You have the following equation:
y = -5x + 3
in order to determine if the point (0,3) is solution of the previous equation, replace the values of x = 0 and y = 3, and verify if the equation is consistent, as follow:
3 = -5(0) + 3
3 = 3
the equation is consistent for the given point, then, the point (0,3) is a olution of the given equation
-3x+5y=-8 solve for x and y
ANSWER
The set of equations has no solution
EXPLANATION
-3x + 5y = -8 ------ equation 1
6x - 10y = 16 -------- equation 2
These two equations can be solve simultaneously either by substitution method or elimination method
To solve for the value of x and y, we will be using the elimination method
-3x + 5y = -8
6x - 10y = 16
Let us eliminate x first.
We need to make the coefficient of x in both equation equal
Hence, multiply equation 1 by 2 and equation 2 by 1
-3x*2 + 5y*2 = -8 x 2
6x * 1 - 10y * 1 = 16 x 1
-6x + 10y = -16 ------------ equation 3
6x - 10y = 16 -------------- equation 4
To eliminate x , add equation 3 and 4 together
-6x + 6x + 10y + (-10y) = -16 + 16
-6x + 6x + 10y - 10y = -16 + 16
0 + 0 = 0
0 = 0
Hence, the set of equations has no solution
Question 2 Find the area of the figure below. Ty below. 24 yd 24 yd 24 yd 40 yd
Answer:
1536 yd²
Explanation:
To find the area of the figure, we need to divide the figure into 2 rectangles as:
So, the area of the first rectangle is equal to:
[tex]\begin{gathered} \text{Area = Base x Height } \\ \text{Area = 24 yd x 24 yd} \\ \text{Area = 576 yd}^2 \end{gathered}[/tex]In the same way, the area of the second rectangle is:
[tex]\begin{gathered} \text{Area = Base x Height } \\ \text{Area = 40 yd }\times24\text{ yd} \\ \text{Area = 960 yd}^2 \end{gathered}[/tex]So, the area of the figure is:
576 yd² + 960 yd² = 1536 yd²
Therefore, the answer is 1536 yd²
If P(6,-2). O(-2,8), R(-4, 3), and S(-9, y). find the value of y so that PO perpendicular to RS.please?
Answer:
y = - 1
Explanation:
Two lines are perpendicular if the product of their slopes is equal to -1.
Additionally, we can calculate the slope of a line with two points (x1, y1) and (x2, y2) as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]If we replace (x1, y1) by P(6, -2) and (x2, y2) by O(-2, 8), we get that the slope of PO is equal to:
[tex]m=\frac{8-(-2)}{-2-6}=\frac{8+2}{-8}=\frac{10}{-8}=-1.25[/tex]In the same way, if we replace (x1, y1) by (-4, 3) and (x2, y2) by (-9, y), we get that the slope of RS is equal to:
[tex]m_{}=\frac{y-3}{-9-(-4)}=\frac{y-3}{-9+4}=\frac{y-3}{-5}[/tex]Then, the product of these two slopes should be equal to -1, so we can write the following equation:
[tex]-1.25\cdot(\frac{y-3}{-5})=-1[/tex]So, solving for y, we get:
[tex]\begin{gathered} (-5)(-1.25)\cdot(\frac{y-3}{-5})=(-5)(-1) \\ -1.25(y-3)=5 \\ y-3=\frac{5}{-1.25} \\ y-3=-4 \\ y=-4+3 \\ y=-1 \end{gathered}[/tex]Therefore, the value of y is equal to -1
What is the probability that the spinner lands on blue?
Answer:
Concept:
The total number of angles in a circle is
[tex]\begin{gathered} =360^0 \\ =120^0+60^0+180^0=360^0 \end{gathered}[/tex]The angle of the sector that represents blue is
[tex]=60^0[/tex]To calculate the probability, we will use the formula below
[tex]\begin{gathered} P(\text{blue)}=\frac{n(\text{blue)}}{n(S)} \\ n(\text{blue)}=60^0,n(S)=360^0 \\ P(\text{blue)}=\frac{n(\text{blue)}}{n(S)}=\frac{60}{360} \\ P(\text{blue)}=\frac{1}{6} \end{gathered}[/tex]Hence,
The final answer is = 1/6
a triangle has side lengths for 8 in and 7 in select all the possible lengths for the third side 6 inches 15 inches 7 inches 20 inches 9 inches
To answer this question, we need to take into account the triangular inequality, that is, in a triangle, the sum of two sides must be greater than one side of the triangle. That is:
[tex]a+b>c,b+c>a,a+c>b[/tex]We can see that two of the sides are:
a = 8 in, and b = 7 in, then, we have:
a + b = 8 + 7 = 15. Therefore:
[tex]15>6,\text{ and 15>7,15>9}[/tex]Therefore, the possible lengths for the third side are:
• 6 inches
,• 7 inches
,• 9 inches
which values are in the domain of the function F(X)= -6x + 11 with a range of (-37 ,-25, -13, -1)? select all that apply a)1b)4c)8d)5e)2f)6g)3h)7
Answers:
2
4
6
8
Explanation:
The domain of the function with a range {-37, -25, -13, -1} will be the set of values of x when f(x) is -37, -25, -13, and -1. So, to find the correct answers, we need to solve the following equations:
If f(x) = -37, we get:
[tex]\begin{gathered} f(x)=-6x+11 \\ -37=-6x+11 \\ -37-11=-6x+11-11 \\ -48=-6x \\ \frac{-48}{-6}=\frac{-6x}{-6} \\ 8=x \end{gathered}[/tex]If f(x) = - 25, we get:
[tex]\begin{gathered} -25=-6x+11 \\ -25-11=-6x+11-11 \\ -36=-6x \\ \frac{-36}{-6}=\frac{-6x}{-6} \\ 6=x \end{gathered}[/tex]If f(x) = - 13, we get:
[tex]\begin{gathered} -13=-6x+11 \\ -13-11=-6x+11-11 \\ -24=-6x \\ \frac{-24}{-6}=\frac{-6x}{-6} \\ 4=x \end{gathered}[/tex]If f(x) = -1, we get:
[tex]\begin{gathered} -1=-6x+11 \\ -1-11=-6x+11-11 \\ -12=-6x \\ \frac{-12}{-6}=\frac{-6x}{-6} \\ 2=x \end{gathered}[/tex]Therefore, the domain is the set of the values of x: {2, 4, 6, 8}
What is the worst part of being a girl?
Answer:
men.
Step-by-step explanation:
just men
Answer:
is this really a question?...
Step-by-step explanation:
1. Find the area of the triangle below. 13 in9in7in18 in63 inches squared91 inches squared126 inches squaredO 45.5 inches squared
ANSWER:
63 square inches
STEP-BY-STEP EXPLANATION:
We have the formula to calculate the area of the triangle is the following:
[tex]A=\frac{b\cdot h}{2}[/tex]Replacing:
[tex]\begin{gathered} A=\frac{7\cdot18}{2} \\ A=63 \end{gathered}[/tex]The area equals 63 square inches
- 23 = -9+7(v - 3)could I please get some help
we have
- 23 = -9+7(v - 3)
apply distributive property right side
-23=-9+7v-21
combine like terms
-23=7v-30
Adds 30 both sides
-23+30=7v-30+30
7=7v
Divide by 7 both sides
7/7=7v/7
1=v
v=1hunter says that there should be a decimal point in the quotient below after 6. is he correct? use number sense to explain your answer. 69.48 ÷ 7.2= 965
Solution
For this case we can do this:
[tex]undefined[/tex]Plot the point given by the following polar coordinates on the graph below. Each circular grid line is 0.5 units apart.(2, -1)
In polar coordinates we must have two things to plot a point, it's the radius and the angle
If we use a negative angle, it just means that we are doing the rotation clockwise.
Therefore the point (2, -π) is
We do a 2 units long line and rotate is by -π, the result is
If you shift the function F(x) = log10 x right three units, what is the newfunction, G(x)?O A. G(x) = log, (x-3)O B. G(x) = log, (x+3)O C. G(x) = 109, *-3O D. G(x) = 109,X+3
Given the function:
[tex]F\mleft(x\mright)=log_{10}x[/tex]You need to remember that, according to the Transformation Rules for Functions:
1. If:
[tex]f(x+h)[/tex]The function is shifted left "h" units.
2. If:
[tex]f(x-h)[/tex]The function is shifted right "h" units.
In this case, you know that F(X) is shifted right three units to obtain the new function G(x), then the transformation has this form:
[tex]F(x-3)[/tex]Therefore, you can determine that:
[tex]G(x)=\log _{10}\mleft(x-3\mright)[/tex]Hence, the answer is: Option A.
Choose the expression that is equivalent to 9w² +3/5(20w² - 15w+10)+2w
The correct answer or equivalent expression is 21w² - 7w + 6.
What is the equivalent of an expression?X-terms and constants should be combined with any other like and similar terms on either side of the equation. By putting the terms in the same order, with the x-term usually comes before the constants. The two phrases or equation are equal if and only if each of their terms is the same.
It is given in the question that 9w² +[tex]\frac{3}{5}[/tex](20w² - 15w+10)+2w
⇒ 9w² + [tex]\frac{3}{5}[/tex] (20w² - 15w+10)+ 2w
⇒ 9w² + [tex]\frac{3}{5}[/tex] × 5 (4w² - 3w+2) + 2w
⇒ 9w² + 3(4w² - 3w+2) + 2w
⇒ 9w² + 12w² - 9w + 6 + 2w
⇒ 21w² - 7w + 6
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Sheridan Company purchased a truck for $79,000. The company expected
the truck to last four years or 120,000 miles, with an estimated residual
value of $12,000 at the end of that time. During the second year the truck
was driven 45,000 miles. Compute the depreciation for the second year
under each of the methods below and place your answers in the blanks
provided.
Units-of-activity
Double-declining-balance
The depreciation in year 2 using the units of activity method is $23,125.
The depreciation in year 2 using the double declining balance is $19,750.
What is the depreciation in year 2?
Depreciation is when the value of an asset declines as a result of wear and tear.
Deprecation in year 2 using the units of activity method = (miles driven in year 2 / total miles) x (cost of the asset - salvage value)
Deprecation = (45,000 / 120,000) x ($79,000 - $12,000)
Deprecation = $23,125
Deprecation using the double declining method = (2/ useful life) x cost of the asset
Depreciation in year 1 = (2/4) x 79,000 = $39,500
Book value in year 2 = 79,000 - $39,500 = $39,500
Depreciation in year 2 = (2/4) x $39,500 = $19,750
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To construct a square, match the corresponding steps to the proper orders. (basically match the words on the left with the number of steps 1-6)
Given:
Construct a square by matching the corresponding steps to the proper orders.
Explanation:
a) The first step would be,
Draw a line segment AB.
Therefore, statement 1 itself is the first step.
b) The second step would be,
Construct a perpendicular line to AB at B.
Therefore, statement 2 itself is the second step.
c) The third step would be,
Measure the distance AB with the compass. Draw an arc on the perpendicular line from B.
Therefore, statement 3 itself is the third step.
d) The fourth step would be,
Label it as C. Draw an arc from C without changing the measurements.
Therefore, statement 4 itself is the fourth step.
e) The fifth step would be,
Place the compass at A. Draw an arc from A without changing the measurements to intersect the previous arc.
Mark it as D.
Therefore, statement 5 itself is the fifth step.
f) The sixth step would be,
Connect ABCD.
Therefore, statement 6 itself is a sixth step.
Determine whether each number is a solution of the given inequality.5b - 7>13
Solve for b:
Add 7 to both sides:
[tex]\begin{gathered} 5b-7+7>13+7 \\ 5b>20 \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} \frac{5b}{5}>\frac{20}{5} \\ b>4 \end{gathered}[/tex]Answer:
b > 4
A town's population is 52,525. About 75 people move out of the town each month. Each month, 200 people on average move into town. A nearby town has a population of 56,375. It has no one moving in and an average of 150 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation Then solve the equation and answer the question.
The required equation to model the given situation is 52,525 - 75x +200x = 56,375 - 150x. the value of x = 14; the populations will be equal in 14 months.
Let x represents the number of months, the first town's population rise is 75x and its drop is 200x. The population of the second town has decreased by 150x.
We want to find m such that the increases and decreases equalize the populations of the towns. In each case, we add the increases and subtract the decreases from the base population.
As per the given situation, the required equation would be as:
52,525 - 75x +200x = 56,375 - 150x
Rearrange the terms likewise and apply the arithmetic operation,
150x + 200x - 75x = 56,375 - 52,525
275x = 3850
x = 3850 / 275
x = 14
Thus, the required equation to model the given situation is 52,525 - 75x +200x = 56,375 - 150x. the value of x = 14; the populations will be equal in 14 months.
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Jaron made a trip of 450 miles in 8hours. Before noon he averaged 60 miles per hour , and afternoon he averaged 50 miles per hour. At what time did he begin his trip and when did he end it?
Data:
Total distance: 450 miles
Total time: 8 h
Average 60 mi/h before noon
Average 50 mi/h afternoon
The relationship between the time, speed (average) and distance is drescribed in the next equations:
[tex]\begin{gathered} s=\frac{d}{t} \\ \\ d=s\times t \\ \\ \end{gathered}[/tex]Then, if you multiply the speed and the time you get the distance:
time before noon: b
time afternoon: a
[tex](60\times b)+(50\times a)=450[/tex]The sum of a and b is the total time:
[tex]a+b=8[/tex]Use the next system of equations to find a and b:
[tex]\begin{gathered} 60b+50a=450 \\ a+b=8 \end{gathered}[/tex]1. Solve a in the second equation:
[tex]\begin{gathered} \text{Subtract b in both sides of the equation:} \\ a+b-b=8-b \\ \\ a=8-b \end{gathered}[/tex]2. Substitute the a in first equation by the value you get in first step:
[tex]60b+50(8-b)=450[/tex]3. Solve b:
[tex]\begin{gathered} 60b+400-50b=450 \\ 10b+400=450 \\ \\ \text{Subtract 400 in both sides of the equation:} \\ 10b+400-400=450-400 \\ 10b=50 \\ \\ \text{Divide both sides of the equation into 10:} \\ \frac{10}{10}b=\frac{50}{10} \\ \\ b=5 \end{gathered}[/tex]4. Use the value of b=5 to solve a:
[tex]\begin{gathered} a=8-b \\ a=8-5 \\ a=3 \end{gathered}[/tex]Then, Jaron begin his trip 5 hours before noon ( at 7:00) and end it 3 hours afternoon (at 15:00)A sandwich shop has 70 stores and 90% of the stores are in California. The rest of the stores are in Nevada. How many stores are in California and how many are in Nevada?There are ____ stores in California and ____ in Nevada.
The sandwich shop has a total of 70 stores, this is the 100% of their stores.
90% of the stores are in California
The rest of the stores, 10%, are in Nevada.
To calculate how many stores correspond to the 90% you can use cross multiplication
100%_____70 shops
90%______x shops
[tex]\begin{gathered} \frac{70}{100}=\frac{x}{90} \\ x=(\frac{70}{100})90 \\ x=63 \end{gathered}[/tex]So the 90% of 70 is 63, this means that there are 63 stores in California.
Now subtract the number of stores in California from the total number of stores
[tex]70-63=7[/tex]And we get that there are 7 stores in Nevada
Kirby wants to run a total of 7 5/8 miles every Tuesday and Thursday. If he runs 4 4/16 miles onTuesday and 3 3/8 miles on Thursday, will he meet his goal for this week? Explain.
Given:
Kirby wants to run a total of 7 5/8 miles every Tuesday and Thursday.
If he runs 4 4/16 miles on Tuesday and 3 3/8 miles on Thursday,
Then, the total miles he will cover is,
[tex]\begin{gathered} 4\frac{4}{16}+3\frac{3}{8}=4\frac{1}{4}+3\frac{3}{8} \\ =\frac{17}{4}+\frac{27}{8} \\ =\frac{34}{8}+\frac{27}{8} \\ =\frac{61}{8} \\ =7\frac{5}{8} \end{gathered}[/tex]Since, he will cover total of 7 5/8 miles.
So, he will meet his goal for this week.
Consider the following set of equations:Equation M: 3y = 3x + 6Equation P: y = x + 2Which of the following best describes the solution to the given set of equations? No solutionOne solutionTwo solutionsInfinite solutions
Solution
Given
Equation M: 3y = 3x + 6
Equation P: y = x + 2
Plot the graph of the two equation
The graph of the two equations are the same. With the same slope and intercept
The graph is shown below
Conclusion:
Because the graph of the equatons are thesame, the system of equations have Infinite solutions
The answer is Infinite solutions
Window45°Apartment450BenchNoah can see a bench in the nearby play area through his window inhis apartment at a 45° angle of depression.If the floor of the apartment that Noah is standing is 25 feet abovethe ground level, what is the horizontal distance from the apartmentto the bench in the play area?
Given:
The angle of depression of the bench with respect to Noah, θ=45° .
The height of the apartment or the height at which Noah is standing with respect to the ground, h=25 feet.
Let x be the horizontal distance from the apartment to the bench.
Now, using trigonometric property in the above triangle,
[tex]\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan \theta=\frac{h}{x} \end{gathered}[/tex]Substitute the values and solve the equation for x.
[tex]\begin{gathered} \tan 45^{\circ}=\frac{25\text{ ft}}{x} \\ 1=\frac{25\text{ ft}}{x} \\ x=25\text{ ft} \end{gathered}[/tex]Therefore, the horizontal distance from the apartment to the bench is 25 ft.
which of the following Roots would be between 8 and 7
To find which of the following roots is between "8" and "7" we can calculate the root of which numbers result in 8 and 7. To do this we will power them by 2, this is done because power is the oposite operation to the root. Doing this gives us:
[tex]\begin{gathered} 8^2=64 \\ 7^2=49 \end{gathered}[/tex]So the root of 64 is 8 and the root of 49 is 7. We need to find the number that is between 49 and 64.
From the options the only one that qualifies is 52. The correct option is b.
Find the z-scores for which 70% of the distribution's area lies between - Z and z.
The values given by z-score tables represent the fraction of the area under a normal curve between -∞ and z. For example, for a given z, the value given by a table represents the following area:
However, in this exercise we must find the area under the curve between -z and z and not between -∞ and z. We are basically looking for an area like this one:
So the z in a z-score table that corresponds to 70% of the area is not the answer.
However, we still can find the value of z using a z-score table. Remember that the total area under this curve is equal to 1. We are told that the area between -z and z is the 70% so this area is equal to 0.7. Then the remaining area i.e. the sum of the areas at the left of -z and at the right of z is equal to 1-0.7=0.3. Another important property of the normal distribution curve is that it's symmetric so the area at the right of z is equal to that at the left of -z then the two green areas are equal and their sum is 0.3. This means that each green area is equal to 0.3/2=0.15. So basically we have the following:
- The area between -∞ and -z is equal to 0.15.
- The area between z and ∞ is equal to 0.15.
Remember that the z-scores tables give us the z-score associated with the area under the curve between -∞ and z. Then if we look at a z-score table and look for the value 0.15 the table will give us the value of -z and with it the value of z. So we must look for 0.15 in a z-score table:
0.14917 is the closest value to 0.15 in this table so it is useful. As you can see it's located at row -1 and column 0.04 which means that it corresponds to -1.04. Then -z=-1.04 and therefore z=1.04. Then the answer is:
[tex]-1.04,1.04[/tex]A van with seven people drove 422 miles six hours. About how many miles did they travel each hour?
Distance travelled by van in six hours is 422 miles.
Determine the distance travelled by the van in one hour.
[tex]\begin{gathered} \frac{422}{6}=70.333 \\ \approx70.3\text{ miles} \end{gathered}[/tex]So, they travel approximately 70.3 miles in each hour.
We estimate that the population of a certain, in t years will be given byp (t) = (2t² + 75) / (2t² + 150) million habitantsAccording to this hypothesis:What is the current population?What will it be in the long term?Sketch the population graph
Given that the population can be represented by the equation;
[tex]P(t)=\frac{2t^2+75}{2t^2+150}[/tex]The current population (Initial population) is the population at time t=0;
Substituting;
[tex]t=0[/tex][tex]\begin{gathered} P(0)=\frac{2t^2+75}{2t^2+150}=\frac{2(0)^2+75}{2(0)^2+150}=\frac{75}{150} \\ P(0)=0.5\text{ million} \end{gathered}[/tex]Therefore, the current population of the habitat is;
[tex]0.5\text{ million}[/tex]The long term population would be the population as t tends to infinity;
[tex]\begin{gathered} \lim _{t\to\infty}P(t)=\frac{2t^2+75}{2t^2+150}=\frac{2(\infty)^2+75}{2(\infty)^2+150}=\frac{\infty}{\infty} \\ \lim _{t\to\infty}P(t)=\frac{4t}{4t}=1 \end{gathered}[/tex]Therefore, the long term population of the habitat is;
[tex]P(\infty)=1\text{ million}[/tex]The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
In this problem
Applying proportion
we have
4/10=x/28
solve for x
x=(4/10)*28
x=11.2
therefore
answer is 11 booksfor a function f(x)=x^2, write an equation for that function stretched vertically by a factor of 4, and shifted 2 units to the right
the initial function is:
[tex]f(x)=x^2[/tex]to stretch the fuction vertically we have to divide by 4 y so:
[tex]\begin{gathered} \frac{f(x)}{4}=x^2 \\ f(x)=4x^2 \end{gathered}[/tex]now to move two units to the right we have to rest 2 in the x so:
[tex]f(x)=4(x-2)^2[/tex]A boat is heading towards a lighthouse, whose beacon-light is 135 feet above the water. The boat's crew measures the angle of elevation to the beacon, 4 deg What is the ship's horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary .
The ship's horizontal distance from the lighthouse is: 1930.59 feet.
What is tangent or tan in trigonometry?
The ratio of the side opposite the angle we know or want to know over the side next to that angle is known as the tangent, which is sometimes abbreviated as T-A-N. The side touching the angle that is NOT the hypotenuse, or the side opposite the right angle, is the neighboring side.
Given in the question,
Height of lighthouse = 135 feet,
angle of elevation = 4 degree,
We know that, tan Θ = perpendicular/ base
Here, height is perpendicular and distance is base,
Putting the values,
tan4° = 135/B
B = 1930.59 feet
Therefore, distance is 1930.59 feet.
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Answer:The answer is 1930.59
Step-by-step explanation:
11.) SOLVE the equation for w by using "factoring by grouping". YOUMUST SHOW ALL STEPS of the grouping process, especially theFIRST STEP of grouping to receive FULL CREDIT. (10 pts)2w3 + 5w2 - 32w - 80 = 0
ANSWER:
w = -5/2, w = 4 and w = -4
STEP-BY-STEP EXPLANATION:
We have the following equiation:
[tex]2w^3+5w^2-32w-80=0[/tex]We solve with the help of factoring by grouping
[tex]\begin{gathered} (2w^3+5w^2)+(-32w-80)=0 \\ w^2\cdot(2w+5)-16\cdot(2w+5)=0 \\ (2w+5)\cdot(w^2-16)=0 \\ 2w+5=0\rightarrow w=-\frac{5}{2} \\ (w^2-16)=0\rightarrow w^2=16\rightarrow w=\pm4\rightarrow w=4,w=-4 \end{gathered}[/tex]The solutions are w = -5/2, w = 4 and w = -4