The given equation is:
ln (x + 2) = -5
Take the exponent of both sides
[tex]e^{\ln (x+2)\text{ }}=e^{-5}[/tex]The exponential cancels the ln on the Left Hand Side:
[tex]\text{x + 2 = e}^{-5}[/tex]Subtract 2 from both sides:
[tex]\begin{gathered} \text{x + 2 - 2 = e}^{-5}-2 \\ x=e^{-5}-2 \end{gathered}[/tex]B. Write the equation of the best fit line. C. Write the Correlation Coefficient(r).D. What does the Correlation Coefficient(r) mean for this scenario? is there a relationship between the fat grams and the total calories in fast food?
B) For the given values the linear equation which best fit is
[tex]y=11.73x+193.85[/tex]where x correspond to the total fat and y to total calories. The slope m is equal to 11.73 and the y-intercept b is equal to 193.85
C) The correlation coefficient r is equal to 0.97.
D) The relationship is almost linear because r=0.97 which is almost 1. The value r=1 means that both variables fit in a line perfectly.
A data set contains an independent and a dependent variable. Which must be true of the data set if a linear function can be used to represent the data?
The set must have a constant additive rate of change.
The set must have a constant multiplicative rate of change.
The values in the set must be positive.
The values in the set must be increasing.
The correct answer is: The set must have a constant additive rate of change.
Let Y be a data set containing an independent and dependent variable.
The standard form of the equation of a line is given by y = mx + b, where x is an independent variable and y is a dependent variable, m is the slope, and b is the y-intercept.
Now, when m = 1,
y = x + c
When m = 2,
y = 2x + c = x + x + c
When m = 3,
y = 3x + c = x + x + x + c
As a result, the set must change at a constant additive rate.In order to avoid the function changing into an exponential function, which is not linear, the set must not have a constant multiplicative rate of change.As the set of real numbers is the domain of the linear function, the values in the set may be positive or negative.And, the values in the set must be rising.Learn more about data set here:
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6. Given WY with W(3, 7) and Y(13, -8), if Xpartitions WY such that the ratio of WX to XYis 3:2, find the coordinates of X.
Answer:
(9, -2)
Explanation:
If a point X partition a segment that starts in point (x1, y1) and ends at point (x2, y2) in a ration a:b, the coordinates of X will be equal to:
[tex](\frac{a}{a+b}(x_2-x_1)+x_1,\frac{a}{a+b}(y_2-y_1)+y_1)[/tex]So, replacing (x1, y1) by point W(3, 7) and (x2, y2) by point Y(13, -8) and the ratio a : b by 3 : 2, we get that the coordinates of X are:
[tex]\begin{gathered} (\frac{3}{3+2}(13-3)+3,\frac{3}{3+2}(-8-7)) \\ (\frac{3}{5}(10)+3,\frac{3}{5}(-15)+7) \\ (6+3,-9+7) \\ (9,-2) \end{gathered}[/tex]Therefore, the coordinates of X are (9, -2)
Identify if the statement is consistent or inconsistent. If the system is consistent, identify wether the equations are dependent or independent.
The solution of the system is: (9, -6)
If a system has at least one solution, it is said to be consistent.
If a consistent system has exactly one solution, it is independent.
Then, the system is consistent and the equations are independent.
Salma wants to cover her rectangular patio in cement. The patio measures 6 yd long and 4 yd wide. She knows the area each bag of cement covers, but only in square meters.
Answer:
Finding the area right? If so, it's 24 m^2
ABC is congruent to DEF.
what is the length of AB and what is angle EDF?
Answer:
10 In the diagram below, DE divides AB and AC proportionally, m∠C = 26°, m∠A = 82°, and DF bisects ∠BDE. The measure of angle DFB is. 1) 36°. 2) 54°. 3) 72°.
Step-by-step explanation:
How many elements does the set A={x∣x is a natural number and x<17}A={x∣xis a natural number andx<17} have?
The list of numbers which are less than 13 is:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. (12 elements)
The answer would be 12.
Find the distance between the points ( – 8, – 8) and (6, – 8).
The distance between the points ( – 8, – 8) and (6, – 8) is 14, according to the definition of distance
Distance between two pointsThe distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.
That is, given the coordinates of two different points (x₁, y₁) and (x₂,y₂), the expression that allows calculating the distance "d" between two different points on the Cartesian plane is:
d= √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance in this caseIn this case, you know:
(x₁, y₁)= (-8, -8)(x₂,y₂)= (6, -8)Substituting in the definition of distance:
d= √[(6-(-8))² + (-8 - (-8))²]
Solving:
d= √[(6+8)² + (-8 +8)²]
d= √[14² + 0²]
d= √14²
d= √196
d= 14
Finally, the distance is 14.
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Solve for x. please and thanks
Answer:
x=9
Step-by-step explanation:
A triangle is equaled to 180
13x+2+3x-4+5x-7=180
Combine like terms
21x-9=180
Add 9 to both side
21x=189
Divide 21 on both sides
x=9
CHECK:
13x+2
Substitute x with 9
13*9+2=119
3x-4
Substitute x with 9
3*9-4= 23
5x-7
Substitute x with 9
5*9-7=38
119+23+38=180
Answer:
x = 9
Step-by-step explanation:
the sum of the interior angles in a triangle is 180°therefore
13x + 2 + 5x -7 + 3x - 4 = 180°
21x -9 = 180°
21 x = 180 + 9
21 x = 189
x = 189 : 21
x = 9
----------------------
check
13 * 9 + 2 + 5 * 9 - 7 + 3 * 9 - 4 = 180 (remember pemdas)
180 = 180
the answer is good
ANSWER PLEASE. FIRST ANSWER WILL BE BRAILIEST!!! DUE TODAY PLEASE HELP!!! WORTH 25 points!!!
The measure of angle C is given as follows:
<C = 80º.
Measure of angle CSegments AD and BE are parallel, hence the angles A and B are congruent, that is, they have the same measure:
<A = <B.
Angle ABE is of 50º, hence the measures of the congruent angles A and B are given as follows:
<A = <B = 50º.
The sum of the measures of the internal angles of a triangle is of 180º, hence the following relation from triangle ABC is established.
<A + <B + <C = 180º.
The measures of angles A and B were already found, hence we can solve for the measure of angle C with the above equation as follows:
<A + <B + <C = 180º.
50 + 50 + <C = 180
<C = 180 - 100
<C = 80º.
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the shorter leg of a right triangle is 7 m shorter than the longer leg. the hypotenuse is 7 m longer than the longer leg. find the side lengths of the triangle. length of the shorter leg:length of the longer leg:length of the hypotenuse:
Answer:
Explanation:
Let the length of the longer leg = x m
The shorter leg of a right triangle is 7m shorter than the longer leg. therefore:
Length of the shorter leg = (x-7) m
The hypotenuse is 7m longer than the longer leg.
Length of the hypotenuse = (x+7) m
We solve for x using Pythagoras Theorem.
[tex]\text{Hypotenuse}^2=\text{Opposite}^2+\text{Adjacent}^2^{}[/tex]This gives us:
[tex]\begin{gathered} (x+7)^2=x^2+(x-7)^2 \\ (x+7)(x+7)=x^2+(x-7)(x-7) \\ x^2+14x+49=x^2+x^2-14x+49 \\ 2x^2-x^2-14x-14x-49+49=0 \\ x^2-28x=0 \\ x(x-28)=0 \\ x-28=0\text{ or x=0} \\ x=28\text{ meters} \end{gathered}[/tex]Therefore:
• Length of the shorter leg: 28-7 = 21 meters
,• Length of the longer leg: 28 meters
,• Length of the hypotenuse: 28+7 = 35 meters
In a certain chemical, the ratio of zinc to copper is 4 to 17. A jar of the chemical contains 459 grams of copper. How many grams of zinc does it contain?
pls im begging u bro.
The grams of zinc that the jar contains is 108.
What is ratio?It should be noted that ratio simply means the comparison of one thing with another thing.
In this case, the ratio of zinc to copper is 4 to 17 and a jar of the chemical contains 459 grams of copper.
Let the grams of zinc be x. This will be illustrated as:
4/17 = x/459
Cross multiply
17x = 4 × 459
x = (4 × 459) / 17
x = 108
It has 108 zinc.
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Classify the symmetry of the function shown on the graph below. A) cannot be determined from the graph B) evenC) neither D) odd
The graph of an even function is symmetrical around the x-axis and the graph of an odd function is symmetrical around the origin.
The graph given does not fulfil neither of this conditions, hence we conclude that the function is neither even nor odd; therefore, the answer is C
Hans is a software salesman. His base salary is $1700, and he makes an additional $70 for every copy of History is Fun he sells. Let P represent his total pay (in dollars), and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 26 coples of History Is Fun.
the equation is:
[tex]P=1700+70N[/tex]so if he sells 26 copies we get that:
[tex]P=1700+26\cdot70=3520[/tex]Below are the times (in days) it takes for a sample of 5 customers from Tony's computer store to pay their invoices.
In this problem, we have the following data sample:
[tex]32,37,24,22,20.[/tex]We must compute the standard deviation of this data sample.
1) First, we compute the mean value which is given by the following formula:
[tex]\bar{x}=\frac{\sum^n_{i\mathop=1}x_i}{n}=\frac{32+37+24+22+20}{5}=\frac{135}{5}=27.[/tex]2) Now, we compute the standard deviation using the following formula:
[tex]\sigma=\sqrt[]{\frac{\sum^n_{i\mathop{=}1}(x_i-\bar{x})^2}{n-1}}=\sqrt[]{\frac{208}{5-1}}\cong7.21.[/tex]Answer
The standard deviation is 7.21.
Last week a pizza restaurant sold 36 cheese pizzas, 64 pepperoni pizzas, and 20 veggie pizzas. Based on these data, what is the probability that the next customer will buy a cheese pizza? Determine the likelihood of this event.
Supposing the same rates, the likelihood of a customer choose a cheese pizza can be calculated by the number of times cheese pizzas were chosen divided by the total of pizzas, so:
[tex]P=\frac{36}{36+64+20}=\frac{36}{120}=\frac{3}{10}[/tex]So, the lokelihood of this event is 3/10, or 30%.
All of the machines are kept cool by circulating cold water through them. The water makes 1 complete cycle through a 30 foot long tube every 12 seconds. Correctly complete the statement about the distance traveled by the water in 3 minutes and number of complete cycles the water makes in 3 minutes
Fill in the blanks to complete the sentence
The water travels ______ feet and completes _____ cycles in 3 minutes
Write
1/10^-3 using a positive exponent.
1/10⁻³ as a positive exponent is 10³.
How to convert a negative exponent to a positive exponent?
The negative exponent instructs us to rewrite the formula by getting the base's reciprocal and then switching the exponent's sign. A positive exponent indicates that the base should be multiplied by that many. Depending on the question at hand, you must flip an exponent from numerator to denominator or from denominator to numerator in order to change its sign.
Given, the exponent is y = 1/10⁻³
Multiplying both numerator and denominator of y with 10³, we get,
y = 10³/(10⁻³×10³) = 10³/1 = 10³
Therefore, 1/10⁻³ as a positive exponent is 10³.
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Calculate the simple interest earned. Round to the nearest cent.P = $4200, r = 7%, t = 1 year
The simple interest formula is defined as
[tex]\begin{gathered} I=Prt \\ \text{where} \\ P\text{ is the principal amount} \\ r\text{ is the rate converted to decimal} \\ t\text{ is time in years} \end{gathered}[/tex]Given
P = $4,200
r = 7% → 0.07 (converted to decimal)
t = 1 year
Substitute the following values and we get
[tex]\begin{gathered} I=(4200)(0.07)(1) \\ I=294 \end{gathered}[/tex]Therefore, the simple interest earned is $294.
6. Sarah made a down payment of $2,000 on a car and pays $210 a month.a. Model this situation with an equationb. Create a table with 5 unique points that represents this situationC. If the car costs $17,750, how long will it take for her to pay it off?
what is 288 divided by 16
Answer:
18
Step-by-step explanation:
16x18=288
The solution is, Yes, because the last digit is 8, which is divisible by 4.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
288 divisible by 16
i.e. 288/16 = 18
so, it is divisible.
now, we know that,
because the last digit is 8, which is divisible by 4.
Hence, The solution is, Yes, because the last digit is 8, which is divisible by 4.
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Need help with question 2 related to literal C of question 1
For the given parabola:
Vertices, foci and asymptotes:
Vertices: (-2, 0) and (2, 0)
Foci: (-5.385, 0) and (5.385, 0)
Asymptotes: y = -(5/2)x and y = (5/2)x
Fundamental rectangle and conjugate axis endpoints:
Endpoints: 5 and -5
graph the equation:
y=-6x+12
What is the gcf of 12 and 86?
factors of 12: 1, 2, 3, 4, 6, 12
factors of 86: 1, 2, 43, 86
Then, the greatest common factor (gcf) is 2
If BC = 5x - 9 and AB = 2x + 21, find the value of x.
Suppose that B is the midpoint of segment AC; therefore, AB=BC
Thus,
[tex]\begin{gathered} AB=BC \\ \Rightarrow2x+21=5x-9 \end{gathered}[/tex]Solve for x as shown below
[tex]\begin{gathered} \Rightarrow3x-9=21 \\ \Rightarrow3x=30 \\ \Rightarrow x=10 \end{gathered}[/tex]Therefore, the answer is x=10Find -x + 10 subtracted from 0.A. 0B. -x + 10C. x - 10
GIVEN:
We are given the following expression;
[tex]-x+10[/tex]Required;
To find the value of this expression subtracted from 0.
Step-by-step solution;
To subtract the expression from zero, we re-write as follows;
[tex]\begin{gathered} 0-(-x+10) \\ \end{gathered}[/tex]Note at this point that a negative times a negative results in a positive.
That is,
[tex]\begin{gathered} -\times(-)=+ \\ \\ Also; \\ \\ -\times(+)=- \end{gathered}[/tex]Therefore, we simplify as follows;
[tex]\begin{gathered} 0-(-x+10) \\ \\ =0+x-10 \\ \\ =x-10 \end{gathered}[/tex]Therefore, the correct answer is option C
ANSWER:
[tex]C:x-10[/tex]Find the amount and the present value of an annuity of P540 payable every end ofthe month at 7% compounded monthly for 4 years and 5 months.
We have to find the present value of a annuity of $540 payable every end of the month at 7% compounded monthly for 4 years and 5 months.
We can express the present value PV as:
[tex]PV=M\cdot\frac{[1-(1+r\/m)^{-n\cdot m}]}{r\/m}[/tex]where M: monthly payment (M = 540), r: annual nominal rate (r = 0.07), m: number of subperiods of compounding per year (m = 12) and n: number of years (n = 4+5/12).
We can replace the variables with its value and calculate PV as:
[tex]\begin{gathered} PV=540\cdot\frac{[1-(1+\frac{0.07}{12})^{-53}]}{\frac{0.07}{12}} \\ PV\approx540\cdot\frac{[1-(1.005833)^{-53}]}{0.005833} \\ PV\approx540\cdot\frac{1-0.7347}{0.005833} \\ PV\approx540\cdot\frac{0.2653}{0.005833} \\ PV\approx540\cdot45.4826 \\ PV\approx24560.60 \end{gathered}[/tex]Answer: The present value of teh annuity is P 24560.60.
Find the GCF (greatest common factor) of the following terms.{4xy^2, 2x^2y^2, x^2y^2}
We need to find the GCF of
[tex]\begin{gathered} 4xy^2 \\ 2x^2y^2 \\ \text{and} \\ x^2y^2 \end{gathered}[/tex]Let's break apart the terms,
[tex]\begin{gathered} 4xy^2=2\cdot2\cdot x\cdot y\cdot y \\ 2x^2y^2=2\cdot x\cdot x\cdot y\cdot y \\ x^2y^2=x\cdot x\cdot y\cdot y \end{gathered}[/tex]We can see that the common factors to all 3 terms are x * y * y, which
[tex]\begin{gathered} x\cdot y\cdot y \\ =xy^2 \end{gathered}[/tex]Thus, the GCF of the 3 terms given is,
[tex]xy^2[/tex]Answer[tex]xy^2[/tex]Quadrilateral WXYZ is a rhombus and m∠XWY=u–44°. What is the value of u?
It is given that
[tex]\angle XWY=u-44^o,\text{ and }\angle YZW=110^o[/tex]Recall that the adjacent angles are supplementary in a rhombus.
[tex]\angle XWZand\text{ }\angle YZW\text{ are supplementary angles.}[/tex]The sum of supplementary angles is 180 degrees.
[tex]\angle XWZ+\angle YZW=180^o\text{.}[/tex][tex]Substitute\text{ }\angle YZW=110^o,\text{ we get}[/tex][tex]\angle XWZ+110^o=180^o\text{.}[/tex][tex]\angle XWZ=180^o-110^o[/tex][tex]\angle XWZ=70^o[/tex][tex]\angle XWZ=\angle XWY+\angle YWZ[/tex]Recall that the diagonals bisect the angles of the rhombus.
[tex]\angle XWY=\angle YWZ[/tex][tex]\angle XWZ=\angle XWY+\angle XWY[/tex][tex]\angle XWZ=2\angle XWY[/tex][tex]Substitute\text{ }\angle XWZ=70^o\text{ and }\angle XWY=u-44^o,\text{ we get}[/tex][tex]70^o=2(u-44^0)[/tex][tex]\frac{70^o}{2}=u-44^0[/tex][tex]35^o=u-44^0[/tex][tex]35^o+44^o=u[/tex][tex]u=79^o[/tex]
Hence the value of u=79 degrees.
What is the distance between a points (3,4) and (-2,-2) (round to the nearest 10th, if necessary) distance between the points (three, four) and (-2, -2) is blank units?
Answer:
The coordinates given in the question are
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(3,4) \\ (x_2,y_2\Rightarrow(-2,-2) \end{gathered}[/tex]Concept:
The distance between two points of a line is given below as
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]By substituting the values, we will have
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(-2-3)^2+(-2-4)^2} \\ d=\sqrt[]{(-5)^2+(-6)^2} \\ d=\sqrt[]{25+36} \\ d=\sqrt[]{61} \\ d=7.8\text{ units} \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow7.8[/tex]