Point A has a coordinate of (7/5, 0) while the straight line l2 is represented by the equation y = 0
The coordinates of point AThe equation of line l1 is given as
5x - 7 = 0
It cuts the x-axis at point A
This means that
5A - 7 = 0
Solve for A
5A = 7
So, we have
A = 7/5
Rewrite as
A = (7/5, 0)
The equation of the straight line l2From the question, we have
Lines l1 and l2 are perpendicular lines
The equation 5x - 7 = 0 has no y variable
So, the slope is undefined
The slopes of perpendicular lines are represented as follows
Slope 1 * Slope 2 = -1
So, we have
Slope 2 = -1/Slope 1
This gives
Slope 2 = -1/undefined
Evaluate
Slope 2 = 0
This means that l2 has a slope of 0
The equation of l2 is calculated as
y = m(x - x₁) + y₁
In this case,
A = x₁ and y₁ = 0
So, we have
y = m(x - A)
This gives
y = 0 * (x - 7/5)
Evaluate
y = 0
Hence, the equation of the straight line l2 is y = 0
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6. Diagram this statement. Then answer the questions (22) that follow. One third of the 60 questions on the test were true false. (a) How many of the questions on the test were true- false? (b) How many of the questions on the test were not true- false? (C) What percent of the questions were true-false?
Select the correct answer. Angela is driving across the state to her friend's house. She just filled her fuel tank to its maximum capacity of 26 gallons. If the amount of gas in her car decreases by 2 gallons every 48 miles, which of the following graphs best represents the number of gallons of fuel remaining?
Let L be the amount of gas Angela has at distance d. At d=0 she has 26, and we know that every 48 miles the gas decreases 2 gallons, so the rate of decrease of gas per mile is
[tex]\frac{2\text{ }}{48}=\frac{1}{24}[/tex]Then, the linear equation that models this problem is
[tex]L=-\frac{1}{24}d+26[/tex](I used the minus sign since the amount decreases).
The gas will run out of gas whe she has driven
[tex]\begin{gathered} 0=-\frac{1}{24}d+26 \\ \frac{1}{24}d=26 \\ d=624\text{ miles} \end{gathered}[/tex]Then the graph that best fits the model is number Z. And the answer is D.
Use trigonometry to find QP. Round to the nearest tenth.
Since this is a right triangle, we can use trig functions
cos theta = adj side/ hypotenuse
cos Q = QP / QR
cos 38 = QP / 25
25 cos 38 = QP
19.70026884= QP
Rounding to the nearest tenth
19.7 = QP
WXYZ is a kite. Use the figure below to fill in the blanks below.
We can assume the kite is simetrycal along line WY, as such
[tex]ZW=XW=10[/tex][tex]m\angle\text{XSW}=90[/tex]because the diagonals of a kite are perpendicular.
Since m∠XSW is 90°, triangle WSX is a right triangle. Thus
[tex]m\angle WXZ=m\angle WXS=180-90-46=44[/tex]By the symmetry we discussed earlier,
[tex]m\angle WYZ=m\angle WYX=18[/tex]And finally
[tex]m\angle XYZ=m\angle WYZ+m\angle WYX=18+18=36[/tex]what angle is Supplementary to angle 2 and what are the Verticle angles in this picture?
Suplementary angle = 180° - angle 2
is Angle 1,
because Angle 2 + Angle 1 = 180°
Part 2. Vertical angles are
Angles 2 and 5
Pls help with the question in the picture. 20 Points and brainliest.
Answer:
**NEED USEFUL ANSWER ASAP, H.W QUESTION**
Given that hotter blackbodies produce more energy than cooler blackbodies, why do cooler red giants have much higher luminosities than much hotter white dwarfs?
Step-by-step explanation:
The price of acorn squash is proportional to the weight in pounds. You pay $6.36 for 4 pounds of acorn squash. How much does3 pounds of acorn squash cost?
In order to calculate the cost for 3 pounds of acorn squash, we can write the following rule of three:
[tex]\begin{gathered} \text{weight}\to\text{cost} \\ 4\text{ pounds}\to6.36 \\ 3\text{ pounds}\to x \end{gathered}[/tex]Then, we can write the following equation and solve it for x:
[tex]\begin{gathered} \frac{4}{3}=\frac{6.36}{x} \\ 4\cdot x=3\cdot6.36 \\ 4x=19.08 \\ x=\frac{19.08}{4} \\ x=4.77 \end{gathered}[/tex]Therefore the cost of 3 pounds is $4.77.
What is the coordinate of the midpoint of S the midpoint of ST write your answer as an integer or a decimal or mixed number in simple Form.
We have a segment ST in a number line.
We can calculate the midpoint M as the average of the position of the endpoints S and T.
The position of S is 11 and the position of T is 13, so the midpoint will be:
[tex]M=\frac{S+T}{2}=\frac{11+13}{2}=\frac{24}{2}=12[/tex]Answer: the midpoint is 12.
The width of a rectangle is [tex] \frac{3}{4} [/tex] its length. The perimeter of the rectangle is 420 ft. What is the length, in feet, of the rectangle?
The width of a rectangle is 3/4 its length.
[tex]w=\frac{3}{4}l[/tex]The perimeter of the rectangle is 420 ft.
Recall that the perimeter of a rectangle is given by
[tex]P=2(w+l)[/tex]Let us substitute the value of the given perimeter and the width
[tex]\begin{gathered} P=2(w+l) \\ 420=2(\frac{3}{4}l+l) \end{gathered}[/tex]Now simplify and solve for length
[tex]\begin{gathered} 420=2(\frac{3}{4}l+l) \\ 420=\frac{3}{2}l+2l \\ 420=3.5l \\ l=\frac{420}{3.5} \\ l=120\: ft \end{gathered}[/tex]Therefore, the length of the rectangle is 120 feet.
Mr. Rodriguez is preparing photos for an international client. The client has requested a photo that is 20 cm by 15 cm. Mr. Rodriguez knows that the formula c = 2.54n can be used to convert n inches to c centimeters. Which formula can he use to convert centimeters to inches?
Given:
The formula to convert from inches to centimeters is c = 2.54n
To find:
The formula that can be used to convert from centimeters to inches
To determine the formula, we need to make n the subject of formula:
[tex]\begin{gathered} \text{c = 2.54n} \\ where\text{ c = value in cm} \\ n\text{ = value in inches} \end{gathered}[/tex][tex]\begin{gathered} To\text{ make n, the subject of formula, we will divide both sides by 2.54:} \\ \frac{c}{2.54}=\text{ }\frac{2.54n}{2.54} \\ n\text{ = }\frac{c}{2.54} \\ This\text{ means when we have a value in cm and substitute, the answer will be in inches} \end{gathered}[/tex][tex]n\text{ = }\frac{c}{2.54\text{ }}\text{ \lparen option B\rparen}[/tex]Can you help me with question number 4 and double check all my other work. (I don’t really understand functions.)
SOLUTION
The relation is a function because each x-value has a unique y-value. That is each domain has only one image. Therefore, the relation is a function
b. (-4,-1) Y= 4/3 x + 6What’s the equation of the line in standard form
When two lines are perpendicular, the slopes of the lines m1 and m2 are related such that
m1m2 = -1
from the given equation comparing with tyhe general form of the equation of a line (y = mx + c)
m1 = 4/3
The slope of the perpendicular line is -3/4
The equation of the line
y- -1 = -3/4(x - -4)
y + 1 = -3/4(x + 4)
y + 1 = -3x/4 - 3
Subtract 1 from both sides
y + 1 - 1 = -3x/4 - 3 - 1
y = -3x/4 - 3 - 1
y = -3x/4 - 4
This is the standard form of the equation
Which of the following data collection methods best describes the situation below?A polling company wants to predict which candidate will win an election. Company employees randomly call 1482 likely voters and ask them how they plan to vote.a. sample surveyb. experimentc. observational studyd. correlation
Answer
Option A is correct.
Explanation
Sample survey refers to the statistic
Create a table of values for the function graphed below using the plotted points. Remember, table of values are written with the -values in order from least to greatest (read the graph from left to right).
To create the table of values, we need to find the coordinates of the given points.
The coordinatesare given by (x,y), where x ican be found by drawing an imaginary vertical line passing through the point, and the x-value is the value of the x-axis where the line intercepts the x-axis.
The y-coordinate is given by the point of interception on the y-axis of a horizontal line passing through the point, so, for the fir tpoint the coordinates are:
[tex]\begin{gathered} (-2,5) \\ x-value\rightarrow-2 \\ y-value\rightarrow5 \end{gathered}[/tex]If we apply the same procedure to the next points, we can find the following coordinates:
[tex]\begin{gathered} (-1,4) \\ (0,3) \\ (1,2) \\ (2,1) \end{gathered}[/tex]Thus, th table of values will be:
x y
-2 5
-1 4
0 3
1 2
2 1
Please help me and I will give the pictures for the choices..
The first compound indequality is:
[tex]x>7\, and\, x<7[/tex]We can view this in the real line:
There is no number that can be both greater AND less than 7, which makes the correct answer "No solution".
The second is:
[tex]x<7\, or\, x>7[/tex]Now, we are not looking for intercetion, we are looking for the union of both. The firts inequality takes all number less than 7 and the second all that are greater than 7, so the only one that is not a solution is 7, which means the correct answer is "all real numbers except 7"
The third is:
[tex]x\ge7\, and\, x\le7[/tex]This is the same as the first one, but now the 7 is included in both:
So, there is only 7 that can be in both indequalitys, thus the correct answer is "one solution, 7".
The fourth is
[tex]x\le7\, or\, x\ge7[/tex]This is similar to the second, but now 7 is included, which means it is also a solution, thus the answer is "all real numbers".
Solve the inequality and graph the solution on the line provided.
< > M >
Inequality Notation:
Number Line:
or
-12 -10 -8 -6
-4 -2
0 2 4
Click and drag to plot line.
2x64 -48
6
8
10 12
Answer:
x ≥ 8Step-by-step explanation:
GivenInequality 2x - 64 ≥ - 48Solution2x - 64 ≥ - 482x ≥ 64 - 482x ≥ 16x ≥ 8To graph the solution, plot the point x = 8, make it closed dot, shade the line to the right from this point.
I will show you the pic
We are given the following system of equations:
[tex]\begin{gathered} 6x-4y=-8,(1) \\ y=-6x+2,(2) \end{gathered}[/tex]To solve this system by substitution we will replace the value of "y" from equation (2) in equation (1)
[tex]6x-4(-6x+2)=-8[/tex]Now we use the distributive property:
[tex]6x+24x-8=-8[/tex]Now we add like terms:
[tex]30x-8=-8[/tex]Now we add 8 to both sides:
[tex]30x-8+8=-8+8[/tex]Solving the operations:
[tex]30x=0[/tex]Dividing by 30:
[tex]x=\frac{0}{30}=0[/tex]Therefore x = 0. Now we replace the value of "x" in equation (2):
[tex]\begin{gathered} y=-6x+2 \\ y=-6(0)+2 \\ y=2 \end{gathered}[/tex]Therefore, the solution of the system is:
[tex](x,y)=(0,2)[/tex]32. Which statement is true if m and n are parallel? A slope m = slope (n)B slope m= -1 (Divide) slope (n)C slope m= 1 (Divide) slope (n)D slope m= -1 x slope (n)
Two lines that parallel, their slopes are equals.
L1 and L2 are parallel only if the slopes of the lines are s1 and s12 are identical
therefore the correct answer is A. slope m = slope (n) since they say that two slopes the same
Emilia and Liam are purchasing a home. They wish to save money for 12 years and purchase a house that has a value of $200,000 which cash. If they deposit money into an account paying 4% interest, compounded monthly, how much do they need to deposit each month in order to make the purchase?
Answer:
Explanation:
Karine invests $6,100 in an account with an annual interest rate of 4.5% compounded daily for 2 years.What is the return on investment for Karine's account?
The return on investment for Katerine's account = 9.4%
Explanation:Amount invested is the principal
Principal, P = $6,100
Annual Interest Rate, r = 4.5% = 0.045
The interest is compounded daily
Number of times the interest is compounded per year, n = 365
Number of years, t = 2 years
The amount after 2 years is calculated as:
[tex]\begin{gathered} A(t)=P(1+\frac{r}{n})^{nt} \\ A=6100(1+\frac{0.045}{365})^{365(2)} \\ A=6100(1.094) \\ A=6673.4 \end{gathered}[/tex]The amount after 2 years = $6673.4
The interest = Amount - Principal
The interest = $6673.4 - $6100
The interest = $573.4
The return on investment is calculated as:
[tex]\begin{gathered} \text{ROI = }\frac{Interest}{Pr\text{incipal}}\times100\text{ \%} \\ \text{ROI}=\frac{573.4}{6100}\times100\text{ \%} \\ \text{ROI = }9.4\text{ \%} \end{gathered}[/tex]The return on investment for Katerine's account = 9.4%
I’m trying to understand where I should shade a graph given the narrative
we have the system
[tex]\begin{gathered} x+y\leq4 \\ y\leq-x+4 \end{gathered}[/tex]The solution to the first inequality is the shaded area below the solid line y=-x+4
[tex]x\ge2[/tex]The solution to the second inequality is the shaded area to the right of the solid vertical line x=2
therefore
The solution to the system is the shaded area below the solid line y=-x+4 and to the right of the solid vertical line x=2
using a graphing tool
see the attached figure below
The solution is the triangular area
(a + 3)-(a + 2) Please help bc im stuck :>
Answer: 1
Step-by-step explanation:
We are given (a + 3) - (a + 2)
To think of this another way, we can distribute the negative sign out into the (a + 2)
(a + 3) -(a) - (2)
Now our expresssion looks like this:
(a + 3) - a - 2
Simplifying, we get
a - a + 3 - 2
The a terms cancel leaving us with
3-2
and that equals
1
Answer:
1
Step-by-step explanation:
1. Rewrite
: (a+3)-(a+2) = a + 3 - a - 2
2. Subtract
: 3-2 = 1 ... so now the equation is a + 1 - a
3. Combine like terms
: a -a = 0 (the a's cancel out) ... now you're left with 1
Since there is nothing left, your answer is 1.
Application machinist is drawing a triangular piece of an industrial machine. Write an equation and solve to find the value of x. Show your work?
Answer:
125
Step-by-step explanation:180=180-(2x+45)+x+80
2x-x=80+45
x=125
One factor of the polynomial x3 − 7x2 + 13x − 3 is (x − 3). What is the other factor of the polynomial? (Note: Use long or synthetic division.) A. (x2 + 4x − 1) B. (x2 − 4x + 1) C. (x − 4) D. (x + 4)
The other factor of the polynomial from what we have here is given as x² - 4x + 1 option B is correct.
How to solve the polynomialWe are required to divide x³ - 7x² + 13x - 3 by x -3
We have this as
x² - 4x + 1
-----------------
x-3 | x³ - 7x² + 13x - 3
we would have
x³ - 3x²
subtract this value by the one that we have above
then we would have
-4x² + 13x
-4x² + 12x
subtract these values from each other to get the value below.
x - 3
Hence the solution to the polynomial would be x² - 4x + 1.
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Consider the following equation: - 6x – 8y =—2A) Write the above equation in the form y = mx + b. Enter the values of m and b in theappropriate boxes below as integers or reduced fractions in the form A/B.)Answer: y =+Preview m: ; Preview b:B) Use your answer in part (A) to find the ordered pair that lies on this line when x = – 40.Answer: (-40,Enter your answer as an integer or a reduced fraction in the form A/B.
we have the equation
-6x-8y=-2
step 1
Isolate the variable y
Adds 6x both sides
-6x-8y+6x=-2+6x
simplify
-8y=6x-2
Divide both sides by -8
-8y/8=(6x-2)/-8
y=-(6/8)x+(2/8)
simplify
y=-(3/4)x+(1/4)therefore
m=-3/4b=1/4Part b
For x=-40
substitute in the equation above
y=-(3/4)(-40)+(1/4)
y=30+1/4
y=121/4
therefore
the answer part b is
(-40,121/4)111. 12 people fit comfortably in a 5 feet by 5 feet area. Use this value to estimate the size of a crowd that is 25feet deep on both sides of the street along a 3-mile section of a parade route (Hint: 1 mile - 5 280 ft)
Answer:
The estimated crowd is of 380160 people.
Step-by-step explanation:
We solve this question applying a proportion on the following format:
People divided by area.
Let's do the drawing:
12 people fit comfortably in a 5 feet by 5 feet area.
So
12 people fitting in an area of 5*5 = 25 ft².
Area of the street:
3 miles = 3*5280 ft = 15840 ft
25 feet on both sides. So, the total area in which the crowd is sparsed is:
A = 15840*25*2= 792000 ft².
Now we apply the ratio:
People over area.
[tex]\frac{12}{25}=\frac{x}{792000}[/tex]Applying cross multiplication:
25x = 12*792000
x = (12*792000)/25
x = 380160
The estimated crowd is of 380160 people.
Prove that if 3/5 x = 9 then x = -15
Given: 3/5 x = 9
Prove: x = -15
There is no proof because X ≠ -15 when 3/5 x = 9
What is multiplication?Multiplication is defined as one of the basic arithmetic operations that is used for the repeated addition of similar figures together.
From the given expression,
3/5x = 9
But X= -15
Substitute X = -15 into the given expression;
That is,
3/5 * -15 = 9
-45/5= 9
-9 = 9
Therefore, there is no proof that in the expression 3/5 x = 9, X ≠ -15 because the final answer is -9 and not ,9.
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-3x + 14y =7 -2x + 13y = -1Should this be solved by elimination or substitution?
ANSWER
Elimination
EXPLANATION
We want to decide what method will be easier to solve the system of simultaneous equations.
From the equation, we see that attempting substitution will be quite difficult because there will be fractions involved thereby making simplification difficult.
On the other hand, elimination will involve multiplying the two equations by certain factors and solving.
Therefore, elimination will be more convenient.
The time spent waiting in the line is approximately normally distributed. The mean waiting time is 5 minutes and the standard deviation of the waiting time is 3 minutes. Find the probability that a person will wait for more than 1 minute. Round your answer to four decimal places.
We were given the following details:
This is a normal distribution. Normal distributions are solved using the z-score
[tex]\begin{gathered} \mu=5min \\ \sigma=3min \end{gathered}[/tex]The z-score for a value, X is calculated using the formula:
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ The\text{ probability that a person will wait more than 1 minute implies that: }X=1 \\ Z=\frac{1-5}{3} \\ Z=-\frac{4}{3} \\ At\text{ Z =}-\frac{4}{3}\text{, pvalue =}0.091759 \\ The\text{ probability that a person waits more than 1 minute is given by:} \\ P=1-0.091759 \\ P=0.908241\approx0.9082 \\ P=0.9082\text{ or }90.82\text{\%} \end{gathered}[/tex]SSS
L
J
++
A) LJ=HF
LK=LG
C)
K
H
G
F
B) LJ LF or
D) ZL=LH
Answer:
A. LJ≅HF
Step-by-step explanation:
Same as last time