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
helpppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
(f o g)(x) = 8x³ + 2x - 6
(g o f)(x) = 2x³ + 2x - 12
Step-by-step explanation:
f(x) = x³ + x - 6; g(x) = 2x
(f o g)(x) = f(g(x))
f(g(x)) = (2x)³ + (2x) - 6
f(g(x)) = 8x³ + 2x - 6
(g o f) = g(f(x))
g(f(x)) = 2(x³ + x - 6)
g(f(x)) = 2x³ + 2x - 12
I hope this helps!
1. Jessica finishes her book in 2 1
3
hours. Eric takes 11
2
times longer than
Jessica to finish his book.
This model represents the amount of time Jessica takes to finish her
book. It has a width of 1 and a length of 2 1
3
. The model is 2 1/3 out of 3
The time taken for Eric to finish the book is 3 1/2 hours.
What is a fraction?A fraction simply means a part of a whole. It van also refer to any number of equal parts.
The information illustrated that Jessica finishes her book in 2 1 / 3 hours and that Eric takes 1 1 / 2
times longer than Jessica to finish his book.
In this case, the time that was used by Eric will be the multiplication of the fractions given. This will be illustrated as:
= 2 1/3 × 1 1/2
Change to improper fraction
= 7/3 × 3/2
= 7 / 2
= 3 1 / 2
Eric used 3 1/2 hours.
This illustrates the concept of multiplication of fractions.
The complete question is written below.
Learn more about fractions on:
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Jessica finishes her book in 2 1/3.hours. Eric takes 1 1/2 times longer than Jessica to finish his book. How long did Eric take yo finish the book?
how do I find the decimal value of the fraction 11/16?
You divide 11 by 16, as follow:
0.6875
16 l 110
-96
140
-128
120
-112
80
-80
0
As you can notice, the result of the division is 0.6875 (here you have used the rules for the division of a number over a greater number, which results in a decimal)
Hurry and answer this pls Bc this have to be turned in
For which equation will x=-2 make the equation true? Equation 1: 2.4x+ 2.6 = 17 Equation 2: 16 = -8(-6 - 2x) X - 4 Equation 3: 3 Equation 4: -6 = -5x - 3+ Óx
We need to check each of the options to determine which equation is true
x = -2
equation1: 2.4x + 2.6 = 17
2.4(-2) + 2.6 = 17
-4.8 + 2.6 = 17
-2.2 = 17
equation2: 16 = -8(-6 - 2x)
16 = -8(-6 -2(-2))
16 = -8(-6+4)
16 = -8(-2)
16 = 16
equation 3: 3
The formula log in a natural logarithm can be written as?
Solution:
Given the logarithmic expression:
[tex]\log_545[/tex]According to the change of base formula,
[tex]\log_BA=\frac{\ln A}{\ln\text{ B}}[/tex]Thus, expressing the logarithm expression in a natural logarithm,
[tex]\log_545=\frac{\ln45}{\ln5}[/tex]Hence, we have
[tex]\frac{\ln45}{\ln5}[/tex]Teresa surveyed 100 students about whether they like pop music or country music. Outof the 100 students surveyed, 42 like only pop, 34 like only country, 15 like both popandcountry, and 9 do not like either pop or country. Complete the two-way frequency table.
SOLUTION
Write out the given information
[tex]\begin{gathered} \text{Total number of student surveyed=100} \\ \text{like pop only=42} \\ \text{like country only=34} \end{gathered}[/tex][tex]\begin{gathered} \text{like both pop and country=15} \\ Do\text{ not like any =9} \end{gathered}[/tex]Construct the two- way frequency table
explain pleaeeeeeeez
Answer:
So first we can assume x= 1 bc there is no number for x
Step-by-step explanation:
So we Evaluate for x=1
1+|2−1|−5
1+|2−1|−5
=−3
Evaluate for x=1
So x+|x-5|+9
1+|1−5|+9
1+|1−5|+9
=14
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!
Answer:
A. reflection over the y-axis
B. translation 3 units right
C. translation 4 down
D. reflection over the x-axis
determine the missing angle measures in each triangle
ANSWER:
50°
STEP-BY-STEP EXPLANATION:
We can calculate the value of the missing angle, since there is a right angle (that is, 90°) and the other is 40 °, we apply the property that says that the sum of all the internal angles of a triangle is equal to 180°, Thus:
[tex]180=90+40+x[/tex]Solving for x:
[tex]\begin{gathered} x=180-90-40 \\ x=50\text{\degree} \end{gathered}[/tex]Each year, a scientist measures the water level of a local lake. Negative numbers indicatethat the water level is below its historical average. Which list shows the water levels in orderfrom highest to lowest?0.7, 0.38, 0.09, – 0.41, – 0.60.7, 0.38, 0.09,-0.6,- 0.41-0.6, 0.38, – 0.41, 0.09, 0.70.38, 0.09, 0.7,– 0.6 – 0.410.38, 0.7, 0.09 – 0.41, -0.6
Answer:
-0.6, -0.41, 0.09, 0.39, 0.7
Step-by-step explanation:
Negative numbers: The higher the absolute number, the lower it is. For example, -2 is lower than -1.
Positive numbers: The lower the absolute number, the lower it is. For example, 1 is lower than 2.
In this question:
We have these following values:
0.7, 0.39, 0.09, -0.41, -0.6
Ranking from lowest to highest, it is:
-0.6, -0.41, 0.09, 0.39, 0.7
Joseph owns a 50 inch TV and it measures 50 inch on the diagonal. if the television is 40 inches across the bottom find the height of the TV
Let's draw the tv with the given values.
Note that we will form a right triangle with heigh of h, base of 40 and a hypotenuse of 50.
The Pythagorean Theorem is :
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse, a and b are the legs of the triangle.
Using the formula above. we will have :
[tex]\begin{gathered} 50^2=40^2+h^2 \\ 2500=1600+h^2 \\ h^2=2500-1600 \\ h^2=900 \\ \sqrt[]{h^2}=\sqrt[]{900} \\ h=30 \end{gathered}[/tex]The answer is 30 inches
John sells plain cakes for $8 and decorated cakes for $12. On a particular day, John started with a total of 100 cakes, and sold all but 4. His sales that day totaled $800.He sold ___plain cakes and ____decorated cakes that day.
INFORMATION:
We know that:
- John sells plain cakes for $8 and decorated cakes for $12.
- On a particular day, John started with a total of 100 cakes, and sold all but 4.
- His sales that day totaled $800.
And we must find the number of plain cakes and decorated cakes that he sold that day.
STEP BY STEP EXPLANATION:
To find them, we can represent the situation using a system of equations
[tex]\begin{cases}x+y={100-4...(1)} \\ 8x+12y={800...(2)}\end{cases}[/tex]Where, x represents the number of plain cakes that he sold and y represents the number of decorated cakes that he sold.
Now, we must solve the system:
1. We must multiply the equation (1) by -8
[tex]\begin{gathered} -8(x+y)=-8(100-4) \\ -8x-8y=-768...(3) \end{gathered}[/tex]2. We must add equations (2) and (3)
[tex]\begin{gathered} 8x+12y=800 \\ -8x-8y=-768 \\ ---------- \\ 0x+4y=32 \\ \text{ Simplifying, } \\ 4y=32...(4) \end{gathered}[/tex]3. We must solve equation (4) for y
[tex]\begin{gathered} 4y=32 \\ y=\frac{32}{4} \\ y=8 \end{gathered}[/tex]4. We must replace the value of y in equation (1) and then solve it for x
[tex]\begin{gathered} x+8=100-4 \\ x=100-4-8 \\ x=88 \end{gathered}[/tex]So, we found that x = 88 and y = 8.
Finally, John sold 88 plain cakes and 8 decorated cakes.
ANSWER:
He sold 88 plain cakes and 8 decorated cakes that day.
What type of number is {-4}{2}
−4/2
start fraction, minus, 4, divided by, 2, end fraction?
Choose all answers that apply:
(Choice A)
Whole number
(Choice B)
Integer
(Choice C)
Rational
(Choice D)
Irrational
Answer:
B and C
Step-by-step explanation:
Whole numbers are:
0, 1, 2, 3, 4, 5, 6...
The number we are looking at is -4/2, which is -2. Whole numbers aren't negative. So not choice A.
Integers are:
...-3, -2, -1, 0, 1, 2, 3...
Positives and negatives are included (just no fractions or decimals) So, -4/2 which is -2 IS an integer.
Rational numbers can be written like a ratio (like a fraction) So -4/2 totally IS a rational number.
Irrational numbers are decimal numbers that go on forever without repeating, like pi and sqrt2 and sqrt5. -4/2 is NOT irrational.
Ana has $75 and saves an additional $13 per week. Which equation can be used to findhow many weeks it will take until she has $452?75 + w = 4520 75 + 13w = 45213w = 75 = 452452 + 13w = 75
Here, we want to get an equation
Firstly, since we do not have the number of weeks, we can represent it with a variable (a letter)
In this case, we shall be representing it with w
Since she saves $13 in a week, in w weeks, the amount saved will be;
13 * w = $13w
Now, recall that she has $75 before she started saving. What this mean is that at the end of the w weeks, the amount she will have will be ;
[tex]13w\text{ + 75}[/tex]We now proceed to equate this to the total she wants to save and we finally have the complete equation below;
[tex]13w\text{ + 75 = 452}[/tex]Write the equation for the quadratic function in vertex form & standard form with the given vertex that passes through the given point.Vertex (2, -8) through the point (4, 3)
We will have the following:
[tex]\begin{gathered} y=a(x-2)^2-8\Rightarrow3=a(4-2)^2-8 \\ \\ \Rightarrow3=4a-8\Rightarrow4a=11 \\ \\ \Rightarrow a=\frac{11}{4} \end{gathered}[/tex]So, the equation in vertex form is:
[tex]y=\frac{11}{4}(x-2)^2-8[/tex]And in standard form:
[tex]\begin{gathered} y=\frac{11}{4}(x^2-4x+4)-8\Rightarrow y=\frac{11}{4}x^2-11x+11-8 \\ \\ \Rightarrow y=\frac{11}{4}x^2-11x+3 \end{gathered}[/tex]***Explanation***
We know that the quadratic expression in vertex form follows:
[tex]y=a(x-h)^2+k[/tex]Where (h, k) is the vertex of the expression. Now, we know that the vertex is (2, -8), so we replace those values and we obtain:
[tex]y=a(x-2)^2+(-8)\Rightarrow y=a(x-2)^2-8[/tex]Now, in order to determine "a" we must replace one point (That is not the vertex) in the expression and solve for "a", and we are told that the point (4, 3) is in one of the solutions, so:
[tex]\begin{gathered} 3=a(4-2)^2-8\Rightarrow3=a(2)^2-8 \\ \\ \Rightarrow11=4a\Rightarrow a=\frac{11}{4} \end{gathered}[/tex]Thus, the expression in vertex form is then:
[tex]y=\frac{11}{4}(x-2)^2-8[/tex]And to determine the standard form, we simply expand the equation in vertex form:
[tex]y=\frac{11}{4}(x^2-4x+4)-8\Rightarrow[/tex]A bird sits on top of a Lamppost. The angle made by the lamp-post and a line from the feet of the bird to the feet of the Observer standing away from the Lamppost is 55°. the distance from the Lamppost and the Observer is 25 ft. estimate the height of the lamp post
A bird sits on top of a Lamppost. The angle made by the lamp-post and a line from the feet of the bird to the feet of the Observer standing away from the Lamppost is 55°. the distance from the Lamppost and the Observer is 25 ft. estimate the height of the lamp post
we have that
see the attached figure to better understand the problem
so
tan(55)=h/25
solve for h
h=25(tan(55))
h=35.7 ftAva graphs the function h(x) = x^2 + 4. Victor graphs the function g(x) = (x + 4)^2. Which statements are true regarding the two graphs? Select three options.Ava’s graph is a vertical translation of f(x) = x^2.Victor’s graph is a vertical translation of f(x) = x^2.Ava’s graph moved 4 units from f(x) = x^2 in a positive direction.Victor’s graph moved 4 units from f(x) = x^2 in a positive direction.Ava’s graph has a y-intercept of 4.
Given,
Ava graphs the function h(x) = x^2 + 4.
Victor graphs the function g(x) = (x + 4)^2.
Required:
Check the correct statement about graph.
The graph of Ava and vector function is:
Here, victor graph was represented by blue curve and ava graph by green curve.
For first statement,
Ava’s graph is a vertical translated by 4 units.
Hence, statement is true.
For second statement,
The graph of victor is not vertically translated.
Hence, statement is false.
For statement three,
The curve of the Ava graph is moved 4 unit up in the positive direction. It is in y axis. Hence, statement is true.
For statement forth,
The curve of the victor graph is moved to negative direction not positive. Hence, statement is false.
For statement fifth,
The graph of Ava has the y intercept at 4. So, statement is correct.
Hence, option A (Ava’s graph is a vertical translation of f(x) = x^2), option C (Ava’s graph moved 4 units from f(x) = x^2 in a positive direction) and option E (Ava’s graph has a y-intercept of 4.) is true.
For the given f(x), solve the equation f(x)=0 analytically and then use a graph of y=f(x) to solve the inequalities f(x)<0 and f(x)≥0. f(x)=ln(x+3)(1) What is the solution of f(x)=0?(2) What is the solution of f(x)<0?(3) What is the solution of f(x)≥0?
Explanation:
f(x) is a logarithmic function. Logarithmic functions are zero when the argument is 1:
[tex]\begin{gathered} f(x)=\ln (x+3)=0 \\ x+3=1 \\ x=1-3 \\ x=-2 \end{gathered}[/tex]For greater values, the function is positive and for less values the function is negative.
Answers:
(1) x = -2
(2) x < -2. In interval notation x:(-∞, -2)
(3) x ≥ -2. In interval notation x:[-2, ∞)
What is the Y intercept of the graph below? A. (0,-2)B. (0,-4) C. (0, 2) D. (0,4)
Recall that the y-intercept of a graph is the point where the graph intersects the y-axis.
From the given graph we get that the line intersects the y-axis at (0,2).
Answer: Option C.
May I please get help with numbers (4), (5), and (6). I have tried multiple times to find the correct answers for each of them but still could not get the accurate or at least correct answers for each of them. I would appreciate it so much if I could get help
EF =21
4) Let's find out the measure of the line segment EF, using the Trapezoid Midsegment Formula:
[tex]M=\frac{B+b}{2}[/tex]4.1) We can plug into that the lengths of AD and BC:
[tex]M=\frac{18+24}{2}=\frac{42}{2}=21[/tex]Note that the Midsegment is the average of the bases of a trapezoid.
4.3) Hence, the answer is 21
what is the LCM of 4 and 6 ?
LCM stands for Least Common Multiple.
And it is defined as the product of the two numbers divided by the GCD (greatest common divisor)
In our case, the product of 4 and 6 is 24, , and the greatest common divisor of 4 and 6 is "2". Therefore, the LCM of 4 and 6 is 24/2 = 12
Let me also use the Venn diagram that your teacher provided:
In the diagram we enter the factors that correspond to both numbers (4 and 6), and in the intersection of the two sets (intersection of the circle) we type a "2" which is the ONLY factor 4 and 6 have in common (the greatest common divisor of the two given numbers) So complete a diagram as follows:
We typed a 2in the area common to both numbers. Then your LCM is the product of 2 times 2 times 3 = 12
Notice the blue set (circle) contains the two factors for 4 (2 * 2) and the orange circle contains the two factor for 6 (2 * 3)
We set in the intersection of the two circles the factor that is common to both.
Do you want me to complete the second question with a Venn diagram as well? Perfect.
The second question is about the LCM of the numbers 12 and 8
Then we create a Venn diagram like the following, considering that the factor in common between 12 and 8 is 4, because 12 = 4 * 3 and 8 = 4 * 2
Again here, the factors 3 and 4 (that give 12) are typed in the blue circle. and the factors that form 8 (4 * 2) are typed inside the orange circle.
The factor that both share is in the middle "4". Therefore, now to find the LCM you simply multiply the three numbers shown in the Venn diagtam: 3 * 4 * 2 = 24
Then 24 is your LCM.
What is the distance from 7 to 0? O A. 7, because 171 = 7 Jurid O B. 7, because 171 = 7 O c. 7, because |-71 = -7 O D. -7, because [7] = -7
The distance from 7 to 0 is 7 because the absolute value of 7 is 7.
Correct Answer: A
NEED HELP ASAP
What is the value of X? Justify each step
The value of x = 3 ,where ,
AC = 32 , AB = 2x , BC = 6x + 8 .
Solution:Here given,
AB = 2x
BC = 6x + 8
AC = 32
AC = (AB + BC) (Rule of addition).
So ,
2x + 6x + 8 = 32 (by applying substitution rule) .
In the equation AB + BC = AC, substitute for AB, BC, and AC.
Simplifying,
8x + 8 = 32
2x + 6x + 8 = 32 (when simplified by incorporating similar terms).
8x = 24
8x = 32 - 8
8x = 24
On dividing both sides by 8
8x / 8 = 24/8
x = 3
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Bella drove her car 81 km and used 9 liters of fuel. She wants to know how many kilometers (x) she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.
Find the proportion between liters of fuel
that is find 22/9 = 2.444
thats how much liters have more to consume
now multiply 2.444 by 81 , the kilometers she has drived
It gives as result 2.444 x 81 = 198 kilometers
Tyler said he swam 23 tenths miles this week. His coach said Tyler swam 2.3 miles this week. To find who is correct, model the distance both Tyler and his coach said Tyler swam. Use the flat as 1 unit. A: What do you need to use?B: What do you know about representing whole numbers and decimals that may help you solve the problem? C: Complete the sentencesAre the models alike or different?Tyler swam _____ tenths, or _____, miles.So, _____________________ are correct.
Answer with explanation:
We need to determine if what Tyler is saying is in fact equal to what his coach said, to get the final answer, we have to concert the resulting units in miles:
Taylor's answer:
[tex]23\times(\frac{1}{10})\text{ miles}\Rightarrow(\frac{23}{10})\text{miles}\Rightarrow2.3\text{ miles}[/tex]Coach's answer:
[tex]2.3\text{ miles}[/tex]In conclusion, The two answers are correct so the two models are indeed alike.
which statement is true
We have to analyze the given options to solve this problem.
Option 1.
The absolute value of -12 is larger than the absolute value of 12.
The absolute value is always a positive number:
[tex]undefined[/tex]creat an espression that includes the zero property of exponents the multiplication property of exponents and the power of a power property of exponents
All in one, or one expression for each property?
a) Zero property
[tex]\text{ (x + y)}^0\text{ = 1}[/tex]b) Multiplication property
[tex]\text{ x}^2\cdot x^5=x^{2+5}=x^7[/tex]c) Power property
[tex]\text{ (x}^2)^3=x^{2\cdot3}=x^6[/tex]d) All in one (this is the expression)
[tex]\mleft\lbrace\text{(x}^0)(x^3)\mright\rbrace\text{ }(x^2)^5[/tex][tex]\text{ }\mleft\lbrace1(x^3\mright)\}(x^{10})[/tex]
What is the probability that a randomly chosen marble is red or small?
We have the next formula
[tex]P\mleft(RorS\mright)=P\mleft(R\mright)+P\mleft(S\mright)-P\mleft(RandS\mright)[/tex]P(R)=0.7
P(S)=0.9
P(RandS)=0.6
The probability that randomly chosen marbñe is red or small is
[tex]\begin{gathered} \\ P(RorS)=0.7+0.9-0.6=1 \end{gathered}[/tex]A person invested $3,700 in an account growing at a rate allowing the money to double every 6 years. How much money would be in the account after 14 years, to the nearest dollar?
Given :
The principal = 3,700
Assume a simple interest
The account growing at a rate allowing the money to double every 6 years.
So,
[tex]\begin{gathered} I=P\cdot r\cdot t \\ I=P \\ 3700=3700\cdot r\cdot6 \\ r=\frac{1}{6} \end{gathered}[/tex]How much money would be in the account after 14 years, to the nearest dollar?
So, we will substitute with r = 1/6, t = 14 years
So,
[tex]\begin{gathered} I=3700\cdot\frac{1}{6}\cdot14=8633.33 \\ \\ A=P+I=8633.33+3700=12333.33 \end{gathered}[/tex]Rounding to the nearest dollar
So, the answer will be $12,333