Let R be the length of the red ribon and let I be the length of the indigo ribbon. We have that the red ribbon is 6 1/4 inches long, then:
[tex]R=6\frac{1}{4}=\frac{25}{4}[/tex]Then, the indigo ribbon is 6 1/4 inches longer than the red ribbon. Then we have:
[tex]I=R+6\frac{1}{4}[/tex]therefore:
[tex]I=\frac{25}{4}+\frac{25}{4}=\frac{50}{4}=\frac{25}{2}=12\frac{1}{2}[/tex]finally, we have that the indigo ribbon is 12 1/2 inches long
use geometric relationship to develop the sequence represented in the table
The first figure has 3 tiles
The second figure has 8 tiles
The third figure has 15 tiles
The 4th figure has 24 tiles
The 5th figure has 35 tiles
The 6th figure has 48 tiles
Each time we increased row and column
So the rule is
a(n) = n(n + 2)
Let us use the rule to find figure 46
n = 46
[tex]a_{46}=46(46+2)=2208[/tex]The number of tiles in figure 46 is 2208
Segment EF is rotated 90° clockwise around the origin and then translated by (-6, y + 7).
The resulting segment E" F" has coordinates E" (-4, 5), F"(-1,-2).
What are the coordinates of the segment EF?
does anyone know this??
Answer:
E = 2,2 F = 5,-9
Step-by-step explanation:
First, you have to add (6, -7) to both coordinates (that being (-4,5)(-1,-2)
This results in E = 2,-2 and F = -5,-9
Next, you need to rotate both coordinates 90 counterclockwise, resulting in: E being (2,-2) and F being (5,-9)
Hope this helped!
Which is the factored form of 3a2 - 24a + 48?а. (За — 8)(а — 6)b. 3a - 4)(a 4)c. (3a - 16)(a − 3)d. 3( -8)(a -8)
Ok, so:
We're going to factor this expression:
3a² - 24a + 48
First of all, we multiply and divide by 3 all the expression, like this:
3(3a² - 24a + 48) / 3
Now, we can rewrite this to a new form:
( (3a)² - 24(3a) + 144) / 3
Then, we have to find two numbers, whose sum is equal to -24 and its multiplication is 144.
And also we distribute:
((3a - 12 ) ( 3a - 12 )) / 3
Notice that the numbers we're going to find should be inside the brackets.
So, these numbers are -12 and -12.
Now, we factor the number 3 in the expression:
(3(a-4)*3(a-4))/3
And we can cancel one "3".
Therefore, the factored form will be: 3 (a - 4) (a - 4)
So, the answer is B.
Find an angle with θ with 0∘ < θ < 360∘ that has the same :
Sine as 220∘ : θ = _______ degrees
Cosine as 220∘ : θ = _______ degrees
The complete trigonometry ratios are sin(220) = -sin(40) and cos(220) = cos(140) and the angles are 40 and 220 degrees
How to determine the measure of the angles?Angle 1
The trigonometry ratio of the angle is given as
sin(220)
Expand the above expression
sin(220) = sin(180 + 40)
Apply the sine rule
sin(220) = sin(180)cos(40) + cos(180)sin(40)
Evaluate the ratios
sin(220) = 0 x cos(40) - sin(40)
So, we have
sin(220) = - sin(40)
So, the measure of the angle is 40 degrees
Angle 2
The trigonometry ratio of the angle is given as
cos(220)
Expand the above expression
cos(220) = cos(360 - 140)
Apply the cosine rule
cos(220) = cos(360)cos(140) + sin(140)sin(360)
Evaluate the ratios
cos(220) = 1 x cos(140) + sin(140) x 0
So, we have
cos(220) = cos(140)
So, the measure of the angle is 140 degrees
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Bobby says the dilation can be represented by (1\3X, 1,\3Y)Betty says the dilation can be represented by (3X, 3Y)who is correct and why?
Bobby is right because the measurements were made smaller so the dilation factor must be a number less than 1, and 1/3 is less than 1
Can I Plss get some help I got stuck I don’t know how to find x
Using Sine of angles to evaluate for x
The formula is,
[tex]sin\theta=\frac{Opposite}{Hypotenuse}[/tex]Given:
[tex]\begin{gathered} Opposite=x \\ Hypotenuse=19 \\ \theta=21^0 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} sin21^0=\frac{x}{19} \\ \therefore x=19\times sin21^0 \end{gathered}[/tex]Simplify
[tex]x=6.80899\approx6.81\text{ \lparen2 decimal places\rparen}[/tex]Hence,
[tex]x=6.81[/tex]A study shows that 28% of the population has high blood pressure. The study also shows that 86% of those who do not have high blood pressure exercise at least 90 minutes per week, while 32% of those with high blood pressure exercise at least 90 minutes per week. Which of the following relative frequency tables could the study provide?
The study can provide relative frequency table 2 (starting from the top)
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. The word per cent means per 100. It is denoted by the symbol “%”.
The total percentage of two or more ratios in a thesame entity is 100. For example, In a population, 28% has HBP (high blood pressure)
This means that number of those that do not have HBP will be 100 - 28 = 72%
86% of those who did not have HBP exercise at least 90 minute per week i.e
86% of no HBP ,exercise >or = 90 = (86/100) × 72 = 62%( nearest whole number)
Those that do exercise <90 minute per week = 72-62= 10%
32% of those with HBP exercise at least 90 minute( >or = 90 minutes) =( 32\100) × 28= 9%( nearest whole number)
Those with HBP and exercise <90= 28- 9= 19%
Therefore Table 2 starting from the top clearly shows this data.
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Classify each Polynomial by degree and number of terms.1. X^3 + 5x 2. X^2 - 2x - 1 3. 5x^4 4. 6x^5 - 3x^2 + 7x + 9 5. -11x - 5 6. 4x^2 + 10 7. 128. 9x^3 - x^2 + 6x - 1]9. -3x^5 + 6x^4 v- 8THESE ARE THE OPTIONS Degree Name using degree 0 Constant 1 Linear 2 quadratic 3 Cubic 4 quartic 5 quintic 6 6th degreeTHESE ARE ALSO THE OTHER OPTIONSTerms NAME USING # OF TERMS1, monomial 2 , binomial3 trinomial4 or more polynomial
The solution to the equation4(x + 2) =3(5-x) is:
ANSWER:
The value of x is 1, that is, the solution of the equation is 1
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]4\cdot(x+2)=3\cdot(5-x)[/tex]Solving for x:
[tex]\begin{gathered} 4x+8=15-3x \\ 4x+3x=15-8 \\ 7x=7 \\ x=\frac{7}{7} \\ x=1 \end{gathered}[/tex]Calculate Sample Variance for the following data collection: 10, 11, 12, 13, 14,18.
The Variance of a set of data is defined as the average of the square of the deviation from the mean.
The first step is to calculate the mean of the data.
[tex]\frac{10+11+12+13+14+18}{6}=13[/tex]Now we take the difference from the mean, square it, and then average the result.
[tex]\frac{(10-13)^2+(11-13^2)+(12-13)^2+(13-13)^2+(14-13)^2+(18-13)^2}{6}[/tex][tex]\Rightarrow\frac{9+4+1+0+1+25}{6}[/tex][tex]\Rightarrow6.67[/tex]Hence, the variance of the data is 6.7 (rounded to the nearest tenth)
Brian is looking to add tile to one wall in his kitchen, each tile is a rectangle that measures
14 inches by 2 inches. The wall that Brian wants to tile is a rectangle that measures
44.25inches by 51 inches. How many bie's will Brian need to cover the wall?
Using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.
What is a rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can also be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.So, tiles needed to cover the wall:
The formula for the area of a rectangle: l × bCalculate the area of a tile as follows:
l × b14 × 228 in²Now, calculate the area of the wall as follows:
l × b44.25 × 512,256.75 in²Then, tiles needed to cover the wall:
2,256.75/2880.59Which means: 80½
Therefore, using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.
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DEF is a right triangle. If FE= 12 and DE= 5, find DF.
Answer:
DF = 13
Explanation:
The Pythagoras theorem says that
[tex]FE^2+ED^2=DF^2[/tex]Now in our case,
FE = 12
ED =
True or false if a set of points all lie on the same plane they are called collinear
We have that a group of points can be:
Coplanar: if they lie in the same plane
Collinear: if they lie in the same line
Answer- False: they are called coplanarWhat is the least common denominator of 1/20 and 7/50
Considering the given fractions
[tex]\frac{1}{20};\frac{7}{50}[/tex]You have to find the least common denominator between the denominators "20" and "50"
For these values, the least common denominator is the least common multiple between both values:
[tex]20\cdot50=100[/tex]So, the least common denominator is 100.
Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible Through (15,5) and (5,15)
Given that the required linepasses through the points (15, 5)and (5, 15).
Find the slope of the line using teo-point formula.
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{15-5}{5-15} \\ =\frac{10}{-10} \\ =-1 \end{gathered}[/tex]Substitute the value of m into theslope-intercept form y = mx+c.
[tex]y=-x+c[/tex]Plug in the point (5, 15)to find c, the y-intercept.
[tex]\begin{gathered} 15=-5+c \\ c=20 \end{gathered}[/tex]Thus, y = -x + 20, which is the required equation of line.
-Зе - 10 - 4Solve and graph the inequality
The given inequality is expressed as
[tex]\begin{gathered} -\text{ 3e - 10 }\leq-4 \\ \end{gathered}[/tex]We would add 10 to both sides of the inequality. It becomes
[tex]\begin{gathered} -\text{ 3e - 10 + 10 }\leq-\text{ 4 + 10} \\ -\text{ 3e }\leq6 \end{gathered}[/tex]We would divide both sides by - 3. This would cause the inequality symbol to reverse. It becomes
[tex]\begin{gathered} \frac{-3e}{-3}\text{ }\ge\frac{6}{-3} \\ e\text{ }\ge-2 \end{gathered}[/tex]The graph would be
The shaded circle at the position of - 2 indicates that- 2 is inclusive
all i need is for question 14 to be answered please help
Given
The path of particle 1 is,
[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]And, the path of second particle is,
[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]To model the path of the two particles in cartesian form and to find whether, the two particles collide.
Explanation:
It is given that,
The path of the first particle is,
[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]That implies,
[tex]x=2t-6,\text{ }y=t^2-2t[/tex]Consider,
[tex]\begin{gathered} x=2t-6 \\ 2t=x+6 \\ t=\frac{x+6}{2} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} y=(\frac{x+6}{2})^2-2(\frac{x+6}{2}) \\ y=\frac{x^2+12x+36}{4}-\frac{2x+12}{2} \\ y=\frac{x^2+12x+36-2(2x+12)}{4} \\ y=\frac{x^2+12x+36-4x-24}{4} \\ y=\frac{x^2+8x+12}{4}\text{ \_\_\_\_\_\_\_\_\_\_\lparen1\rparen} \end{gathered}[/tex]Also, the path of second particle is,
[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]That implies,
[tex]x=\sqrt{t+6},\text{ }y=-3+2t[/tex]Consider,
[tex]\begin{gathered} y=-3+2t \\ 2t=y+3 \\ t=\frac{y+3}{2} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} x=\sqrt{t+6} \\ \Rightarrow x^2=(t+6) \\ \Rightarrow x^2=(\frac{y+3}{2})+6 \\ \Rightarrow x^2=\frac{y+3+12}{2} \\ \Rightarrow2x^2=y+15 \\ \Rightarrow y=2x^2-15\text{ \_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]Hence, y=(x^2+8x+12)/4, y=2x^2-15 are the paths of the two particles respectively.
The graph of the path of the two particles are,
From, this it is clear that the particle collide at the points (-2.686, -0.568) and (3.829, 14.324).
what is the driving distance between the police station and Art Museum
First, locate the coordinate points (x,y) of each place, by looking at the graph:
Police station = (0,-4)
Art museum = (6,1)
Apply the distance formula:
[tex]D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Replacing:
[tex]D=\sqrt[]{(6-0)^2+(1-(-4))^2}=\sqrt[]{6^2+5^2}=\sqrt[]{36+25}=\sqrt[]{61}=7.81[/tex](I don't know if there are tutors here right now at this time but it's worth a try.) Please help me I really really don't understand this, it's going to take me a while to understand this. X(
by the distributive law x(y+z)=zy+xz, we have
[tex]\begin{gathered} 3b+3(5)=4(2b)-4(5) \\ 3b+15=8b-20 \end{gathered}[/tex]Then we use the properties of inequalities, we can switch both sides, and if we add or multiply something on both sides the equality remains
[tex]\begin{gathered} 3b+15=8b-20 \\ \end{gathered}[/tex]we want the variables and the numbers without variables to be in different side, so, first we add 20 to both sides, note that the -20 will be cancelled
[tex]\begin{gathered} 3b+15+20\text{ = 8b-20+20} \\ 3b+15+20=8b \end{gathered}[/tex]we want to left all the numbers with variable on the right side so we substract 3b (add -3b) to both sides. Same as before, the 3b will be cancellated (we can change the order in the sum)
[tex]\begin{gathered} -3b+3b+15+20=-3b+8b \\ 15+20=8b-3b \end{gathered}[/tex]of course, you're welcome
I was asking if you have understood my explanation so far
tell me
it doesn't matter the order, in fact, when you get used to the method you can work with both at the same time
any other question?
yes, you could substrac 3b first
For example
[tex]\begin{gathered} 2+3x=6-x \\ 2+3x+x=6-x+x \\ 2+3x+x=6 \\ -2+2+3x+x=-2+6 \\ 3x+x=6-2 \\ 4x=4 \\ \end{gathered}[/tex]sadly I will need to leave since my shift is over, but if you ask another question one of my partners will help you
Have a nice evening!!!!
then we add like terms and switch both sides
[tex]5b=35[/tex]And then we multiply by 1/5 both sides
[tex]\begin{gathered} 5\frac{1}{5}b=\frac{35}{5} \\ b=\frac{35}{5} \\ b=7 \end{gathered}[/tex]{x|x ≤ - 6}
Write written interval motion and graph the interval
The inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).
What exactly is interval notation?
The number line's left to right location in the solution is indicated using interval notation (i.e., which part of the number line is shaded). Endpoints that are part of the solution are denoted by parentheses, while those that are not are denoted by brackets.For instance, the expressions -3x2, [-3,2], and xR|-3x2 denote that x is between -3 and 2 and might be either endpoint.Interval Notation x<-6. x<−6 x < - 6.
Convert the inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).
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Jackie planted a tomato plant that was 4 inches tall. The plant grew by 150% of its height after 3 weeks. How tall was the plant after the 3 weeks?
1) Problems like these, we can solve by writing an equation.
2)Since that tomato plant grew 150% after three weeks we can write the following
[tex]\begin{gathered} 4\cdot(1+1.5)= \\ 4(2.5)=10 \\ \end{gathered}[/tex]Note that in the parentheses we have the factor of growth. Since it's 150% we can add to 1 and write 1 +1.5=2.5
3) Thus, the answer is:
[tex]10\:inches[/tex]What is the answer to 6x + =5
Answer:
x = 5/6 or x = 0.83
Step-by-step explanation:
6x + =5
6x + 0 = 5
6x = 5
6x/6 = 5/6
x = 5/6 or x = 0.83
An online bookstore is having a sale. All paperback books are $6.00 with a flat shipping fee of $1.25. you purchase "b" booms and your total is "c". What is the independent variable?$6.00"c" cost"b" books$1.25
Let:
c = total
a = cost of each book
w = flat shipping fee
Therefore, the total is given by:
[tex]c=ab+w[/tex]where:
b = number of books
[tex]c=6x+1.25[/tex]The independent variable is:
"b" books
Create three different proportions that can be used to find BC in the figure above. At least one proportion must include AC as one of the measures.
We are given two similar triangles which are;
[tex]\begin{gathered} \Delta AEB\text{ and }\Delta ADC \\ \end{gathered}[/tex]Note that the sides are not equal, but similar in the sense that the ratio of two sides in one triangle is equal to that of the two corresponding sides in the other triangle.
To calculate the length of side BC, we can use any of the following ratios (proportions);
[tex]\frac{AE}{ED}=\frac{AB}{BC}[/tex][tex]\frac{AB}{AC}=\frac{AE}{AD}[/tex][tex]\frac{AE}{AB}=\frac{AD}{AC}[/tex]Using the first ratio as stated above, we shall have;
[tex]\begin{gathered} \frac{AE}{ED}=\frac{AB}{BC} \\ \frac{8}{5}=\frac{6.5}{BC} \end{gathered}[/tex]Next we cross multiply and we have;
[tex]\begin{gathered} BC=\frac{6.5\times5}{8} \\ BC=4.0625 \end{gathered}[/tex]ANSWER:
[tex]BC=4.0625[/tex]evaluate B-( - 1/8) + c where b =2 and c=- 7/4
Answer: 3/8
Step-by-step explanation:
Given:
[tex]B-(-\frac{1}{8} )+c[/tex]
replace variables with their given values: b = 2 and C = 7/4
[tex]2-(-\frac{1}{8})+\frac{-7}{4}[/tex]
to make subtracting and addition easier, make each number has the same common denominator.
[tex]\frac{16}{8} -(-\frac{1}{8})+(\frac{-14}{8})[/tex]
Finally, solve equation.
***remember that subtracting a negative is the same as just adding and adding by a negative is the same as simply subtracting.
[tex]\frac{16}{8} -(-\frac{1}{8})+(\frac{-14}{8})=\frac{16}{8} +\frac{1}{8}-\frac{14}{8}[/tex]
= 3/8
Answer:
3/8
Step-by-step explanation:
2 - (-1/8) + (-7/4)
= 17/8 - 7/4
= 17/8 + -7/4
= 3/8
Select the correct answer from each drop-down menu.Glven: W(-1, 1), X(3, 4), Y(6, 0), and Z(2, -3) are the vertices of quadrilateral WXYZ.Prove: WXYZis a square.
ANSWER
all four sides have a length of 5
EXPLANATION
The distance between two points (x₁, y₁) and (x₂, y₂) is,
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Let's find the distance between each pair of points, WX, XY, YX, and WZ,
[tex]WX=\sqrt{(3-(-1))^2+(4-1)^2}=\sqrt{(3+1)^2+(4-1)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]XY=\sqrt{(6-3)^2+(0-4)^2}=\sqrt{(3)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex][tex]YZ=\sqrt{(2-6)^2+(-3-0)^2}=\sqrt{(-4)^2+(-3)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]WZ=\sqrt{(2-(-1))^2+(-3-1)^2}=\sqrt{(2+1)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]Hence, using the distance formula we found that all four sides have a length of 5.
polynomials: classifying, simplifying adding and subtracting polynomials write in standard formplease do minimum steps
41 increased by 4 is what number ?
The statement
41 increased by 4
The word increase mean adding to the given number 41
Hence,
The statement can be expressed as
[tex]41+4[/tex]Simplifying the result gives
[tex]41+4=45[/tex]Therefore, the answer is
[tex]45[/tex]Solve the System of Equations8x + 15y = -1174x + 9y=-75Write your answer as an ordered pair: (x,y)
We have to solve the system of linear equations:
[tex]\begin{gathered} 8x+15y=-117 \\ 4x+9y=-75 \end{gathered}[/tex]We can substract 2 times the second equation for the first equation and solve for y:
[tex]\begin{gathered} (8x+15y)-2(4x+9y)=-117-2(-75) \\ 8x+15y-8x-18y=-117+150 \\ 0x-3y=33 \\ y=\frac{33}{-3} \\ y=-11 \end{gathered}[/tex]Now, we can solve for x:
[tex]\begin{gathered} 4x+9y=-75 \\ 4x+9(-11)=-75 \\ 4x-99=-75 \\ 4x=-75+99 \\ 4x=24 \\ x=\frac{24}{4} \\ x=6 \end{gathered}[/tex]Answer: (x,y)=(6,-11)
need help with this problem, find the length of the darkened arc. C is the center of the circle
Notice that the central angle measures 138 degrees, We have a property of the circle that says that the measure of a central angle is equal to the arc between its sides.
Therefore, the arc measures 138 degrees
