The value of angle 3 is 63.3⁰.
The sum of angle 3 and angle 4 is determined as 126.6⁰.
What is the measure of angle 1?
The value of angle labelled 1 is calculated by applying the following method;
angle 1 = angle 3 (alternate angles are equal)
The value of angle 3 is calculated as;
∠3 + 79.4⁰ + 37.3⁰ = 180⁰
∠3 + 116.7⁰ = 180⁰
∠3 = 180 - 116.7⁰
∠3 = 63.3⁰
The value of angle 4 is calculated as follows;
∠3 = ∠4 (the vertical opposite angle of angle 3 is the corresponding angle of angle 4)
∠4 = 63.3⁰
∠4 + ∠3 = 2 x 63.3⁰ = 126.6⁰
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Item 3 You fill bags with cookies to give your friends. You bake 45 chocolate chip cookies, 30 peanut butter cookies, and 15 oatmeal cookies. You want identical groups of cookies in each bag with no cookies left over. What is the greatest number of bags you can make? The greatest number of identical bags you can make is
Answer:
30 in each bag
Step-by-step explanation:
2/3 - 4x + 7/2 = -9x + 5/6 need help asap please!
Answer:
X= Negative 2/3 or -0.6
Step-by-step explanation:
here you go
How can the zeros and end behavior of a polynomial function allow a graph to be sketched?
Given a polynomial of the following form:
\(f(x)\text{ = (x-1)}(x+1)^2(x^2-4)\)Equaling f(x) to zero:
\(0=(x-1)(x+1)^2(x^2-4)\)
If we know that f(x) is equal to zero, then at least one term or all terms are equal to zero.
Equaling each term to zero as shown as follows:
x-1 = 0 (x+1)^2 = 0 x^2-4 = 0
Isolating the x:
x=1 x=-1 x=± 2
Now, looking at the degree of the power of each term.
(x-1)^1 --> m=1 [odd] (x+1)^2--> m=2 [even] (x^2-4)^1-->m=1 [odd]
Now, we can draw the graph:
Yesterday, a movie theater sold 279 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, the movie theater made $567 from popcorn sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.
Answer:
x=96 and y=183
Step-by-step explanation:
Your welcome
Which tool could be used to model wave motion during a scientific investigation?
A: beam balance
B: mirror
C: prism
D: slinky spring
Answer:
D: slinky spring
Step-by-step explanation:
Gerri says that if a number is a multiple of 9 it is also a multiple of 3.Do you agree? Explain.
rationalize the denominator of
1/3+√2
Answer:
(-√2 + 3)/7
Step-by-step explanation:
To rationalize the denominator, we need to multiply by the conjugate:
1/(3 + √2)*(3 - √2)/(3 - √2)
(3 - √2)/(9 - √4)
(3 - √2)/(9 - 2)
(-√2 + 3)/7
what is the slope of the line perpendicular to the line through the points (-1,6) and (3,-4)
Answer:
The slope of the perpendicular line is 2/5.
Step-by-step explanation:
We want to find the slope of the line that is perpendicular to the line that passes through the points (-1, 6) and (3, -4).
Recall that the slopes of perpendicular lines are negative reciprocals of each other.
Find the slope of the original line:
\(\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{(-4)-(6)}{(3)-(-1)}=\frac{-10}{4}=-\frac{5}{2}\)
The slope of the perpendicular line will be its negative reciprocal.
Thus, the slope of the perpendicular line is 2/5.
The slope of the line perpendicular to the line through the points (-1,6) and (3,-4) is -5/2.
Step-by-step explanation:We have to find the slope of the line perpendicular to the line through the points (-1,6) and (3,-4).
using the formula;-
m = (y²-y¹) / (x²-x¹)
Where,
m = slope ( y² - y¹) = ( -4 -6 )( x² - x¹) = ( 3 - 1)plug the value and simplify.
m = ( (-4 ) - 6)/(3 - (- 1)
m = - 10 / 4
m = - 5/2
Hence, The slope of the line perpendicular to the line through the points (-1,6) and (3,-4) is -5/2.
what is the value of 6 in the number 7689
Answer:
7 6 8 9
The value of 6 is in the hunderth place and represents 600
Hope this helps!! <3
Consider the point (-4, -2). What will be the coordinates of the new point if we
-Reflect it across the line y=x
-Translate it 2 units to the right and 3 units up?
The coordinates of the new point after applying the given set of transformation is given by the ordered pair (0, -1).
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.
Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is given by this transformation rule:
(x, y) → (y, x)
Ordered pair A = (-4, -2) → Ordered pair A' = (-2, -4).
Next, we would apply a translation of 2 units to the right and 3 units up:
(x, y) → (x + 2, x + 3)
Ordered pair A' = (-2, -4) → (-2 + 2, -4 + 3) → Ordered pair A' = (0, -1).
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Alice,barbra, and carol are sisters. alice is 3 years younger then barbara is 5 years younger then carol. together the sisters are 68 years old. how old is barbara?
The age of Barbra is 22 years.
What is method of substitution?The algebraic method for solving simultaneous linear equations is the substitution method. A quantity of one variable through one expression is replaced in the second equation, as the name implies.
Now, according to the question.
Let 'a' be the age of Alice.
Let 'b' be the age of Barbra
Let 'c' be the age of Carol.
The sum of age of all three sisters is 68 years.
Thus, a + b + c = 68
Now, as Alice is three years younger than Barbra.
a = b - 3
and, Barbra is 5 years younger than Carol.
b = c - 5
c = b + 5
By substitution of values of a and c in total age.
(b - 3) + b + (b + 5) = 68
3b - 3 + 5 = 68
On solving the expression.
b = 22
Therefore, the age of Barbra is 22 years.
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Question 42: Which equation represents the line that passes through the points
(-1, -2) and (3, 10)? *
O y = 3x + 1
O y = 3x - 1
O y = 4x + 2
O y = 4x - 2
Answer:
y = 3x + 1
Step-by-step explanation:
first we need to find the slope
m = (y2-y1) / (x2-x1)
m = (10 - -2) / (3 - -1) = 3
note that it does not matter which points you chose to be second or first
then use slope point equation again it does not matter which point you use
y - y1 = m ( x - x1 )
y - 10 = 3 ( x - 3)
y - 10 = 3x -9
y = 3x -9 + 10
y = 3x +1
Use the slope formula below (Rise Over Run)
\( \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }\)
We are given two points. Substitute those points in the equation. Remember that it is (x,y) and not (y,x).
\( \large{m = \frac{10 - ( - 2)}{3 - ( -1)} } \\ \large{m = \frac{10 + 2}{3 + 1} \longrightarrow m = \frac{12}{4} } \\ \large \boxed{\purple{m = 3}}\)
Next we will be using the point-slope form then convert into slope-intercept form. You can also use the slope-intercept form to substitute one of these points and solve for the y-intercept. However, I will be using the point-slope form instead.
\( \large \boxed{y - y_1 = m(x - x_1)}\)
The equation above is in point-slope form. Next we can substitute one of given points. I will choose (-1,-2) to substitute (You can use another point as well since the outcome would be the same.)
\( \large{y - ( - 2) = 3(x - ( - 1))}\)
We substitute x1 = -1, m = 3 and y1 = -2. Next, we simplify the equation and convert it in slope-intercept form.
\( \large{y + 2 = 3(x + 1)} \\ \large{y = 3(x + 1) - 2} \\ \large{y = 3x + 3 - 2} \\ \large \boxed{ \red{y = 3x + 1}}\)
Answer
y = 3x+1Jonczyk Company is considering two different, mutually exclusive capital expenditure proposals. Project A will cost $454,000, has an expected useful life of 13 years and a salvage value of zero, and is expected to increase net annual cash flows by $68,000. Project B will cost $300,000, has an expected useful life of 13 years and a salvage value of zero, and is expected to increase net annual cash flows by $47,000. A discount rate of 9% is appropriate for both projects. Click here to view PV table.
Calculate the net present value and profitability index of each project. (If the net present value is negative, use either a negative sign preceding the number e.g. -45 or parentheses e.g. (45). Round present value answers to 0 decimal places, e.g. 125 and profitability index answers to 2 decimal places, e.g. 15.52. For calculation purposes, use 5 decimal places as displayed in the factor table provided, e.g. 1.25124.)
Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.
A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.
Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14
Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96
The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.
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Someone explain please
Answer:
SA = 94 ft²
Step-by-step explanation:
To find the surface area of a rectangular prism, you can use the equation:
SA = 2 ( wl + hl + hw )
SA = surface area of rectangular prism
l = length
w = width
h = height
In the image, we are given the following information:
l = 4
w = 5
h = 3
Now, let's plug in the information given to us to solve for surface area:
SA = 2 ( wl + hl + hw)
SA = 2 ( 5(4) + 3(4) + 3(5) )
SA = 2 ( 20 + 12 + 15 )
SA = 2 ( 47 )
SA = 94 ft²
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Find the circumference of a circle that has a radius of 7 cm. Use 3.14 for .
Answer:
C = 2rπ
C = 2(7)(3.14) = 53.38
Step-by-step explanation:
The product –2 • (–5) is shown on the number line. A number line shows an arrow from 0 to negative 5 labeled negative 5, another arrow from negative 5 to negative 10 labeled negative 5, and another arrow from 0 to 10 labeled the opposite of 2 times negative 5. Complete the sentences to explain how the model on the number line could be used to find the answer. Starting at 0 move twice to the left______ spaces. 2 • (–5) = ______. The answer is the opposite of that value, ______ .
Answer:
Starting at 0 move twice to the left___5___ spaces. 2 • (–5) = ___-10___. The answer is the opposite of that value, ___10___ .
Step-by-step explanation:
The required blank space is filled by the numbers, 5, -10, and 10.
Given that,
Starting at 0 move twice to the left______ spaces. 2 • (–5) = ______. The answer is the opposite of that value, ______ . To determine the solutions for the blank spaces.
A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
here,
The number line 2(-5), shows that move twice to the left 5 spaces.
And This results in -10 spaces having to move, and the outcome is the opposite of the number 10.
Thus, A complete solution is "Starting at 0 move twice to the left 5 spaces. 2 • (–5) = -10. The answer is the opposite of that value, 10.
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The circumference of a circle is 11π m. What is the area, in square meters? Express your answer in terms of π.
The ceiling of Katie’s living room is a square that is 15 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Katie can buy rolls that each contain 20 ft of crepe paper. What is the minimum number of rolls she should buy? Show your work.
Answer:
6 rolls because the total perimeter is 102 ft and five rolls is only 100 feet. So she needs 6 rolls.
Step-by-step explanation:
to find perimeter, add up all the side lengths.
so 15*4 (it's easier than 15+15+15...)
60 ft.
now we have to use Pythagorean's Theorum to find corner to corner.
so \(a^2+b^2=c^2\)
we have a and b
\(15^2+15^2=c^2\)
do the math...
225+225= 450
square root of 450=
21.213
double that because it's used twice (corner to corner and corner to corner)
42.426
now add it all up
42.426 + 60 = 102.426
we can round
102
20*5 = 100
so she needs 6
MY ORIGINAL ERROR WAS 5, BUT 5 TIMES 20 IS ONLY 80, SO THEREFORE 6 IS REQUIRED SO THERE IS ENOUGH TO COVER 102.
Answer:
Katie needs 6 crepe rolls.
Step-by-step explanation:
Hello!
Katie originally needed ~5.1 crepe rolls, but since its a question on how many rolls she should by, she should get 6.
There are a couple of steps in order to solve this.
Brainly is being weird- so I put an explanation to the problem in the image below- hope it helps!
Mr.Eastman drew triangle JKL,with a height of 12 inches and a base of 12 inches, and triangle XLZ, with a height of 8 inches and a base of 16 inches.Which trangle has the greater area?
Answer:
Step-by-step explanation:
Area of triangle = 1/2 × Base × Height
Mr.Eastman drew triangle JKL,with a height of 12 inches and a base of 12 inches
Area of JKL = 1/2 × 12 inches × 12 inches
= 72 Square inches
triangle XLZ, with a height of 8 inches and a base of 16 inches. Which triangle has the greater area?
A bubble originating at the bottom of a lake rises to the surface within 10.0 seconds with an acceleration of 10.0 meters/second2. what is the depth of the lake? a. 100 meters b. 200 meters c. 300 meters d. 400 meters e. 500 meters
The depth of the lake is 500 meters.
According to the question
Acceleration = 10 m/s²
Time = 10 sec
Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
The distance covered in a certain time of accelerated motion:
D = (1/2) × A × T²
Distance covered= (1/2) (Acceleration) (Time squared) .
The question gives us the acceleration and the time.
Let's plug them into the formula.
Distance = (1/2) (10 m/s²) (10 sec)²
= (5 m/s²) (100 sec²)
= 500 meters.
The depth of the lake is 500 meters.
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in the diagram below of triangle KLM, N is the midpoint of KM and O is the midpoint of LM if NO equals 3+ 7X and KL equals 4X +16 what is the measure of no
If O is the midpoint of LM and N is the midpoint of KM then the measure of NO is 10.
What are Linear equations?Linear equations are a combination of constants and variables where the value of the variable is calculated using mathematical operations.
We have given that Triangle KLM, N is the midpoint of KM and O is the midpoint of LM if NO equals 3+ 7X and KL equals 4X +16, we are supposed to find the measure of NO.
Using the Midpoint theorem, we can say that in Triangle KLM;
NO = KL / 2
Substituting values,
3+ 7X = 4X +16/ 2
3+ 7X = 2X + 8
7x - 2x = 8 - 3
5x = 5
x = 1
NO = 3+ 7X
NO = 3+ 7(1) = 10
NO equals 10
Hence the measure of NO is 10.
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The quadratic function h(t) = 16t2 models the height (in feet) at time t (in seconds). A person drops an egg off the roof of a building from a height of 92 feet.
a) How long does it take the egg to pass by a window at a height of 20 feet?
The time it take the egg to pass by a window at a height of 20 feet is 2.18 secs
What are quadratic equations?Given the quadratic equation that models the height as h(t) = 16t^2If a person drops an egg off the roof of a building from a height of 92 feet, then;
96 - 20= 16t^2
t^2 = 76/16
t = 2.18secs
Hence the time it takes the egg to pass by a window at a height of 20 feet is 2.18 secs
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What is a 2 step equation that equals to 14
Answer:
2x + 1 = 29
Step-by-step explanation:
There are a lot of answers.
2x + 1 = 29
2x + 1 = 29 Subtract 1 from both sides
2x = 28 Divide both sides by s
x = 14
Start off knowing that x will be 14, then multiply 14 by some number and then add or subtract some number from that and put that on the other side of the equal sign.
x = 14
14 x 2 = 28 and then add 1 to that to get 29
2x + 1 = 29
Answer: Do you want x=14 or for it to equal 14, because I have it both ways. For x=14, an acceptable two step equation would be 2x-5=23. If you want it to equal 14, then you can write 5x-1=14
Step-by-step explanation:
For x=14:
2x-5=23
Add 5 on both sides
2x=28
x=14
For the equation to equal 14:
5x-1=14
Add one on both sides
5x=15
x=3
Which number sentence is true? A. 8.565 < |-13.23| B. 7/8 < 0.78 C. 4/11 < -4.11 D. 23.5 < 2 3/5
Answer:
A
Step-by-step explanation:
beacuse the rest are false
G(x)=4x^2+9x ; find g(3x)
Answer:
12xto the 3 + 27x squared
which expression is a possible leading term for the polynomial function graphed below? –18x14 –10x7 17x12 22x9
Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.
The leading term of a polynomial function is the term containing the highest power of the variable. Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.
The degree of a polynomial function is the highest degree of any of its terms.
If a polynomial has only one term, then the degree of that term is the degree of the polynomial and is also called a monomial.
For example, consider the given function:Now, observe the degree of the function, which is 14, as the highest exponent of the function is 14.
Thus, the term containing the highest power of the variable x is -18x¹⁴.
Therefore, among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.
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is this the correct answer?
Answer:
Yes that answer is correct
Step-by-step explanation:
Im literally god
Evaluate the following: (d) \( (-4 i)^{3 i} \); (e) \( \sin (-3-i) \); (f) \( \tan (4 i) \).
d) \((-4i)^{(3i)\) simplifies to \(e^{(3i ln(4) - 3\pi/2)\).
e) sin(-3 - i) simplifies to (\(e^{(3i - 1)} - e^{(-3i + 1)\)) / (2i)
To evaluate the given expressions, let's go through each one:
(d) \((-4i)^{(3i)\):
To evaluate \((-4i)^{(3i)\), we can use Euler's formula, which states that \(e^{(i\theta)\) = cos(θ) + i sin(θ). We'll express -4i in Euler's form and then raise it to the power of 3i.
-4i = 4\(e^{(i(3\pi/2))\) [Using Euler's formula]
Now, we can raise it to the power of 3i:
\((-4i)^{(3i)\) =\((4e^{(i(3\pi/2))})^{(3i)\)
Apply the exponent rule \((a^b)^c = a^{(b*c)\):
= \(4^{(3i)} * e^{(-3\pi/2)\)
The real number 4 raised to the power of a complex number can be expressed as:
\(4^{(3i)\) = \(e^{(3i ln(4))\)
Substitute this back into the expression:
= \(e^{(3i ln(4))} * e^{(-3\pi/2)\)
Apply the rule \(e^{(a+b)} = e^a * e^b\):
= \(e^{(3i ln(4) - 3\pi/2)\)
Thus, \((-4i)^{(3i)\) simplifies to \(e^{(3i ln(4) - 3\pi/2)\).
(e) sin(-3 - i):
To evaluate sin(-3 - i), we can use the formula:
sin(x) = \((e^{(ix)} - e^{(-ix)})\) / (2i)
Let's substitute -3 - i into the formula:
sin(-3 - i) = \((e^{((-3 - i)i)} - e^{(-(-3 - i)i)})\) / (2i)
= (\(e^{(3i + i^2)} - e^{(-3i - i^2)\)) / (2i)
= (\(e^{(3i - 1)} - e^{(-3i + 1)\)) / (2i)
Therefore, sin(-3 - i) simplifies to (\(e^{(3i - 1)} - e^{(-3i + 1)\)) / (2i)
(f) tan(4i):
To evaluate tan(4i), we can use the formula:
tan(x) = (sin(2x)) / (cos(2x))
Substituting 4i into the formula:
tan(4i) = (sin(2 * 4i)) / (cos(2 * 4i))
= (sin(8i)) / (cos(8i))
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Consider the quadratic function f(x)= 2(x + 4)² − 6. Does the graph open up or down
Answer:
up
Step-by-step explanation:
a is positive
Solve for P please
17.5 - 6.3p =
The value of p from the equation 17.5 - 6.3p = 25 is 1.19
What are algebraic expression?Algebraic expression can be defined as a mathematical expression that are variables, terms, factors, constants and coefficients.
These expressions are also composed of mathematical or arithmetic operations, which includes;
DivisionAdditionSubtractionFloor divisionMultiplicationBracketParenthesesFrom the information given, we have that;
17.5 - 6.3p = 25
Now, let's take the following steps
collect like terms
-6.3p = 25 - 17.5
subtract the like terms
-6.3p = 7.5
Divide both by the coefficient of p, we get;
p = 7.5/-6.3
p = 1.19
Hence, the value is 1.19
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Complete question:
Solve for P please
17.5 - 6.3p = 25