SOLUTION
We want to find which of the following values makes the inequality
x ≥ −14 to be true.
This inequality means that x is equal to -14 or greater than -14. So the values that make this true are from -14 to more than -14
-24 is less than -14 so it is not among these values. -16 is also less than -14, so it is not among these numbers. So the numbers that fall under this are
-14, 5.3, 12, and 0.
Hence the answers are b, c, d, f
is 70 foot four string of lights will be attached to the top of 70 ft pole for Holiday display how far from the base of the pole should the end of the string of lights be anchored
Using pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ c=74ft \\ a=70ft \\ b^2=c^2-a^2 \\ b^2=576 \\ b=\sqrt[]{576} \\ b=24ft \end{gathered}[/tex]Answer:
24ft
movement of the progress bar may be uneven because questions can be worth more or less (including zero) dependingMatch each expression on the left with an equivalent expression on the right.√64a5 b6-4a²b√√a-√64ab54ab²a²-64a7b³-8|a³|b² √b
Explanation
let's remember some properties of the exponents and roots
[tex]\begin{gathered} \sqrt{ab}=\sqrt{a}*\sqrt{b} \\ \sqrt[n]{a}\text{ = }a^{\frac{1}{n}} \\ \sqrt[n]{a^m}\text{ = }a^{\frac{m}{n}} \\ a^{m+n}=a^m*a^n \end{gathered}[/tex]so
Step 1
given the first expression on the left
[tex]\begin{gathered} \sqrt[3]{64a^5b^6} \\ hence \\ \sqrt[3]{64a^5b^6\text{ }}\text{ =}\sqrt[3]{64}\sqrt[3]{a^5}\text{ }\sqrt[3]{b^6}=4\sqrt{a^3a^2}\sqrt[3]{(b^2)^3}=4a\sqrt[3]{a^2}*b^2 \\ so \\ \sqrt[3]{64a^5b^6}\text{ =4ab}^2\sqrt[3]{a^2}^ \end{gathered}[/tex]Step 2
second expression
[tex]\begin{gathered} -\sqrt{64a^6b^5} \\ hence \\ -(\sqrt[]{64}\sqrt[]{a^6}\text{ }\sqrt[]{b^5})=-(4a^3\sqrt{b^4b}\text{ \rparen=-}(4a^3b^2\sqrt{b}) \end{gathered}[/tex]so, the full answer is
I hope this helps you
Express (2x – 1)(x + 5) - 1x2as a trinomial in standard form.
The given expression can be expressed in the trinomial in standard form as,
[tex]\begin{gathered} (2x-1)(x+5)-\frac{1}{2}x^2=\lbrack2x(x+5)-1(x+5)\rbrack-\frac{1}{2}x^2 \\ =\lbrack2x^2+10x-x-5\rbrack-\frac{1}{2}x^2 \\ =\lbrack2x^2+9x-5\rbrack-\frac{1}{2}x^2 \\ =\frac{3}{2}x^2+9x-5 \end{gathered}[/tex]Thus, the above expression is the requried trinomial.
A business's total profit in January was $19,540. Since January, the total profit has consistently increased by a rate of 8% each month. Write a function to model the businesses profit over time.
The profit at January = $19,540
RS ll TU, m<5 = (3x-10) and m<3 = (2x + 5)What is m<3?
in this problem we have that
m<5 and m<3 are alternate interior angles
that means
m<5=m<3
substitute teh given values
3x-10=2x+5
solve for x
3x-2x=5+10
x=15
Find the measure of angle 3
m<3=2(15)+5
m<3=35 degreesWhich equation expresses the relationship between the pairs of values of X and why shown in the table below
We are given a table that relates values of "x" and values of "y". To determine which equation expresses the relationship we need to substitute the values of "x" and we should get the values of "y". We will begin with x = 1. For the first equation we have:
[tex]y=3x-2[/tex]Substituting x = 1 we get:
[tex]\begin{gathered} y=3(1)-2 \\ y=3-2 \\ y=1 \end{gathered}[/tex]Therefore, this is a possible solution. Now for the second equation, we get:
[tex]y=2x[/tex]Substituting the value we get:
[tex]\begin{gathered} y=2(1) \\ y=2 \end{gathered}[/tex]We got 2 instead of 1 as shown in the table, therefore, we can discard this equation as a possible solution.
Now, we use the third equation:
[tex]y=2x+1[/tex]Substituting the value we get:
[tex]\begin{gathered} y=2(1)+1 \\ y=2+1 \\ y=3 \end{gathered}[/tex]We got 3 instead of 1, therefore, we can discard this equation as a possible solution.
Now the fourth equation:
[tex]y=x[/tex]Substituting the value we get:
[tex]y=1[/tex]Therefore, this is also a possible solution.
Now we use the value x = 2, we will substitute in the first and fourth equations which are the ones we haven't discarded yet. For the first equation we get:
[tex]\begin{gathered} y=3(2)-2 \\ y=6-2 \\ y=4 \end{gathered}[/tex]Therefore, this is a possible solution. Now for the fourth equation:
[tex]y=2[/tex]We got 2 instead of 4, therefore, this is not a solution, therefore, the right equation must be the first equation. To be sure we can replace the remaining values of "x" and we should get the corresponding values of "y".
l>lo3. A city parking garage charges a flat rate of $3.00 for parking 2 hours or less, and $0.50 per hour for eachadditional hour. Write a linear relation that gives the total charge in terms of additional hours parked.
Answer:
Let h be the number of additional hours parked, then the total charge in dollars is:
[tex]C=3.00+0.50h\text{.}[/tex]Use the center of rotation point C and rotatepoint P clockwise around it 90°. Label the image P'. With point C as a center of rotation also rotate point P 180°. Label this image P".P':__; P'':__
Solution
We have a point P=(a=7,b=6) and we need to rotate around C=(x= 4,y=1)
And we can use the following formula:
We can change the origin and the new coordinates are now:
C (0,0), P= (3 ,5)
Then the rotated point is:
Px' = (5, -3)
And the real value would be:
P' = (5+4, -3+1)= (9,-2)
For the second case the new coordinate is:
Px'' = (-5, -3)
And with the transformation we have:
P'' =(-5+4, -3+1)= (-1, -2)
Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including allanswers in [0, 2x) and indicating the remaining answers by using n to represent any integer. Round your answer to four decimal places, if necessary. If there is nosolution, indicate "No Solution."272cos(x) + 2 = 0
Given the trigonometric equation:
2√2 cos (x) + 2 = 0
We can rewrite it, as:
2√2 cos (x) = - 2
Dividing both sides by two:
√2 cos (x) = - 1
Rationalizing:
cos (x) = - √2/2
Solving for cos(x):
[tex]\begin{gathered} x\text{ = }\frac{3\pi}{4} \\ \\ x\text{ = }\frac{5\pi}{4} \end{gathered}[/tex]Which equation represents a line that is parallel to y = -4x + 3 and passes through the point (-3, 2)?a. y = -4X – 10b. y = -4x + 2c. y = -4x + 5d. y = 1/4x - 7/2e. y = 1/4x + 11/4
when 2 lines are parallels , have the same slope
the slope of
[tex]y=-4x+3[/tex]is -4 because is the coefficient of x
so I write the general equation of the line and replace the slope
[tex]\begin{gathered} y=mx+b \\ \\ y=-4x+b \end{gathered}[/tex]to find b, I replace the point (-3,2) since this must be fulfilled
so
[tex]2=-4(-3)+b[/tex]and solve b
[tex]\begin{gathered} 2=12+b \\ b=2-12 \\ b=-10 \end{gathered}[/tex]the equation of the parellel line is
[tex]y=-4x-10[/tex]so the right option is A
1) Put these numbers in order from greatest to lea 7/8 0.89 5/8
Solve the fractions to convert it into decimal numbers
[tex]\frac{7}{8}=0.875[/tex][tex]\frac{5}{8}=0.625[/tex]Now, we can order these numbers from greatest to least:
0.89
0.875
0.625
It means the correct order is: 0.89, 7/8, 5/8.
Simplify the expression showing steps 1+4.25n+3/2p-3+(-2p)+5/4n
The given expression is
[tex]1+4.25n+\frac{3}{2}p-3+(-2p)+\frac{5}{4}n[/tex]We have to reduce like terms.
[tex]\begin{gathered} 4.25n+\frac{5}{4}n+\frac{3}{2}p-2p-3+1 \\ 4.25n+1.25n+1.5p-2p-3+1 \\ 5.5n-0.5p-2 \end{gathered}[/tex]Therefore, the simplest form of the given expression is[tex]5.5n-0.5p-2[/tex]I need help I don’t know how to solve this problem using estimates please help
To solve this problem, you will need to approximate the values to the nearest whole dollars.
Hence, 18.79 ecomes $19
2.11 becomes $2
1.92 becomes $1.9
while lastly, 17.28 becomes $17
Hence, we can rewrite the given expression as follows;
$19 + $2 -$2 + $17 = $19 + $17 = $36
Solve a quadratic equation by the square root method and write the solution in radical form simplify the solutions
The quadratic equation is given to be:
[tex]3x^2=36[/tex]Divide both sides by 3:
[tex]\begin{gathered} x^2=\frac{36}{3} \\ x^2=12 \end{gathered}[/tex]Recall the rule:
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]Therefore, we have that:
[tex]x=\pm\sqrt{12}[/tex]Simplifying the radical, we have:
[tex]\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}[/tex]Therefore, the solution is:
[tex]x=2\sqrt{3}\text{ or }-2\sqrt{3}[/tex]send picfind area of figure
we must find the are of the triangle and the area of the half circle and sum them
Triangle
[tex]A_1=\frac{b\times h}{2}[/tex]where b is the base and is 16 because is the diameter of the circle and h is the height 15
so replacing
[tex]\begin{gathered} A_1=\frac{16\times15}{2} \\ \\ A_1=120 \end{gathered}[/tex]the area is 120 cm2
Half circle(area of the circle between 2)
[tex]A_2=\frac{\pi\times r^2}{2}[/tex]where r is the radius 8
[tex]\begin{gathered} A_2=\frac{\pi\times8^2}{2} \\ \\ A_2=32\pi\approx100.5 \end{gathered}[/tex]the area is 100.5 cm2
Total area
[tex]A_T=A_1_{}+A_2^{}[/tex][tex]\begin{gathered} A_T=120+100.5 \\ A_T=220.5 \end{gathered}[/tex]the total area is 220.5cm2
What are the bounds of the solution to the inequality -9 m +2 > -36?
We have the following:
[tex]-9|m+2|\ge-36[/tex]solving for m
[tex]\begin{gathered} -\frac{9}{9}|m+2|\ge-\frac{36}{9} \\ |m+2|\ge-4 \\ m+2\ge-4 \\ m+2\leq4 \\ -4\leq m+2\leq4 \\ -4-2\leq m+2-2\leq4-2 \\ -6\leq m\leq2 \\ \lbrack-6,2\rbrack \end{gathered}[/tex]Danielle Works 40 hours every week she earns $12 per hour part of Danielle's pay stub is shown the numbers on the page that represents our taxes deductions, net income, and gross income for one week.
Answer: OPTION D
Danielle works 40 hours every week and she earns $ 12 per hour
The amount she earned weekly can be calculated as
Gross income = 40 x 12
Gross income =$480
Net income = Gross income - all expenses
Net income is the amount Danielle takes home after all the deduction has been mad
$401 is Danielle's net income because that is the amount she takes home.
what is the pemdas method
EXPLANATION
The Pemdas methd give us the
PEMDAS is the order that you solve a problem.
PEMDAS stands for:
Parenthesis
Exponents
Multiplication and Division
Addition and Subtraction
If you have an equation or expression that you need to solve, you solve it in this order. You do the parenthesis first, then you solve the exponents, then you do the multiplication and division from left to right, and last you do addition and subtraction from left to right.
In the equation
2 + 3 * 5,
first you would do 3 * 5 because multiplication is before addition.
2 + 15
Then you would do the addition to get the answer:
17.
Please give brainliest
the answer answer is red give the step by step by how u get the answer
In order to simplify the following expressions you use the one of the square root properties:
√a√b = √(ab)
5)
√(5n^3)√(20n) = √((5n^3)(20n)) = √(100n^4) = 10n^2
6)
√(8p)√(5p^3) = √((8p)(5p^3)) = √(40p^4) √(4*10p^4) = 2p^2√10
7)
3√(15n^2)√(5n^2) = 3√((15n^2)(5n^2)) = 3√(75n^4) = 3√(25*3n^4) = 15n^2√3
8)
√(3p^3)√(3p) = √((3p^3)(3p)) = √9p^4 = 3p^2
Which equation is equivalent to7x – 2y = 8
7x =2(y+4)
7x-2y-8 and y= 7/2x -4
1) An equivalent number equation is an equation that has the same result on the right side.
In algebra, we can have equivalent equations by algebraic manipulation.
So for that:
7x-2y=8
We can say that, for example
7x =2(y+4) Factoring out 2y and 4
7x-2y-8=0 Placing the 8 on the left side of the equation
and
y= 7/2x -4 Writing that on the Standard linear equation form, dividing by 2
are Equivalent equations.
write a linear equation with the coordinates of (-4,4) and (4,-2)
The line equation is typically represented as
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-4}{4+4}=\frac{-6}{8}=-\frac{3}{4} \end{gathered}[/tex]Let find b
[tex]\begin{gathered} y=mx+b \\ 4=-\frac{3}{4}(-4)+b \\ b=1 \end{gathered}[/tex]The linear equation is
[tex]y=-\frac{3}{4}x+1[/tex]Let S = {1,2,3,...,18,19,20) be the universal set.Let sets A and B be subsets of S, where:Set A = {2, 3, 4, 6, 11, 13, 15, 16, 19, 20}Set B = {1, 2, 3, 4, 5, 6, 10, 11, 14, 16, 17, 18, 19}LIST the elements in Set A and Set B: {LIST the elements in Set A or Set B: {Enter the elements as a list, separated by commas. If the result is the empty set, enter DNEYou may want to draw a Venn Diagram to help answer this question.
a) Set (A and B) = {2, 3, 4, 6, 11, 16, 19}
b) Set (A or B) = {1, 2, 3, 4, 5, 6, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20}
Explanation:Given:
S = {1,2,3, ... ,18,19,20) be the universal set
Set A = {2, 3, 4, 6, 11, 13, 15, 16, 19, 20}
Set B = {1, 2, 3, 4, 5, 6, 10, 11, 14, 16, 17, 18, 19}
To find:
a) the elements in Set A and Set B
b) the elements in set A or set B
a) Elements in set A and set B will include the numbers common to both sets
Set (A and B) = {2, 3, 4, 6, 11, 16, 19}
b) Elements in set A or set B will include the union of elements in set A and elements in set and any repetition will be written once
Set (A or B) = {1, 2, 3, 4, 5, 6, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20}
A mom took her daughter shopping with her allowance. Together, they spent $20. The mom spent 8 more than 4 times the amount of the daughter. Find the amount they each spent. x is the daughter's spending and y is the mother's spending
Given that, they spent a total of 20 dollars.
Therefore, the first equation becomes,
[tex]x+y=20[/tex]Also, mom spent 8 more than 4 times the amount of daughter.
Therefore, the second equation becomes,
[tex]y=4x+8[/tex]Substitute 4x+8 for y in the equation x+y=20 implies,
[tex]\begin{gathered} x+4x+8=20 \\ 5x=12 \\ x=2.4 \end{gathered}[/tex]Use the equation x+y=20 to find the value of y.
[tex]\begin{gathered} y=20-x \\ y=20-2.4 \\ y=17.6 \end{gathered}[/tex]Therefore, daughter's spending is 2.4 dollars and mom's spending is 17.6 dollars
A manufacturing company performs a quality control analysis on the ceramic tile it produces. Suppose a batch of 22 tiles has 6 defective tiles. If 5 tiles are sampled at random, what isthe probability that exactly 1 of the sampled tiles is defective?How many ways can 5 tiles be selected from 22 tiles?ways(Type a whole number)Help Me Solve ThisView an ExampleGet More HelpClear AllCheck Answer
ANSWER:
The probability is 0.4147
26334 ways
STEP-BY-STEP EXPLANATION:
The first thing is to calculate numbers of ways of choosing 5 out of 22 (without replacement), just like this:
[tex]\begin{gathered} \text{nCr}=\frac{n!}{r!\cdot(n-r)!} \\ \text{ replacing} \\ 22C5=\frac{22!}{5!\cdot(22-5)!}=26334 \end{gathered}[/tex]Out of 22 tiles, 6 are defective and remaining 16 are not defective.
Let a = number of defective among randomly selected 5 tiles.
Here a follows hypergeometric distribution with parameters N = 22, k = 6, n = 5.
PMF is given: P(a = k), in this case:
[tex]P(a=1)=\frac{(\text{choose 1 of 6 defective)}\cdot(\text{choose 4 of 16 not defective) }}{(\text{select 5 from 22 total)}}[/tex]replacing:
[tex]P(a=1)=\frac{\frac{6!}{1!\cdot(6-1)!}\cdot\frac{16!}{4!\cdot(16-4)!}}{\frac{22!}{5!\cdot(22-5)!}}=\frac{6\cdot1820}{26334}=0.4147[/tex]If 1 mile equals 1,760 yards, then how many miles are in 10,208 yards?
Answer:
5.8 miles.
Step-by-step explanation:
You simply divide 10,208 by 1,760. Then you get 5.8 miles
10,208/1,760
5.8
Pls mark Brainliest with the crown
two point four divided by eighty
Given:
[tex]\frac{2.4}{8}[/tex]Solution:
[tex]\begin{gathered} =\frac{2.4}{8} \\ =\frac{24}{80} \\ =0.3 \end{gathered}[/tex]value of 2.4 divided by 8 is 0.3.
-1-2-51-68-9State the domain and the range of the function shown in the mappingdiagram.
The first column in a mapping diagram represents the domain of a function and the second column represents the range of the function.
The domain of the function is {1, -5,-6, -9}
The probability of meeting a random person who has the same birthday as you is365• whichis approximately 0.27%. What is the probability that the 25th person you meet is the firstperson who has the same birthday as you?00.27%00.14%00.25%00.03%
Given:
The same birthday probability is
[tex]\begin{gathered} =\frac{1}{365} \\ \\ =0.27\% \end{gathered}[/tex]Find:-
Person who has the same birthday
Explanation-:
The probability of meeting a random person who has the same birthday is:
[tex]=\frac{1}{365}[/tex]Probability of meeting a random person who does not has same birthday as you
[tex]\begin{gathered} =1-\frac{1}{365} \\ \\ =\frac{365-1}{365} \\ \\ =\frac{364}{365} \end{gathered}[/tex]The required probability that the 25th person you meet is the first person who has the same birthday as
[tex]\begin{gathered} =\text{ Probability that the first 24 persons we meet did not have same birthday \rparen}\times(\text{ probability that the first 25 person we meet has same birthday\rparen} \\ \end{gathered}[/tex]Therefor,
[tex]\begin{gathered} P=(\frac{364}{365})^{24}\times\frac{1}{365} \\ \\ =(0.9972)^{24}\times0.27 \\ \\ =0.9362\times0.27 \\ \\ =0.25\% \end{gathered}[/tex]Find the surface area of the cylinder and round to the nearest tenth. (It is recommended that you use the # button on your calculator) (Note: Remember the radius is half of the diameter.) 2 ft. 2 ft. Surface Area ft2
To answer this question, we need to know the formula to find the surface area of a cylinder:
[tex]SA=2\pi rh+2\pi r^2[/tex]The first part of the formula corresponds to the lateral part of the cylinder. The other part represents the area of the two circles in the cylinder.
Then, we have:
r = D/2 ---> D = 2ft ---> r = 2ft /2 ---> r = 1ft.
h = 2ft
Now, we can apply the above formula:
[tex]SA_{\text{cyl}}=2\cdot\pi\cdot1\cdot2+2\cdot\pi\cdot(1)^2=4\pi ft^2+2\pi ft^2=6\pi ft^2=18.8495559215ft^2[/tex]If we round this area to the nearest tenth, we have that the area is equal to 18.8 sq. feet.
Given square ABCD, find the following measures.АBEraDGiven thin the diOm AED=hij in blankmZACD= fill in blankhis...뿔g=45dl.
The angles of the four corners of the square are right angles, which means that they have a measure of 90º.
Each diagonal bisects the corner angles, this means that the diagonals divide the 90º angles into two equal angles:
[tex]\frac{90}{2}=45º[/tex]Each resulting angle measures 45º
The diagonals bisect each other so that they form 4 isosceles triangles.
The diagonals of the square are perpendicular, this means that the angles formed when they intersect each other are right angles. So the 4 central angles are right angles.
So you can conclude that the angles have the following measures:
∠AED= 90º
∠ACD= 45º