Elimination Method : In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
The given system of equation:
7x + 5y = -1 (1)
4x - y = -16 (2)
Multiply the equation (2) by 5 :
5(4x -y ) = 5(-16)
20x - 5y = -80 (3)
Add equation (3) & (1)
(7x + 5y) + (20x -5y ) =(-1) + (-80)
7x + 5y + 20x - 5y = -1 - 80
27x = -81
x = -81/ 27
x = -3
Substitute the value of x =3 in the equation (1)
7x + 5y = -1
7(-3) + 5y = -1
-21 + 5y = -1
5y = -1 +21
5y = 20
y =20/5
y = 4
Thus, the solution of system is (x, y) = (-3, 4)
Answer : x =-3, y = 4
7. Angela bought some sugar and strawberries to make strawberry jam.Sugar costs $1.80 per pound, and strawberries cost $2.50 per pound.Angela spent a total of $19.40. Which point on the coordinate plane couldrepresent the pounds of sugar and strawberries that Angela used to makejam?
Equation of the Line
Let's use the following variables:
x = pounds of sugar
y = pounds of strawberries
Angela spent a total of $19.40 to make strawberry jam, thus:
1.80x + 2.50y = 19.40
The equation of the line represents the relationship between x and y. Any point that solves the problem must lie in the line.
The image shows the graph of a line, but we need to be sure it represents the equation above. A small checkup will be done as follows:
For x = 0, solve for y:
1.80*(0) + 2.50y = 19.40
y = 19.4 / 2.5 = 7.76
This point corresponds to the y-intercept (0, 7.76). It can be correctly found on the graph.
For y = 0, solve for x:
1.80x + 2.50*(0) = 19.40
x = 19.40 / 1.8 = 10.78
This point corresponds to the x-intercept at (10.78, 0). It can also be found on the graph.
Now we are sure the line is the representation of our equation, the only point that lies on that line is B(8, 2).
If we substitute x = 8, y = 2:
1.80*(8) + 2.50*(2) = 19.40
14.4 + 5 = 19.40
19.40 = 19.40
The equation is satisfied, thus, the answer is:
Point B
Art club has 12 members. Each member paysmonthly dues of $12.60. On the first day of themonth, 4 members paid their dues. The remainingmembers paid their dues on the second day of themonth. How much money was collected in dues onthe second day of the month?
Given:
Total number of members in a club is 12
Each member pays $12.60 on every month.
[tex]\begin{gathered} \text{Number of members paid the dues on second day=12-4} \\ \text{Number of members paid the dues on second day=}8 \end{gathered}[/tex][tex]\begin{gathered} \text{Money collected on the second day=8}\times12.60 \\ \text{Money collected on the second day= \$100.80} \end{gathered}[/tex]Money collected on the second day of the month is $100.80
Answer:
100.8
Step-by-step explanation:
12-4 = 8
the 4 is the people who payes the first day the 8 is the people who payes the second day
12.60 eight times = 12.60•8= 100.8
the eight people each payes 12.60 so that would be 12.60 8 times
Solve the equation without using a calculator
[tex]x^2+\big(4x^3-3x\big)^2=1[/tex]
Answer:
[tex]x= \dfrac{\sqrt{2}}{2}, \quad x=-\dfrac{\sqrt{2}}{2},\\\\x=\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x=-\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x= \dfrac{\sqrt{2 + \sqrt{2}}}{2}, \quad x= -\dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]x^2+(4x^3-3x)^2=1[/tex]
Expand and equal the equation to zero:
[tex]\begin{aligned}x^2+(4x^3-3x)^2&=1\\x^2+(4x^3-3x)(4x^3-3x)&=1\\x^2+16x^6-24x^4+9x^2&=1\\16x^6-24x^4+x^2+9x^2-1&=0\\16x^6-24x^4+10x^2-1&=0\end{aligned}[/tex]
Let u = x²:
[tex]\implies 16u^3-24u^2+10u-1=0[/tex]
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x)
[tex]\textsf{As\;\;$f\left(\dfrac{1}{2}\right)=0$\;\;then\;$\left(u-\dfrac{1}{2}\right)$\;is a factor of $f(u)$}.[/tex]
Therefore:
[tex]\implies \left(u-\dfrac{1}{2}\right)\left(16u^2+bu+2\right)=0[/tex]
Compare the coefficients of u² to find b:
[tex]\implies b-8 = -24[/tex]
[tex]\implies b = -16[/tex]
Therefore:
[tex]\implies \left(u-\dfrac{1}{2}\right)\left(16u^2-16u+2\right)=0[/tex]
Factor out 2:
[tex]\implies 2\left(u-\dfrac{1}{2}\right)\left(8u^2-8u+1\right)=0[/tex]
[tex]\implies \left(u-\dfrac{1}{2}\right)\left(8u^2-8u+1\right)=0[/tex]
Zero Product Property
If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Using the Zero Product Property, set each factor equal to zero and solve for u.
[tex]\implies u-\dfrac{1}{2}=0 \implies u=\dfrac{1}{2}[/tex]
Use the quadratic formula to solve the quadratic:
[tex]\implies u=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(8)(1)}}{2(8)}[/tex]
[tex]\implies u=\dfrac{8 \pm \sqrt{32}}{16}[/tex]
[tex]\implies u=\dfrac{8 \pm 4\sqrt{2}}{16}[/tex]
[tex]\implies u=\dfrac{2 \pm \sqrt{2}}{4}[/tex]
Therefore:
[tex]u=\dfrac{1}{2}, \quad u=\dfrac{2 - \sqrt{2}}{4}, \quad u=\dfrac{2 + \sqrt{2}}{4}[/tex]
Substitute back u = x²:
[tex]x^2=\dfrac{1}{2}, \quad x^2=\dfrac{2 - \sqrt{2}}{4}, \quad x^2=\dfrac{2 + \sqrt{2}}{4}[/tex]
Solve each case for x:
[tex]\implies x^2=\dfrac{1}{2}[/tex]
[tex]\implies x=\pm \sqrt{\dfrac{1}{2}}[/tex]
[tex]\implies x=\pm \dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies x^2=\dfrac{2 - \sqrt{2}}{4}[/tex]
[tex]\implies x=\pm \sqrt{\dfrac{2 - \sqrt{2}}{4}}[/tex]
[tex]\implies x=\pm \dfrac{\sqrt{2 - \sqrt{2}}}{2}[/tex]
[tex]\implies x^2=\dfrac{2 + \sqrt{2}}{4}[/tex]
[tex]\implies x=\pm \sqrt{\dfrac{2 + \sqrt{2}}{4}}[/tex]
[tex]\implies x=\pm \dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]
Solutions
[tex]x= \dfrac{\sqrt{2}}{2}, \quad x=-\dfrac{\sqrt{2}}{2},\\\\x=\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x=-\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x= \dfrac{\sqrt{2 + \sqrt{2}}}{2}, \quad x= -\dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]
Class Work...Exit Ticket... 11.25.2020 Malik picked forty-five oranges in five minutes. At this rate, how many oranges will she pick per minute. Classwork/Participation. 5 points
Malike picked 45 oranges in 5 minutes
Work = Rate x time
If she can pick 45 oranges in 5 minutes
Mathematically
45 oranges ========= 5minutes
x oranges ========== 1 minute
Introduce cross multiplication
45 * 1 = 5 * x
45 = 5x
Divide both sides by 5
45/5 = 5x/5
x = 45 / 5
x = 9 oranges
Malik can pick 9 oranges in 1 minute
The answer is 9 oranges
Complete each equation in order to obtain the indicated solution
Question 13.
Part (a).
Given the solution:
All real numbers
We have the expression:
3(4x + 2) = ________
Let's complete the equation in order to obtain the indicated solution.
For a solution to be all real numbers, the equation must be true.
hence, we have:
[tex]\begin{gathered} 3(4x+2)=3(4x+2) \\ \end{gathered}[/tex]After solving we have:
0 = 0
This means the system has infinitely many solutions, therefore, the solution is all real numbers.
ANSWER:
3(4x + 2) = 3(4x + 2)
I need help with 4 problems
1)
[tex]c^2=5^2+5^2[/tex]then the solution is
[tex]c=\sqrt[]{25+25}=\sqrt[]{50}=5\sqrt[]{2}\approx7.1[/tex]what is 8 1/2 / 11 as a mixed number or fraction
Answer: 17/22
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer:
3.68181818182=33409090909150000000000
Showing the work
Rewrite the decimal number as a fraction with 1 in the denominator
3.68181818182=3.681818181821
Multiply to remove 11 decimal places. Here, you multiply top and bottom by 1011 = 100000000000
3.681818181821×100000000000100000000000=368181818182100000000000
Find the Greatest Common Factor (GCF) of 368181818182 and 100000000000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 2,
368181818182÷2100000000000÷2=18409090909150000000000
Simplify the improper fraction,
=33409090909150000000000
In conclusion,
3.68181818182=33409090909150000000000
what is a like term?
In an expression, two or more terms are like terms if they have the same variable and exponents.
For example the terms:
2a and -8a → these terms have the same variable "a" and the same exponent "1"
9y³ and 8x⁴ → these terms have different variables "y" and "x" and different exponents "3" and "4", so they are not like terms.
Constants, for example, -10 or 6, are also considered to be like terms.
If Carl wants to buy a $23,999 truck and put a 15% down payment on it, how much money should he save for a down payment?
Money Carl should save for a down payment is $3699.85.
A percentage is a number or ratio expressed as a fraction of 100. A percentage is a dimensionless number, it has no unit of measurement.
Calculation:-
Cost of truck = $23,999
Downpayment = 15% of truck price
So, downpayment value = $23,999 × 15/100
= $3699.85
To calculate the average percent, add all probabilities together as numbered values and divide by the sum of all the sets. Then multiply by using a hundred. The percentage may be calculated by dividing the price with the aid of the entire fee, after which multiplying the end result by a hundred. The method used to calculate the percent is: (value/general price)×100%.
Learn more about percentages here:-https://brainly.com/question/24877689
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4^3/(-12+ 2^2)
(2x2)^2 + (-5 x 2 x 3 ) + 2
[tex] \frac{4^3/(-12 +2^2)}{(2x3)^2 +(-5 x2 x 3)+2} [/tex]
i need help!!
Answer:
-1
Step-by-step explanation:
[tex]\frac{\frac{64}{-12+4}}{(6)^2+(-30)+2} \\ \\ =\frac{\frac{64}{-8}}{36-30+2} \\ \\ =\frac{-8}{8} \\ \\ =-1[/tex]
Describe a situation that could be represented by theequation y=x-0.3x.Be sure to explain what x and y mean in your situation,
We are asked to describe a situation that could be represented by the equation
[tex]y=x-0.3x[/tex]Suppose that y is the number of liters of water in a tank.
And x is the number of hours.
Each hour, 30% (0.3) of the water is evaporated from the tank. (subtracted)
So the equation completely models the above scenario.
[tex]y=x-0.3x[/tex]For example:
What will be the amount of water in the tank after 10 hours?
[tex]undefined[/tex]f(x)= - 9x+2 Find the domain of the function. Type answer in interval notation.
ANSWER:
Domain: (-∞, ∞)
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=-\:9x+2\:[/tex]The domain of a function is the set of all possible input values of the function. In this case, it would be the interval of values that x can take.
In this function, x can take any value in real numbers.
Therefore, in that case, it will be:
[tex]D=(-\infty,\infty)[/tex]2x - 11 = -3
What does x equal?
Answer :x=4
Step-by-step explanation:
x equals a point. If you are in the same exact area but at a different x, you dont know how to get to the area where x is. It is important to note that x does not equal a point, but a location.
how we do this this is hoighs chbool clac 1 i failed it and i have to reatek it
The equation of the curve is given by:
[tex]y=5+\cot(x)-2\csc(x)[/tex]Differentiating both sides of the equation with respect to x, we have:
[tex]\frac{dy}{dx}=2\cot(x)\csc(x)-\csc^2(x)[/tex]Therefore, the slope of the tangent is given by the value of dy/dx when x= π / 2
[tex]2\cot(\frac{\pi}{2})\csc(\frac{\pi}{2})-\csc^2(\frac{\pi}{2})=-1[/tex]Using the point slope formula, it follows that:
[tex]\begin{gathered} y-3=-1(x-\frac{\pi}{2}) \\ y=-x+\frac{\pi}{2}+3 \end{gathered}[/tex]Therefore, the equation of the tangent at P is given by:
y = -x + π /2 + 3
natural number is also a whole number.TrueFalse
Answer
The statement istrue.
Natural numbers are also whole numbers.
Explanation
Natural numbers are counting numbers.
They are the numbers that are numerically used to count things.
Hence, all natural numbers (counting numbers) are whole numbers.
Hope this Helps!!!
9. For each fraction, decimal, or percent, write the equivalent number from the list below 0.52, 38, 50, 0.35, 40% , 50 UN 76% 0.82 7 20 13 25
We have
In order to convert a fraction to a decimal, we divide the numerator between the denominator.
[tex]\frac{2}{5}=0.4=40\text{\%}[/tex][tex]0.82=\frac{82}{100}=\frac{41}{50}[/tex][tex]\frac{13}{25}=0.52[/tex][tex]76\text{\%}=\frac{76}{100}=\frac{38}{50}[/tex][tex]\frac{7}{20}=0.35[/tex]ANSWER
2/5=40%
0.82=41/50
13/25=0.52
76%=38/50
7/20=0.35
Answer the questions below.(a) Here are the prices (In thousands) for 10 houses for sale in a local neighborhood:$285, $286, $287, $290, $292, $295, $300, $301, $306, $307.which measure should be used to summarize the data?MeanMedianMode(b) in a survey, a soft drink company asks people to name as many brands of soft drinks as they can.Which measure glves the most frequently mentioned brand?MeanMedianMode(c) In the past 9 days, Kira has received the following numbers of email advertisements per day:40, 41, 43, 45, 48, 49, 50, 52, 85.Which measure should be used to summarize the data?O MeanMedianMode$2
a.
The data set shows the prices for houses.
Looking at the values, they lie near to the same value.
In this case, we can summarize the prices with the mean or median.
b. The survey was made to find how many names of brands of soft drinks they know. In this case, is important to know which soft drinks are the most popular.
Hence, the measure that gives the most frequently mentioned brand is the mode.
c. Kira has received many emails per day.
The emails also lie near to the same value except for the number of 85.
Where 85 represents an outlier (a value in a data set that is very different).
When we have outliers is better to use the median.
blank +0=9 is a associative b. commutativec identity property
It is an identity property
Any number plus zero will give that number
Rain equation of a hyperbola given the foci and the asymptotes
The equation for a hyperbola that opens up and down has the following general form:
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]Where the foci of the hyperbola are located at (h,k+c) and (h,k-c) with c given by:
[tex]c^2=a^2+b^2[/tex]And asymptotes with slopes given by a/b and -a/b.
The hyperbola with the equation that we have to find has these two foci:
[tex](3,2-\sqrt{26})\text{ and }(3,2+\sqrt{26})[/tex]This means that:
[tex]\begin{gathered} (h,k-c)=(3,2-\sqrt{26}) \\ (h,k+c)=(3,2+\sqrt{26}) \end{gathered}[/tex]So we get h=3, k=2 and c=√26.
The slope of the asymptotes have to be 5 and -5 which means that:
[tex]\frac{a}{b}=5[/tex]Using the value of c we have:
[tex]c^2=26=a^2+b^2[/tex]So we have two equation for a and b. We can take the first one and multiply b to both sides:
[tex]\begin{gathered} \frac{a}{b}\cdot b=5b \\ a=5b \end{gathered}[/tex]And we use this in the second equation:
[tex]\begin{gathered} 26=(5b)^2+b^2=25b^2+b^2 \\ 26=26b^2 \end{gathered}[/tex]We divide both sides by 26:
[tex]\begin{gathered} \frac{26}{26}=\frac{26b^2}{26} \\ b^2=1 \end{gathered}[/tex]Which implies that b=1. Then a is equal to:
[tex]a=5b=5\cdot1=5[/tex]AnswerNow that we have found a, b, h and k we can write the equation of the hyperbola. Then the answer is:
[tex]\frac{(y-2)^2}{5^2}-\frac{(x-3)^2}{1^2}=1[/tex]Find the values that form the boundaries of the critical region for a two-tailed test with a = .05 for eachof the following sample sizes:a. n = 4b. n = 15c. n = 24
Given
a). n = 4
b). n = 15
c). n = 24
Find
values that form the boundaries of the critical region for a two-tailed test with a = .05
Explanation
a) n = 4
degree of freedom = n - 1 = 4 - 1 = 3
so , the t value for critical region =
[tex]\begin{gathered} \pm t_{0.05,3} \\ \pm3.182 \end{gathered}[/tex]b) n = 15
degree of freedom = 15 - 1 = 14
so , t- value =
[tex]\begin{gathered} \pm t_{0.05,15} \\ \pm2.131 \end{gathered}[/tex]c) n = 24
degree of freedom = 24 - 1 = 23
so , t - value =
[tex]\begin{gathered} \pm t_{0.05,23} \\ \pm2.069 \end{gathered}[/tex]Final Answer
Hence , the values that form the boundaries of the critical region for a two-tailed test with a = .05 are
a)
[tex]\pm3.182[/tex]b)
[tex]\pm2.131[/tex]c)
[tex]\pm2.069[/tex]Subtract 14 from 11 the difference is
First it is important to remember that, by definition, the result of a subtraction is called "Difference".
In this case you need to subtract 14 from 11. This can operation can be expressed as following:
[tex]11-14[/tex]Notice that , since 14 is greater than 11 and it is also a negative number, the sign of the result (the difference) must be negative too.
Therfefore, keeping the above on mind, you obtain that the difference is the following:
[tex]11-14=-3[/tex]Write 12.5% as a decimal.
12.5% as a decimal is 0.125.
To convert a percentage in to a decimal, we divide the percentage by 100:
[tex]12.5\div100=0.125[/tex]Select the correct answer from each drop-down menu.Wayne, Winston, and Wilfred walked for an hour. Winston and Wilfred walked the same number of miles. Winston walked 2 miles less than 2 themiles Wayne walked. Wilfred walked 2 miles more than 3 the miles Wayne walked.A variable selected to solve this problem should represent the number of mileswalked in an hour.In that hour, Wayne would have walkedmiles and Winston and Wilfred would have walkedmiles each. So, WaynewalkedWinston and Wilfred.
SOLUTION:
Winston =
[tex]Win\text{ston = }\frac{3}{2}\text{ (Wayne) - 2}[/tex][tex]\text{Wilfred = }\frac{1}{3\text{ }}\text{ wayne }+\text{ }\frac{3}{2}[/tex][tex]\frac{3}{2}\text{ wayne - 2 = }\frac{1}{3}\text{ wayne }+\frac{3}{2}[/tex][tex]\frac{3}{2}\text{ wayne - }\frac{1}{3}\text{ wayne = }\frac{3}{2}\text{ + 2}[/tex]Upon simplification, the number of miles wayne walked was 3
Substituting wayne = 3 into the second equation
[tex]\text{Wilfred = }\frac{1}{3\text{ }}\text{ (3) }+\text{ }\frac{3}{2}[/tex]Wilfred = 2.5
Since Wilfred and Winston walked the same number of miles,
Winston = 2.5
The first drop menu is Wilfred
The second drop menu is 3
The third drop menu is 2.5
The fourth drop menu is faster than.
sin data cos data tan datacsc date sec data cot data
P (7/25, 24/25)
Sin data= 24/25
Cos data = 7/25
Tan data= (24/25)/(7/25)= 24/7
Csc data= 1/(24/25)= 25/24
Sec data= 1/(7/25)= 25/7
Cotan data= 1/(24/7)= 7/24
Triangle is rotated 180° around the origin. What will be the coordinates for Triangle J'K'L'? A(6,7)(6,2)(3,7)B(7,-6)(2,-7)(-3,-7)C(-6,-7)(-6,-2)(-3,-7)D(-7,6)(2,-6)(-7,3)
Answer:
A. (6,7)(6,2)(3,7)
Explanation:
From the graph, the coordinates of J, K and L are:
[tex]J(-6,-7),K(-6,-2)\text{ and L}(-3,-7)[/tex]When a point (x,y) is rotated 180° around the origin, we have the transformation rule:
[tex](x,y)\to(-x,-y)[/tex]Therefore, the coordinates for Triangle J'K'L' are:
[tex]J^{\prime}(6,7),K^{\prime}(6,2)\text{ and L'}(3,7)[/tex]The correct choice is A.
what is the sum of a 7-term geometric series if the first term is -11, the last term is -45056, and the common ratio is -4
Answer:
[tex]-171,875[/tex]Explanation:
Here, we want to find the sum of the geometric series
Mathematically, we have the mathematical formula to calculate this as follows:
[tex]S_n\text{ = }\frac{a(1-r^n)}{1-r}[/tex]where:
a is the first term which is given as -11
n is the number of terms wich is 7
r is the common ratio which is -4
Substituting the values, we have it that:
[tex]\begin{gathered} S_n\text{ = }\frac{-11(1-(-4))\placeholder{⬚}^7}{1+4} \\ \\ S_n\text{ = }\frac{-11(5)\placeholder{⬚}^7}{5}\text{ = -11 }\times\text{ 5}^6\text{ = -171,875} \end{gathered}[/tex]Which expression has a quotient of 63? 1) 4650÷752) 2867÷473) 3276÷52
To find the term with quotient in 63 in from the given option divide each quotient with 63. If the quatiend is divisible that term contain the quotient 63.
The quotient in the first option is 4650. Divide the quotient with 63.
[tex]\frac{4650}{63}=72.38[/tex]The final answer contains decimal places. Thus, there first option does not contain 63 as quotient.
The quotient in the second term is 2867. Divide the quotient with 63.
[tex]\frac{2867}{63}=45.190[/tex]The final answer contains decimal places. Thus, there second option does not contain 63 as quotient.
The quotient in the second term is 3276. Divide the quotient with 63.
[tex]\frac{3276}{63}=52[/tex]The final answer does not contain any decimal places. Thus, the third option contains 63 as quotient.
Thus, the correct option is option 3) 3276÷52.
The two lines y y = x and y = x + 1 are parallel lines.
True
False
By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
The equation of a line that passes through the Origin has the following form:
[tex]y=mx[/tex]Where "m" is the slope of the line.
In this case, you have the first line that passes through the Origin:
[tex]y=x[/tex]You can identify that its slope is:
[tex]m_1=1[/tex]You also know the second equation, which is written in Slope-Intercept form:
[tex]y=x+1[/tex]You can identify that:
[tex]\begin{gathered} m_2=1 \\ b=1 \end{gathered}[/tex]By definition, the slopes of parallel lines are equal. Then, since:
[tex]m_1=m_2[/tex]These lines are parallel.
The answer is: True.
I NEED HELP WITH THIS ASAP 100 POINTS IF SOMEONE GETS THIS RIGHT.
Question 12(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
For triangle XYZ, m∠X = (4g + 13)° and the exterior angle to ∠X measures (3g + 48)°. Find the measure of ∠X and its exterior angle.
Interior angle = 48°; exterior angle = 74.25°
Interior angle = 74.25°; exterior angle = 48°
Interior angle = 81°; exterior angle = 99°
Interior angle = 99°; exterior angle = 81°
Answer:
Interior angle = 81°; exterior angle = 99°.
Step-by-step explanation:
For triangle XYZ:
m∠X = (4g + 13)° exterior angle to ∠X = (3g + 48)°Angle X and its exterior angle form a straight line.
Angles on a straight line sum to 180°.
Therefore:
⇒ (4g + 13)° + (3g + 48)° = 180°
⇒ 4g + 13 + 3g + 48 = 180
⇒ 7g + 61 = 180
⇒ 7g + 61 - 61 = 180 - 61
⇒ 7g = 119
⇒ 7g ÷ 7 = 119 ÷ 7
⇒ g = 17
To find the measure of ∠X and its exterior angle, substitute the found value of g into the angle expressions:
⇒ m∠X = (4(17) + 13)°
⇒ m∠X = (68 + 13)°
⇒ m∠X = 81°
⇒ exterior angle to ∠X = (3(17) + 48)°
⇒ exterior angle to ∠X = (51 + 48)°
⇒ exterior angle to ∠X = 99°
Therefore:
Interior angle = 81°Exterior angle = 99°Answer: C
Step-by-step explanation: did the practice test!
h (t) = 2t - 2 g(t) = 4t + 5 Find (h(g(t))
ANSWER:
[tex]h(g(t))=8t-8[/tex]STEP-BY-STEP EXPLANATION:
We have the following functions:
[tex]\begin{gathered} h(t)=2t-2 \\ g(t)=4t+5 \end{gathered}[/tex]To calculate h (g (t)) we must do the following:
[tex]\begin{gathered} h\mleft(g\mleft(t\mright)\mright)=2\cdot(4t+5)-2 \\ h(g(t))=8t+10-2 \\ h(g(t))=8t-8 \end{gathered}[/tex]