Answer:
see below
Step-by-step explanation:
4(5n-7)+10n+2
Distribute
20n -28 +10n+2
Combine like terms
30n-26
Assuming you meant =
4(5n-7)=10n+2
Distribute
20n -28 =10n+2
Subtract 10n from each side
20n-10n-28 = 10n-10n+2
10n-28 =2
Add 28 to each side
10n-28+28=28+2
10n=30
Divide by 10
10n/10 =30/10
n=3
9(x+3)=4x-3
Distribute
9x+27 = 4x-3
Subtract 4x from each side
9x-4x+27 = 4x-4x-3
5x +27 =-3
Subtract 27 from each side
5x+27-27 = -3-27
5x = -30
Divide by 5
5x/5 = -30/5
x=-6
2(12-8x)=x-11x
Combine like terms
2(12-8x) = -10x
Divide by 2
12-8x = -5x
Add 8x to each side
12-8x+8x = -5x+8x
12 = 3x
Divide by 3
12/3 =3x/3
4=x
Answer:
See explaination
Step-by-step explanation:
Assuming that these are three different problems:
1) 4(5n-7) = 10n+2
Distribute:
4(5n-7) = 10n+2
20n - 28 = 10n + 2
Combine like terms, isolate, and solve:
10n = 30
n = 3
2) 9(x+3) = 4x-3
Distribute:
9(x+3) = 4x-3
9x+27 = 4x - 3
Combine like terms, isolate, and solve:
5x = -30
x = -6
3) 2(12-8x) = x-11(i assumed the extra x was a typo)
distribute:
24-16x = x-11
Combine like terms, isolate, and solve:
35 = 17x
x = 35/17
PLEASE HELP ASAP 100 PTS WILL MARK BRAINLYIEST If f(x) = (x + 7)^2, which of the following is g(x), based on the translation? g(x) = (x + 9)^2 g(x) = (x + 5)^2 g(x) = (x + 7)^2 + 2 g(x) = (x + 7)^2 − 2
Answer: g(x)=(x+7)²-2
Step-by-step explanation:
For this problem, you will need to know what each part fo the function does. You can see that g(x) is the bottom function and f(x) is the to function. F(x) has traveled down to -2. You know that the y-intercept is -2. The only answer choice with -2 as y-intercept is g(x)=(x+7)²-2.
Answer:
g(x) = (x + 7)^2 -2
Step-by-step explanation:
f(x) = (x + 7)^2
We are shifting the function down 2 units
f(x) -b where b is 2
g(x) = f(x) -2
g(x) = (x + 7)^2 -2
Tony and Tiffany collect semi-precious stones. At the rock hound hut, Tiffany paid $38 for 9 pounds of snowflake obsidian. At the solid rock shop, tony paid $19 for 3 pounds of the same type of the stone. Who made the better buy?
Answer:
Tiffany made the better buy
Step-by-step explanation:
Based on the information provided within the question it can be said that Tiffany made the better buy in this scenario. Mainly because Tiffany paid a less amount per pound than Tony did. This can be calculated by dividing the total amount each paid by the total amount each of them received, like so...
Tiffany: $38 / 9 = $4.22 per pound
Tony: $19 / 3 = $6.33 per pound
Therefore we can see that Tiffany paid $4.22 per pound and Tony paid $6.33 per pound a whole $2.11 more than Tiffany, thus making Tiffany purchase the better buy.
Pls help with this question.
This recipe makes 16 portions of potato soup.
Richard follows the recipe but wants to make 4 portions.
Complete the amounts of each ingredient that he needs.
Answer:
24 ml oil
60 g onions
360 g potatoes
400 ml milk
Step-by-step explanation:
The recipe makes 16 portions and you only need 4 portions. Since 16 is 4 times bigger than what you need, just divide everything you've been given by 4.
*you can choose to convert into the correct units of measurement before or after dividing. I converted after dividing. Either way works fine though.
1) 96/4 = 24 ml
2) 240/4 = 60 g
3) 1.44/4 = 0.36 kg
They want it in grams, so times it by 1,000 to convert. this gives you 360 g.
4) 1.6/4 = 0.4 l
They want it in ml, so times it by 1,000 to convert. this gives you 400 ml.
Hope this helped : )
A 6.5 foot street sign casts a 10-foot shadow while a telephone pole casts a 40-foot shadow. How tall
is the telephone pole?
Answer:
26
Step-by-step explanation:
10 x 4 = 40
6.5 x 4 = 26
The height of the telephone pole is 26 foot.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Shadow of 6.5 foot street sign = 10 foot
Let the height of telephone pole = h foot
According to given condition,
Shadow of h foot telephone pole = 40 foot
Since, 10 foot shadow cast by 6.5 foot street sign
To find the height of the pole,
Use Ratio property,
10/6.5=40/h
⇒h=26 foot
The height of telephone pole is 26 foot
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What is the leading coefficient of the polynomial?
5x3 + 17 − 8x5 − 9x4
A) −8
B) −9
C) 17
D) 5
Answer:
-8
Step-by-step explanation:
Write the polynomial from highest power to smallest
− 8x^5 − 9x^4+5x^3 + 17
The leading coefficient is the first number in front of the highest power
What is the HIGHEST common factor
of the set of numbers (54, 72, 90}?
Answer:
18
Step-by-step explanation:
54/18=3
72/18=4
90/18=5
Answer:
18
Step-by-step explanation:
GCF of 54, 72, 90 is:
54÷3= 18
72÷4= 18
90÷5= 18
The GCF of 54, 72, and 90 is 18.
Jacob wants to know the favorite sport among sixth grade students. Which types of survey below with give Jacob valid results?
A) randomly survey students in the middle school
B) randomly survey six grade students inside the football store
C) randomly survey six grade students inside the school cafeteria
D) randomly survey six grade students inside the tennis shop
Answer I think
:randomly survey six grade students in the school cafeteria
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Randomly surveying 6th graders in the school cafeteria would give jacob valid results because A wouldn't be reliable, because he just wants 6th graders, and B and D would be selective as it would be inside a football store, implying that most 6th graders in there would be tending towards football, and D would be inside a tennis shop, which would imply that most 6th graders there would prefer football. Therefore, the cafeteria would yield the most reliable results.
Find the value of x
Answer:
98
Step-by-step explanation:
Angles in a triangle: 180
Supplementary Angles: 180
180-122=58
58+24=82
180-82=98
the probability of rolling factors of 6 on both dice
Answer:1/6
Step-by-step explanation:
Verify sin^4x-sin^2x=cos^4x-cos^2x is an identity. Please dumb it down, i don't get this lesson.
Answer:
Step-by-step explanation:
cos^2+sin^2 = 1 ( rule)
cos^4x-cos^2x simplify
- cos^2( -cos^2 +1 ) -cos^2 common
or -cos^2 ( 1-cos^2)
since cos^2 + sin^2 = 1
substitute : -cos^2 ( sin^2 )
substitute : -(1-sin^2 ) ( sin^2)
multiply : -sin^2 + sin^4 or sin^4 - sin^2
it is verified that sin^4 -sin^2= cos^4-cos^2
hope it helps
Re-write the statement 19+7÷2×6+1 by including two pairs of brackets to make the total value equal to 2.
(19+7)(2×6+1)
Step-by-step explanation:
(19+7)/(2×6+1) = 2
26/13 = 2
2 = 2
3:15=12:60 then find the sum of the mean
Answer:
The means of the proportion 3/15 = 12/60 are 15 and 12. The means of the proportion 3/15 = 12/60 are 15 and 12
A triangular prism has a height of 9 m. The area of a triangular base measures 16 m². What is the volume of a triangular prism?
Possible answers are 15,60,72,144 cubic meters. What one is correct?
Answer:
144m^3
Step-by-step explanation:
Sophie and Jackson are reading the same book. At the beginning of the month, Sophie was on page 20 and Jackson was on page 50. Sophie will read 10 pages per day and Jackson will read 5 pages per day. Let S represent the page of the book that Sophie is on at the end of t days into the month, and let J represent the page of the book that Jackson is on at the end of t days into the month. Graph each function and determine after how many days t Sophie and Jackson will be on the same page of the book.
Answer:
t = 6 days
Step-by-step explanation:
We can model both cases with linear equations in the form:
y = ax + b
Sophie was on page 20 and she reads 10 pages per day, so her equation is:
S = 20 + 10t
Jackson was on page 50 and he reads 5 pages per day, so his equation is:
J = 50 + 5*t
The graph of those equations are in the image attached (The blue line is for Sophie and the orange line is for Jackson)
To find after how many days they will be on the same page, we can make S = J and then find the value of t:
20 + 10t = 50 + 5t
5t = 30
t = 6 days
What else would need to be congruent to show that ABC= ADEF by AAS?
B
10
10
30"
30°7
A
С
D
•F
.
A. ZA ZD
B. ZA= 2C
C. AC = DF
O D. BC = EF
To show that ABC =DEF by AAS congruent postulate, (A) [tex]\angle A \cong \angle D[/tex]
How to complete the congruent postulate?The given parameters are:
AB = DE = 10
[tex]\angle C \cong \angle F = 30^o[/tex]
The above highlight show that one side and one angle of the triangle are congruent
To complete the AAS postulate, one other corresponding angle must be congruent.
From the figure, points A and D are corresponding points
Hence, to show that ABC =DEF by AAS congruent postulate, (A) [tex]\angle A \cong \angle D[/tex] must be true
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The reason needs to show the triangles are congruent by AAS is ∠A ≅ ∠D.
What are congruent triangles?Two triangles are said to be congruent if their corresponding parts are congruent with each other.
Given that, triangles ΔABC, and ΔDEF, need to be congruent by AAS rule,
∠C ≅ ∠F, AB = DE, we need to find one more reason,
AAS rule :-
AAS or Angle Angle Side congruence rule states that if two pairs of corresponding angles along with the opposite or non-included sides are equal to each other then the two triangles are said to be congruent.
So, the reason must be ∠A ≅ ∠D.
Hence, the reason needs to show the triangles are congruent by AAS is ∠A ≅ ∠D.
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A car with 16 gallons of gas drives 416 miles until the tank is empty. Write a linear equation that describes the amount of gas left in the car, y, after driving x miles.
The base of a right circular cone has a radius of 4 inches and a slant height of 9 inches. If the radius and the slant height are multiplied by 6, by what factor is the surface area multiplied? A. 6 B. 36 C. 24 D. 54
Answer:
Correct option: B -> 36
Step-by-step explanation:
The surface area of a circular cone is given by the formula:
Surface area = pi * radius * (radius + slant height)
If the inicial radius is 4 in and the slant height is 9 in, we have:
Surface area = pi * 4 * (4 + 9) = 52pi in2
The radius and the slant height are multiplied by 6, so we have:
radius = 6 * 4 = 24 in
slant height = 6 * 9 = 54 in
So the new surface area is:
New surface area = pi * 24 * (24 + 54) = 1872pi in2
The factor of the surface areas is:
New surface area / Surface area = 1872pi / 52pi = 36
Correct option: B
Answer:
b
Step-by-step explanation:
Which of the following terms have a GCF of 6x^3? Select two options. 12p^3r 27p^4q 45p^3q^6 54p^3 63p^3q^6
Answer:
A. and D. are correct
Step-by-step explanation:
The correct answers are Option A, Option D.
The terms which have the GCF of [tex]6x^3\\[/tex] are [tex]12p^3r[/tex] and [tex]54p^3[/tex].
Given data:
To find the greatest common factor (GCF) of the given terms, we need to find the highest power of x that divides into all the terms and the highest power of p that divides into all the terms.
For [tex]12p^3r[/tex] , the highest power of x that divides into this term is [tex]x^0[/tex](since x^0 = 1), and the highest power of p that divides into this term is [tex]p^3[/tex]. Therefore, the GCF is [tex]1 * p^3 = p^3.[/tex]
For 54p^3, the highest power of x that divides into this term is [tex]x^0[/tex] (since x^0 = 1), and the highest power of p that divides into this term is [tex]p^3[/tex]. Therefore, the GCF is [tex]1 * p^3 = p^3.[/tex]
Hence, the terms are [tex]12p^3r[/tex] and [tex]54p^3[/tex].
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Observa las figuras y contesta lo siguiente de cada figura ¿cuantos cubos la forman? ¿Cuantos cubos tiene de alto? ¿Cuantos cubos tiene de largo? ¿Cuantos cubos tiene de ancho?
Answer:
The figures are shown in the image attached.
Figure 1.Notice that the figure is a cube with side of 3 cubes long. That means the total number of cubes that form the figure are
[tex]V=3^{3}=27[/tex]
27 cubes in total.
Its height is formed by 3 cubes.
Its length is formed by 3 cubes.
Its width is formed by 3 cubes.
Figure 2.
The second figure has:
Its height formed by 5 cubes.
Its length formed by 1 cube.
Its width formed by 3 cubes.
Which gives: [tex]V= 5 \times 1 \times 3 = 15[/tex]
There are 15 cubes in total.
Figure 3.The third figure has
Its height formed by 3 cubes.
Its length formed by 2 cube.
Its width formed by 3 cubes.
Which gives: [tex]V= 3 \times 2 \times 3 = 18[/tex]
There are 18 cubes in total.
Figure 4.The fourth figure has
Its height formed by 1 cubes.
Its length formed by 2 cube.
Its width formed by 7 cubes.
Which gives: [tex]V= 1 \times 2 \times 7 = 14[/tex]
There are 14 cubes in total.
plzzz help me i will mark you as brainliest
Answer:
10/12
Step-by-step explanation:
6*2=12 so
5*2=10
What is the smallest prime that is a factor of the sum 51 + 1?
Answer:
2
Step-by-step explanation:
51+1 = 52
Since 52 is even, obviously the answer is 2.
Hope this helps.
Good Luck
What is the equation, in point-slope form, of the line that is
perpendicular to the given line and passes through the
point (-4, 3)?
y-3 = -2(x + 4)
Y-3 = -
2(x+4)
y-3 = {(x + 4)
Y-3 = 2(x + 4)
Answer:
y=1/2x+5
Step-by-step explanation:
the perpendicular line equation's slope is a negative reciprocal, so the new equation's slope is 1/2. so now you have y=1/2x+b plug in (-4,3) to find b. so you will do 3=1/2(-4)+b. 3=-2+b and then you solve for b. you would get b=5. so, the new equation is y=1/2x+5
The shortest leg of a right triangle measures 9 centimeters and the hypotenuse measures 3 centimeters more than the longer leg. Find the length of the hypotenuse. Use the Pythagorean Theorem Formula.
I'm not sure how to set this up
Answer:
The triple is 9, 12, 15
The hypotenuse is 15.
Step-by-step explanation:
Pythagorean Theorem Formula: a²+b²=c² where a & b are the short legs and c is the hypotenuse.
9²+b²=(b+3)²
81+b²=(b+3)²
Small list of the Pythagorean Triples that contain 9:
9,12,15
9,40,41
So as you can see, there are only 2 examples in my list that contain 9 in them. The only one that fits our criteria is the triple, 9, 12 and, 15
You don't need to use the Pythagorean Formula for this as I have just proved.
Answer:
12 cm
Step-by-step explanation:
I don't think u have to use the phytagores theorem b/c the hypotenuse is 9+3=12. but if u have to use this.
[tex] {?a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {9}^{2} + {b}^{2} = {9 + 3}^{2} [/tex]
[tex]81 + {b}^{2} = 9(9 + 3) + 3(9 + 3)[/tex]
[tex]81 + {b}^{2} = 81 + 54 + 9[/tex]
[tex]81 + {b}^{2} = 144[/tex]
[tex] {b}^{2} = 144 - 81 = 63[/tex]
[tex] {b}^{2} = \sqrt{53} = b = 7.93[/tex]
so if u found b then u can find c by using the same formula.
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {9}^{2} + {7.93}^{2} = {c}^{2} [/tex]
[tex]81 + 63 = {c}^{2} [/tex]
[tex] {c}^{2} = 81 + 63 = 144[/tex]
[tex] \sqrt{c} = \sqrt{144} [/tex]
[tex]c = 12[/tex]
The volume of prism A is 60 cubic units, and the volume of prism B is half the volume of prism A. What is the value of a?
Answer:
5
Step-by-step explanation:
V= Bh
volume of figure A is 60, and the volume of figure B is half.
figure B:
B= 3*4
B= 12
60=12*h
5=h
the value of a is 5.
The value of a in the prism is 3 units.
What is prism?In three-dimensional space,
a prism is a polyhedron where two ends are similar.
Given:
The volume of prism A is 60 cubic units,
and the volume of prism B is half the volume of prism A.
The base area of the prism B is 20 square units.
The volume of the prism,
V = Ba, where B is the base area and a is the height.
So,
60 = 20a
a = 3 units
Therefore, the value of a is 3 units.
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The complete question:
The volume of prism A is 60 cubic units, and the volume of prism B is half the volume of prism A. The base area of the prism B is 20 square units.
What is the value of a?
A circular cardboard piece is needed for the base of a volcano model. The volcano is 46 centimeters tall and has a volume of 890 cubic centimeters. Which equation can be used to find the area of the circular base?
Answer: its A
sorry if im wrong
The equation 890 = 1/3 B(46) can be used to find the area of the circular base .
What is Area ?Area is the space enclosed within the perimeter of the given shape.
It is given in the question that Area of the base of a volcano has to be determined.
The structure of a volcano is that of a Cone
Area of a conical structure is given by
V = (1/3) * height * (radius)²
890 = 1/3 (radius)²(46)
V = 890 h = 46
area of a circle = π (radius)²,
890 = 1/3 B(46)
If B = (radius)²
Therefore Option D is the correct answer
890 = 1/3 B(46) equation can be used to find the area of the circular base .
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Please solve the question.
Answer:
a = 125°, b = 20°, c = 35°, d = 90°, e = 55°
Step-by-step explanation:
Quadrilateral PQRS is inscribed in a circle, therefore it is a cyclic quadrilateral.
PQ is diameter, SR is chord and PR is transversal such that:
PQ || SR... (given)
[tex] m\angle PRQ = 90°..(\angle \: inscribed \: in\: semicircle) \\
\huge \red {\boxed {\therefore d = 90°}} \\\\
m\angle RPQ= m\angle PRS .. (alternate \: \angle s) \\
\huge \purple {\boxed {\therefore c = 35°}} \\\\
In\: \triangle PQR, \\
c + d + e = 180°\\
35° + 90° + e = 180°\\
125° + e = 180°\\
e = 180° - 125°\\
\huge \orange {\boxed {\therefore e = 55°}} \\\\
a + e = 180°...(opposite \:\angle 's \: of \: cyclic \: quadrilateral) \\
a + 55°= 180°\\
a = 180°- 55°\\
\huge \blue {\boxed {a = 125°}} \\\\
In\: \triangle PSR, \\
a + b + 35°= 180°\\
125° + b + 35° = 180°\\
160° + b = 180°\\
b = 180° - 160°\\
\huge \pink {\boxed {b = 20°}}
[/tex]
Which object shown below could we slice perpendicular to its base/face to create a trapezoid cross-section
Answer:
B
Step-by-step explanation:
Which number produces a rational number when multiplied by
1/3
Answer:
Any integer multiplied can give rational number
Step-by-step explanation:
100 students in a classroom like iPhone or Samsung or both of them. Out of them, 40 like both mobiles. If the ratio of the number of students who like iPhone and Samsung is 3:2, Find the number of students who like iPhone only.
Answer:
36 like iphone only
Step-by-step explanation:
You know that 40 people like both so you can already get them out of the way. That leaves you with 60 people and if we are dividing them into 5ths then 1/5 = 12 people. If the ratio is 3:2 then you can just multiply 3 x 12 to get 36 and then 2 x 12 to get 24 and that equals 60 and added to your 40 who like both, you get 100 students.
A scale drawing of a room is shown below. In the drawing, the room is 7 1/2 inches long and 5 inches wide. What is the actual area of the room? Please help
Answer:
The area of the room is 37.5 square inches.
Step-by-step explanation:
Consider that the room is rectangular in shape.
The dimensions of the rooms are:
Length (l) = 7.5 inches
Breadth (b) = 5 inches
The area of a rectangle is:
Area = l × b
Compute the area of the room as follows:
Area = l × b
[tex]=7.5\times 5\\=37.5[/tex]
Thus, the area of the room is 37.5 square inches.
