The given equation is
[tex]y=-x+2[/tex]We have to find a new line perpendicular to the given line and must pass through P(-5,7).
First, we use the definition of perpendicularity for two lines.
[tex]m_1\cdot m_2=-1[/tex]Where one of the slopes is equal to -1 because the coefficient of x in the given equation is -1. Let's find the other slope.
[tex]\begin{gathered} m\cdot(-1)=-1 \\ m=1 \end{gathered}[/tex]This means the new perpendicular line has a slope of 1.
Now, we use the slope we found, the point P, and the point-slope formula, to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-7=1(x-(-5)) \\ y-7=x+5 \\ y=x+5+7 \\ y=x+12 \end{gathered}[/tex]Therefore, the equation of the new perpendicular line is y = x + 12.c and 217 more is equal to 198
c and 217 more means c+217
equal to 198 means =198
the complete sentence means
c+217=198
From 2014-2015 to 2024-2025, the number of students enrolled in an associate degree program is projected to increase by 21.3%. If the enrollment in associatedegree programs in 2014-2015 is 7,800,000, find the increase and the projected number of students in an associate degree program in 2024-2025.The increase is(Round to the nearest whole number as needed.)The projected number of students in an associate degree program in 2024-2025 is(Round to the nearest whole number as needed)
First, let's convert the percentage into a decimal:
[tex]\frac{21.3}{100}\rightarrow0.213[/tex]And multiply it by the initial amount:
[tex]7800000\cdot0.213=1661400[/tex]This way, the increase would be 1,661,400 , and the proyected number of students would be 9,461,400
Hello! I'm having a hard time solving and graphing this
Answer:
A = 25π units² = 78.5 units²
Explanation:
The circle with a center at (-1, 2) that passes through (-6, 2) has a radius equal to 5 because the distance between the center and the point is calculated as
-1 - (-6) = -1 + 6 = 5
Then, the area of the circle is equal to
A = πr²
A = π(5)²
A = 25π
Replacing π = 3.14, we get
A = 25(3.14)
A = 78.5
Therefore, the answer is
A = 25π units² = 78.5 units²
The question is in the image. Answer the question 4.
Step 1
Given;
[tex]coordinate\text{ points\lparen5,-12\rparen}[/tex]Required; To find the value of θ
Step 2
We use the trigonometric function Toa to find the required angle.
[tex]\begin{gathered} tan\theta=\frac{opposite}{Adjacent} \\ opposite=-12 \\ adjacent=5 \\ tan\theta=\frac{-12}{5} \\ \end{gathered}[/tex][tex]\begin{gathered} Using\text{ pythagoras} \\ (-12)^2+(5)^2=hypotenuse^2 \\ hypotenuse=\sqrt{144+25}=13 \\ Sin\theta=\frac{opposite}{Hypotenuse}=\frac{-12}{13} \end{gathered}[/tex][tex]\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse}=\frac{5}{13} \\ csc\theta=\frac{1}{sin\theta}=\frac{1}{\frac{-12}{13}}=\frac{13}{-12} \end{gathered}[/tex][tex]\begin{gathered} sec\theta=\frac{1}{cos\theta}=\frac{1}{\frac{5}{13}}=\frac{13}{5} \\ cot\theta=\frac{1}{tan\theta}=\frac{1}{\frac{-12}{5}}=\frac{5}{-12} \end{gathered}[/tex]←
Which postulate or theorem could you use to prove AXYZ AABC?
Choose the correct answer below.
O SSS postulate
OSAS postulate
O ASA postulate
O AAS theorem
Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x² + 4x - 5. If there is more than one x-Intercept, separate them with commas.DD:x-intercept(s):5?vertex:00
SOLUTION
Step 1 :
In this equation, we are expected to find the x-intercept(s)
of the vertex and the co-ordinates of the vertex of the parabola :
[tex]y=x^2\text{ + 4x - 5}[/tex]Step 2 :
[tex]\begin{gathered} \text{Given y = x}^2\text{ + 4 x - 5,} \\ y=x^2\text{ + 4 x + (}\frac{4}{2})^2\text{ - 5 - (}\frac{4}{2})^2\text{ ( Completing the square method )} \\ \\ y=(x+2)^2\text{ - }9 \\ \text{The vertex of the parabola, ( h, k ) }=\text{ ( -2 , -9 )} \end{gathered}[/tex]Step 3 :
We need to solve for the x-intercepts,
[tex]\begin{gathered} \text{Given y = x}^2\text{ + 4 x - 5} \\ \text{Factorising the Quadratic Function, we have that:} \\ y=x^2\text{ - x + 5 x - 5 } \\ y\text{ = x ( x -1 ) + 5 ( x - 1 )} \\ y\text{ = ( x - 1 ) ( x + 5 )} \\ \text{Setting y = 0, we have ( x - 1 ) = 0 or ( x + 5 ) = 0} \\ x\text{ = 1 or x = -}5\text{ } \end{gathered}[/tex]CONCLUSION:
The vertex of the parabola, ( h, k ) = ( -2 , -9 )
The x - intercepts are : x = 1 or x = -5
insert parentheses to make the expression true, 382/292-101+8=10
Answer:
(382/(292-101))+8=10
(382/191)+8=10
(2)+8=10
10=10
Х о 1 2 3 4 у -5 4 13 22 31
We can take any 2 points both from x and y and use the equation of a line formula to find out the equation of the line represented by the points in the table.
Let's take the points:
[tex]\begin{gathered} (x_1,y_1)=(0,-5) \\ (x_2,y_2)=(1,4) \end{gathered}[/tex]The equation of a line formula is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Let us plug in the points into this formula and do a little algebra to re-arrange the equation in the slope-intercept form, which is y = mx + b. The steps are shown below:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-(-5)=\frac{4-(-5)}{1-0}(x-0) \\ y+5=\frac{4+5}{1}(x) \\ y+5=\frac{9}{1}(x) \\ y+5=9x \\ y=9x-5 \end{gathered}[/tex]The slope-intercept form is given by:
[tex]y=9x-5[/tex]Where 9 is the slope and -5 is the y-intercept (y-axis cutting point)
what is 30% off 10? How u get answer
We are asked to find out what is 30% off 10?
30% off 10 means that there is a discount of 30% and you are supposed to pay only the remaining 70%
100% - 30% = 70%
So you can simply find the 70% of 10
[tex]70\%\: of\: 10=\frac{70}{100}\times10=7[/tex]Therefore, 30% off 10 is equal to 7
There is another way to find out 30% off 10
First, you find 30% of 10 and then subtract the result from the original amount
[tex]\begin{gathered} 30\%\: of\: 10=\frac{30}{100}\times10=3 \\ 10-3=7 \end{gathered}[/tex]Therefore, 30% off 10 is equal to 7
Suppose that $6500 is placed in an account that pays 3% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.
Given
Part A
[tex]\begin{gathered} P=\text{ \$6,500} \\ r=3\text{ \%} \\ t=1 \end{gathered}[/tex]Formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} A=6,500(1+\frac{0.03}{1})^{1\times1} \\ \\ A=6,500(1.03) \\ A=\text{ \$}6,695 \end{gathered}[/tex]Part B
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ P=6500 \\ R=3\text{ \%} \\ t=2 \end{gathered}[/tex][tex]\begin{gathered} A=6500(1+\frac{0.03}{1})^{1\times2} \\ \\ A=6500(1.03)^2 \\ A=6500(1.0609) \\ A=\text{ \$}6895.85 \end{gathered}[/tex]The final answer
According to the manual, a battery in a cellular phone loses 2% of its charge eachday. Assume the battery is 100% charged. Write an equation to represent thepercent charge, P, as a function of the number of days, d, since the battery wascharged and use it to determine the number of days until the battery in only 50%charged.
a.) According to the manual, a battery in a cellular phone loses 2% of its charge each
day.
b.) Assume the battery is 100% charged.
Let,
P = the percent charge
d = the number of days since the battery was charged
The equation will be:
P = 100 - 2d
Let's determine the number of days until the battery in only 50% charged.
P = 100 - 2d
50 = 100 - 2d
2d = 100 - 50
2d = 50
2d/2 = 50/2
d = 25
Therefore, the battey will be only 50% charged in 25 days.
i need to know what box i drag each , i tried to attach all them but it didnt allow me .
Triangle ABC has two angles measuring 59º and 88º. The third angle can be found by using the fact that the three angles of a triangle must sum up to 180º.
So, we have:
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \\ 88^{\circ}+\angle B+59^{\circ}=180^{\circ} \\ \\ 147^{\circ}+\angle B=180^{\circ} \\ \\ \angle B=180^{\circ}-147^{\circ} \\ \\ \angle B=33^{\circ} \end{gathered}[/tex]Now we know the measures of all angles and sides of the given triangle, let's analyze each of the congruence cases.
• For, triangle DEF, we see that:
Side DE is congruent to side AB (because they are represented using the same symbol)
Side EF is congruent to side BC (again, they both are represented by the same symbol)
The angle between sides DE and EF is congruent to the angle between sides AB and BC (they both measure 33º).
Thus, triangle DEF has a pair of sides, and the angle between them congruent two a pair of sides and the angle between them of triangle ABC.
Therefore, those two triangles are congruent by the Side-Angle-Side theorem. Or, for short: SAS.
• For ,triangle GHI ,we see that:
It has a pair of angles, 33º and 59º, that are congruent to a pair of angles of triangle ABC. Also, the side HI between those angles is congruent to side BC.
Thus, triangle GHI and triangle ABC are congruent by the Angle-Side-Angle Theorem. Or, for short: ASA.
For triangle
Algebraic proof write a reason for every step4x = 12x + 32
DAC BAD.What is the length of BD?Round to one decimal place.
Notice that we have two triangles with the SAME angle, abd with also a common side (the same length) AD.
we can use the law os sines in the smaller triangle and specially using the sides that are known.
for example, we can state in the first (smaller) triangle that:
[tex]\frac{\sin(\theta)}{2}=\frac{\sin (D)}{5.9}=\text{ }\frac{\sin(C)}{AD}[/tex]For the full triangle ABC we have the following law of sines:
[tex]\frac{\sin(2\theta)}{2+\text{?}}=\text{ }\frac{\sin(C)}{8.1}=\frac{\sin (B)}{5.9}[/tex]For the medium triangle ADB the law of sines goes as:
[tex]\frac{\sin(\theta)}{?}=\frac{\sin(B)}{AD}=\frac{\sin(180-D^{})}{8.1}=\frac{\sin (D)}{8.1}[/tex]Now, we need to find common variables to combine equations based on the law of sines.
Notice as well that sin(180-a) = sin(a) this is a trig identity, so we are going to replace this in the last trig identity for triangle ADB
Now, we have the following relationships from the veri first law of sines:
[tex]\sin (\theta)=\frac{2\cdot\sin (D)}{5.9}[/tex]and from the last law of sines we have the folloowing relationship:
[tex]\sin (\theta)=\frac{?\cdot\sin (D)}{8.1}[/tex]so we can equal both sine expressions since they are from the same angle, and try to solve for the unknown "?" in the equation:
[tex]\begin{gathered} \frac{2\cdot\sin(D)}{5.9}=\frac{?\cdot\sin (D)}{8.1} \\ \frac{2}{5.9}=\frac{?}{8.1} \\ \frac{2\cdot8.1}{5.9}=\text{?} \end{gathered}[/tex]whre we have eliminated sin(D) as common factor in both equations (this is correct as long as sin*D) is not equal to zero, which cleary is not the case here)
Therefore our unknown "?" is 2*8.1 / 5.9 = 2.7457 which rounded to one decimal is 2.7
k= 12, r=4%, po=$10,000, n=25 using the compound interest formula
The compound interes formula is given by:
[tex]P_N=P_0(1+\frac{r}{k})^{Nk}[/tex]where P0 is the principal (the initial amount), r is the interes rate (in decimal form), k is the number of times the interest is compounded and N is the time elapsed.
Plugging the values given we have:
[tex]\begin{gathered} P_N=10000(1+\frac{0.04}{12})^{12\cdot25} \\ =27,137.65 \end{gathered}[/tex]Therefore the future amount is $27,137.65 and the interest earned is $17,137.65.
A department store is holding a drawing to give away free shopping sprees. There are 9 customers who have entered the drawing: 3 live in the town of Gaston, 2 live in Pike, and 4 live in Wells. Two winners will be selected at random. What is the probability that both winners live in Pike? Write your answer as a fraction in simplest form.
We need to find the probability that the two winners line in Pike.
We know that 2 out of the 9 customers who entered the drawing live in Pike.
Thus, the probability of the first winner line in Pike is:
[tex]\frac{2}{9}[/tex]Then, considering the first winner live in Pike, there are left 8 customers, and 1 of them live in Pike. Thus, the probability that the second winner lives in Pike is:
[tex]\frac{1}{8}[/tex]Now, the probability that the first one lives in Pike and the second one also lives in Pike is the product of the two probabilities we found:
[tex]\frac{2}{9}\times\frac{1}{8}=\frac{2}{9\times8}=\frac{1}{9\times4}=\frac{1}{36}[/tex]Therefore, the probability that both winners live in Pike is:
[tex]\frac{1}{36}[/tex]Diamond form and grouping to factored form a(x-r1)(x-r2) for the first problem on the picture
Given the expression:
[tex]6x^2-13x-5[/tex]We will factor the expression as follows:
The factors of 6 = 2 x 3 or 1 x 6
The factors of 5 = 1 x 5
The difference must be = -13
So, we will use the factors of 6 = 2 x 3
So, the factoring will be as follows:
[tex]6x^2-13x-5=(3x+1)(2x-5)[/tex]We will write the expression in the form a(x-r1)(x-r2) as follows:
[tex]\frac{1}{6}(x+\frac{1}{3})(x-\frac{5}{2})[/tex]2.90change repeating decimal to fraction?
The given number is 2.90.
As you can notice this is a decimal number which is also rational. To express as a fraction, we divide it by 100 to get rid of the decimal point, then we simplify, as follows
[tex]\frac{290}{100}=\frac{145}{50}=\frac{29}{10}[/tex]Therefore, the equivalent fraction is 29/10.Which of the following is equivalent to the radical expression below when x is greater than or equal to 7
SOLUTION
The radical expression given is
[tex]\sqrt[]{x-7}.\sqrt[]{x+1}[/tex]Applying the rule
[tex]\sqrt[]{a}\times\sqrt[]{b}=\sqrt[]{ab}[/tex]We obtain
[tex]\sqrt[]{x-7}\times\sqrt[]{x+1}=\sqrt[]{(x-7)(x+1)}[/tex]Expanding the parenthesis, we have
[tex]\begin{gathered} \sqrt[]{(x(x+1)-7(x+1)} \\ =\sqrt[]{x^2+x-7x-7} \\ =\sqrt[]{x^2-6x-7} \end{gathered}[/tex]The radical expression is equivalent to
[tex]\sqrt[]{x^2-6x-7}[/tex]The right option is A
if the spinner was fair and spun 300 times,each outcome would be expected to be observed_____times.
ANSWER
Each outcome would be expected to be observed 75 times.
EXPLANATION
We have to find the theoretical probability of each outcome. If the spinner is fair, each outcome is equally probable. If we were to spin it 300 times, and the spinner has 4 sections, we would expect that each outcome to be observed:
[tex]\frac{300}{4}=75[/tex]75 times each section.
What is the standard deviation of the data?Some teenagers collected trash for a beach cleanup.The data for the number of pounds of trash collected byeach teenager are shown below.26, 26, 21, 22, 20, 25, 35O pounds4.66 pounds5.03 poundso 25.33 pounds
1. Ingrid will start college next year. She wasapproved for 10-year unsubsidized Federal Loanfor the amount of $15,000 at 4.29%a) How much interest will Ingrid accrue for 4.5 yearsnonpayment period?b) What will the new principal be when she beginsmaking loan payments?c) How much interest will she pay over the life of theloan?2. Suppose Ingrid only paid the interest during her 4years of school and the six-month grace period.What will she now pay in interest over the term ofthe loan?3. Ingrid made her last monthly interest only paymenton September 1 Her next payment is due onOctober 1. What will be the amount of interestonly payment?4. Suppose Ingrid has decided to apply for a privateloan rather then a federal loan. She has beenapproved for a 10 year loan with APR of 7.8%a) What is her monthly payments?b) What is the total amount she will pay back?c) What is total interest amount?
Given:
[tex]\begin{gathered} Principal=15,000 \\ rate(r)=4.9\%=0.049 \\ time(t)=10years \end{gathered}[/tex]To Determine: (a) How much interest will Ingrid accrue for 4.5 years non payment period
Solution
Calculate the amount accrued for 4.5years
The formula for finding amount for compound interest is
[tex]A=P(1+r)^{nt}[/tex]Substitute the given into the formula
[tex]\begin{gathered} A=15000(1+0.049)^{4.5} \\ A=15000(1.049)^{4.5} \\ A=18602.91 \end{gathered}[/tex]Step 2: Calculate the interest accrued for 4.5 years
[tex]\begin{gathered} I=A-P \\ I=18602.91-15000 \\ I=3602.91 \end{gathered}[/tex](a) Hence the interest Ingrid will accrued for 4.5 years non-payment period is $3,602.91
(b) The new principal when she begins making loan payments will be the amount accrued for 4.5years nonpayment period. This is as calculated above, which is
$18,602.91
(c) To Determine how much interest will she pay over the life of the loan
Note that the life of the loan is 10 years
[tex]So,t=10[/tex]Substitute the given into the formula for finding the amount as shown below
[tex]\begin{gathered} A=15000(1+0.049)^{10} \\ A=15000(1.049)^{10} \\ A=24201.71 \end{gathered}[/tex]Use the amount to calculate the interest of the life of the loan
[tex]\begin{gathered} I=A-P \\ I=24201.71-15000 \\ I=9201.71 \end{gathered}[/tex]Hence, the interest she would pay over the life of the loan is $9,201.71
Line c passes through the points (3, - 5) and (6, 1) . Line d passes through the points (6, - 4) and (2, - 2) Find the slope of each line and determine whether lines c and d are parallel , perpendicular , or neither . Explain your answer ...
Answer:
The slope of line c is 2.
The slope of line d is -1/2.
Lines c and d are perpendicular
Step-by-step explanation:
Slope of a line:
When given two points of a line, the slope is given by the change in y divided by the change in x.
Parallel lines: Have the same slope
Perpendicular lines: The multiplication of their slopes is -1.
Line c:
Passes through points (3,-5) and (6,1).
Change in y: 1 - (-5) = 1 + 5 = 6
Change in x: 6 - 3 = 3
Slope: 6/3 = 2
The slope of line c is 2.
Line d:
Passes through points (6,-4) and (2,-2)
Change in y: -2 - (-4) = -2 + 4 = 2
Change in x: 2 - 6 = -4
Slope: 2/-4 = -1/2
The slope of line d is -1/2.
Relationship between the lines:
They have different slopes, so they are not parallel.
Multiplication of the slopes:
2*(-1/2) = -2/2 = -1
Since the multiplication of their slopes is -1, Lines c and d are perpendicular.
How do you graph Y=5 on a graph. This is a linear equation. I know how to do it when they give an x too. But I don’t know what to do with just a y=5?
The equation y=5 represents something we know as a constant function. In a constant function, y, always, no matter what, takes the same value and is the value of the constant. In this case, the constant is 5, it means that for all values of x, y will always be 5.
In a graph, a constant function is an horizontal line, parallel to the x axis, that cuts the y axis at y=c, c is the constant. It means that the graph of y=5 will be an horizontal line that has a y intercept of 5.
estimate 8426 divided by 36 so that it only has one non zero digit.
Given:
[tex]\frac{8426}{36}[/tex]Required:
To estimate 8426 divided by 36.
Explanation:
[tex]\begin{gathered} \text{ 234.05} \\ 36)8426 \\ \text{ 72} \\ ----- \\ \text{ 1226} \\ \text{ 108} \\ ------- \\ \text{ 146} \\ \text{ 144} \\ ------ \\ \text{ 200} \\ \text{ 180} \\ -------- \\ \text{ 20} \end{gathered}[/tex]Therefore,
[tex]\frac{8426}{36}=234.05555[/tex]Final Answer:
[tex]234.05[/tex]Calculate the X value a. 4: 7 = x: 5x: 8 = 99 :5
Start writing the proportion as a fraction
[tex]\begin{gathered} 4\colon7\rightarrow\frac{4}{7} \\ x\colon5\rightarrow\frac{x}{5} \end{gathered}[/tex]then, the ratios must be the same meaning we can equal the fractions
[tex]\begin{gathered} \frac{4}{7}=\frac{x}{5} \\ \text{cross-multiply and solve for x } \\ x=4\cdot\frac{5}{7} \\ x=\frac{20}{7} \end{gathered}[/tex]repeat the same procedure for b
[tex]\begin{gathered} x\colon8\rightarrow\frac{x}{8} \\ 99\colon5\rightarrow\frac{99}{5} \\ \text{then,} \\ \frac{x}{8}=\frac{99}{5} \\ x=8\cdot\frac{99}{5} \\ x=\frac{792}{5} \end{gathered}[/tex]at Mr.neelys farm, there were 75 sheep and 60 cows what is the ratio number of cows to the number of sheep's at Mr.neelys farm
Answer:
The ratio of the number of cows to the number of sheeps in the farm is;
[tex]\begin{gathered} \frac{4}{5} \\ Or \\ 4\colon5 \end{gathered}[/tex]Explanation:
Given that;
there were 75 sheep
and 60 cows
We want to find the ratio of the number of cows to the number of sheeps in the farm;
[tex]\text{ratio}=\frac{\text{ number of cows }}{\text{ number of sh}eeps}=\frac{60}{75}[/tex]reducing the ratio to the least form;
[tex]\text{ratio=}\frac{60}{75}=\frac{4}{5}[/tex]Therefore, the ratio of the number of cows to the number of sheeps in the farm is;
[tex]\begin{gathered} \frac{4}{5} \\ Or \\ 4\colon5 \end{gathered}[/tex]determine the slope of a vertical line, and the slope of a horizontal line.
The slope of a vertical line is undefine
The slope of a horizontal line is zero
"The sum of 5 and a number results in 14."
We are given the phrase "The sum of 5 and a number results in 14." which suggest that we should find such a number. Let x be the number we are looking for, the phrase "The sum of 5 and a number" translates to the equation x+5,, since we are adding 5 to the number.
The part "results in 14" means that after adding 5, we end up having 14 as a result, this means we have
[tex]x+5=14[/tex]Now, we proceed to solve this equation for x by simply subtracting 5 on both sides. Once we do so, we get
[tex]x=14-5=9[/tex]so in this case the number we were looking for is x=9.
???? help pls !$!! !!!!
Answer:
I'm pretty sure congruent means if you split them in half will they be the same shape
Step-by-step explanation:
so Yes they are congruent because if you cut a diamond in half it's going to be two triangles two triangles that are the exact same size and if you fold them they're going to be the same