Answer:
Factors are (x +1) ( x -7) .
Step-by-step explanation:
Given : x² – 6x – 7.
To find : Factor.
Solution : We have given x² – 6x – 7.
On factoring
x² – 7x + 1x – 7.
On taking x common from first two terms and 1 from last two terms.
x ( x -7) +1( x -7)
On grouping
(x +1) ( x -7)
Factors are (x +1) ( x -7) .
Therefore, Factors are (x +1) ( x -7) .
Evaluate: 5C2
20
25
10
60
...?
A piece of wood that is 3/4 meter long is being cut into smaller pieces that are each 1/10 meter long.which equation could be solved to find the number of pieces,n,that can be made?
What is 27.38 rounded to the nearest wholenumber?
What is 20 times greater than 0.08?
Grace caught a fish after 38 minutes of fishing. Grace started fishing at8:49 a.m.
9:27
she caught it just add 38 MINSA
how to do rational numbers
A car manufacturer announced that next year the price of a certain model car would increase by 5.5 %.This year the price is $17,891. Find the increase and the new price.
Kala made 20000 in taxable income last year. Suppose the income tax rate is 0.15 for the first 8500 plus 0.19 for the amount over 8500 . How much must Kala pay in income tax for last year?
Triangle ABD equal to triangle CBD. Name the theorem or postulate that justifies the congruence.
(There is a diagram)
When you get your answer could you please tell me how you got it? Thank you!
Answer:
SAS postulate
Step-by-step explanation:
Triangle ABD equal to triangle CBD.
The postulate that justifies the congruence is - Side angle side.
The Side Angle Side postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
Here, AD and CD sides are equal and the two triangles ABD and CBD share a common right angle , so these are congruent or equal as per SAS postulate.
AD and CD sides are equal and the two triangles ABD and CBD share a common right angle , so these are congruent or equal as per SAS postulate.
Triangle ABD equal to triangle CBD.
The postulate that justifies the congruence is - Side angle side
The Side Angle Side postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
Here, AD and CD sides are equal and the two triangles ABD and CBD share a common right angle , so these are congruent or equal as per SAS postulate.
Which of the following is equivalent to45/46 ?
88/92
135/138
46/45
90/93
Five people are sitting around a circle. Some always tell the truth, whilst others always lie. Each person claims to be sitting between two liars. How many of them are telling the truth?
A 0 B 1 C 2 D 3 E 4
The answer is: B. 1 - Only one of the five people is telling the truth.
In this scenario, we are given that five people are sitting around a circle. Some always tell the truth, while others always lie. Each person claims to be sitting between two liars.
Let's analyze the possibilities:
If all five people were telling the truth, each person's claim of sitting between two liars would be true. However, this would mean that all five people are telling the truth, which contradicts the given information.
If none of the five people were telling the truth, each person's claim of sitting between two liars would be false. However, this also contradicts the given information.
Given these two possibilities, we can conclude that there must be a combination of truth-tellers and liars among the five people.
Considering the options given:
A. 0: This suggests that none of the people are telling the truth. However, this contradicts the given information that some people always tell the truth.
B. 1: This suggests that only one person is telling the truth. In this case, this person's claim of sitting between two liars would be true, while the claims of the other four people would be false. This option aligns with the given information and is a valid possibility.
C. 2, D. 3, E. 4: These options suggest that multiple people are telling the truth. However, if more than one person tells the truth, their claims of sitting between two liars cannot all be true.
Based on the analysis, the answer is:
B. 1 - Only one of the five people is telling the truth.
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The quotient of a number and –1.5 is 21
Find the solution set for the open sentence with the given replacement set.
2x + 7 = 19, {4, 5, 6, 7}
what is the expression in factored form 16x^2+8x
Final answer:
The expression 16x^2+8x in factored form is 8x(2x + 1), obtained by factoring out the greatest common factor, which is 8x.
Explanation:
To factor the expression 16x^2+8x, we look for common factors in each term. Here, we can see that both terms contain a power of x and the number 8 is a common factor. We can factor out 8x from each term.
Step-by-step, this looks like:
Identify the greatest common factor (GCF): both terms have an x and an 8 in common.Factor out the GCF: 16x^2 + 8x = 8x(2x + 1)We've now expressed the original expression in factored form.
In the diagram, which angle is part of a linear pair and part of a vertical pair?
The options of the question are
A.)BFC B.)CFG C.)GFD D.)EFA
we know that
A linear pair forms a straight angle which contains [tex] 180 [/tex]º, so you have [tex] 2 [/tex] angles whose measures add to [tex] 180 [/tex] degrees, which means they are supplementary.
Vertical Angles are two angles whose sides form two pairs of opposite rays (straight lines).Vertical angles are congruent
in this problem
Part a) Linear Pair
1) m∠EFA+m∠EFD=[tex] 180 [/tex]°
angles ∠EFA and ∠EFD are a linear pair
2) m∠BFD+m∠EFD=[tex] 180 [/tex]°
angles ∠BFD and ∠EFD are a linear pair
3) m∠BFD+m∠BFA=[tex] 180 [/tex]°
angles ∠BFD and ∠BFA are a linear pair
4) m∠BFA+m∠AFD=[tex] 180 [/tex]°
angles ∠BFA and ∠AFD are a linear pair
Part b) Vertical angles
1) m∠EFA=m∠BFD
angles ∠EFA and ∠BFD are a vertical angles
2) m∠AFB=m∠EFD
angles ∠AFB and ∠EFD are a vertical angles
therefore
the answer is the option
D.) EFA
A four-character secret code can begin with any two of the five vowels and end with any two numerals, from 0 to 9. How many different four-character secret codes are possible?
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 3 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.
the cone = 150.8
the cylinder= 301.6 the cones volume is 2x smaller than the cylinders volume. two cones equal one cylinder.
What is the 40th term of the arithmetic sequence?
21,18,15,12,9....
A: -99
B: -96
C: 6
D: 138
The 40th term of the arithmetic sequence 21,18,15,12,9.. is -96
using Arithmetic progression formula,
a = first term = 21
common difference = d = 18 - 21 = - 3
Therefore,
aₙ = a + (n - 1)d
a₄₀ = 21 + (40 - 1)-3
a₄₀ = 21 +(39)(-3)
a₄₀ = 21 - 117
a₄₀ = -96
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Marquis has a gross pay of $816. By how much will his gross pay be reduced if Marquis has the following items withheld?
federal tax of $92
Social Security tax that is 6.2% of his gross pay
Medicare tax that is 1.45% of his gross pay
state tax that is 22% of his federal tax
Answer:
His gross pay would be reduced $174.66.
Step-by-step explanation:
Gross pay of Marquis = $816
His withholding are :
Federal tax = $92.00
Social security tax = 6.2% of $816
= 0.062 × 816
= $50.592
Medicare tax = 1.45% × 816
= 0.0145 × 816
= $11.832
State tax = 22% × 92
= 0.22 × 92
= $20.24
Total withholding = 92 + 50.59 + 11.83 + 20.24
= $174.66
His net pay = $816 - $174.66 = $641.34
His gross pay would be reduced $174.66
(04.02 LC)
Triangle ABC is similar to triangle PQR, as shown below:
Two similar triangles ABC and PQR are shown. Triangle ABC has sides AB = c, BC = a, and AC = b. Triangle PQR has sides PQ = r,
Which ratio is equal to b:q? (1 point)
b:a
c:r
r:a
q:c
∆ABC~∆PQR
AB~PQ , c~r
c:r
Answer:
The correct option is 2.
Step-by-step explanation:
It is given that triangles ABC and PQR are similar triangles.
The sides of the triangle ABC are AB = c, BC = a, and AC = b. Triangle PQR has sides PQ = r, QR=p and PR=q.
If two triangles are similar, then their corresponding sides proportional.
Since ABC and PQR are similar triangles, therefore
[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}[/tex]
[tex]\frac{c}{r}=\frac{a}{p}=\frac{b}{q}[/tex]
It can be written as
[tex]\frac{c}{r}=\frac{b}{q}[/tex]
[tex]\frac{a}{p}=\frac{b}{q}[/tex]
Therefore b:q is equal to c:r or a:p. Option 2 is correct.
Brand X soda advertises, "We will give you 20% more soda than Brand Y for a total price that is 10% less than Brand Y's price!" What is the ratio of the unit price of Brand X soda to the unit price of Brand Y soda? Express your answer as a common fraction. ...?
Answer:
3/4
Step-by-step explanation:
its 3/4 k
I will fan and medal if you help!
Part A Find the value of x
A. x=9
B. x=15
C. x=41
D. x=77
Part B Find the measure of each of the unlabeled angles in the previous question
A. one angle measures 87° and the other measures 273°
B. one angle measures 161° and the other measures 179°
C. both angles measure 155°
D. both angles measure 25°
if you can explain how you did these questions instead of just the answer that'd be great
Factor out the greatest common factor: 16a3 - 8a5
Suppose you are making yourself a sandwich. How many different sandwiches can you make if you have four choices in bread, two choices in meat, and five choices in cheese?
Please Hhhellp!! Given AB, explain how to construct a square with sides of length AB
1.A
2.C
3.C
4.C
5.C
6.B
7.D
8.C
Unit 4 Lesson 9 100%
Step-by-step explanation: Short answers you have to look up
Identify the type of conic section that has the equation 9x^2+ 16y^2 = 144 and identify its domain and range.
Answer:
B ) ellipse.Domain: { -4 ≤ x ≤ 4 }Range: { -3 ≤ y ≤ 3 }
posted whole test on jiskha under RandomSophomore
The equation [tex]\(9x^2 + 16y^2 = 144\)[/tex] represents an ellipse. Its domain is \([-4, 4]\) and its range is \([-3, 3]\).
The equation [tex]\(9x^2 + 16y^2 = 144\)[/tex] represents an ellipse. To identify its domain and range, we need to understand its shape and orientation.
Step 1: Standard Form of an Ellipse
The standard form of an ellipse with its center at the origin is [tex]\( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)[/tex], where \( a \) and \( b \) are the semi-major and semi-minor axes lengths, respectively.
Step 2: Compare Equations
Comparing the given equation [tex]\( 9x^2 + 16y^2 = 144 \)[/tex] with the standard form, we see that [tex]\( a^2 = \frac{144}{9} = 16 \)[/tex] and [tex]\( b^2 = \frac{144}{16} = 9 \).[/tex]
Step 3: Determine Axis Lengths
This means the semi-major axis length \( a \) is [tex]\( \sqrt{16} = 4 \)[/tex]and the semi-minor axis length \( b \) is [tex]\( \sqrt{9} = 3 \).[/tex]Step 4: Shape of the Ellipse
Since \( a > b \), the ellipse is stretched more horizontally than vertically, meaning it's wider than it is tall.
Step 5: Domain and Range
The domain of the ellipse is determined by the values of \( x \) and the range by the values of \( y \). For this ellipse, the \( x \)-values vary from \( -4 \) to \( 4 \) (domain), and the \( y \)-values vary from \( -3 \) to \( 3 \) (range).
Therefore, the domain is \([-4, 4]\) and the range is \([-3, 3]\).
Nine wolves, eight female and one male, are to be released into the wild three at a time.
If the male wolf is to be in the first released group and order does not matter, in how many ways can the first group of three wolves be formed?
The correct answer is 28 ways.
Please give me brainiest and have a great day.
Answer:
Hence, we can form a group of three wolves in:
28 ways.
Step-by-step explanation:
We are given:
Nine wolves, eight female and one male.
We have to release three at a time also the male wolf is to be in the first released group and order does not matter
Then we have to choose 2 female wolves out of 8
as the order does not matter so we have to use combination
Hence, it is given as:
[tex]8_C_2=\dfrac{8!}{2!\times (8-2)!}\\\\8_C_2=\dfrac{8!}{2!\times 6!}\\\\8_C_2=28[/tex]
Hence, we can form a group of three wolves in:
28 ways.
If ABCDE is a regular pentagon and diagonals EB and AC intersect at O, then what is the degree measure of angleEOC?
If ABCDE is a regular pentagon and diagonals EB and AC intersect at O, then the degree measure of angle EOC is 108°.
In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:
Sum of interior angles = 180 × (n - 2)
Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.
Sum of interior angles = 180 × (5 - 2)
Sum of interior angles = 180 × 3
Sum of interior angles = 540°.
Therefore, the measure of each interior angle is given by;
Interior angle of a pentagon = 540°/5
Interior angle of a pentagon = 108°
From triangle EAO, we have:
2m∠EOA = 180° - (54 + 54)°
m∠EOA = 72°/2
m∠EOA = 34°
Now, we can determine the measure of angle EOC;
m∠EOC = 180° - (34 + 34)°
m∠EOC = 108°
The area of egypt is 386,700 square miles. the area of wyoming is about 97,818 square milesegypt is about how many times as large as wyoming?explain how you solved the problem
To borrow money, you pawn your guitar. Based on the value of the guitar, the pawnbroker loans you $960. One month later, you get the guitar back by paying the pawnbroker $1,472. What annual interest rate did you pay? Round to the nearest tenth of a percent. ...?
The annual interest rate paid for the pawned guitar is calculated to be 640%, which is obtained by dividing the interest paid by the original loan amount to find the monthly rate and then multiplying by 12.
Explanation:To calculate the annual interest rate paid for pawning the guitar, we need to first determine the total interest paid, then the monthly interest rate, and finally convert that to an annual rate. The interest paid is the difference between the amount received from pawning the guitar and the amount paid to redeem it, which is $1,472 - $960 = $512.
As the loan was for one month, we can determine the monthly interest rate by dividing the interest paid by the principal amount. This gives us $512 / $960 = 0.5333 or 53.33%. To find the annual interest rate, we multiply the monthly rate by 12 (the number of months in a year). Thus, the annual interest rate is 53.33% * 12 = 640%.
It's important to note that this is an extremely high rate of interest, which is not uncommon for pawnshop loans or other short-term high-risk loans.