Answers
Step-by-step explanation:
For a RIGHT triangle , remember S-O-H-C-A-H-T-O-A ?
Cos (Φ) = Adjacent leg / Hypotenuse
so cos D = sqrt (78) / DF = sqrt (78) / 28
Related Questions
Two distinct number cubes are rolled together. Each number cube has sides numbered 1 through 6.
What is the probability that the outcome of the roll is an even sum or a sum that is a multiple of 3?
Enter your answer, in simplest fraction form, in the box.
Answers
Answer:
2/3
Step-by-step explanation:
asking whether the linear system corresponding to an augmented matrix [a1 a2 a3 b] has a solution amounts to asking whether b is in span {a1, a2, a3}.
Answers
To determine if the linear system corresponding to an augmented matrix [a1 a2 a3 b] has a solution, we can check whether the vector b is in the span of the vectors {a1, a2, a3}.
In linear algebra, the augmented matrix represents a system of linear equations. The columns a1, a2, and a3 correspond to the coefficients of the variables in the system, while the column b represents the constants on the right-hand side of the equations. To check if the system has a solution, we need to determine if the vector b is a linear combination of the vectors a1, a2, and a3.
If the vector b lies in the span of the vectors {a1, a2, a3}, it means that b can be expressed as a linear combination of a1, a2, and a3. In other words, there exist scalars (coefficients) that can be multiplied with a1, a2, and a3 to obtain the vector b. This indicates that there is a solution to the linear system.
On the other hand, if b is not in the span of {a1, a2, a3}, it implies that there is no linear combination of a1, a2, and a3 that can yield the vector b. In this case, the linear system does not have a solution.
Therefore, determining whether the vector b is in the span of {a1, a2, a3} allows us to determine if the linear system corresponding to the augmented matrix [a1 a2 a3 b] has a solution or not.
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i need the find the area of a rectangle. the length is 6.5x + 5ft and the width is 15 ft
Answers
Answer:
Area= l+b) ×2
6.5x+5ft +5ft
13x+20ft
solve 5^2x+1-5^2x=150 with steps
Answers
Answer:
x = 2.98
Step-by-step explanation:
5^2x + 1 - 5^2x = 150
25x + 1 + 25x = 150
50x + 1 = 150
50x = 149
x = 2.98
5^2x + 1 - 5^2x = ?
5^2(2.98) + 1 - 5^2(2.98) = ?
25(2.98) + 1 + 25(2.98) = ?
74.5 + 1 + 74.5 = ?
149 + 1 = ?
150 = ?
The value of x is 2.98
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given an equation, 5^2x+1-5^2x=150
5^2x + 1 - 5^2x = 150
25x + 1 + 25x = 150
50x + 1 = 150
50x = 149
x = 2.98
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Molly and Brian are playing a game .Molly is counting by 8s. Brian is counting by 6s. They pace the counting so they will say the first common number together. What is the first number they both say together? »
Answers
Answer:
I believe it would be 24.
Step-by-step explanation:
Hope this helps :)
4
Write the equation of the line in slope-intercept form given the following:
Slope 3, yintercept (0,8)
5
Write the equation of the line in point-slope form given the following:
Point : (-5,2), Slope : -3
1
Show Your Work
Answers
Answer:
\bold{\text{Slope (m)}=\dfrac{1}{4}}Slope (m)=41
Step-by-step explanation:
A linear equation is of the form: y = mx + b where
m is the slope
b is the y-intercept (where it crosses the y-axis)
x + 4y = 16
4y = -x + 16
y = -\dfrac{1}{4}x+\dfrac{16}{4}y=−41x+416
y=-\dfrac{1}{4}x+4y=−41x+4
The y-intercept (b) = 4
Next, find the slope given point (4, 5) and b = 4
\begin{gathered}y=mx+b\\\\5=m(4)+4\\\\1=4m\\\\\dfrac{1}{4}=m\\\\\\\\\large\boxed{Slope (m)=\dfrac{1}{4}}\end{gathered}y=mx+b5=m(4)+41=4m41=mSlope(m)=41
The temperature is 8 degrees below zero the next day it went up to 5 degrees followed by a decrease of 7 degrees what is the temperature
Answers
Answer:
The Temperature is 10 degrees below zero.
I NEED HELP I CANT FIGURE THIS OUT
Answers
Answer:
B
Step-by-step explanation:
Hi there!
We are given line segment DG, which equals 10.
Point O belongs to DG, which splits DG into DO and OG, which are parts of the line segment.
DO=x+1, and OG=2x-15
We want to find the value of x
There is a postulate in Geometry called the Parts Whole Postulate, which states that a whole is equal to the sum of its parts. In other words, DO + OG = DG
Now we can substitute x+1 as DO, 2x-15 as OG, and 10 as DG.
x+1+2x-15=10
Combine like terms.
3x-14=10
Add 14 to both sides
3x=24
x=8
The answer is B
Hope this helps!
The lines AB and CD are perpendicular to each other. If the slope of line AB is 2/3 then what is the slope of line CD
Answers
Answer:
-3/2
Step-by-step explanation:
you can find the perpendicular slope by putting the slope in 1/-m. M is the current slope you have or really you can flip it and change the signs so for example, 1/-(2/3) = -3/2
The slope of line CD is = -3/2
What are Perpendicular lines?A perpendicular is a straight line that makes an angle of 90° with another line.
Given that the lines AB and CD are perpendicular to each other, the slope of line AB is 2/3.
Slope of perpendicular lines are negative reciprocal of each other, so,
Hence, The slope of line CD is = -3/2
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x2 + bx – 12 where b is some whole number (no
A polynomial is written as
decimals). If we're able to factor the polynomial, what are all the possible values of b?
Explain how you know.
Answers
Find the total Surface area of the prism. this is a test for math please help a broda out
Answers
To find the total surface area of a prism, calculate the sum of the areas of all its faces. Each face of the prism contributes to the total surface area, which can be calculated using the formula for the area of each face.
To find the total surface area of a prism, we need to calculate the sum of the areas of all its faces. The total surface area includes the areas of the bases and the lateral faces.
The formula for the area of each face depends on the shape of the prism's base. For example, if the base is a rectangle, the area of each rectangle face is given by the formula length * width. If the base is a triangle, the area of each triangular face is given by the formula (1/2) * base * height.
To calculate the total surface area, sum up the areas of all the faces. If there are n faces, the formula for the total surface area (TSA) is:
TSA = Area of Face 1 + Area of Face 2 + ... + Area of Face n
Calculate the area of each face according to its shape and dimensions, and then add them together to find the total surface area of the prism.
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IT IS 2AM AND ITS DUE IN LIKE AN HOUR PLEASE HELP
Answers
14) Using the same steps in 13, I found the factors. As the zeros are x=-6 and x=0, I got the factors (x) and (x+6). Then, I multiplied them and got x^2+6x, which is the answer.
15) x=1, x=1, x=2. These become the factors (x-1), (x-1), and (x-2). Then, by multiplying (x-1) and (x-1) you get x^2-2x+1. Multiply that by (x-2) to get your final answer, x^3-4x^2+5x-2.
16) Zeros are x=-1, x=5, and x=-2. You get the factors (x+1), (x-5), and (x+2). Multiply (x+1) and (x-5) to get x^2-4x-5. Multiply that by the other factor, (x+2), to get your final answer, x^3-2x^2-13x-10.
The rule for the repeating pattern is “5,7,2,8” tell me what will be the 25th number in the pattern explain
Answers
Answer:
8
Step-by-step explanation:
The repeating pattern of “5,7,2,8” has a length of 4. To find the 25th number in the pattern, we need to divide 25 by 4 to get a quotient of 6 with a remainder of 1. This means that the pattern repeats 6 times, and we need to find the first number in the pattern plus the remainder. The first number in the pattern is 5, and the remainder is 1, so the 25th number in the pattern is 8.
A pound of strawberries costs $3.28 and a pound of apples costs $4.63. What is the combined cost of 0.7 pound of strawberries and 1.4 pounds of apples? Round your answer to the nearest cent.
Answers
Answer:
$8.78
Step-by-step explanation:
cost = 3.28(0.7) + 1.4(4.63)
= 2.296 + 6.482
= 8.778
= $8.78
Which type of interest can be described as interest that is earned on the principal amount only
Answers
Simple interest is the type of interest that is earned on the principal amount only.
What is Interest?Interest in simple terms is the extra amount that you have to pay if you borrow money or the extra money you get if you lend the money.
Simple interest is one of the type of interest.
Simple interest is defined as the interest obtained over the principal amount on a certain rate.
Suppose that, a certain transaction has an annual interest rate of 2% for a period of 10 years.
If the principal amount is P, then in simple interest, interest will be a fixed amount, that is, 2% of P, in the whole period.
In compound interest, the interest will be compounded each of the year or month or quarterly depending on the criterion.
Hence the type of interest described here is simple interest.
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P and Q are two geometrically similar solid shapes. The total surface area of shape P is 240 cm². The total surface area of shape Q is 2160 cm². The volume of shape P is 960 cm³. Calculate the volume of shape Q. Optional working + Answer cm³
Answers
The volume of the shape Q is 25,920 cm³.
What is the equation for a sphere's surface area and how does it relate to the volume of the sphere?The isoperimetric inequality describes the relationship between a sphere's volume and surface area. This inequality indicates that the sphere has the biggest volume among all forms with a fixed surface area. The sphere also has the lowest surface area among all forms with a fixed volume. Due to its ability to increase volume while reducing surface area, the sphere is sometimes referred to as the "most efficient" form.
Let us suppose the scale factor = k.
Given that, total surface area of shape P is 240 cm².
Then surface area of Q can be written as:
k² × surface area of shape P = surface area of shape Q
k² × 240 cm² = 2160 cm²
k² = 9
k = 3
The volume of shape Q is:
k³ × volume of shape P = volume of shape Q
3³ × 960 cm³ = 27 × 960 cm³ = 25,920 cm³
Hence, the volume of the shape Q is 25,920 cm³.
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Ernie is . All of these points on the same line because the slope between (0, 0) and (3, 3) equal to -4.
Answers
Answer:
Ernie is incorrect.
Step-by-step explanation:
I suppose that we want to see if Ernie statement is correct or not.
Suppose that we have a line that passes through the points (x₁, y₁) and (x₂, y₂)
The slope of that line can be calculated as:
slope = (y₂ - y₁)/(x₂ - x₁)
In this case, we know that the line passes through (0, 0) and (3, 3), then the slope of this line is:
slope = (3 - 0)/(3 - 0) = 3/3 = 1
Then Ernie got the slope wrong, which means that he is wrong.
f(x) → 4x - 7. Find f(9)
Answers
Answer:
29
Step-by-step explanation:
f(x) = 4x -7
f(9) = 4(9)-7
=36-7
=29
A line includes the points (2, 4) and (3, 10). What is its equation in slope-intercept form?
Answers
Answer:
6
Step-by-step explanation:
formula is y2-y1 / x2-x1
Step-by-step explanation:
first off find the gradient dy/dx
-6÷-1=6
y=6x+c
now substitute (2,4)
4=12+c
c=-8
y=6x-8
given g (x) = -x -2, find g (-5)
Answers
Answer:
g(-5)=3
Step-by-step explanation:
g(-5)=-(-5)-2=5-2=3
Substitute x with -5.
g(-5) = -(-5) - 2
g(-5) = 5 - 2
g(-5) = 3
Best of Luck!
At a real estate agency, an agent sold a house for $327,000. The commission rate is 7.5% for the real estate agency and the commission rate for the agent is 20% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission? The agency made $ nothing on the house. The agent earned $ nothing in commission.
Answers
During the month of May there were 130 births, of which 127 were full-term births and three were premature births. There were five newborn deaths. The newborn death rate is
Answers
During the month of May, there were 130 births, of which the newborn death rate is 38.4615.
According to the question,
There were 130 births, of which 127 were full-term births and three were premature births. There were five newborn deaths.
In order to find the newborn death rate we have the formula:
= \(\frac{number of death under 28 days of age }{Total live births in the same year}\) × 1000
= \(\frac{5}{130}\) × 1000
=\(\frac{5000}{130}\)
=38.4615
Hence, the new born death rate is 38.4615.
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An online fax company, EFaxlt.com, has a customer plan where a subscriber pays a monthly subscription fee of $12.75 dollars and can send/receive 40 fax pages at no additional cost. For each page sent or received past the 40 page limit, the customer must pay an overage fee of $0.06 per page. The following expression gives the total cost, in dollars, to send p pages beyond the plan's monthly limit. C = 0.06p + 12.75
If the monthly bill under this plan comes out to be $16.47, what was the total number of pages that were sent or received?
Answers
The number of pages that were sent or received beyond the 40 page limit under the plan was 70 pages.
Given that an online fax company, EFaxlt.com, has a customer plan where a subscriber pays a monthly subscription fee of $12.75 dollars and can send/receive 40 fax pages at no additional cost. For each page sent or received past the 40 page limit, the customer must pay an overage fee of $0.06 per page.
Let p be the number of pages that were sent or received beyond the 40 page limit under the plan. Thus, the total number of pages sent or received within the plan is (40 + p).Since the monthly bill under this plan comes out to be $16.47, the total cost, in dollars, to send p pages beyond the plan's monthly limit is given byC = 0.06p + 12.75= $16.47Therefore,0.06p + 12.75 = 16.47Solve for p,0.06p = 16.47 - 12.750.06p = 3.72p = 3.72/0.06p = 62
Therefore, the number of pages that were sent or received beyond the 40 page limit under the plan was 70 pages (p + 40)
The total number of pages that were sent or received beyond the plan's monthly limit was 70 pages.
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What is the equation of the line through the points (1, 1), (5, 4), (9, 7) and (13, 10)?
Answers
Answer:
Its y=3/4x+1/4
Step-by-step explanation:
90+27 apply the distributive property to factor out the greatest common factor
Answers
Given:
90 + 27
Let's apply the distributive property to factor out the greatest common factor.
First find greatest common factor of 90 and 27
Greatest common Factor of 90 and 27 = 9
Thus, we have:
\(\begin{gathered} 9(\frac{90}{9}+\frac{27}{9})\text{ } \\ \\ =\text{ 9(10 + 3)} \end{gathered}\)Applying distribuive property, we could rewrite as: 9(10 + 3)
ANSWER:
9(10 + 3)
express in kg: 3470 grams
4 kg 8 g
Answers
Answer:
Step-by-step explanation:
This Makes no sense but this is 4kg and 8g converted to Kg :
4kg - 8g = 4.008 kg
I need help with these questions pls
Answers
Answer:
Step-by-step explanation:
I NEED HELP ON THIS ASAP! PLEASE HELP!! I WILL GIVE YOU BRAINLIEST!!
Answers
A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.
A graph of the system of inequalities is shown on the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of HD Big View television produced in one day.Let the variable y represent the number of Mega Tele box television produced in one day.Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox television takes 3 person-hours to make, a linear equation to describe this situation is given by:
2x + 3y = 192.
Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;
x + y = 72
For the constraints, we have the following system of linear inequalities:
x ≥ 0.
y ≥ 0.
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Compare the age of the earth to the age of the oldest known rocks found
Answers
The Earth is estimated to be around 4.54 billion years old, while the oldest known rocks found on Earth date back to about 4 billion years ago.
Determining the age of the Earth is a complex process that involves a variety of scientific disciplines. Geologists and other scientists have used a variety of methods to estimate the age of the planet, including radiometric dating, which involves measuring the decay of radioactive isotopes in rocks and other materials.
The age of the oldest known rocks found on Earth has also been determined using radiometric dating techniques. These rocks, which are primarily found in Western Greenland, have been dated to around 3.8 to 4.0 billion years old. The rocks are believed to have formed during the Hadean Eon, a period of Earth's history when the planet was still in its early stages of formation and was subject to intense meteorite bombardment.
It's important to note that the age of the Earth and the age of the oldest known rocks found on its surface are not precise measurements.
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Help!!!! I will Mark Brainiest!!!!! Use the graph of f(x) to answer the question!
Answers
Answer:
1.2
Step-by-step explanation:
The point on the graph (- 6, 1.2 ) gives the value of f = 1.2 when x = - 6
Then when x = - 6, the output f = 1.2