Therefore, the answer is:
b. 2 and 3
The diagram below shows a pennant in the shape of an isosceles triangle. The equal sides each measure 13, the altitude is x+7, and the base is 2x. 13 x + 7 2x 13 What is the length of the base? Your answer
we have that
the altitude divide the isosceles triangle into two congruent right triangles
so
Applying the Pythagorean Theorem
(x+7)^2=13^2+x^2
solve for x
x^2+14x+49=169+x^2
simplify
14x+49=169
14x=169-49
14x=120
x=120/14
simplify
x=60/7
Find the length of the base
2x=2(60/7)=120/7
answer is 120/7 unitsThe height of a triangle is 3 feet less than the base. The area of the triangle is 230 square feet. Find the length of the baseand the height of the triangle,
Let b be the base of the traingle
Let h be the height of the triangle
The height of a triangle is 3 feet less than the base:
[tex]h=b-3[/tex]The area of the triangle is 230 square feet.
The area of a triangle is:
[tex]A=\frac{1}{2}(b\cdot h)[/tex]For the given triangle:
[tex]\begin{gathered} A=\frac{1}{2}(b\cdot(b-3)) \\ \\ 230=\frac{1}{2}(b\cdot(b-3)) \end{gathered}[/tex]Solve b in the equation above:
[tex]\begin{gathered} 230=\frac{b^2-3b}{2} \\ \\ 2\cdot230=b^2-3b \\ \\ 460=b^2-3b \\ \\ b^2-3b-460=0 \end{gathered}[/tex]Use the quadratic formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} b=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(1)(-460)}}{2(1)} \\ \\ b=\frac{3\pm\sqrt[]{9+1840}}{2} \\ \\ b=\frac{3\pm\sqrt[]{1849}}{2} \\ \\ b=\frac{3\pm43}{2} \\ \\ b_1=\frac{3+43}{2}=\frac{46}{2}=23 \\ \\ b_2=\frac{3-43}{2}=-\frac{40}{2}=-20 \end{gathered}[/tex]As the length of the base cannot be a negative quantity you use the solution 1.
The base of the triangle is 23ft
Use the value of b to find the heigth:
[tex]\begin{gathered} h=b-3 \\ h=23-3 \\ h=20 \end{gathered}[/tex]Then, the given triangle has the next dimensions:base: 23ftheight: 20ftThe area a of a circle is pi times the radius R squared as an equation
Answer:
pi r squared
Step-by-step explanation:
A=pir2
pi is 3.14
hope it helps
Which exponential function models this situation ?
Exponential function models is v(x) = 9,000(0.9)ˣ
Lets take two year data (0,9000) and (1,8100)
using the general form of exponential function y = abˣ and substitute value of x and y as (0,9000)
9000 = ab⁰
9000 = a.1
9000 = a
Again using general form of exponential function and taking x and y as (1 , 8100)
8100 = ab¹
substitute a = 9000 in above equation
8100 = 9000×b
b = 8100/9000
b=0.9
putting value of a and b in general form of exponential function
v(x) = 9000(0.9)ˣ is required exponential function model
correct answer is option B
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What is the missing value in the proportion 4/4=x/30 A.6B.24C.37.5D.29
Answer
x = 30
Explanation
We need to find the value of x in the proportion
[tex]\begin{gathered} \frac{4}{4}=\frac{x}{30} \\ \text{Cross multiply} \\ 4x=120 \\ \text{Divide both sides by 4} \\ \frac{4x}{4}=\frac{120}{4} \\ x=30 \end{gathered}[/tex]Hope this Helps!!!
You have 400000 saved for retirement. your account earns 7% interest. how much will you be able to pull out each month if you want withdraws for 25 years
Answer:
$1,426.7
Step-by-step explanation:
Let's say the unit currency is dollars
$400,000
7% of $400,000
= $28,000
400,000 + 28,000
= $428,000
For 25 years,
= 25 × 12
= 300
$428,000/300
= $1,426.7
~ $1,427
What is the equation of the line that passes through the point (-8,-8)(−8,−8) and has a slope of 22?
The slope intercept form of the required line is 2x - y = -8
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Slope of the line = 2
The line passes through (-8, -8)
Equation of the required line-
[tex]y - (-8)= 2(x - (-8))\\y + 8 = 2(x + 8)\\y + 8 = 2x + 16\\2x - y = 8 -16\\2x - y = -8[/tex]
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Can I get some help on this please?Options 1: reflection accross the y-axis, 90 degree counterclockwise rotation about the point a, 90 degree clockwise rotation about the point a, 90 degree counterclockwise rotation about point bOptions 2: clockwise rotation about point b and a translation 20 units down, reflection across the y-axis and 20 units down, reflection across the x-axis and 15 units down, reflection across the y-axis and 25 units down
Answer:
The sequence of transformation that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a 90 degrees counterclockwise rotation about point A followed by reflection across the y-axis and a translation of 20 units down.
Explanation:
The sequence of transformations are described in the following figure:
Therefore, the first transformation is a rotation of 90 degrees counterclockwise about point A. After that transformation, we get the figure A'B'C'D'
Then, we reflect the figure across the y axis, so we get A''B''C''D''
Finally, we translate the figure 20 units down to get GHIJ
So, the answers are:
The sequence of transformation that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a 90 degrees counterclockwise rotation about point A followed by reflection across the y-axis and a translation of 20 units down.
Sydney measured a line to be 4.9 inches long. If the actual length of the line is 5.2 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
The percent error of the measurement will be 5.8%.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Sydney measured a line to be 4.9 inches long.
And, The actual length of the line is 5.2 inches.
Now,
The percent error is calculated as;
The difference between the measures = 5.2 - 4.9
= 0.3 inches
So, The percent error = 0.3/5.2 x 100
= 5.76%
Thus, The percent error of the measurement to the nearest tenth of a percent will be 5.8%.
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Ethanol fuel mixtures have "E" numbers that indicate the percentage of ethanol in the mixture by volume. For example, E10 is a mixture of 10% ethanol and 90% gasoline. How much E7 should be mixed with 4000 gal of E10 to make an E9 mixture?
We have to blend two mixtures of ethanol (E7 and E10) to make an E9 mixture.
We know that the amount of E10 mixture is 4000 gal.
Let x be the amount of E7 mixture.
As we have x gallons of E7 and 4000 gallons of E10, the volume of the E9 mixture will be (x+4000).
The volume of ethanol in the E7 mixture will be 0.07*x gallons.
The volume of ethanol in the E10 mixture is 0.1*4000 = 400 gallons.
The volume of ethanol in the E9 mixture will be 0.09*(x+4000) gallons.
As the sum of the ethanol volume in the E7 and E10 mixtures has to be equal to the ethanol in the E9 mixture, we can write:
[tex]0.07\cdot x+0.1\cdot4000=0.09\cdot(x+4000)[/tex]We can use this equation to solve for x:
[tex]\begin{gathered} 0.07\cdot x+0.1\cdot4000=0.09\cdot(x+4000) \\ 0.07x+400=0.09x+0.09\cdot4000 \\ 0.07x+400=0.09x+360 \\ 0.07x-0.09x=360-400 \\ -0.02x=-40 \\ x=\frac{40}{0.02} \\ x=2000 \end{gathered}[/tex]Then, the volume of the E7 mixture has to be 2000 gallons.
Answer: 2000 gallons of E7 mixture.
What is the sum of -12, 5, and -10?
0-27
0-17
O 17
O 27
Answer:
The answer is -17
Step-by-step explanation:
Add all the numbers together:
-12-10 is -22
Then -22+5= -17
Please help fast f(x) = 4x2 - 2x + 4 Find f(-9)
Answer:
346
Step-by-step explanation:
substitute the -9 for the x and solve. you will get 346 that will be the function of -9 for this equation
Just help with the problem and do it quickly please
SOLUTION
In 2020 black engineers under 30 is 70% of 500, which is
[tex]\frac{70}{100}\times500=350[/tex]In 2021 500 members joined making a total of 1000 members.
The black engineers together are now 50% of 1000, which is 500
So the numbers of black engineers that joined in 2021 becomes
[tex]500-350=150[/tex]Hence the answer is 150
Porch areas of successful sales are given below decide what study uses population in Parameter
Remember that a population parameter is a number that describes something about an entire group or population.
The only study that states a conclusion about an entire group or population is the one in the first option.
Answer: Option 1
it takes james 15 minutes to cut a log into 4 pieces. find how long it will take him to cut a log into 15 pieces.
It will take 56.25 minutes to cut the log into 15 pieces.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, James takes 15 minutes to cut the log into 4 pieces, which can be represented by:
4 pieces = 15 minutes
1 piece = 15/4 minutes
15 pieces = (15/4)×15 minutes
15 pieces = 56.25
Hence, it will take 56.25 minutes to cut the log into 15 pieces.
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Determine if each expression is equal to (2) (-3) (-4)(6) (-4)(-3) (8)(12) (2)(-4) (-6)
The product of the numbers (2) (-3) (-4) is:
[tex]2\times-3\times-4=24[/tex]By verifying the options one after the other, to check which is also equal to 24, we have:
[tex](6)(-4)=-24[/tex][tex](-3)(8)=-24[/tex][tex](12)(2)=24[/tex][tex](-4)(-6)=24[/tex]Hence, the correct options are C and D
What is the slope of the line shown?
A. slope = 3
B.slope = 12
C. slope = 2
D. slope = -3
The slope of the line shown is 0.5 .
How to find the slope of a given line?
For a line passing through the points (x₁, y₁) and (x₂, y₂), the slope for the same can be defined with the mathematical value of m i.e.,
m = (y₂ - y₁)/(x₂ - x₁)
Given, the line in picture passes through the points (0, -3) and (6, 0).
Following the formula established in the literature above, the given line has slope as m, which is:
m = (y₂ - y₁)/(x₂ - x₁) = (0 - (-3))/(6 - 0) = 3/6 = 0.5
Thus, the slope of the given line in question is 0.5 .
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.
Tyler owns a food truck that sells chicken wings and hamburger sliders. Each order of
chicken wings sells for $7.25-while each order of hamburger sliders sells for $3. On
Friday, Tyler made a total of $595 in revenue from all sliders and wings-sales. There
were twice as many chicken wing orders sold than there were sliders sold.
The number of chicken wing orders is 90 and the number of sliders is 45.
According to the question,
We have the following information:
Each order of chicken wings sells for $7.25-while each order of hamburger sliders sells for $3. On Friday, Tyler made a total of $595 in revenue from all sliders and wings-sales. There were twice as many chicken wing orders sold than there were sliders sold.
Now, let's take the number of sliders to be x and the number of chicken wing orders to be y.
y = 2x
Now, we have the following expression:
7.25x+3(2x) = 595
7.25x+6x = 595
13.25x = 595
x = 45 (This value is rounded off to a whole number)
Now, the number of wing sales:
y = 2*45
y = 90
Hence, the number of chicken wing orders is 90 and the number of sliders is 45.
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DCF = FB and AE = EBCB = 38 and AB = 22DE = [?]EBFLLEnter
Given
Also, CF = FB and AE = EB, CB = 38 and AB = 22.
To find the length of DE.
Explanation:
It is given that,
Also, CF = FB and AE = EB, CB = 38 and AB = 22.
That implies,
By using midpoint theorem of triangle, we have,
[tex]DE=\frac{1}{2}BC[/tex]Therefore,
[tex]\begin{gathered} DE=\frac{1}{2}\times38 \\ =19 \end{gathered}[/tex]the measure of two angle are (8x+24) and (12x-16) what is the value of x if theses angle ar congruent
Answer: 10
Step-by-step explanation: Congruent means they are the same, so you set up the problem as 8x+24=12x-16. Then you just solve for x. Subtract 8x from both sides to get 24=4x-16. Then add 16 to both sides. 40=4x. Then divide by 4 into both sides to get x=10.
DIRECTIONS: Use this diagram to answer Parts A and B. 60° 55° Part A Find the value of x in the diagram.
By using the properties of triangles and straight lines we get the values of x as 65° and the value of y as 115°
A) In the given triangles we know that the sum of all the angles is 180 .
Hence :
60 + 55 + c = 180
or, c = 180° - 115°
or, c = 65°
Now the angle marked x is vertical angle to the angle c , hence the value of x is also 65°.
B) Now we know that the value of x is 65°
Again x + y = 180°
Therefore : 65° + y = 180° or, y = 180° - 65° or, y = 115°
Three vertices, three sides, and three angles make up a closed triangle. PQR serves as the symbol for a triangle with the vertices P, Q, and R.
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how do I find the value of xfor the following triangles
Given at the figure 1
A right triangle of legs of 10 and 16
We need to find the angle x
The side of 16 represent the opposite side of the angle x
The side of 10 represents the adjacent side of the angle x
According to the known sides, we can find x using tan function :
So,
[tex]\begin{gathered} \tan x=\frac{opposite}{adjacent} \\ \\ \tan x=\frac{16}{10}=1.6 \\ \\ x=\tan ^{-1}1.6=57.995 \end{gathered}[/tex]Rounding to the nearest degree
So, the measure of angle x = 58
Solve: -4x + 3 > 27
Please explain and show your work step-by-step.
The value of x is less than -6.
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, -4x + 3 > 27
-4x + 3 > 27
-4x + 3 - 3 > 27 - 3 → (subtracting 3 from both sides)
-4x > 24
-4x/4 > 24/4 → (dividing by 4 both the side)
-x > 6x
x < -6
Hence, x < -6
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10. Two classes work together on a project. One class has 18 students,8 of whom are girls. The other class has 10 girls and 7 boys.What is the ratio of boys to the total number of students working on theproject? Express your answer as a fraction.lo0OOOOOOCOOOOO
Solution
For this case we have the following info:
Class 1: Total 18 students, 8 girls and 10 boys
Class 2: Total 17 students, 10 girls and 7 boys
The total of students are: 18+17 = 35
Total of boys: 10 + 7 = 17
Then the ratio of boys to the total number of students is given by:
r = 17/35
PLEAS HELP ME TYYYYYYY
Answer:I would say if there are 15 leaches then there will be 20 toads
Step-by-step explanation: I multiplied the 4 times 5
Write an equation of the line passing through point P(0, −1) that is parallel to the line y = −2x+3.
Answer:
y = -2x - 1
Step-by-step explanation:
Equation of line: y =mx + bHere, m is the slope and 'b' is the y-intercept
y = -2x + 3
m = -2
Parallel lines have same slope.
Substitute m = -2 in the equation,
y = -2x + b
The line is passing through (0 ,-1). So, substitute this point in the equation and find the value of b.
-1 = -2*0 + b
-1 = b
Equation of line:
[tex]\sf \boxed{y = -2x - 1}[/tex]
Solve for g: g + 8 > 10
Given the inequality:
[tex]g+8>10[/tex]Solve for g, subtract 8 from both sides
[tex]\begin{gathered} g+8-8>10-8 \\ \\ g>2 \end{gathered}[/tex]so, the answer will be:
[tex]g=(2,\infty)[/tex]6 chairs cost £84 in total.
How much does 1 chair cost?
Give your answer in pounds (£).
Answer: £14
Step-by-step explanation:
Divide the pounds from the chairs, in this case £84 / 6 is £14. So each chair costs £14.
Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 400 minus quantity y minus 110 end quantity squared over 2304 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number. please help look at the image
100 meters
50 meters
48 meters
40 meters
The width of the cooling tower at the base of the structure is 40 meters.
What is defined as the ellipse?An ellipse is a closed curve made up of points for whom distances from two points (foci) each add up to a single value. The center is the midpoint between the foci. One property of the an ellipse that the reflection of a line from one focus off its boundary will pass across the other.For the given question,
The equation modelling the cooling tower's walls is -
x²/400 - (y-110)²/2,304 = 1
This can be written as;
x²/20² - (y-110)²/48² = 1
Comparing the equation with the standard form of ellipse;
(x-h)²/a² - (y-k)²/b² = 1
The base of the ellipse will be its major axis,
That is 2a.
Thus,
For the width of the colling tower.
Cooling tower width =2√400
Cooling tower width = 2×20
Cooling tower width= 40 meters
Thus, the width of the cooling tower at the base of the structure is 40 meters.
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4. Felix and Oscar applied for the same credit card from the same bank.
The bank checked both of their FICO scores. Felix had an excellent
credit rating, and Oscar had a poor credit rating.
a. Felix was given a card with an APR of 12%. What was his
monthly percentage rate?
b. Oscar was given a card with an APR of 15%. What was his
monthly payment?
c. If each of them had an average daily balance of $800 and had to
pay a finance charge, how much more would Oscar pay than Felix?
A) The monthly percentage rate of Felix is; 1%
B) The monthly percentage rate of Oscar is; 1.25%
C) The amount that Oscar will pay more than Felix is; $2
What is the monthly Percentage Rate?A monthly interest rate is simply how much percentage interest you would be charged in one month while annual percentage interest rate is defined as the percentage interest rate you will be charged annually.
A) We are told that Felix was given a card with APR of 12%.
Thus;
Monthly percentage rate = 12%/12 = 1%
B) We are told that Oscar was given a card with an APR of 15%. Thus;
Monthly percentage rate = 15%/12 = 1.25%
C) We are told that each of them had an average daily balance of $800 for a specific month.
Thus;
Amount paid by Felix = 800 * 1%
Amount paid by Felix = $8
Amount paid by Oscar = 800 * 1.25%
Amount paid by Oscar = $10
Difference in Payments = $10 - $8 = $2
Thus, Oscar pays $0.96 more than Felix.
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