Answer:
a/b =6
Step-by-step explanation:
We want to evaluate a/b
a=24, b=4
Substitute these values into the expression
a/b =24/4
= 6
Final answer:
When evaluating the expression a/b with a=24 and b=4, the result is 6, as you simply divide 24 by 4.
Explanation:
The expression to evaluate is a/b, where a=24 and b=4.
To calculate this, simply divide the value of a by the value of b:
Step-by-step calculation:
Insert the known values into the expression: a/b = 24/4.
Divide 24 by 4 to get the result.
24 divided by 4 equals 6.
Therefore, if a=24 and b=4, the value of a/b is 6.
Which method can you use to prove that the triangles are congruent?
A. HL
B. ASA
C. SAS
D. SSS
E. AAS
Answer:
The answer is ASA.
Step-by-step explanation:
There is one other angle in the middle which is congruent to its self.
ASA (Angle-Side- Angle) method can we use to prove that the triangles are congruent
Two triangles are called to be congruent if their sides have the equal length and angles have equal measure.
Thus, two triangles can be superimposed side to side and angle to angle.
If any two angles and the side of the angles of triangle are equivalent to the corresponding, then the two triangles are said to be congruent by ASA rule.
There is one other angle in the middle which is congruent to its self
ASA (Angle-Side- Angle)
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Find the measure of the angle
Answer:
? = 113
Step-by-step explanation:
The angles are alternate interior angles. Alternate interior angles are equal if the lines are parallel. Since the lines are parallel, the angles are equal.
? = 113
Determine the ratio in which the point (–6, m) divides the join of A(–3, –1) and B(–8, 9). Also, find the value of m.
Answer:
Ratio = 3 : 2 and value of m = 5.
Step-by-step explanation:
We are given the end points ( -3,-1 ) and ( -8,9 ) of a line and a point P = ( -6,m ) divides this line in a particular ratio.
Let us assume that it cuts the line in k : 1 ratio.
Then, the co-ordinates of P = [tex]( \frac{-8k-3}{k+1},\frac{9k-1}{k+1} )[/tex].
But, [tex]\frac{-8k-3}{k+1}[/tex] = -6
i.e. -8k-3 = -6k-6
i.e. -2k = -3
i.e. [tex]k = \frac{3}{2}[/tex]
So, the ratio is k : 1 i.e [tex]\frac{3}{2} : 1[/tex] i.e. 3 : 2.
Hence, the ratio in which P divides the line is 3 : 2.
Also, [tex]\frac{9k-1}{k+1}[/tex] = m where [tex]k = \frac{3}{2}[/tex]
i.e. m = [tex]\frac{\frac{9 \times 3}{2}-1}{\frac{3}{2}-1}[/tex]
i.e. m = [tex]\frac{27-2}{3+2}[/tex]
i.e. m = [tex]\frac{25}{5}[/tex]
i.e. m = 5.
Hence, the value of m is 5.
Answer:
m=5
Step-by-step explanation:
Given: Point [tex]C(x_3,y_3)=(-6,m)[/tex] divides the join of point [tex]A(x_1,y_1)=(-3,-1)[/tex] and point [tex]B(x_2,y_2)=(8,9)[/tex]
Let the line AB divides by Point C in a ratio m:n=k:1
Then, Using section formula [tex](x_3,y_3)=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}[/tex]
Applying formula,
[tex]x_3,y_3=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}[/tex]
[tex]x_3,y_3=\frac{-8k-3}{k+1},\frac{9k-1}{k+1}[/tex]
But, [tex]x_3=-6[/tex]
Therefore, [tex]x_3=\frac{-8k-3}{k+1}[/tex]
[tex]-6=\frac{-8k-3}{k+1}[/tex]
[tex]-6k-6=-8k-3[/tex]
[tex]2k-3=0[/tex]
[tex]k=\frac{3}{2}[/tex]
Therefore, C divides line AB in 3:2
Now, [tex]m=\frac{9k-1}{k+1}[/tex] where, k=3/2
[tex]m=\frac{9\frac{3}{2}-1}{\frac{3}{2}+1}[/tex]
[tex]m=\frac{\frac{25}{2}}{\frac{5}{2}}[/tex]
[tex]m=\frac{25\times2}{2\times5}[/tex]
[tex]m=5[/tex]
Jack makes W dollars an hour. He will get a $2 an hour raise. Write an expression for his new hourly wage
Answer:
2w
Step-by-step explanation:
you multiply 2 by how many hours you have worked (w)
As a clinical trials monitor, you recruit subjects for a new study. You want 175 subjects per group for 3 groups. How many subjects should you recruit for the whole study?
Answer:
You should recruit a total of 525 subjects for the whole study.
Step-by-step explanation:
The question states that you want 175 subjects per group for 3 groups. This indicates that we need to either multiply 175 times 3, or we can add 175 three times to get the total number of subjects we would need to recruit. Group 1 should have 175, Group 2 should have 175 and Group 3 should have 175. Whether we multiply 175 x 3 or add 175+175+175, we get a final anser of 525.
Harvey is finding the area that can be divided into 2 trapezoids.the basis of each trapezoid is 14 and 24. The height of each is 8. What is the area of the figure?
Answer:
Area of the figure is 304 sq. units
Step-by-step explanation:
The area is divided into two identical trapezoids of height 8 units and bases 14 and 24 units.
Area of a trapezoid = (1/2) * (Sum of base lengths) * height
So, area of 1 one trapezoid = (1/2)*(14+24)*8=152
The area of the figure is twice the area of the trapezoid.
So, area of figure = 2 * 152 = 304 sq. units
∴ Area of the figure is 304 sq. units
Harold can buy 2 pounds of bananas for $7. Write and equation to represent the cost , c , for b bananas
So far in math class, a student's quiz scores are 86%, 82%, 72%, and 69%. What score does the student need on the fifth quiz to have a mean quiz score of 79%? All the quizzes have equal weights. a 86% b 77.25% c 79% d 87%
Answer:
a
Step-by-step explanation:
the mean = [tex]\frac{total score}{count}[/tex]
let the fifth score be x and count = 5, hence
[tex]\frac{86+82+72+69+x}{5}[/tex] = 79 ( multiply both sides by 5 )
309 + x = 395 ( subtract 309 from both sides )
x = 86
the student requires a score of 86% → a
Can someone help me please
Another math question because that’s my weak point 30 points
Answer:
4j-3 = j is an equation
2 + 66÷11 -3*2 is an expression
g+h>f is an inequality
Step-by-step explanation:
An equation has an equals sign =
An expression has no equals sign or greater or less than signs
An inequality has ( ≤,≥,<,>) greater than or equal to, less than or equal to, greater than, less than signs
I also need help with this one
Which is the graph of f(x)= 4[1/2]^x ?
Answer:
B
Step-by-step explanation:
A
f(1) = 4*(1/2)^1 = 4/2 = 2
(1,1) is not the same thing.
B
B is the answer.
C
f(0)=4 not 2 C is incorrect. C is not the answer
D
Same problem as C
PLZ DO ASAP NEED LIKE NOW HELP ME PLZ
What is the equation of this graphed line? y = mx + b m is the slope b is the y intercept (where does the line cross the y - ordered pair) x and y can be a point on the line m = y2 - y1/x2 - x1 A graph with a line running through coordinates (-4, -6) and coordinates (2, 6) Enter your answer in slope-intercept form in the box.
Answer:
y = 2x+2
Step-by-step explanation:
When we have 2 points, we can find the slope from
m = (y2-y1)/(x2-x1)
= (6--6)/(2--4)
= (6+6)/(2+4)
= 12/6
= 2
The slope is 2
We can use the point slope form of the equation for a line
y-y1 = m(x-x1)
y-6 = 2(x-2)
We need to get this in slope intercept form
Distribute the 2
y-6 = 2x-4
Add 6 to each side
y-6+6 = 2x-4+6
y = 2x+2
Answer:
y = 2x + 2
Step-by-step explanation:
the equation of a line in slope-intercept form is
y = mx + b ( m is the slope and b the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 4, - 6) and (x₂, y₂ ) = (2, 6)
m = [tex]\frac{6+6}{2+4}[/tex] = [tex]\frac{12}{6}[/tex] = 2, hence
y = 2x + b is the partial equation
to find b substitute either of the 2 points into the partial equation
using (2, 6), then
6 = 4 + b ⇒ b = 6 - 4 = 2
y = 2x + 2 ← equation in slope-intercept form
graph the equation y=2x-3 using slope and y-intercept
Answer: The slope of the graph is 2x. In other words, rise over run: move up 2 and move to the right 1 because it is 2 over 1. The y-intercept is -3, which means you move down 3 on the y-axis.
If triangle XYZ’s points are X (-2, 1), Y (-4,-3), and Z (0,-2) what are the new coordinates of X’, Y’, and Z’ if the triangle is transformed using the rule (x - 1, y + 3) to form triangle X’Y’Z’.
Answer:
The coordinates of image are X'(-3,4), Y'(-5,0) and Z'(-1,1).
Step-by-step explanation:
The vertices of triangle XYZ are X(-2,1), Y(-4,-3) and Z(0,-2).
It is given that the triangle translated by rule
[tex](x,y)\rightarrow (x-1,y+3)[/tex]
The coordinates of image of XYZ are
[tex]X(-2,1)\rightarrow X'(-2-1,1+3)[/tex]
[tex]X(-2,1)\rightarrow X'(-3,4)[/tex]
[tex]Y(-4,-3)\rightarrow Y'(-4-1,-3+3)[/tex]
[tex]Y(-4,-3)\rightarrow Y'(-5,0)[/tex]
[tex]Z(0,-2)\rightarrow Z'(0-1,-2+3)[/tex]
[tex]Z(0,-2)\rightarrow Z'(-1,1)[/tex]
Therefore coordinates of image are X'(-3,4), Y'(-5,0) and Z'(-1,1).
van someone please help me with this i dont need an explaination i just need a. b. c. or d. please and thank you
Answer:
option C
[tex]f(x)=-\sqrt{x+3}+8[/tex]
Step-by-step explanation:
we have
[tex]f(x)=-2\sqrt{x-3}+8[/tex]
using a graphing tool
see the attached figure N[tex]1[/tex]
The range is the interval--------> (-∞,8]
[tex]y\leq 8[/tex]
case A) [tex]f(x)=\sqrt{x-3}-8[/tex]
using a graphing tool
The range is the interval--------> [-8,∞)
[tex]y\geq -8[/tex]
case B) [tex]f(x)=\sqrt{x-3}+8[/tex]
using a graphing tool
The range is the interval--------> [8,∞)
[tex]y\geq 8[/tex]
case C) [tex]f(x)=-\sqrt{x+3}+8[/tex]
using a graphing tool
The range is the interval--------> (-∞,8]
[tex]y\leq 8[/tex]
case D) [tex]f(x)=-\sqrt{x-3}-8[/tex]
using a graphing tool
The range is the interval--------> (-∞,-8]
[tex]y\leq -8[/tex]
9x-6a=-7,find x when a =-7
Answer:
Step-by-step explanation:
Plug in -7 for the variable a.
9x - 6(-7) = -7
Follow PEMDAS. Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x.
Multiply -6 with -7
9x - 6(-7) = -7
9x + 42 = -7
Isolate the variable x. Subtract 42 from both sides
9x + 42 (-42) = -7 (-42)
9x = -49
Divide 9 from both sides
(9x)/9 = (-49)/9
x = (-49)/9
x = ~5.44 (rounded)
~
HELP QUICK IM GIVING 21 POINTS AND A BRAINLIEST AWARD
Peter had a 12:00 noon appointment that was 60 miles from his home. He drove from his home at an average rate of 40 miles per hour and arrived 15 mins late. At what time did Peter leave home
Answer:
10:45
Step-by-step explanation:
v...speed = 40 mph
s...distance = 60
t...time
if he was 15 min late he arrived at 12:15
v=s/t => t=s/v
t = 60/40 = 1.5 h = 1h and 30 min
if he arrived at 12:15 and he was driving for an hour and a half just substract
12:15 - 1:30 = 11:15 - 0:30 = 10:45
he left at 10 45
Write Y=3x^2+6x+8 In Vertex form
5x + 3 < 3(x+2 need help
Answer:
x < [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
distribute the parenthesis on the right side
5x + 3 < 3x + 6 ( subtract 3x from both sides )
2x + 3 < 6 ( subtract 3 from both sides )
2x < 3 ( divide both sides by 2 )
x < [tex]\frac{3}{2}[/tex]
Answer:
x < [tex]\frac{3}{2} \\[/tex]
What ordered pair doesn't belong in the solution set of y>2x+1? (1,4), (1,6), (3,8), (2,5)?
Put the coordinates of the points to the inequality and check.
y > 2x + 1
for (1, 4):
4 > 2(1) + 1
4 > 2 + 1
4 > 3 CORRECT
for (1, 6):
6 > 2(1) + 1
6 > 2 + 1
6 > 3 CORRECT
for (3, 8):
8 > 2(3) + 1
8 > 6 + 1
8 > 7 CORRECT
for (2, 5):
5 > 2(2) + 1
5 > 4 + 1
5 > 5 FALSE
Answer: (2, 5).7y+44=12y+11, I need help!
Answer:
y = 33/5 or 6.6
Step-by-step explanation:
7y + 44 = 12y + 11
-11 -11
7y + 33 = 12y
-7y -7y
33 = 5y
Divide both sides by 5
= 33/5 or 6.6
Answer:
[tex]y=6\frac{3}{5}[/tex]
Step-by-step explanation:
We are given the following equation for which we have to solve for y:
[tex]7y+44=12y+11[/tex]
So first of all, we will rearrange the terms by putting the like terms together (variables on one side of the equation and constants on the other side) to get:
[tex]12y-7y=44-11[/tex]
Then solving for y:
[tex]5y=33\\\\y=\frac{33}{5}[/tex]
Therefore, the value of y is equal to [tex]y=6\frac{3}{5}[/tex] (rewriting y in a mixed fraction form).
Rafael's art class is 6 hours long. How long is his class in minutes?
Answer:
360 Minutes Long
Step-by-step explanation:
There are 60 minutes in an hour. Multiply 60*6, and you get 360 minutes.
Answer:
The art class would be 360 mins long.
Step-by-step explanation:
Is my answer correct
Answer:
yes
Step-by-step explanation:
the box would typically be closer to the left than in the middle
Answer:
Yes you are correct because the box plot's data is skewed left
Step-by-step explanation:
Your welcome and don't forget to say Thanks
Line AB passes through points A(–6, 6) and B(12, 3). If the equation of the line is written in slope-intercept form, y = mx + b, then m = –1/6.
and b = ?
Put the value of slope to the equation of the function:
[tex]y=-\dfrac{1}{6}x+b[/tex]
Put the coordinates of the point B(12, 3) to the equation:
[tex]3=-\dfrac{1}{6}(12)+b[/tex]
[tex]3=-2+b[/tex] add 2 to both sides
[tex]5=b[/tex]
Answer: b = 5Answer:
The value of b is 5.
Step-by-step explanation:
Consider the provided information.
It is given that the slope intercept form is, y = mx + b
Where m is the slope and b is the y intercept.
Also, it is given that the slope of the line is -1/6.
Line AB passes through points A(–6, 6) and B(12, 3).
That means Point A and B must satisfy the equation of line.
Substitute [tex]m=\frac{-1}{6}, x=-6\ \text{and}\ y = 6[/tex] in slope intercept form:
[tex]6=\frac{-1}{6}\times(-6)+b[/tex]
[tex]6=1+b[/tex]
[tex]5=b[/tex]
Thus, the value of b is 5.
In which number is the value of the 7 ten times the value of the 7 in the number 1,273
Answer:
Your answer would require a 7 in the hundreds place
Step-by-step explanation:
1,273
The 1 is in the thousands place. 1 * 1000
The 2 is in the hundreds place. 2 * 100
The 7 in in the tens place. 7 * 10
The 3 is in the ones place. 1 * 1
To get from 10 to 100, we would multiply by 10, so to get from the tens place to the hundreds place is 10 times greater.
Your answer would require a 7 in the hundreds place
In the number system, each place to the left is ten times the place to its right. Therefore, for the value of the 7 to be ten times greater than the 7 in 1,273, it must be in the tens place, such as in numbers like 702, 770, or 170.
Explanation:The value of a digit in a number depends on its place or position. In the number system, each place is ten times the place to its right. Therefore, in the number 1,273, the value of the 7 is simply 7 (because it's in the units place). However, for the 7 in the new number to be ten times greater than the 7 in 1,273, it must be in tens place. Therefore, the new number could be 7x10 = 70 (with the 7 in the tens place). So, any number with 70 in the tens place (like 702, 770, or 170) has a 7 that's ten times the 7 in 1,273.
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2 Emma buys 33 yards of blue fabric and some yellow fabric at a store. She buys a total of 53 yards of fabric. The equation 1 2 5333can be used to represent this situation, where y is the number of yards of yellow fabric she buys. How much yellow fabric does she buy?
Step-by-step explanation:
your answer is 99
Kameko bought a home in Homewood, Illinois, for $230,000. He put down 20% and obtained a mortgage for 25 years at 8%. What's the total interest cost of the loan?
Final answer:
The total interest cost of the loan is $28,999.
Explanation:
To find the total interest cost of the loan, we need to calculate the amount of interest paid over the 25-year period. First, we need to find the amount of the mortgage by subtracting the down payment from the purchase price. 20% of $230,000 is $46,000, so the mortgage is $230,000 - $46,000 = $184,000.
To calculate the interest cost, we can use the formula: Interest Cost = Total Repayment - Principal Amount.
Principal Amount = Mortgage Amount = $184,000.
Number of Payments = Number of years x Number of payments per year = 25 x 12 = 300.
Monthly Interest Rate = Annual Interest Rate / Number of payments per year = 8% / 12 = 0.00667.
Total Repayment = Monthly Payment x Number of Payments = [(Monthly Interest Rate x Principal Amount) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments)) ] x Number of Payments = [(0.00667 x $184,000) / (1 - (1 + 0.00667)^(-300))] x 300 = $526.67 x 300 = $157,001.
Interest Cost = Total Repayment - Principal Amount = $157,001 - $184,000 = $28,999.
Find all the whole values of a for which the solution of the equation ax = 6 is a whole number.
Answer:
[tex]a=1,\ 2,\ 3,\ 6.[/tex]
Step-by-step explanation:
A whole number is any number of a set [tex]\{0,\ 1,\ 2,\ 3,...\}[/tex]
The equation [tex]ax=6[/tex] has a solution [tex]x=\dfrac{6}{a},\ a\neq 0.[/tex]
If [tex]a=1,[/tex] then [tex]x=\dfrac{6}{1}=6[/tex] is a whole number.
If [tex]a=2,[/tex] then [tex]x=\dfrac{6}{2}=3[/tex] is a whole number.
If [tex]a=3,[/tex] then [tex]x=\dfrac{6}{3}=2[/tex] is a whole number.
If [tex]a=6,[/tex] then [tex]x=\dfrac{6}{6}=1[/tex] is a whole number.
For all other values of [tex]a[/tex] equation [tex]ax=6[/tex] will have solution that is not a whole number.
Twice the sum of a number and eleven is twenty-two less than three times the number. Find the number.