Answer: (1, 2)
Step-by-step explanation:
y = -x² + x + 2
y = -x + 3
1. Set the two equations equal to each other:
-x² + x + 2 = -x + 3
2. move one of the equations to the other side:
-x² + 2x - 1
3. Factor out a -1:
-1 (-x² + 2x - 1) = 0
x² - 2x + 1
4. Factor:
(x - 1)(x - 1)
x = 1
5. Plug in 1 to one of the equations:
y = -x + 3
y = -(1) + 3
y = 2
6. Write as coordinates:
(1, 2)
(05.07) A square pyramid is shown. What is the surface area?
A square based pyramid, with bases labeled 3.5 centimeters and side length of triangle labeled 7 centimeters.
19.25 cm2
30.625 cm2
49.625 cm2
61.25 cm2
The surface area of the square based pyramid is 61.25 centimetre square
How to find the surface area of a square base pyramid?surface area of the pyramid = A + 1 /2 ps
where
A = area of the base
p = perimeter of the base
s = slant height
Therefore,
A = 3.5² = 12.25 cm²
p = 4(3.5) = 14 cm
s = 7 cm
Therefore,
surface area of the pyramid = 12.25 + 1 /2 × 14 × 7
surface area of the pyramid = 61.25 cm²
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which is a solution to x - 3x + 9 equals negative 27
Answer:
x = 18
Step-by-step explanation:
[tex]\sf x - 3x+9= - 27[/tex]
Let's first combine like terms.
[tex] \sf - 2x+9= - 27[/tex]
Subtract 9 from both sides.
[tex]\sf - 2x= - 27 - 9[/tex]
[tex] \sf - 2x= - 36[/tex]
Divide both sides by −2.
[tex]\sf x=18[/tex]
Decide whether you have enough information to determine that the triangles are congruent. If they are congruent, explain why.
Pls ingore all of the questions below, but help me with the attached image
What is the only number that has the same number of letters as it's meaning? ...
What number doesn't have its own Roman numeral? ...
What is the only even prime number? ...
What is the smallest perfect number? ...
What is our current numerical system based on? ...
Is Pi a rational or irrational number?
Answer:
t = 110°
Step-by-step explanation:
Triangle BCD is isosceles, so its base angles are congruent. This means m<CBD = m<CDB. Since m<CBD is 35, m<CDB is also 35.
The sum of angles in a triangle is 180, so the following equation can be written:
180 = m<CBD + m<CDB + m<BCD
We can substitute m<CBD and m<CDB with 35 and m<BCD with t and solve:
[tex]180 = 35 + 35+ t\\180=70+t\\t=110[/tex]
So t = 110°
Which part of a story shows how the climax affected the characters?
Falling action
Rising action
Exposition
Resolution
Answer:
Falling action
Step-by-step explanation:
Falling action in a basic plot structure is the events that happen after the climax and before the resolution. This part of your story is often used to show the consequences of the climax and how it affects the characters.
HELP PLEASE ITS DUE TOMMOROW
Answer:
Hope the picture will help you...............
WILL MARK BRAINLIEST The amount (A) that principal (P) will be worth after t years at interest rate (r) compounded annually is
A = P(1 + r)
t
Suppose $6,000 is invested at 5.5% and yields a total of $7,255. How many years was it invested?
Put in the formula
[tex]\\ \rm\Rrightarrow A=P(1+r)^t[/tex]
[tex]\\ \rm\Rrightarrow 7255=6000(1+0.055)^t[/tex]
[tex]\\ \rm\Rrightarrow 1.20917=(1.055)^t[/tex]
[tex]\\ \rm\Rrightarrow ln1.20917=tln1.055[/tex]
[tex]\\ \rm\Rrightarrow t=\dfrac{ln1.20917}{ln1.055}[/tex]
[tex]\\ \rm\Rrightarrow t=3.5years[/tex]
Answer:
4 years (nearest year) or
3.5 years (nearest tenth) or
3 years, 6 months and 17 days (most accurate)
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
A = $7,255P = $6,000r = 5.5% = 0.055Substitute the given values into the formula and solve for t:
[tex]\implies \sf 7255=6000(1+0.055)^t[/tex]
[tex]\implies \sf 7255=6000(1.055)^t[/tex]
[tex]\implies \sf \dfrac{7255}{6000}=(1.055)^t[/tex]
Take natural logs of both sides:
[tex]\implies \sf \ln \left(\dfrac{7255}{6000}\right)= \ln (1.055)^t[/tex]
[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\implies \sf \ln \left(\dfrac{7255}{6000}\right)= t\ln (1.055)[/tex]
[tex]\implies \sf t=\dfrac{\ln \left(\dfrac{7255}{6000}\right)}{\ln (1.055)}[/tex]
[tex]\sf \implies t=3.547416819...[/tex]
Therefore, the number of years the principal was invested is:
4 years (nearest year)3.5 years (nearest tenth)3 years, 6 months and 17 daysLearn more about compound interest here:
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What is the height of the trapezoid?
Answer:
11 units
Step-by-step explanation:
The height of a trapezoid is the distance between the parallel bases.
__
Here, one base lies on the horizontal line y=5, and the other lies on the horizontal line y = -6. The distance between them is ...
5 -(-6) = 5 +6 = 11
You can also find this distance by counting the grid squares between the two parallel lines.
The height of the trapezoid is 11 units.
_____
Additional comment
The base lengths are ...
AB = 2 -(-5) = 7
CD = 8 -(-7) = 15
The area is 1/2(b1 +b2)h = (1/2)(7 +15)(11) = 121 square units.
the perimeter of a rectangle is 26 and the area is 30. what are the dimensions of the rectangle ?
Answer:
Step-by-step explanation:
Can someone explain how to solve this I’m confused
Answer:
x = 61°
Step-by-step explanation:
(2x + 3)°+ (x - 6)° = 180°
2x + x + 3 - 6 = 180°
3x - 3 = 180°
3x = 180° + 3
3x = 183°
x = 183°/3
x = 61°
Write a sine function that has an amplitude of 5, a midline of 4 and a period of
4
Answer:
See below
Step-by-step explanation:
Start with sin x
amplitude of 5
5 sin x
midline 4
5 sin (x) + 4
period of 4
2 pi / 4 = pi/2
5 sin ( x pi/2 ) + 4
Type the correct answer in each box.
A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is ____? units. The point (-7, __?) lies on this circle.
Answer:
the answer is 5 and (-7,5)
Step-by-step explanation:
The radius is 5, and the points (-7, 5) and (-7, -1) both lie on the circle.
Given that:
The points at which the circle is centered are (-3,2)
Passing points = (1,5)
The radius is calculated using the distance formula:
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]
Substituting the coordinates, we have:
d =[tex]\sqrt{({1 - (-3))^2 + (5 - 2)^2[/tex]
= [tex]\sqrt{(1 + 3)^2 + (5 - 2)^2[/tex]
=[tex]\sqrt{(4^2 + 3^2)[/tex]
= [tex]\sqrt{(16 + 9)[/tex]
= 5
Therefore, the radius of the circle is 5 units.
The equation of a circle with center (h, k) and radius r is given by:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Substituting the values, we have:
[tex][-7 - (-3)]^2 + (y - 2)^2 = 5^2[/tex]
[tex](-7 + 3)^2 + (y - 2)^2 = 25[/tex]
[tex](-4)^2 + (y - 2)^2 = 25[/tex]
[tex]16 + (y - 2)^2 = 25[/tex]
[tex](y - 2)^2 = 9[/tex]
Taking the square root of both sides, we have:
y - 2 = ±3
Solving for y, we have two possible values:
y - 2 = 3
y = 5
y - 2 = -3
y = -1
The points (-7, 5) and (-7, -1) both lie on the circle.
Thus, the radius is 5, and the points (-7, 5) and (-7, -1) both lie on the circle.
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4. Make a table and graph the function. (1 point)
y = 4x + 2
4) Carlo finished answering his homework at 7:20 p.m. If he started at 6:50 p.m., how many minutes did he spend in answering his homework?
a. What is asked?
b. What are given?
c. What is/are the operation/s to be used?
d. What is the number sentence?
e. What is the answer?
Answer:
a. the time spent answering homework
b. time finished and time started
c. subtraction
d. 7:20-6:50 (unsure how this is supposed to be laid out)
e. Carlo spent 30 minutes answering his homework
Pedro is sailing his boat and maps his route on a coordinate plane. He starts at the origin and then sails 1.2 kilometers west, 1.5 kilometers south, 2 kilometers west again, and 2.8 kilometers north.
Pedro's total distance moved is 7.5 kilometers
How to determine the total distance?The given parameters are:
West = 1.2 kilometersSouth = 1.5 kilometers West = 2 kilometersNorth = 2.8 kilometersThe total distance is the sum of the above distances i.e.
Total = 1.2 km + 1.5 km + 2 km + 2.8 km
Evaluate
Total = 7.5 km
Hence, Pedro's total distance moved is 7.5 kilometers
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If the temperature today is 3 more than twice what it was yesterday and the temperature today is 66, what was the temperature yesterday?
Using algebra to solve this problem, which of the following is one step that you will take?
Step-by-step explanation:
x is the temperature yesterday
Answer:
Step-by-step explanation:
The correct answer is
Write the equation 66=2y+3.
What is the length of the hypotenuse?
Answer:
Step-by-step explanation:
First things first, let's explain what a right triangle is. The definition is very simple and might even seem obvious for those who already know it: a right-angled triangle is a triangle where one and only one of the angles is exactly 90°. The other two angles will clearly be smaller than the right angle because the sum of all angles in a triangle is always 180°. In a right angled triangle the sides are defined in a special way. The side opposing the right angle is always the biggest in the triangle and receives the name of "hypotenuse". The other two sides are called catheti. The hypotenuse is opposite the right angle and can be solved by using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c, Pythagoras' theorem states that: a² + b² = c².
To solve for c, take the square root of both sides to get c = √(b²+a²). This extension of the Pythagorean theorem can be considered as a "hypotenuse formula".
Steps to solve:
[tex]c=\sqrt{a^{2} +b^{2} } \\c=\sqrt{1.3^{2} +6.1^{2} } \\c=\sqrt{1.69+37.21} \\c=\sqrt{38.9} \\c=6.236986[/tex]
Simplify 5(xy+z)-2xy.
Answer:
3xy+5z
Step-by-step explanation:
5(xy+z)-2xy
=5xy+5z-2xy
3xy+5z
Sam Bought a shirt for $27 after a discount, He said he bought the shirt at a 10% discount, What was the original selling price of the shirt?
Answer:$37.00
Step-by-step explanation: hope it helps
is 300 greater than 8/9?
Answer:
yes.
Step-by-step explanation:
300>8/9
300>0.888888889
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Is 300 greater than 8/9?
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
Yes, 300 is greater than [tex]\bold{\dfrac{8}{9}}[/tex].
Remember, proper fractions (fractions with a numerator less than the denominator) are less than 1.
When comparing an integer (like 300) with a fraction (like 8/9), first you need to work out whether or not the fraction is a proper fraction.
Then, you also need to pay attention to the signs, because they may seem trivial, but they are in fact highly significant.
Therefore,
300>8/9 (300 is definitely greater than a number less than 1, right?)
(and the ">" sign means "greater than"
Good luck with your studies.[tex]\rule{200}{2}[/tex]
A. On place 20000 f à intérêt composé au taux annuel t%. Au
bout d'un an on complète par un dépôt de 20000 f. Un an
après ce nouveau placement on retire la totalité soit :
44298 f. Calculer le taux t.
Answer:
Step-by-step explanation: Après un an on a 20000(1+t%)+20000
Après 2 ans on a 20000(1+t%)^2+20000(1+t%)^1=44298
On a donc 20000[(1+t%)^2+(1+t%)^1]=44298
En résolvant l’équation de second degré dans R, on obtient : t = 7%
3. Mick recorded the rainfall, in inches, each day for the last 8 days. What is the difference between the most amount of rainfall and the least amount of rainfall?
Answer: 2 inches
At 8 days there will be 8/4 = 2
Difference = 2 - 0 = 2 inches
in a hostel of 400 students, it was discovered that 70% like to drink tea and 60% like to drink coffee . if 10% students didn't like to drink tea or coffee , represent the information in a venn-diagram and find the number of students who like 1)coffee only,tea, bothtea and coffee ,neither tea nor coffee
Of the 400 students, 120 students like to drink coffee, 80 students like to drink tea, 160 students like both and 40 students do not like any of these drinks.
How many students like to drink coffee, tea, or none?Cofee: 70% of 400 = 280 students
Tea: 60% of 400 = 240 students
None: 10% of 400= 40 students
This means that 360 students like coffee, tea or both.
How many students like both drinks?280 + 240 (students who drink either coffe or tea)= 520 - 360 (real number of students who like coffee or tea) = 160 (students who like both coffee and tea.
Moreover, it can be inferred 80 students like tea and 120 studetns like coffee.
How to represented it in a Venn diagram?Set A: Students who like coffee 120 students.Set B: Students who like tea 80 students.Set A^B: Students who ike both drinks 160 studentsOutside the sets 40 students who do not like any of the drinks.
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Which is not a reason an athlete uses technology to assess performance?
A. To monitor development.
B. To tailor to their training program.
C. To send to college recruiters.
D. To analyze technique.
The reason for which an athlete does not use technology to assess performance is To send to college recruiters.
What is technology?Technology is the culmination of collected knowledge and the application of skills, methods, and procedures utilized in manufacturing and scientific research. Technology is incorporated into the functioning of all machinery, with or without a thorough understanding of its function, for an organization's stated purpose.
The reason for which an athlete does not use technology to assess performance is To send to college recruiters.
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In November 2005, an international study to assess public opinion on the treatment of suspected terrorists was conducted (“Most in U.S., Britain, S. Korea, and France Say Torture is OK in at Least Rare Instances,” Associated Press, December 7, 2005). Each individual in random samples of 1000 adults from each of 9 different countries was asked the following question: “Do you feel the use of torture against suspected terrorists to obtain information about terrorism activities is justified?” Responses from Italy, Spain, France, the United States, and South Korea are summarized in the table below. Based on these data, is it reasonable to conclude that the response proportions are not the same for all five countries? Use a = 0.01 to test the appropriate hypotheses.
Based on the responses, the significance level, and the p-value, we can conclude that the response proportions are not the same for the countries.
What can be concluded about the response proportions for these countries?The null hypothesis is that the response proportions are the same. The alternate hypothesis is that the response proportions are not the same.
The sample size is large enough for a Chi-Square test to be used because the expected counts are all greater than 5.
Running a Chi-Square analysis shows that the P-value to be 0.000.
The P-Value is less than the significance level of 0.01 so the null hypothesis is rejected. This means that the alternate hypothesis of the response proportions not being the same is true.
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What is the approximate area of the shaded sector in the circle shown below?
100°
c
18 cm
O A. 31.4 cm2 O B. 565 cm O C. 15.7 cm O D. 283 cm2
Answer:
C
Step-by-step explanation:
Formula to get the area
A = r^2π
A = 16^2π
A= 804.24 cm^2
As per the given data, the approximate area of the shaded sector is 283 square cm, which is option D.
What is area?Area is a measure of the amount of space inside a two-dimensional shape or a flat surface. It is typically measured in square units, such as square meters or square feet.
To find the area of the shaded sector, we need to first find the area of the whole circle, and then multiply it by the fraction of the circle that is shaded.
The area of a circle is given by the formula:
A = [tex]\pi r^2[/tex]
Where r is the radius of the circle. In this case, we are given that the radius of the circle is 18 cm, so we can substitute this value into the formula:
A = [tex]\pi 18^2[/tex]
A = 324π
So, the area of the whole circle is 324π square cm.
The shaded sector has a central angle of 100 degrees, which is a fraction of the total central angle of 360 degrees. So, the fraction of the circle that is shaded is:
100° / 360° = 5/18
Therefore, the area of the shaded sector is:
A = (5/18) * 324π
A = 90π
Using 3.14 as an approximation for π, we get:
A ≈ 90 * 3.14
A ≈ 283
Thus, the approximate area of the shaded sector is 283 square cm, which is option D.
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what is "the power" of something (mathematically).
The power of a number says how many times to use the number in a multiplication.
--
For instance 6 to the power of 2
This means
6²Which is also equal to 36
what is the volume of a cylinder, in cubic feet, with a height of 8 feet and a base diameter of 18 Round to the nearest place
The sum of four consecutive even numbers is 60. Find the smallest of the four number.
Answer:
answer = 12
Step-by-step explanation:
Let the smallest number be x
So
X+(x+2)+(x+4)+(x+6)=60
4x+12=60
4x=48
X=12
Please solve with explanation (high points)
Both ∠AKL and ∠AKC have a value of 45 degrees. The rationale is that the regular polygons BKLC (rectangle) and ABCD are bisected by lines AK and KC respectively. Since the sum of angles in a right angle is 90°, thus half of that is 45°.
What is a regular polygon?A regular polygon is a polygon that has two dimensions and can be made or drawn using at least three lines joined together.
Because, the sum of angles in a right angle is 90° and half of that is 45°, we can thus conclude that the values of ∠AKL and ∠AKC are both 45° each.
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