The given equations are:
[tex]\begin{gathered} -10x+8y=-44\ldots\ldots(1) \\ 4x+8y=40\ldots\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]Subtract equation 1 from 2, we get,
[tex]\begin{gathered} 4x+10x+8y-8y=40+44 \\ 14x=84 \\ x=\frac{84}{14}=6 \end{gathered}[/tex]Now, substitute the value of x in equation 2, we get
[tex]\begin{gathered} 4\times6+8y=40 \\ 8y=40-24=16 \\ y=\frac{16}{8}=2 \end{gathered}[/tex]Thus, the solution is x = 6 and y = 2
I need help with number ten please and thank you for your help today
We know that there are 3 feet in 1 yard, so:
27 feet < 8 yards.
Which is the equation of the graph?
y = -2/3|x|
y = 3/2|x|
y = -3/2|x|
y = 2/3|x|
Answer:
y= -2/3|x| is the right answer
Step-by-step explanation:
If you substitute x and y values from the graph, this equation turns true.
For example take the value (6; -4) and (-6; -4) from the graph and substitute in the funxtion:
a) -4 = -2/3 |6|
-4 = -4
b) -4 = -2/3 |-6|
-4 = -2/3* 6
-4 = -4
18. Find the total surface area of the right triangular prism. .1112
We are asked to find the total surface area of the right triangular prism.
Recall that the total surface area of a right triangular prism is given by
[tex]TSA=P\cdot h+2B[/tex]Where P is the perimeter of the base, h is the height of the prism, and B is the area of the base.
From the figure, we see that
height = 11
side 1 = 9
side 2 = 12
We can apply the Pythagorean theorem to find the length of the third side. (hypotenuse)
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=9^2+12^2 \\ c^2=81^{}+144 \\ c^2=225 \\ c=\sqrt[]{225} \\ c=15 \end{gathered}[/tex]Now we can find the perimeter of the base,
[tex]\begin{gathered} P=s_1+s_2+s_3 \\ P=9+12+15 \\ P=36 \end{gathered}[/tex]The area of the base is given by
[tex]\begin{gathered} B=\frac{1}{2}\cdot b\cdot h \\ B=\frac{1}{2}\cdot12\cdot11 \\ B=66 \end{gathered}[/tex]So, the total surface area of the right triangular prism is
[tex]\begin{gathered} TSA=P\cdot h+2B \\ TSA=36\cdot11+2(66) \\ TSA=396+132 \\ TSA=528\: \text{unit}^2 \end{gathered}[/tex]Therefore, the total surface area of the right triangular prism is 528 square units.
problem here to solve
Answer:
Step-by-step explanation:
-8.4=c/-2+-5.4
We subtract -5.4 from both sides.
3=c/-2
multiply both sides by -2
-6=c
A weather researcher compared average monthly temperature data for CapeTown, South Africa, and Luxor, Egypt.Cape TownLuxorMean63.5°F78°FRange21°F29.4°FBased on these data, which statements are true?OA. On average, Cape Town has a higher monthly temperature,However, Luxor's temperatures vary more.O B. On average, Luxor has a higher monthly temperature. However,Cape Town's temperatures vary more.C. On average, Luxor has a higher monthly temperature. Its monthlytemperatures also vary more.D. On average, Cape Town has a higher monthly temperature. Itsmonthly temperatures also vary more.
Given
average monthly temperature data for Cape Town, South Africa, and Luxor, Egypt.
Find
Which statement is true?
Explanation
As we know that mean is given by the sum of the observations divided by the number of observations.
Range is the difference between highest and lowest .
so, considering the mean and range concept , it is found that the correct option is C.
Final Answer
The correct option is C that is On average, Luxor has a higher monthly temperature. Its monthly temperatures also vary more.
The rat population in a major metropolitan city is given by the formula n(t)measured in years since 2001 and n(t) is measured in millions.66e0.015€ where t isWhat was the rat population in 2001 ?ratsWhat does the model predict the rat population was in the year 2020 ?rats
The given formula is:
[tex]n(t)=66e^{0.015t}[/tex]Where t is measured in years since 2001 and n(t) is measured in millions.
a. What was the rat population in 2001?
Since t is measured in years since 2001, then we need to subtract 2001 from the year we want to analyze. So:
[tex]t=2001-2001=0[/tex]By replacing t=0 into the formula we obtain:
[tex]\begin{gathered} n(0)=66e^{0.015*0} \\ n(0)=66e^0 \\ n(0)=66*1 \\ n(0)=66\text{ millions} \end{gathered}[/tex]As n(t) is measured in millions, thus, the rat population in 2001 was 66000000 rats.
b. What does the model predict the rat population was in the year 2020?
t in the year 2020 is:
[tex]t=2020-2001=19[/tex]Then:
[tex]\begin{gathered} n(19)=66e^{0.015*19} \\ n(19)=66e^{0.285} \\ n(19)=66*1.33 \\ n(19)=87.764294\text{ millions} \end{gathered}[/tex]In the year 2020 the predicted rat population was 87764294 rats.
Juan made $1000 in taxable income last year.Suppose the income tax rate is 15% for the first $ 7000 plus 17% for the amount over $7000. How much must Juan pay in income tax for last year?
step 1
$1,000 < $7,000
so
the tax rate is 15%
15%=15/100=0.15
0.15*1,000=$150
therefore
The answer is $150Select the correct answer. Simplify (8x + 5) + (4x+6) A. 4x - 11 B. 12x-1 C. 12x + 11 D 4x + 1
we are given the following expression:
[tex]\mleft(8x+5\mright)+(4x+6)[/tex]First, we will associate like terms, that is terms that have the same variable elevated to the same exponent:
[tex](8x+4x)+(5+6)[/tex]Adding like terms:
[tex]12x+11[/tex]Since we can't simplify any further, this is the final answer.
Distance between P1 and P2
Answer:
Can't solve
Step-by-step explanation:
Theres no image.
I nee someone to answer this and actually explain it to me please.
Given Data:
[tex]\begin{gathered} a=1.4 \\ b=-2.6 \\ c=5.2 \end{gathered}[/tex]Here the point d is the horizontal distance, it can be found by adding the distance 'a' and 'c', since 'a' and 'c' are horizontal measurements. Th distance 'b' is given in vertical measurements. Thus, the distance 'b' can be ignored while finding the value of d.
[tex]\begin{gathered} d=a+c \\ d=1.4+5.2 \\ d=6.6 \end{gathered}[/tex]Thus, the distant d is in 6.6 unit from the origin, or from the y-axis.
When summarizing the distribution of a data set with Strong outlier the what number summary is a better choice than the mean and standard deviation?
Since the mean and the standard deviations are "sensible" to outliers, that is, t
I already found the range of the logarithmic function, so if you could just help me find the domain.
The domain of a logarithmic function:
[tex]f(x)=\log _ax[/tex]will always be all the positive numbers, that is the domain is:
[tex](0,\infty)[/tex]b) 10x-8 = 8x
e) 2x+3 = x-9
h) 5x+8 = 7x-32
Answer:
b) x = 4
e) x = -12
h) x = 20
Step-by-step explanation:
b) 10x - 8 = 8x
10x - 8 + 8 = 8x + 8
10x = 8x + 8
10x - 8x = 8x + 8 - 8x
2x = 8
[tex]\frac{2x}{2} = \frac{8}{2}[/tex]
x = 4
e) 2x +3 = x - 9
2x +3 -3 = x - 9 -3
2x = x - 12
2x -x = x -12 -x
x = -12
h) 5x + 8 = 7x - 32
5x + 8 - 8 = 7x -32 -8
5x = 7x - 40
5x - 7x = 7x - 40 -7x
-2x = -40
[tex]\frac{-2x}{-2} = \frac{-40}{-2}[/tex]
x = 20
Hello, how do I solve these equations when the domain is restricted to 0 ≤ θ <2πa) 5cot(θ) -2 = 3cot(θ) - 2b) 2sinθ = tanθc) 3cos^2θ - sin^2θ = 2
a)
The given equation is
[tex]5cot\theta-2=3cot\theta-2[/tex]Subtract 3cot(theta) from each side
[tex]\begin{gathered} 5cot\theta-3cot\theta-2=3cot\theta-3cot\theta-2 \\ 2cot\theta-2=-2 \end{gathered}[/tex]Add 2 to both sides
[tex]\begin{gathered} 2cot\theta-2+2=-2+2 \\ 2cot\theta=0 \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{2cot\theta}{2}=\frac{0}{2} \\ \\ cot\theta=0 \end{gathered}[/tex]cot(theta) = 0 at theta = pi and theta = 3/2pi
[tex]\theta=\pi,\frac{3}{2}\pi[/tex]b)
[tex]2sin\theta=tan\theta[/tex]Change tan(theta) to sin(theta)/cos(theta)
[tex]\begin{gathered} tan\theta=\frac{sin\theta}{cos\theta} \\ \\ 2sin\theta=\frac{sin\theta}{cos\theta} \end{gathered}[/tex]Multiply both sides by cos(theta)
[tex]2sin\theta cos\theta=sin\theta[/tex]Subtract sin(theta) from both sides
[tex]2sin\theta cos\theta-sin\theta=0[/tex]Take sin(theta) as a common factor on the left side
[tex]sin\theta(2cos\theta-1)=0[/tex]Equate each factor by 0
[tex]\begin{gathered} sin\theta=0 \\ \theta=0,\pi \end{gathered}[/tex][tex]\begin{gathered} 2cos\theta-1=0 \\ 2cos\theta=1 \\ cos\theta=\frac{1}{2} \\ \theta=\frac{\pi}{3},\frac{5\pi}{3} \end{gathered}[/tex][tex]\theta=0,\frac{\pi}{3},\pi,\frac{5\pi}{3}[/tex]c)
[tex]3cos^2(\theta)-sin^2(\theta)=2[/tex]Change sin^2(theta) to 1 - cos^2(theta)
[tex]\begin{gathered} 3cos^2\theta-(1-cos^2\theta)=2 \\ 3cos^2\theta-1+cos^2\theta=2 \\ 4cos^2\theta-1=2 \\ 4cos^2\theta=3 \\ cos^2\theta=\frac{3}{4} \end{gathered}[/tex]Take a square root for each side
[tex]cos\theta=-\frac{\sqrt{3}}{2},cos\theta=\frac{\sqrt{3}}{2}[/tex]The values of theta are
[tex]\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}[/tex]Write an equation that could be used to solve for x. 7% – 5 6x + 10 8 See where to Hell
Both angles are alternate exterior angles.
Since both parallel lines are crossed by a transversal, alternate exterior angles are equal:
7x-5=6x+10
19) Determine if the number is rational (R) or irrational (I)
Given the number:
[tex]20.455566...[/tex]Irrational numbers cannot be expressed as the ratio of two integers.
ANSWER
Irrational.
what is 620÷3? i keep getting 6.02 as the answer
explain with long division pleasee
Answer:
206.67 round it
Step-by-step explanation:
what does being independent or mutually exclusive do to the way we calculate the probability??
If two events are independent, it means that the probability of one event happening does not depend on the probability of the other happening. If A and B are 2 independent events, the probability of them happening is the product of their seperate probabilities. P(A) x P(B)
If two events are mutually exclusive, it means that they cannot occur together. If A and B are 2 mutually exclusive events, the probability of them happening is together is 0
The students in Mr.Collins class used a surveyors measuring devices to find the angle from their location to the top of a building. The also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building. A.36ft B.137ft C.32ft D.154ft
Given:
The angle from the location of surveyors is 63 degrees and the distance to the bottom of the building is 70 ft.
To find:
The height of the building
Solution:
We can solve the question, using the trigonometric function tangent.
From the figure, the tangent of the angle is:
[tex]\begin{gathered} \tan 63=\frac{x}{70} \\ 1.96=\frac{x}{70} \\ x=70\times1.96 \\ x=137.2 \end{gathered}[/tex]Thus, the height of the building is approximately 137 ft.
Thus. option B is correct.
What is a rule for the translation of ARST to AR'S'T' ? Select all that apply.RSГуRISतकT-2이erA. T-7,3)B. 7 units down; 3 units rightC. 7 units right; 3 units downD. T7.-3
Given :
R'S'T' is the image of RST
we will find the rule of translation using the coordinates of :
[tex]\begin{gathered} R=(-4,5) \\ R^{\prime}=(3,2) \end{gathered}[/tex]So, the rule will have the form :
[tex]\begin{gathered} R\rightarrow R^{\prime} \\ (x,y)\rightarrow(x+h,y+k) \end{gathered}[/tex][tex]\begin{gathered} 3=-4+h\rightarrow h=7 \\ 2=5+k\rightarrow k=-3 \end{gathered}[/tex]So, the answer is :
T(7,-3)
7 units right ; 3 units down
I need help on in the answer to this question
Notice that angle z and the angle with measure 70⁰ is a linear pair. Hence, it follows that they are supplementary (they'll sum up to 180⁰):
[tex]z+70^{\circ}=180^{\circ}[/tex]Solve for z in the equation:
[tex]\begin{gathered} z=180^{\circ}-70^{\circ} \\ \Rightarrow z=110^{\circ} \end{gathered}[/tex]Using the Angles formed by two intersecting chords theorem: If two chords intersect inside a circle, then the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle , it follows that:
[tex]z=\frac{1}{2}(w+79^{\circ})[/tex]Substitute z=110⁰ into the equation and solve for w:
[tex]\begin{gathered} 110^{\circ}=\frac{1}{2}(w+79^{\circ}) \\ \text{Cross multiply:} \\ \Rightarrow2\times110^{\circ}=w+79^{\circ} \\ \Rightarrow220^{\circ}=w+79^{\circ} \\ \Rightarrow w=220^{\circ}-79^{\circ} \\ \Rightarrow w=141^{\circ} \end{gathered}[/tex]The value of w is 141.
function G is an exponential function passing through two points
mariana races on a BMX bike with 12-in-radius wheels. when she is traveling at a speed of 24 ft/sec, how many revolutions per minute are her wheels making?
First, we have to calculate the circumference of the wheels:
Circumference (c) = pi x 2radius
C = pi x 2(12)
C= 75.4 inches
Convert into feet:
Since 1 ft =12 inches
75.4 in / 12 in/ft = 6.28 ft
Multiply the speed by 60 to convert into ft/min
1minute =60 seconds
24 ft/sec x 60 sec = 1,440 ft/min
Divide the speed by the circumference:
1,440 / 6.28 = 229.3 revolutions per minute
A magazine asks its readers to complete a brief survey and respond by mailing back their responses in an envelope. This survey may be biased because
The magazine asks its readers to complete a survey and respond by mailing.
The fact that the survey could be biased can only be that occurs a problem with the delivery.
With this argument, we can discard the other options, having in mind the context.
Then, the correct answer is A.
Please help I need an answer ASAP!!!!!!!!
The domain is the set of x-values for the points on the graph:
{-5, -3, 1, 2, 3}
Graph a line trough the given point with the given slope. Point:(4, 4) slope ( -4/3
Given:
point =(4,4) slope(m)=-4/3
x₁=4 y=4
We find the intercept
substitute into y=mx + b
4=4(-4/3)+ b
4 = -16 /3 + b
4+16/3 = b
[tex]\frac{12+16}{3}=b[/tex][tex]b=\frac{28}{3}[/tex]The equation can be form by substituting the value of m and b into y=mx+b
[tex]y=-\frac{4}{3}x+\frac{28}{3}[/tex]To be able to sketch the graph, we need two points, the x and y-intercept.
To find the y-interpet, substitute x=0 into the equation
y = 28/3
Hence, the y-intercept is (0, 9.3)
To find the x-intercept, put y=0 and solve for x
[tex]\begin{gathered} 0=-\frac{4}{3}x+\frac{28}{3} \\ \\ \frac{4}{3}x=\frac{28}{3} \\ \\ x=\frac{28}{3}\times\frac{3}{4} \\ x=\frac{28}{4} \end{gathered}[/tex]The x-intercept is (7,0)
So we can now sketch the graph
F(x) = 2^x and G(x) = x; graph F-G
Given the two functions
[tex]F(x)=2^x,G(x)=x_{}[/tex]We are tasked to plot (F-G)(x).
The first step here is to get the resulting function (F-G)(x). We have
[tex](F-G)(x)=2^x-x[/tex]Now, we need to assign values of x and evaluate them at the function (F-G)(x) to get a value. We will get coordinate points and we will plot them at the cartesian coordinate plane. I will use values of x = [-3,3]. We get the following results
[tex]\begin{gathered} (F-G)(-3)=2^{-3}-(-3)=3.125\rightarrow\rightarrow(-3,3.125)_{}_{} \\ (F-G)(-2)=2^{-2}-(-2)=3.125\rightarrow\rightarrow(-2,2.25)_{} \\ (F-G)(-1)=2^{-1}-(-1)=3.125\rightarrow\rightarrow(-1,1.5)_{} \\ (F-G)(0)=2^0-0=1\rightarrow\rightarrow(0,1)_{} \\ (F-G)(1)=2^1-1=1\rightarrow\rightarrow(1,1)_{} \\ (F-G)(2)=2^2-2=2\rightarrow\rightarrow(2,2)_{} \\ (F-G)(3)=2^3-3=5\rightarrow\rightarrow(3,5)_{} \end{gathered}[/tex]The plot is provided by the image below.
Where would 1 2/3 be on a number line
So we want to put the number:
[tex]1\frac{2}{3}[/tex]on a number line.
Remember that, this number can be expressed as:
-Taking values between 1 and 2 and divide this interval in three parts. The second part will be the location of the number. If we draw:
So the correct answer is A.
triangle ABC has the following verticles A (-4,6)B (6,6)C( 1,-3) is triangle ABC an equilateral traingle and why?
we know that
An equilateral truangle has three equal length sides
so
If triangle ABC is an equilateral triangle
then
AB=BC=AC
so
step 1
Find out the distance AB
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^2+(x2-x1)^2}[/tex]we have
A (-4,6)
B (6,6)
substitue in the formula
[tex]\begin{gathered} d=\sqrt{(6-6)^2+(6+4)^2} \\ d=\sqrt{(0)^2+(10)^2} \\ dAB=10\text{ units} \end{gathered}[/tex]step 2
Find the distance BC
we have
B (6,6)
C( 1,-3)
substitute the values in the formula
[tex]\begin{gathered} d=\sqrt{(-3-6)^2+(1-6)^2} \\ d=\sqrt{(-9)^2+(-5)^2} \\ d=\sqrt{81+25} \\ dBC=\sqrt{106\text{ units}} \end{gathered}[/tex]we have that
AB is not equal to BC
therefore
Is not an equilateral triangle
Is not necessary calculate the distance AC
55x[78+9]+3 Solve it for me??
first solve for the equation inside the bracket
55×(87)+3
=55×87+3
4785+3
=4788