The length of the base is 13 yards and the height of the triangle is 10 yards.
Let h = ht of the triangle
let (h + 3) = base of triangle
A = (1/2)bh is the formula for the area of a triangle
65 = (1/2) (h + 3)h
130 = [tex]h^2[/tex] + 3h
[tex]h^2[/tex] + 3h - 130 = 0
(h + 13)(h - 10) = 0
h = -13, h = 10
Height = 10 yards, base = 13 yards
What is geometry ?
Geometry is one of the oldest branches of mathematics, along with arithmetic. It concerns the properties of space, like the distance, shape, size and relative position of figures. A mathematician who works in geometry is called a geometer.
Three geometries
History of Euclidean geometry and non-Euclidean geometry. Spherical geometry. Hyperbolic geometry.To learn more geometry, visit;
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Figure NN is the result of a transformation on Figure MM. Which transformation would accomplish this?
The transformation that is used is a translation of 3 units upwards.
Numerous different coordinate systems can be used to describe geometrical figures.
The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system. For example, if the polar axis on a plane is the positive x axis and the origins of the Cartesian coordinates (x, y) and the polar coordinates (r), respectively, are the same. The transformation of the coordinates from the polar to the Cartesian coordinate system is x = r cos α and y = r sin α.From the diagram of the graph we can see that the transformation that is used is translation of 3 units upwards.
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INSTRUCTIONS: INSTRUCTIONS: Find the slope of the line and enter it here: 1. Find the slope of the line and enter it here: Find the y-intercept of the line & enter it here: Find the y-intercept of the line the enter it here: Write the equation of the line in form y=mx +b Write the equation of the line in form y=x+h 126 27 17
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]from the graph we notice that the line passes through the points (0,2) and (3,0), plugging this values into the equation above we have:
[tex]\begin{gathered} m=\frac{0-2}{3-0} \\ m=-\frac{2}{3} \end{gathered}[/tex]therefore the slope is m=-2/3.
The y intercept is the value of y when x=0; from the graph we conclude that b=2.
The equation of the line is:
[tex]y=-\frac{2}{3}x+2[/tex]a wildfire organization wants to fence off an area of a beach. The organization can only fence 100 yd². what length (x) and width (y) should the organization use the Least amount of fencing as possible
It is given that the total area of the beach is 100 yd².
We have to find the length x and the width y that the organization shoul use to use the least amount of fencing as possible. it means that we have to find the dimensions for which parameter is leasr.
The perimeter of a rectangle is:
[tex]P=2\times(l+w)[/tex]In option 1, the length is 50 yards and the width is 20 yards. then the perimeter will be (using the previous formula) equal to 140.
In option too the perimeter will be 130.
in option 3 the perimeter will be 134.44
and, in option 4 it will be 146.36
therefore the least perimeter is 130 when the length is 40 yd and the width is 25 yd.
What is 159,100 rounded to nearest thousand
Answer: 159,000
Step-by-step explanation:
The number after the nine (one) is under five, so you keep the number the same instead of rounding up :)
I will send a picture of the equations because if I type it here it won't make sense.
Hence option A is the correct answer
Julieta has p pennies and n nickels. She has at most $1 worth of coins altogether.
Write this situation as an inequality.
Julieta has at most $1 worth of coins altogether, then the inequality of the given situation is $0.1p + $0.25n ≤ $1.00.
Based on the given conditions,
Julieta has p pennies and n nickels.
He has at most $1 worth of coins altogether.
What is a Inequality :Inequality, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Since p time = $0.1
So n times = $(0.1)n
Since p quarter = $0.25
So n quarters = $(0.25)n
Total of p times and n quarters = $[(0.1)p + (0.25)n]
This total answer has a minimum of $1 worth of mins all to get he.
So,
$[(0.1p + 0.25n)] ≤ 1
Therefore,
Julieta has at most $1 worth of coins altogether, then the inequality of the given situation is $0.1p + $0.25n ≤ $1.00.
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Make a table and a graph of y = 4x - 2.
To make the table first replace the given values of x in the equation, operate, and with it, you get their corresponding coordinates in y. Then you have
If x = -2
[tex]\begin{gathered} y=4x-2 \\ y=4(-2)-2 \\ y=-8-2 \\ y=-10 \\ \text{Then you have the ordered pair (-2,-10)} \end{gathered}[/tex]If x = -1
[tex]\begin{gathered} y=4x-2 \\ y=4(-1)-2 \\ y=-4-2 \\ y=-6 \\ \text{Then you have the ordered pair (-1,-6)} \end{gathered}[/tex]If x = 0
[tex]\begin{gathered} y=4x-2 \\ y=4(0)-2 \\ y=0-2 \\ y=-2 \\ \text{Then you have the ordered pair (0,-2)} \end{gathered}[/tex]If x = 1
[tex]\begin{gathered} y=4x-2 \\ y=4(1)-2 \\ y=4-2 \\ y=2 \\ \text{Then you have the ordered pair (1,2)} \end{gathered}[/tex]If x = 2
[tex]\begin{gathered} y=4x-2 \\ y=4(2)-2 \\ y=8-2 \\ y=6 \\ \text{Then you have the ordered pair (2,6)} \end{gathered}[/tex]Finally, the table of the equation
and its corresponding graph will be
Therefore, the correct answer is option A.
I need help with this problem
Solving a percent makes your prom using a system of linear equations
Water :60 ounces
Salt solution:60 ounces
Explanation
Step 1
set the equations
Let x represent the amoun of water forthe solution
let y represents the amount of solution ( 40% salt)
so
a)the scientific mixes water with the solution to obtain 120 ounces, so
[tex]x+y=120\Rightarrow equation\left(1\right)[/tex]b)the mixture is 20% salt
so
salt fromwater+salt from solution( 40%) = salt in the solution (20%)
so
[tex]\begin{gathered} 0+0.4y=120*0.2 \\ 0.4y=24 \\ divide\text{ both sides by 0.4} \\ \frac{0.4y}{0.4}=\frac{24}{0.4} \\ y=60 \end{gathered}[/tex]hence, the amount of salt solution is 60 ounces
,now to find x, replace the y value in equation (1)
[tex]\begin{gathered} x+y=120\Rightarrow equation\left(1\right) \\ x+60=120 \\ subtract\text{ 60 in both sides} \\ x+60-60=120-60 \\ x=60 \end{gathered}[/tex]so, water : 60 ounces
therefore, the answer is
Water :60 ounces
Salt solution:60 ounces
I hope this helps you
Find P(z > -0.24)Use the Normal table and give answer using 4 decimal places.
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given z-score
[tex]P(z>-0.24)[/tex]STEP 2: Draw the required region on a graph
STEP 3: Find the probability using the normal distribution tabele
-0.24 = -(0.20 + 0.04)
It can be seen from the table above that the Probability will be the circled portion on the table.
Hence,
[tex]P(z>-0.24)\approx0.5948[/tex]6 ft
11 ft
How do I solve this problem
Answer:
the answer is 66
Step-by-step explanation:
multiply
Find the area of the figure given to the right. The hexagon is regular. Round to the nearest whole number.
We can divide the hexagon into 6 equilateral triangles, and call the side 'x'. I will draw the situation:
Every line is x because the hexagon is regular (all sides have the same length). Therefore we can find x, because two times x is 18'':
[tex]2x\text{ = 18}[/tex][tex]x\text{ = 9 inches}[/tex]The hexagon has the same area of 6 equilateral triangles with the side equal to x. The formula of the area of an equilateral triangle is:
[tex]Area\text{ = }\frac{x^2\sqrt[]{3}}{4}[/tex]Therefore the area of the hexagon will be:
[tex]\text{AreaHexagon = 6}\times\frac{x^2\sqrt[]{3}}{4}^{}[/tex][tex]\text{AreaHexagon = 6}\times\frac{9^2\sqrt[]{3}}{4}^{}[/tex][tex]\text{AreaHexagon }\cong210.44\text{ square inches}[/tex]Rounding it will be 210 square inches.
Think about what is different here? What makes this a challenge? Can you use skills you already know to figure out the intercepts here?
We are given the following line equation:
[tex]4x+5y=20[/tex]We are asked to determine the x and y-intercepts of the line. To do that, we will convert the given equation into the following form:
[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]Written in that form the value of "a" is the x-intercept and the value of "b" is the y-intercept. Therefore, we need to divide the given equation by 20 in order to get a 1 on the right side:
[tex]\frac{4x}{20}+\frac{5y}{20}=\frac{20}{20}[/tex]Simplifying we get:
[tex]\frac{x}{5}+\frac{y}{4}=1[/tex]Therefore, the y-intercept is 4 and the x-intercept is 5.
Theo is saving $8 per week for a vacation he is taking. He started off with some money in savings, but less than $8. At the end of his weeks savings, he had a total of $52. How much money did theo start of with?
To find the money at start let us use an equation
Since he puts $8 per week
Then his rate is 8
Since he has a total of $52 after some weeks
We must find the nearest number to 52 in table 8
Since 6 * 8 = 48 the nearest number to 52 in table 8
Then he did that for 6 weeks
52 = 8(6) + x
Let us find x
52 = 48 + x
Subtract 48 from both sides
52 - 48 = 48 - 48 + x
4 = x
He started with $4
Type the correct answer in each box. Use numerals instead of words.What is the yintercept of this quadratic function?f(3) -52 + 101 - 22).-The y-intercept of function fis (ResetNext
The quadratic function is expressed as
f(x) = - x^2 + 10x - 22
The y intercept is the value of y or f(x) when x = 0
Thus, to find the y intercept, we would substitute x = 0 into the function. Thus, we have
f(0) = - 0^2 + 10 * 0 - 22
f(0) = 0 + 0 - 22
f(0) = - 22
Thus, the y intercept of the function f is (0, - 22)
Verify algebraically if the function is odd, even, or neither. Need # 6 help
As given by the question
(6)
There are given that the function:
[tex]h(x)=x^9+1[/tex]Now,
For the even:
[tex]h(-x)=h(x)[/tex]So,
From the function
[tex]\begin{gathered} h(x)=x^9+1 \\ h(-x)=(-x)^9+1 \\ =x^9+1 \\ h(-x)\ne h(x) \end{gathered}[/tex]So, the given function is not even.
Then,
For odd:
[tex]\begin{gathered} h(-x)=-h(x) \\ h(-x)=(-x)^9+1 \\ h(-x)=-(x)^9+1 \\ h(-x)\ne-h(x) \end{gathered}[/tex]So, the given function is not odd.
Hence, the given function is neither odd nor even.
determine the number of different ways the given number can be written as the sum of 2 primes? 50
the prime numbers smaller than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
let's find the sums that give us 50:
3+47=50
7+43=50
13+37=50
19+31=50
so the answer is four different ways.
Find the value of the following expression: (3^8•2^-5•9^0)^-2•(2^-2/3^3)^4•3^28 Write your answer in simplified form.
Answer:
4
Step-by-step explanation:
Given expression:
[tex](3^{8} \cdot 2^{-5} \cdot 9^{0})^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
Any number to the power of zero is 1:
[tex]\implies (3^{8} \cdot 2^{-5} \cdot 1)^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\implies (3^{8} \cdot 2^{-5})^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b \cdot c^d)^p=a^{bp}\cdot c^{dp}:[/tex]
[tex]\implies 3^{(8 \cdot -2)} \cdot 2^{(-5 \cdot -2)} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{\left(2^{-2}\right)^{4} }{\left(3^{3}\right)^{4} } \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{2^{(-2 \cdot 4)}}{3^{(3\cdot 4)}} \cdot 3^{28}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{2^{-8}}{3^{12}} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot 2^{-8} \cdot 3^{-12} \cdot 3^{28}[/tex]
Gather like terms:
[tex]\implies 2^{10} \cdot 2^{-8} \cdot3^{-16} \cdot 3^{-12} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 2^{(10-8)}\cdot3^{(-16-12+28)}[/tex]
[tex]\implies 2^{2}\cdot3^{0}[/tex]
Any number to the power of zero is 1:
[tex]\implies 2^{2}\cdot 1[/tex]
[tex]\implies 2^2[/tex]
Therefore, the solution is:
[tex]\implies 2^2=2 \times 2=4[/tex]
Some help I will mark Brain liest
Answer:
-2.86, -0.37, 0.19, 0.91, 1.46
Step-by-step explanation:
the negatives will always be the least, hope this helps!
Write an equation of the line passing through (4,-2) that is parallel to the line -3x minus 4y =5
Answer:
Step-by-step explanation:
y=4x3
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
First, rearrange -3x - 4y = 5 into y = mx + c form.
-3x - 4y = 5
-4y = 3x + 5
y = -3/4x - 5/4
Since parallel lines have the same gradient, equation of line is y = -3/4x + c.
Substitute (4,-2) into the equation to find c.
-2 = -3/4(4) + c
c = 1
Hence, equation of line is y = -3/4x + 1.
The Busy Bee store bottles fresh jars of honey at a constant rate. In 3 hours, it bottles 36 jars, and in 7 hours, it bottles 84 jars of honey.
Determine the constant of proportionality.
36
12
4
0.08
The constant of proportionality is 12
Number of fresh jars of honey stored by The Busy Bee in 3 hours= 36 jars
Number of fresh jars of honey stored by The Busy Bee in 7 hours= 84 jars
So, In 3 hours = 36 jars
In 1 hour = 36/3 = 12 jars
Similarly, In 7 hours = 84 jars
In 1 hour = 84/7 = 12 jars
So, 12 is the constant number
Let x represent the number of hours and y the total number of jars stored by The Busy Bee after x hours
So, the equation can be formulated as:
y = 12x
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In a survey of 630 randomly selected U.S. companies, 535 reportedthat they performed drug testing on their employees and/or applicantslast year. At the 1% significance level, is there sufficient evidence toconclude that the percentage of U.S. firms that drug-tested last yearexceeds the previous year's figure of 74%? Formulate and carry outthe one-population z-test.Mean = 300Your answer should include:a) a statement of the hypothesesb) the critical value for the testc) the value of the test statisticd) a statement of conclusionTo get you started, here is the null hypothesis:H.p = 0.74
Given the following:
[tex]\begin{gathered} \alpha=0.05 \\ p=0.74 \\ \mu=300 \end{gathered}[/tex]a)
[tex]\begin{gathered} H_0\colon P=0.1 \\ H_1\colon P<0.1 \end{gathered}[/tex][tex]\begin{gathered} z=\frac{\hat{P}-P}{\sqrt[]{\frac{P(1-P)}{\mu}}} \\ \\ =\frac{0.09-0.1}{\sqrt[]{\frac{0.1\mleft(0.9\mright)}{300}}}=-0.58 \end{gathered}[/tex]b) The critical value is -1.645
Also
[tex]\begin{gathered} p<-0.58 \\ =0.28 \end{gathered}[/tex]c) Conclusion:
We fail to reject the test, since there is no enough evidence to conclude that the proportion of wrong tests is less than 10%
Find the points on
y = x³ + 6x² - 15x + 1 at which the
gradient is zero.
Answer:
(-5, 101) or (1, -7)
Step-by-step explanation:
The gradient of a function is zero when its first differential is zero
Taking first derivative of y = x³ + 6x² - 15x + 1
we get
[tex]\dfrac{dy}{dx} = \dfrac{d}{dx}(x^3+6x^2-15x\:+\:1)[/tex]
[tex]= \dfrac{d}{dx}(x^3)+ \dfrac{d}{dx}(6x^2) - \dfrac{d}{dx}(15x)\:+\: \dfrac{d}{dx}(1)\\\\[/tex]
[tex]= 3x^2 + 2(6x) - 15 + 0\\\\\\= 3x^2 + 12x - 15x\\[/tex]
Set this first differential to 0, find the solution set for x
[tex]3x^2 + 12x - 15x =0[/tex]
This is a quadratic equation which will have 2 solutions for x.
First divide throughout by 3
[tex]= > x^2 + 4x - 5 = 0[/tex]
Factor the term:
[tex]= > x^2 + 4x - 5 = 0\\\\== > (x -1)(x + 5) = 0\\== > x - 1 =0 \text { or } x + 5 =0\\\\[/tex]
This means x = 1 or x = -5 is the solution set
To find the y value corresponding to these values of x, plug in each of these x values in the original equation and solve for y
Plug in x = 1 into equation x³ + 6x² - 15x + 1
=> 1³ + 6(1)² - 15(1) + 1
=> 1 + 6 - 15 + 1
=> -7
So one point is (1, -7)
Looking at the choices we can eliminate the first and last choices
Looking at choices 2 and 3 we see that only one of them has x = -5 which is the other solution value. This is the second choice
So the correct answer is second choice
(-5, 101) or (1, -7)
Note we did not have to go through the pain of computing y for x = -5
The pentagonal prism below has a cross-sectional area of
27 cm² and a length of 3 cm.
Calculate the volume of the prism.
Give your answer in cm³.
Answer:
81 cm³
Step-by-step explanation:
For a normal distribution, it is known that the mean is zero and the standard deviation is 1. Be sure to draw and label a normal distribution for each problem. Find the probability that a z score is between -1.15 and 1.98.
To find the probability between two z-scores on a normal distribution, we can use a z-score table.
A z-score table gives the probability of a data less than the corresponding z-score, like in the picture:
So, if we want the probability between 1.98 and -1.15, we need to do the following:
[tex]P(-1.15However, usually z-score tables go only from z = 0 and above, so we need a way to consult the negative z.Since the normal distribution in symmetric around z = 0, we have that:
[tex]P(z<-1.15)=P(z>1.15)[/tex]And since the whole distribution give a 100% probability, or an area of 1, we have that:
[tex]\begin{gathered} P(z<1.15)+P(z>1.15)=1 \\ P(z>1.15)=1-P\mleft(z<1.15\mright) \end{gathered}[/tex]So, in the end, we have:
[tex]\begin{gathered} P(-1.151.15) \\ P(-1.15So, we can consult the values for the probabilities of z < 1.98 and z < 1.15 on the z-score table:[tex]\begin{gathered} P(z<1.98)\approx0.9761 \\ P(z<1.15)\approx0.8749 \end{gathered}[/tex]So, the total probability is:
[tex]\begin{gathered} P(-1.15So, the probability is approximately 0.8510.Not sure I’m doing this correctly or I’m missing something please help ! The wheel has a radius of 32 feet and the distance from the center of the Ferris wheel to the ground is 40 feet.
a)
From the information given, the ferris wheel makes a complete rotation in 16 minutes.
A complete rotation is 360 degrees. This means that each angle is
360/12 = 30 degrees
Lets us assume that the starting point is A. As the ferris wheel move towards the highest point at D, the angle covered is 30 + 30 + 30 = 90 degrees
We have the following equations
360 = 16
90 = (90 x 16)/360 = 4
b) Recall, 1 minute = 60 seconds
Thus, 16 minutes = 16 x 60 = 960 seconds
It x
Which of the following can be modeled by a linear function?
A taxi driver charges $3.50 per ride and $0.80 per mile driven.
The relationship between the height of a ball after being kicked from the ground and the distance the ball is from the kicker.
The balance in a savings account that acquires 0.7% interest compounded monthly.
The relationship between the time passed and the speed of a car as it slows down for a curve then accelerates back to its regular speed.
Taxi fares start at $3.50 and go up to $0.80 for every mile traveled is an example of a linear equation. Then the correct option is A.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
Taxi fares start at $3.50 and go up to $0.80 for every mile traveled. This relationship is given by the linear equation.
the link between a ball's height after being kicked off the ground and its proximity to the kicker. This relationship is given by the quadratic equation.
The amount in a savings account earns 0.7% interest each month compounded. This relationship is given by the exponential equation.
A car's slowing down for a curve and then reaccelerating to its usual speed. Its links time and speed. This relationship may be given by the linear equation.
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Fill in the missing amounts (do not use commas or decimal points.)
A$
B$
C$
D$
E$
F$
The missing amount is A. 790 B. 20 C. 90 D. 75 E. 20 F. 275
Subtract non-cash assets from total current assets. This number represents the cash amount on the balance sheet. Below is a simple way to calculate income, capital, and total cost of income: Net Income = Ending Equity Starting Equity from the Balance Sheet Total Expenses = Net Income Net Income.
Everything a company owns must come from debt-equity owners or equity so the equation must be balanced. Equity equals the balance sheet total minus all liabilities. All these figures are on the company's balance sheet. For homeowners, equity is the value of the home minus any outstanding mortgage debt or liens.
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Write an equation in slope - intercept form for the line that passes through the given paint andis parallel to the given equation.4.(-4, 2), y = -1/2x+ 6
When two equation are parallel it means they have the same slope.
You have the equation:
[tex]y=-\frac{1}{2}x+6[/tex]You can identify the slope(m) as the number next to the x in equation that follow the next form:
[tex]y=mx+b[/tex]Then, the equation parallel to the given equation has an slope of:
m= - 1/2Now, if we have a point of the equation we can find the value of the b (y-intercept) in the slope - intercept form of a lineal equation:
[tex]y=mx+b[/tex]The given point is ( -4 , 2)
You have the next values:
m= - 1/2
y= 2
x= -4
Then we substitute that values:
[tex]2=-\frac{1}{2}(-4)+b[/tex]And clear the b:
[tex]2=\frac{4}{2}+b[/tex][tex]2=2+b[/tex][tex]2-2=2-2+b[/tex][tex]0=b[/tex]Now, we get the value of the slope (m= - 1/2) and the y-intercept (b=0)
We can write the equation in slope - intercept form:
[tex]y=-\frac{1}{2}x+0[/tex]or:
[tex]y=-\frac{1}{2}x[/tex]Evaluate lc2 + b21, given a = 5, b=-3, and c= -2. A. 13 B. 6 C. 2 D. 10
We have the function:
[tex]|c^2+b^2|[/tex]We then replace the values of b and c, that is:
[tex]|(-2)^2+(-3)^2|=13[/tex]From this expression, we have that the solution is 13.
