CAN SOMEONE HELP WITH THIS QUESTION?✨
The exponential function passes through the points (-1,4/5) and (1,20) will be y = 4 × [tex]5^{x}[/tex].
What is an exponential function?In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.
In other meaning, an exponential function is that function above which a variable x has imposed.
Suppose the exponential function as
y = a[tex]e^{bx}[/tex]
Substitute, (-1,4/5)
4/5 = a[tex]e^{-b}[/tex] (1)
Substitute, (1,20)
20 = a[tex]e^{b}[/tex] (2)
Multiply (1) with (2)
(4/5)20 = a[tex]e^{-b}[/tex] × a[tex]e^{b}[/tex]
4 × 4 = a²
a = 4
Substitute, a = 4 into (2)
20 = 4[tex]e^{b}[/tex]
[tex]e^{b}[/tex] = 5
Take log on both sides of the above equation,
ln [tex]e^{b}[/tex] = ln 5
b = ln 5
Substitute a = 4 and b = ln 5 into y = a[tex]e^{bx}[/tex]
y = 4 e^(x(ln 5)) = 4 e^(ln5^x)
y = 4 × [tex]5^{x}[/tex]
Hence "The exponential function passes through the points (-1,4/5) and (1,20) will be y = 4 × [tex]5^{x}[/tex]".
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Write and graph the inverse of y=-x²+5
Write the inverse of y=-x²+5
y=
Answer:
Below
Step-by-step explanation:
y = - x^2 + 5 solve for x
y-5 = - x^2
x^2 = 5-y
x = ± sqrt (5-y) now switch the x's and y's
y = ± sqrt(5-x)
Here is a picture:
what is the average rate of change
The required average rate of change in the amount of Kendall's account is $50 per month.
What is rate?Rate is a measurement to determine the change in one quantity with respect to another quantity.
Given that,
The amount of the end of the 8th month in Kendall's account = $450,
And at the end of the 11th month, the saved amount = $600.
To find the rate of change in saving amount
The increased amount = 600 - 450 = 150.
Since, In 3 months the amount increased by 150.
So, the average rate of change in amount
= 150 / 3.
= 50.
The average rate of change in the amount is $50 per month.
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Write the equation of the line that is parallel to z = 4 and passes through (-3, 7).
Answer:
x = -3
Step-by-step explanation:
If you look at the graph.
x = 4 is a vertical line.
Another vertical line that would be parallel to this can contain the point (-3, 7) would be the line x = -3
The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 80.2% of their carbon-14. How old were the bones at the time they were discovered?
The age of the bones when they were discovered is 13439.66 years
What is half-life of an element?
The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value
The decay constant λ is = 0.693/t½
where t½ is the half-life of the element
Given data ,
The radioactive element carbon-14 has a half-life of 5750 years
So , the value of t½ = 5750 years
Now , the decay constant λ = 0.693 / t½
Substituting the values in the equation , we get
Decay constant λ = 0.693 / t½
Decay constant λ = 0.693 / 5750
Decay constant λ = 1.205 x 10⁻⁴
N=N₀e ^ −λt
where N₀ = Mass of radioactive element initially
N = Mass of radioactive element after time t
Apply natural logarithm on both the sides of the equation , we get
ln N = ln N₀ - λt
Let N0 be 100 then N will be 100 - 80.2 = 19.8
Substituting the values in the equation , we get
ln 19.8 = ln 100 - 1.205 x 10⁻⁴ ( t )
ln [ 19.8 / 100 ] = - 1.205 x 10⁻⁴ ( t )
-1.61948 = -1.205 x 10⁻⁴ ( t )
Therefore , the value of t is
t = -1.61948 / -1.205 x 10⁻⁴
t = 1.343966 x 10⁴
t = 13439.66 years
Therefore , the value of t is 13439.66 years
Hence ,
The age of the bones when they were discovered is 13439.66 years
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-24 – x = -34 pls help
Answer:
x = 10
Step-by-step explanation:
Given equation,
→ -24 - x = -34
Now the value of x will be,
→ -24 - x = -34
→ -x = -34 + 24
→ -x = -10
→ [ x = 10 ]
Hence, the value of x is 10.
Answer: x=10
1. Rearrange the terms
-24 - x= -34
-x - 24= -34
2. Add 24 to both sides
-x - 24= -34
-x - 24= -34
+24 +24
3. Simplify(add the numbers)
-x=-10
4. Divide both sides by the same factor
-x=-10
-x/-1 = -10/-1
Simplify (cancel terms, divide numbers)
X=10
Step-by-step explanation:
What are the coordinates of the point on a directed line segment from (-8,8) to (-2,-10) that partitions the segment into a ratio of 1 to 2
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-8,8)\qquad B(-2,-10)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-8,8)=1(-2,-10)[/tex]
[tex](\stackrel{x}{-16}~~,~~ \stackrel{y}{16})=(\stackrel{x}{-2}~~,~~ \stackrel{y}{-10}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-16 -2}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{16 -10}}{1+2} \right)} \\\\\\ C=\left( \cfrac{ -18 }{ 3 }~~,~~\cfrac{ 6}{ 3 } \right)\implies {\Large \begin{array}{llll} C=(-6~~,~~2) \end{array}}[/tex]
What is the slope of a line perpendicular to the line whose equation is 4x-6y=-604x−6y=−60. Fully simplify your answer.
The slope of the line perpendicular to 4x - 6y = - 60 is (-3/2).
What is slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is
y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.
We know lines perpendicular to each other have slopes that are negative reciprocals of each other.
Given line is 4x - 6y = - 60 ⇒ - 6y = - 4x - 60 ⇒ y = (2/3)x + 10.
Now the line perpendicular to it will have a slope of (-3/2).
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Convert 5pi/7 radians to degrees.
(Use pi = 3.14 when necessary and round your final answer to the hundredths place.)
5pi/7radians=________ degrees
well, since we know there are 180° in π/2 radians, then, what's 5π/7 radians?
[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\frac{\pi }{2}\\[1em] d&\frac{5\pi }{7} \end{array}\implies \cfrac{180}{d}~~ = ~~\cfrac{\frac{\pi }{2}}{ ~~ \frac{5\pi }{7} ~~ }\implies \cfrac{180}{d}=\cfrac{\pi }{2}\cdot \cfrac{7}{5\pi } \\\\\\ \cfrac{180}{d}=\cfrac{7}{10}\implies 1800=7d\implies \cfrac{1800}{7}=d\implies 257.14^o\approx d[/tex]
ASAP!! Which graph could be used to find the distance between the points (−3, −13) and (11, 9)?
graph of a right triangle with hypotenuse beginning at negative 13 comma negative 3 and ending at 9 comma 11
graph of a right triangle with hypotenuse beginning at negative 3 comma negative 13 and ending at 11 comma 9
graph of a right triangle with hypotenuse beginning at negative 11 comma negative 9 and ending at 3 comma 13
graph of a right triangle with hypotenuse beginning at negative 9 comma negative 11 and ending at 13 comma 3
The graph that could be used to find the distance between the points
(-3, -13) and (11, 9) is given as follows:
B. graph of a right triangle with hypotenuse beginning at negative 3 comma negative 13 and ending at 11 comma 9.
What is distance between two points?
The distance between two points in a plane is the length of the line segment separating the two points. Typically, the equation
d=√((x2 - x1)^2 + (y2 - y1)^2) is used to calculate the distance between two points.
Suppose we have a pair of points, with the coordinates given as follows:
[tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].
The two points form a right triangle, in which the sides are given as follows:
[tex]y_2-y_1\\x_2-x_1[/tex]
The distance between these two points is given by the hypotenuse of the right triangle.
Hence, applying the Pythagorean Theorem, the distance is obtained as follows:
[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
In this problem, the coordinates of the points are given as follows:
(−3, −13) and (11, 9).
Hence the correct option is given by option B.
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In triangle WXY, the measure of W is 10 less than the measure of X and the measure of Y is 14 less than the measure of X. Find the measure of each angle
X = 63°
W = 60°
Y = 57° are the measure of each angle in triangle.
In math, what is a triangle?
A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.
W = X - 10
Y = X - 14
X + W + Y = 180 substitute
X + (X - 10) + ( X - 14)
= 3 X - 24 = 180
3X = 180 + 24.
X = 204/3
X = 68
W = 58
Y = 54
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B. Hannah approximates the areas of circles using the equation A=3 r², and records areas of circles with different radius lengths in a table.
a. Graph the ordered pairs from the table.
b. Is the relation a function? Explain.
Use the number line to represent the solution to x + 3 > 5. Select the ray. Move the point on the ray to the correct place on the number line.
Hence, the point on the ray is [tex]x > 2[/tex].
What is the number line?
A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides
Here given that,
Use the number line to represent the solution to [tex]x + 3 > 5.[/tex]
i.e.,
[tex]x+3 > 5\\\\x > 5-3\\\\x > 2[/tex]
Hence, the point on the ray is [tex]x > 2[/tex].
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One fisherman and 6 his friends were fishing and they spent the night on
the island putting all fish in a box. Fishermen fell asleep, but one decided to go
home. He took 48 fish which was 3/7 of all fish in the box. Then he sees that
his friends did not get any fish, He put fish he took back into the box and tried
to divide fish evenly among his friends. He took his part, and went home. How many fish does each person get
Each person got 16 fish equally divided among 7 fishermen.
What is a numerical expression?A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.
Given, One fisherman and 6 his friends were fishing.
So, The total no. of people is (6 + 1) = 7.
one decided to go home so he took 48 fish which was 3/7 of all fish in the box.
Let, 'x' be the total no. of fish.
Therefore, (3/7)x = 48.
x = 48×(7/3).
x = 112.
Now, by dividing the total no. of fish by total no. of fishermen
we get, (112/7).
= 16.
So, Each person got 16 fish.
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In a study comparing 4 types of batteries, 60 batteries (15 of each type) were tested, and their lifetimes were compared. (Here, k = 4, and N-60) (a) The hypotheses are Part of the ANOVA summary table is given below. Sum of Squares df Mean SquaresF MSB/MSW MS SS/df Between (Factor) 25.7375 Within (Error) 75 (b) Complete the table. (Remember that the df for the numerator (Between Groups) is k-1, and the df for the denominator (Within Groups) is N-k. (c) Use the Fcdf on your calculator to find the p-value. (Go to 2nd is Fcdf( F, 10000, df Between, df Within).) DISTR VARS and choose FEeff. The syntax and choose Fcdf. The syntax (d) State your decision and conclusion.
a) The hypotheses for this study would be the Null hypothesis and Alternative hypothesis.
b) The completed ANOVA summary table would be the Sum of Squares.
c) The calculator would give a p-value of approximately 0.03.
d) The results of the ANOVA test may not be reliable.
(a) The hypotheses for this study would be:
Null hypothesis ([tex]H_0[/tex]): There is no difference in the average lifetime of the four types of batteries.
Alternative hypothesis ([tex]H_1[/tex]): There is a difference in the average lifetime of the four types of batteries.
(b) The completed ANOVA summary table would be:
Sum of Squares (SS) df Mean Squares (MS) F
Between (Factor) 25.7375 3 8.578 3.77
Within (Error) 75 56 1.34
Total 100 59
(c) To find the p-value, you would use the Fcdf function on your calculator. The syntax for this would be Fcdf(F, 10000, df Between, df Within). In this case, the F value is 3.77, the df Between is 3, and the df Within is 56. Plugging these values into the calculator would give a p-value of approximately 0.03.
(d) Based on the p-value, we can reject the null hypothesis and conclude that there is a significant difference in the average lifetime of the four types of batteries. This suggests that the type of battery has an effect on its lifetime. However, it is important to note that this conclusion is based on the assumptions of the ANOVA test, including the assumption of equal variances among the groups. If these assumptions are not met, the results of the ANOVA test may not be reliable.
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
The relationship between the cone cylinder and sphere is sphere takes up two-thirds of the volume of the cylinder, the cone takes up one-third of the volume of the cylinder.
What is the properties of the cone cylinder and sphere?Similar to a prism, a cylinder has two bases, however they are circles rather than polygons. A cylinder's sides are also curved rather than flat. A cone has a vertex that is not on the base and a single circular base. The sphere is a form in space with equal distances between each of its points and the centre.Any sphere has a volume that is 2/3 the size of any cylinder with an equivalent radius and height.While CYL, or cylinder, is the amount of lens power required to correct astigmatism, SPH, or sphere, is the amount of lens power required to correct nearsightedness or farsightedness. People frequently allude to their SPH value while discussing their eye degree or "power."Answers of blank :
Blank 1 = 1/3
Blank 2 = Three
Blank 3 = Two
Blank 4 = 2/3
Blank 5 = 1/3
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Add
900-200= 700
and then add 700 + 700 =
Answer =
Answer:1400
Step-by-step explanation:
Samuel and his children went into a movie theater and he bought $43.75 worth of bags of popcorn and candies. Each bag of popcorn costs $5 and each candy costs $4.75. He bought a total of 9 bags of popcorn and candies altogether. Write a system of equations that could be used to determine the number of bags of popcorn and the number of candies that Samuel bought. Define the variables that you use to write the system.
In linear equation, Samuel bought 7 bags of popcorn and 10 bags of candies.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Let x represent the number of bags of popcorn and y represent the number of candies that Samuel bought.
She bought $43.75 worth of bags of popcorn and candies. Hence:
5x + 4.75y = 43.75 ........... (1)
She bought a total of 17 bags of popcorn and candies altogether. Hence:
x + y = 9 (2)
Solving equations 1 and 2 simultaneously gives:
x = 4, y = 5
Therefore Samuel bought 4 bags of popcorn and 5 bags of candies.
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The table shows the proportional relationship between the price for a certain number of buckets of golf balls at a driving range.
hurry pls
Buckets 3 5 7
Price (dollars) 28.50 47.50 66.50
Determine the constant of proportionality.
The constant of proportionality will be 9.5 when the table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.
Given that,
The table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.
We have to find the constant of proportionality.
We know that,
What are ratio and proportion?A collection of consecutively ordered numbers a and b expressed as a/b, where b is never equal to zero, is referred to as a ratio. A statement is considered proportionate when there is equality between two items.
The table displays the proportional relationship between the price for a particular quantity of golf ball cans at a driving range.
Buckets 3 5 7
Price (dollars) 28.50 47.50 66.50
The constant of proportionality is calculated as,
⇒ 25.8 / 3
⇒ 9.5
Therefore, The constant of proportionality will be 9.5 when the table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.
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Answer:
9.5
Step-by-step explanation:
I took the exam and got it right
The monthly cost of water use is a linear function of the amount of water used (HCF). The cost for using 16 HCF of water is $39.04, and the cost for using 44 HCF is $79.64. What is the cost for using 22 HCF?
Answer:
The cost for using 22 HCF is $47.74------------------------------
Equation of line:
y = mx + b, where m- slope, b- y-intercept
Given values can be interpreted as pairs of coordinates of the two points:
(16, 39.04) and (44, 79.64)Find the slope of the line:
m = (79.64 - 39.04)/(44 - 16) = 40.6/28 = 1.45Find the y-intercept, by substituting coordinates of one point:
39.04 = 1.45*16 + b39.04 = 23.2 + bb = 39.04 - 23.2b = 15.84The equation becomes:
y = 1.45x + 15.84Find the value of y when x = 22:
y = 1.45*22 + 15.84 = 31.9 + 15.84 = 47.74Ms. Bobadilla has a 24 ounce coffee. I drink 8 ounces. What percent of the coffee is left? 7th grade math
The required percent of the coffee left is given as 66.67%.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
24 ounces of coffee Ms. Bobadilla,
And 8 ounces of coffee has been drinking,
Applying the percentage evaluation, in order to calculate the remaining coffee to Ms. Bobadilla.
Percentage of coffee remaining = 24 - 8 / 24 × 100%
Percentage of coffee remaining = 0.6667 × 100%
Percentage of coffee remaining = 66.67%
Thus, the percentage is given as 66.67%.
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B + 6 divided by 4 when b = 1.5
Answer:
Step-by-step explanation:
Write it out
[tex](B+6)/4[/tex]
plug in the value
[tex](1.5+6)/4[/tex]
solve
[tex](1.5+6)/4\\7.5/4\\= 1.875[/tex]
A radio tower is located 400 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 26∘ and that the angle of depression to the bottom of the tower is 20∘. How tall is the tower?
340 ft high
d = 400' distance from building to tower
26° from the window to the top of the tower and 20° from the window to the bottom of the tower
Tan 26 = h2/d
Tan 20 = h1/d
h2 = 400Tan26
h1 = 400Tan20
on solving the equations,
h=a+b
Tower = 340 ft high
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A research department wants to test the hypothesis that caffeine from organic coffee more safely stimulates mental alertness than caffeine from nonorganic coffee. Which of the following would most effectively provide the desired primary data?
Experimentation, one form of primary research,can produce data suggesting cause and effect
The most effectively provide the desired primary data is experimentation
Experimentation is the step in the scientific method that helps people decide between two or more competing explanations—or hypotheses. These hypotheses suggest reasons to explain a phenomenon or predict the results of an action.
With an experiment, you run a test and see what the results are. If you don't get good results, you can try another option, and run another test. Then you can see what the outcomes of the choices are (the info you didn't have when first thinking about the decision), and you can make a better-informed decision now.
According to the question,
A research department wants to test the hypothesis that caffeine from organic coffee more safely stimulates mental alertness than caffeine from nonorganic coffee. Experimentation, one form of primary research, can produce data suggesting cause and effect
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Construct a confidence interval that will capture the true population mean with 95% confidence. Population standard deviation is unknown.
Data: 18
19,19,19,19,19,19,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21, 22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,24,24,24,24,24,24,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,26,26,26,26,26,26,26,26,,26,26,26,27,27,27,27,27,28,28,28,28,28,28,28,28,28,28,29,29,29,30,30,30,31
A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459 , 24.8293 ) .
What is population mean?
A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.
Data: 18
for given data
[tex]$$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$$[/tex]
as population variance is unknown so we used sample variance
[tex]$$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$$[/tex]
Now
[tex]\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$[/tex]
hence 95 % of population mean is
As n=101 which is large so critical value is 1.98397
[tex]$$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$$[/tex]
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Find the volume of the figures
1. The volume of the cylinder is 942 m³.
2. The volume of the cone is 33.16 mm.
3. The volume of the sphere is 33.50 in³.
4. The volume of the cuboid is 672 in³.
What is volume?Volume is defined as how much of a three-dimensional object occupies
a space.
We know the volume of a cylinder is πr²h.
∴ The volume of the given cylinder is = π(5)²×12 m³ = 942 m³.
We know the volume of a cone is = (1/3)πr²h.
∴ The volume of the given cone is = (1/3)π(2)²×8 mm³ = 33.16 mm.
We know the volume of a sphere is (4/3)π×r³.
∴ The volume of the given sphere is = (4/3)×π×(r³) in³ = 33.50 in³.
We know the volume of a cuboid is = (length×width×height).
∴ The volume of the given cuboid is = (7×8×12) in³ = 672 in³.
The volume of the object in figure 8 is the sum of the volume of a cuboid and a pyramid.
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Please help anyone. I need help especially with #4
Answer:
#4 x=70
Step-by-step explanation:
Because this is an Isosceles triangle, we know that the 2 base angles have to be equivalent. So subtract 40 from 180 which leaves you with 140, then divide 140 by 2 because there are 2 base angles. Then arrive at the answer of x=70.
-Hope this helped & Happy Holidays!
Describe and correct error
Answer Questions 9 to 11 using the lines shown in the coordinate grid below.
1. Is it true that m parallel to n?Include any relevant measurements and calculations.
2. Is it true that m is congruent to p?include relevant measurements and calculations.
3.Is it true that n is congruent to p? Include any relevant measurements and calculations.
The solution to the parallel lines identification and congruency are;
1) They are not parallel.
2) They are not congruent.
3) They are not congruent.
How to Identify Parallel lines?
Parallel lines are defined as lines in a plane that are always the same distance apart. Parallel lines never intersect.
1) Looking at lines m and n , for them to be parallel, it means that they must be the same width all through. However, we see that along the x-axis they are 6 units while going further down, it is not always 6 units as some are 5.5 units. Thus, they are not parallel.
2) No, m is not congruent to p because it is not the same distance from the x and y-axis at similar points.
3) No, n cannot be congruent to p because we see that the distance between the marked points are not congruent.
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SOLVE FOR R
-7 - 7r= -10r + 8
R =
Answer:
the answer is 5
Step-by-step explanation:
(Add 10r to both sides)
-7-7r+10r= 8
Then -7+3r = 8
(Add 7 to both sides)
3r = 8+7
3r = 15
Divide both sides by 3.
r = 5