Answer:
2 quarts
Step-by-step explanation:
We know that an automobile's radiator has a capacity of fifteen quarts and currently carries twelve quarts of a thirty percent antifreeze solution.
We are to find the number of quarts of pure antifreeze that must be added to strengthen the solution to forty percent.
We can write the following equation for this and solve it:
[tex] 12 + x = y \\ 12 (.30) + 1 x = y ( . 4 0 ) [/tex]
[tex]3.6 + x = 0.4y[/tex]
[tex]0.4(12 + x) = 3.6 + x&\\4.8 + 0.4x = 3.6 + x[/tex]
[tex]x-0.4x=4.8-3.6[/tex]
[tex]0.6x=1.2[/tex]
[tex]x=2[/tex]
Therefore, 2 quarts are needed.
It’s Choose More than one answer Just to let you know ..and can someone please help ..please
Answer:
Step-by-step explanation:
Answer x = 0
1 < 0 and 13<0
Find the greatest common factor 7x^3a+7x^2a^2
Answer:
7x^2a
Step-by-step explanation:
7x^3a+7x^2a^2
7x^3a = 7 xxxa
7x^2a^2= 7 xxaa
The common terms are 7xxa
7x^2a
This is the greatest common factor
what would be the values of f(f-1(17)) and f-1(f(2))? FAST HELP
Answer:
f(f-1(17)) = 17
f-1(f(2)) = 2
Step-by-step explanation:
Lemma;
If f(x) and g(x) are inverses, then the compositions f(g(x)) = g(f(x)) = x.
In both situations, we are determining the composite of inverse functions;
f and f-1
whats the exanded expression for -7(k-3)
Answer:
-7k+21
Step-by-step explanation:
Distributive Property:
↓
[tex]A(B+C)=AB+AC[/tex]
A=-7, B=K, and C=3
-7k+7*3
Multiply by the numbers from left to right to find the answer.
7*3=21
-7k+21 is the correct answer.
For his long distance phone service, bill pays a $7 monthly fee plus 7 cents per minute. Last month, bill’s long distance bill was $18.27. For how many minutes was bill billed?
Answer:
161 minutes
Step-by-step explanation:
$1827-$7=$11.27
$11.27/.07=161
Answer:
161 minutes
Step-by-step explanation:
Bill pays a monthly fee for his long distance phone service = $7.00
and call charges per minute = 7 cents
1 dollar = 100 cents
Therefore 7 cents = [tex]\frac{7}{100}[/tex] = $0.07
Last month, Bill's long distance bill was $18.27.
Let Bill used the phone service for x minutes
The equation for his uses in minutes :
7.00 +(0.07x) = 18.27
0.07x = 18.27 - 7.00
0.07x = 11.27
x = [tex]\frac{11.27}{0.07}[/tex]
x = 161 minutes
Bill was billed for 161 minutes.
36
Which expression is equivalent to (h2 + 9h - 1)(-4h + 3)?
F -413 - 33h2 +31h - 3
G463 + 39h2 – 23h - 3
H -463 – 39h2 + 23h + 3
j
4h3 + 33h2 – 31h + 3
Answer:
I THINK IT IS THE SECOND ANSWER
Step-by-step explanation:
Answer:
it is -413 - 33h2 +31h - 3
F is the answer I did the math
News cameras take an overhead picture of a part of a crowd at an outdoor event. Journalists then count the number of people in the picture and use the sample to estimate the total number of people in the crowd. This process is an example of
Answer:
cluster system
Step-by-step explanation: For edgunity
This process is an example of cluster system.
The following information should be considered:
A cluster refers to a group of inter-connected computers where it work together for support applications and middleware (e.g. databases). In a cluster, each & every computer is known to be a “node”.learn more: https://brainly.com/question/4804019?referrer=searchResults
A dilation maps (4, 6) to (2, 3). Under the same dilation, (-1,3) would be mapped to
Answer:
(-1/2,3/2)
Step-by-step explanation:
The rule for dilation about (0,0) by a scale factor is given as:
(x,y)----------(kx,ky)
So if (4,6) was mapped to (2,3) by dilation it means;
x=4
kx=2
k=2/4 =1/2
Hence in this case, the dilation rule is ;
(x,y)---------(1/2x ,1/2y)
For (-1,3) ---------(1/2*-1, 1/2*3)
(-1/2, 3/2)
Answer:
[tex](-\frac{1}{2}, \frac{3}{2})[/tex].
Step-by-step explanation:
Since, the rule of dilation about origin by the scale factor k is,
[tex](x,y)\rightarrow (kx,ky)[/tex]
Given,
The dilation maps (4, 6) to (2, 3).
Let k be the scale factor for this dilation,
⇒ 4k = 2 ⇒ k = [tex]\frac{2}{4}=\frac{1}{2}[/tex],
Thus, under the dilation rule would be,
[tex](x,y)\rightarrow (\frac{1}{2}x,\frac{1}{2}y)[/tex]
Hence, (-1,3) would be mapped to [tex](-\frac{1}{2}, \frac{3}{2})[/tex].
Substitute w=1 and w=3 to determine if the two expressions are equivalent. 4(3w+4) 16w+12 Which statements are true? Check all that apply.
A: The value of both expressions when w=1 is 28.
B: The two expressions are equivalent.
C: The value of both expressions when w=1 is 16.
D: The two expressions are not equivalent.
E: The value of both expressions when w=3 is 52.
F: The value of both expressions when w=3 is 60.
Answer:
A: The value of both expressions when w=1 is 28.
D: The two expressions are not equivalent.
Step-by-step explanation:
Given expressions are:
4(3w+4)
and
16w+12
For w=1
First Expression:
4(3w+4)
= 4[3(1)+4]
=4(3+4)
=4(7)
=28
Second expression:
16w+12
= 16(1)+12
=16+12
=28
For w=3
First Expression:
4(3w+4)
= 4[3(3)+4]
=4(9+4)
=4(13)
=52
Second expression:
16w+12
= 16(3)+12
=48+12
=60
Now looking at the statements:
A: The value of both expressions when w=1 is 28.
The statement is true because our calculated values of both expressions are 28 for w=1.
B: The two expressions are equivalent.
The two expressions are not equivalent because their values at w=3 are not same.
C: The value of both expressions when w=1 is 16.
The value of both expression when w=1 is 28 so this statement is not correct
D: The two expressions are not equivalent.
We can see by comparing the values that both expressions are not equivalent.
E: The value of both expressions when w=3 is 52.
F: The value of both expressions when w=3 is 60.
Both statements are false because both expressions have different values at w=3 ..
A. The value of both expressions when w=1 is 28. D. The two expressions are not equivalent. Statements A and D are true.
To determine if the two expressions are equivalent, we need to substitute w=1 and w=3 into both expressions. The first expression is 4(3w+4) and the second expression is 16w+12.
Step-by-step:
Substitute w=1:For 4(3w+4): 4(3(1)+4) = 4(3+4) = 4*7 = 28For 16w+12: 16(1)+12 = 16+12 = 28Substitute w=3:For 4(3w+4): 4(3(3)+4) = 4(9+4) = 4*13 = 52For 16w+12: 16(3)+12 = 48+12 = 60Based on these calculations:
A: The value of both expressions when w=1 is 28. (True)B: The two expressions are equivalent. (False, they are only equal at w=1)C: The value of both expressions when w=1 is 16. (False)D: The two expressions are not equivalent. (True, they give different values for w=3)E: The value of both expressions when w=3 is 52. (True for first expression, false for second)F: The value of both expressions when w=3 is 60. (True for second expression, false for first)Let R be the region bounded by y=x and y=x^2.
Find the area of R.
Find the volume of the solid that results when R is revolved about the x-axis(using the shell method).
Answer:
2pi/15
Step-by-step explanation:
The intersection of y=x and y=x^2 is (0,0) and (1,1)
Washer method
Prefered this method for this one since slices are perpendicular to axis of rotation
Integrate(Big circle - Small Circle)dx
Integrate(pi*(x)^2-pi*(x^2)^2)dx on x=0..1
Integrate(pi*x^2-pi*x^4)dx on x=0..1 is 2pi/15
Shells method
So I have to solve for x since I will be integrating with respect to y
The height of the the shell will be sqrt(y)-y
The radius will be y since that is the distance between axis of rotation in a point within the shell
Integrate(2*pi*r*h ) dy
Integrate(2*pi*(sqrt(y)-y)*y) dy on y=0..1 is 2pi/15
If f(x) = 2x-1 + 3 and g(x) = 5x-9, what is (f-g)(x)?
Answer:
-3x+11
Step-by-step explanation:
f(x) = 2x-1 + 3 =2x+2
g(x) = 5x-9
(f-g)(x)= 2x+2 - (5x-9)
Distribute the minus sign
= 2x+2 - 5x +9
Combine like terms
= -3x+11
What value of X is in the solution set of 2(3x-1)>4x-6
Answer:
negative 1
2(3x-1)>4x-6
Answer:
Step-by-step explanation:
-1
The first few steps in solving the quadratic equation 8x2 + 80x = −5 by completing the square are shown.
8x2 + 80x = −5
8(x2 + 10x) = −5
8(x2 + 10x + 25) = −5 + ______
Which number is missing in the last step?
Answer:
200
Step-by-step explanation:
8x^2 + 80x = −5
Factor out an 8
8(x^2 + 10x) = −5
Take the coefficient of the x term, divide by 2 and then square it
10/2 = 5, 5^2=25
Remember we have the 8 outside, so we are multiplying by 8
8*25 =200
Add 200 to each side
8(x^2 + 10x + 25) = −5 + 200
Answer:
Missing number is 200.
Step-by-step explanation:
In the completing the square method we follow the following steps,
Step 1 : Move constant term to the right side,
Step 2 : Make 1 as the coefficient of [tex]x^2[/tex]
Step 3 : Add square of the half of the coefficient of x in the left side and balance the equation,
Here, the given equation,
[tex]8x^2+ 80x = -5[/tex]
[tex]8(x^2 + 10x) = -5[/tex]
∵ coefficient of x = 10,
Half of 10 = 5,
Square of 5 = 25,
Thus, we need 25 inside the bracket in left side,
For this, add 200 on both side,
[tex]8(x^2 + 10x+25) = -5+200[/tex]
Hence, missing number in the last step is 200.
Convert 12 and a half of 30
Answer:
375
Step-by-step explanation:
12½[30] → 25⁄2[30]
Multiply 25 by 30 [750] then divide by 2 to get 375.
I am joyous to assist you anytime.
Identify the linear term in the function of y = 2x2 − 5x − 12
Answer:
The linear term is -5x
Step-by-step explanation:
The linear term is the term that has the degree equal to 1.
The given function is
y = 2x^2 − 5x − 12
here 2x^2 = quadratic term i.e having degree 2
-5x = linear term i.e having degree 1
-12 = constant
so, The linear term is -5x
The equation tan(559)= 15 can be used to find the length of AC.
What is the length of AC? Round to the nearest tenth
Answer:
10.5
Step-by-step explanation:
b=15/tan(55 degrees)=10.5
AC=10.5
Can someone help me please
Answer:
Multiply [tex] \frac { 3 } { 4 } [/tex] by 8.
Step-by-step explanation:
We are given the following expression and we are to find its quotient:
[tex] \frac { 3 } { 4 } [/tex] ÷ [tex] \frac { 1 } { 8 } [/tex]
This can also be written as:
[tex]\frac{\frac{3}{4}}{\frac{1}{8} }[/tex]
Since the two fractions are being divided so to change this division sign into a multiplication sign, we will take the reciprocal of the fraction in the denominator and multiply 3/4 by 8.
[tex]\frac{3}{4} \times 8[/tex] = 6
For this case we must find the quotient of the following expression:
[tex]\frac {\frac {3} {4}} {\frac {1} {8}} =[/tex]
Applying double C we have:
[tex]\frac {3 * 8} {4 * 1} =\\\frac {24} {4}[/tex]
This is equivalent to the following expression:
[tex]\frac {3} {4} * 8 = \frac {24} {4}[/tex]
Answer:
Option B
Using the figure below, select the two pairs of alternate interior angles.
A:point 1 and point 4
B :point 2 and point 3
C:point 6 and point 6
D:point 5 and point 7
Answer:
B :point 2 and point 3
Step-by-step explanation:
The only interior angles are 6, 2, 3, and 7
The angles equal to each other are 6 and 7 or 2 and 3
6 and 7 is not an option so 2 and 3 are the correct answer.
What’s the value of Y? I’m stuck on this
Answer:
B 65
Step-by-step explanation:
The measure of the exterior angle is equal to the sum of the opposite interior angles
130 = y+y
130 = 2y
Divide by 2
130/2 = 2y/2
65= y
PLEASE HELP ME ASP! Brainlist and 25 points!
Answer:
Answer is in the explanation
Step-by-step explanation:
I don't know exactly word from word what your choices look like...
but I can describe per each box what happened in my own words:
First box: They multiply first equation by 3 and the second equation by 2 to obtain the equations in that first box.
Second box: They subtracted the two equations in the first box to obtain 1x+0y=2 which means 1x=2 or x=2 (this is called solving a system by elimination
Third box: They used their first original equation (before the multiplication manipulation) and plug in the value they got for x which was 2 giving them 3(2)-2y=10
Fourth box: They simplified the equation 3(2)-2y=10 by performing the multiplication 3(2) giving them 6-2y=10
Fifth box: They subtracted 6 on both sides giving them -2y=4
Sixth box: They divided both sides by -2 giving them y=-2
I will summarize then what I wrote above:
1st box: Multiplication Property of Equality
2nd box: Elimination
3rd box: Substitution (plug in)
4th box: Simplifying
5th box: Subtraction Property of Equality
6th box: Division Property of Equality
the circumference of a circle is 64 cm.find the diameter ,the radius,the length of an arc of 190
The diameter of the circle is approximately 20.37 cm, the radius is approximately 10.18 cm, and the length of an arc measuring 190 degrees is approximately 33.8 cm.
Explanation:The subject at hand concerns the properties of a circle, more specifically its circumference, diameter, radius, and arc length.
In this case, we know that the circumference of the circle is 64 cm. The circumference of a circle is calculated by the formula 2πr (where r is the radius), or can also be viewed as πd (where d is the diameter). If we equate 64 = 2πr, we can thus find the radius, r = 64/(2π), resulting in roughly a radius of 10.18 cm. The diameter of the circle is simply twice the radius, hence in this context, it would be roughly 20.37 cm.
The length of an arc is calculated by multiplying the radius by the angle (in radian measure), which is represented as θ = s/r. In this case, the arc length is not given directly but we are given an angle of 190, and this seems to denote 190 degrees. Although it's important to mention that the standard measure for calculating arc length is radians, if we convert 190 degrees into radians, we get about 3.32 rad. Thus the length of this specific arc will be r*θ=10.18*3.32, resulting in an arc length of about 33.8 cm.
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The radius of the circle with a circumference of 64 cm is approximately 10.18 cm, the diameter of the circle is 20.36 cm and the length of an arc of 190 degrees in this circle is approximately 33.78 cm.
Explanation:The given circumference is 64 cm. In a circle, the circumference is given by the formula 2πr = Circumference, where r is the radius and π is a constant approximately equal to 3.14. We can rearrange this formula to find the radius: r = Circumference / 2π. Substituting the given value of the circumference, we have r = 64 cm / 2π ≈ 10.18 cm. This is the radius of the circle.
The diameter of a circle is twice the radius, hence the diameter of the circle is 2 * 10.18 cm = 20.36 cm.
Now, to find the length of an arc of 190 degrees in this circle, we first understand that the total angle in a circle is 360 degrees. Hence, the length of the arc corresponding to 190 degrees will be the ratio of 190 to 360 times the circumference. Therefore, arc length = (190/360) * 64 cm ≈ 33.78 cm.
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Which mathematical property is demonstrated below?
a + b + 7 = 7+ b + a
Step-by-step explanation:
the demonstrated property is the commutative property
The equation a + b + 7 = 7 + b + a demonstrates the commutative property of addition, which means that the order of addition does not change the sum.
The mathematical property demonstrated by the equation a + b + 7 = 7 + b + a is the commutative property of addition. This property states that the order in which two numbers are added does not affect the sum. In other words, swapping the operands does not change the result. As shown in the equation and the principles outlined, whether you add a to b or b to a, the sum remains the same. This is true for the addition of ordinary numbers as well— you get the same result whether you add 2 + 3 or 3 + 2, for example.
Positive integer A has 2 different prime factors: p and q (p<q) such that A = pq. Positive integer B is greater than A and the quotient A^2/B is an integer. How many possible values of B are there? PLEASE GIVE AN EXPLANATION WITH YOUR ANSWER!
Answer:
4
Step-by-step explanation:
The integer A^2 will have 9 divisors:
1, p, q, p^2, pq, q^2, p^2q, pq^2, p^2q^2
Of these, the last 4 are greater than A. Hence there will be these 4 values of B.
Answer:
it removed body waste like and instructions
The volume of an object is equal to the ratio of its mass to density, V = . The mass of a spherical grape is 8.4 grams and its density is 2 grams per cubic centimeter.
What is the radius of the grape? Round to the nearest tenth of a centimeter.
Step-by-step explanation:
Mass = Volume x density
Mass = 8.4 gm
Density = 2.4 g/cc
Substituting
8.4 = Volume x 2.4
Volume = 3.5 cm³
[tex]\texttt{Volume of sphere =}\frac{4}{3}\pi r^3[/tex]
We need to find radius, r
Substituting volume value
[tex]\texttt{Volume of sphere =}\frac{4}{3}\pi r^3=3.5\\\\r^3=0.836\\\\r=0.941cm=1cm[/tex]
Radius of grape = 1 cm
To solve the problem we must know about volume.
The radius of the sphere is whose mass is 8.2 grams and has a density of 2 grams per cubic centimeter is 1 cm.
What is volume?
The volume can be defined as the space occupied by the three-dimensional object.
It is given by the ratio of mass(m) and density(ρ).
[tex]\text{Volume of the object} = \dfrac{m}{\rho}[/tex]
Given to us
Mass of the object, m = 8.4 grams
Density of the object, ρ = 2 gram/cm³
As it is already mentioned that the volume is equal to the ratio of its mass to density. therefore,
[tex]\text{Volume of the object} = \dfrac{m}{\rho}\\\\\text{Volume of the object} = \dfrac{8.4}{2}\\\\\text{Volume of the object} = 4.2\ cm^3[/tex]
Thus, the volume of the object is 4.2 cm³.
To find the radius of the sphere we will use the formula of the volume of the sphere.
[tex]\text{Volume of sphere} = \dfrac{4}{3}\pi r ^3[/tex]
Substitute the values,
[tex]4.2 = \dfrac{4}{3}\pi r ^3\\\\r = 1\rm\ cm[/tex]
Hence, the radius of the sphere is whose mass is 8.2 grams and has a density of 2 grams per cubic centimeter is 1 cm.
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what is 7x-7=4x+14 equal
What is the Celsius temperature that is equal to 94 degrees Fahrenheit using the formula F=9/5 C+32
Answer:
34.4°C (rounded up to nearest tenth)
Step-by-step explanation:
Given; F = [tex]\frac{9}{5}[/tex]C + 32
94°F = [tex]\frac{9}{5}[/tex]C + 32
[tex]\frac{9}{5}[/tex]C = 94 - 32 = 62
C = [tex]\frac{62 * 5}{9}[/tex] = 34.44444444°C
And is equal to: 34.4°C (rounded up to nearest tenth)
The Celsius temperature equaling 94 degrees Fahrenheit is 34.44°C.
To find the Celsius temperature equivalent to 94 degrees Fahrenheit using the formula F = (9/5)C + 32:
Substitute 94 for F: 94 = (9/5)C + 32
Then solve for C: C = (94 - 32) / (9/5) = 34.44°C
The Celsius temperature equaling 94 degrees Fahrenheit is 34.44°C.
What makes a trapezoid an isosceles trapezoid?
A. Its legs are congruent.
B. its bases are congruent
C. Its opposite angles are congruent.
D. Its diagonals bisect each other
Answer:
A. Its legs are congruent.
Step-by-step explanation:
It is a parallelogram if ...
the bases are congruent,opposite angles are congruent, orthe diagonals bisect each other.A daycare center charges a $75 enrollment fee plus $100 per week. Which of the following represents the cost of sending a child to daycare for 14 weeks?
Answer:
$1,475
Step-by-step explanation:
times 100 by 14 which is 1400
but then add 75 onto that
Answer:
$1475
Step-by-step explanation:
One week costs $100.
Note that:
The $75 enrollment fee is a one-time payment.
$100 per week is the amount that is paid per week, and can change depending on the amount of week they pay for.
In this case, the child would be there for 14 weeks. Set the equation. Let x = amount of weeks, and t = total cost:
100x + 75 = t
We know that the child will be there for 14 weeks, so plug in 14 for x.
(100)(14) + 75 = t
t = (100 * 14) + 75
Simplify. Remember to follow PEMDAS. Multiply first, then add:
t = (1400) + 75
t = 1475
The total cost for 14 weeks is $1475.
~
The original price of a phone was reduced by $200.
If p = the phone's original price in dollars, which algebraic expression
represents the reduced price?
Answer:
r=reduced price
r=p-200
Step-by-step explanation:
Answer:
P = P - 200$
Step-by-step explanation:
P represents the phone's original price, and the phone's original price dropped 200$. Original price minus 200$.
The equation c = 6.5h represents the cost, c, of renting a bicycle for h hours. The table below can be used to show the same information.
Cost for Renting Bicycles
Number of Hours (h)
0
2
4
6
Cost (c)
If Francesca rents a bicycle for 2 hours and Phil rents a bicycle for 6 hours, how much more does Phil pay?
Answer:
$26
Step-by-step explanation:
To find your answer, simply plug in Francesca's time and Phil's time to your cost equation.
Francesca can be represented by the following equation:
[tex]c=6.5(2)\\c=13[/tex]
Phil can be represented by the following equation:
[tex]c=6.5(6)\\c=39[/tex]
As such, Francesca pays $13 and Phil pays $39. Next, since you want to find how much more Phil paid, all you have to do is subtract 13 from 39. That will give you $26.