Answers
To find the maximun height (y) given a quadratic equation as above you find the coordinates of the vertex (maximum or minimun point of a parabola)
1. Use the next formula to find the x- coordinate of the vertex
[tex]\begin{gathered} y=ax^2+bx+c \\ \\ x=-\frac{b}{2a} \end{gathered}[/tex][tex]\begin{gathered} x=-\frac{\frac{24}{9}}{2(-\frac{4}{9})} \\ \\ x=-\frac{\frac{24}{9}}{-\frac{8}{9}}=\frac{-24}{-8}=3 \end{gathered}[/tex]2. Use the value of x above to find y-coordinate in the vertex:
[tex]\begin{gathered} y=-\frac{4}{9}(3)^2+\frac{24}{9}(3)+12 \\ \\ y=-\frac{4}{9}(9)+\frac{72}{9}+12 \\ \\ y=-4+8+12 \\ \\ y=16 \end{gathered}[/tex]Then, the maximum height of the diver is 16 feetRelated Questions
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
√70 = 8.3 is between 8 and 9
-√5 = -2.2 is between -3 and -2
√81 = 9 (exactly 9)
-2√4 = -2 × 2 = -4 (exactly -4)
4√8 = 8√2 = 11.3 is between 11 and 12
What is the probability of rolling a 2 or a 3 when rolling a fair six-sided die?
Answers
Answer:
It would be a 2/6 chance, or a 1/3 chance.
Step-by-step explanation:
0=9 means no solution one solution or infinite solution?
Answers
Answer:
no solution
Step-by-step explanation:
If you end up with a false equality, then the initial statement is false, meaning that there are no solutions.
Describe how to go from 1. The computer store A to the food store B.2. the computer store A, to the hardware store C.3. The hardware store C, to the food store B.Use words like left, right, up, down, north, south, east, and west. Each square on the coordinate plane is a city block.
Answers
Explanation
In the question, we are required to go through the image and describe how to move in the given directions. The solution can be seen below.
Number 1: The computer store A to the food store B.
Answer: In this case, the individual would move down for 6 city blocks
Number 2: The computer store A, to the hardware store C.
Answer: In this case, the individual will move down for one block then move right for 5 blocks
Number 3: The computer store A, to the hardware store C.
Answer: In this case, the individual will move down for five blocks and move left for 5 blocks
The American Water Works Association reports that the per capita water use in a single-family home is 69 gallons per day. Legacy Ranch is a relatively new housing development. The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences. Thirty-six owners responded, and the sample mean water use per day was 64 gallons with a standard deviation of 8.8 gallons per day.
At the .10 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average?
What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0: µ ≥ 69 when the test statistic is less than ____.
Answers
a. The decision rule for this question would be to reject the null hypothesis if test statistic is less than the critical value.
b. The test statistic is given as: -3.4091
What is the hypothesis?We have the null hypothesis as
h0 : μ ≥ 69
The alternate hypothesis is
H1 : μ < 69
a. The decision rule would be to reject the null if the test statistic is greater than the critical value
at α = 0.10 the degree of freedom = 36 - 1 = 35
the critical value is -1.306
The test statistic calculation
[tex]t =\frac{ x - u}{s/\sqrt{n} }[/tex]
[tex]t = \frac{64-69}{8.8/\sqrt{36} }[/tex]
t = -3.4091
The decision rule would be to Reject H0: µ ≥ 69 when the test statistic is less than -1.306.
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Consider the quadratic f(x)=x^2-x-30Determine the following ( enter all numerical answers as integers,fraction or decimals$The smallest (leftmost) x-intercepts is x=The largest (rightmost)x-intercepts is x=The y-intercept is y=The vertex is The line of symmetry has the equation
Answers
ANSWER
Smallest x-intercept: x = -5
Largest x-intercept: x = 6
y-intercept: y = -30
The vertex is (1/2, -121/4)
Line of symmetry x = 1/2
EXPLANATION
Given:
[tex]f(x)\text{ = x}^2\text{ - x - 30}[/tex]Desired Results:
1. Smallest x-intercept: x =
2. Largest x-intercept: x =
3. y-intercept: y =
4. The vertex is
5. Equation of Line of symmetry
1. Determine the x-intercepts by equating f(x) to zero (0).
[tex]\begin{gathered} 0\text{ = x}^2-x-30 \\ x^2-6x+5x-30\text{ = 0} \\ x(x-6)+5(x-6)=0 \\ (x-6)(x+5)=0 \\ x-6=0,\text{ x+5=0} \\ x\text{ = 6, x = -5} \end{gathered}[/tex]The smallest and largest x-intercepts are -5 and 6 respectively.
2. Determine the y-intercept by equating x to 0
[tex]\begin{gathered} y\text{ = \lparen0\rparen}^2-0-30 \\ y\text{ = -30} \end{gathered}[/tex]y-intercept is -30
3a. Determine the x-coordinate of the vertex using the formula
[tex]x\text{ = -}\frac{b}{2a}[/tex]where:
a = 1
b = -1
Substitute the values
[tex]\begin{gathered} x\text{ = -}\frac{(-1)}{2(1)} \\ x\text{ = }\frac{1}{2} \end{gathered}[/tex]3b. Determine the y-coordinate of the vertex by substituting x into the equation
[tex]\begin{gathered} y\text{ = \lparen}\frac{1}{2})^2-\frac{1}{2}-30 \\ y\text{ = }\frac{1}{4}-\frac{1}{2}-30 \\ Find\text{ LCM} \\ y\text{ = }\frac{1-2-120}{4} \\ y\text{ = -}\frac{121}{4} \end{gathered}[/tex]4. Determine the line of symmetry
In standard form the line of symmetry of a quadratic function can be identified using the formula
[tex]\begin{gathered} x\text{ = -}\frac{b}{2a} \\ x\text{ = }\frac{1}{2} \end{gathered}[/tex]which of the following properly describes "slope"? select all that apply. A. y2 - y1/ x2 - x1 B. x2-x1/y2-y1 C. run/rise D. rise/run E. ratio of change in y values (rise) for a segment of the graph to the corresponding change in x values (run)
Answers
The formula to calculate the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]A is right
also, the slope can be calculated with rise and run
[tex]m=\frac{rise}{run}[/tex]the correct formula is D.
and also apply E
the answer will be A,D and E
Sarah wanted to lose some weight, so she planned a day of exercising. She spent a total of 4 hours riding her bike and jogging. She biked for 35 miles and jogged for 6 miles. Her rate for jogging was 10 mph less than her biking rate. What was her rate when jogging?
Answers
Consider the relation,
[tex]\text{Speed}=\frac{\text{ Distance}}{\text{ Time}}[/tex]The total time taken by Sarah for biking and jogging is 4 hours.
Given that her speed for biking was 10 mph, the time taken to bike 35 miles is calculated as,
[tex]\begin{gathered} T_b=\frac{35}{10} \\ T_b=3.5\text{ hours} \end{gathered}[/tex]So, out of the total 4 hours of exercise, Sarah spent 3.5 hours riding her bike.
The remaining 0.5 hour must have been spent on jogging,
[tex]undefined[/tex]A credit card bill for $562 was due on September 14. Purchases of $283 were made on September 19, and $12 was charged on September 28. A payment of $350 was made on September 25. The annual interest on the average daily balance is 19.5%. Find the finance charge due (in dollars) on the October 14 bill. (Use 365 for the number of days in a year. Round your answer to the nearest cent.)
Answers
The annual interest on a daily basis with 19.5%, then the finance charge due on October 14 will be $623.
What is interest?In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed).
So, the finance charge will be;
(+) $ 562 due on sep 14, $ 562 x (19.5 x31) / (100 x 365) = $ 9.20
(+) purchase $ 283 on Sep 19, $ 283 x (19.5x26 ) / (100 x365) = $ 2.42
(+) finance charge on sep 28, $ 18 x(19.5 x17 ) / (100 x 365) = $ 0.17
(-) Repayment on 25 sep , $ 250 x (19.5 x20 ) / (100 x 365) = (2.745)
Finance charges from 14 sep to 14 oct will be $ 9.7= appr. 10
The Amount due on 14 October = $562 +$283 +$15+$11.855- $250
= $ 623
Therefore, The annual interest on a daily basis with 19.5%, then the finance charge due on October 14 will be $623
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Angles A and B are supplementary angles. The measure of angle A is
73∘
What is the measure of angle B?
Answers
Answer:
17
Step-by-step explanation:
73+b=90
b=90-73
b=17
The school band bought cheese and pepperoni pizzas in the ratio represented in the tape diagram for their end of year party. Based on the ratio how many pepperoni pizzas did they buy if they bought 12 cheese pizzas?
Answers
The cheese pizza is represented by 3 rectangles while the pepperoni pizza is represented by 1 rectangle.
Therefore, the ratio of cheese to pepperoni pizza is:
3 : 1
This means that if there are 3 cheese pizzas, then there will be 1 pepperoni pizza
Therefore, since they bought 12 cheese pizzas, it means that:
CCC + CCC + CCC + CCC = 12 cheese pizzas ( where C is cheese)
P + P + P + P = 4 pepperoni pizzas ( where P is pepperoni)
Thus, they bought 4 pepperoni pizzas
I'm not sure what to do for this question I have already tried could you help me with this?
Answers
1) Take into account that a linear relation can be written as follow:
y = mx + b
where m is the slope of the line and the constant b the y-coordinate of the y-intercept.
Due to Rocco started to count from a distance of 4 miles, this is a constant number, which is equivalent to b, that is, b = 4.
If the constant rate of the walk is 3 miles per 2 hours, then, m = 3/2 (because the slope is also a constant rate of change).
Then, you have the following linear equation for the relation between the distance traveled by Rocco and the time.
y = 3/2*x + 4
y is the number of miles of the Rocco walking
x is the time (in hours) he takes for the walking
2) Now, based on the previous equation, you have for the table:
3) The relation between the given variables is proportional because a change in x makes that y changes too.
The distance traveled by Rocco is given by the value of y when x = 4. As you can notice on the table, such a distance is 10 miles.
After a translation, the image of P(-3, 5) is P'(-4, 3). Identify the image of the point (1, 6) after this same translation.
Answers
The image of the point (1, 6) after the translation is (0, 4).
What is named as translation?In geometry, translation refers to a function that shifts an object a specified distance. The object is not elsewhere altered. It has not been rotated, mirrored, or resized.Every location of the object should be relocated in the same manner and at the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, as well as the object that after translation is referred to as the image.For the given question,
The image of point P(-3, 5) after a translation is P'(-4, 3).
In this, there is a shift of 1 units to the left of x axis and shift of 2 units up on the y axis.
Thus, do the same translation for the point (1, 6).
After translation image will be (0, 4)
Thus, image of the point (1, 6) after the translation is (0, 4).
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Kyree needs to fill up his truck with gasoline to drive to and from school. Gas costs $2.79 per gallon, and his truck holds a maximum of 28 gallons.Domain:Range:
Answers
Let x represent the cost per gallon of gasoline.
Let y or f(x) represent the cost of x gallons of gasoline.
Given that the cost per gallon is $2.79,
The function would be
f(x) = 2.79x
The domain refers to all possible values of x that can fit into the function. Given that the truck holds a maximum of 28 gallons, the maximum value of x is 28. When the truck is empty, the minimum value of x is 0. Therefore, the domain is 0 to 28
The range refers to all possibel values of y or f(x) that can satisfy the function.
When x = 0, f(x) = 2.79 * 0 = 0
When x = 28, f(x) = 2.79 * 28 = 78.12
The range would be 0 to 78.12
Domain: 0 to 28
Range: 0 t0 78.12
100 Points
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degrees and classifications of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for the multiplication of polynomials?
Answers
The expression that represents the area of the rectangle is 6x² + 29x + 35. The degree of the expression will be 2. And the closure property of multiplication is also demonstrated.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
Area of the rectangle = L × W square units
The sides of a rectangle are (2x + 5) units and (3x + 7) units, respectively. Then the area of the rectangle will be given as,
A = (2x + 5)(3x + 7)
A = 2x(3x + 7) + 5(3x + 7)
A = 6x² + 14x + 15x + 35
A = 6x² + 29x + 35
The degree of the expression will be 2. And the closure property of multiplication is also demonstrated.
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Answer:
[tex]\textsf{A.} \quad \textsf{Area}=(2x+5)(3x+7)[/tex]
B. Degree = 2.
Classification = Quadratic trinomial.
C. Part A demonstrates the closure property for the multiplication of polynomials as the multiplication of the two given polynomials (side measures) produces another polynomial (area).
Step-by-step explanation:
Part AArea of a rectangle
[tex]\boxed{A=lw}[/tex]
where l is the length and w is the width.
Given that a rectangle has sides measuring (2x + 5) units and (3x + 7) units, the area can be expressed as a product of the two sides:
[tex]\implies \textsf{Area}=(2x+5)(3x+7)[/tex]
Part BFOIL method
[tex]\boxed{(a + b)(c + d) = ac + ad + bc + bd}[/tex]
Expand the brackets of the equation found in part A by using the FOIL method:
[tex]\implies \textsf{Area}=6x^2+14x+15x+35[/tex]
[tex]\implies \textsf{Area}=6x^2+29x+35[/tex]
The degree of a polynomial is the highest power of a variable in the polynomial equation. Therefore:
The degree of the function is 2.A polynomial is classified according to the number of terms and its degree.
The number of terms in the polynomial is three, therefore it is a trinomial.The degree of the function is 2, therefore it is quadratic.Part CClosure property under Multiplication
A set is closed under multiplication when we perform that operation on elements of the set and the answer is also in the set.
Therefore, Part A demonstrates the closure property for the multiplication of polynomials as the multiplication of the two given polynomials (side measures) produces another polynomial (area).
A random survey of 10 students recorded their number of hours of activity each week and their Body Mass Index (BMI). The results are shown in the table below. Student Body Mass Number of Hours of Activity Each Week Index Which of the following best describes the data? O linear positive association linear negative association no association O non-linear association
Answers
According to the given table, the dataset does not describe a linear-relationhip because they do not show a linear relation between the variables, they are too far away from each other.
Hence, the answer is D.If r is the nominal rate and n is the number of times interest is compounded annually, then R=(1+r/n)^(n)-1 is the effective rate. Here, R represents the annual rate that the investment would earn if simple interest were paid. Use this formula to determine the effective rate for $1 invested for 1 year at 4.8% compounded semiannually.
Answers
Effective Rate in Compound Interest
Given r as the nominal rate of investment and n the number of times the interest is compounded annually, the formula for the effective rate is:
[tex]R=\mleft(1+\frac{r}{n}\mright)^n-1[/tex]We are required to find the effective rate for a rate of r=4.8% compounded semiannually. This means the value of n is 2 since there are two periods where interest is added to the principal per year.
Substituting the given values in the formula (recall r must be used as a decimal value, i.e. r=4.8/100=0.048):
[tex]R=(1+\frac{0.048}{2})^2-1[/tex]Calculating:
[tex]R=(1.024)^2-1=0.048576[/tex]The effective rate is 4.86%
Use the figure below to find the value of x. (x + 20) y (x + 10° (y – 40)
Answers
Answer:
The value of x is 75;
[tex]x=75[/tex]Explanation:
From the diagram;
[tex](x+20)^0+(x+10)^0=180^0[/tex]Reason; supplementary angles.
Solving the equation, we have;
[tex]\begin{gathered} x+x+20+10=180 \\ 2x+30=180 \\ 2x=180-30 \\ 2x=150 \\ x=\frac{150}{2} \\ x=75 \end{gathered}[/tex]Therefore, the value of x is 75;
[tex]x=75[/tex]Which function below has the following domain and range?Domain: {-9, - 5, 2, 6, 10}Range: { -2, 0, 8}
Answers
ANSWER :
A.
EXPLANATION :
From the problem, we have the domain and range :
[tex]\begin{gathered} Domain:\lbrace-9,-5,2,6,10\rbrace \\ Range:\lbrace-2,0,8\rbrace \end{gathered}[/tex]The x coordinates must only have the values of the domain
and the y coordinates must only have the values of the range.
The only option that satisfies this condition is :
[tex]\lbrace(2,0),(-5,-2),(10,8),(6,0),(-9,-2)\rbrace[/tex]use the formula Sn to find the sum of the first five terms of the geometric sequence.
Answers
First, find the common ratio r:
-4/9 : 4/3 = -1/3
4/3 : -4 = -1/3
-4:12 = -1/3
r= -1/3
[tex]Sn=\frac{a(r^n-1)}{r-1}[/tex]Where:
a= first term = 12
n= number of terms = 5
Replacing:
[tex]Sn=\frac{12(-\frac{1^{}}{3}^5-1)}{-\frac{1}{3}-1}[/tex]Sn= 244/27 = 9 1/27
Use the Distributive Property and partial
products to find 5 × 727
Answers
The required product of the given expression [tex]5\times727[/tex] is [tex]3635[/tex].
Distributive property is defined as sum of two or more addends is multiplied by a number gives the same result by multiplying each addends separately and add the products.
For example:
[tex]a\times (b+c)=a\times b + a\times c[/tex]
Partial product is defined as the product of each digit of a number is multiplied by each digit of other number separately.
Solving the expression using Distributive property and partial products:
[tex]5 \times 727 = 5 \times ( 700 + 27 )\\[/tex] {∵ [tex]727=700+27[/tex]}
Here, Applying the distributive property we get:
[tex]= 5 \times700 + 5 \times27\\ = 3500 + 135\\ = 3635[/tex]
Hence, the required value of the expression [tex]5\times727[/tex] is [tex]3635[/tex].
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The product of the 5×727 is 3635.
The definition of a distributive property states that when the sum of two or more addends is multiplied by a number, the results are the same whether the addends are multiplied individually or all at once. Like a×(b+c) = a × b + a × c.
The definition of a partial product is the result of multiplying each digit of one integer by each digit of the other number separately.
Given in question, 5 × 727
Using distributive property and partial product,
5 × 727 = 5 × (700 + 27)
= 5 × 700 + 5 × 27
= 3500 + 135
= 3635
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f(x+h)-f(x)
h
lim:
h→0
i) The average rate of change of f(x) over the interval [x, x + h]
ii) The slope of the line tangent to f(x) at the point (x, f(x))
iii) The slope of the line secant to f(x) over the interval [x, x + h]
iv) The derivative of f(x)
O A. ii and iii
O B. i and iii
O c. ii
OD. i
...
O E.
i and iv
O F. ii and iv
Answers
Answer: F
Step-by-step explanation:
(i) The interval is meant to have infinitesimal width because the limit is approaching 0.
(ii) This gives the derivative at [tex](x, f(x))[/tex], which is the same as the slope of the tangent line.
(iii) False, this deals with the tangent line, not the secant.
(iv) True by definition.
About how much more is the total weight of the pacific halibut and conger than the weight of the yellowfin tuna ? Explain
Answers
The weight of pacific halibut is 459 pounds and weight of yellowfin tuna is 387 pounds.
There is 72 pounds more is the total weight of pacific halibut than the yellowfin tuna.
1) The perimeter of a rectangular garden is 344M. If the width of the garden is 76M, what is its length?
Equation:
Solution:
(I need the equation and solution)
2) The area of a rectangular window is 7315CM^2 (^2 is squared). If the length of the window is 95CM, what is its width?
Equation:
Solution:
(Once again, I need the equation and solution)
3) The perimeter of a rectangular garden is 5/8 mile. If the width of the garden is 3/16 mile, what is its length?
4) The area of a rectangular window is 8256M^2 (^2 is squared). If the length of the window is 86M, what is its width?
5) The length of a rectangle is six times its width. The perimeter of the rectangle is 98M, find its length and width.
6) The perimeter of the pentagon below is 58 units. Find VW. Write your answer without variables.
Answers
The length of the rectangle is 96 m, the width of the rectangle is 77 cm , the length of the rectangle is 1/8 mile, the length and width of the rectangle is 7 m and 42 m respectively, VW is 11 units.
According to the question,
1) Perimeter of rectangle = 344 M
Width = 76 M
Perimeter of rectangle = 2(length + width)
2(length+76) = 344
length+76 = 172
length = 172-76
Length of the rectangle = 96 M
2) Area of a rectangular window = 7315 [tex]cm^{2}[/tex]
Length of the window is 95 cm.
Area of rectangle = length*width
95*width = 7315
width = 7315/95
Width of the rectangle = 77 cm
3) The perimeter of a rectangular garden is 5/8 mile.
The width of the garden is 3/16 mile.
Perimeter of rectangle = 2(length+width)
2(length+3/16) = 5/8
length+3/16 = 5/(2*8)
length = 5/16-3/16
Length of the rectangle = 2/16 or 1/8 mile
4) The area of a rectangular window is 8256 [tex]m^{2}[/tex].
The length of the window is 86 m.
Area of rectangle = length*width
86*width = 8256
width = 8256/86
Width of the rectangle = 96 m
5) The length of a rectangle is six times its width. The perimeter of the rectangle is 98 m.
Let's take width of the rectangle to be x m.
Length of rectangle = 6x m
2(length+width) = 98
2(6x+x) = 98
2*7x = 98
14x = 98
x = 98/14
x = 7 m
Width = 7 m
Length = 7*6 m or 42 m
6) The perimeter of the pentagon is 58 units.
3z+10+z+3+2z-1+10 = 58
6z+10+3-1+10 = 58
6z+22 = 58
6z = 58-22
6z = 36
z = 36/6
z = 6 units
VW = 2z-1
VW = 2*6-1
VW = 12-1
VW = 11 units
Hence, the answer to 1 is 96 m , 2 is 77 cm, 3 is 1/8 mile , 4 is 96 m , 5 is 7 m and 42 m and 6 is 11 units.
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4 Evaluate: 2 (1) - O 1 16 2 ( ) V2 O O 1 2
Answers
To answer this question, we need to apply the following rule:
[tex]x^{-m}=\frac{1}{x^m}[/tex]This rule is known as the negative exponent rule. We also need to remember that when we have an exponent of 1/2 is the same as finding the square root for a number. Then, we have:
[tex](\frac{1}{4})^{-\frac{1}{2}}=\frac{1}{(\frac{1}{4})^{\frac{1}{2}}}=\frac{1}{\frac{\sqrt[]{1}^{}}{\sqrt[]{4}}}[/tex]Therefore, we have:
[tex]\frac{1}{\frac{1}{2}}=2[/tex]Thus, we have that:
[tex](\frac{1}{4})^{-\frac{1}{2}}=2[/tex]In summary, the correct answer is 2 (second option).
I need help with this practice problem Having a tough time solving properly
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
r = 7 sin (2θ)
Step 02:
polar equation:
r = 7 sin (2θ):
r = a sin nθ
n odd ==> n petals
n even ===> 2n petals
n = 2 ===> 2*2 petals = 4 petals
graph:
length of the petals:
r = 7 sin (2θ)
θ = 45°
r = 7 sin (2*45°) = 4.95
The answer is:
4.95
If 1 is divided by a number, the quotient is less than the number.If 1 is divided by -2, the result is (enter your response here), which is (your response) -2. A. greater than B. Less thanC. Equal to
Answers
Let us revise an important note
Positive numbers are increasing from 0 to positive infinity
Negative numbers are increasing from negative infinity to 0
If we divide 1 by 2, then the answer is 1/2 which is less than 2
That means the quotient is less than the divisor
If we divide 1 by -2, then the answer is -1/2 which is greater than -2
That means the quotient is greater than the divisor
Then the answer is
The result is greater than the number
The answer is A
Ethan's income is 4500 per month a list of some of his expenses appear below what percent of Ethan's expenses is insurance
Answers
Ethan's income is given as $4500
she pays $95 in insurance
percentage of Ethan's slary in insurance =
[tex]\begin{gathered} =\frac{95}{4500}\times100 \\ =2.11 \end{gathered}[/tex]Answer=2.11%
To the nearest hundredth, what is the value of x? X 40°
Answers
The given triangle is a right angle triangle,
Apply the trignometry ratio of tan
[tex]\tan \emptyset=\frac{Perpendicular}{Base}[/tex]From the given figure we have,
Perpendicular=x and base=72 and angle =40 degree
[tex]\begin{gathered} \tan 40^{\circ}=\frac{x}{72} \\ 0.839=\frac{x}{72} \\ x=0.839\times72 \\ x=60.408 \\ x=60.41 \end{gathered}[/tex]So the value of x is 60.41
Can you help to solve for number 5. Solving for X.
Answers
We will work at first with the small triangle ADC
[tex]m\angle DAC+m\angle C=m\angle ADB[/tex]mm[tex]m\angle DAC=55-20=35^{\circ}[/tex]We will use the sine rule
[tex]\frac{65}{\sin35}=\frac{AD}{\sin 20}[/tex]By using the cross multiplication
[tex]\begin{gathered} AD\times\sin 35=65\times\sin 20 \\ AD=\frac{65\sin 20}{\sin 35} \end{gathered}[/tex]In triangle ABD
We will use
[tex]\sin 55=\frac{x}{AD}[/tex]Then
[tex]x=AD\sin 55[/tex]Substitute AD by its value above
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