Answer:
The correct answer is "x = 4" and "x = -12".
Step-by-step explanation:
The given equation is:
⇒ [tex]x^2+8x-30=18[/tex]
On subtracting "18" from both sides, we get
⇒ [tex]x^2+8x-30-18=18-18[/tex]
⇒ [tex]x^2+8x-48=0[/tex]
On applying factorization, we get
⇒ [tex]x^2+12x-4x-48=0[/tex]
On taking common, we get
⇒ [tex]x(x+12)-4(x+12)=0[/tex]
⇒ [tex](x-4)(x+12)=0[/tex]
⇒ [tex]x-4=0[/tex]
[tex]x=4[/tex]
or,
⇒ [tex]x+12=0[/tex]
[tex]x=-12[/tex]
Activity 1: Keep Trying
Direction: Read, understand, analyze the given problem and solve it by applying the suggested
steps. Write your answer on the box provided.
1. Esther gave birth to a new-born baby weighing 5 kg at birth. Her friend told her that
the monthly average weight gained by a baby is 2 kg. If the rate of increase of the baby's
weight every month is constant, what is the weight of the baby after five months?
Perlom
Solution
Step 5
ernalia
Step 1
Step 2
Step 4
Step 3
nent anar
lia
The weight of the baby after five months is 15 Kg.
Step 1:
Given:
New-born baby weight = 5kg
Monthly average weight gained = 2kg
To find:
The weight of the baby after 5 months.
Average Weight of Baby:
Birth weight is the weight of the baby at birth. [1] The average birth weight of babies of European descent is 3.5 kilograms, with a normal range of 2.5 to 4.5 kilograms (5.5 to 9.9 pounds). On average, South Asian and Chinese babies weigh about 3.26 kg. The prevalence of low birth weight infants decreased slightly from 7.9% (1970) to 6.8% (1980), then increased slightly to 8.3% (2006) and is currently at 8.2% (2016).
Step 2:
Represent the unknown.
Let x-the number of months .
Let y-weight of the baby after 5 months.
Step 3:
Formulate the equation.
The mathematical equation is:
5+2x = y
Step 4:
Solve the equation.
5+2x = y
5+2(5) = y
5+10 = y
y = 15
Thus, the baby weight is 15kg after 5 months.
Step 5:
Using the equation 5+2x=y.
5+2x = y
5+2(5) = 15
5+10 = 15
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Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1). Determine the scale factor used.
1
1/2
3
1/3
If Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1) then the scale factor used is 1/3
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1).
A(−3, −3)---->A(−3/3, −3/3)---->A′(−1, −1)
B(3, 3)---->B(3/3, 3/3)---->B′(1, 1)
C(0, 1)---->C(0/3, 1/3)---->B′(0, 1/3)
Hence, the scale factor used is 1/3.
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Scale Factor
Smaller Figure:
Larger Figure:
Please please help, no links
Answer:
2/3
Step-by-step explanation:
you reduce the fraction to get the scale factor. so 8/12 reduces down to 2/3 which is the scale factor
Tom says that he needs 6 rolls to obtain each possible outcome on a 6-sided die. On the fourth roll, he rolls his second "3”. Tom says that the die is loaded and that each outcome is not equally likely. Is Tom correct here? If you think Tom is incorrect, how many rolls should Tom make until he sees each number occurring about 1/6 of the time?
I DON'T KNOW HOW TO SOLVE FOR HOW MANY ROLLS (the last part)
Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.
Answer:
The correct option - Figure A
Step-by-step explanation:
The exact question is as follows :
Given - Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.
1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3
To find - Which box plot shows this data set?
Solution -
Given the data is -
1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3
Firstly,
Arrange the data from smallest to largest
0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 7
Now,
Find the median
Median is the middle value - i.e. (15 + 1)/2 = 8th value
So, we get Median = 2
Now,
Find the Quartile -
The first quartile is the median of the data points to the left of the median.
i.e. Median of 0, 0, 0, 0, 0, 1, 1
so, we get
Q1 = 0
The third quartile is the median of the data points to the right of the median.
i.e. Median of 2, 2, 2, 3, 3, 5, 7
so, we get
Q3 = 3
Now,
Compute the min and the max
Minimum value = 0
Maximum value - 7
So,
five number summary is -
0, 0, 2, 3, 7
And we draw the box as follows -
So,
The correct option - Figure A
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 9 inches, and the length of the base is 7 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.
Answer:
26.3
Step-by-step explanation:
The altitude splits the 7-inch base into two 3.5-inch pieces find the missing sides:
3.5^2+9^2=c^2
9.656603=c
7+9.657+9.657=the perimeter
26.314 or 26.3
WILL MARK BRAINLIEST ANSWER IF RIGHT
ILL BRAINLIEST YOU PLEASE HELP ME
Answer: x = 34
Step-by-step explanation: ok so when you put 2 triangles together and make a rectangle the length and width will still be the same! so the answer is 34ft
A sequence is represented by the explicit formula
The value of a₂₆ in the arithmetic sequence aₙ= 14 + 9n is 248.
The correct option is D.
What is an arithmetic sequence?A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
An arithmetic sequence,
aₙ= 14 + 9n
We have to find the value of a₂₆.
That means, n = 26.
Substitute the value of n = 26 to the sequence,
a₂₆ = 14 + 9(26)
a₂₆ = 14 + 234
a₂₆ = 248
Therefore, the value of a₂₆ is 248.
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I need help on this math question !!! All the questions are on the second screenshot and there is a graph included .
The blank words are 5 cm, 5 cm, 5 cm, 5 cm, adjacent, equal, 3/4, -4/3, 3/4, -4/3, adjacent, perpendicular, equal.
What is quadrilateral?
A quadrilateral in geometry is a four-sided polygon with four edges and four corners.
I will prove that quadrilateral KLMN is a square by demonstrating that
all sides are of equal measure,
and adjacent sides are perpendicular.
To prove all sides are equal:
KL = 5 cm
LM = 5 cm
MN = 5 cm
NK = 5 cm
The four sides are of 5 measure.
To prove adjacent sides are perpendicular:
slope of KL = 3/4
slope of LM = -4/3
slope of MN = 3/4
slope of NK = -4/3
The slopes of any pair of adjacent sides are perpendicular.
That being the case, those sides are equal.
Therefore, 5 cm, 5 cm, 5 cm, 5 cm, adjacent, equal, 3/4, -4/3, 3/4, -4/3, adjacent, perpendicular, equal are the blank words.
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What does the letter "B" represent?
Seth built a wooden step stool out of two rectangular prisms and two cubes. Before fastening the components together, he stained each component to give it its final color.
To completely stain the bottom rectangular prism, Seth had to cover
square inches of wood. For one of the cubes to be completely stained, he had to cover
square inches of wood. To completely stain the top rectangular prism, he had to cover
square inches of wood.
Once the stool was fastened together, he applied a coat of sealant to all exposed surfaces of the stool, including the bottom, to cover a total of
square inches.
To complete stain the bottom rectangular prism, he needs to cover 624 square inches.
What is surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up.
Given that:
Bottom rectangular prism:
Length = 22 in
Width = 8 in
Height = 6 in
The surface area of the rectangular prism is:
SA = 2( lh + wh + lw)
SA = 2((22)(6) + (8)(6) + (22)(6))
SA= 624 square inches.
To complete stain the bottom rectangular prism, he needs to cover 624 square inches.
Square:
Side = 4 in
The surface area of the cube is:
[tex]SA = 6a^2[/tex]
[tex]SA = 6 (4)^2\\\\SA= 96[/tex]square inches.
To completely stain two squares, he needs to cover 96 * 2 = 196 square inches.
Top rectangular prism:
Length = 18 in
Width = 5 in
Height = 2 in
The surface area of the rectangular prism is:
SA = 2( lh + wh + lw)
SA = 2((18)(2) + (5)(2) + (18)(5))
SA = 136 square inches
Hence to completely stain top rectangular prism, he needs to cover 136 square inches.
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what is the probability of spinning the pointer on the spinner below and getting a 2 or 4
Answer:
The probability would be 2/5
Step-by-step explanation:
There is five numbers on the spinning and the chance of getting one certain number would be 1/5, and if you add the two probabilities together would be 2/5, I am pretty sure.
Becca hiked a total distance of 8.8 miles on three different trails.
• She hiked 4.8 miles on the first trail.
• She hiked 2.2 miles on the second trail.
What is the number of miles Becca hiked on the third trail?
Answer:
1.8
Step-by-step explanation:
4.8 + 2.2 = 7
8.8 - 7 = 1.8
margin of error of 1 percentage and use a confidence level of 90%.
The sample size needed for a margin of error of 1%, for a confidence level of 90%, is of:
6,766.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error of the interval is defined as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.
We have no prior estimate, hence the proportion is given as follows:
[tex]\pi = 0.5[/tex]
For a margin of error of M = 0.01, the needed sample size n is obtained as follows:
[tex]0.01 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.01\sqrt{n} = 1.645 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{1.645 \times 0.5}{0.01}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645 \times 0.5}{0.01}\right)^2[/tex]
n = 6,766.
(rounding up, as for a sample size of 6,765 the margin of error would be slightly above 0.01).
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The function m(L)=0. 00001L3 gives the mass m in kilograms of a red snapper of length L centimeters. Determine the function that gives the length L in centimeters of a red snapper as a function of its mass m in kilograms. Then find the length of a four-year-old snapper that weights about 1. 5 kilograms
Therefore , the solution of the given problem of area comes out to be AB/DC =5 Imagine that your square is made out of more compact unit squares.
What is area?Area is the quantity that describes how much space .A surface or an object's shape occupy. Use a pencil to mark a square on the paper. Specifically, a 2-D figure. A shape's area on paper is referred to as its "Area" in this sentence. Imagine that your square is made out of more compact unit squares.
Since the heights of both trapezoids are equal, and the area of ABEF is twice the area of FECD, AB+ EF/2 = 2(DC+EF /2) AB + EF / 2= DC + EF,
AB + EF = 2DC + 2EF. EF is exactly halfway between AB and DC, so EF = AB + (AB+ DC)/2 = 2DC+ AB + DC, so 3/2 AB + 1/2DC = 3DC+AB, 1/2AB =5/2DC => AB/DC =5 Therefore , the solution of the given problem of area comes out to be AB/DC =5.
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B. ) For Service B, is the additional charge per mile greater or less than 30 cents per
mile of the trip? Explain your reasoning.
The additional charge per mile for Service B is less than 30 cents per mile of the trip. This is because the rate for Service B is 20 cents per mile plus a flat fee of $10, which works out to less than 30 cents per mile for longer trips.
For a trip of 10 miles, Service B would cost
(10 x 0.20) + 10
= $12.
For a trip of 20 miles, Service B would cost
(20 x 0.20) + 10
= $22.
Therefore, the additional charge per mile for Service B is
(12/10)
= 1.2 for the 10 mile trip and
(22/20)
= 1.1 for the 20 mile trip.
Both of these are less than 30 cents per mile.
The additional charge per mile for Service B is less than 30 cents per mile of the trip because the rate for Service B is 20 cents per mile plus a flat fee of $10, which works out to less than 30 cents per mile for longer trips. To demonstrate this, for a 10 mile trip, the total cost would be $12, and for a 20 mile trip, the total cost would be $22. This works out to an additional charge per mile of 1.2 and 1.1 cents respectively, which are both less than 30 cents per mile.
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Is y 4 a vertical line?
y = 4 is a horizontal line.
The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.
Now, According to the question:
Let's know:
What is Horizontal lines?
If we are given the equation of y equal to a number, our graph will be a horizontal line. Is this equation a function? The answer would be yes since it passes the vertical line test. The vertical line test tells us if we draw a vertical line through any point of the graph and it goes through only one point at each line, then it is a function. If it passes through more than one point, it does not. The slope of a horizontal line is zero.
The equation is y = 4.
The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.
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The complete question is this :
Is y = 4 a vertical line?
Cierra has 1 bag and 1 jar of marbles. The bag contains 6 yellow marbles, 4 blue marbles, 2 purple marbles, and 3 pink marbles. The jar contains 12 yellow marbles, 8 blue marbles, 4 purple marbles, and 6 pink marbles. If Cierra randomly selects 1 marble from the bag and 2 marble form the jar, what is the probability that she will select a pink marble from each?
Answer:
3/15 probability she will select a pink from the bag and 6/30 she will select from the jar.
Step-by-step explanation:
If you simplify she has just as equal a probability of selecting a pink from the jar and the bag
Select the interval where the graph f is positive
Answer: A
Step-by-step explanation:
Based on the graph, we know that it is positive if it is above the x-axis. It is also indicated by the positive labels.
A: correct
Looking at choice A, it says the interval is from -2<x<-1. This means we have to find x=-2 and x=-1. On the graph, that interval is above the x-axis, so it is positive.
B: incorrect
Looking at choice B, it says the interval is from -1<x<0. This means we have to find x=-1 and x=1. On the graph, that interval is below the x-axis, so it is negative.
C: incorrect
Looking at choice C, it says the interval is from 0<x<1. This means we have to find x=0 and x=1. On the graph, that interval is below the x-axis, so it is negative.
Therefore, A is the correct answer.
Notice the number of edge tiles (column 3) is equal to two less than the number of tiles on one side (column 1) multiplied by four. Knowing this relationship, if we built a 10 by 10 square mirror, write a numerical expression that would help us calculate the number of edge tiles we would need.
A numerical equation using addition as the only operator, for instance, is 2 + 17.
What is meant by numerical expression?An expression that uses only numbers and one or more operation symbols is referred to as a numerical expression. Operations like addition, subtraction, multiplication, and division are represented by symbols. Additionally, the square root sign or the absolute value symbol can be used to represent it. A numerical equation using addition as the only operator, for instance, is 2 + 17. An equation with three operators, 11 + 43 x (-4), starts with addition and moves through multiplication and subtraction. Operations are applied to numbers in numerical expressions. Numerical expressions include things like 2(3 + 8). At least one variable and one operation are included in algebraic expressions (addition, subtraction, multiplication, division). An algebraic expression is, for instance, 2(x + 8y).To learn more about numerical expression, refer to:
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Geometry: Applications of All Right Triangles
Look at the attachments below to answer this question.
Given:
A length of a side of an equilateral triangle = 32 cm
Formula Used:
If in an equilateral triangle with side length 'a' then,
Area of an equilateral triangle = [(√3)/4] × a2
Calculations:
Area of an equilateral triangle = [(√3)/4] × 322
⇒ (1024 × √3)/4
⇒ 256√3 cm2
Wyatt is paying back a loan with a nominal interest rate of 13.62%. if the interest is compounded quarterly, how much greater is wyatt’s effective interest rate than his nominal interest rate?
a. 0.96 percentage points
b. 0.40 percentage points
c. 0.25 percentage points
d. 0.71 percentage points
please select the best answer from the choices provided a b c d
0.71 percentage points greater is wyatt’s effective interest rate than his nominal interest rate.
What is intrest?Interest is a fee paid by a borrower to a lender for the use of borrowed money. It is calculated as a percentage of the amount borrowed, and is usually paid periodically at intervals. Interest is generally considered to be a form of compensation for the time and risk taken by the lender in providing a loan or other form of credit.
The effective interest rate is calculated by taking the (1 + nominal interest rate/number of compounding periods per year) to the number of compounding periods per year power minus 1. In this case, the effective interest rate would be 0.1362 x (1 + 0.1362/4)^4 - 1, which is 0.1439 or 14.39%. The difference between the nominal interest rate of 13.62% and the effective interest rate of 14.39% is 0.71 percentage points.
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Y'all actually expect people to conduct experiments or to write whole essays for you?
What is the correct equation for a slope of 2 and a y-intercept of -7
Answer:
y=2x-7
Step-by-step explanation:
y=mx+b ==> m is the slope and b is the y-intercept
y=(2)x + (-7) ==> plugin 2 for m=slope and -7 for b = y-intercept
y=2x-7 ==> simplify
Use the quadratic formula to solve for the zeros: 2x^2 + 39 = -18
Answer:
18
Step-by-step explanation:
2
2
+
3
9
=
−
1
8
2x^{2}+39=-18
2x2+39=−18
2
2
+
3
9
−
(
−
1
8
)
=
0
The newest streaming service costs $9.24 per month with
tax. If tax is 5%, how much is the streaming service before
tax and how much does a year of the service cost?
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Answer:
Step-by-step explanation:
express 8 to the power of 1 in exponential form
Answer:
8¹
Step-by-step explanation:
The given expression is :
8 to the power 1.
We need to write it in exponential form.
If we write 10³, here 10 is base and 3 is exponent.
8 to the power 1 = 8¹
The base is 8 and exponent is 1.
Hence, the exponential form is 8¹.
Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. What will his monthly payments be? Round to the nearest cent.
If Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. His monthly payment is $87.31.
What is monthly payment?Monthly payment can be defined as the amount a person received on a monthly basis.
Now let find the monthly payment
Monthly payment = 7900 (0.0429/12) ( 1+ 0.0429/12)^12×10 ÷ ( 1+ 0.0429/12)^12×10 -1
Monthly payment = 7900 (0.003575) ( 1+ 0.003575)^120÷ ( 1+ 0.003575)^120 -1
Monthly payment =7900 (0.003575) ( 1.003575)^120 ÷ ( 1.003575)^120 -1
Monthly payment = $87.31
Therefore the monthly payment is $87.31.
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The complete question is:
Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. Suppose that Rich had decided to apply for a private loan rather than a federal loan. He is considering a 10-year lo"an with an interest rate of 5.9% .What will his monthly payments be?