Answer: Area = l × w
= 3.5 × 2.8
= 9.8 meters2
Step-by-step explanation:
Created by Cortin Lyons riables on Both Sides #3 2.12r – 14 = 8x + 16 12x – 14 = 6x + 16 as with Distributive Property
Problem N 2
we have
12x-14=8x+16
solve for x
subtract 8x both sides
12x-14-8x=8x+16-8x
4x-14=16
Adds 14 both sides
4x-14+14=16+14
4x=30
divide by 4 both sides
x=30/4
x=7.5
Problem N 4
we have
12x-14=6x+16
solve for x
subtract 6x both sides
12x-14-6x=6x+16-6x
6x-14=16
adds 14 both sides
6x=16+14
6x=30
divide by 6 both sides
x=30/6
x=5
Find a.Round to the nearest tenth:a10 cm150°12°с=a = [ ? ]cmLaw of Sines: sin A=sin Bbasin cСEnter
Answer:
24.0 cm
Explanation:
To find the value of a, we will use the Law of sines, so
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}[/tex]So, replacing A = 150°, B = 12°, and b = 10 cm, we get:
[tex]\frac{\sin150}{a}=\frac{\sin 12}{10}[/tex]Now, we need to solve for a. First, cross multiply
[tex]10\cdot\sin 150=a\cdot\sin 12[/tex]Then, divide by sin12
[tex]\begin{gathered} \frac{10\cdot\sin150}{\sin12}=\frac{a\cdot\sin 12}{\sin 12} \\ \frac{10\cdot(0.5)}{0.208}=a \\ 24.0=a \end{gathered}[/tex]Therefore, a = 24.0 cm
find the value of the expression 4d ÷ c when c=3and d=6 simplify your answer
Perform the indicated operation by removing the parentheses and combining like terms.(5x + 3) + (x2 – 8x + 4)
Given the sum of the functions expressed as:
[tex]\mleft(5x+3\mright)+x^2-8x+4[/tex]Collecting the like terms:
[tex]x^2+5x-8x+3+4[/tex]Group the terms based on their degrees
[tex]x^2+(5x-8x)+(3+4)[/tex]Simplify the result to determine the final answer:
[tex]\begin{gathered} x^2+(5x-8x)+(3+4) \\ x^2+(-3x)+7 \\ x^2-3x+7 \end{gathered}[/tex]Hence the required sum of the functions is x^2 - 3x + 7
how can you obtain the points for the log below from its inverse?
Answer
Check Explanation
Explanation
The laws of logarithms will come in handy in helping to obtain the points for the log from its inverse.
Before we commence, the two laws of logarithms that we will be using is that
log₄ 4ᶜ = c (log₄ 4)
And
log₄ 4 = 1
So, no matter the value of inverse given, a simple mathematical evaluation will give the log points.
when x = 1
f(x) = log₄ x
f(1) = log₄ 1 = log₄ 4⁰ = 0 log₄ 4 = 0 × 1 = 0
when x = 4
f(x) = log₄ x
f(4) = log₄ 4 = log₄ 4¹ = 1 (log₄ 4) = 1 × 1 = 1
when x = 16
f(x) = log₄ x
f(16) = log₄ 16 = log₄ 4² = 2 (log₄ 4) = 2 × 1 = 2
when x = 64
f(x) = log₄ x
f(64) = log₄ 64 = log₄ 4³ = 3 (log₄ 4) = 3 × 1 = 3
Hope this Helps!!!
Hello! I need some help with this homework question, please? The question is posted in the image below. Q17
The function being one-to-one implies that every value of x, has one one vaue of y, and every value of y, has one value of x.
The inverse uses the output(y value) as an input(x value) and spits it out to get the original x value inputted into f.
Using the given point ( 2, -5 ), it implies of f(2) = -5. Since the function is one-to-one, this implies that:
[tex]f^{-1}(-5)=2[/tex][tex]\text{Thus, the point on the graph of f}^{-1}\text{ is }(-5,2\text{ )}[/tex]Hence, the correct option is option B
13х-17y+16z= 73
-11x + 15y + 17z= 61
46x+10y-30z = -18
The solution of the linear system of three simultaneous equations is presented as follows; x = 2, y = 1 and z = 4
What is a set of simultaneous equation?Simultaneous system of equations consists of a finite set of equations for which a solution to the equation system is required.
The linear system of three equations can be presented as follows;
13•x - 17•y + 16•z = 73...(1)
-11•x + 15•y + 17•z = 61...(2)
46•x + 10•y - 30•z = -18...(3)
The above system of equations can be solved using common multiples of the coefficients as follows;
Multiply equation (2) by 2 and equation (3) by 3 to get;
2 × (-11•x + 15•y + 17•z) = 2 × 61 = 122
-22•x + 30•y + 34•z = 122...(4)3 × (46•x + 10•y - 30•z) = 3 × (-18) = -54
138•x + 30•y - 90•y = -54...(5)Subtracting equation (4) from equation (5) gives;
138•x + 30•y - 90•z - (-22•x + 30•y + 34•z) = -54 - 122 = -176
138•x - (-22•x) + 30•y - 30•y - 90•z - 34•z = -176
160•x - 124•z = -176
40•x - 31•z = 44
[tex] \displaystyle {z = \frac{(44 + 40\cdot x)}{31}}[/tex]
Plugging in the value of z in equation (1) and (2) gives;
1043•x - 527•y + 704 = 73 × 31 = 2236...(6)
Which gives;
[tex] \displaystyle {y = \frac{(1043\cdot x - 1559)}{527}}[/tex]
339•x + 465•y + 748 = 61 × 31 = 1891...(7)
Which gives; [tex] \displaystyle {y = \frac{(381 - 113\cdot x )}{155}}[/tex] which gives;
[tex] \displaystyle { \frac{(1043\cdot x - 1559)}{527}= \frac{(381 - 113\cdot x )}{155}}[/tex]
Therefore; 221216•x - 442432 = 0
x = 442432 ÷ 221216 = 2
x = 2
y = (1043×2 - 1559)÷527 = 1
y = 1
z = (44 + 40×2) ÷ 31 = 4
z = 4
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polynomials: classifying, simplifying adding and subtracting polynomials write in standard formplease do minimum steps
Solve the following inequality. Graph the solution set and then write it in interval notation .
Given:
-2x ≥ 6
Solve for x
Divide both sides by -2
-2x/-2 ≤ 6/-2
x ≤ -3
Graph:
Interval notation (-∞, -3 ]
Solving Equations ** Reminder need to show ALL work **
solution
For this case we have the following equation:
[tex]\frac{3}{4}x-5=4[/tex]Then we can add 5 in both sides and we got:
[tex]\frac{3}{4}x=9[/tex]Then we can multiply both sides by 4/3 and we got:
[tex]x=9\cdot\frac{4}{3}=12[/tex]And the final solution for this case is x= 12
Finding Slope
HELP ME PLS
The slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
The first point = (-5,6)
The second point = (-9,-6)
The slope of the line defined as the change in y coordinates with respect to the change in x coordinates.
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = [tex]\frac{-6-6}{-9-(-5)}[/tex]
= -12/-4
= 3
Hence, the slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
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Given the equation y = x (x - 3)(2x + 7), find the rational roots. Complete theexplanation.The rational roots are x =, and. I found my answers bygraphing the equation, then finding where the equation crossed the (select) ▼4'
ANSWER
[tex]0,3,-\frac{7}{2}[/tex]EXPLANATION
The roots are the x values where the equation intercepts the x-axis.
A firm incurs $70,000 in interest expenses each year. If the tax rate of the firm is 30%, what is the effective after-tax interest rate expense for the firm?
Answer:
After tax interest expenses = Interest expenses x (100 - Tax Rate)
= 70000 x (100 - 30)%
= 70000 x 70%
= $49,000.00
Step-by-step explanation:
When you are on the 2nd step of factoring this trinomial,you should be listing the factors of?
Given:
The trinomial equation is given as,
[tex]3v^2-4v-7[/tex]The objective is to choose the correct value for which the factors are to be obtained for factorization.
Explanation:
From the step 1, to perform the factorization the values of a and c has to be multiplied.
Then in step 2, the factors need to be calculated for the product of a and c.
Product of a and c :
The product of a and c will be,
[tex]a\times c=3\times7=21[/tex]Thus, factors are to be listed for the number 21.
Hence, option (1) is the correct answer.
What is a feature of function g if g(x) = log (x-4) -8
The domain and range of the logarithmic function are
[tex]\begin{gathered} \text{domain}(\log x)=(0,\infty) \\ \text{range}(\log x)=(-\infty,\infty) \end{gathered}[/tex]Therefore, if
[tex]g(x)=\log (x-4)-8[/tex]We require that
[tex]\begin{gathered} x-4>0 \\ \Rightarrow x>4 \end{gathered}[/tex]Notice that the -8 term does not affect the range of function g(x); thus,
[tex]\begin{gathered} \text{domain}(g(x))=(4,\infty) \\ \text{range}(g(x))=(-\infty,\infty) \end{gathered}[/tex]Set g(x)=-8; then,
[tex]\begin{gathered} \Rightarrow\log (x-4)-8=-8 \\ \Rightarrow\log (x-4)=0 \\ \Rightarrow x=5 \end{gathered}[/tex]Therefore, y=-8 is not an asymptote of g(x), and, as shown above, the domain and range of g(x) are x>4, y->all real numbers.
Calculate the limit when x->4 as shown below,
[tex]\lim _{x\to4}g(x)=(\lim _{x\to4}\log (x-4))-8=(-\infty)-8=-\infty[/tex]Therefore, there is a vertical asymptote at x=4
Answer:
Hope this helps ;)
Step-by-step explanation:
#11 When you were born, your grandparents deposited $10,000 in a CD. for your college education. If theaccount earns 5% interest, compounded monthly, how much will be in the account for your collegeeducation?
Replacing with the values we already know, we have:
PV = 10,000
i = 5% or 0.05 but it is compounded monthly, then it is 0.05/12
n = 18 years or 216 months
10,000 = FV * 0.4073
FV = 10,000/0.4073
FV = $ 24,551.93
It is very close to option D, where the term "about" is included.
Slope =
y-intercept = (0,
Answer:
y intercept= (0,-3)
slope= 2/1 or simplified 2
Step-by-step explanation:
The area of a rectangular garden is 1,432 meters. If the length of the garden is 40 meters,
what is the width of the garden?
Answer: 35.8
Step-by-step explanation: 40x?=1432
40x35.8=1432
Question 8 > Find the area of the trapezoid shown below 9 19 18 21 23 I Question Help ve
288 u²
1) Let's calculate the area of that trapezoid by plugging into the formula below the measures of the altitude, larger base, smaller one:
[tex]\begin{gathered} S=\frac{(B+b)h}{2} \\ S=\frac{(23+9)18}{2} \\ S=288 \end{gathered}[/tex]2) So that trapezoid has an area of 288 u²
Joe bought 8 comic books for $36. How much does 1 comic book cost?
Answer:
1 comic book costs $4.5
Explanation:
Given that 8 comic books cost $36
To know how much 1 comic book costs, let x be the cost of 1 comic book, then, we have:
8 comic books = $36
1 comic book = x
Then we have the equation
8x = 36
where we can solve for x
Divide both sides by 8
8x/8 = 36/8
x = 4.5
Therefore, 1 comic book costs $4.5
Brian is looking to add tile to one wall in his kitchen, each tile is a rectangle that measures
14 inches by 2 inches. The wall that Brian wants to tile is a rectangle that measures
44.25inches by 51 inches. How many bie's will Brian need to cover the wall?
Using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.
What is a rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can also be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.So, tiles needed to cover the wall:
The formula for the area of a rectangle: l × bCalculate the area of a tile as follows:
l × b14 × 228 in²Now, calculate the area of the wall as follows:
l × b44.25 × 512,256.75 in²Then, tiles needed to cover the wall:
2,256.75/2880.59Which means: 80½
Therefore, using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.
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do an addition in binary (inverse code) on following numbers:
00011101
+ 111111101
please, help asap thank u
The first complement of the binary addition is 00011111.
The binary addition operation works similarly to the base 10 decimal system, except that it is a base 2 system. The binary system consists of only two digits, 1 and 0.
Given that, the addition of the given number
00011101 + 11111101
In the binary addition,
0+1 = 1
1+0 = 1
1+1 = 0
00011101 + 11111101 = 11100000
Then inverse code means first complement of the answer.
In the first complement, 0 is the inverse of 1 and 1 is inverse of 0.
11100000 = 00011111
Hence, The first complement of the binary addition is 00011111.
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I need to write this equation that has a infinite number of solutions
2 (8x+4) -x =
Simplify the equation:
2(8x)+2(4) -x
16x +8 -x
15x +8
If both sides of the equation are equal o equivalent, there is an infinite number of solutions.
2 (8x+4) -x = 15x + 8
Classify the triangle with side lengths 8,13,20. a) Acute b) Right c) Obtuse
for right angles triangle,
hyposenuse square should be equal to sum of square of other two sides
it fails that law so its not right angled triangle
Rectangle ABCD has vertex coordinates
A(1, -2), B(4, -2), C(4, -4), and D(1,
-4). It is translated 1 unit to the left and 1 3 units up. What are the coordinates
of B?
A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.
Response: C
What is a graph's vertex?A node of a graph, or one of the points on which the graph is defined and which may be connected by graph edges, is referred to as a "vertex" in computing.
For instance, a rectangle's four sides result in its four vertices.
Response: C . The coordinates are obtained by first subtracting 1 from 4 to obtain 3 and then adding 3 to -2 to obtain 1. (3, 1)
The vertex is the collective endpoint. Vertex, on the other hand, refers to the common terminal point where two rays converge to make an angle. In a similar manner, we must understand an angle's arm. The term "arm of an angle" refers to the two rays that unite to make an angle.
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suppose s is between r and t use the segment addition postulate to solve for each variable RS equals 2z plus 6 St equals 4z - 3 RT = 5z + 12
If s is between r and t, then:
RS + ST = RT
Where RS = 2z + 6
ST = 4z - 3
RT = 5z + 12
So, we get:
(2z + 6) + (4z - 3) = 5z + 12
Solving for z, we get:
2z + 6 + 4z - 3 = 5z + 12
6z + 3 = 5z + 12
6z + 3 - 5z = 12
z + 3 = 12
z = 12 - 3
z = 9
Answer: z = 9
A company has developed a new deluxe AAA battery that is supposed to last longer than its regular AAA battery. However these new batteries are more expensive to produce. So the company would like to be convinced that they really do last longer. Based on years of experience, the company knows that its regular AAA batteries last lor 45 hours of continuous use. On average. The company selects an SRS Of 50 new batteries and uses them continuously until they are completely drained. The Sample mean lifetime is X =46.9 hours with a Standard deviation of S=4.6 hours A) Check for the conditions for the situation B) Calculate the test statistic for this situation C) What is the P value for this situation? D) What conclusion do you draw with 5% significance level? why? E) What type of error could you possibly make here? I
1 sample t-test
[tex]\mu=the\text{ true mean lifetime of new AAA batteries}[/tex][tex]\begin{gathered} H_0\colon\mu=45\text{ hours} \\ H_a\colon\mu>45\text{ hours} \end{gathered}[/tex][tex]n=50[/tex]B)
Calculating t test statistic
[tex]\begin{gathered} t=\frac{statistic-parameter}{s\tan dard\text{ deviation of statistic}} \\ t=\frac{\bar{x}-\mu_0}{\frac{s_x}{\sqrt[]{n}}} \end{gathered}[/tex]Plugging in the values, we have:
[tex]\begin{gathered} t=\frac{\bar{x}-\mu_0}{\frac{s_x}{\sqrt[]{n}}} \\ t=\frac{46.9-45}{\frac{4.6}{\sqrt[]{50}}} \\ t=\frac{1.9}{0.6505} \\ t=2.9207 \end{gathered}[/tex]C)t test statistic = 2.9207
degrees of freedom = n - 1 = 50 - 1 = 49
Using a calculator, we can calculate the p-value.
[tex]p-\text{value}=0.002633[/tex]D)Since p value is less than significance level (p value < alpha), then we will reject H_0 and take the alternate hypothesis.
Thus the test suggests that the new batteries do last more than 45 hours.
E)
We could've done Type I error here.
Type I error or α: Reject the null when it’s true.
james harmon pays 850.80 per year for his life insurance. if he where to the premiums quarterly, the payments would would be 221.21 what percentage more is mr hamrmon paying for the year using yhe quarterly rate
Percent is given by the expression:
[tex]\begin{gathered} \text{Total}\cdot\frac{\text{percent}}{100}=\text{Equivalent number to the percent} \\ 850.8\cdot\frac{x}{100}=221.21 \\ x=\frac{221.21\cdot100}{850.8} \\ x=26\text{ percent} \end{gathered}[/tex]So, he is paying 74% more using the quarterly rate
Use long division or a calculator to write 4/99 as a decimal. Then tell whether the decimal is terminating or repeating
0.0404
Repeating decimal (periodic)
1) Let's proceed with the long division of 4 by 99:
1.1) Since 4 is way smaller than 99 let's add one zero to the dividend and another for the quotient followed by a dot.
But 40 is still lesser than 99, so let's add another zero after the dot to make it 400. Now we can divide 400 by 99
1.2) Again to proceed with that division we'll need to write a zero at that 4 and another one in the quotient.
As and we can see already this a repeating decimal or periodic. This division will yield 0.0404040404.....
2) Hence, the answer is 0.0404
Select the correct answer.Using long division, what is the quotient of 3r4 + 2023 + 1422 + 17= + 30 and I + 67
EXPLANATION
we are asked to use the long division method to solve the division
[tex]\frac{3x^4+20x^3+14x^2+17x+30}{x+6}[/tex]We will have