The base of the triangle = 4(x + 1)
Explanations:The Area of a triangle is given by the formula:
[tex]\text{Area = }\frac{1}{2}\times\text{ base }\times\text{ height}[/tex][tex]\begin{gathered} \text{Area = 2x}^2-2x-4 \\ \text{Height = x -2} \end{gathered}[/tex]Substituting these expressions into the formula for the area of a triangle:
[tex]\begin{gathered} 2x^2-2x-4\text{ = }\frac{1}{2}\times\text{ b }\times(x-2) \\ 2(2x^2-2x-4)\text{ = b (x - 2)} \\ 4x^2-4x-8\text{ = b (x-2)} \\ 4x^2-8x\text{ + 4x - 8 = b (x - 2)} \\ 4x(x\text{ - 2) + }4(x\text{ - 2) = b(x-2)} \\ (4x+4)(x-2)\text{ = b(x-2)} \\ b\text{ = }\frac{(4x+4)(x-2)}{(x-2)} \\ b\text{ = 4x + 4} \end{gathered}[/tex]b = 4 (x + 1)
The base of the triangle = 4(x + 1)
Julie has a jewelry box shaped like a cube. If the volume is
216 cm³, what is the edge length of Julie's jewelry box?
A 14.7 cm
B 108 cm
C 6 cm
D 72 cm
Answer: C) 6cm
Step-by-step explanation:
6³= 6x6x6
6x6x6= 216
Answer:
Choice C: 6 cm
Step-by-step explanation:
The sides of a cube are all of equal length
If each side is a cm, then the volume = a x a x a = a³ cubic cm
So a = ∛V where V is the volume
Since we are given V = 216 cm³,
each side = ∛21 = 6 cm
3 and 20
Drag each pair of numbers to show if their greatest common factor (GCF) is less than
5, equal to 5, or greater than 5.
12 and 30
GCF is less than 5.
DRAG AND
DROP ITEMS
HERE
25 and 30
E
[
15 and 20
6 and 33
GCF is equal to 5.
DRAG AND
DROP ITEMS
HERE
20 and 30
CLEAR CHECK
GCF is greater than 5.
DRAG AND
DROP ITEMS
HERE
A
The matching pairs of the greatest common factor (GCF) of the numbers is given as follows:
3 and 20: less than 5.12 and 30: greater than 5.25 and 30: equals to 5.15 and 20: equals to 5.6 and 33: less than 5.20 and 30: greater than 5.How to find the greatest common factor between two numbers?As the common word states, the greatest common factor between two numbers a and b is the greatest number by which both numbers a and b are divisible by.
Hence, the GCFs for the pairs in this problem are given as follows:
3 and 20 = 1, as 3 is prime(only divisible by 1 and by itself), hence less than 5.12 and 30 = 6, as 12/6 = 2 and 30/6 = 5, hence greater than 5.25 and 30 = 5, as 25/5 = 5 and 30/5 = 6, hence equals to 5.15 and 20 = 5, 15/5 = 5 and 20/5 = 4, hence equals to 5.6 and 33 = 3, as 6/3 = 2 and 33/3 = 11, hence the GCF of 3 is less than 5,20 and 30 = 10, as 20/10 = 2 and 30/10 = 3, hence the GCF of 10 is greater than 5.More can be learned about the greatest common factor at https://brainly.com/question/219464
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Determine the values of x in the equation x2 = 81.
A. x = −9
B. x = ±9
C. x = ±40.5
D. x = 40.5
Answer:
The Answer Is C X = 40.5
Step-by-step explanation: Half of 81 = 40.5 and 40.5 x 2 = 81 (x only multiplies 40.5 by 2 which equals 81)
Someone help pls tysm
Answer:
youd get 0.25 off and yes you would save 25 cents the difference would be 2.25 dollars instead of 2.50
Step-by-step explanation:
im so so sorry if im wrong so so sorry
Guenther drove 260 miles in 5 hours. He has 494 more miles to drive on his trip. If he continues at this same average speed, what will his driving time in hours be for the remainder of his trip?
The driving time in hours for the remainder of Guenther's trip would be = 9.5 hours.
What is average speed?Average speed of a moving object is defined as the average change in distance divided by change in time.
The first distance covered by Guenther = 260 miles.
The time it took to cover the first distance= 5 hours.
The remaining distance = 494 miles
The time it will take to cover the remaining distance= X hours
But if , 260 miles = 5 hours
494 miles = X hours
Make X the subject of formula;
X hours= 494 × 5 / 260
X hours = 2,470 / 260
X hours = 9.5 hours.
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The line parallel to y=1/4x+1 that passes through the point (6,-2)
Answer:
y = [tex]\frac{1}{4}[/tex] x - [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{4}[/tex] x + 1 ← is in slope- intercept form
with slope m = [tex]\frac{1}{4}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute (6, - 2 ) into the partial equation
- 2 = [tex]\frac{3}{2}[/tex] + c ⇒ c = - 2 - [tex]\frac{3}{2}[/tex] = - [tex]\frac{7}{2}[/tex]
y = [tex]\frac{1}{4}[/tex] x - [tex]\frac{7}{2}[/tex] ← equation of parallel line
In the figure below, points D, E, and F are the midpoints of the sides of ABC. suppose DF =34, AC =48, and BC =78. find the following lengths.
For any given Triangle ABC, its medial triangle is constructed by finding the midpoints of its three sides (Segments AB, BC, and AC) and constructing segments to join these midpoints.
An important property of the medial triangle is that it divides the original triangle into four smaller, congruent triangles that are each similar to the original triangle.
With this in mind we now that the four triangles are congruent. Then:
[tex]CF=DE[/tex]but we know that CF is half of BC, then:
[tex]DE=\frac{78}{2}=39[/tex]From the figure we also notice that:
[tex]\begin{gathered} BE=DF \\ BE=34 \end{gathered}[/tex]Ans that AB is twice BE, then
[tex]AB=68[/tex]Summing up we have:
[tex]\begin{gathered} DE=39 \\ AB=68 \\ BE=34 \end{gathered}[/tex]during december the average daily temperature in a town is -1.7.the average daily temperature in the same town is 3.2 lower in january what is the average daily temperature in january?
Answer:
the average daily temperature in January is -4.9
a truck delivers 35 cases of books to the library. each case holds 12 books. the librarian plans to place 8 books on each shelf. what is the fewest number of shelves the librarian will need to hold all of the books delivered by the truck?
Answer:
52
Step-by-step explanation:
35×12÷8
35×12
8
(Cross out the common factor which is 8 and 12)
35×3 = 105
2 2
(find the largest integer less than or equal to 105 which is 52.)
2
-16 = -8x solve for x simplify your answer as much as possible
Answer:
x = 2
Step-by-step explanation:
-16 = -8x
divide both sides by -8:
-16/-8 = -8x/-8
x = 2
Answer:
x=2
Step-by-step explanation:
[tex]x = \frac{ - 16}{ - 8} [/tex]
[tex]x = 2[/tex]
Write a function in any form that would match the graph shown below.
......................
Two neighbors are draining swimming pools. Mr. Zoetrope’s pool has 10,858 gallons and is
draining 150 gallons per minute. Mrs. Horner’s pool has 9,650 gallons and is draining 110
gallons per minute. Write and solve an equation to determine the number of minutes ( ) m the
two pools must drain to have the same amount of water
Step-by-step explanation:
I hope this answers your problem
Kyle invests $600 which earns 3% annual simple interest for 5 years Use A(t)=P (1+rt) to determine how much money he will have after 5 years. Interpret the rate of change in this situation
The amount of money that Kyle will have after 5 years is $690.
How to calculate the interest?From the information, Kyle invests $600 which earns 3% annual simple interest for 5 years.
The formula for the amount is given as:
A(t)=P (1+rt)
where P = principal = $600
R = rate = 3%
T = time = 5 years
This will be:
A(t)=P (1+rt)
A = 600 [ 1 + (3% × 5)]
A = 600 (1 + 0.15)
A = 600(1.15)
A = 690
The amount is $690.
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What percent of 933 is 391.86?
Solve these 3 equations 1. (x - 8) (2x + 5) = 52. x² + 13x + 40 = 03. x² - 6x - 20 = 7
1. (x - 8) (2x + 5) = 5
2. x² + 13x + 40 = 0
3. x² - 6x - 20 = 7
Part 1
apply distributive property left side
2x^2+5x-16x-40=5
2x^2-11x-45=0
Apply the formula to solve quadratic equation
we have
a=2
b=-11
c=-45
substitute
[tex]\begin{gathered} x=\frac{11\pm\sqrt[\square]{(-11^2)-4(2)(-45)}}{4} \\ \\ x=\frac{11\pm\sqrt[\square]{481}}{4} \end{gathered}[/tex]the solutions are[tex]\begin{gathered} x1=\frac{11+_{}\sqrt[\square]{481}}{4} \\ \text{and} \\ x2=\frac{11-\sqrt[\square]{481}}{4} \end{gathered}[/tex]Part 2
x² + 13x + 40 = 0
we have
a=1
b=13
c=40
Apply the formula
[tex]\begin{gathered} x=\frac{-13\pm\sqrt[\square]{13^2-4(1)(40)}}{2} \\ \\ x=\frac{-13\pm\sqrt[\square]{9}}{2} \\ \\ x=\frac{-13\pm3}{2} \end{gathered}[/tex]so
x=-5 and x=-8Part 3
x² - 6x - 20 = 7
x² - 6x - 27=0
so
a=1
b=-6
c=-27
Apply the formula
[tex]\begin{gathered} x=\frac{6\pm\sqrt[\square]{(-6^2)-4(1)(-27)}}{2} \\ \\ x=\frac{6\pm\sqrt[\square]{144}}{2} \\ \\ x=\frac{6\pm12}{2} \end{gathered}[/tex]so
x=9 and x=-3
5. Holly ran 3/5 mile on Saturday and 3/5 mile on Sunday. How many miles did Holly run in those 2 days?
Answer: He did not convert the fractions into the like fraction to add.
Step-by-step explanation:Given: The distance Jonah runs on Sunday= milesThe distance Jonah runs on Monday= milesThe total distance he ran = Since both the fractions are not like , thus multiply 2 to the numerator and the denominator of the first fraction [to add fractions first convert them into like fractions], we get The total distance he ran = The right answer is "The total distance he ran ="
can anyone help me with this mixed number question pls.
7 2/3 + 2 1/5
Answer: The value of 7 2/3 + 2 1/5 is 9 13/15
Explaination: The lowest common multiple of 3 and 5 is 15. Therefore, 7 2/3 + 2 1/5 will be calculated thus:
= 7 2/3 + 2 1/5
= [7 + 2/3× 15] + [2 1/5 × 15]
= 7 10/15 + 2 3/15
= 9 13/15
In conclusion, the value of the fraction 7 2/3 + 2 1/5 is 9 13/15
ninety-two percent (92%) of parents/guardians surveyed indicated that they were "involved" in making decisions about their underage child’s healthcare treatment, and 7% stated that they were "almost always" involved.
The probability that three parents are involved" in making decisions about their underage child’s healthcare treatment is 0.7787.
What is probability?It should be noted that probability simply means the likelihood that something will happen.
In this case, ninety-two percent (92%) of parents/guardians surveyed indicated that they were "involved" in making decisions.
The probability of the involvement of the three parents will be:
= P(involvement)³
= (92%)³
= 0.92 × 0.92 × 0.92
= 0.7787
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Ninety-two percent (92%) of parents/guardians surveyed indicated that they were "involved" in making decisions about their underage child’s healthcare treatment, and 7% stated that they were "almost always" involved. Find the probability that three parents are involved" in making decisions about their underage child’s healthcare treatment,
Solve the formula Aa + By = C for B.
Answer: B = -(Aa)/y + C/y
By = -Aa + C
B = -(Aa)/y + C/y
hope this helps! <3
Solve the compound inequality.
- 3x≤ - 9 or 5x-18 ≥ 12
Answer:341623456245
Step-by-step explanation:78325687345
Quinn knit a total of 4 centimeters of scarf over 2 nights. how many nights will quinn have to spend knitting in order to knit a total of 70 centimeters of scarf?
The nights required by Quinn in order to knit a total of 70 centimeters of the scarf is equal to 35.
The number of nights required by Quinn in order to knit a total of 70cm of the scarf can be calculated using multiplication. Multiplication can be described as one of the four basic arithmetic operations in which we perform the repeated addition of the same number or value. This problem can be solved using cross-multiplication as follows;
2 nights = 4 cm of scarf
x nights = 70 cm of scarf
70 × 2 = 4(x)
140 = 4(x)
x = 140 / 4
x = 35
Therefore, Quinn will have to spend 35 nights knitting in order to knit a total of 70 centimeters of the scarf.
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3(3x - 6) = 18 solve for x simplify your answer as much as possible
the state of new hampshire has the approximate shape of a triange with base 90 mi and height 180 mi. estimate the area of new hampshire
Answer:
[tex]A = 8100mi^{2}[/tex]
Step-by-step explanation:
Are of a triangle: [tex]A = \frac{hb}{2}[/tex], where A is the area, h is height and b is base.
[tex]A = \frac{hb}{2}\\A = \frac{(180)(90)}{2}\\A = \frac{16200}{2}\\A = 8100mi^{2}[/tex]
The aproxiate area of NH is 8100mi^2
Use the equality to find the ratio a : b . a/5=b/7
ANSWER QUICK I WILL GIVE BRAINLIEST
Solve 3x + 2 = 5.
A) x = 1
B) x = 2
C) x = 3
D) x = 4
Answer:
x = 1
Step-by-step explanation:
3x + 2 = 5
3x + 2 - 2 = 5 - 2
3x = 3
3x/3 = 3/3
x = 1
Hope this helps! :)
Answer:
I think it's A, hope this helps
nine times the sum of a number and 4 equals 7.
Answer: the answer is 17
Step-by-step explanation:
Answer: The equation would be 9(x+4)=7
Divide both sides by the numeric factor on the left side, then solve.
Exact Form: x= −29/9
Mixed Number Form: x= −3 2/9
two sides of a triangle are 18 ft and 23 ft. Find the range for the measure of the third side.
Answer:
5<x<41
Step-by-step explanation:
Assume the unknown side to be x
By triangle inequality theorem
Difference of two known sides < x< Sum if two known sides
⇒23-18<x<23+18
⇒5<x<41
Therefore the possible values for unknown side x lies between 5 ft and 41 ft.
The ground temperature at an airport is 11 °C. The temperature decreases by 7 °C for every increase of 1 kilometer above the ground. What is the temperature outside a plane flying at an altitude of 5 kilometers?
The temperature outside a plane flying at an altitude of 5 kilometers is
°C.
Under the linear assumption of temperature and altitude, the temperature outside the plane is - 24 °C.
What is the temperature outside a plane flying at a given altitude?
In this problem we must determine the temperature outside the plane on the assumption that the temperature decreases linearly with the altitude:
T(z) = T' + (ΔT / Δz) · z
Where:
T' - Temperate at ground level, in degrees Celsius.Δz - Level change, in kilometers.ΔT - Temperature change, in degrees Celsius.If we know that T' = 11, Δz = 1 and ΔT = - 7, then the temperature at an altitude of 5 kilometers is:
T(5) = 11 + (- 7 / 1) · 5
T(5) = 11 - 35
T(5) = - 24
The temperature outside the plane is - 24 °C.
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3) -7y + 9 = 3y + 49
Answer:
y = -4
Step-by-step explanation:
first add 7y to both sides
9 = 10y + 49
second subtract 49 from both sides
-40 = 10y
flip it
10y = -40
now divide both sides by 10
y = -4
that is your answer
Answer: 7y+9=3y+49
We move all terms to the left:
-7y+9-(3y+49)=0
We get rid of parentheses
-7y-3y-49+9=0
We add all the numbers together, and all the variables
-10y-40=0
We move all terms containing y to the left, all other terms to the right
-10y=40
y=40/-10
y=-4
Question 5(Multiple Choice Worth 1 points)
(01.05 LC)
What is the converse of the following statement?
"If the shoes are clean, then the shoes are new."
O If the shoes are not clean, then the shoes are not new.
O If the shoes are clean, then the shoes are not new.
O if the shoes are not new then the shoes are not clean.
O If the shoes are new, then the shoes are clean.
The converse of the statement on shoes being clean and new is If the shoes are new, then the shoes are clean.
How to write a converse statement?When converting a statement that involves two clauses to a converse statement, you should exchange the position of the two clauses to make a converse statement.
This means that if you had a statement as (if a then b) the converse statement is (if b than a). The statement, "If the shoes are clean, then the shoes are new" would then be "If the shoes are new, then the shoes are clean."
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