are:
[tex]68=2^2\cdot17[/tex]Then, we can rewrite the area as follows:
[tex]A_{\text{rectangle}}=\sqrt[]{17}\cdot\sqrt[]{2^2\cdot17}=\sqrt[]{17}\cdot2\cdot\sqrt[]{17}=2\cdot\sqrt[]{17}\cdot\sqrt[]{17}=2\cdot(17)^{\frac{1}{2}}_{}\cdot(17)^{\frac{1}{2}}[/tex]And, finally, we have:
[tex]A_{\text{rectangle}}=2\cdot(17)^{\frac{1}{2}+\frac{1}{2}}=2\cdot17^1=34\Rightarrow A_{rec\tan gle}=34u^2[/tex]In summary, the area of the rectangle ABCD is equal to 34 square units (last option).
The graph of the absolute value function y = -a| x | is reflected over thex-axisy-axisy = xy = -x
When there is - sign multiplying the absolute value, accompanied by any constant, the graph is reflected over the x-axis. You can confirm this by putting some points in the cartesian plane and plotting them. Therefore, the correct answer is x-axis
Josh and Daniel each want to save $600 to attend a sports camp. Josh has saved 60% ofthe amount. Daniel has saved $320. Who has saved more money? How much more?
The total amount to save is $600
Josh saved 60%. This is the same as below
[tex]\begin{gathered} 60\text{ \% of \$600} \\ =\frac{60}{100}\times600 \\ =\frac{36000}{100} \\ =360 \end{gathered}[/tex][tex]\begin{gathered} \text{ 60\% } \\ =\frac{60}{100}=\frac{360}{600} \end{gathered}[/tex]Josh has saved $360.
Daniel has saved $320
It can be observed that $360 is more than $320, so Josh saved more money
The difference tells how much more
[tex]\begin{gathered} \text{ \$360 - \$320} \\ =\text{ \$40} \end{gathered}[/tex]Hence,
1. 60/100= x/600
2. Multiply both sides by 600
3. Josh has saved $360
4. Josh saved more money. Josh saved $40 more than Daniel
Determine whether ACDE is similar to AFGHi Answerby i AnswerNoYesAngles not congruentAA similaritySides not proportionalSSS similaritySAS similarity
Given
Graph of triangles
Procedure
CDE to FGH
[tex]\frac{DE}{GH}=\frac{35}{24}=1.4583[/tex][tex]\frac{DC}{FH}=\frac{28}{20}=1.4[/tex][tex]\frac{CE}{GF}=\frac{21}{16}=1.3125[/tex]Answer NO
SIDES NOT PROPORTIONAL
show the stepsHow do the graphs of y=1/x and y = 5/(x+6) compare?
• Slightly shifted up
,• Horizontally translated to the left 6 units
1) Consider this:
[tex]y=\frac{1}{x}[/tex]This is the parent function from the familiar of rational functions.
2) Note that on the other hand, the function below:
[tex]y=\frac{5}{x+6}[/tex]This is a transformed function from the first one. Take a look at the graph with both functions plotted:
In Rational functions the greater the numerator the farther from the origin is, shifting up the graph and the addition of 6 in the bottom number translates horizontally to the left.
3) Thus, we can state the answer as:
The graph of y=5/(x+6) is:
• Slightly shifted up
,• Horizontally translated to the left 6 units
Find the measure of angle DAC if point P is the incenter of triangle AEC.
Given that P is the incenter of the triangle, then angles EAD and DAC are congruent. Therefore, the measure of angle DAC is 33°
How many 1 --liter bottles of water does it take to fill a 16-liter jug?
What is the area of a circle with a radius of 4.6Area:
The formula for the area of a circle with radius R is;
[tex]A=\pi(R^2)[/tex]With R = 4.6 units
[tex]\begin{gathered} A=\pi\times4.6^2 \\ A=66.48\text{ square units.} \end{gathered}[/tex]Therefore the area of the circle is 66.48 square units.
i have a question on one of my assignments i need to do its homework
the initial height is when the number of days is 0 from the graph we can notice is 4Cm
The graph is relationship lineal because is a line
The graph is relationship proportional because if time increases the size also increases
can someone please help me find the area of the following?
Mya, this is the solution:
Let's recall that the formula to solve for the surface area of a cylinder is:
A = 2 * π * r * h + 2 * π * r²
In our exercise, we have:
r = 8 cm
h = 7 cm
In consequence, replacing these values in the formula:
A = 2π * 7 * 8 + 2π * 8²
A = 2π * 56 + 2π * 64
A = 112π + 128π
A = 240π cm²
The correct answer is D. 240π cm²
Complete each equation so that it is true for no values of x
By definition, an equation has no solution when does not exist a value of the variable that makes the equation true.
• In this case, you have this expression on the left side of the first equation:
[tex]3x+6_{}_{}[/tex]Then, knowing part of the right side, you can set up the following:
[tex]3x+6=3(x+1)[/tex]Notice that you need to write a value different from 6, in order to make the equation false, In this case, you cannot complete the missing value with 2, because;
[tex]3\cdot2=6[/tex]Then, having that equation. you can solve it as follows:
[tex]\begin{gathered} 3x+6=3x+3 \\ 3x-3x=3-6 \\ 0=-3\text{ (False)} \end{gathered}[/tex]• Given the second equation that has this left side:
[tex]x-2[/tex]The missing value must be:
Solve for Angle x given: 11x+30=54-5x 4. Od 3
hello
to solve for angle x, let's collect like terms
[tex]11x+30=54-5x[/tex]step 1
collect like terms to do this, we'll take variables of x one side of the eqaution and keep non-variables at the other side
[tex]\begin{gathered} 11x+30=54-5x \\ 11x+5x=54-30 \\ 16x=24 \\ \text{divide both sides by 16} \\ \frac{16x}{16}=\frac{24}{16} \\ x=\frac{24}{16}=\frac{6}{4} \end{gathered}[/tex]plot on a number line . 3| y+4 | >12
3 |y + 4| > 12
| y + 4 | > 12/3 = 4
| y + 4 | > 4
Two solutions:
y + 4 > 4 ==> y > 0
y + 4 < -4 ==> y < -8
how do I show my work for (3 + 1/2) x 14
this is
[tex](3+\frac{1}{2})\times14=(\frac{7}{2})\times14=\frac{98}{2}=49[/tex]If PAJB)= PA). state the relationship between events Aand B.
The condition is:
[tex]P(A\uparrow B)=P(A)[/tex]Then we know that they are overlapping events so is option (D)
Find the quotient and the remainder using the long division method
The question is to evaluate the quotient and remainder of the division using the long division method:
[tex]\frac{-3x^3+13x^2-14x+9}{x-3}[/tex]Step 1: Write out the problem in the long division format
Step 2: Divide the leading term of the dividend by the leading term of the divisor. Write down the calculated result in the upper part of the table. Multiply it by the divisor and subtract the dividend from the obtained result
[tex]\begin{gathered} \frac{-3x^3}{x}=-3x^2 \\ -3x^2(x-3)=-3x^3+9x^2 \end{gathered}[/tex]Step 3: Apply the steps from 2 above to the remainder at the bottom
[tex]\begin{gathered} \frac{4x^2}{x}=4x \\ 4x(x-3)=4x^2-12x \end{gathered}[/tex]Step 4: Apply the steps from 3 above
[tex]\begin{gathered} \frac{-2x}{x}=-2 \\ -2(x-3)=-2x+6 \end{gathered}[/tex]Step 5: Since the degree of the remainder is less than that of the divisor, we are done with the division. The quotient is the polynomial at the top and the remainder is at the bottom
[tex]\frac{-3x^3+13x^2-14x+9}{x-3}=-3x^2+4x-2+\frac{3}{x-3}[/tex]ANSWER
The quotient is:
[tex]-3x^2+4x-2[/tex]The remainder is
[tex]3[/tex]-11. Given points (x, y) and (x2, y2), derive the two-point form of a line. , , , 10. 13. Given that a line is parallel to the x-axis through (x, y), derive the parallel to x-axis form a line.
11. Given the two points (x1, y1) & (x2, y2) we will have the following line and we derivate it:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]y-y_1=m(x-x_1)\Rightarrow y=mx-mx_1+y_1[/tex]It's derivative is:
[tex]\frac{\delta y}{\delta x}=m=\frac{y_2-y_1}{x_2-x_1}[/tex]This is since the derivative of constants is 0 and the only variable accompanied m. This is proof that the derivative of a function can be interpreted as the slope of the function at that point.
13. If we have that the line is parallel to the x-axis and passes through the point (x1, y1), we will have that the line is a constant function, so when we derivate no matter the point, it will be equal to 0.
That is:
[tex]y=x_1[/tex][tex]\frac{\delta y}{\delta x}=0[/tex]***Explanation:
point 11:
Since we are given two points (x1, y1) & (x2, y2), we will always have that the slope of the line that passes through those points will always have the form:
The decay of a radioactive substance is given byA = 200(1/2) t/10. Which answer is an equivalent equationfor the decay that shows the approximate amount of/decayin 4 years?
The decay of a radioactive substance is given by
A = 200(1/2) t/10.
The equivalent equation for the decay that shows the approximate amount of decay in 4 years
Hence the correct option that approximately amounts to decay in 4years is
[tex]A=151.57(0.933)^{t-4}[/tex]Option C is the correct answer cause it matches the red image