Since we're in a right triangle, we'll have that:
[tex]\cos 26=\frac{x}{28}[/tex]Solving for x :
[tex]\cos 26=\frac{x}{28}\rightarrow28\cos 26=x\rightarrow x=25.17[/tex]Therefore, x = 25.17
What are the coefficients in the expression 32x + 24y - 15z?
Answer:
32, 24, 15
Step-by-step explanation:
A coefficient is a number that comes before a variable, so therefor 32 24 and 15 are the coefficients.
Carol is depositing $1500 into an account earning 3% compounded semiannually. How much money will be in the account after 25 years?
ANSWER
$3157.86
EXPLANATION
We have that Carol is depositing $1500 into an account earning 3% that is compounded semiannually.
The formula for amount for a compound interest is:
[tex]A\text{ = }P(1\text{ + }\frac{r}{n})^{n\cdot t}[/tex]where P = principal (amount deposited)
r = interest rate
t = number of years
n = number of times interest is compounded
Since the interest is compounded twice a year (semiannually), n = 2.
From the question:
P = $1500
r = 3% = 0.03
t = 25 years
So, the amount of money that will be there after 25 years is:
[tex]\begin{gathered} A\text{ = 1500(1 + }\frac{0.03}{2})^{2\cdot25} \\ A=1500(1+0.015)^{50} \\ \text{A = 1500(1.015)}^{50} \\ A\text{ = \$3157.86} \end{gathered}[/tex]Given that a function, g, has a domain of -1 ≤ x ≤ 4 and.a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, seleccould be true for g.OOg(3) = 18g(2)=4g(1) = -2g(5) = 12Submit
Answer:
[tex]g(3)\text{ = 18 is possible}[/tex]Explanation:
Here, we want to get the possible true value for the function
From the given range values, g(x) cannot be negative since the lowest number is 0
Thus, g(-1) = 2 is wrong
Looking at the domain also, we have values existing from -1 to 4
This means that g(5) does not exist
Now, we are left with g(3) = 18 and g(2) = 4
We already have g(2) = 8
g(2) cannot possess two values
Thus, the possible correct value is g(3) = 18
how much does Taryn charge to mow a lawn she mowed ,9 lawns time spent mowing lawns in an hour 7.5 and money earned $112.50
step 1
Find the unit rate
Taryn
(9,112.50)
Divide 112.50 by 9
112.50/9=$12.50 per law
Alastair
Divide 122.50 by 7
122.50/7=$17.5 per law
Find out how much Taryn earn per hour
Divide 112.50 by 7.5
112.5/7.5=$15 per hour
Find out how much Alastair earn per hour
Divide 122.50 by 5
122.5/5=$24.5 per hour
therefore
Alastair earns more per hour
Which of the following expressions are equivalent to -19/8.(-50)?Choose all answers that apply.
To answer this question we notice the result of the original expression is positive; now, using the law of sign we notice that the negative sign in the fraction in option A will cancel out, leaving only the outer minus sign; after that if we make the product the result will be positve. This does not happens in option B, in this case the final result will be negative.
Therefore, the answer is A.
16For an arithmetic series a₁ = -10 and S6 = -285, find the common difference.A-35B-25C -15D -5
Given:
An arithmetic series a₁ = -10 and S6 = -285
We will find the common difference (d) using the formula of the sum.
[tex]S=\frac{n}{2}(2a+(n-1)d)[/tex]Substitute S= -285, a = -10, n = 6
[tex]\frac{6}{2}(2(-10)+(6-1)d)=-285[/tex]Solve the equation to find (d):
[tex]\begin{gathered} 3(-20+5d)=-285 \\ -20+5d=-\frac{285}{3} \\ \\ -20+5d=-95 \\ 5d=-95+20 \\ 5d=-75 \\ \\ d=-\frac{75}{5}=-15 \end{gathered}[/tex]So, the answer will be option C) -15
QuestionThe population of deer in a national forest has consistently increased by 5% each year. This year, thepopulation of deer is 5, 000. If the population increases at the same rate, what number of deer isexpected to be in the national forest next year?
Answer:
5250 deer
Explanation:
We know that the deer population increases by 5% each year. This means That if we start with a population of 5000, then next year the population will be 100% + 5% = 105% of 5000.
Now, what is 105% of 5000?
The answer is
[tex]5000\times\frac{105\%}{100\%}[/tex][tex]=5250[/tex]Hence, the deer population after one year will be 5250.
We can solve the same problem with a somewhat different approach.
We know that the deer population increases by 5% per year. Then what is the deer population next year if we start with 5000 deer?
Next year the population will have increased by 5%.
Now, what is 5% of 5000?
The answer is
[tex]5000\times\frac{5\%}{100\%}[/tex][tex]=250[/tex]This means the population has increased by 250.
Therefore, the population next year is 5000 + 250 = 5250 deer.
What is the range of the function?Type the answer using interval notation example : (#,#]
To analyze the range we need to look at the Y values. In this case the lowest Y value is 0 and the highest Y value it can go all the way up to positive infinity. So the range would be [0, +∞)
What is the location of the point (5, 0) translates 4 units to the down and reflected across the y-axis?
STEP-BY-STEP EXPLANATION:
Given information
The given ordered point = (5, 0)
Step 1: We need to translate the point 4 units down
To translate down means we will be subtracting a value from the y--axis
Hence, we have
[tex]\begin{gathered} (x,\text{ y) }\rightarrow\text{ (x, y-b)} \\ \text{where b = 4} \\ (5,\text{ 0) }\rightarrow\text{ (5, 0 - 4)} \\ (5,\text{ 0) }\rightarrow\text{ (5, -4)} \end{gathered}[/tex]When translated 4 units down, we got (5, -4)
Step 2: Reflect over the y-axis
The general rule for reflecting over the y-axis is (-x, y)
This means the value of x will be negated and the value of y will remain the same
[tex]\begin{gathered} \text{Over the y-ax}is \\ (x,\text{ y) }\rightarrow\text{ (-x, y)} \\ (5,\text{ -4) }\rightarrow\text{ (-5, -4)} \end{gathered}[/tex]Step 3: the graph the point
You deposit $300 in an account that pays 1.48% annual interest. What is the balance after 1 year if the interest is compound daily?
We are going to use the compound interest formula to solve:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
P = initial balance
r = interest rate
n = number of times compounded annually
t = time
1.48% to a decimal
[tex]\frac{1.48}{100}=0.0148[/tex]Since the interest is compounded daily, we will use 365 for n. Therefore:
[tex]A=300(1+\frac{0.0148}{365})^{365(1)}=300(1+\frac{0.0148}{365})^{365}=304.47[/tex]Answer: $304.47
What makes 3 + 7 + 2 = 0 + 2 true?
Assuming that the question for this case is:
[tex]3+7+2=x+0+2[/tex]We can subtract in both sides of the equation 2 and we got:
[tex]x=3+7+2-2=10[/tex]And the solution for this case would be 10
last Friday Adam had $22.33 over the weekend, she received some money for cleaning the attic period. He now had 32 dollars period, how much money did he receive.
Word Problem Leading to Simple Equation.
Last Friday Adam had $22.33 : 22.33
He received some money for cleaning: Let the amount of money he received be x, so that she now has:
[tex]22.33+x[/tex]He is left with $32, meaning his total money is now $32 :
Mathematically, we write:
[tex]\begin{gathered} 22.33+x=32 \\ \text{Collecting like terms, we get,} \\ x=32-22.33 \\ x=\text{ \$9.67} \end{gathered}[/tex]Hence, the correct answer is $9.67
1. Which of the below is a binomial factor of thepolynomial shown?
The given polynomial is
[tex]\begin{gathered} 3x^2+11x+10^{} \\ \text{ By factoring completely, we obtain two paired factors 6 and 5,} \\ \text{ whose sum is 11 (the coefficient of x), and product 30 found from } \\ \text{ the product of the constant 10 and 3 (the coefficient of x}^2) \end{gathered}[/tex][tex]\begin{gathered} 3x^2+11x+10^{} \\ 3x^2+6x+5x+10 \\ 3x(x+2)+5(x+2) \\ (3x+5)(x+2) \end{gathered}[/tex]Therefore, a binomial factor of the polynomial is (x + 2) [Option A]
-x + 2y = 11 three points graphed please help !
We can see that we have the following equation:
[tex]-x+2y=11[/tex]And we can see that this is a linear equation in standard form:
[tex]Ax+By=C[/tex]And we need to graph the linear equation. To achieve that, we can proceed as follows:
1. We can find the intercepts of the linear function, and then we will have two points we can use to graph the line equation. We can find another point to graph it easier.
2. To find the x-intercept (the point where the line passes through the x-axis, and when y = 0) is as follows:
[tex]\begin{gathered} -x+2y=11\rightarrow y=0 \\ \\ -x+2(0)=11 \\ \\ -x=11\Rightarrow x=-11 \end{gathered}[/tex]Therefore, the x-intercept is (-11, 0).
3. To find the y-intercept (the point where the line passes through the y-axis, and when x = 0) is as follows:
[tex]\begin{gathered} -x+2y=11\rightarrow x=0 \\ \\ 2y=11 \\ \\ \frac{2y}{2}=\frac{11}{2} \\ \\ y=5.5 \end{gathered}[/tex]Therefore, the y-intercept is 5.5 (0, 5.5).
4. Since we have a decimal, and to be more precise, we can find another point. To do that, we can try with x = 5:
[tex]\begin{gathered} -x+2y=11 \\ \\ -5+2y=11 \\ \\ -5+5+2y=11+5 \\ \\ 2y=16\Rightarrow y=\frac{16}{2}=8 \\ \\ y=8 \\ \end{gathered}[/tex]Then we have another pair to graph the function: (5, 8).
5. We can find another point, using x = -5. Then we have:
[tex]\begin{gathered} -x+2y=11 \\ \\ -(-5)+2y=11 \\ \\ 5+2y=11\Rightarrow5-5+2y=11-5 \\ \\ 2y=6 \\ \\ \frac{2y}{2}=\frac{6}{2}\Rightarrow y=3 \end{gathered}[/tex]Therefore, another point is (-5, 3)
5. Now, with these values, we can sketch the graph of the line as follows (we will use (-5, 3) and (5, 8), and we will see that the line passes through the point (0, 5.5):
• (-11, 0),, (-5, 3),, (0, 5.5), ,(5, 8)
Therefore, we can see the points: (-5, 3), (0, 5.5), and (5, 8) are three points that solve the equation -x + 2y = 11, since they lie on that line:
[tex]\begin{gathered} -(-5)+2(3)=11 \\ \\ 5+6=11 \\ \\ 11=11\text{ \lparen It is true\rparen} \\ \\ \text{ And we can follow the same steps for the other two points:} \\ \\ -(0)+2(5.5)=11 \\ \\ 11=11 \\ \\ \text{ And} \\ \\ -5+2(8)=11 \\ \\ -5+16=11 \\ \\ 11=11 \end{gathered}[/tex]Therefore, in summary, we graphed the linear function as follows, and we found that the three points on the graph solve the equation -x + 2y = 11, that is, (-5, 3), (0, 5.5), and (5, 8):
Which expressions are equivalent to the one below? Check all that apply. 212 32
Given:
[tex]\frac{21^x}{3^x}[/tex]Aim:
We need to find the equivalent expression for the given expression.
Explanation:
[tex]Use\text{ }\frac{a^n}{b^n}=(\frac{a}{b})^n.\text{ Here a=21, b=3 and n=x.}[/tex][tex]\frac{21^x}{3^x}=(\frac{21}{3})^x[/tex][tex]Use\text{ 21=7}\times3\text{ in the given expression.}[/tex][tex]\frac{21^x}{3^x}=\frac{(7\times3)^x}{3^x}[/tex][tex]Use\text{ }(a\times b)^x=a^x\times b^x.\text{ Here a=7, b=3 and n=x.}[/tex][tex]\frac{21^x}{3^x}=\frac{7^x\times3^x}{3^x}[/tex]Cancel out common terms.
[tex]\frac{21^x}{3^x}=7^x[/tex]Final answer:
[tex]B.\frac{7^x\times3^x}{3^x}[/tex][tex]C.\text{ }7^x[/tex][tex]D.\text{ }(\frac{21}{3})^x[/tex]
For Items 9-11, determine the length of each segmentwith the given endpoints.9. C(1, 4) and D(11, 28)10. Y(-2, 6) and Z(5, -8)11. P(-7,-7) and Q(9,5)
Use the following formula:
d = √((x2-x1)² + (y2-y1)²)
9.
C(1,4) = (x1,y1)
D(11,28) = (x2,y2)
d = √((11-1)² + (28-4)²) = √((10)²+(24)²) = 29.73213749
10.
Y(-2,6) = (x1,y1)
Z(5,-8) = (x2,y2)
d = √((5-(-2))² + (-8-6)²) = √((7)² + (-14)²) = 15.65247584
11.
P(-7,7) = (x1,y1)
Q(9,5) = (x2,y2)
d = √((9-(-7))² + (5-(-7))²) = √((16)²+(12)²) = 20
Donna run 7 miles in 60 minutes. At the same rate, how many miles would she run in 24 minutes?
We know how many miles she runs in 60 mins, we can make a rule of three to find the miles in 24 mins
So if she runs 7 miles in 60 mins
how many x miles in 24mins
x = (24mins*7miles)/60mins = (24*7miles)/60 = 2.8 miles
So, Donna runs 2.8 miles in 24mins.
1. Select all values of x that are solutions to the equation: -2(x + 4)(3x - 18) = 0A) -6B) -4C) -2D) OE) 2F) 4G) 6
x = -4 OR x = 6
The correct options are B and G
Having trouble understanding
Since the value of the coin collection rises proportionally every year, this functions exponentially.
What are exponential functions?The exponential function in mathematics is represented by the symbols f(x)=exp or ex. The word, unless otherwise stated, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras. f(x) = bx, where b > 0 and b 1, is the formula for an exponential function. B is referred to as the base and x is referred to as the exponent, just like in any exponential expression. Bacterial proliferation is an illustration of an exponential function. Some bacteria grow by two folds per hour. The exponent is the independent variable, or x-value, in an exponential function, while the base is a fixed value. An exponential function would be, for instance, y = 2x. Here is what that appears to be.
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A population of beetles are growing according to a linear growth model. The initial population (week 0) is Po = 9, and the population after 4 weeks is P4 = 25. Find an explicit formula for the beetle population after n weeks. Pn = After how many weeks will the beetle population reach 113?
Pn = 4n + 9
it will take 26 weeks
Explanation:Po = 9
P4 = 25
the linear model will be in the form of linear equation:
y = mx + c
where c = Po
x = 4
y = P4 = 25
we insert to get the m = slope or rate of change
25 = m(4) + 9
25 = 4m + 9
25 - 9 = 4m
16 = 4m
m = 16/4
m = 4
Inserting the m and c into the equation of line:
y = 4x + 9
We are told represent the number of weeks with n. Hence, we replace our x with n.
Also, y = Pn
Pn = 4n + 9
when Pn = 113, n = ?
Pn = 4n + 9
113 = 4n + 9
113 - 9 = 4n
104 = 4n
104/4 = n
n = 26
Therefore, it will take 26 weeks for the beetle population to reach 113
Find the equation of the line in standard form that passes through the following points. Eliminate anyfractions and simplify your answer.(4, -8) and (9, 11)
We want to find the equation of the line that passes through the points:
(4 , -8) and (9 , 11)
First, we're going to find the slope between these points using the fact that:
If we have two points that lie on a line:
[tex](x_1,y_1)\text{ and }(x_2,y_2)[/tex]The slope between them can be found using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]If we replace our values:
[tex]\begin{gathered} (x_1,y_1)=(4,-8) \\ (x_2,y_2)=(9,11) \\ x_1=4 \\ x_2=9 \\ y_1=-8 \\ y_2=11 \end{gathered}[/tex]The slope will be:
[tex]m=\frac{11-(-8)}{9-4}=\frac{11+8}{5}=\frac{19}{5}[/tex]Now, we could apply the point-slope equation. This equation tells us that we can find the equation of the line if we got a point (x1,y1) on the line, and the slope m:
[tex]y=y_1+m(x-x_1)[/tex]Replacing our values:
[tex]\begin{gathered} y=-8+\frac{19}{5}(x-4) \\ y=-8+\frac{19}{5}x-\frac{76}{5} \\ y=\frac{19}{5}x-\frac{116}{5} \end{gathered}[/tex]This, is the general form. We want to express the last equation as a standard form like this:
[tex]Ax+By=C[/tex]If we re-write:
[tex]\begin{gathered} y=\frac{19x-116}{5} \\ \\ 5y=19x-116 \\ 19x-5y=116 \end{gathered}[/tex]Therefore, the standard for the equation of the line that passes through (4 , -8) and (9, 11) is:
19x-5y=116
Determine the radius of the circle with center at (7,-4) and a point on the circle (-2, 5). Show organized work to support your answer. Round your answer to the nearest tenth.
The radius of the circle with center at (7,-4) and a point on the circle (-2, 5). is 9√2
Radius is the line segment extending from the center of a circle or sphere to the circumference or bounding surface, it is the distance betwee the center of the circle to a point on the circumference
the circle with center at (7,-4) and a point on the circle (-2, 5).
We can find the radius by using the distance formula
r = √((x₂ - x₁)² + (y₂ - y₁)²)
r = √((-2 -7)² + 5 - (-4)²)
r = √(9² + 9²)
r = 9√2
Therefore, the radius of the circle with center at (7,-4) and a point on the circle (-2, 5). is 9√2
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A book sold 37,900 copies in its first month of release. Suppose this represents 9.1% of the number of copies sold to date. How many copies have been sold to date? Round your answer to the nearest whole number.
We know that 9.1% of the total copies sold are 37,900.
If we call N to the total amount of copies sold and see that 9,1% correspond to a proportion of 9.1/100=0.091, we can calculate N as:
[tex]\begin{gathered} 0.091\cdot N=37,900 \\ N=\frac{37,900}{0.091} \\ N\approx416,484 \end{gathered}[/tex]Answer: the total number of copies sold is approximately 416,484.
Find the value of y at which the maximum occurs
Given
Z = 2x + y
Find
Find the value of y at which the maximum occurs
Explanation
objective function is maximum at point (12 , 0)
so , here value of x = 12
and value of y = 0
therefore ,
value of y at which the maximum occurs = 0
Final Answer
hence , x = 12 and y = 0
Find the diameter of the circle with an area of 14π squared inches. Round to the nearest hundredths. Please solve using this formula: Area= πr^2r=radius
Given:
Area of the circle
[tex]A=14\pi\text{ in.}^2[/tex]Required:
To find the diameter of the circle.
Explanation:
The area of the circle is given by the formula:
[tex]A=\pi r^2[/tex]Where r = radius of the circle
Put the given value of A.
[tex]\begin{gathered} 14\pi=\pi r^2 \\ r^2=14 \end{gathered}[/tex]Take the square root on both sides.
[tex]\begin{gathered} r=\sqrt{14} \\ r=3.741\text{ in.} \end{gathered}[/tex]Now the diameter D= 2r
[tex]\begin{gathered} D=2\text{ }\times3.741 \\ D=7.482\text{ in.} \end{gathered}[/tex]Final answer:
The diameter of the circle D= 7.482 in,
In the picture provided, describe the three dimensional figure that will be produced if the rectangle is rotated about the vertical axis.A. a cylinder with radius of 5 cm and height of 3 cm B.a cylinder with height of 5 cm and radius of 3 cm C. a cylinder with diameter of 5 cm and height of 3 cm D. a cylinder with height of 5 cm and diameter of 3 cm
To answer this question, we need to do a drawing like this:
If we see the figure from above, we will see that the figure will have a radius of 5 cm, and, therefore, a diameter of 10 cm. The height will be always 3 cm.
Therefore, if the rectangle is rotated about the vertical axis, we will have a cylinder of radius equal to 5 cm and a height of 3 cm.
Hence, the answer is option A: a cylinder with a radius of 5 cm and a height of 3 cm.
Graph the equation-6x + 2y = 10 2. Compare and Contrast this graph to the graph from the previous problem. pleas be SPECIFIC:)
we have the equation
6x + 2y = 10
To graph the line we need at least two points
Find out the first point
For x=0
6(0)+2y=10
2y=10
y=5
The first point is (0,5)
Find out the second point
For x=3
6(3)+2y=10
2y=10-18
2y=-8
y=-4
the second point is (3,-4)
Plot the points and join them to graph the line
using a graphing tool
what is the range of this exponential function?1) all real numbers 2) { y | y > 0 }3) { y | y ≥ 0 }4) { y | y ≤ 0 }5) { y | y < 0 }
Remember that
The range is the data set of all possible values of y
In this function
y>0
the range is the interval (0, infinite)
therefore
answer is the second option
v-7/3 = 0...........
Answer
Explanation
The question to be solved is
What is the surface area of the cylinder with height of 6cm and radius of 7cm?Round your answer nearest thousanddth
The radius of cylinder is r=7 cm.
The heighht of cylinder is h= 6 cm
Determine the surface area of the cylinder.
[tex]\begin{gathered} SA=2\pi rh+2\pi(r)^2 \\ =2\pi\cdot7\cdot6+2\pi\cdot(7)^2 \\ =572 \end{gathered}[/tex]So answer is 572 centimeter square.