We have that Alex filled
[tex]\frac{2}{7}\text{ and }\frac{4}{7}[/tex]of his binder.
We just add both fractions.
Then, in total he filled:
[tex]\frac{2}{7}+\frac{4}{7}[/tex]Since both fractions have the same denominator, 7, we add them just by adding the numerators:
[tex]\frac{2}{7}+\frac{4}{7}=\frac{2+4}{7}=\frac{6}{7}[/tex]Then, he filled 6/7 of his binder in those two days.
Answer: 6/7
Which of the following ratios is equivalent to1/2?1:21:12:1
The correct equivalent expression for 1/2 is:
1 : 2
Given cos theta= -7/25 and theta lies in quadrant II Find tan 2 theta
Answer:
336/527
Explanation:
If cos θ = -7/25, then we can represent these angle as:
Because -7 is the adjacent side and 25 is the hypotenuse of the triangle.
So, to know what is tan θ, we need to find the value of x. Then, using the Pythagorean theorem, we get that x is equal to:
[tex]\begin{gathered} x=\sqrt[]{25^2-(7)^2} \\ x=\sqrt[]{625-49} \\ x=\sqrt[]{576} \\ x=24 \end{gathered}[/tex]Now, tan θ is equal to:
[tex]\begin{gathered} \tan \theta=\frac{Opposite\text{ side}}{\text{Adjacent side}} \\ \tan \theta=\frac{24}{-7} \\ \tan \theta=-\frac{24}{7} \end{gathered}[/tex]Then, there is a trigonometric identity that says that tan 2θ is equal to:
[tex]undefined[/tex]Find the unit rate:3 tablespoons for 1.5 servings.
Explanation
A unit rate is a rate where the bottom number is 1 (also called a single-unit rate),it can be found using the expression
[tex]\text{unit rate = }\frac{total\text{ amount}}{\text{total el}emets}[/tex]Step 1
Let
total amount = 3 tablespoons
total elements = 1.5 serving, so replacing
[tex]\begin{gathered} \text{unit rate = }\frac{total\text{ amount}}{\text{total el}emets} \\ \text{unit rate =}\frac{3\text{ tablespoons}}{1.5\text{ servings}}=2\text{ tablespoons per serving} \\ \text{unit rate =}2\frac{tablespoon}{\text{serving}} \end{gathered}[/tex]therefore, the answer is
[tex]\text{unit rate =}2\frac{tablespoon}{\text{serving}}[/tex]I hope this helps you
Jonh is building a stage for a school play. The stage is 15 1/2 feet long and 20 feet wide. Select ALL options that represent the area of the stage, in square feet. A. 31/2 X 1/20B. 30/2 X 20 C. 31/2 X 20D. 300E. 310
To solve this problem, recall that the area of a rectangle is given by the following formula:
[tex]A=wide\times length.[/tex]Therefore, the area of the stage is:
[tex](15\frac{1}{2}\times20)ft^2.[/tex]Converting the mixed number to an improper fraction, you get:
[tex]15\frac{1}{2}\times20=\frac{31}{2}\times20.[/tex]Computing the multiplication you get:
[tex]310.[/tex]Answer: [tex]310,\frac{31}{2}\times20.[/tex]simplify the following inequalitywrite your answer in inequality notation ? graph the inequalitywrite your answer in interval notation
We will have the following:
First, we simplify:
[tex]\begin{gathered} 5x+3<-27\Rightarrow5x<-30 \\ \Rightarrow x<-6 \end{gathered}[/tex]And:
[tex]2x+0\ge0\Rightarrow x\ge0[/tex]So, the solution in interval notation is:
[tex](-\infty,-6)\cap\lbrack0,\infty)[/tex]How would I solve the system of inequalities?Is the procedure correct?
To plot the line of the inequality , we begin by inserting the values x = 0 and y = 0 one after the other.
[tex]\begin{gathered} 4x+5y>20 \\ \text{When x = 0, then} \\ 4(0)+5y=20 \\ 5y=20 \\ y=4 \\ \text{That gives us the point (0, 4)} \\ \text{Similarly when y = 0, then} \\ 4x+5(0)=20 \\ 4x=20 \\ x=5 \\ \text{That gives us the point (5, 0)} \\ \text{With these two points we can now plot a line by joining both points with a ruler} \\ \text{Note also that the inequality can now be expressed as;} \\ 4x+5y>20 \\ 5y>20-4x \\ y>\frac{20-4x}{5} \\ y>\frac{20}{5}-\frac{4x}{5} \\ y>4-\frac{4}{5}x \\ y>-\frac{4}{5}x+4 \end{gathered}[/tex]Letus now derive two points for the second inequality given just like we did for the first one above;
[tex]\begin{gathered} -3x+7y\ge7 \\ \text{When x = 0, then } \\ -3(0)+7y=7 \\ 7y=7 \\ y=1 \\ \text{This gives us the point (0, 1)} \\ \text{Also, when y = 0, then} \\ -3x+7(0)=7 \\ -3x=7 \\ x=-\frac{7}{3}\text{ (OR x=-2}\frac{1}{3}) \\ \text{That gives us the point (-2}\frac{1}{3},0) \\ \text{The equation can now be expressed as} \\ -3x+7y\ge7 \\ 7y\ge7+3x \\ y\ge\frac{7+3x}{7} \\ y\ge\frac{7}{7}+\frac{3x}{7} \\ y\ge1+\frac{3}{7}x \\ y\ge\frac{3}{7}x+1 \end{gathered}[/tex]The graph of both inequalities is now shown below;
Observe carefully that the solution lies in the region shaded BLUE and RED.
One point in this region is (4, 4)
The blue and red graphs are represented by;
[tex]\begin{gathered} y>-\frac{4}{5}x+4\text{ (RED graph)} \\ y\ge1+\frac{3}{7}x\text{ (BLUE graph)} \end{gathered}[/tex]Can you please help me
The formula to find the area of a circle is
[tex]\begin{gathered} A=\pi r^2 \\ \text{ Where A is the area and} \\ r\text{ is the radius of the circle} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} r=21ft \\ \text{ Because} \\ \text{radius =}\frac{\text{ diameter}}{2} \\ \text{radius =}\frac{42ft}{2} \\ \text{radius =}21ft \end{gathered}[/tex][tex]\begin{gathered} A=\pi(21ft)^2 \\ A=\pi\cdot441ft^2 \\ A=1385.44ft^2 \end{gathered}[/tex]Therefore, the area of this circle is 1385.44 square feet.
graph on the coordinate plane 4.5, 2
The given points are, (-5, 5) and (4.5, 2).
To ordered pairs are noted as (x, y), that is first value corresponds to the value on the x axis and the second one corresponds to the value on the y aixs. Therefore we have,
(a)What is the domain of the relation ? Enter a value on the same line , separated by commas (b)What is the range of the relation ? Enter a value on the same line , separated by commas
Answer:
• Domain: {1,2,3,7,9}
,• Range: {1,4,6,7,8}
Explanation:
Given the relation in the table, we are required to find the domain.
Domain
The domain is defined as the set of all the values of x that satisfies the relation.
From the table, the domain is:
[tex]\{1,2,3,7,9\}[/tex]Range
The range is defined as the set of all the values of y that satisfies the relation.
From the table, the range is:
[tex]\{1,4,6,7,8\}[/tex]Basilico's 27 equal strips from a 6-yard spoon of ribbon which expression shows the number of yards used for one strip of ribbon
∵ The 27 equal strips made from a 6-yard ribbon
∴ The length of each strip is
[tex]\frac{6}{27}[/tex]Each strip is 6/27 yards
The answer is A
7. An equation is shown.7 m = 105 What is the value for m that makes the equation true?
In order to find the value of m in this equation, we just need to divide both sides of the equation by 7.
So we have that:
[tex]\begin{gathered} 7m=105 \\ \frac{7m}{7}=\frac{105}{7} \\ m=\frac{105}{7} \\ m=15 \end{gathered}[/tex]So the value of m that makes the equation true is m = 15.
Write the rate as unit rate 702 riders in 9 subway cars
Given:
702 riders in 9 subway cars.
Required:
To write the rate as a unit.
Explanation:
Consider 702 numerator part and 9 in denominator part.
Therefore, the unit rate is
[tex]\begin{gathered} =\frac{702}{9} \\ =78 \end{gathered}[/tex]Final Answer:
Unit rate is 78.
Which of the figures below is the correct construction of an angle bisector?
The final step coincides with option 4
Which of the following expressions are equivalent to…I will take a screenshot of the expression I need help with.
Given:
[tex]-\frac{2}{-13}[/tex]You can move the negative anywhere or in front of the fraction.
[tex]-\frac{2}{-13}=\frac{-2}{-13}=-\frac{-2}{13}[/tex]
Answer:
A. and B.
I need an answer a b c or d I know how to do the scratch workdetermine the angle measures in the polygon
The sum of the interior angles of a pentagon is 540°. A pentagon is a polygon with five sides and five vertices.
So, in this case, you have
[tex]x\text{\degree}+135\text{\degree}+x\text{\degree}+x\text{\degree}+135\text{\degree}=540\text{\degree}[/tex]Now, you can solve for x
[tex]\begin{gathered} x\text{\degree}+135\text{\degree}+x\text{\degree}+x\text{\degree}+135\text{\degree}=540\text{\degree} \\ \text{ Add similar terms} \\ 3x\text{\degree}+270\text{\degree}=540\text{\degree} \\ \text{ Subtract 270\degree{}from both sides of the equation} \\ 3x\text{\degree}+270\text{\degree-270\degree}=540\text{\degree-270\degree} \\ 3x\text{\degree}=270\text{\degree} \\ \text{ Divide by 3 into both sides of the equation} \\ \frac{3x\text{\degree}}{3}=\frac{270\text{\degree}}{3} \\ x=90\text{\degree} \end{gathered}[/tex]Therefore, the angle measures in the polygon are 90°,135°,90°,90°,135°.
Suppose a ball is dropped from an initial height of 10 feet and loses 40% of its height after every bounce. Complete the table to give the heights of the ball after the first 4 bounces. Bounce Height after Bounce 1 ? 2 ?3 ?4 ?Write the equation for the height of the ball, y, after x bounces, and fill out the chart.
Answer:
[tex]y=10(0.9)^x[/tex]Explanation:
The ball is dropped from an initial height of 10 feet.
It loses 10% of its height after every bounce.
• An equation for the height of the ball, y, after x bounces is derived below:
[tex]\begin{gathered} y=10(1-10\%)^x \\ y=10(1-0.1)^x \\ y=10(0.9)^x \end{gathered}[/tex]Substitute the values of x=1,2,3 and 4 respectively:
[tex]\begin{gathered} When\; x=1,y=10(0.9)^1=9\text{ feet} \\ When\; x=2,y=10(0.9)^2=8.1\text{ feet} \\ When\; x=3,y=10(0.9)^3=7.29\text{ feet} \\ When\; x=4,y=10(0.9)^4=6.561\text{ feet} \end{gathered}[/tex]What is the solution to the system of linear equations graphed below? a) (0,1) b) (7,0) c) Infinitely Many Solutions d) No Solution y у 11- 3 3 2 1 2 3 4 5 6 8 9 10 D
As shown in the figure:
The graphed lines are parallel, because the difference of y-coordinates are constant.
So, there is no intersection between the lines
So, The answer is option d) No solution
Nancy has 8 pieces of string that are exactly the same length. Which equation the total length of string she has
Nancy has 8 pieces of strings that are exactly the same length each. That means each of the piece of strings have the same length.
Let
Fine, and radians in degrees, the inclination theta of the line with the equation -5x - 13y - 66 =0
Given
[tex]-5x-13y-66=0[/tex]Transform it into its slope-intercept form, as shown below
[tex]\begin{gathered} \Rightarrow y=-\frac{5}{13}x-\frac{66}{13} \\ \end{gathered}[/tex]Then, the slope of the line is -5/13.
On the other hand, the inclination angle of a line is given by the formula below
[tex]\begin{gathered} m=tan\theta \\ \Rightarrow\theta=\tan^{-1}(m) \\ \theta\rightarrow\text{ inclination angle} \\ m\rightarrow\text{ slope} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} \Rightarrow\theta=\tan^{-1}(-\frac{5}{13}) \\ \Rightarrow\theta=-0.3671738...\text{ radians} \\ or \\ \theta=-21.04\degree \end{gathered}[/tex]Thus, the answer is -0.3671738... radians or -21.04°What do you know to be true about the values of a and b?bº775aA. abD. Can't be determined
The answer is D. can't be determined
we need more details t
1. A marine biologist recorded the number of deaths of specific fish species from the last 10 years (1 point)due to pollution in a specific area off the Pacific coast. She was curious to see if there was atrend. Identify the best mathematical model with its corresponding R? value and tell whether itis a good model.
We have to see which model (quadratic or linear) best represents the data.
We can use software to fit this data set.
Linear model:
Quadratic model:
The quadratic model has a slightly better fit than the linear model.
But the value of R² = 0.176 shows that the fit is very weak, so we can conclude that this is not a good model for the data.
Answer:
Quadratic model, 0.176.
No, 0.176 is a very low R² value.
Write each number in standard form. Include Commas and decimal points when necessary! Double check your answer before submitting.
Given:
[tex]2.54\times10^2[/tex]Let's write the given expression in standard form.
To write in standard form, since the exponent is positive 2 we are to move the decimal point two places to the right.
Thus, we have the standard form below:
[tex]2.54\times10^2=254[/tex]Therefore, the number in standard form is = 254
ANSWER:
[tex]254[/tex]LINEAR GRAPH A linear graph must be a straight line. UNEAR NON-LINEAR R o #4 #3 С
Linear graph
As stated in the question, a linear graph must be represented by a straight line.
Curved lines cannot be classified as linear graphs.
From the choices presented, the following are linear graphs:
#1. Is a linear graph, or a horizontal line
#4 is a linear graph, or a slanted line
#2 is non-linear because it's a circle
#3 is non-linear because it's curved
Find a polynomial f(x) of degree 4 that has the following zeros. -5, 9 (multiplicity 2), 0
We are to find a polynomial f(x) of degree 4 that has the following zeros.
-5, 9 (multiplicity 2), 0
So,
The degree 4 polynomial of the given zeros is:
But recall, that there is a multiplicity which tells the number of times a factor occurs
So, x = 9 occurred twice.
Therefore, the degree 4 polynomial of the given zeros:
f(x) = x(x + 5)(x - 9)(x - 9)
So in a factored form:
f(x) = x(x + 5)(x - 9)(x - 9)
VE FULL CREDIT The formula te convert Fahrenheit to Celsius is C = (F - 32). a) Solve the formula for F. b) How would you dress for outdoor weather if the temperature is 30°C7 Show work to support your answer
solve for C:
Multiply both sides by 9/5:
[tex]\frac{9}{5}C=F-32[/tex]Add 32 to both sides:
[tex]F=\frac{9}{5}C+32[/tex]---------------------------------------------------------
for C = 30:
[tex]\begin{gathered} F=\frac{9}{5}(30)+32 \\ F=54+32 \\ F=86 \end{gathered}[/tex]Answers:
a)
[tex]F=\frac{9}{5}C+32[/tex]b)
[tex]F=86[/tex]help!!!!! this ends in 12 minutes Find the value of x. The diagram is not to scale. Given: RS , ST, MZRTS - 5x - 18. mZSTU- 6x T O 18 108 © 20 23
Given Data:
[tex]\begin{gathered} RS\cong ST \\ \angle RTS=5x-18 \\ \angle STU=6x \end{gathered}[/tex]Using the property of linear pair,
[tex]\begin{gathered} \angle RTS+\angle STU=180 \\ 5x-18+6x=180 \\ 11x=198 \\ x=18 \end{gathered}[/tex]Thus, option (A) is the correct answer.
Calculate the monthly percentage rate if the APR is 16.99%. Round your monthly percentage rate to the nearest hundredth of a percent.
Given:
APR = 16.99%
The Annual Percentage Rate is the interest rate charged yearly.
Given that there are 12 months in a year, to find the monthly percentage, divide the APR by 12.
Therefore, we have:
[tex]\text{Monthly percentage = }\frac{16.99}{12}=1.42^{}\text{ percent}[/tex]Therefore, the monthly percentage rate to the nearest hundreth of a percent is 1.42%
ANSWER:
1.42%
The area of the rectangle shown is 34 square inches.4 inchesWhat is the length of the base of the rectangle in inches?
The formula for any give rectangle is just that you multiply it's lenght by it's width, or as expressed by the equation;
[tex]\text{Area}=length\text{ x width}[/tex]Since in the picture we are given a side of the rectangle measuring 4 inches, with it's length as unkown, we can only assume that the 4 inches there is the width therefore for a sqaure with an area of 34 square inches, we can express it as;
[tex]\begin{gathered} \text{Area = lenght x width , where Area = 34, and width = 4} \\ 34\text{ = lenght x 4 , then divide both sides by 4} \\ \frac{34}{4}=\frac{4}{4}(lenght)\text{ , and remember that }\frac{4}{4}\text{ = 1} \\ \text{lenght = }\frac{34}{4} \\ \text{lenght = 8.5} \end{gathered}[/tex]Therefore the lenght of the rectangle in our question is 8.5 inches.
Solve the equation 6+(c+8)=136-(c+8)-131+7(t+2)=854(A+4)-9(A-4)=3711=7-(1-y)3+7(p-10)= -38-(5-3p)20+5(3-5A)=-5(A-6)+5
Let's solve the next equation:
[tex]6+(c+8)=13[/tex]We need to find the value for c, this value is correct when we replaced it with a number and the equality equation becomes true.
First, subtract both sides by 6
[tex]6-6+(c+8)=13-6[/tex][tex]c+8=7[/tex]Now, subtract both sides by 8
[tex]c+8-8=7-8[/tex][tex]c=-1[/tex]Replacing the c value to verify:
[tex]6+(-1+8)=13[/tex][tex]6+7=13[/tex]The c value is correct.
mary question word problem please can u show work on the picture for me to understand it get confusing when it's not marked what question
a. The company produces 52 boxes per hour. Then, after 3 hours they produce 52*3 = 156 boxes. If they had 404 boxes after 3 hours, then they started with 404 - 156 = 248 boxes.
Given that they produce 52 boxes per hour, then after h hours, they produce 52h boxes. Therefore, the number of boxes, b, as a function of the number of hours, h, is:
b = 248 + 52h
b. Replacing with h = 8, we get:
b = 248 + 52(8)
b = 248 + 416
b = 664
There will be 664 boxes after an 8-hour shift