Answer:Q(2,-3)
Step-by-step explanation:
Find ST R. 12.5 x + 5 V 7.5 S X-5 T O A 25 B. 20 O C. 10 OD. 15
Here, we want to calculate the value of ST
To do this, we need to check for similar triangles
As we can see; we have similar triangles and thus, will use the bisector theorem
We have this as;
[tex]\begin{gathered} \frac{x-5}{x+5}\text{ = }\frac{7.5}{12.5} \\ \\ 12.5(x-5)\text{ = 7.5(x+5)} \\ 12.5x\text{ - 62.5 = 7.5x + 37.5} \\ 12.5x\text{ - 7.5x = 37.5 + 62.5} \\ 5x\text{ = 100} \\ x\text{ = }\frac{100}{5} \\ \text{ x = 20} \end{gathered}[/tex]But ST is x-5
Simply substitute the value of x in the expression
We have this as; 20-5 = 15
The question is in the photo. Complete the fourth one.
Question number 4
Given:
One side of a right-angled triangle 6 and the hypotenuse of the triangle 10
Required:
Another side of the triangle
Explanation:
For the right-angled triangle, Pythagorean theorem is applied which is
[tex]a^2+b^2=c^2[/tex]where
a=side of the right triangle
b=side of the right triangle
c=hypotenuse
so hypotenuse =
[tex]\sqrt{(10^2-6^2)}=8[/tex]Final Answer:
8
7x - 2xy + 9xy - 2x + 5Like terms
we have given Question is 7x-2xy+9xy+5
now we will rearrange it to like terms
7x-2x+9xy-2xy+5
we use simple addition and subtraction for like terms
5x+7xy+5
so here is the answer
5x+7xy+5
we can write it as below
5+5x+7xy=0
The 2017 Toyota Prius is EPA-rated at 54 mi/gal (miles per gallon) for city driving and 50 mi/gal for highway driving. The 2017 Toyota Yaris is rated at 30 mi/gal city and 36 mi/gal highway. How many gallons of gas, to the nearest tenth, would each vehicle consume for:(A) 300 mi of city driving plus 100 mi of highway driving.(B) 100 mi of city driving plus 300 mi of highway driving.
A) For 300 mi of city driving plus 100 mi of highway driving:
Toyota Prius will need
[tex]\frac{300\text{ mi}}{54\text{ mi/gal}}+\frac{100\text{ mi}}{50\text{ mi/gal}}=5.6\text{gal}+2\text{gal}=7.6\text{gal}[/tex]Toyota Yaris will need
[tex]\frac{300mi}{30\text{ mi/gal}}+\frac{100mi}{36\text{ mi/gal}}=10gal+2.8gal=12.8gal[/tex]B) For 100 mi of city driving plus 300 mi of highway driving:
Toyota Prius will need
[tex]\frac{100mi}{54\text{ mi/gal}}+\frac{300mi}{50\text{ mi/gal}}=1.9gal+6gal=7.9gal[/tex]Toyota Yaris will need
[tex]\frac{100mi}{30\text{ mi/gal}}+\frac{300mi}{36\text{ mi/gal}}=3.3gal+8.3gal=11.6\text{gal}[/tex]BRAINLIEST (statistics) (please help fast) The parallel dotplots below display the number of absences for students in each of two classes.
2 dotplots titled class absences. The number lines go from 0 to 10 and are labeled number of absences. Class D, 0, 7; 1, 11; 2, 4; 3, 3. Class C, 0, 8; 1, 10, 2, 4; 3, 1; 5, 1; 10, 1.
Which of the following statements is true?
The range for the distribution of the number of absences is larger for class D.
The range for the distribution of the number of absences is larger for class C.
The IQR for the distribution of the number of absences is larger for class D.
The IQR for the distribution of the number of absences is larger for class C.
The true statements are,
The range for the distribution of the number of absences is larger for
class D.
The IQR for the distribution of the number of absences is larger for class C.
What is IQR or interquartile range?The interquartile range serves as a gauge for where a data set's "middle fifty" lies. An interquartile range (IQR) measures where the majority of the values lay, whereas a range measures where a set's start and finish are.
Given, Are 2 dot plots titled class absences.
Arranging the data set For class D,
0, 1, 2, 3, 3, 4, 7, 11.
So, The range of the data set D is 11 - 0 = 11.
The IQR for the absences for class D is Q₃ - Q₁ = 7 - 1 = 6.
Arranging the data set For class C,
0, 1, 1, 1, 1, 2, 3, 4, 5, 8, 10, 10.
So, The range of the data set C is 10 - 0 = 10.
The IQR for the absences for class C is Q₃ - Q₁ = 8 - 1 = 7.
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Determine the check digit (d) for the UPC bar code number 2-91273-05213-d. Show your work?
the given UPC bar code digit is
2- 91273 - 05213 - d
for determining d we will follow the rule
first, we sum up all the odd place numbers
like
2 + 1 + 7 + 0 +2 + 3 = 15
then multiply with 3
15 * 3 = 45
then
we sum up all the even place numbers,
9 + 2 + 9 +5 + 1 = 26
now we will add these two results
26 + 45 = 71
now we can see that 71 is 9 less than the next multiple of 10 that is 80 in this case'
80 - 71 = 9
so the answer is
d = 9 .
Which of the following is a true stateme 3/4 < 4/6; 5/6 > 10/12; 8/16 = 1/4; 11/15 < 4/5
Answer:
11/15 < 4/5
Step-by-step explanation:
this is because:
3/4 < 4/6 is the same as 9/12 < 8/12 which is incorrect
5/6 > 10/12 is the same as 10/12 > 10/12 which is incorrect
8/16 = 1/4 is the same as 8/16 = 4/16 which is incorrect
therefore the only possible answer is 11/15 < 4/15 because:
it is the same as 11/15 < 12/15 which is CORRECT
What percent of 27 is 12?
Solution
For this case we can do the following procedure:
[tex]\frac{12}{27}\cdot100=44.4[/tex]then the answer is: 44.4%
Fill in the boxes with numbers and operations to reflect the equation of the circle after the transformations
Given the equation of the circle:
[tex]x^2+4x+y^2-12y=-24[/tex]We will complete the squares for x and y to write the equation of the circle as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h,k) is the coordinates of the circle and r is the radius of the circle
so, the equation will be:
[tex]\begin{gathered} (x^2+4x+4)+(y^2-12y+36)=-24+4+36 \\ \\ (x+2)^2+(y-6)^2=16 \\ \\ (x+2)^2+(y-6)^2=4^2 \end{gathered}[/tex]So, the radius of the circle = 4
And the center of the circle = ( -2, 6 )
Now, we will make the transformation for the circle:
Shift 1 unit up, the center will be = ( -2, 7 )
shift 2 units right, the center will be = ( 0, 7 )
Reflection across the x-axis, the center will be = ( 0, -7)
So, the equation of the circle after transformation will be:
[tex](x-0)^2+(y+7)^2=4^2[/tex]So, the answer will be:
[tex](x-0)^2+(y+7)^2=16[/tex]3y+12=-6 I need help please
3y + 12 = 6
subtrac 12 from both sides of the equation:
3y + 12 -12 = 6 -12
3y = -6
divide both sides by 3
3y/3 = -6/3
y= -2
Need help with this one. Instructions are: Determine whether the triangles are similar. If so, write a similarity statement. If not,what would be sufficient to prove the triangles similar? Explain your reasoning.
ANSWER :
Triangles UWY and UXZ are similar
EXPLANATION :
Two triangles are similar if the ratio of their corresponding sides is the same.
We can try UW/UX, WY/XZ, and UY/UZ
[tex]\begin{gathered} \frac{UW}{UX}=\frac{8}{8+3.2}=\frac{8}{11.2}\quad or\quad\frac{5}{7} \\ \\ \frac{WY}{XZ}=\frac{10}{14}=\frac{5}{7} \\ \\ \frac{UY}{UZ}=\frac{5}{5+2}=\frac{5}{7} \end{gathered}[/tex]Since the ratios are the same, then the triangles are similar.
Francesca leaves her home and Drive South 150 km. Then she drives West 70 km. At this point, she drives North 30 km. Finally, she drives east 20 km. How far is she from her home? Included diagram of her trip.
To find the distance between her home and her latest position:
According to the question, the diagram is,
Consider the right triangle,
AB=120 km
BC=50 km
To find AC:
Using Pythagoras theorem,
[tex]\begin{gathered} AC^2=AB^2+BC^2_{} \\ =120^2+50^2 \\ =14400+2500 \\ =16900 \\ =130\text{ km} \end{gathered}[/tex]Hence, the distance between the new position and her home is 130 km.
I need help please with math
Answer:
A = (1, 1i)
B = (-7, 3i)
C = (-4, -7i)
Step-by-step explanation:
Complex numbers makes the x axis the "real" axis and the y axis the "imaginary" axis. Therefore, your "y" coordinates will have an "i" attached to them to signify that they are imaginary.
Domain: 100, 200,300, 425, 575
Range: 100, 25, 200, 50, 75
Is this a function? Why or why not
Reason:
There aren't any repeated items in the domain. Each x input goes to exactly one y output. This is why we have a function.
The y values can repeat, but the function wouldn't be one-to-one (i.e. injective).
1.6) What is the solution to the system? x+3y = 5 5x-3y = 7
The given system of equations is expressed as
x + 3y = 5
5x - 3y = 7
The first step is to add both equations.
The tree diagram below shows the possible outcomes. Use the diagram to answer the questions
Outcomes are the possible pairings of crust and pizza that Heather can choose. Based on the tree diagram, we see that there are 12 possible pairings starting from (thin, onions) to (pan mushrooms). Hence, there are 12 outcomes.
Based on the list of outcomes, there is only 1 outcome in which both the regular crust and sausage are chosen.
Lastly, for pepperoni OR mushroom being chosen, let's take a look and count.
There are 6 outcomes in which pepperoni or mushrooms were chosen.
Evaluate e3.32 Round your answer to the nearest tenth, and do not include "e3.32 =" in your answer.
You would need a scientific calculator for this exercise.
On your calculator you simply enter the symbol e. (Please ensure your calculator has nothing on display before this)
After pressing the e button, you press the x raised to the power of y symbol and then input 3.32, as shown below;
[tex]\begin{gathered} e\text{ (step 1)} \\ x^y\text{ (step 2)} \\ 3.32(step\text{ 3)} \\ \text{This displays the result shown below;} \\ 27.66035055851675 \\ \text{Rounded to the nearest tenth;} \\ e^{3.32}=27.7 \end{gathered}[/tex]Please help me with my geometry
Answer:
m∠E = 52°
Step-by-step explanation:
You seem to want a step-by-step explanation of the logic to find the measure of angle E.
There are a number of approaches you might take to this. Here is one.
[tex]\begin{array}{ccc}\text{Step}&\text{Angle}&\text{Reason}\\1&m\angle C=64^\circ&\text{Given}\\2&m\angle ADE=64^\circ&\textsf{Corresponding angles}\\3&m\angle DAB=64^\circ&\textsf{Alternate interior angles}\\4& m\angle DAE=64^\circ& \textsf{Angle bisector de}\textsf{finition}\\5& m\angle E=52^\circ&\textsf{Sum of angles in a triangle}\end{array}[/tex]
The measure of angle E is 52°.
Find the value of r so the line that passes through each pair of points has the given slope.
(r, 7),(3, 4), m=−35
Answer: 102/35
Step-by-step explanation:
Substituting into the slope formula,
[tex]\frac{7-4}{r-3}=-35\\\\\frac{3}{r-3}=-35\\\\\frac{r-3}{3}=-\frac{1}{35}\\\\r-3=-\frac{3}{35}\\\\r=102/35[/tex]
The figure below can be used to prove the Pythagorean Theorem. Use the drop-down menusto complete the proof.aababClick the arrows to choose an answer from each menu.The expression Choose... represents the area of the figure as the sum of the area of theshaded triangles and the area of the white square.The equivalent expressions Choose...use the length of the figure torepresent the area.Setting two of these area expressions equal to each other and subtracting Choose...from both sides of the equation results in the Pythagorean Theorem, a? + b2 = c?.
2ab + c²
(a+b)² and a² + 2ab + b²
2ab
1) Examining that picture, we can state the following about that:
The shaded triangles area:
[tex]\frac{1}{2}ab\text{ +}\frac{1}{2}ab+\frac{1}{2}ab+\frac{1}{2}ab=2ab[/tex]Note that the area of the triangle is 1/2 the product of the base by its height.
The area of that white inner square is given by c² since the Area of a square is equal to the side length raised to the 2nd powe.
2) Then
The expression 2ab + c² represents the area...
The equivalent expressions (a+b)² and a² + 2ab + b² use the length of the figure (a square) raised to the 2nd power. As explained above.
For the last statement let's calculate it:
2ab + c² = (a+b)²
a² +2ab + b² = 2ab +c² Subtracting 2ab
a² +b² = c²
3) Hence, the answers are:
2ab + c²
(a+b)² and a² + 2ab + b²
2ab
d. Henrich has $195,000 of taxable income, which includes $50,000 of long-term capital gain that is taxed at preferential rates.
Assume his modified AGI is $210,000.
Income tax
Net investment income tax
Total tax liability
$
Amount
0.00
Net Income tax payable $41,516.75 (f + g)
As per the data are given in the above question it is given that,
Henrich has $195,000 of taxable income,
i.e. Taxable Income (a) $195,000
Which includes $50,000 of long-term capital gain that is taxed at preferential rates.
i.e. Preferentially taxed income (b) $50,000
Assume his modified AGI is $210,000.
Therefore Income taxed at ordinary rates ( c) $145,000
Tax on c above (d) $33,636.75 = $18,558.75 + [($145,000 - $91,150) x 28%]
Tax on b above ( e) $7,500.00 = $50,000 x 15%
Total Income tax (f) $41,136.75 (d + e)
Investment Income, if any (g) $380 Only $10,000 is taxed at 3.8%, only ($210,000 - $200,000) i.e. $10,000
Net Income tax payable $41,516.75 (f + g)
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17. You divide 5 1/2 cups of juice evenly among 6 glasses. How much juice is in each glass?
Answer:
11/12
Step-by-step explanation:
hopes this helps, I am sorry if I am wrong
5 1/2 ÷ 6
11/2 ÷ 6
11/2 × 1/6
11/12
The number of bank robberies that occur in Lagos is modeled to be Poisson distributed with mean of 1.8 per day. Find the probability of getting exactly three robberies in a day.
The Poisson distribution is a discrete distribution that calculates the likelihood that a certain number of events will occur within a certain amount of time.
The probability of getting exactly three robberies in a day is 0.1607.
What is meant by poison distribution?The Poisson distribution is a discrete probability distribution used in probability theory and statistics to express the likelihood that a given number of events will occur within a specified time or space interval if they occur at a known constant mean rate and regardless of the interval since the last event.
The Poisson distribution is a discrete distribution that calculates the likelihood that a certain number of events will occur within a certain amount of time.
In the poison distribution a discrete random variable X has the following probability mass function,
[tex]$P(X=x)=\frac{e^{-\lambda} \cdot \lambda^x}{x !}$[/tex], where [tex]$\lambda$[/tex] is the mean of the distribution and [tex]$x=0,1,2,3 \ldots \ldots$[/tex]
Given that [tex]$\lambda=1.8$[/tex]
The required probability, [tex]$P(X=3)=\frac{e^{-1.8} .(1.8)^3}{3 !}=0.1607$[/tex]
Therefore, the probability of getting exactly three robberies in a day is = 0.1607.
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The sphere at the right fits snugly inside a cube with 4-in. edges. What is the approximate volume of the space between the sphere and cube?
As given by the question
There are given that the inside edge is 4 in.
Now,
Since sphere fits snugly inside a cube therefore diameter of sphere will be equal to side of the cube
So,
[tex]\begin{gathered} \text{diameter}=4\text{ inches} \\ \text{radius}=\frac{dameter}{2} \\ \text{radius}=\frac{4}{2} \\ \text{radius}=2 \end{gathered}[/tex]Then,
Volume of the sphere is given by:
[tex]\begin{gathered} \frac{4}{3}\times\pi\times r^3=\frac{4}{3}\times3.14\times2^3 \\ =\frac{4}{3}\times3.14\times8 \\ =33.5 \end{gathered}[/tex]And,
The volume of a cube is:
[tex]\begin{gathered} \text{Volume of cube=side}\times side\times side \\ =4\times4\times4 \\ =64\text{ inches} \end{gathered}[/tex]Then,
The volume of the space between the sphere and cube = 64-33.5 = 30.5.
Hence, the answer is 30.5 cube inches.
Find the area of the triangle 4 m 7 m The area of the triangle is v (Type a whole number.)
Find the area of the triangle;
[tex]\begin{gathered} \text{Area}=\frac{1}{2}bh \\ b=\text{base (7)} \\ h=\text{vertical height (4)} \\ A=\frac{1}{2}\times7\times4 \\ A=\frac{1}{2}\times28 \\ A=14 \end{gathered}[/tex]The area of the triangle is 14 square units
**Please Note; The instruction is to type in a whole number, so you may exclude "Square Units" from your answer
Last week, a share stock gained a total of 1.64 points. Express this gain as a mixed number in simplest form.
Answer: [tex]1\frac{16}{25}[/tex]
Step-by-step explanation:
1.64 is 1 64/100. Now to get the simplest form find a number you can divide both the numerator and the denominator by, like 4. Now you have 1 16/25. 16 and 25 do not have a common number you can divide both by so it is the simplest form.
for a circle with a diameter of 4 centimeters, what is its exact area?
Solution
The area of a circle with diameter d is
[tex]\begin{gathered} A=\pi(\frac{d}{2})^2 \\ \\ A=\pi(\frac{4}{2})^2 \\ \\ A=4\pi \end{gathered}[/tex]Therefore, the exact area is 4π centimeters square.
Miguel mixes plant food with water to feed his plants. The instructions on the
plant food say to mix 1 teaspoon of plant food into every 4 cups of water.
b. How much plant food should Miguel add to 7 cups of water? Use a model to show your work
The plant food should Miguel add to 7 cups of water is 336 plant food
What is Algebra?
One of the many different mathematical disciplines is algebra. Algebra, a common thread that runs through nearly all of mathematics, is the study of mathematical symbols and the rules for using them in formulas.
To feed his plants, Miguel combines water and plant food. According to the directions on the plant food, you should add 1 teaspoon to every 4 cups of water. To demonstrate the relationship between cups of water (w) and teaspoons of plant food (f), create an equation.
48 teaspoons = 1 cup.
1 teaspoon = plants food
4 cups = water.
= 48 teaspoons x 4.
= 192 teaspoons
The formula is:
water in cups = w
Teaspoon of nourishment for plants equals f
The mixture = 192w + f
The relation between f and w is f = kw.
1 teaspoon = plant food
7 cups = water.
= 48teaspoon x 7
= 336teaspoon
The formula is:
water in cups = w
Teaspoon of nourishment for plants equals f
The mixture = 336w + f
Hence, 336 plant food should Miguel add to 7 cups of work
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4. Select all systems that are equivalent to this system: {
6d+4.5e = 16.5
45d +4.5e = 4
^{
${
B.
<{
D.
{
{
E.
F.
30d +22.5e 82.5
5d + 0.5e = 4
30d +22.5e 82.5
30d +
3e = 24
f6d+4.5e
16.5
6d+0.6e = 4.8
12d + 9e = 33
10d + 0.5e = 8
6d+4.5e = 16.5
11d + 5e = 20.5
6d+4.5e = 16.5
Sd+0.5e = 4
The system that are equivalent to the system
6d+4.5e = 16.5
45d +4.5e = 4 are
30d +22.5e= 82.5
5d + 0.5e = 4,
30d +22.5e 82.5
30d +3e = 24 and
6d+4.5e=16.5
6d+0.6e = 4.8
What is substitution method?
Substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
In equation two,
30d +22.5e= 82.5
5d + 0.5e = 4
5(6d + 4.5e) = 5 (16.5)
5d + 0.5e = 4
similarly, the equation 3
5(6d +4.5e) = 5(16.5)
6(5d + 0.5e) = 6(4)
Similarly, the equation 4
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4) How many solutions does the system of linearequations have?2x + 3y = 6-8x - 12y = -20image
Answer
Explanation
To know how many solutions this system of linear equations have, we willl need to solve it.
2x + 3y = 6
-8x - 12y = -20
Making x the subject of formula in the first equation
2x + 3y = 6
2x = -3y + 6
Divide through by 2
(2x/2) = (-3y/2) + (6/2)
x = (-3y/2) + 3
Substituting this for x in the second equation
-8x - 12y = -20
x = (-3y/2) + 3
-8 (-3
