Answer:
20 feet²Step-by-step explanation:
triangle area formula: A = 1/2 × b × h
Find the base7 +3 = 10 ft
Find Area1/2 10 × 4 =
5 × 4 =
20 feet²
-5x - 7<3 and -5x-7> -42
Answer:
x<-2, x>-7
Step-by-step explanation:
1st one
add 7 to 3 =10
-5 divide by 10 = -2
2nd one
add 7 to -42 = -35
-35 divided by 5 = -7
Find the Value of X in each case. RSM geo Lesson 9, 24d
The value of x in the triangle is 17 degrees.
How to find angle in a triangle?A triangle is a polygon with three sides and angles.
The sum of angles in a triangle is 180 degrees.
Therefore, ABC is a triangle and CDE is a also a triangle.
Let's find the angle x in the triangle CDE.
Hence,
∠ACB = 180 - 4x - 49 (sum of angles in a triangle is 180 degrees)
∠ACB = 180 - 49 - 4x
∠ACB = 131 - 4x
Therefore,
180 = ∠DCE + ∠DEC + ∠CDE
∠CDE = 100°
∠DEC = x
∠DCE = ∠ACB = 131 - 4x
Hence,
180 = 131 - 4x + x + 100
180 = 231 - 4x + x
180 - 231 = -3x
-51 = -3x
divide both sides by -3
x = -51 / -3
x = 17
Therefore,
x = 17
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¡¡¡Help with this!!!
The value of sin 2x=0.8304 ,cos 2x=0.557,tan 2x=1.498 when the value of tan x is 8/15 and using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).
What is trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
sin 2x=2 tan x/(1+(tan x)²)
cos 2x=(1-(tan x)²)/(1+(tan x)²)
tan 2x=sin 2x/cos 2x=2 tan x/(1-(tan x)²)
Here,
tan x=8/15
sin 2x=2 tan x/(1+(tan x)²)
= 2*8/15/(1+(8/15)²)
=(16/15)/(289/225)
=(16*15)/(289)
≈0.8304
cos 2x=(1-(tan x)²)/(1+(tan x)²)
=(1-(8/15)²)/(1+(8/15)²)
=(225-64)/(225+64)
≈0.557
tan 2x=sin 2x/cos 2x
tan 2x= 0.8304/0.557
=1.498
≈1.5
When the value of tan x is 8/15, the values of sin 2x=0.8304, cos 2x=0.557, and tan 2x=1.498 using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.
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what is y= –12x–6 on a graph
The graph of the equation y = –12x – 6 is attached in the solution.
We can find the x and y intercept of the line to find make the graph.
Putting x = 0 in the given equation, we get:-
y = -12(0) - 6 = 0 - 6 = -6
Hence, the x -intercept is (0,-6).
Putting y = 0 in the given equation, we get:-
0 = -12x - 6
6 = -12x
x = 6/(-12)
x = -1/2
Hence, the y -intercept is (-1/2,0).
We can find another point on the line.
Putting x = -1 in the given equation, we get:-
y = -12(-1) - 6
y = 12 - 6 = 6
y = 6
Hence, another point on the line is (-1,6).
Plotting these points we can graph the equation of the line.
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Evaluate. 34+(12+14)2⋅2 Enter your answer as a mixed number in simplest form by filling in the boxes. $$
The result of 34+(12+14)2.2 in the mixed fraction is [tex]91\frac{1}{5}[/tex]
The expression is
34+(12+14)2.2
The mixed fraction is defined as the fraction that consist of one whole number part and a simple fraction part. simple fraction is the fraction that consist of numerator and denominator as whole numbers. The top term of the simple fraction is called numerator and bottom term of the simple fraction is called denominator.
The expression is
=34+(12+14)2.2
First do the arithmetic operation in the bracket
= 34 + 26×2.2
Do the Multiplication
= 34+57.2
= 91.2
Convert the decimal form to simple fraction
91.2 = 456/5
Convert the simple fraction to the mixed fraction
456/5 = [tex]91\frac{1}{5}[/tex]
Hence, The result of 34+(12+14)2.2 in the mixed fraction is [tex]91\frac{1}{5}[/tex]
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28-6x=2x-84
Prove: x = 14
28-6x = 2x -84
Add 6x to both sides:
28 = 8x -84
Add 84 to both sides
112 = 8x
Divide both sides by 8
X = 112/8
X = 14
4 2/15 / 3.1 (I NEED HELP NOW!!!!!!!!!!!)
Answer:
The answer would be 1.3, and the three is repeating.
Step-by-step explanation:
First, make 4 2/15 into a improper fraction.
4 2/15= 62/15
Now, when we divide fraction, use the rule Keep, Change, Flip.
Keep the 62/15.
Change the division sign into a multiplication sign.
To make the 3.1 into a fraction, put a one over it.
3.1/1
Now, flip the fraction.
3.1/1= 1/3.1
Your equation will look like this:
62/15x1/3.1
Multiply across.
62/46.5
Now simplify.
The answer would be 1.3, and the three is repeating.
Robert gets a loan from the bank. agrees to borrow 6000 , his interest rate is 7 %. he agrees to pay back over a 10 year period. how much money wil he have paid back by then?
The amount to be paid after paying interest of 7% for 10 years is 10,2000
The amount to be borrowed from the bank = 6000
Interest rate for the amount per year = 7%
The total time period of the loan = 10 years
Thus , the final amount can be calculated by using the formula
A = P(1 + rt)
where A is the final amount
P is the principal amount to be borrowed
r is the rate of interest
t is the time period
Now, let us substitute the known values in the above equation , we get
A = 6000 ( 1 + 0.07 x 10)
= 6000 (1 + 0.7)
= 6000 (1.7)
A = 10,200
Therefore , the final amount to be paid is 10,200
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which is an equation of the line through the origin and (-5,6)
The equation of a line through the origin and (-5,6) is y = -1.2x
How to determine the equationIt is important to note that the equation of a line is expressed as;
y = mx + c
Where;
y is the point on the y - axism is the slope of the linex is the point on the x - axisc is the intercept on the y axisFrom the information given, we have the points;
(0, 0) and ( -5, 6)
The formula for slope is given as;
slope, m = y₂ - y₁/ x₂ -x₁
slope, m = 6 - 0/ -5 - 0
slope, m = 6/ -5
slope, m = - 1. 2
To determine the intercept, we have;
6 = -1. 2(-5) + c
expand the bracket
c = 6 - 6
c = 0
The equation is given as;
y = -1.2x
Hence, the equation is y = -1.2x
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The equation for line s can be written as y = 3/10x + 8. Line t is parallel to lines and passes through (-7, -2). What is the equation of line t? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
A line's equation written using a single point on the line and the line's slope is referred to as the point-slope form. The slope is the rise over run, or the ratio of the change in the y values over the change in the x values, and the point form is denoted as (x,y).
What is the line's slope-intercept form?The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.y= 3 / 10x + 8
The slope-intercept form isy=mx+b, where
m is the slope and b is the y-intercept.y=mx+b
Reorder termsy=3/ 10x+8
Use the slope-intercept form to find the slope and y-intercept.Using the formula y = m x + b, determine the values of m and b.m=3/10 b=8
The value of m represents the line's slope, and the value of b represents the y-intercept.Slope: 3/ 10, and the y-intercept is at (0, 8).
Two points can be used to graph any line. To determine the corresponding y values, enter the equation with two chosen x values.Phrase reordering y = 3 /10 x + 8The x and y values should be put into a table.x y
0 8
10 11.
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Consider the polynomial function p(x)=-4x³-6x²+16+24. find the end behavior of the graph of p(x). explain your answer
I will ask my question here
is p(x)
[tex]\begin{gathered} p(x)=-4x^3-6x^2+16x+24 \\ \lim _{x\to\infty}-4x^3-6x^2+16x+24=\lim _{x\to\infty}-4x^3=-4\lim ^{}_{x\to\infty}x^3=-4\infty=-\infty \\ \\ \end{gathered}[/tex]bye :)
Can someone solve this I don’t understand the graph
The graph given in the problem is the function of cosine that is;
y = -cos x
How to find the function which was used to make a graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it. If the function crosses x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
Suppose that we've got:
f(x) = a cos (bx - c) + d
Then, this function has the Amplitude (the maximum distance of the graph from the middle line) = a
Period = [tex]\dfrac{2\pi}{b}[/tex]
Phase shift = [tex]\dfrac{c}{b}[/tex]
Maximum value: a + d
Minimum value: -a + d
Here we can see that the graph is the function of cosine that is;
y = -cos x
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Write an exponential expression equivalent to 8^3 that has a base of 2.
Answer:
2^9
Step-by-step explanation:
8 is [tex]2^3\\[/tex], so we can replace [tex]8^3[/tex] for [tex](2^3)^3[/tex]
Exponents separated by parenthesis, multiply.
So [tex](2^3)^3=2^9[/tex]
4. The density of gold is 18 g/cm3. If the volume of a plece of gold is 13cm, how many grams will it be?
ANSWER:
Therefore there are about 234 grams
STEP-BY-STEP EXPLANATION:
We have that the density is given by this formula
[tex]\begin{gathered} d=\frac{m}{V} \\ \text{where m is the mass and V the volume} \end{gathered}[/tex]We have the value of the density and the volume, therefore we can calculate the number of grams as follows:
[tex]\begin{gathered} 18=\frac{m}{13} \\ m=18\cdot13 \\ m=234 \end{gathered}[/tex]-0.5f - 4.52 = -25.52 + f HELP PLEASE
Answer:
-0.5f - 4.52 = -25.52 + 1f
-1.5f = 21
f = 14
Answer:
14
Step-by-step explanation:
-4.52 + 25.52 = f + 0.5f
21 = 1.5f
f = 14
If Santa drives at an average speed of 60 miles per hour for a distance of 1,260 miles, how long will Santa's trip take?
Step 1: Speed is defined as the rate of covering a distance, mathematically it is given by
[tex]\begin{gathered} S\text{peed}=\frac{\text{distance}}{\text{time}} \\ S=\frac{d}{t} \end{gathered}[/tex]Step 2: Make the time (t) of the subject in the above speed formula
[tex]t=\frac{d}{S}[/tex]Step 3: Given the distance covered and the average speed used during the trip as
[tex]\begin{gathered} S=60\text{miles per hour} \\ d=1260\text{ miles} \end{gathered}[/tex]Step 4: Substitute the values for distance and speed in the time formula in step 2
[tex]\begin{gathered} t=\frac{d}{S} \\ t=\frac{1260}{60} \\ t=21\text{ hours} \end{gathered}[/tex]Hence, Santa's trip will take up to 21 hours
Answer:
To find out the time required to travel the distance of 1260 miles we need to divide the total distance travelled by the distance travelled in one hour.
[tex]1260/60=21[/tex]
So, it tool 21 hours for Santa to complete the trip
I just need the answer
At x=0
[tex]\begin{gathered} f(x)=14 \\ c=14 \end{gathered}[/tex]at x=1
[tex]\begin{gathered} f(x)=10.5 \\ a+b=10.5-14 \\ a+b=-3.5 \end{gathered}[/tex]at x=2
[tex]\begin{gathered} f(x)=8 \\ 4a+2b=8-14 \\ 4a+2b=-6 \end{gathered}[/tex]a=1/2
So correct option is (c).
20, 33, 44, 53, 69, 75, 89, 90 Find the mean and the standard deviation. Round to the nearest thousandth.
The mean and the standard deviation of the following numbers 20, 33, 44, 53, 69, 75, 89, 90 are 59.125 and 22.461 respectively
What are mean and standard deviation?The mean is the average value in a collection and a standard deviation is the average amount of variability in a data.
mean= sum of data in the collection/ number of data
= (20+33+44+53+69+75+89+90)/8 = 473/8 = 59.125( nearest thousandth)
standard deviation= sum of √(x- mean)^2/ number of data while x is each number in the data
finding (x- mean)^2 for each value of x
(20-59.125)^2=848.266
(33-59.125)^2=682.516
(44-59.125)^2=228.766
(53-59.125)^2=37.516
(69-59.125)^2=102.516
(75-59.125)^2= 260.016
(89-59.125)^2= 907.516
(90-59.125)^2= 968.766
S.D= √(848.266+682.516+228.766+37.516+102.516+260.016+907.516+968.766)/8 =
√504.484
Therefore S.D =22.461 ( to the nearest thousandth)
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Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
= 6; = 2
P(5 ≤ x ≤ 9) =
The probability P(5 ≤ x ≤ 9) is 0.6847
Assume that x has a normal distribution
We have been the mean and standard deviation μ = 6; σ = 2.
To calculate this probability we use the standardized normal distribution and the z-value for 5 and 9.
z = (5 - 6)/2
= -0.5
and z = (9 - 6)/2
= 1.5
Then the probability is calculated as:
P(x ≤ 5) = 0.3085
P(x ≤ 9) = 0.9932
P(5 ≤ x ≤ 9) = 0.9932 - 0.3085
P(5 ≤ x ≤ 9) = 0.6847
Therefore, the probability P(5 ≤ x ≤ 9) is 0.6847
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I haven’t came across one of these questions so not sure how to solve
m∠F = 140º
1) Since that trapezoid is a quadrilateral, then we can affirm that the Sum of their interior angles is:
[tex]\begin{gathered} S_i=180(n-2) \\ S_i=180(4-2) \\ S_i=180(2) \\ S_i=360 \end{gathered}[/tex]Note that "n" refers to the number of sides:
Notice also that angle H is a right angle since this is not an Isosceles Trapezoid
So we can write out the following
9x +14x +4x + 90 = 360º
27x = 360 -90
27x = 270
x =10
Alternatively, angles between parallel lines are supplementary
2) To find out the measure of angle ∠F We'll need to plug x=10 into that expression:
m∠F = 14x
m∠F = 140º
when 9 times a number is increased by 30, the answer is the same as when 140 is decreased by the number. Find this number
Answer: 11
Step-by-step explanation:
Let the number be x.
[tex]9x+30=140-x\\\\10x=110\\\\x=11[/tex]
PLEASE HELP
50 POINTS
Answer:
9. [tex]256u^8 v^{16}[/tex]
10. [tex]-32x^{10} y^{35}[/tex]
11. [tex]-x^{12}y^{20}[/tex]
12. 1
13. [tex]\frac{2}{3xy^3}[/tex]
14. [tex]\frac{h^8}{3j^6k^6}[/tex]
15. [tex]\frac{1}{4z}[/tex]
Answer:
9. 256u^8 v^16
10. -32x^10 y^35
11. x^12 y^21
12. 1
Step-by-step explanation:
If you can, please give me a Brainliest; thank you! I put a lot fo times to solve it !
Solve for u.u^2-u-12=0If there is more than one solution, separate them with commas.If there is no solution, click on "No solution."
we have the quadratic equation
[tex]u^2-u-12=0[/tex]we have that
a=1
b=-1
c=-12
Applying the formula to solve a quadratic equation
[tex]u=\frac{-(-1)\pm\sqrt{-1^2-4(1)(-12)}}{2(1)}[/tex][tex]u=\frac{1\pm7}{2}[/tex]The values of u are
u=4 and u=-3
therefore
The answer is
u=-3,42x^2-5x-11=1
factor pls
Answer:
(2x+3)(x-4) = 0
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the blue graph? G(x) = _ A. G(x) = x2 + 5 B. G(x) = (x + 5)2 C. G(x) = x2 - 5 D. G(x) = (x - 5)2
The blue graph is represented by the equation g(x) = (x - 5)²
How to determine the equation represented by the blue graph?The possible graph that completes the question is added as an attachment
From the attached graph, we have the following parameters
Red graph = f(x)Blue graph = g(x)Also from the graph, we have the equation of the function f(x) to be
f(x) = x²
Solving further, we can see that:
The function g(x) is on the same level as the function f(x) Also, the function has the same size as .f(x)The only difference is that, f(x) is shifted to the right by 5 units
This means that
g(x) = f(x - 5)
So, we have
g(x) = (x - 5)²
Hence, the blue graph equation is g(x) = (x - 5)²
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A magical basket of pennies doubles every day. If the basket if full on the 15th day, on what day was the basket one-quarter full?
The basket of pennies will be 1/4 full on the 13th day
How to determine the day?From the question, the given parameters are:
Rate of change, r = 2 i.e. doubleFull basket, = 15th dayThe above parameters illustrate an exponential function
An exponential function is represented as
A(n) = A * (r)ⁿ⁻¹
Where
A represents the initial value
It is full on the 15th day
So, we have
1 = A *(2)¹⁵⁻¹
Evaluate
1 = A *(2)¹⁴
Divide by (2)¹⁴
A = (2)⁻¹⁴
Substitute A = (2)⁻¹⁴ in A(n) = A * (r)ⁿ⁻¹
A(n) = (2)⁻¹⁴ * (2)ⁿ⁻¹
When it is one-quarter full, we have
1/4 = (2)⁻¹⁴ * (2)ⁿ⁻¹
Multiply by (2)¹⁴
(2)¹² = (2)ⁿ⁻¹
By comparison, we have
n - 1 = 12
Add 1 to both sides
n = 13
Hence, the basket will be one-quarter full on the 13th day
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Suppose that 13 inches of wire costs 52 cents.
At the same rate, how many inches of wire can be bought for 36 cents?
Answer:
9 inches
Step-by-step explanation:
Set it up like a fraction ratio and solve for x. as the price (denominator) and amount (numerator) have a set ratio, you can cross-multiply for your answer.
[tex]\frac{13}{52} =\frac{x}{36\\}\\[/tex]
13*36 = 468
468/52 = 9
Another way would be to divide 13 by 52 and multiply by 36, but then you end up with decimals and cross multiplication will be easier in the long run.
Which equations pass through the points (1, 3) and (7 9)?
Answer:
f(x)=x+2 Passes through
x-y=2 DOES NOT pass through
Step-by-step explanation:
Method- plug in x and see if the y matches the points. (1,3) (7,9)
f(x)=x+2
f(1)=1+2=3
f(7)=7+2=9
Matches!
x-y=2
1-y=2 --> y=-1
Does not match
Dilate this figure by a scale factor of 1.5. Is the image a stretch or compression?
Answer:
compression
Step-by-step explanation:
If b>1 then the graph will compress
Question number three in the photo provided.
Using the Central Limit Theorem, the formulas are given as follows:
Standard deviation: [tex]\sigma_{\overline{p}} = \sqrt{\frac{p(1 - p)}{n}}[/tex].Mean: [tex]\overline{p} = p[/tex].What does the Central Limit Theorem state?The Central Limit Theorem states that a random variable X with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] can have the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
A distribution of proportions, with a proportion p in a sample of size n, also respects the Central Limit Theorem, as the the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation given as follows:
Mean: [tex]\overline{p} = p[/tex].Standard deviation: [tex]\sigma_{\overline{p}} = \sqrt{\frac{p(1 - p)}{n}}[/tex].More can be learned about the Central Limit Theorem at https://brainly.com/question/25800303
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