$7969.24 invested at 8% and $3930.76 invested at 5%
From given information,
Amount invested = $11,900
Rate of interest for first part = 8%
Rate of interest for second part = 5%
Let the amount invested for 8% be 'x'.
Let the amount invested for 5% be 'y'
According to question, we get an equation,
0.08x - 0.05y = 441
x + y = 11,900
x = 11,900 - y
0.08(11,900 - y) - 0.05y = 441
952 - 0.08y - 0.05y = 441
-0.13y = -511
y = (-511)/(-0.13)
y = 3930.76
so, x = 11,900 - 3930.77
x = 7969.23
Therefore, $7969.24 invested at 8% and $3930.76 invested at 5%
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Problem 29) Find the point of inflection and concavity.
29. f(x)=4/x²+1
The function given f(x) = 4/x² + 1 concaves upward on (-∞,0)∪(∞,0) and has no point of inflection.
Point of Inflection and ConcavityA point of inflection of the graph of a function f(x) is a point where the second derivative f′′(x) is 0. We have to wait a minute to clarify the geometric meaning of this.
A piece of the graph of f is concave upward if the curve ‘bends’ upward. For example, the popular parabola y=x2 is concave upward in its entirety.
A piece of the graph of f is concave downward if the curve ‘bends’ downward. For example, a ‘flipped’ version y=−x² of the popular parabola is concave downward in its entirety.
The relation of points of inflection to intervals where the curve is concave up or down is exactly the same as the relation of critical points to intervals where the function is increasing or decreasing. That is, the points of inflection mark the boundaries of the two different sort of behavior. Further, only one sample value of f′′ need be taken between each pair of consecutive inflection points in order to see whether the curve bends up or down along that interval.
In the function f(x) = 4 / x² + 1 has no points of inflection but it's concave upwards along (-∞, 0) ∪ (0, ∞)
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y = x² + 6x + 3 y = 3x - 7
The given system of equations has no solution.
What is the general equation of a Straight line and a quadratic equation?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The general equation of a quadratic equation is -
y = ax² + bx + c
We have the following equations -
y = x² + 6x + 3
y = 3x - 7
Plot the graph of both equations and the points of intersection would be the solution set. Refer to the graph below. There are no points of intersection, hence these set of equations have no solution.
Therefore, the set of equations of line -
y = x² + 6x + 3
y = 3x - 7
have no solution
Therefore, the given system of equations has no solution.
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HELPPP PLEASEEEE VERY IMPORTANTTTTTTTTTT
The possible real zeros for the function will be:
Positive: 4 or 2
Negative: 1
The Descartes rule of sign is technique which helps us to find no. of real positive/negative and imaginary zeros a function has.
To apply the rule:
1. Arrange the function in the decreasing value of exponents of variables.
2. The no. of positive real zeros of f(x) will be either equal to the number of sign change or less than the number of sign changes by an even number.
3. For real negative real zeros it will be the same but we will check the sign change of f(-x).
now let's look at the function.
f(x) = 6[tex]x^{7}[/tex] -3[tex]x^{4}[/tex] + 6[tex]x^{3}[/tex] + 9[tex]x^{2}[/tex] - 7x + 4
The sign change here is 4 times so the value of +ve zeros of f(x) will be either 4 or 2.
similarly let's take f(-x) for negative zeros.
f(x) = 6[tex](-x)^{7}[/tex] -3[tex](-x)^{4}[/tex] + 6[tex](-x)^{3}[/tex] + 9[tex](-x)^{2}[/tex] - 7(-x) + 4
Here sign change is 1 which cannot be decreased by an even no. so it is the only value.
Therefore the positive and negative zeros of the function will be 2 or 4 and 1 respectively.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
A line that represent the "rise" and the "run" of the line is shown in the image attached below. Also, a slope of this line in simplest form is equal to 0.25.
How to determine the slope of a line?Mathematically, the slope of a line is also referred to as pitch or gradient and can be calculated by using this formula:
Slope, m = V/H
Where:
V represents the rising vertical distance (rise) of an object.H represents the horizontal distance (run) an object runs through.From the graph of this line, we would choose the following data points to represent both the rise and run:
Rise (x, y) = (-5, 0)
Run (x, y) = (7, 3)
Substituting the selected data points into the slope formula, we have;
Slope (pitch), m = (3 - 0)/(7 - (-5))
Slope (pitch), m = (3 - 0)/(7 + 5)
Slope (pitch), m = 3/12
Slope (pitch), m = 0.25
At point (-5, 0), the equation of this line would be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the data points.Substituting the parameters into the formula, we have;
y - 0 = 0.25(x - (-5))
y - 0 = 0.25(x + 5)
y = 0.25x + 1.25
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HELP ME PLEASEE!! I can’t do fractions!! I will give a brainliest too!!
The value of fractions are
11/12 11/9203/155/16259/8819/123/467/2061/205/211/699/20The given Fractions are :
1. [tex]\frac{3}{4} +\frac{1}{6} =\frac{3*3+2*1}{12} = \frac{9+2}{12} = \frac{11}{12}[/tex]
2. [tex]\frac{8}{9} +\frac{1}{3} =\frac{8*1+3*1}{9} =\frac{8+3}{9} =\frac{11}{9}[/tex]
3. [tex]8\frac{5}{6} +4\frac{7}{10} = \frac{53}{6} +\frac{47}{10} =\frac{5*53+3*47}{30} =\frac{406}{30}= \frac{203}{15}[/tex]
4. [tex]\frac{3}{4} -\frac{7}{16} =\frac{12-7}{16} =\frac{5}{16}[/tex]
5. [tex]9\frac{11}{24} -7\frac{3}{8} =\frac{227}{22} -\frac{59}{8} =\frac{908 - 649}{88} =\frac{259}{88}[/tex]
6. [tex]2\frac{5}{6} -1\frac{1}{4} =\frac{17}{6} -\frac{5}{4} =\frac17*2-3*5}{12} =\frac{34-15}{12} =\frac{19}{12}[/tex]
7. [tex]\frac{2}{3} +\frac{1}{12} = \frac{4*2+1*1}{12} =\frac{8+1}{12} =\frac{9}{12} =\frac{3}{4}[/tex]
8. [tex]5\frac{4}{5} -2\frac{9}{20} =\frac{29}{5} -\frac{49}{20} =\frac{4*29-49*1}{20} =\frac{116-49}{20} =\frac{67}{20}[/tex]
9. [tex]1\frac{3}{4} +1\frac{3}{10} =\frac{7}{4}+\frac{13}{10} =\frac{35+26}{20} = \frac{61}{20}[/tex]
10. [tex]6 -3 \frac{1}{2} = \frac{6}{1} -\frac{7}{2} =\frac{12-7}{2} =\frac{5}{2}[/tex]
11. [tex]3\frac{1}{2} -1\frac{2}{3} =\frac{7}{2} -\frac{5}{3} =\frac{21-10}{6} =\frac{11}{6}[/tex]
12. [tex]8\frac{3}{4} -3\frac{4}{5} =\frac{35}{4} -\frac{19}{5} =\frac{175-76}{20} =\frac{99}{20}[/tex]
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How far is the distance from sprinkler head to ?
The distance from sprinkler head B to C is?
.B (-14,-5)
C(-14, 7)
The distance between the points B and C is 12m
What is the distance between two points?Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
for the coordinates B (-14,-5) and C(-14, 7), then x1 = -14 ,x-2= -14 , y1= -5 and y2= 7
therefore d =√((x2 – x1)² + (y2 – y1)²) = √((-14– -14)² + (-5 – 7)²)
d=√((0)² + 12²)
d=√144
d= 12m
therefore the distance between the points B and C is 12m.
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Urgent 80-90 points if completed!
Complete the table (information you can use and table in images.)
The required cost function is c(b) = 35b + 475, and the completed table is shown.
What is a function?A function is a relation where every input is connected to only one possible output from a set of available inputs.
Given that, the cost of the plane ticket is $475 and the cost per checked bag is $35.
The cost of b checked bags is $35b.
Therefore, the total cost is:
c(b) = 35b + 475
The completed table is:
Number of bags(b) Total cost c(b)
0 475
1 510
2 542
3 580
4 615
6 685
8 755
Hence, the required cost function is c(b) = 35b + 475.
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This square root equation has 2 solutions. What is the extraneous solution?
2x+29−−−−−−√−7=x
Enter your answer in the box.
x =
Answer:
See below
Step-by-step explanation:
Sqrt(2x + 29) - 7 = x <===answering this version
add 7 to both sides to get
sqrt(2x+29) = x+7 square both sides
2x+29 = x^2 + 14x + 49 simplify
x^2 +12x + 20 = 0 factor
(x+10)(x+2) = 0 shows x can be -10 or -2
sub in these values in the original equation to find only the answer
x = -2 works then the answer x = -10 is extraneous answer
find x in angle ABC
............
Answer:
x = 5.59
Step-by-step explanation:
tan 90⁰ = 16/x
x = atan 90⁰/16
= 5.5852 (to 5 significant figures)
= 5.59 (to 3 significant figures)
What’s the answer PLEASEE asap 4(x - 2)
Answer:x=2
Step-by-step explanation:
4(x-2) goes to 4x -8 which then goes to 4x=8 which then divided by 4 equals x=2
Erica solved the equation -5x - 25 = 78; her work is shown below. Identify the error and where it was made. 5
points)
-5x - 25 = 78
Step 1: -5x - 25 - 25 = 78
25
Step 2: -5x = 53
-5X
53
Step 3: -5 = -5
Step 4: x =
53
• Step 1: She should have added 25 to each side.
Step 1: She should have divided both sides by -5.
Step 3: She should have divided both sides by -5.
Step 3: She should have multiplied both sides by -5.
Answer:
-103/5Step-by-step explanation:
-5x-25=78
-5x-25+25=78+25
-5x=103
divide both sides by -5
-5x/-5 = 103/-5
x=-103/5
Write an equation of a line in slope-intercept form given the slope (m) and the y-intercept (b).
Answer:
D: y = -4/7x + 7
Step-by-step explanation:
Answer:
[tex]y=-\frac{4}{7}x+7[/tex] or option D
Step-by-step explanation:
y=mx+b is the form where m is the slope and b is the y intercept so just fill those in
y=-4/7x+7
Hopes this helps please mark brainliest
Help please 20 points
Answer: x=18 inches.
Step-by-step explanation:
You can use the Pythagorean Theorem for help.
To find the length of the third side of a right triangle, you have to do
10 square + 15 square=x square.
100+225=x square
325=x square
x= [tex]\sqrt{325}[/tex].
The nearest inch would be x= 18 inches.
Answer: The correct answer is 18 inches
Step-by-step explanation:
Using the Pythagorean Theorem:
c= [tex]\sqrt{a^2+b^2}[/tex]
c=[tex]\sqrt{10^2+15^2}[/tex]
c=18.02776
c= 18 inches
The length of a rectangle is three times it’s width. The area of the rectangle is 108cm power of 2 what is its perimeter
The perimeter of the rectangle with area of 108 cm is 48 cm.
How to find the perimeter of a rectangle?The perimeter of a rectangle is the sum of the whole sides of the rectangle. A rectangle is a quadrilateral with opposite side equal to each other.
Therefore,
area of a rectangle = lw
where
l = side lengthw = widthTherefore,
l = 3w
108 = 3w(w)
108 = 3w²
w² = 108 / 3
w = √36
w = 6
Hence,
length = 3(6) = 18
Therefore,
perimeter of the rectangle = 2(l + w)
perimeter of the rectangle = 2(18 + 6)
perimeter of the rectangle = 2(24)
perimeter of the rectangle = 48 cm
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Match the reasons to the statement ( will mark brainiest if optional)
Match the reasons to the statements.
a) Reflexive Property
b) Angle Congruence Postulate
c) Definition of Supplementary
d) Segment Addition Postulate
e) Definition of Right Angle
f) Symmetric Property
g) Substitution Property of Equality
h) Definition of Complementary
i) Segment Congruence Postulate
j) Angle Addition Postulate
k) Linear Pair Postulate
The reasons for the possible congruency statements obtained from a similar question on the website are as follows;
Statement [tex]{}[/tex] Reason
7. ∠BAD ≅ ∠CAD
[tex]\overline{AD}[/tex] ≅ [tex]\overline{AD}[/tex] ⇒[tex]{}[/tex] Reflexive property
8. ∠2 ≅∠3
m∠2 = m∠3 ⇒ [tex]{}[/tex] Angle congruency postulate
9. [tex]\overline{BE}[/tex] ≅ [tex]\overline{CE}[/tex]
[tex]\overline{DE}[/tex] ≅ [tex]\overline{AE}[/tex]
[tex]\overline{BE}[/tex] = [tex]\overline{CE}[/tex] [tex]{}[/tex] ⇒ Segment Congruence Postulate
[tex]\overline{DE}[/tex] = [tex]\overline{AE}[/tex] [tex]{}[/tex] ⇒ Segment Congruence Postulate
10. AE + BE = AB [tex]{}[/tex] ⇒ Segment Addition Postulate
11. [tex]\overline{AB}[/tex] ≅ [tex]\overline{DE}[/tex]
[tex]\overline{DE}[/tex] ≅ [tex]\overline{AB}[/tex] [tex]{}[/tex] ⇒ Symmetric property
What are congruent geometric figures?Geometric figures are congruent if their shape and or size are the same.
Reflexive property of congruency
The reflexive property of congruency states that a shape is congruent to itself.
Angle congruency postulate
The angle congruency postulate states that if the measure of two angles are the same, then they are congruent
Segment congruency postulate
The segment congruency postulate states that if the length of two segments are the same, then the segments are congruent
Segment Addition Postulate
The segment addition postulate states a point B is located on a segment AC if and only if AB + BC = AC
Symmetric property of congruency
The symmetric property congruency states that if a geometric figure, A, is congruent to another geometric figure, B, then B is congruent to A
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Question 10
Three students in the Math Club are analyzing the expressions (10x+8) and (x+13) + 3(x+5) for all values of x. Each student
claims the expressions are related according to the results in the table. Which student is correct?
Student 1 (10x+8)
Student 2(10x +¹8) >
Student 3 (10x+8)
=
<
Student Select Choice is correct.
-(x+13) + 3(x+5)
-(x+13) + 3(x+5)
-(x+13) + 3(x+5)
1/4(10x+8)= -(1/2x+13) + 3(x+5) being examined by three Math Club members for all possible values of x.
Given that,
The formulas 1/4(10x+8) and -(1/2x+13) + 3(x+5) are being examined by three Math Club members for all possible values of x. According to the findings in the table, each student asserts that the expressions are connected.
We have to find which student is right.
Take the
1/4(10x+8) = 10/4x+8/4 = 5/2x+2
-(1/2x+13) + 3(x+5) = -1/2x-13+3x+15 = 5/2x+2
So, 1/4(10x+8)= -(1/2x+13) + 3(x+5)
Therefore, 1/4(10x+8)= -(1/2x+13) + 3(x+5) being examined by three Math Club members for all possible values of x.
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3/10 - 1/5=
Find the missing fraction.
Please answer need to turn it in
Answer:
85,000 i think
Step-by-step explanation:
if the equation of y = 19x - 8, what are the coordinates of the point where the line crosses the y axis?
Answer:
(0, -8)
Step-by-step explanation:
The y-intercept of the line is -8, meaning the coordinate point is (0, -8),
help me ou asap thanks
Answer:
I think it's =
Step-by-step explanation:
they both equal 32.
Answer:
=
Step-by-step explanation:
6^2 - 2^2
36 - 4
32
4 (6 + 2)
24 + 8
32
1
Two Truths & One
Which of the 3 statements below
Explain how you made your deci
x = 2
y = 5
Z=7
69
by=64
2
bz
bx=65
3
68
bx=68
Answer:
3
Step-by-step explanation:
1) Substitute x with 2
b^8
b^2
2) subtract the index
b^8-2
=b^6
3)b^6 ≠ b^8
therefore, 3 is a lie
The medical practice you are working it has seen an average of 22.4 patients a day for the past three months 3/4 of those patients have insurance and one form or another describe nowhere written paragraph how you analyze this scenario in the process you were used to arrive at an answer, please express to the nearest whole number how many of these patients on average per day do not have insurance and thus pay cash price for their visits
The number of these patients on average per day that do not have insurance and thus pay cash price for their visits would be = 504 people.
What is insurance coverage?An insurance coverage is defined as the official coverage an individual has over unforseen and inexperienced financial demands.
The average number of patients seen in a day = 22.4.
The number of months patients where seen = 3 months = 90 days
Total number of patients seen would be= 22.4 × 90 = 2,016
The fraction of patients that has insurance= 3/4
Therefore the fraction that doesn't have insurance= 1/4 of 2,016
= 2,016/4
= 504 people.
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Two mechanics worked on a car. The first mechanic charged
$55
per hour, and the second mechanic charged
$115
per hour. The mechanics worked for a combined total of
20
hours, and together they charged a total of
$1400
. How long did each mechanic work?
pie charts help is greatly apprieciated
Answer:
Brown 180°
Ginger 84°
Blonde 96°
Step-by-step explanation:
Brown 360 x 15/30 = 180
Ginger 360 x [tex]\frac{7}{30}[/tex] = 84
Blonde 360 x [tex]\frac{8}{30}[/tex] = 96
The point A (-5,3)is translated by the rules (x,y)- (x+3,y-3) what are the coordinates of A?
the coordinates of A after translation is (-2, 0)
What is a co-ordinate?
In geometry, a coordinate system may be a system that uses one or a lot of numbers, or coordinates, to unambiguously confirm the position of the points or alternative geometric components on a manifold like Euclidean space.
Main body:
point A = (-5,3)
According to question:
translated by the rules (x,y)- (x+3,y-3)
we need to add 3 to x coordinate and subtract 3 from y coordinate.
New coordinate of A are (-5+3 , 3-3)
Hence New coordinate of A are (-2,0)
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Simplify the expression completely:
8x + 4 - 6y - 3x + y =
The simplified expression of 8x + 4 - 6y - 3x + y is 5x - 5y + 1
Expression:
An expression is any mathematical statement that consists of numbers, variables and an arithmetic operation between them.
Given,
Here we have the expression 8x + 4 - 6y - 3x + y.
Now, we have to simplify the expression.
To simplify the expression, first we have to write the given expression,
=> 8x + 4 - 6y - 3x + y
Now, we have to combine the like terms, then we get,
=> (8x - 3x) + (-6y + y) + (4 - 3)
Now, we have to perform the appropriate arithmetic operations on it, then we get,
> 5x + (-5y) +1
Therefore, the simplified form of the given expression is 5x - 5y + 1
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When the system is solved, the result is:
3x + y = -7
4x − y = -14
(3, -2).
(3, 2).
(-3, 2).
(-3, -2).
None of these choices are correct.
Y=6x-2 function rule
The table considering the numeric values of the function y = 6x - 2 is given as follows:
x | y
-1 | -8
0 | -2
1 | 4
5 | 28
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
In this problem, the function is:
y = 6x - 2.
Hence the numeric values are obtained replacing the lone instance of x by it's attributed value.
At x = -1, the numeric value is:
y = 6(-1) - 2 = -6 - 2 = -8.
At x = 0, the numeric value is:
y = 6(0) - 2 = 0 - 2 = -2.
At x = 1, the numeric value is:
y = 6(1) - 2 = 6 - 2 = 4.
At x = 5, the numeric value is:
y = 6(5) - 2 = 30 - 2 = 28.
Missing InformationThe problem asks to complete the table with the numeric values as follows:
x | y
-1 | _
0 | _
1 | _
5 | _
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Antonia is making a cake.
She uses currants, raisins and sultanas in the ratio
currants: raisins: sultanas = 4:3:5.
The total mass of the three ingredients is 3.6 kilograms.
Calculate the mass of sultanas.
The mass of sultanas is 1.5 kilograms which were found using the given data and ratio.
What is the definition of ratio?Simply said, a ratio is a number that may be used to indicate one quantity as a fraction of another. A ratio's two numbers can only be compared if they share the same unit. To compare two objects, we utilize ratios.What are some examples of ratios?A ratio in mathematics displays the multiplicative relationship between two numbers. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio of 4:3).Given:
Ratio of currants: raisins: sultanas = 4:3:5.
The total mass of the three ingredients is 3.6 kilograms.
Let,
number of currants = 4x
number of raisins = 3x
number of sultanas = 5x
We know that,
4x + 3x + 5x = 3.6
12x = 3.6
x = 0.3
So, the mass of sultanas = 5x = 5(0.3) = 1.5
Therefore, the mass of sultanas is 1.5 kilograms which were found using the given data.
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in the equation (m) what is the value of x
Answer:
x is equal to 10 times 5 is the ans
