Sarah sold her stock for $56.25 A share, which reflected a ROI of 7.7%. What was the original price of her stock?
Triangle ABC is similar to triangle PQR, as shown below:
Which ratio is equal to r:c?
A. c:p
B. p:a
C. r:a
D. q:c
rotate the triangles so r and c line up
when you do that Q=B, a=p, C=R, b=q, A=P
so answer would be B. p:a
we know that
If triangle ABC is similar to triangle PQR
then
the corresponding sides are proportional
so
[tex]\frac{RQ}{CB} =\frac{RP}{AC}= \frac{PQ}{AB}[/tex]
substitute the values
[tex]\frac{p}{a} =\frac{q}{b}= \frac{r}{c}[/tex]
therefore
[tex]\frac{r}{c}[/tex]
is equal to
[tex]\frac{q}{b}[/tex] and [tex]\frac{p}{a}[/tex]
the answer is the option B
[tex]\frac{p}{a}[/tex]
Write an equation in slope-intercept form of the line through point (6, –1) with slope m=4. Question 6 options: y + 1 = 4(x – 6) y = 4x – 1 y = 4x – 25 y + 6 = 4(x – 1)
Maria was given a 5% raise on her weekly salary of $375.
Select from the drop-down menu to correctly complete the sentence.
A. 0.005(400)
B. 0.05(400)
C. 0.5(400)
D. 5(400)
Please explain your answer so I can understand it Thanks!
Factor 9y 2 - 12y + 4.
Answer:
Factors of the expression given in the question i.e 9y² - 12y + 4 is (3y -2)(3y -2) .
Step-by-step explanation:
As the expression is given in the question be .
= 9y² - 12y + 4
Simplify the above
= 9y² -6y -6y + 4
= 3y (3y -2) -2 (3y - 2)
= (3y-2)(3y-2)
Therefore factors of the expression given in the question i.e 9y² - 12y + 4 is (3y -2)(3y -2) .
Write a function rule (equation) that represents each table.
graph the function for the given domain. y=2x D:{ -2,0,2,4}
We want to graph the given function for the given domain.
The graph can be seen at the end of the answer.
The given function is:
y = 2*x
The given domain is D: {-2, 0, 2, 4}
To graph this, we need to evaluate the function in the given values of the domain, we will get four points.
y = 2*(-2) = -4
Then we have the point (-2, -4)
y = 2*0 = 0
Then we have the point (0, 0)
y = 2*2 = 4
Then we have the point (2, 4)
y = 2*4 = 8
Then we have the point (4, 8)
Then we need to graph these four points, the graph can be seen below:
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Given: ∆ABC, AB = CB
BD − altitude to AC
P ∈ BD, PB = PC
m∠ABC = 48°
Find: m∠PCD
Answer: The measure of angle PCD is 42 degree.
Explanation:
It is given that in ∆ABC,
AB = CB
BD − altitude to AC
P ∈ BD, PB = PC
∠ABC = 48°
Since the AB and CB are equal therefore by property of isosceles triangle the angle BAC and angel BCA are equal.
According to the angle sum property the the sum of interior angles of a triangle is 180.
[tex]\angle ABC+\angle BAC+\angle BCA=180^{\circ}[/tex]
[tex]48^{\circ}+2\angle BAC=180^{\circ}[/tex]
[tex]\angle BAC=66^{\circ}[/tex]
The altitude BD on AC divides the angle b in two equal parts because triangle ABC is an isosceles triangle.
[tex]\angle PBC=\frac{48}{2}=24^{\circ}[/tex]
Since PB=PC , so triangle BPC is an isosceles triangle.
[tex]\angle PBC=\angle PCB=24^{\circ}[/tex]
From the figure it is noticed that,
[tex]\angle PCD+\angle PCB=\angle BCA[/tex]
[tex]\angle PCD+24^{\circ}=66^{\circ}[/tex]
[tex]\angle PCD=66^{\circ}-24^{\circ}[/tex]
[tex]\angle PCD=42^{\circ}[/tex]
Therefore, the measure of angle PCD is 42 degree.
Mohave Community College reimburses faculty members $.298 cents per mile to go to a workshop. Professor Boes submitted her travel log for a total of 650.11 miles. What reimbursement can Professor Boes expect? (Round to the nearest cent.)
Three zeroes of a fifth degree polynomial function are 1/3, 4-6i and -2 +11i. Determine the remaining zeroes of the function.
Answer:
Answer is option A
Step-by-step explanation:
Given that there is a fifth degree polynomial. The three zeroes are given as
1/3, 4-6i, -2+11i
Since the polynomial having real coefficients will have imaginary roots occurring in conjugates only we can say that the imaginary roots will have conjugates also as zeroes of the polynomial.
We have one real root 1/3.
The imaginary roots are 4-6i and -2+11i
Hence these conjugates will be zeroes
i.e. [tex]4-6i, -2-11i[/tex] are the other zeroes
Option A is right.
Which number is not in scientific notation?
a. 1.1 x 10^213
b. 7.8 x 10^8
c. 3.02 x 10^-10
d. 35 x 10^4
At the annual dogs show chantel noticed that there were three more Scottie’s than schnauzers. She also realized that the number of wire haired terriers was five less than twice the number of schnauzers if there were 78 dogs in all how many schnauzers were their?
a dime has the circumference of about 56.27 millimeters. What is the radius of the dime? Round to two decimal places!
what times 8 equals 36
The result of dividing 36 by 8 is 4.5. This means that there is no whole number that when multiplied by 8 equals 36; the closest is 4, giving us 32, with a remainder that results in 4.5 as the exact quotient.
The question the student is asking relates to basic arithmetic multiplication. Specifically, they're looking for a number that, when multiplied by 8, results in 36. To solve for this, we would generally divide 36 by 8.
However, because 36 is not a multiple of 8, we cannot get a whole number as the result. Instead, the closest we can get without going over is 4, because 4 multiplied by 8 equals 32. If we divide 36 by 8, the result is 4 with a remainder, or 4.5 (which can be expressed as 41/2).
The correct approach to find the quotient is to perform the division 36 / 8, which equals 4.5. To understand this better, you can think of it as having 36 objects that you want to divide into groups of 8 and trying to see how many full groups you can make. You would be able to make 4 full groups with 4 objects left over, or you could see it as making 4 and a half groups.
the first side of a triangle is 3 m shorter than the second side. the third side is 4 times as long as the first side . the perimeter is 27 m. find the length of each side
HELP please I have a bunch of these and I’m stressing cause I have like 50 tests tomorrow
What percent of 67.5 is 7.02 ? Answer in proportions
The percent of 67.5 is equal to 7.02 is for the number 10.4.
To find what percent of 67.5 is 7.02, we can use proportions.
Let's represent the unknown percentage as 'x'. The proportion can be set up as follows:
(7.02 / 67.5) = (x / 100)
Now, solve for 'x':
7.02 × 100 = 67.5 × x
702 = 67.5x
x = 702 / 67.5
x ≈ 10.4
Therefore, 7.02 is approximately 10.4 percent of 67.5.
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The Smiths want to buy a 9 ft. by 12 ft. carpet and center it in a 15 ft. by 20 ft. room.
What is the area of the area NOT covered by the carpet?
Answer: The required area of the room that is NOT covered by the carpet is 192 ft².
Step-by-step explanation: Given that the Smith wants to buy a 9 ft. by 12 ft. carpet and center it in a 15 ft. by 20 ft. room.
We are to find the area of the room that is NOT covered by the carpet.
We know that the area of a rectangle is given by the product of its length and breadth.
So, the area of the carpet bought by Smith is
[tex]A_c=9\times12=108~\textup{ft}^2,[/tex]
and the are of the room is
[tex]A_r=15\times 20=300~\textup{ft}^2.[/tex]
Therefore, area of the room that is NOT covered by the carpet will be
[tex]A=A_r-A_c=300-108=192~\textup{ft}^2.[/tex]
Thus, the required area of the room that is NOT covered by the carpet is 192 ft².
5x+4x2(2x+7)-6x2-9x+(x+3)(x-8)
Write this expression as a polynomial in standard form
a. If m<7 = 37 , what is in m<4 ?
b. If m<7 = 37 , what is in m<2 ?
c. Describe the relationship between <4 and <8 .
d. Describe the relationship between <3 and <5 .
Answer:
a). m∠4 = 143°
b). m∠2 = 37°
c). ∠4 ≅ ∠8
d). ∠3 + ∠5 ≅ 180°
Step-by-step explanation:
a). Given m∠7 = 37°
Since m∠7 ≅ m∠6 [Vertically opposite angles]
and m∠6 + m∠4 = 180° [Sum of interior angles formed by parallel lines l, m and transverse.]
Therefore, 37°+ m∠4 = 180°
m∠4 = 180 - 37
= 143°
b). Since m∠6 ≅ m∠2 [Corresponding angles]
and m∠6 ≅ m∠7 [Vertically opposite angles]
Therefore, m∠2 ≅ m∠6 ≅ m∠7 ≅ 37°
c). ∠4 ≅ ∠8 [Corresponding angles]
d). ∠3 + ∠5 ≅ 180° [Interior angles of parallel lines m, l and a transverse].
HELP!
Solve for x.
−1/3x≤−6
Enter the solution to the inequality in the box.
Answer:
x [tex]\geq[/tex] 18
Step-by-step explanation:
Factor this polynomial expression. x2 – 18x + 81
Factorizing the polynomial expression x² - 18x + 81 = (x - 9)²
What is factorization?Factorization is the simplification of an expression into a smaller expression using its factors.
To factor this polynomial expression. x² - 18x + 81, we proceed as follows
Since we have the polynomial expression x² - 18x + 81, we multiply x² by 81 to get x² × 81 = 81x².
Now, we look for the factors of 81x² such that the sum of those factors equal - 18x
So, we have that 81x² = -9x × (-9x)
So, -18x = -9x - 9x
So, replacing this with -18x, we have that
x² - 18x + 81 = x² - 9x - 9x + 81
Now, factorizing, we have that
x² - 9x - 9x + 81 = x(x - 9) - 9(x - 9)
= (x - 9)(x - 9)
= (x - 9)²
So, factorizing x² - 18x + 81 = (x - 9)².
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If the following two triangles are similar, find X.
Show work please
The cooking time for a ham is 2/5 of an hour for each pound. A.) How long should you cook a ham that weighs 12 3/4 pounds? B.) Dinner time is 4:45 pm. What time should you start cooking the ham?
To cook a 12 3/4 pounds ham which requires 2/5 of an hour for each pound, it will take approximately 5.1 hours. If dinner is at 4:45 pm, you should start cooking around 11:39 am.
Explanation:The subject of your question is Mathematics. To solve this problem, let's understand first that the cooking time for a ham is 2/5 of an hour for each pound. This means that for each pound of ham, it should be cooked for 2/5 hour.
A.) To find how long you should cook a ham that weighs 12 3/4 pounds, you need to multiply that weight by 2/5. (12 3/4) * (2/5) ≈ 5.1 hours. So, you would need to cook the ham for approximately 5.1 hours.
B.) If dinner time is at 4:45 pm, and you know that the ham takes about 5.1 hours to cook, simply subtract 5.1 hours from the dinner time to find out when you should start cooking. 4:45pm - 5.1 hours ≈ 11:39am. Hence, you should begin cooking at around 11:39am to have the ham ready by 4:45pm.
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Giorgio surveyed 45 randomly selected shoppers at the mall and found that approximately 24% believe that the food court needs to be remodeled. To the nearest percent, with a confidence level of 99% (z*-score 2.58), what is the confidence interval for the proportion of shoppers who believe the food court needs to be remodeled? E = z* and C = + E
Answer with explanation:
Number of People Surveyed (S)= 45
Confidence Level = 99%
Percentage of population who believe that food court needs to be remodeled =24 %
→So, 24% of 45
[tex]=\frac{24}{100}\times 45=10.80[/tex]
= 11 people
Probability of population who thinks that food court needs to be remodeled(P)
[tex]=\frac{11}{45}[/tex]
[tex]Z_{99 percent}= 2.58[/tex]
Confidence level for a population is given by
[tex]=P \pm Z\sqrt{\frac{P*(1-P)}{S}}[/tex]
Substituting the values, of Z, P and S in above equation
[tex]=0.25\pm 2.58\sqrt{\frac{0.25*0.75}{45}}\\\\=0.25 \pm 2.58*0.064549\\\\=0.25 \pm 0.17\\\\= 0.25 - 0.17 , 0.25+0.17\\\\=0.08 , 0.42[/tex]
→→0.08 ≤proportion of shoppers who believe the food court needs to be remodeled≤0.42
→→8%≤proportion of shoppers who believe the food court needs to be remodeled≤42%
. Earl purchased a living room set for $3,592 using a 12-month deferred payment plan. The interest rate after the introductory period is 21.80%. A down payment of $275 is required as well as a minimum monthly payment of $112. What is the balance after the introductory period if only the minimum payment is made until then?
Answer:
The required answer is $2839.25.
Step-by-step explanation:
[tex]112\times12=1344[/tex] dollars
Plus down payment = [tex]1344+275=1619[/tex] dollars
Now, compound interest is found as:
[tex]A=p(1+\frac{r}{n})^{nt}[/tex]
p = 3592
r = 21.80% or 0.2180
n = 12
t = 1
Substituting the values in formula:
[tex]A=3592(1+\frac{0.2180}{12})^{12}[/tex]
=> [tex]A=3592(1.018167)^{12}[/tex]
A = $4458.25
So, Balance = [tex]4458.25-1619=2839.25[/tex] dollars
Therefore, the required answer is $2839.25.
identify a pattern and find the next number in the pattern -0.8, -3.2, -12.8, -51.2
A:-358.4
B:-204.8
C:-51.2
D:4
The next number in the pattern -0.8, -3.2, -12.8, -51.2 is -204.8.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
The numbers are -0.8, -3.2, -12.8, -51.2.
To find the pattern:
Divide the number to find the proportionate rate,
-3.2/-0.8 = 4
-12.8/-3.2 = 4
-51.2 /-3.2 = 4
So, the proportionality relationship is,
number = 4 x previous number.
So, the next number,
-51.2 x 4
= -204.8
Therefore, the number is -204.8.
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How many feet of fencing are need to enclose a triangular lot?
Give three examples of when negative numbers are used in daily life
Given right triangle ABC. To the nearest degree, find the measure of angle B.
Answer:
Step-by-step explanation:
We have the length of AC which is opposite angle B; we also have the length of the hypotenuse. We will use trig here to solve for angle B. The sin ratio is the one that fits.
sin(B) = side opposite / hypotenuse:
[tex]sin(B)= \frac{ 4.8}{ 5.1}[/tex] so
sin(B) = .9411764706
Now we will use the 2nd button on our calculators. This will give us the missing angle value. Press 2nd then sin and you will see on your screen:
[tex]sin^{-1 ([/tex]
Enter that decimal after the open parenthesis and hit "enter" to get
B = 70.25 or 70°