∠1 is 31.5°
∠2 is 148.5°.
Given:
∠1 = x
∠2 = 5x-9
The measure of ∠1 and ∠2 are supplementary angles.
First, the value of x can be calculated as,
[tex]\begin{gathered} \angle1+\angle2=180\degree \\ 5x-9+x=180\degree \\ 6x-9=180\degree \\ 6x=180+9 \\ 6x=189 \\ x=\frac{189}{6} \\ x=31.5 \\ x=\angle1 \end{gathered}[/tex]Substitute the value of x in ∠2.
[tex]\begin{gathered} \angle2=5x-9 \\ =5(31.5)-9 \\ =157.5-9 \\ =148.5 \end{gathered}[/tex]Hence, the measure of ∠1 is 31.5° and the measure of ∠2 is 148.5°.
A shoe salesman earns a commission of 30%
of all shoe sales made.
Yesterday he sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80
each. How much did he earn in commission yesterday?
Answer: $111 is earn by shoe salesman as commission .
Step-by-step explanation:
As given the statement in the question be as follow.
Shoes salesman sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80 each.
Total cost of the pair of shoes = 3 × 70 + 2 × 80
= 210 + 160
= $ 370
As given
shoe salesman earns a commission of 30% of all shoe sales made.
30% is written is decimal form
= 0.30
Commission earns = 0.30 × Total cost of the pair of shoes .
= 0.30 × 370
= $ 111
Therefore $111 is earn by shoe salesman as commission .
If a,b ,and c represent the set of all values of x that satisly the equation below, what is the value(A+ b+ c) + (abc)?X^3-20x = x^2(A) -1(B) 0(C) 1(D) 9
First, we need to find the solutions a, b, and c of the equation:
[tex]x^3-20x=x^2[/tex]We can rewrite it as:
[tex]\begin{gathered} x^3-x^{2}-20x=0 \\ \\ x(x^{2}-x-20)=0 \\ \\ x=0\text{ or }x^{2}-x-20=0 \end{gathered}[/tex]Thus, one of the solutions is a = 0.
To find the other solutions, we can use the quadratic formula. We obtain:
[tex]\begin{gathered} x=\frac{-(-1)\pm\sqrt[]{(-1)^{2}-4(1)(-20)}}{2(1)} \\ \\ x=\frac{1\pm\sqrt[]{1+80}}{2} \\ \\ x=\frac{1\pm\sqrt[]{81}}{2} \\ \\ x=\frac{1\pm9}{2} \\ \\ b=\frac{1-9}{2}=-4 \\ \\ c=\frac{1+9}{2}=5 \end{gathered}[/tex]Now, we need to find the value of the expression:
[tex]\mleft(a+b+c\mright)+abc[/tex]Using the previous solutions, we obtain:
[tex]\mleft(0-4+5\mright)+0(-4)(5)=1+0=1[/tex]Therefore, the answer is 1.
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The value of x is -2.
We are given a graph of a function f(x).
We have to find the value of x when the value of f(x) is -3.
We know that x- axis represents x and the y-axis shows f(x).
Hence, the x and y coordinates of a point on the line will be (x, f(x)).
To find the value of x , I will check the coordinates of the point (x, -3) because it is given that f(x) is -3.
Using the graph, we found the coordinates of that point to be (-2,-3).
Hence, we can say that,
x = -2
To learn more about function, here:-
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Which inference about the man is best supported by the events in the text?
a storage container for oil is in the shape of a cylinder with a diameter of 10ft and a height of 17ft. what is the volume if the storage container in cubic feet?
To calculate the volume, w will use the formula:
[tex]V=\pi r^2h[/tex]where r is the radius and h is the height
From the question,
diameter = 10
This implies that; r=d/2 = 10/2 = 5
h = 17
susbtitute the values into the formula
[tex]V=\pi\times5^2\times17[/tex][tex]=425\pi\text{ cubic feet}[/tex]If we substitute the value of pie= 22/7
[tex]V=\frac{22}{7}\times425[/tex][tex]\approx1335.71\text{ cubic f}eet[/tex]3/5 ÷ 1/3 = ?????????
Change the division sign to multiplication and then invert 1/3
That is;
[tex]\frac{3}{5}\times3[/tex][tex]=\frac{9}{5}\text{ =1}\frac{4}{5}[/tex]Create a polynomial of degree 6 that has no real roots. Explain why it has no real roots. Is it possible to have a polynomial with an odd degree that has no real roots? Explain.
Create a polynomial of degree 6 that has no real roots.
y = ( x^2 + 4) ( x^2 +7 ) ( x^2+5)
Multiplying all the terms together
y =x ^6 + 16 x^4 + 83 x^2 + 140
Using the zero product property
0= x^2 +4 x^2+7 =0 x^2 + 5 =0 will each give a complex solution
x^2 = -4 x^2 = -7 x^2 = -5
This means x = 2i or -2i x = i sqrt(7) or -i sqrt(7) x = i sqrt (5) or - i sqrt(5)
These solutions can be in the form a+bi
Therefor it will have no real roots
y = x^6 + 16 x^4 + 83 x^2 + 140 has no real solutions
Complex solutions come in pairs, so an odd degree must have a real solution
is the number 6.35 a whole number and a integer
Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity. This includes all numbers that can be written as a decimal.
Hence, 6.35 is a natural number. It is natural number, whole number, integer, and rational number.
3. What is the slope of a line that is parallel to the line that contains these
two points: (-2,5) and (-3,1).
Answer:
4
Step-by-step explanation:
The slope of the line through the points is
[tex]\frac{1-5}{-3-(-2)}=4[/tex]
Parallel lines have the same slope, so the answer is 4.
please help me work through this homework problem! thank you!
Given:
Given the function
[tex]y=3+\frac{3}{x}+\frac{2}{x^2}[/tex]and a point x = 3.
Required: Equation of the line tangent to y at x = 3.
Explanation:
The derivative of a function is he slope of the tangent line of the function at a given point. So, finding the derivative gives the slope of the tangent line.
[tex]y^{\prime}=-\frac{3}{x^2}-\frac{4}{x^3}[/tex]Substitute 3 for x into the derivative.
[tex]\begin{gathered} y^{\prime}|_{x=3}=-\frac{3}{3^2}-\frac{4}{3^3} \\ =-\frac{31}{27} \end{gathered}[/tex]Therefore, the slope of the tangent line is -31/27.
Substitute 3 for x into y.
[tex]\begin{gathered} y|_{x=3}=3+\frac{3}{3}+\frac{2}{3^2} \\ =3+1+\frac{2}{9} \\ =4+\frac{2}{9} \\ =\frac{38}{9} \end{gathered}[/tex](3, 38/9) is the only point on the tangent line where it intersects the original graph.
Plug these coordinates along with slope into the general point-slope form to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-\frac{38}{9}=-\frac{31}{27}(x-3) \end{gathered}[/tex]Solving for y will give the equation in slope-intercept form.
[tex]\begin{gathered} y=-\frac{31}{27}(x-3)+\frac{38}{9} \\ =-\frac{31}{27}x+\frac{69}{9} \end{gathered}[/tex]Final Answer: The equation of the tangent line is
[tex]y=-\frac{31}{27}x+\frac{69}{9}[/tex]
find the slope of the line passing through the points (-5,4) and (3,-3)
P1 = (-5, 4)
P2 = (3, -3)
Formula
[tex]\text{slope = }\frac{(y2\text{ - y1)}}{(x2\text{ - x1)}}[/tex]Substitution
[tex]\begin{gathered} \text{ slope = }\frac{(-3-4)}{(3\text{ + 5)}} \\ \text{ slope = }\frac{-7}{8} \end{gathered}[/tex]Result
[tex]\text{ slope = }\frac{-7}{8}[/tex]When point A'(-2,4) is reflected over they-axis, where is the image A"?(2,-4)(2,4)(4,-2)
Answer:
Explanation
Given a coordinate (x, y), If this coordinate reflected over y axis, the resulting coordinate will be expressed as (-x, y). Note that only the sign of the x coordinate axis was
4x squared- 5x +4-(9x squared +3x -1)
hello
the question here requires the subtraction of polynomials
[tex]\begin{gathered} 4x^2-5x+4 \\ - \\ 9x^2+3x-1 \end{gathered}[/tex]if we are to do this, we have to subtract the polynomials based on their degree
this would be equal to
[tex]-5x^2-8x+5[/tex]the above polynomial is the result after subtraction, but we can as well, decide to multiply through by -1, to make or eilimate the negative sign on the second degree polynomal
[tex]\begin{gathered} (-5x^2-8x+5)\times-1 \\ = \\ 5x^2+8x-5 \end{gathered}[/tex]find the slope. A. y= -1/2x - 19/2.
The equation of the line follows the following general structure:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y intercept.
Find the corresponding values in the given formula, this way:
In the given equation, m has a value of -1/2, it means the slope is -1/2.
2) A humane society claims that 30% of U.S. households own a cat. In a random sample of 210 U.S. households, 80 say they own a cat. Is there enough evidence to show this percent has changed? Use a level of significance of 0.05.
ANSWER:
There is enough evidence to reject the humane society claims
STEP-BY-STEP EXPLANATION:
Given:
p = 0.3
q = 1 - p = 1 - 0.3 = 0.7
n = 210
x = 80
Therefore:
[tex]\hat{p}=\frac{x}{n}=\frac{80}{210}=0.381[/tex]The critical values are:
[tex]Z_0=\pm1.96\text{ due }\alpha=0.05[/tex]The test statistic is:
[tex]\begin{gathered} Z=\frac{\hat{p}-p}{\sqrt[]{\frac{pq}{n}}} \\ \text{ replacing:} \\ Z=\frac{0.381-0.3}{\sqrt{\frac{0.3\cdot0.7}{210}}} \\ Z=2.56 \end{gathered}[/tex]Observe that
Z < 1.96
Therefore, reject the null hypothesis
There is enough evidence to reject the humane society claims
ANSWER:
There is enough evidence to reject the humane society claims
STEP-BY-STEP EXPLANATION:
Given:
p = 0.3
q = 1 - p = 1 - 0.3 = 0.7
n = 210
x = 80
Therefore:
[tex]\hat{p}=\frac{x}{n}=\frac{80}{210}=0.381[/tex]The critical values are:
[tex]Z_0=\pm1.96\text{ due }\alpha=0.05[/tex]The test statistic is:
[tex]\begin{gathered} Z=\frac{\hat{p}-p}{\sqrt[]{\frac{pq}{n}}} \\ \text{ replacing:} \\ Z=\frac{0.381-0.3}{\sqrt{\frac{0.3\cdot0.7}{210}}} \\ Z=2.56 \end{gathered}[/tex]Observe that
Z < 1.96
Therefore, reject the null hypothesis
There is enough evidence to reject the humane society claims
2/3 divided 17/28 equals what?
Solve for the unknown: 6(B+2) = 30
The unknown is B
[tex]6(B+2)=30[/tex][tex]\begin{gathered} 6B+12=30 \\ 6B+12-12=30-12 \\ 6B=18 \\ B=\frac{18}{6} \\ B=3 \end{gathered}[/tex]Lucky's Market purchased a new freezer for the store.When the freezer door stays open, the temperatureinside rises. The table shows how much thetemperature rises every 15 minutes. Find the unit rate.temperature (°F) =10number of minutes =15(answer) °F per minute
Notice that the information in the table can be modeled using a linear function. To find the slope (rate of change) given two points, use the formula below
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow slope=m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (15,10),(30,20) \\ \Rightarrow slope=\frac{20-10}{30-15}=\frac{10}{15}=\frac{2}{3} \end{gathered}[/tex]Given f(x), find g(x) and h(x) such that f(x)= g(h(x)) and neither g(x) nor h(x) is solely x.
Given:
[tex]\begin{gathered} f(x)=g(h(x)) \\ f(x)=\sqrt[]{-4x^2-3}+2 \end{gathered}[/tex]Solve :
[tex]g(h(x)=\sqrt[]{-4x^2-3}+2[/tex]The function g(x) convert then x is equal to h(x) then:
[tex]\begin{gathered} h(x)=-4x^2 \\ g(x)=\sqrt[]{x-3}+2 \end{gathered}[/tex]Rick's average score on his first three tests in math is 80. What must he score on his next test to raise his average to 84?
SOLUTION
Now, we don't know the scores for his first three tests. But we are told that the average score for the first three tests was 80.
So, let the scores of the first three tests be a, b, and c. That means
[tex]\frac{a+b+c}{3}=80[/tex]Also, let's assume the total score for his first three tests was x, This means that
[tex]\begin{gathered} a+b+c=x \\ or \\ x=a+b+c \end{gathered}[/tex]Comparing with the first equation it means that
[tex]\begin{gathered} \frac{a+b+c}{3}=80 \\ \frac{x}{3}=80 \\ x=3\times80 \\ x=240 \end{gathered}[/tex]Now we are asked "What must he score on his next test to raise his average to 84?"
So this means the total tests becomes 4. Hence
[tex]\begin{gathered} \frac{a+b+c+d}{4}=84 \\ \frac{x+d}{4}=84 \\ \frac{240+d}{4}=84 \\ 240+d=84\times4 \\ 240+d=336 \\ d=336-240 \\ d=96 \end{gathered}[/tex]So he must score 96 to raise his average score to 84.
Hence, the answer is 96
Julie is 6 feet tall if she stands 15 feet from the flagpole and holds a cardboard square the edges of the square light up with the top and bottom of the flagpole approximate the height of the flagpole
Using tangent function:
[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{adjacent} \\ \frac{6}{15}=\frac{15}{x-6} \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 6(x-6)=15^2 \\ 6x-36=225 \\ 6x=225+36 \\ 6x=261 \\ x=\frac{261}{6} \\ x=43.5ft \end{gathered}[/tex]What is the length of the side adjacent to angle 0?
To answer this question, we always need to take into account the reference angle in a right triangle. The reference angle here is theta, Θ, and we have that:
Then, the length of the side adjacent to theta is equal to 15.
In summary, we have that the length of the side adjacent to the angle Θ is equal to 15.
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[tex]\sqrt{25*7x^{4}*x^{1} } \\=\sqrt{25*x^{4}*7 *x^{1} } \\=\sqrt{25x^{4} } *\sqrt{7x}\\=5x^{2} \sqrt{7x}[/tex]
Option B is the answer.
Answer: C
i hope you can see my handwriting
Graph two or more functions in the same family for which the parameter being changed is the slope, m. and is less than 0.Refer to the graph of f(x) = x + 2
We have the expression:
[tex]f(x)=x+2[/tex]If the slope is changing being less than 0, that is:
Find the simple interest owed for the following loan. Principal = 2775 Rate = 7.5% Time = 5 1/2 years
We would apply the simple interest formula which is xpressed as
I = PRT/100
Where
I represents interest
P represents principal or amount borrowed
T represents time in years
R represents rate.
From the information given,
P = 2775
R = 7.5
T = 5 1/2 = 5.5
I = (2775 * 7.5 * 5.5)/100
I = 1144.6875
Rounding to the nearest cent,
I = 1144.69
Find the zero for the polynomial function and give the multiplicity for each zero. State whether the graph crosses to x axis or touch the x axis and turn around, at each zero.
we have the function
f(x)=2(x-6)(x-7)^2
REmember that the zeros of the function are the values of x when the value of the function is equal to zero
In this problem
the zeros of the function are
x=6 -------> multiplicity 1 (the graph crosses to x axis)
x=7 ----- multiplicity 2 (touch the x axis and turn around)
see the attached figure to better understand the problem
In a nearby park, a field has been marked off for the neighborhood Pop Warner football team. If the field has a perimeter of 310 yd and an area of 4950 yd', what are the dimensions of the field?
Answer:
The dimension of the field is ( 110 x 45)
Exolanations:
Perimeter of the field, P = 310 yd
Area of the field, A = 4950 yd²
Note that the shape of a field is rectangular:
Perimeter of a rectangle, P = 2(L + B)
Area of a rectangle, A = L x B
Substituting the values of the perimeter, P, and the Area, A into the formulae above:
310 = 2(L + B)
310 / 2 = L + B
155 = L + B
L + B = 155...............................................(1)
4950 = L x B...............(2)
From equation (1), make L the subject of the formula:
L = 155 - B...................(3)
Substitute equation (3) into equation (2)
4950 = (155 - B) B
4950 = 155B - B²
B² - 155B + 4950 = 0
Solving the quadratic equation above:
B² - 110B - 45B + 4950 = 0
B (B - 110) - 45(B - 110) = 0
(B - 110) ( B - 45) = 0
B - 110 = 0
B = 110
B - 45 = 0
B = 45
Substitute the value of B into equation (3)
L = 155 - B
L = 155 - 45
L = 110
The dimension of the field is ( 110 x 45)
4. Which of the following rules is the composition of a dilation of scale factor 2 following (after) a translation of 3 units to the right?
ANSWER
A. (2x + 3, 2y)
EXPLANATION
Let the original coordinates be (x, y)
First, there was a dilation of scale factor 2.
This means that the coordinates become:
2 * (x, y) => (2x, 2y)
Then, there was a translation of 3 units to the right. That is a translation of 3 units on the horizontal (or x axis).
That is:
(2x + 3, 2y)
So, the answer is option A.
Segment AB and segment CD intersect at point E. Segment AC and segment DB are parallel.
To begin we shall sketch a diagram of the line segments as given in the question
As depicted in the diagram, line segment AC is parallel to line segment DB.
This means angle A and angle B are alternate angles. Hence, angle B equals 41 degrees. Similarly, angle C and angle D are alternate angles, which means angle C equals 56.
Therefore, in triangle EAC,
[tex]\begin{gathered} \angle A+\angle C+\angle AEC=180\text{ (angles in a triangle sum up to 180)} \\ 41+56+\angle AEC=180 \\ \angle AEC=180-41-56 \\ \angle AEC=83 \end{gathered}[/tex]The measure of angle AEC is 83 degrees
Using the Rational Roots Theorem which of the values shown are potential roots of ) = 32-132-3x + 457 Select all that apply. +1/3 +5 +5/3 +9 +1 +15 +3 +45
To solve this problem, you find the value of x that will make the function to be = 0 by substituting the likely values from the option into the eqaution and checking if after the simplification the value is 0
so checking
[tex]\begin{gathered} \text{The factors betwe}en\text{ }3\text{ and 45 are } \\ 1,3,5,9,15,45 \\ \text{factors of 3 are 1,3} \end{gathered}[/tex]we have
[tex]\begin{gathered} =3x^{^3}-13x^2-3x\text{ +45} \\ \pm1,\text{ 3, 5,9, 15,45} \\ \pm\frac{1}{3},\text{ 1, 5/3, 3, 5 , 15} \\ \text{values that apply are +3 twice and -5/3} \end{gathered}[/tex]