Answer:
24x − 8y
Step-by-step explanation:
8(3x-y)
apply distributive property;
1. 8 (3x) + 8 (−y)
multiply 3 by 8 ;
2. 24x + 8 (-y)
multiply -1 by 8;
3. 24x - 8y
Regroup terms ;
4. 24x − 8y
Fabio has run five eighths of the race. What fraction of the race remains?
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
Fractionssince [tex]\frac{5}{8}[/tex] has been completed
the remaining would be :
[tex]\frac{8}{8} -\frac{5}{8}[/tex]
since denominators are the same
= [tex]\frac{8 - 5}{8} \\\\[/tex]
= [tex]\frac{3}{8}[/tex]
the fraction of the race that is remaining is 3/8
what two numbers multiply into (-24) and adds up to (-10)?
Two numbers multiply into (-24) and adds up to (-10) are 2 & -12
Step-by-step explanation:
Here we need to find two numbers , with the following info:
Let us assume that two numbers are x & y .
two numbers multiply into (-24):
Two numbers are x and y , and there multiply is -24 i.e.
⇒ [tex]x(y) = -24[/tex]
two numbers adds up to (-10):
Two numbers are x and y , and there addition is -10 i.e.
⇒ [tex]x+y = -10[/tex] . .............. (1)
Let's solve this :
We know that , [tex](x+y)^2 = x^2 +y^2 +2xy[/tex]
⇒ [tex](x+y)^2 = x^2 +y^2 +2xy[/tex]
⇒ [tex](-10)^2 = x^2 +y^2 +2(-24)[/tex]
⇒ [tex]100 = x^2 +y^2 -48[/tex]
⇒ [tex]x^2 +y^2 =148[/tex]
Now,
⇒ [tex](x-y)^2 = x^2 +y^2 -2xy[/tex]
⇒ [tex](x-y)^2 = (148) -2(-24)[/tex]
⇒ [tex](x-y)^2 = (148) +48=196 = 14^2[/tex]
⇒ [tex]x-y = 14[/tex] .......... (2)
Let's solve equation 1 & 2 by adding (1)+(2):
⇒ [tex](x+y)+(x-y) = -10 +14[/tex]
⇒ [tex]2x=4[/tex]
⇒ [tex]x=2[/tex]
Putting value of [tex]x=2[/tex] in [tex]x-y = 14[/tex] :
⇒ [tex]2-y = 14[/tex]
⇒ [tex]y = -12[/tex]
Therefore, two numbers multiply into (-24) and adds up to (-10) are 2 & -12.
Bobby catches 8 passes in 3 football games. At this rate, how many passes does he
catch in 15 games?
Answer:
40 passes
Step-by-step explanation:
we know that
Bobby catches 8 passes in 3 football games
so
using proportion
Find out how many passes does he catch in 15 games
[tex]\frac{8}{3}=\frac{x}{15}\\\\x=8(15)/3\\\\x=40\ passes[/tex]
Answer: 40 passes
Step-by-step explanation:
Hi, to answer this we have to use proportions:
Proportion = Passes catched/ football games
Bobby catches 8 passes in 3 football games: 8/3
For 15 games: x/15
8 /3 = x/15
Solving for x
(8/3)15 =x
40 = x
He catches 40 passes in 15 games.
Feel free to ask for more if needed or if you did not understand something.
solve: 43x = 42
a: x= -3/2
b: x= -2/3
c: x=2/3
d: x=3/2
Answer: C
it's C) 2/3
Answer:
C! X = 2/3
Step-by-step explanation:
Next part on edge is
(C) X=1
at a local school the ratio of boys to girls was 8 to 9 if there were 117 girls how many boys were enrolled in the school?
i need help
The number of boys in the schools is 104.
Step-by-step explanation:
Given,
The ratio of boys and girls is 8:9
Number of girls = 117
Let us take,
Number of boys = 8x
Number of girls = 9x
To find the number of boys.
According to the problem,
9x = 117
or, x = [tex]\frac{117}{9}[/tex]
= 13
Hence, the number of boys = 13×8 = 104
3x^2(2x^2+3)=0
please help quick
Answer:
x=0 and x=sqrt(3/2)i
Step-by-step explanation:
3x^2(2x^2+3)=0
Make into two equations due to Zero Product Property:
3x^2=0 and 2x^2+3=0
x^2=0 2x^2=-3
x=0 x^2=-3/2
x=sqrt(3/2)i
f(4) if f(x) = 3x - 1
Answer:
f(4) = 11
Step-by-step explanation:
To evaluate f(4) substitute x = 4 into f(x)
f(4) = 3(4) - 1 = 12 - 1 = 11
PLEASE HELP ME!!!!!!!!
A polygon has the following coordinates: A(3,-3), B(-3,-2), C(-5,1), D(-5,4), E(-4,6), F(-2,6), G(3,2). Find the length of CD.
A. 4 units
B. 6 units
C. 3 units
D. 5 units
The right answer is Option C: 3 units
Step-by-step explanation:
Given coordinates are;
A polygon has the following coordinates: A(3,-3), B(-3,-2), C(-5,1), D(-5,4), E(-4,6), F(-2,6), G(3,2).
For finding length of CD, we will find the distance between C and D.
C(-5,1) and D(-5,4)
Here;
[tex]x_1=-5, y_1=1\\x_2=-5, y_2=4[/tex]
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
[tex]Distance=\sqrt{(-5+5)^2+(4-1)^2}\\Distance=\sqrt{(0)^2-(3)2}\\Distance=\sqrt{(3)^2}\\Distance = 3[/tex]
Therefore;
The length of CD is units.
The right answer is Option C: 3 units
Answer:
2
Step-by-step explanation:
Simplify the numerical expession 5-2 + 12 + 4?
Answer:
The answer is 19
Step-by-step explanation:
Answer:so easy its 19 it's right i promise you
(7+x)+7x simplify each expression
Step-by-step explanation:
[tex](7 + x) + 7x \\ = 7 + x + 7x \\ = 7 + (x + 7x) \\ = 7 + 8x \\ = 8x + 7[/tex]
how so you slove 4^2x-1 = 8^x+2 ?
Answer:
x = [tex]\frac{ln(16)}{ln(2)}[/tex]
Step-by-step explanation:
[tex]4^{2x-1} =8^{x+2}[/tex]
ln both sides like you would add the same number to both sides to keep the equation equivalent
[tex]ln4^{2x-1} = ln 8^{x+2}[/tex]
using log rules, exponents can be brought down as a constant multiplying ln
[tex](2x-1)ln(4) =(x+2)ln(8)[/tex]
use distributive property to remove parentheses
2xln(4) - ln(4) = xln(8) + 2ln(8)
isolate x
2xln(4) - xln(8) = 2ln(8) + ln(4)
rewrite the logs using log rules: ln(x) - ln(y) = ln([tex]\frac{x}{y}[/tex]) and the exponent rule stated above
xln([tex]4^{2}[/tex])-xln(8) = ln([tex]\frac{8^{2} }{4}[/tex])
factor out x
x(ln[tex]4^{2}[/tex]-ln8) = ln([tex]\frac{8^{2} }{4}[/tex])
again use log rules: ln(x) - ln(y) = ln([tex]\frac{x}{y}[/tex])
x* [tex]ln(\frac{4^{2} }{8}[/tex][tex])[/tex]= ln([tex]\frac{8^{2} }{4}[/tex])
now simplify the stuff inside the ln parentheses
x*ln(2) = ln(16)
x = [tex]\frac{ln(16)}{ln(2)}[/tex]
Whats 33.33% into a decimal number
Answer:
0.3333
Step-by-step explanation:
To convert 33.33% to decimal, simply divide 33.33 by 100.
Answer: 0.3333
Step-by-step explanation:
33.33% = 33.33 / 100 = 0.3333.
Since 100 has 2 zeros, you count the decimal point in 33.33 forward twice.
-7=z/-6 solve for z pls help it 7th grade math and it’s on khan ;cc
Answer:
42
Step-by-step explanation:
I think it's 42 because 42/-6 is -7
Answer:
z = 42
Step-by-step explanation:
Given -7 = z/-6
Cross multiply
-7 x -6 = z
Negative times negative gives you positive.
42 = z
z = 42
35 more than 5 times a number, w, is -10, what is the number w?
Answer: w= -9
Step-by-step explanation:
Set up an equation, 5 times a number is 5w, and 35 more, means plus 35. All of this is equal to -10, so the equation will be:
5w+35=-10
Subtract 35 from both sides
5w=-45
Divide by 5 on both sides
w= -9
Hope this helped!
You draw two cards from a standard deck of 52 cards. What is the probability of drawing a club and then a diamond consecutively from the deck without replacement? A) 13 51 B) 13 105 Eliminate C) 13 204 D) 13 408
Answer:
There are 13 cards for each suit so the first fraction is 13/52 and the next one is 13/51 as there is no replacement for the first card you pulled.
Multiplying them you get: 13/52*13/51= 169/2652,
Then you divide both sides by 13 to get: 13/204
So, the answer is C.
I hope this helps!
The probability of drawing a club and then a diamond consecutively from the deck without replacement is 13/204.
Option C is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of cards = 52
Number of clubs = 13
Number of diamonds = 13
Now,
The probability of drawing a club.
= 13/52
And,
The probability of drawing a diamond consecutively from the deck without replacement.
= 13/51
[ There will be only 51 cards in total since we are not replacing ]
Now,
The probability of drawing a club and then a diamond consecutively from the deck without replacement.
= 13/52 x 13/51
= 13/4 x 1/51
= 13/204
Thus,
13/204 is the probability of drawing a club and then a diamond consecutively from the deck without replacement.
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Apples weigh 12 ounces each.Ronald bought 4 apples.How many pounds of apples did he buy?
how do you work out how many 1/3 cup servings are in 6 cups of pecans
Answer:
18 servings
Step-by-step explanation:
Because 6 divided by 1/3 is the same as 6*3, we can just do it that way so it makes more sense.
6*3= 18
And there you have your answer!
if a+b = 8, a²-b²=16, then ab is?
Answer:
a=5 and b=3
Step-by-step explanation:
a+b=8
okay, so the numbers that can make 8 are 4+4, 5+3, 6+2, and 7+1
Try 5+3
so plug them in
5+3=8
5*5=25
3*3=9
25-9=16
that's your answer
Fill in the blank: in the table of exponential function,————————- by the same amount each time to get to the next number
Answer: multiplies
Explain: this is because exponentially is multiplication.
The table of exponential multiplies by the same amount each time to get to the next number.
What is an exponential function?In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.
In another meaning, an exponential function is that function above which a variable x has imposed.
For example [tex]3^{x}[/tex] , [tex]7^{x}[/tex] like that.
Let a general exponential function [tex]a^{x}[/tex] where a is constant.
Let x = 1,2,3,4,5....
At x = 1 ⇒ a¹ = a
At x = 2 ⇒ a² = a × a = previous numebr × (a)
At x = 3 ⇒ a³ = a² × a = previous number × (a)
So,
It is clear that in exponential function each term multiplies the same amount each time to get to the next number.
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Cindy rode her bicycle 6 miles less than four times the number of miles that Scotty road. If Cindy rode his bicycle 42 miles, how many miles did Scotty ride?
Answer:
12
Step-by-step explanation:
42+6=48
48/4=12
log 32 (16)= 5 4 exponential form
Answer: _(32)(16)=(4)/(5)
Step-by-step explanation:
which ordered pair is a a solution of the equation ?
y= 3x+5
A. only (2,11)
B. only (3,13)
C. both (2,11) and (3,13)
D.neither
Answer:
A
Step-by-step explanation:
when you plug in 2,11
11 = 3*2 +5 that is correct
13 = 3*3 +5 that is not correct
only 2,11 works
Answer:
A. only (2,11)
Step-by-step explanation:
Concrete Works manufactures and sells cement trucks. For the previous year, their taxable income was $6,775,989.00. They have
to pay a federal tax rate of 35%, a state tax rate of 8%, and a local tax rate of 2%. As part of their loan package for the business, the
company has to pay $3,200,000.00 after the taxes are paid each year to go against the principal amount of the loan. The profit after
taxes and principal reduction can be determined by the equation
p() = 0.586041 - 3,200,000,
where x is their taxable income. How much profit does the company have after paying taxes and reducing the principal on the loan?
You have the right equation.
p(x) = 0.586041x - 3,200,000
3200000 of course represents the deduction from the loan
0.586041 - this number represents the amount of money left after taxes (58.6041% of the total is left)
We get this by taking into account all the taxes on top of another...
35% federal tax = 65% left
35% federal tax and 8% state tax = 65% x 92% left
35% federal tax and 8% state tax and 2% local tax = 65% x 92% x 98% left = 58.6041%
To get the profit plug in the given taxable income for x.
p(6775989) = 0.586041(6775989) - 3,200,000 = $771,007.37 approx.
answer: $771,007.37 approx.
What is true about triangle AMB?
It is congruent to triangle ABC.
It is an obtuse triangle.
It is an isosceles right triangle.
It is a scalene triangle.
Answer:option c
Step-by-step explanation:
An Isosceles Right Triangle is a right triangle that consists of two equal-length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.
So the correct answer is option c. It is an isosceles right triangle.
What are the sides of an isosceles right triangle?
Since the two sides are equal it makes the corresponding angle congruent. Thus, in an isosceles right triangle two sides are congruent and the corresponding angles will be 45 degree each which sums to 90 degree. So the sum of three angles of the triangle will be 180 degrees.
What is the formula for an isosceles right triangle?
The area of the isosceles right triangle follows the general formula of the area of a triangle that is (1/2) × Base × Height. In ∆QPR shown above with side lengths PQ = QR = x where PQ represents the height and QR represents the base, the area of isosceles right triangle formula is given by 1/2 × PQ × QR = x2/2 square units.
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What is the value of y in the equation,
y = -3x + 4, if x = 3?
Answer:y= -5
Step-by-step explanation:
-3(3)+4= -5
-3(3)= -9
-9 + 4= -5
Answer:
-5
Step-by-step explanation:
y = -3x + 4
If x = 3
Plug the value into the expression
We have
y = -3(3) + 4
= -9 + 4
= -5
You are writing the inequality for age. At an amusement park, children ages 3 and under are free. Write an inequality.
Answer:
Step-by-step explanation:
So you would do x as other ages, 3 as well obviously 3.
x < 3
THE < WILL HAVE A LINE UNDER IT!
The line stands for less than or EQUAL to. In this case, you have to be 3 or younger. Do not forget the line under the <. I am unable to type it!
The question is about writing an inequality to represent the ages of children who can enter an amusement park for free. The correct mathematical expression according to the given scenario is 'age ≤ 3'.
Explanation:The subject of the question deals with the practical application of inequalities in a real-world context. In this case, the inequality would represent the ages at which children could enter an amusement park for free. According to the amusement park policy, children ages 3 and under are free. In mathematical terms, this can be expressed as 'age ≤ 3'. The symbol '≤' represents 'less than or equal to', indicating that the age could be any number less than or equal to 3.
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10 is decreased by four times the quantity of 8-3. One is an added to that result.
2x - y = 10
y = -x - 1
Solve the system of equations
A (9.8)
B (3.-4)
C no solution
Answer: option is C
Step-by-step explanation:
What customary unit would you use to estimate? A car is about 15 _____ long. inches meters yards feet
Answer:
feet
Step-by-step explanation:
1. Find the area and perimeter of the triangle.
16 cm
20.9 am
27 cm
Answer:
Perimeter = 63.9 cm.
Area = 166.96 cm^2 to the nearest hundredth.
Step-by-step explanation:
The perimeter = 16+20.9+27 = 63.9 cm.
To find the area you can use Heron's Formula.
Area = √ [ s(s-a)(s-b)(s-c)] where s = the semi-perimeter and a, b and c are the lengths of the 3 sides.
s = 63.9 / 2 = 31.95.
Area of the triangle = √ (31.95(31.95-16)(31.95-20.9)(31.95-27)]
= 166.96 cm^2.