Area of the triangle is 225 sq. cm.
Given:
The base of the triangle is, b = 30cm.
The height of the triangle is, h = 15cm.
The objective is to find the area of the triangle.
The formula to find the area of the triangle is,
[tex]A=\frac{1}{2}\times b\times h[/tex]Now, substitute the given values in the above formula.
[tex]\begin{gathered} A=\frac{1}{2}\times30\times15 \\ A=225cm^2 \end{gathered}[/tex]Hence, the area of the triangle is 225 sq. cm.
Ethan and Evan are twins. They each deposit $3,000 into separate bank accounts.Their accounts each accrue interest annually as shown in the tables below.
Part A.
Ethan's account can be model as a linear equation since it is increasing at a constant rate of the form:
[tex]y=240x+3000[/tex]And Evan's account can be model as a exponential equation of the form:
[tex]y=3000(1.08)^x[/tex]Part B:
Evaluate the 1st and 2nd equation for x = 5:
[tex]\begin{gathered} y=240(5)+3000=4200 \\ y=3000(1.08)^5=4407.98 \\ so\colon \\ \frac{4407.98}{4200}=1.05 \end{gathered}[/tex]It would be 1.05 higher
A contractor bought 10.8 ft² of sheet metal. He has used 3.5 ft² so far and has $219 worth of sheetmetal remaining. The equation 10.8x - 3.5x = 219 represents how much sheet metal is remainingand the cost of the remaining amount. How much does sheet metal cost per square foot?
The first step to do is to combine 10.8x - 3.5x and that is equal to 7.3x.
[tex]7.3x=219[/tex]The next step is to divide both sides by 7.3 to solve for x.
[tex]\begin{gathered} \frac{7.3x}{7.3}=\frac{219}{7.3} \\ x=30 \end{gathered}[/tex]Therefore, the remaining sheet metal is 7.3 ft² and the cost per square foot of sheet metal is $30.
find the exact values of the six trigonometric functions of the angle 0 shown in the figure(Use the Pythagorean theorem to find the third side of the triangle)
The right angled triangle is given with reference angle theta.
The opposite side (facing the reference angle) is 3, while the hypotenuse (facing the right angle) is 5. The adjacent shall be calculated using the Pythagoras' theorem as follows;
[tex]\begin{gathered} \text{Adj}^2+3^2=5^2 \\ \text{Adj}^2=5^2-3^2 \\ \text{Adj}^2=25-9 \\ \text{Adj}^2=16 \\ \text{Adj}=\sqrt[]{16} \\ \text{Adj}=4 \end{gathered}[/tex]Therefore, the trigonometric functions of angle theta are shown as follows;
[tex]\begin{gathered} \sin \theta=\frac{opp}{hyp}=\frac{3}{5} \\ \cos \theta=\frac{adj}{hyp}=\frac{4}{5} \\ \tan \theta=\frac{opp}{adj}=\frac{3}{4} \\ \csc \theta=\frac{hyp}{opp}=\frac{5}{3} \\ \sec \theta=\frac{hyp}{adj}=\frac{5}{4} \\ \cot \theta=\frac{adj}{opp}=\frac{4}{3} \end{gathered}[/tex]jessica bought 4 gallons of paint. Jessica needed to use 3/4 of the paint to paint her living room and dining room. How many gallons did she use, write the number of gallons.
Jessica bought 4 gallons of paint. Of that, she used 3/4 to paint. So the ammount she used was
[tex]4\cdot(\frac{3}{4})=\frac{4\cdot3}{4}=3[/tex]So she used 3 gallons of paint.
A cubic equation has zeros at -2, 1, and 3 a) Write an eqn for a polynomial function that meets the given conditions.b) Draw the graph of a polynomial function that meets the given conditions.
we know that
A cubic equation has zeros at -2, 1, and 3
so
the factors of the cubic equation are
(x+2), (x-1) and (x-3)
Part a
The equation of a polynomial is
[tex]P(x)=(x+2)\cdot(x-1)\cdot(x-3)[/tex]Applying distributive property
[tex]\begin{gathered} P(x)=(x^2-x+2x-2)\cdot(x-3) \\ P(x)=(x^2+x-2)\cdot(x-3) \end{gathered}[/tex]Applying distributive property again
[tex]P(x)=x^3-3x^2+x^2-3x-2x+6[/tex]Combine like terms
[tex]P(x)=x^3-2x^2^{}-5x+6[/tex]Part b
using a graphing tool
see the attached figure below
Mr.Gonzalez spent $50 more than Mr.Silva on school supplies. together, they spent $174. How much money did each of them spent?
Answer: You need to spend more than $5.00
Step-by-step explanation:
Which of the following pairs of numbers do not have a geometric mean of 12? A 11 and 13 B 20 and 7.2 C 3 and 48 D 5 and 28.8
Answer
Option A contains two numbers that do not have a geometric mean of 12.
11 and 13 do not have a geometric mean of 12.
Explanation
The geometric mean of two numbers, a and b, is given as
Geometric mean = √(a × b)
So, we want to find which two numbers will have a geometric mean of 12
12 = √(a × b)
Taking the square of both sides, we see that
144 = (a × b)
So, whichever two numbers give a product of 144 is our answer.
Option A
11 × 13 = 143
Option B
20 × 7.2 = 144
Option C
3 × 48 = 144
Option D
5 × 28.8 = 144
Hope this Helps!!!
Indicate the transformation that has occurred.2.A. (x,y)-->(-x+3.y-5) C. (x,y) --> (-x,y-5)B. (x,y) --> (x +3,y-5) D. (x,y) --> (x-1,-y)
So we have a transformation that maps a triangle into another one. This is made by transforming the points X, Y and Z into X', Y' and Z'. In order to find out which of the four options is the correct one we must verify that points X, Y and Z actually transform into X', Y' and Z'.
We have:
[tex]X=(2,5)\rightarrow X^{\prime}=(1,0)[/tex]Let's see which of the four transformations do this. So for A:
[tex]\begin{gathered} (x,y)\rightarrow(-x+3,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(-x+3,y-5)=(-2+3,5-5) \\ X^{\prime}=(1,0) \end{gathered}[/tex]So transformation A is a possible answer, let's see the rest.
For C:
[tex]\begin{gathered} (x,y)\rightarrow(-x,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(-x,y-5)=(-2,5-5) \\ X^{\prime}=(-2,0)\ne(1,0) \end{gathered}[/tex]So the X' that we calculate with transformation C is different that the one we are looking for so we discard this option.
For option B we have:
[tex]\begin{gathered} (x,y)\rightarrow(x+3,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(x+3,y-5)=(2+3,5-5)=(5,0) \\ X^{\prime}=(5,0)\ne(1,0) \end{gathered}[/tex]Like what happened with C, transformation B is discarded.
Let's see what happens with D:
[tex]\begin{gathered} (x,y)\rightarrow(x-1,-y) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(x-1,-y)=(2-1,-5)=(1,-5) \\ X^{\prime}=(1,-5)=(1,0) \end{gathered}[/tex]So D is also discarded. This would mean that A is the correct option but just in case, let's check if it tansform points Y=(0,2) and Z=(3,1) into Y'=(3,-3) and Z'=(0,-4):
[tex]\begin{gathered} (x,y)\rightarrow(-x+3,y-5) \\ \text{If} \\ Y=\mleft(0,2\mright) \\ \text{Then} \\ Y^{\prime}=(-0+3,2-5)=(3,-3) \\ \text{If} \\ Z=\mleft(3,1\mright) \\ \text{Then} \\ Z^{\prime}=(-3+3,1-5)=(0,-4) \end{gathered}[/tex]So Y' and Z' are (3,-3) and (0,-4) which definetely means that option A is the correct one.
A population grows according to an exponential growth model. The initial population is 224 and the population after one year is 263. Complete the formula where P is the population and n is the number of years.: P=224*(___)n
Round your answer to three decimal places.
The equation of the population function is is P = 224(1.17)ⁿ
How to complete the equation?From the question, the given parameters are:
Initial population = 224Population after one year = 263The above parameters imply that the rate of change of the population every year is
Rate = Population after one year/Initial population
Substitute the known values in the above equation
So, we have
Rate = 263/224
Evaluate the quotient
Rate = 1.17
The exponential function can be represented as
P = Initial population * (Rate)ⁿ
So, we have
P = 224(1.17)ⁿ
Hence, the complete equation is P = 224(1.17)ⁿ
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The required rate of the increase in the population is 17% and the equation is fulfilled as P = 224 (1.17)ⁿ.
As per the question, the population of the 2 years are given as 224 and the preceding year's population is 263 and equation is illustrated the exponential growth is given as P = 224(__)ⁿ. The blank space in the equation is to be filled.
The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
The given function of the population is incomplete as rate of growth is missing, So,
The rate is given as,
Rate = 263 - 224 / 224
Rate = 0.17 or 17%
Growth = 1 + 0.17 = 1.17
now, put this growth rate in the blank space.
So,
P = 224 (1.17)ⁿ
Thus, the required rate of the increase in the population is 17% and the equation is fulfilled as P = 224 (1.17)ⁿ.
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Question 4 of 10 In the function y + 3 = (2x)2+1, what effect does the number 2 have on the graph, as compared to the graph of y=x"? 2 A. It shrinks the graph vertically to 1/2 the original height. B. It stretches the graph vertically by a factor of 2. C. It stretches the graph horizontally by a factor of 2. O OD. It shrinks the graph horizontally to 1/2 the original width
The parental function of the graph is,
[tex]y+3=(x)^2+1[/tex]The transformed function of the graph is,
[tex]y+3=(2x)^2+1[/tex]The transformation between the parent function and the transformed function will be resolved graphically.
From the graph above, the parent function is represented with red while the transformed image is represented with green colour.
We can conclude that the parent function was shrinked horizontally by 1/2.
Hence, it shrinks the graph horizontally to 1/2 the original width.
The correct option is Option
can I please getsome help with this question here, I can't really figure out how to find side PQ
SOLUTION
The following diagram will help us solve the problem
(a) From the diagram, the height of the parallelogram is given as TR, and it is 40 mm
Now we can use the area which is given to us as 3,600 square-mm to find the base of the parallelogram, which is PQ
So,
[tex]\begin{gathered} \text{Area }of\text{ a parallelogram = base}\times height \\ So\text{ } \\ 3600=PQ\times TR \\ 3600=PQ\times40 \\ 3600=40PQ \\ \text{dividing by 40, we have } \\ \frac{3600}{40}=\frac{40PQ}{40} \\ PQ=90 \end{gathered}[/tex]Hence PQ is 90 mm
(b) Now, note that the side
[tex]PS=QR[/tex]So, we will find QR
Also, since we have PQ, we can find TQ, that is
[tex]\begin{gathered} PQ=PT+TQ \\ 90=60+TQ \\ TQ=90-60 \\ TQ=30mm \end{gathered}[/tex]Note that triangle QRT is a right-angle triangle, and QR is the hypotenuse or the longest side
From pythagoras
[tex]\text{hypotenuse}^2=opposite^2+adjacent^2[/tex]So,
[tex]\begin{gathered} QR^2=TR^2+TQ^2 \\ QR^2=40^2+30^2 \\ QR^2=1600+900 \\ QR^2=2,500 \\ QR=\sqrt[]{2,500} \\ QR=50mm \end{gathered}[/tex]Now, since
[tex]\begin{gathered} PS=QR \\ \text{then } \\ PS=50mm \end{gathered}[/tex]Hence PS is 50 mm
Determine whether the graph represents a function.
A, the relation is not a function
in order for something to be a function, x (the input) can't repeat itself more than once
Question 6 What is the factored form of the expression below? 7 - 16 O OD (x-8)(x - 8) (x - 4)(x + 4) (x - 4)(x - 4) (x-8)(x + 8) Oo
If :
[tex]x^2-16[/tex][tex]\begin{gathered} \sqrt[]{x^2}=x \\ \sqrt[]{16}=4 \end{gathered}[/tex]Then:
[tex]x^2-16\text{ =(x-4)(x+4)}[/tex]Answer: ( x - 4 ) ( x + 4 )
Use the following data set to answer the question below.8 12 15 9 101212 18 14 1510 11 12 9 17What is the range for the data set?
Given the following set of data:
8 12 15 9 10 12 12 18 14 15 10 11 12 9 17
We will find the range of the data.
We need to find the maximum and the minimum
The maximum = 18
The minimum = 8
So, the range = maximum - minimum = 18 - 8 = 10
So, the answer will be The range = 10
Which compound inequality does the number line represent
The compound ineqality which the number line represents will be 5x ≥ -15 or 5x ≤ 10 so option (B) must be correct.
What is inequality?
A difference between two values reveals whether one is greater, smaller, or fundamentally different from the other.If the sides are not equal, an expression in mathematics is said to be unequal. The result of comparing any two values is a determination of whether one is smaller, bigger, or equal to the value on the opposite side of the equation.In option (B) given that
5x ≥ -15
⇒ x ≥ -15/5
⇒ x ≥ -3
And
5x ≤ 10
⇒ x ≤ 10/5
⇒ x ≤ 2
By looking at the number line it is clear that the blue line is greater than -3 and less than 2 hence it will be correct.
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Which of the following is not a correct way to name the plane.
For this case the first option is correct Plane P
What is the complement of P(A) if P(A) = 0.52P(A) =
Given
P(A) = 0.52
Find
complement of P(A)
Explanation
As we know sum of probabilities is equal to one,
so ,
[tex]\begin{gathered} P(A)+P^{\prime}(A)=1 \\ P^{\prime}(A)=1-0.52 \\ P^{\prime}(A)=0.48 \end{gathered}[/tex]Final Answer
Therefore, the complement of P(A) = 0.48
What is the distance between (-5, 5) and (1, -2)
Answer:
[tex]\displaystyle d=\sqrt{85}\text{, or about 9.22 units}[/tex]
Step-by-step explanation:
We will use the distance formula to solve.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(1--5)^2 +(-2-5)^2}[/tex]
[tex]\displaystyle d=\sqrt{(6)^2 +(-7)^2}[/tex]
[tex]\displaystyle d=\sqrt{36+49}[/tex]
[tex]\displaystyle d=\sqrt{85}\text{, or about 9.22 units}[/tex]
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HELP ASAP
QUESTION IS ATTACHED!
Answer:
(2,8) and (-6,0)Step-by-step explanation:
(3,9)
(-5*3) +( 3*9) > 12
-15 + 27 > 12
12 > 12
not true
(-5,5)
(-5*5) + (3*5) > 12
-25 + 15 > 12
-10 > 12
not true
(3,-6)
(-5*3) + (3*-6) > 12
-15 + -18 > 12
-33 > 12
not true
(-2,-5)
(-5*-2) + (3*-5) > 12
10 + -15 > 12
5 > 12
not true
(2,8)
(-5*2) + (3*8) > 12
-10 + 24 > 12
14 > 12
true(-6,0)
(-5*-6) + (3*0) > 12
30 + 0 > 12
30 > 12
truehelp me please i'm stuck Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks. Myra owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 3 small tiers and 4 large tiers, which will serve a total of 226 guests. The second one includes 1 small tier and 1 large tier, which is enough servings for 62 guests. How many guests does each size of tier serve? A small tier will serve ? guests and a large tier will serve ? guests.
the number of guests a small tier can serve is 22
the number of guest a large tier serves is 40
Explanation
Step 1
Set the equations
a) let
x represents the number of guest one small tier serves
y represents the number of guests one large tier serves
b) translate into math term
i)The first cake consists of 3 small tiers and 4 large tiers, which will serve a total of 226 guests,so
[tex]3x+4y=226\Rightarrow equation(1)[/tex]ii) The second one includes 1 small tier and 1 large tier, which is enough servings for 62 guests,so
[tex]x+y=62\Rightarrow equation(2)[/tex]Step 2
solve the equations:
[tex]\begin{gathered} 3x+4y=226\Rightarrow equation(1) \\ x+y=62\operatorname{\Rightarrow}equat\imaginaryI on(2) \end{gathered}[/tex]a) isolate the x value in equation (2) and replace in equatino (1) to solve for y
[tex]\begin{gathered} x+y=62\Rightarrow equation(2) \\ subtract\text{ y in both sides} \\ x=62-y \end{gathered}[/tex]replace into equation(1) and solve for y
[tex]\begin{gathered} 3x+4y=226\Rightarrow equation(1) \\ 3(62-y)+4y=226 \\ 186-3y+4y=226 \\ add\text{ like terms} \\ 186+y=226 \\ subtrac\text{ 186 in both sides} \\ 186+y-186=226-186 \\ y=40 \end{gathered}[/tex]so, the number of guest a large tier serves is 40
b)now, replace the y value into equation (2) and solve for x
[tex]\begin{gathered} x+y=62\Rightarrow equation(2) \\ x+40=62 \\ subtract\text{ 40 in both sides} \\ x+40-40=62-40 \\ x=22 \end{gathered}[/tex]so, the number of guests a small tier can serve is 22the number of guests a small tier can serve is 22
I hope this helps you
Point Q is shown on the number line. Which Value is best represented by point Q? 15 6
According to the given graph, the point Q is between 5 and 5.50.
Therefore, the number that best describes point Q is
[tex]\sqrt[]{29.5}\approx5.4[/tex]Since it's between 5 and 5.50 too.
What are the lengths of segments PQ and QR? input the lengths. then click done.
Write the expression as a complex number in standard form.
(-2+6i)-(2-3i)=
Answer:
-4 +9i
Step-by-step explanation:
complex number in standard form.
(-2+6i)-(2-3i)=
Combine like terms
-2 -2 +6i +3i
Standard form is a+bi
-4 +9i
I Need some help on this assignment Also the second half to the problem how much will be spent on the job from the 10 to 20th day
Explanation
[tex]f(x)=4.1x+1.9[/tex]
where x is the number of days since the start of the job
and f(x) is the rate of change
Step 1
a)find the total expenditure if the job takes 12 days
so, as x represents the number of days, just replace and calculate
let x= 12
[tex]\begin{gathered} f(x)=4.1x+1.9 \\ f(12)=4.1(12)+1.9 \\ f(12)=49.2+1.9 \\ f(12)=51.1 \end{gathered}[/tex]so
a) 51.1
Step 2
now, let's find the total spent on the job from the 10 to 20th day
a) find the x value ( number of days since the job started)
x= 20 days-10dys= 10
so
x= 10
Omar has $84 and maryam has $12. how much money must Omar give to maryam so that maryam will have three times as much as omar? let x be the amount of dollars Omar will give maryam. which equation best represents the situation described above? A.) 84 - x = 3(12) + xB.) 3(84 - x) = 12 - xC.) 3(84 - x ) = 12 + xD.) 3x = 84 - (12 + x)
Given data:
The given money Omar has $84.
The given money maryam has $12.
The expression for the money Omar give to maryam so that maryam will have three times as much as omar.
[tex]3(84-x)=12+x[/tex]Thus, the final expression is 3(84-x)=12+x.
Solve the following system of equations using the elimination method. Give the final answer in (x,y) form.
Anisha used the substitution method to solve the system of equations.
She is missing the value of y.
To find it we plut the value of x in the first equation, then:
[tex]y=4-5=-1[/tex]Therefore the solution is (4,-1)
How do you Graph g(x)=x^5-2x^4 ?
Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values.
Finding a polynomial of a given degree with given zeros: Complex zeros
Given:
• Degree of polynomial = 3
,• Zeros of the polynomial: 2, 3 - 2i
Let's find the polynomial.
Since the polynomail is of degree 3, it's highest exponent will be 3.
Equate the zeros to zero:
x = 2
Subtract 2 from both sides:
x - 2 = 2 - 2
x - 2 = 0
x = (3 - 2i)
Since this root is a complex conjugate, we have the other complex root: (3 + 2i)
Hence, we have:
(x - (3 - 2i)) and (x - (3 + 2i)).
Therefore, to write the function, we have:
[tex]f(x)=(x-2)(x-(3-2i))(x-(3+2i))[/tex]Now, simplify the expression:
[tex]\begin{gathered} f(x)=(x-2)(x-3+2i)(x-3-2i) \\ \\ f(x)=x(x-3+2i)-2(x-3+2i)(x-3-2i) \\ \\ f(x)=x^2-3x+2ix-2x+6-4i(x-3-2i) \\ \\ f(x)=x^2-5x+2ix-4i+6(x-3-2i) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} f(x)=x(x^2-5x+2ix-4i+6)-3(x^2-5x+2ix-4i+6)-2i(x^2-5x+2ix-4i+6) \\ \\ f(x)=x^3-5x^2+2ix^2-4ix+6x-3x^2+15x-6ix+12i-18-2ix^2+10ix-4i^2x-8-12i^{} \end{gathered}[/tex]Combine like terms:
[tex]\begin{gathered} f(x)=x^3-5x^2-3x^2-4ix-6ix+10ix+2ix^2-2ix^2+6x+15x+12i-12i-8-16 \\ \\ f(x)=x^3-8x^2+25x-26 \end{gathered}[/tex]ANSWER:
[tex]f(x)=x^3-8x^2+25x-26[/tex]If I complete this review, then I will do well on the test. If I do well on the test. If I do well on the test, then I will get an “A” on my progress report. Make a conclusion using the law of syllogism
Law of syllogism:
If p, then q
If q, then r
Conclude:
If p, then r
Given situation:
p: complete this review
q: do well on the test
r: get an “A” on my progress report
If p, then q: If I complete this review, then I will do well on the test
If q, then r: If I do well on the test, then I will get an “A” on my progress report
Conclusion:
If p, then r: If I complete this review, then I will get an “A” on my progress report
Option 1: Piecewise Defined Functions
A t-shirt company is looking to buy t-shirts from a distributor. They are trying to decide which distributor would be best for them when they buy about 80 shirts for their weekly order. Justify your answer with a piece wise function and discuss what you would do if you were in charge. A review on this topic can be found in the Instruction of Piecewise Defiined functions slide 15.
Company 1:
Shirts are $11 a piece for the first 100. After the first 100 each additional shirt is $7.50.
Company 2
$12 a piece for the first 50, $9.50 each additional shirt.
Answer:
-105$
Step-by-step explanation:
