Answer:
$90, $135, $189
Step-by-step explanation:
Since the first part of the ratio is two- thirds of the second, then
first part = [tex]\frac{2}{3}[/tex] × 5 = [tex]\frac{10}{3}[/tex]
The ratio is then
[tex]\frac{10}{3}[/tex] : 5 : 7
Sum the 3 parts of the ratio
[tex]\frac{10}{3}[/tex] + 5 + 7 = [tex]\frac{46}{3}[/tex]
Divide the amount to be shared by the sum to find the value of one part of the ratio.
$414 × [tex]\frac{3}{46}[/tex] = $27 ← value of 1 part of the ratio, then
[tex]\frac{10}{3}[/tex] × $27 = $90
5 × $27 = $135
7 × $27 = $189
The 3 parts are $90, $135, $189
A fountain shoots a water arc that can be modeled by the graph of the equation y=-0.006x^2+1.2x+10, where x is the horizontal distance (in feet) from the river's north shore and y is the height (in feet) above the river. Does the water arc reach a height of 50 feet? If so, about how far from the north shore is the water arc 50 feet above the water?
ANSWER
The water arc is 50 ft above the water approximately 42ft and 158ft from the north shore.
EXPLANATION
The water arc is modeled by the function:
[tex]y = - 0.006 {x}^{2} + 1.2x + 10[/tex]
We write this function in vertex form:
[tex]y = - 0.006 ({x}^{2} - 200x )+ 10[/tex]
[tex]y = - 0.006 ({x}^{2} - 200x + ( - 100)^{2} ) - - 0.006( - 100)^{2} + 10[/tex]
[tex]y = - 0.006 ( x- 100)^{2} ) + 60+ 10[/tex]
[tex]y = - 0.006 ( x- 100)^{2} ) +70[/tex]
The vertex of this function is at
(100,70).
This means that the water arc reached a height of 50ft.
We put y=50 and solve for x.
[tex]- 0.006 ( x- 100)^{2}+70 = 50[/tex]
[tex]- 0.006 ( x- 100)^{2} = - 20[/tex]
[tex]( x- 100)^{2} = \frac{10000}{3} [/tex]
[tex]x = 100 \pm \frac{100 \sqrt{3} }{3} [/tex]
x=42.3 or x=157.7
Hence the water arc is 50 ft above the water approximately 42ft and 158ft from the north shore.
The water arc does reach a height of 50 feet, and it is about 42.27 feet and 157.73 feet from the north shore when it is 50 feet above the water.
1.Set up the equation:
[tex]\[ -0.006x^2 + 1.2x + 10 = 50 \][/tex]
2. Simplify the equation:
Subtract 50 from both sides:
[tex]\[ -0.006x^2 + 1.2x + 10 - 50 = 0 \] \[ -0.006x^2 + 1.2x - 40 = 0 \][/tex]
3. Solve the quadratic equation:
We can use the quadratic formula
[tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = -0.006 \), \( b = 1.2 \), and \( c = -40 \).[/tex]
[tex]\[ a = -0.006, \quad b = 1.2, \quad c = -40 \][/tex]
[tex]\[ \Delta = b^2 - 4ac \] \[ \Delta = 1.2^2 - 4(-0.006)(-40) \] \[ \Delta = 1.44 - 0.96 \] \[ \Delta = 0.48 \][/tex]
[tex]\[ x = \frac{-b \pm \sqrt{\Delta}}{2a} \] \[ x = \frac{-1.2 \pm \sqrt{0.48}}{2(-0.006)} \][/tex]
Calculate the square root of 0.48:
[tex]\[ \sqrt{0.48} \approx 0.6928 \][/tex]
Now, find the two values of x:
[tex]\[ x_1 = \frac{-1.2 + 0.6928}{-0.012} = \frac{-0.5072}{-0.012} \approx 42.27 \] \[ x_2 = \frac{-1.2 - 0.6928}{-0.012} = \frac{-1.8928}{-0.012} \approx 157.73 \][/tex]
Therefore, the water arc reaches a height of 50 feet at approximately [tex]\( x = 42.27 \) feet and \( x = 157.73 \)[/tex] feet from the north shore.
The low temperature in Chicago was -3 °F. The low temperature in Milwaukee was -11 °F. Which statement is true?
-11 is greater than -3, so it was colder in Chicago.
-3 is greater than -11, so it was colder in Chicago.
-11 is greater than -3, so it was colder in Milwaukee.
-3 is greater than -11, so it was colder in Milwaukee.
Answer:
The statement -11 is greater than -3, so it was colder in Milwaukee is true.
Answer:
-11 is greater than -3, so it was colder in Milwaukee.
Step-by-step explanation:
Answer 1 (-11 is greater than -3, so it was colder in Chicago) is incorrect because it was -3 in Chicago, not -11.
Answer 2 (-3 is greater than -11, so it was colder in Chicago) is incorrect because -3 is not greater than -11.
Answer 3 is correct because -11 is greater than -3 and the cities are labeled correctly.
Answer 4 (-3 is greater than -11, so it was colder in Milwaukee) is incorrect because -3 is not greater than -11. Milwaukee was also -11, not -3.
I hope this helps!
I need to find the measure of each angle indicated
1. From the given right-triangle, the side opposite to [tex]\theta[/tex] is 6.8 units.
The adjacent side to [tex]\theta[/tex] is 4 units.
Recall the mnemonics, SOH-CAH-TOA.
We use the tangent ratio to obtain:
[tex]\tan \theta=\frac{Opposite}{Adjacent}[/tex]
[tex]\tan \theta=\frac{4}{6.8}[/tex]
[tex]\tan \theta=\frac{10}{17}[/tex]
[tex]\implies \theta=\tan^{-1}(\frac{10}{17})[/tex]
[tex]\implies \theta=30.5\degree[/tex] to the nearest tenth.
2. This time we were given the hypotenuse to be 15.7 units and the adjacent side is 6 units.
We use the cosine ratio to obtain:
[tex]\cos \theta=\frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos \theta=\frac{6}{15.7}[/tex]
[tex]\cos \theta=\frac{60}{157}[/tex]
[tex]\implies \theta=\cos^{-1}(\frac{60}{157})[/tex]
[tex]\implies \theta=67.5\degree[/tex] to the nearest tenth.
Answer:
25). 55.02°
26). 30.46°
Step-by-step explanation:
Points to remember
Trigonometric ratios
Sin θ = Opposite side/Hypotenuse
Cos θ = Adjacent side/Hypotenuse
Tan θ = Opposite side/Adjacent side
To find the answer of question 25
Cos θ = Adjacent side/Hypotenuse
= 9/15.7 = 0.573
θ = Cos⁻¹(0.573) = 55.02°
To find the answer of question 26
Tan θ = Opposite side/Adjacent side
= 4/6.8 = 0.588
θ = Tan⁻¹(0.588) = 30.46°
Which is the graph of logarithmic function ?
Answer:
Graph C on edge
Step-by-step explanation:
I Just did the Assignment
The second graph is the graph of logarithmic function
What is a logarithm functionLogarithmic functions are the inverses of exponential functions. The logarithmic function [tex]y=1og_ax[/tex]is defined to be equivalent to the exponential equation [tex]x=a^y[/tex].
The logarithmic function is similar in shape to the square root function. To graph a logarithmic function it is better to convert the equation to its exponential form.
The second graph is the graph of logarithmic function
Find out more on Logarithm function at: https://brainly.com/question/13473114
Plz help me with this
Answer: B) A = 750(1.04)ⁿ
Step-by-step explanation:
The formula for compounded annually is: A = P(1 + r)ⁿ where
A (amount accrued) = unknownP (amount invested) = $750r (interest rate) = 4% -->(0.04)t (time in years) = unknownA = 750(1 + 0.04)ⁿ
= 750(1.04)ⁿ
Use the given information to write an equation of the circle.
center at (-7,-3), radius 2
Answer:
(x + 7)² + (y + 3)² = 4Step-by-step explanation:
The equation of a circle in the standard form:
[tex](a-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (-7, -3) and the radius r = 2. Substitute:
[tex](x-(-7))^2+(y-(-3))^2=2^2\\\\(x+7)^2+(y+3)^2=4[/tex]
Jackson works as a veterinarian technician and earns $12.20 per hour Jackson normally works 40 hours a week in a normal week what is his total pay before taxes and other deductions Jackson works as a veterinarian technician earns $12.20 per hour Jackson normally works 40 hours a week in normal week what is his total pay before taxes and other deductions
Answer:
Multiply $12.40 times 40. Remember to use a dollar sign in your answer.
Step-by-step explanation:
The vertex form of the equation of a parabola is y=5(x-3)^2 -6? What is the standard form of the equation? Please show steps
So , at first we should calculate the power because in calculating order we have:
first power or radical
then multiply or division
then + or -
so according to the rules we must do:
1)(x-3)^2=x^2 -6x +9
2)5(x^2 -6x +9)=5x^2 -30x +45
3)then -6 and we have:
Y=5x^2 -30x +39
Help me find the value of x!!!
The value of x is B. 8.
Enter the values for the following composite transformation.
Translate Answer
0,0
Incorrect units left and _____ units down, then rotate _____°.
Enter the three numbers with commas and no spaces. Example: 5,7,270
do u have the answer
a number from 1 to 10 is chosen at random what is the probability of choosing a 4 or an odd number
Probably to get a 4 or 1,3,5,7,8 so is the probability of getting 1,3,4,5,7,8 so answer is 6/10=3/5
Answer:
6/10 or 0.6 or 60%
Step-by-step explanation:
The options for numbers are 1,2,3,4,5,6,7,8,9,and 10. There are 5 odd numbers from 1-10, 1,3,5,7, and 9. This woud be 50/50 odds. If you add four as an option, there would be 6 numbers, 1,3,4,5,7, and 9. the odds would be 6/10 which would be 60%.
Point B is on a line that has a slope of 2. Which of these could be the coordinates of another point on the line?
I actually don't have enough information to complete this question but if you have a positive slope the line goes either up and right or down and left but when it is negative it goes down left or up right.
Answer:
Since theres no graph i cant really explain it to you. What i do know is that on TTM the answer would be (1,2)
Step-by-step explanation:
please help! will give brainlist, only answer if youre 100% surre
Simplify. 1/4y+1 1/2 + 2− 13/4y − 12 Enter your answer in the box
Answer:
-3y-8 1/2
Step-by-step explanation:
1/4y-13/4y=-12/4y=-3y
1.5+2-12=-8.5 or 8 1/2
Answer:
-17y+13/4y
use m.a.t.h.w.a.y
Step-by-step explanation:
which one of these tables represent a non-linear function
Answer:
NUMBER3
Step-by-step explanation:
Table no 3 is representing here a non-linear function.
Why table 3 is a non-linear function?A nonlinear function, as its name suggests, is a function that is not linear. In other words, the graph of a nonlinear function is not a line, its graph can be anything other than a line
Since a nonlinear function is a function that is not a linear, its equation can be anything that is not of the form f(x) = ax+ b. One examples of nonlinear functions is, f(x) = x2 is nonlinear as it is a quadratic function.
The right answer is option 3.
Learn more about non-linear function, refer:
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The volume of a cube can be found using the equation v=s3 where v is the volume and a is the measure of one side of the cube
Answer:
s = ∛2560
Step-by-step explanation:
The volume of a cube is found by V = s³. To solve for the side of a cube with a specific volume, we use inverse operations to find it. s = ∛V. If the volume is 2560 then the s = ∛2560.
Answer:
it's the last one
Step-by-step explanation:
I took the K12 test
IMPORTANT PLEASE HURRY!!
what is the surface area of a box if it’s volume is 2244 inches cubed?
I wasn’t given any measurements, just the volume.
For this case we have that if the box is cubed, then the volume is given by:
[tex]V = l ^ 3[/tex]
Where:
l: It's the side of the cube
We have to:
[tex]l ^ 3 = 2244\\l = \sqrt [3] {2244}\\l = 13,09204886[/tex]
So, l is the side of the box. The surface area of a cube is given by:
[tex]SA = 6l ^ 2\\SA = 6 * (13.09204886) ^ 2\\SA = 1028.41046012[/tex]
Rounding off we have that the surface area of the cube is:
[tex]1028.4 \ in ^ 2[/tex]
Answer:
[tex]1028.4 \ in ^ 2[/tex]
Which number completes this number sentence? [ ? ] > -6
A.-8
B.-7
C.-6
D.0
Answer:
It is 0
Step-by-step explanation:
Unlike the positive side of the number line which increases its value as it goes up in numbers, the negative side of a number line increases its value as it goes goes down in numbers as the more closer a negative number is to the positive side of infinity, the greater value it has. In this instance, zero is the greater number than -6 and all other negative numbers.
If you were to spin the spinner once, what is the probability of not landing on 3?
Answer:
5/6
Step-by-step explanation:
Answer:
5/6 i think
hope this helps pls if mine is right make it the brainlest thx
What is the measure of CAD?
I am pretty sure 52 degrees
Answer:
the answer is D
Step-by-step explanation:
because the measurements for CAD is 92
Which of the following linear equations in standard form contains points (-2,4) and (3,9)?
Answer:
y=x+6
Step-by-step explanation:
If you need to find a standard linear equation from two points, you have to first find the slope, then find the y intercept.
To find the slope, you should do the change in y over the change in x.
that would be:
(4-9)/(-2-3)
(-5)/(-5)
the slope is 1
plug that in along with values of x and y taken from known point (3,9) to the standard equation of a linear relationship:
y=mx+b
m=1
y=9
x=3
b=?
9=(1)(3)+b
9=3+b
b=6
The equation of the line would be y=x+6
Answer:
x - y = - 6
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (3, 9)
m = [tex]\frac{9-4}{3+2}[/tex] = [tex]\frac{5}{5}[/tex] = 1, hence
y = x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 9), then
9 = 3 + c ⇒ c = 9 - 3 = 6
y = x + 6 ← equation in slope- intercept form
Subtract y from both sides
0 = x - y + 6 ( subtract 6 from both sides )
- 6 = x - y, thus
x - y = - 6 ← in standard form
The box plots show the average gas mileage of cars and minivans tested by a certain company.
Josef says that the range for the car data is greater than the range for the minivan data because the box in the box plot for the car data is wider. Which explains Josef’s error?
Josef confused the range and the interquartile range.
Josef confused the range and the median.
Josef should have compared the medians and minimum values.
Josef should have compared the medians and maximum values.
Josef's error will be Josef confused the range and the interquartile range.
What is an interquartile range?The interquartile range is a measurement of a data set's "middle fifty." A range is a measurement of where a set's beginning and end are located.
Given that:-
Josef says that the range for the car data is greater than the range for the minivan data because the box in the box plot for the car data is wider.From the given statement we can conclude that Josef confused the range and the interquartile range.
Therefore Josef's error will be Josef confused the range and the interquartile range.
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A cylinder and a cone have the same volume. The cylinder has a radius of 2 inches and a height of 3 inches . The cone has a radius of 3 inches. What is the height of the cone ?
Answer:
The height of the cone is [tex]4\ in[/tex]
Step-by-step explanation:
step 1
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi (r)^{2}(h)[/tex]
substitute the values
[tex]V=\pi (2)^{2}(3)=12\pi\ in^{3}[/tex]
step 2
Find the height of the cone
The volume of the cone is equal to
[tex]V=(1/3)\pi (r)^{2}(h)[/tex]
Remember that the volume of the cone is equal to the volume of the cylinder
substitute the given values and solve for h
[tex]12\pi=(1/3)\pi (3)^{2}(h)[/tex]
Simplify
[tex]36=9(h)[/tex]
[tex]h=36/9=4\ in[/tex]
Plz help me with this
Answer: [tex]\bold{C)\quad y=2sin(x+\dfrac{3\pi}{4})}[/tex]
Step-by-step explanation:
A sin graph is a cosine graph shifted to the left [tex]\dfrac{\pi}{2}[/tex] units.
[tex]y=2cos(x + \dfrac{\pi}{4})\qquad \implies y=2sin(x+\dfrac{\pi}{4}+\dfrac{\pi}{2})\\\\\\.\qquad \qquad \qquad \qquad \quad \implies \large\boxed{y=2sin(x+\dfrac{3\pi}{4})}[/tex]
Please help as I don’t understand!
well, she knows that the mass of chocolate is 1.8 times that of powered sugar.
it just so happen that powered sugar is 100 grams for one cup, and since chocolate is 1.8 times "that", then in one cup of chocolate there must be 1.8 times 100 grams, or 1.8*100 = 180 grams.
the recipe uses 1/2 cup of chocolate, well, half a cup of chocolate, namely half of 180 grams is just 90 grams.
the number √21 is a ____ number because ___
Answer:
composite number
Step-by-step explanation:
When the length of a rectangle with a width of 1/6 foot was increased by 2/3 foot, the area of the rectangle became 11/72 square feet. Find the original length of the rectangle. Explain your reasoning.
Answer:
1/4 is the original length
Step-by-step explanation:
The original length of the rectangle is 11/72 square feet. To get the area of a rectangle, you multiply the length x width.
You already know the width in this problem. The width is 1/6 feet. So, divide the area (11/72 feet) by the width (1/6 feet) to get the length, 11/12 feet.
However, the original length was increased by 2/3 feet. So, take our new length (11/12 feet) and subtract the increased length (2/3 feet) from it. When you do that, you get 1/4 feet.
Therefore, the answer is 1/4 feet. Hope this helps! :)
Find the missing lengths of the sides
ANSWER
The correct answer is C
EXPLANATION
The given triangle is a right triangle. Since two angles are equal, it is a right isosceles triangle.
This implies that, x=8 units.
Using Pythagoras Theorem,
[tex] {y}^{2} = {8}^{2} + {8}^{2} [/tex]
This implies that:
[tex]{y}^{2} = 64 + 64[/tex]
[tex]{y}^{2} =128[/tex]
Take positive square root,
[tex]{y} = \sqrt{128} [/tex]
[tex]{y} = 8 \sqrt{2} [/tex]
The correct answer is C
Answer:
Correct choice is C. [tex]x=8[/tex], [tex]y=8\sqrt{2}[/tex].
Step-by-step explanation:
Apply formula [tex]\sin\left(\theta\right)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sin\left(45^o\right)=\frac{8}{y}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{8}{y}[/tex]
[tex]y=8\sqrt{2}[/tex]
Apply formula [tex]\tan\left(\theta\right)=\frac{opposite}{adjacent}[/tex]
[tex]\tan\left(45^o\right)=\frac{8}{x}[/tex]
[tex]1=\frac{8}{x}[/tex]
[tex]x=8[/tex]
Hence correct choice is C. [tex]x=8[/tex], [tex]y=8\sqrt{2}[/tex].
A random sample of 110 children who play instruments were asked if they prefer milk or juice. The results are shown in the table. Milk Juice Girls 18 27 Boys 23 42 Select a word or phrase from the drop-down menus to correctly complete the statements describing the association. Of the boys surveyed, more . Of the girls surveyed, more . There appear to be an association between gender and beverage preference.
Answer:
Juice, Juice, and no association
Step-by-step explanation:
For f(x) = -x -7, find f(-5)
Answer: -2
Step-by-step explanation:
f(-5) - (-5) - 7
+5 -7
-2
Answer:
-2
Step-by-step explanation:
=-(-5)-7
Which is the first incorrect step in the solution shown above ?
Answer:
Step 2 is incorrect
Step-by-step explanation:
Step 2 is incorrect
step 1: 3x + 15 = 2x + 35
step 2: subtract 2x from both sides
3x + 15 - 2x = 2x + 35 - 2x
x + 15 = 35
Answer:
Step 2
Step-by-step explanation:
2x was moved to 3x just to add.
It was supposed to be 3x - 2x = x