Answer:
462 mi
Step-by-step explanation:
Gloria gets 420 mi/tank.
10 % of 420 is
420 × 0.10 = 42 mi
She will be able to drive an extra 42 mi.
420 + 42 = 462 mi
With her new tires, a tank of gas will take her 462 mi.
Answer:
462
Step-by-step explanation:
to find 10% of 420 you take
420 x .10 = 42
then add 42 to 420
420+42=462
Using the Law of Detachment, find the conclusion for the following: If two triangles are similar, then their corresponding angles are congruent.
Triangle ABC and Triangle XYZ are similar.
Question 8 options:
AB≅XY
ABC≅XYZ
The statements are not valid.
Answer:
∠ABC ≅ ∠XYZ
Step-by-step explanation:
Given: ΔABC is similar to ΔXYZ.
If two triangles are similar, then
1. the corresponding angles are congruent
2. the corresponding sides are proportional
From the options given,
AB ≅ XY is not applicable for similar triangles. Hence the option is wrong.
∠ABC ≅ ∠XYZ since ΔABC ≅ ΔXYZ
Hence the answer is ∠ABC ≅ ∠XYZ
Factor completely 7x3y +14x2y3 − 7x2y2.
Answer:
7x^2y(x +2xy^2 -y)
Step-by-step explanation:
7, x^2, and y are factors of every term, so we can start by factoring those out.
... = 7x^2y(x +2xy^2 -y)
The trinomial does not factor further, so this is it.
Answer:
7x^2y(x +2xy^2 -y)
Step-by-step explanation:
7x^3y +14x^2y^3 − 7x^2y^2
WE find out GCF
7x^3y= 7*x*x*x*y
14x^2y^3= 7*2*x*x*y*y*y
7x^2y^2 = 7 *x*x*y*y
GCF is 7x^2y
Factor out GCF from the given expression. when we factor out 7x^2y we divide each term by GCF. we put GCF 7x^2y outside
7x^2y(x +2xy^2 -y)
What is the volume of this rectangular prism?
3ft by 6 1/4 ft by 14 ft
To convert 6 weeks to days, the first ratio is 1 week/7 days . To set up the proportion, the second ratio must be _____
Answer:
6/x weeks
Hope this helps
Answer:
6/x weeks
Step-by-step explanation:
This is the correct answer, credits to the other person who answered.
There are 18 gallons of water in the tank. The tank is 3/4 full. How many gallons of water g can the tank hold
Answer:
24 gallons
Step-by-step explanation:
18 divided by 3 is 6
6 x 4 = 24
so there are 24 gallons as a whole
You said . . . . . 18 = 3/4 g
Multiply each side by 4 . . . 72 = 3g
Divide each side by 3 . . . 24 = g
A) Between x 2 and x 3, which function has a greater average rate of change than f(x)=1/6^-x
Answer:
4^x+1
Step-by-step explanation:
because i got it wrong
Answer:
[tex]y= 4^{x+1}[/tex]
Step-by-step explanation:
A grocer sells 30 loaves of bread a day. The cost is $2.50 per loaf. The grocer estimates that for each $0.50 increase in cost, 2 fewer loaves of bread will be sold per day. Let x represent the number of $0.50 increases in the cost of a loaf of bread.For what number of $0.50 increases in the cost of a loaf of bread will the grocer's generated revenue be greater than zero?
A. The grocer's generated revenue will be greater than zero for any number of $0.50 increases greater than 20.
B. The grocer's generated revenue will be greater than zero for any number of $0.50 increases less than 20.
C. The grocer's generated revenue will be greater than zero for any number of $0.50 increases greater than 15
.
D. The grocer's generated revenue will be greater than zero for any number of $0.50 increases less than 15.
Answer:
none of the above
Step-by-step explanation:
The grocer's revenue will be the product of the number of loaves sold (30-2x) and their price (2.50+0.50x).
Revenue will be positive for values of x between those that make these factors be zero. The number of loaves sold will be zero when ...
... 30 -2x = 0
... 15 -x = 0 . . . . . divide by 2
... x = 15 . . . . . . . add x
The price of each loaf will be zero when ...
... 2.50 +0.50x = 0
... 5 + x = 0 . . . . . . . multiply by 2
... x = -5 . . . . . . . . . . subtract 5
Revenue will be positive for any number of increases greater than -5 and less than 15.
_____
D is the best of the offered choices, but it is incorrect in detail. -5 is a number less than 15, but will give zero revenue.
how do you prove this?
Answer:
Show ΔBCD ≅ ΔGFE, so ∠C ≅ ∠F. Base angle of an isosceles triangle are congruent, so ΔACF is isosceles.
Step-by-step explanation:
Informally, subtract DE from CE and DF. This will show CD ≅ EF.
Then ΔBCD ≅ ΔGFE by the HL theorem for right triangles.
Corresponding parts of congruent triangles are congruent, namely the angles C and F.
Since base angles of ΔACF are congruent, it is isosceles.
what is the equation of the circle with center (0,0) the passes through the point (5,-5). please help
x² + y² = 50
Step-by-step explanation:The circle centered at (h, k) with radius r has equation ...
... (x -h)² + (y -k)² = r²
You have (h, k) = (0, 0), so all we need to do is find r². We can do that by choosing r² so that the equation is true at the given point.
... x² + y² = (5)² + (-5)² = 25 + 25 = 50
Your equation is x² + y² = 50.
The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm greater than its other side. Find the side of the square, if it’s known that the area of the square is 30 cm^2 less than the area of the rectangle.
36 cm
Step-by-step explanation:Let s represent the side of the square in cm. Then s+3 and s-2 are the sides of the rectangle of interest.
The area of the rectangle is the product of its side lengths:
... rectange area = (s+3)(s-2) = s² +s -6
The area of the square is the product of its side lengths, both of which are s.
... square area = s²
The difference of these areas is 30 cm², so ...
... rectangle area - square area = 30
... (s² +s -6) -(s²) = 30
... s = 36 . . . . . . . . . . . . simplify, add 6
The side of the square is 36 cm.
_____
Check
The rectangle dimensions are 39 cm by 34 cm, so its area is
... (39 × 34) cm² = 1326 cm²
The area of the square is (36 cm)² = 1296 cm²
The difference in areas is (1326 -1296) cm² = 30 cm², as required.
The lengths of the sides of a triangle are 15 cm, 20 cm, 30 cm. What are the lengths of the sides of a similar triangle that has a perimeter of 26 cm ?
Answer:
6 cm,12 cm,8 cm
Step-by-step explanation:
add the perimeter of the first triangle to get 65
then divide 65 by 26 to get 2.5
then divide all the side lengths by 2.5
15/2.5=6
20/2.5=8
30/2.5=12
The lengths of the sides of a similar triangle that has a perimeter of 26 cm are 6 cm, 8 cm, and 12 cm and this can be determined by using the given data.
Given :
The lengths of the sides of a triangle are 15 cm, 20 cm, 30 cm.
The following steps can be used in order to determine the lengths of the sides of a similar triangle that has a perimeter of 26 cm:
Step 1 - The formula of the perimeter of the triangle is given below:
[tex]\rm P = a + b + c[/tex]
where a, b, and c are the length of the sides of the triangle.
Step 2 - Now, determine the perimeter of the triangle whose sides are 15 cm, 20 cm, 30 cm.
P' = 15 + 20 + 30
P' = 65 cm
Step 3 - Now, divide both the perimeters of the triangles, that is:
[tex]=\dfrac{65}{26}[/tex]
= 2.5
Step 4 - So, the side length of the sides of a similar triangle is given below:
[tex]\rm \dfrac{15}{2.5} = 6\;cm[/tex]
[tex]\rm \dfrac{20}{2.5}=8 \;cm[/tex]
[tex]\rm \dfrac{30}{2.5}=12\;cm[/tex]
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If your car gets 26 miles per gallon, how much does it cost to drive 430 miles when gasoline costs $3.00 per gallon?
Answer:
$51
Step-by-step explanation:
To solve this, we must divide the total amount of miles by the miles per gallon, and multiply that by the cost per gallon.
430 / 26 = 16.53
Because this is talking about gallons, we should round up to 17.
17 * 3 = 51
It costs $51 to drive 430 miles when gasoline costs $3 per gallon.
Answer:
$49.62
Step-by-step explanation:
We know that the car travels for 26 miles in 1 gallon. So we will find out the number of gallons it requires to travel for 430 miles by simple ratio method.
[tex]\frac{1 gallon}{x} =\frac{26 miles}{430}[/tex]
[tex]x=\frac{430}{26}[/tex]
[tex]x=16.54[/tex]
Now that we know that the car needs 16.54 gallons of gasoline to drive for 430 miles, we can simply multiply the number of gallons by the cost per gallon to find its total cost.
Total cost of gasoline to drive 430 miles = 16.54 x 3 = $49.62
Which of the following represents the equation y = mx + b, where m is a positive integer, written in standard form?
Select one:
A. x+y=mb
B. mx−y=−b
C. −mx+y=0
D. 2y+x=−mb
B. mx−y=−b
Step-by-step explanation:Start with ...
... y = mx +b
Subtract mx.
... -mx +y = b
You want the leading coefficient positive, so multiply by -1.
... mx -y = -b . . . . matches selection B
Answer: B. mx−y=−b
Step-by-step explanation:
The equation of a line in standard form is given by :-
[tex]Ax+By=C[/tex]
, where A is a positive integer , B and C are integers.
The given equation : [tex]y = mx + b[/tex]
, where m is a positive integer.
The convert it into standard form , we subtract y and b from both sides , we get
[tex]y -y-b= mx + b-y-b[/tex]
Simplify,
[tex]-b= mx -y[/tex]
Or we can write it as [tex] mx -y=-b[/tex] → Standard form.
Thus , the equation of line in standard form = [tex] mx -y=-b[/tex] , where m is a positive integer.
Hence, the correct answer is B. mx−y=−b
Translate the difference of five squared and n into symbols.
5^2- n
5^2+ n
5^2x n
5^2 ÷ n
Answer:
5² - n
Step-by-step explanation:
Five squared = 5²
n = n Subtract n from 5²
Diff. = 5² - n
We indicate "taking the difference" by a "minus" sign, so all the other options are wrong.
Answer:
5² - n
Step-by-step explanation:
Five squared is written as = 5²
The symbol of n is n.
The term difference is subtraction.
The difference of five squared and n ⇒ 5² - n
Noel has 5/6 of a yard of purple ribbon and 9/10 of a yard of pink ribbon. How much ribbon does she have altogether?
triangles abc and def are similar. The length of each side of triangle abc is 8 times the length of each corresponding side of triangle def. How many times greater is the area of triangle abc than the area of triangle def
64
Step-by-step explanation:If each side length is multiplied by 8, the product of two side lengths will be multiplied by 8×8 = 64.
Area is proportional to the product of two side lengths, so will be multiplied by 64.
I just need help with Number 17 when it comes to writing out the equation
Answer:
132(X) + 64(2X) = $1040.00
Step-by-step explanation:
equations
64a +132s = 1040a = 2ssolution
Adult ticket: $8Student ticket: $4Step-by-step explanation:a. It usually works well to let a variable represent the quantity the problem statement is asking you to find. I like to choose variable names that help me remember what the variable stands for. (x and y rarely do that) So, let's choose "a" for the cost of an adult ticket, and "s" for the cost of a student ticket.
The equations express the relationships described by the problem statement. The first relationship expresses the total revenue in terms of the numbers of tickets sold. You know that multiplying the number of tickets by the cost of the ticket will give the revenue from sales of that ticket. So, the total revenue is ...
... 64a +132s = 1040
The problem statement also tells you the relationship between the costs. An adult ticket is twice the cost of a student ticket, so ...
... a = 2s
These equations are your system of linear equations.
_____
b. The solution can be found using substitution. Since the second equation gives an expression for "a", we can use that in the first equation.
... 64(2s) +132s = 1040
... 260s = 1040 . . . . . . . . simplify
... 1040/260 = s = 4
... a = 2s = 2·4 = 8
An adult ticket costs $8; a student ticket costs $4.
Krys bought x boxes of pastries to bring to a party. Each box contains 12 pastries. She decides to keep two boxes for herself. She brings 60 pastries to the party. Which equation can be used to find the number of boxes, x, Krys bought? a. 2x − 12 = 60 b. 12x − 2 = 60 c. 12x − 24 = 60 d. 24 − 12x = 60
Answer:
c. 12x − 24 = 60
Step-by-step explanation:
x is the number of boxes Krys bought.
12x is the number of pastries in those boxes. 2·12 = 24 is the number of pastries in the boxes Krys kept for herself. Then the number of pastries Krys brought to the party is ....
... 12x -24
We are told that number is 60, so we can use this equation to find x:
... 12x -24 = 60
Answer:
Option C : 12x − 24 =60
Step-by-step explanation:
Given :
Krys bought x boxes of pastries to bring to a party.
Each box contains 12 pastries.
She decides to keep two boxes for herself.
She brings 60 pastries to the party.
To Find : Equation can be used to find the number of boxes, x, Krys bought.
Solution :
Krys bought x boxes of pastries .
Each box contains 12 pastries.
So, total pastries she bought = 12 x
She decides to keep two boxes for herself.
Since 1 box contain 12 pastries .
Thus two box contains pastries = 12*2 =24 pastries
Now total pastries she bought is 12 x . Out of which she decides to keep 24 pastries . after keeping 24 pastries from 12 x pastries she bought 60 pastries to the party i.e.
⇒ 12 x - 24 = 60
Thus,Equation can be used to find the number of boxes, x, Krys bought:
12 x - 24 = 60
Hence Option C is correct .
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SEE ATTACHMENT
-3 is a solution of y > -2
Answer:
i think it is true and true
Step-by-step explanation:
Answer:
35. False
36. True
Step-by-step explanation:
35. [tex]-3\:<\:-2[/tex]
On the number line [tex]-3[/tex] is to the left of [tex]-2[/tex].
Therefore [tex]-3[/tex] is not greater than [tex]-2[/tex].
[tex]-3[/tex] is rather less than [tex]-2[/tex].
36. [tex]y\leq 3[/tex] includes three as a possible solution.
The reason is that, the inequality contains an equal sign in it, the boundary is also inclusive, therefore 3 is itself a possible solution.
In order words, the statement
[tex]3\leq3[/tex] is a truth statement.
Jack signs up for a credit card that has a APR of 13.99%. Use the periodic (monthly) interest rate to calculate how much interest he owes on his unpaid February balance of $345.67?
Answer:
$3.46
Step-by-step explanation:
Unpaid February balance = $345.67
Annual Percentage Rate(APR) = 13.99 %
= [tex]\frac{13.99}{100}[/tex]
= 0.1399 (converted into decimal)
Periodic (monthly) interest rate = [tex]\frac{0.1399}{12}[/tex] (since there are 12 months in a year)
= 0.01
Interest he owes on his unpaid February balance of $345.67
= Periodic (monthly) interest rate * unpaid February balance
= 0.01 * 345.67
= 3.456
= $3.46 (rounded off to the hundredth place)
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Name Score Julia 650 Andrew 550 Jason 380 Cathy 720 Jessica 710 Robert 550 The table gives the scores of 6 students from a class of 25 in a competitive exam. The point estimate of the mean score for the students is . (Round off your answer to the nearest tenth.)
Answer:
Mean score for the students = 593.3
Step-by-step explanation:
Name Score
Julia 650
Andrew 550
Jason 380
Cathy 720
Jessica 710
Robert 550
1) Mean Score = [tex]\frac{Sum of the scores}{Total number of students}[/tex]
= [tex]\frac{650+550+380+720+710+550}{6}[/tex]
= 593.33
2) Upon rounding off to the nearest tenth, we get
Mean Score = 593.3 (since the hundredth digit is lesser than 5, the tenth digit is not increased)
Answer:
593.3
Step-by-step explanation:
Assuming random sample, assuming "point estimate of mean score" means "estimate of mean score in points",
(650+550+380+720+710+550)/6 is 593.3
Sample size 6 population size 25 is irrelevant except to note estimate might not be very good.
Solve the logarithmic equation.
y = log4 0.25
What does y equal?
[tex]\bf \textit{exponential form of a logarithm} \\\\ log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y=\log_4(0.25) ~\hfill 0.\underline{25}\implies \cfrac{025}{1\underline{00}}\implies \cfrac{1}{4}\implies 4^{-1} \\\\\\ y=\log_4\left( 4^{-1} \right)\implies 4^y=4^{-1}\implies y=-1[/tex]
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Answer:
B) 6
Step-by-step explanation:
It is 45, 45, 90 degrees right triangle, the ratio of the triangle 1:1:√2
Hypotenuse = 3√2*√2
= 3*2
= 6
Thank you.
Answer:
6
Step-by-step explanation:
Hypotenuse is the side that is opposite of the 90 degree angle (the longest side as well).
As seen in the triangle, the side opposite of 45° angle is known AND we want to find the hypotenuse.
Which trigonometric ratio relates opposite with hypotenuse?
SINE
We can write:
[tex]sin(A)=\frac{opposite}{hypotenuse}\\sin(45)=\frac{3\sqrt{2}}{h}[/tex]
We let hypotenuse be [tex]h[/tex]. Also we know that [tex]sin(45)=\frac{1}{\sqrt{2}}[/tex]
Now we can solve for [tex]h[/tex]:
[tex]sin(45)=\frac{3\sqrt{2}}{h}\\h*sin(45)=3\sqrt{2}\\h=\frac{3\sqrt{2}}{sin(45)}\\h=\frac{3\sqrt{2}}{\frac{1}{\sqrt{2}}}\\h=3\sqrt{2}*\frac{\sqrt{2}}{1}\\h=6[/tex]
(we used the identity [tex](\sqrt{a})(\sqrt{a})=a[/tex])
2nd answer choice is right. Hypotenuse is 6.
What is -2 1/2 divided by 6?
A. -2 1/6
B. 5/12
C. 2 1/6
D. -5/12
Answer:
D -5/12
Step-by-step explanation:
2 1/2 = 2·(2/2) + 1/2 = 5/2
Dividing by 6 is the same as multiplying by 1/6.
... (-5/2)×(1/6) = -5·1/(2·6) = -5/12
a) Find a polynomial, which, when added to the polynomial 5x2–3x–9, is equivalent to: 18
b) Find a polynomial, which, when added to the polynomial 5x2–3x–9, is equivalent to: 0
Answer:
a) [tex]-5x^{2}+3x+27[/tex]
b) [tex]-5x^{2}+3x+9[/tex]
Step-by-step explanation:
a) Let the required polynomial be p(x).
We have the relation, [tex]5x^{2}-3x-9[/tex] + p(x) = 18
i.e. p(x) = 18 [tex]-5x^{2}+3x+9[/tex]
i.e. p(x) = [tex]-5x^{2}+3x+27[/tex]
b) Let the required polynomial be q(x).
We have the relation, [tex]5x^{2}-3x-9[/tex] + q(x) = 0
i.e. q(x) = 0 [tex]-5x^{2}+3x+9[/tex]
i.e. q(x) = [tex]-5x^{2}+3x+9[/tex]
Answer:
(a) [tex]-5x^2+3x+27[/tex]
(b) [tex]-5x^2+3x+9[/tex]
Step-by-step explanation:
(a)
Let the polynomial be Q(x).
Given polynomial P(x) = [tex]5x^2-3x-9[/tex]
As per the given statement: A polynomial(Q(x)) which, when added to the polynomial [tex]5x^2-3x-9[/tex], is equivalent to 18.
[tex]P(x)+Q(x) = 18[/tex]
[tex]5x^2-3x-9 +Q(x) = 18[/tex]
⇒[tex]Q(x) = 18 -(5x^2-3x-9)[/tex]
or
[tex]Q(x) = 18 -5x^2+3x+9[/tex]
Simplify:
[tex]Q(x) =-5x^2+3x+27[/tex]
Therefore, the polynomial is, [tex]-5x^2+3x+27[/tex]
Check:
[tex]P(x)+Q(x)[/tex] = [tex]5x^2-3x-9 +(-5x^2+3x+27)[/tex]
= [tex]5x^2-3x-9 -5x^2 +3x+27[/tex]
= 18
(b)
Let the polynomial be Q(x).
Given polynomial P(x) = [tex]5x^2-3x-9[/tex]
As per the given statement: A polynomial(Q(x)) which, when added to the polynomial [tex]5x^2-3x-9[/tex], is equivalent to 0.
[tex]P(x)+Q(x) = 0[/tex]
[tex]P(x) = -Q(x)[/tex]
⇒[tex]Q(x) = -(5x^2-3x-9)[/tex]
or
[tex]Q(x) = -5x^2+3x+9[/tex]
Therefore, the polynomial is, [tex]-5x^2+3x+9[/tex]
Check:
[tex]P(x)+Q(x)[/tex]=[tex]5x^2-3x-9 +(-5x^2+3x+9)[/tex]
= [tex]5x^2-3x-9-5x^2 +3x+9[/tex]
= 0
15x+8y=56 in slope intercept form
The equation 15x + 8y = 56 can be rewritten in slope-intercept form (y = mx + b) as y = -15/8x + 7, where -15/8 is the slope and 7 is the y-intercept.
Explanation:To convert the equation 15x + 8y = 56 into slope-intercept form (y = mx + b), we want to isolate y. Here are the steps:
Subtract 15x from both sides of the equation, which gives us 8y = -15x + 56.Divide every term by 8 to solve for y. This gives us y = -15/8x + 7.In this equation, -15/8 is the slope, and 7 is the y-intercept. This means the line intersects the y-axis at y = 7, and for every 8 units increase in x, there is a 15 unit decrease in y, as the slope is negative.
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A graph has a constant of proportionality of 2.54. Let y represent centimeters and x represent inches.
What is the unit rate of the relationship?
Enter your answer, as a decimal, in the box
______cm/in.
2.54 cm/in
Step-by-step explanation:In this context, "constant of proportionality" and "unit rate" mean the same thing.
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Answer:
[tex]<\:3[/tex] is the angle of elevation from the boat to the lighthouse.
Step-by-step explanation:
From the boat, the angle through which you will raise your head to see the light house is the angle of elevation, which is [tex]<\:3[/tex].
See graph for the illustration.
The correct answer is A
Answer:
The angle of elevation from the boat to the lighthouse is:
First option: <3
Step-by-step explanation:
The angle of elevation from the boat to the lighthouse is the angle of the visual since the boat to the lighthouse with the horizontal, according with the graph this angle is <3 (First option)
Given: y varies directly as x. If y = 5 when x = 4, what is the value of y when x = 12? A) 9.6 B) 10 C) 12 D) 15
Answer:
D) 15
Step-by-step explanation:
We know the formula for direct variation is
y=kx
Substituting y=5 and x=4 we can calculate k
5=k4
Divide each side by 4
5/4 =k
Now y= 5/4 x
If x =12
y =5/4*12
y = 15
Use the information in the diagram to determine the height of the tree to the nearest foot.
the diagram is not to scale.
A. 60
B. 30
C. 28
D. 120
Answer:
The correct option is A. The height of tree is 60 ft.
Step-by-step explanation:
From the given figure it is noticed that the building is creating a right angle triangle from a point and the tree divides the hypotenuse and base in two equal part.
According to midpoint theorem of triangle: In a triangle, if a line segment connecting the midpoints of two sides, then the line is parallel to third side. The length of line segment is half of the length of third side.
Using midpoint theorem of triangle, we can say that the length of tree is half of the building.
[tex]Tree=\frac{1}{2}\times Building[/tex]
[tex]Tree=\frac{1}{2}\times 120[/tex]
[tex]Tree=60[/tex]
Therefore correct option is A. The height of tree is 60 ft.