Given:
the terminal side θ passes through the point (8,-7)
so,
[tex](x,y)=(8,-7)[/tex]The point lying in quarter number 4
so,
[tex]\begin{gathered} \tan \theta=\frac{y}{x}=-\frac{7}{8} \\ \\ \theta=\tan ^{-1}(-\frac{7}{8})=-41.186 \\ \\ \theta=360-41.186=318.814 \end{gathered}[/tex]
Lin is reading a 47 page book. She read the first 20 pages in 35 minutes. If she continues to read at the same rate will she be able to complete in under an hour? If not, how much more time is needed?
Answer:
No, 40 pages would take 70 minutes.
Step-by-step explanation:
20 more pages would take 35 more minutes which would be 40 pages at 70 minutes, then you will divide your 7 pages left by the 35 minutes it took to read the the first two 20 page sections of the book.
35 min.+ 35 min = 70 min. 35 mins./7 pages = 5 minutes
So it took a total of 75 minutes for Line to read her 47 page book.
basketball player made 76 out of 100 attempted free throws. What percent of free throws was made?
Percentages measure the frequency of occurrence of a certain event with respect to the occurrence of another event.
This is measured as a division or ratio:
[tex]P=\frac{\text{frequency of event 1}}{frequency\text{ of event 2}}[/tex]The basketball player made 76 out of 100 attempts. Here, our event 1 is the basketball player making a free throw. Event 2 is the player throwing the ball, regardless of its result.
Since he/she made 76 out of 100, the percent is:
[tex]P=\frac{76}{100}=0.76[/tex]The percent is 0.76*100 = 76%
is (8, -44) a solution of the equation y = -7x + 6?
The ordered pair (8, -44) is not a solution of the equation
How to determine the true statement?The equation of the function is given as
y = -7x + 6
The possible solution of the equation is given s
(8, -44)
This means that
x = 8 and y = -44
Substitute x = 8 and y = -44 in the equation y = -7x + 6
So, we have the following equation
-44 = -7 x 8 + 6
Evaluate the products
So, we have the following equation
-44 = -56 + 6
Evaluate the sum
So, we have the following equation
-44 = -50
The above equation is false
Hence, the solution is not a solution
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Help me pls this is hard :,)
Answer: My friend could rewrite the fraction as a percent and compare that to the given percent. This is a good strategy if the denominator is `5`, `10`, `20`, or `50`. She could also turn the percent into a fraction by writing the percent over `100`. This is a good strategy if the new fraction can be simplified to have a common denominator with the original fraction.
Step-by-step explanation: BOOM I'M A PRO
I got you
find f(6). evaluate the function graphically.
F(6) IS TRYING TO ASK YOU WHAT IS THE VALUE OF Y WHEN X IS EQUAL TO 6 IN THE GRAPH.
VALUE OF Y WHEN X IS EQUAL TO 6 IN THE GRAPH.IF TOU CHECK IN THE GRAPH YOU WILL FIND THAT WHEN X=6 Y=8
THE ANSWER IS 8.
A line passes through the point (8, -3) and has a slope of 5/4.
Write an equation in slope-intercept form for this line.
Answer: y = 5/4x - 13
Step-by-step explanation:
m = 5/4
y = mx + b
substitute the coordinate into the equation to find b
-3 = 5/4(8) + b
b= -13
Consider the following equation.
7x +9y = 5y-6
Step 2 of 2: Find the equation of the line which passes through the point (-8,-6) and is perpendicular to the given line. Express your answer in slope-intercept
form. Simplify your answer.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]7x+9y=5y-6\implies 7x+4y=-6\implies 4y=-7x-6 \\\\\\ y=\cfrac{-7x-6}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{7}{4}}x-\cfrac{3}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-7}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{-7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{-7}\implies \cfrac{4}{7}}}[/tex]
so we're really looking for the equation oif a line whose slope is 4/7 and it passes through the point (-8 , -6)
[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{4}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ \cfrac{4}{7}}(x-\stackrel{x_1}{(-8)}) \implies y +6= \cfrac{4}{7} (x +8) \\\\\\ y+6=\cfrac{4}{7}x+\cfrac{32}{7}\implies y=\cfrac{4}{7}x+\cfrac{32}{7}-6\implies {\Large \begin{array}{llll} y=\cfrac{4}{7}x-\cfrac{10}{7} \end{array}}[/tex]
help meeeeeeeeee pleaseee
Inequalities define the relationship between two non-equal values. Inequality means being unequal.
option C is the correct Graph.
Relation { x | -7 < x < 3} .
solution in interval notation ( -7 , 3 ) .
Why do we study inequalities?To comprehend inequality, one must first comprehend the modern world and the forces that shaped it. More specifically, understanding inequality is a prerequisite for overcoming it: that is, for healing past wounds, generating social solidarity, and rebuilding a more just society.According to experts, inequality stifles economic growth and fosters political dysfunction. Because rich households spend less of their income than poorer households, concentrated income and wealth reduces the level of demand in the economy. Reduced opportunities for low-income households can also have a negative impact on the economy.To learn more about : Inequality,
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A typical passenger vehicle emits about 4.7 metric tons of carbon dioxide per year. Assuming there are 253 million cars and trucks in the U.S, estimate the total emitted weight of carbon dioxide in the U.S
To estimate this quantity we can multiply the quantities given in the problem:
[tex]253\cdot4.7=1189.1[/tex]The estime total emmited weight of carbon dioxide in the U.S. is about 1189.1 millions of tons
9. Higher Order Thinking The table shows
the temperatures of the water in
14 different beakers. What is the average
temperature, rounded to the nearest tenth
of a degree?
Temperatures in Beakers
Temperature 4.5°C 3.7°C 4.3°C 4.1°C 2.9°C
Frequency
3
4
2
3
2
The Average temperature of the given distribution is; 3.3°C
What is the average temperature?When given the values of the input and their frequencies of occurrence, the average mean can be calculated from the formula;
x' = ∑fx/∑f
Thus;
∑fx = ((4.5 * 3) + (3.7 * 4) + (4.3 * 2) + (4.1 * 3) + (2.9 * 2))
∑fx = 13.5 + 14.8 + 8.6 + 12.3 + 5.8
∑fx = 46.4
∑f = 3 + 4 + 2 + 3 + 2
∑f = 14
Thus;
Average temperature = 46.4/14 = 3.3°C
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which ratio is equivalent to 1 and 8 a.7 to 14b. 7 to 9c.6 to 41d.6 to 48
we can see that
[tex]\frac{6}{48}=\frac{6}{6\cdot8}=\frac{1}{8}[/tex]hence, the answer is d).
A store owner buysy scooter for $40.99 and sells it for $94. What is the percent of increase for the price of the scooter? Round to the nearest tenth if necessary.
Percentage increase in the price of scooter = 129.3%
What is percentage?The word "percentage" refers to a figure that is stated as a percentage of 100, a relative value that denotes hundredths of any amount. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
For example 2% means [tex]\frac{2}{100}[/tex]. Here 2 is expressed as a fraction of 100.
Cost price of scooter = $40.99
Selling price of scooter = $94
Increase in price of the scooter = $(94 - 40.99)
= $53.01
Percentage increase in the price of scooter = [tex]\frac{53.01}{40.99}\times 100[/tex]
= 129.3%
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In a circle, the perpendicular bisector of a chord contains the center of the circle.Given : O X with L the 1 bisector of WY.Prove: L contains the center of O X.
All radii of the circle are congruent.Therefore, the radii XW and XY are congruent
[tex]\begin{gathered} XW\cong XY \\ \end{gathered}[/tex]The histogram to the right represents the weights (in pounds) of members of a certain high-school programming team.What is the class width? What are the approximate lower and upper class limits of the first class?
Looking at the given histogram
we have that
120-110=10
130-120=10
140-130=10
150-140=10
160-150=10
170-160=10
180-170=10
therefore
The class width is 10 lbs
First-class is 110-120 lbs
lower-class limit=110
upper class limit=120
sovle the equation 8x-11=9x+2
Given the equation:
[tex]8x-11=9x+2[/tex]To solve this equation for x, the first step is to pass the x-term to the left side of the equation and the number to the right side. For this, you have to apply the opposite operation to both sides of the equal sign, that is, to subtract 9x and to add 11:
[tex]\begin{gathered} 8x-9x-11=9x-9x+2 \\ -x-11=2 \end{gathered}[/tex][tex]\begin{gathered} -x-11+11=2+11 \\ -x=13 \end{gathered}[/tex]Note that the x-term is negative, but the objective is to determine the value of x, so we have to multiply it by (-1) to reverse its sign, and to keep the equality valid, you have to multiply both sides of the equation by (-1)
[tex]\begin{gathered} (-1)(-x)=(-1)\cdot13 \\ x=-13 \end{gathered}[/tex]70) Approximately how many feet tall is thestreetlight?A. 12.8B. 15.4C. 16.8D. 23.8
The height of the street light represent the opposite side.
The adjacent is 20ft
the angle is 40 degrees
using trigonometry ratio for tangent
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 40^0=\frac{x}{20} \\ \text{where x=height of the stre}etlight \end{gathered}[/tex][tex]\begin{gathered} x=20\times\tan 40 \\ =20\times0.8390 \\ =16.78 \end{gathered}[/tex]Therefore the streetlight is approximately 16.8ft
The right option is C
8. James is at a gift sale where everything costs $4 (tax included).James has $50.James must have at least $28 rer ining when he is finished buyinggifts.What is the greatest number of gifts James can buy?
Let the number of gift be x
The total amount James has is $50
Since he must have $28 remaining
Thus, the amount he would spend must not exceed
[tex]\text{ \$50-\$28=\$22}[/tex]Therefore,
If for every gift, $4 tax is included
[tex]x\text{ }\times\text{ \$4 =\$4x}[/tex]The number of gift James can buy
[tex]\begin{gathered} 4x\leq22 \\ x\leq\frac{22}{4} \\ x\leq5.5 \end{gathered}[/tex]Hence, the maximum number of gift James can buy is 5
charles walked on a treadmill 16 3/4 miles over 4 days. how many miles did he walk per day. write the answer as a simplified fraction or mix number
Belinda is altering dance costumes for an upcoming recital. The number of costumes
she can alter varies directly with the amount of time spent working. If Belinda can
alter four costumes in one hour, find the number of costumes she can alter in four
and a half hours.
Answer: c
Step-by-step explanation: the equation asks for the divison of the two equal libruims and u subtract the numeriator by the scound stance
Help please thanks please. Solve for the value of d to the nearest tenth place
d = √74
d = 8.6 (to the nearest tenth place)
Explanations:Given the expression to calculate the distance between the coordinates (-2, 1) and (5, -4) as shown:
[tex]d=AB=\sqrt{(5-(-2))^2+(-4-1)^2}[/tex]Simplify
[tex]\begin{gathered} d=\sqrt{(5+2)^2+(-5)^2} \\ d=\sqrt{7^2+5^2} \\ d=\sqrt{49+25} \\ d=\sqrt{74} \\ d\approx8.6 \end{gathered}[/tex]Hence the simplified form of the expression is √74 or 8.6
Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:
o Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50)
o Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50)
What is Val’s margin of error, rounded to the nearest whole number? (The formula is 1.96 (std dev) /
If the average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.
Given that the average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows.
We are required to find the margin of error of Val's data.
Margin of error is basically the difference between the actual data and the calculated data.
Margin of error=1.96*σ/[tex]\sqrt{n}[/tex]
In our case σ=50 and n is 100.
Margin of error=1.96*50/[tex]\sqrt{100}[/tex]
=1.96*50/10
=1.96*5
=9.80
Hence if the average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.
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Fred has 5/8 of a pizza left to share with 3 people. If it is split up evenly, how much of the pizza will each person get?
Evaluate f(x) at the given values of x.
f(x) = 4x x = -5, 3
Step-by-step explanation:
x=-5 f(x)=4x
f(x)=4(-5)
f(x)=-20
x=3 f(x)=4(3)
f(x)=12
m=1/4(w+d) solve for d , how do I solve for this equation?
The value of d in the equation is d= 4m-w
How to calculate the value of d ?The first step is to write out the equation given
m=1/4(w+d)
The value of d can be calculated as follows
m= w + d/4
Cross multiply both sides
4m= w + d
collect the like terms
4m -w= d
d= 4m-w
Hence the value of d in the equation is 4m-w
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Determine the slope of the line passing through the points (5,6) and (-5,-1)m=____
GIVEN:
We are given two points on a line and these are;
[tex]A=(5,6),\text{ }B=(-5,-1)[/tex]Required;
We are required to determine the slope of the line passing through these points.
Step-by-step solution;
The slope of a line is given by the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The variables are;
[tex]\begin{gathered} (x_1,y_1)=(5,6) \\ \\ (x_2,y_2)=(-5,-1) \end{gathered}[/tex]We can now substitute these into the formula and then simplify;
[tex]\begin{gathered} m=\frac{-1-6}{-5-5} \\ \\ m=\frac{-7}{-10} \\ \\ m=\frac{7}{10} \end{gathered}[/tex]ANSWER:
The slope of the line passing through the given points is;
[tex]m=\frac{7}{10}[/tex]Evaluate sin 315º without using a calculator.O A. 132DIRO B.B. -12OC, V22O D. - 12
Answer:
Choice D.
Explanation:
Another way to write 315 degrees is
[tex]315-360=-45[/tex]In other words, when measured clockwise, 315 degrees = -45 degrees; therefore, our problem becomes
[tex]\sin 315^o=\sin -45^o[/tex]since
[tex]\sin \theta=-\sin -\theta[/tex][tex]\sin 45=-\sin -45[/tex][tex]\frac{\sqrt[]{2}}{2}=-\sin -45[/tex][tex]\sin -45=-\frac{\sqrt[]{2}}{2}[/tex]Therefore,
[tex]\boxed{\sin 315^o=-\frac{\sqrt[]{2}}{2}}[/tex]which is our answer!
Mike can make 7 holiday cards with the cardstock he already has on hand. He is also buying more paper, and he can make 12 additional cards with each package of cardstock he buys. Write an equation that shows how the total number of cards Mike can make, y, depends on the number of packages of cardstock he buys, x.
Answer:y = 12x + 7
Step-by-step explanation:
24 lemons are required to make 32 gallons of lemonade. How many lemons are needed to make 4 gallons of lemonade?
Answer:
Step-by-step explanation:
Simple:
24:32
?:4
This means just divide by 8 to get four. This also means to divide 8 for 24 also
24/8:4=
3:4 as answer
5 pointsWhich is the image of vertex Lafter the triangle is rotated 180 degrees about the origin?
The image of vertex L after the triangle is rotated 180 degrees about the origin= (-2, -1).
Option B.
First let's stae the the original location of the figure on the graph.
From the graph:
L (2, 1)
W(1, -3)
O (-1, -2)
A rotation of 180 degrees about the origin will change the x and y axis of each location to the opposite of those numbers;
Positive numbers becomes negative and negative numbers becomes positive.
The new location for L = L'
L' = (-2, -1)
The new location for W = W'
W' = (-1, 3)
The new location for O = O'
O' = (1, 2)
Hence, the image of vertex L after the triangle is rotated 180 degrees about the origin= (-2, -1).
Option B.
Please help me with this problem i am not sure if what I calculated is correct please help.Let f(x)=12x2+4. The function g(x) is a vertical stretch of f(x) by a factor of 4. What is the equation of g(x)? Enter your answer in the box.g(x) = ---------
SOLUTION
The given equation is
[tex]f(x)=\frac{1}{2}x^2+4[/tex]Recall the definition of vertical stretch
vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1
For a vertical stretch of a scale factor of 4 on f(x) g(x) will be
[tex]g(x)=4(\frac{1}{2}x^2+4)_{}[/tex]Expand the bracket
[tex]g(x)=2x^2+16[/tex]Therefore, the answer is
[tex]g(x)=2x^2+16[/tex]