∠DFG and ∠JKL are complementary angles
Measure of each angle
[tex]m<DFG=48\\m<JKL= 42[/tex]
Given :
∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5,
and m∠JKL = x − 1
When two angles are complementary then the sum of angles is 90 degrees
∠DFG and ∠JKL are complementary angles.
So, [tex]m<DFG+m<JKL =90[/tex]
Now replace the expressions and solve for x
[tex]x+5+x-1=90\\2x+4=90\\2x=90-4\\2x=86\\x=43[/tex]
Now replace x with 43 and find out each angle
[tex]m<DFG= x+5\\m<DFG= 43+5=48\\\\m<DFG=48\\m<JKL=x-1=43-1=42[/tex]
[tex]m<DFG=48\\m<JKL= 42[/tex]
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graph of the quadratic function f(x)=‒(x+4)(x‒6) is shown on the coordinate grid below.
Which statement is not true?
A.
The maximum of this function occurs when y=25.
B.
The function increases in the interval 1 to 6.
C.
The has a zero at (‒4,0).
D.
The function positive in the interval ‒4 to 6.
Answer:
Option B is not true.
Step-by-step explanation:
The quadratic function is f(x) = -(x + 4)(x - 6)
Now we check each option given
Option A.
It is clear from the graph function is maximum at y = 25.
TRUE.
Option B.
Function increases in the interval 1 to 6.
Let's check this at x = 2 and x = 3
f(2) = -(2 + 4)(2 - 6)
= -(6)(-4)
= 24
f(3) = -(3 + 4)(3 - 6)
= - (7)(-3)
= 21
So we find this function is decreasing in this interval.
So the given option is FALSE.
Option C.
The function has a zero at (-4, 0)
f(-4) = -(-4 + 4)(-4 + 6) = 0
So the function has a zero at (-4, 0).
Option is True.
Option D.
The function is positive in the interval -4 to 6
f(x) = -(x + 4)(x - 6)
f(-3) = -(-3 + 4)(-3 - 6)
= -(1)(-9)
= 9
f(0) = -(0 + 4)( 0 - 6)
= 24
Therefore, this function is positive in this interval so the option is TRUE.
Option B is not true.
An 8 foot length of 4 inch wide crown molding costs $16. How much will it cost to buy 40 feet of crown molding?
If a refrigerator is a heat pump that follows the first law of thermodynamics, how much heat was removed from food inside of the refrigerator if it released 492J of energy to the room? Joules
What is the slope of the line passing through the points (−1, 7) and (4, −1)?
2nd picture is the choices I have.
mr chu is slicing 4 cantaloupes for his class . There are 24 students in the class. If he cuts the cantal to make an equal portion for each student how much of a whole cantal will each student get
What are the coordinates of the point?
A:(4, −2)
B:(2, 4)
C:(−4, −2)
D:(−2, 4)
A coordinate grid with a dot placed in the second quadrant. The dot is to the left of positive 4 on the y axis and above negative 2 on the x axis
During a 4-month-long drought, the water level in a lake changed by
−3 1/2 feet. The water level changed at the same rate each month.
What is amount the water level changed in 1 month?
Answer:
-7/8
Step-by-step explanation:
i did the 3.15 Unit Test
A container holds 6 gallon of juice how many in pints
3/4 x 3 2/3 in simplest form
Use the diagram to find the value of x?
147 32 33 150
calculate the length of the hypotenuse
hypotenuse =sqrt( a^ + b^
10^2 = 100
14^2 = 196
196+100 = 296
sqrt(296) = 17.20
Answer is D. 17.20
A 180 day $3 million negotiable cd has a 4.25% annual rate quote. if you buy the cd, how much will you collect in 180 days?
At the beginning of a bake sale mary set aside 4 pies for herself karen bought half of the remaining pies for her birthday party and 5 more pies were sold during the sale. When the sale was over there were 19 pies remaining. How msny pies were there before the bake sale started
There were 52 pies before the bake sale started as per the provided condition.
Let's break down the information given step by step:
At the beginning of the bake sale, Mary set aside 4 pies for herself. So, the number of remaining pies is the total number of pies minus 4.
Karen then bought half of the remaining pies for her birthday party. This means the number of remaining pies is now half of the previous remaining pies.
Next, 5 more pies were sold during the sale. Therefore, the number of remaining pies is further reduced by 5.
Finally, when the sale was over, there were 19 pies remaining.
Let's use variables to solve the problem. Let's say the initial number of pies before the sale started is "x."
After Mary set aside 4 pies, the number of remaining pies is (x - 4).
Karen bought half of the remaining pies, so the number of remaining pies becomes (x - 4)/2.
5 more pies were sold, reducing the number of remaining pies to (x - 4)/2 - 5.
According to the given information, (x - 4)/2 - 5 equals 19.
Now, we can solve the equation to find the value of x:
(x - 4)/2 - 5 = 19
Simplifying the equation, we have:
(x - 4)/2 = 24
(x - 4) = 48
x = 52
Therefore, there were 52 pies before the bake sale started.
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The volume of a rectangular box can be found using the formula lwh where l represents the length, w represents the width, and h represents the height of the box. What is the volume of a box with the following dimensions?
l = 4 centimeters
w = 5 centimeters
h = 6 centimeters
120 cm 3
456 cm 3
15 cm 3
34 cm 3
multiply the 3 dimensions together
4*5 = 20 *6 = 120 cm^3
9+(6-6)x4-(-7-(-2)) solved in order of operations
The solution of the given expression will be 14.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Given expression as; 9+(6-6)x4-(-7-(-2))
We have to solved in order of operations
1. (6-6)=0
2. (-7+2)=-5
3. Now, substitute the values in the expression;
9 + 0×4 + 5 = 14
Therefore, the solution of the given expression will be 14.
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If 1/3 of a sum of money is $21, what is the sum of money?
I have a rug has a length that is 2 times the width the area of the rug is 8 square feet What is the length and width of the rug
Why i hundred 4 tens and 14 tens name the same number
A television game has 6 shows doors, of which the contests must pick 2. behind two of the doors are expensive cars, and behind the other 4 doors are consolation prizes. Find the probability that the contestant wins exactly 1 car? no car? or atleast one car?
Answer:
In this question, there are 4 consolation door and 2 car doors of total 6 doors. That means for the first door the chance to get consolation is 4/6 and car is 2/6. In second door, only 5 remains so the chance to get consolation is either 4/5 (if 1st door car) or 3/5(if 1st door consolation)
Win 1 car condition:
1. 1st door car, 2nd door consolation = 2/6 * 4/5 =8/30
2. 1st door consolation, 2nd door car= 4/6 * 2/5 = 8/30
8/30+8/30= 16/30
No car condition
1. 1st door consolation, 2nd door consolation= 4/6 * 3/5= 12/30
At least one car condition
1. 1st door car, 2nd door car = 2/6 * 1/5 =2/30
2. 1st door car, 2nd door consolation = 2/6 * 4/5 =8/30
3. 1st door consolation, 2nd door car= 4/6 * 2/5 = 8/30
2/30 + 8/30 + 8/30= 18/30
Find the vertices and foci of the hyperbola with equation (x+1)^2/16-(y+5)^2/9=1
Answer:
B on edge
Step-by-step explanation:
On the pic explanation is right on.
In triangle FGH, GJ is an angle bisector of ∠G and perpendicular to FH.
What is the length of FH?
___ units
we know that
in the right triangle FGJ
[tex]cos(FGJ)=\frac{GJ}{FG}= \frac{GJ}{3x-8}[/tex] ----> equation A
in the right triangle GJH
[tex]cos(JGH)=\frac{GJ}{GH}= \frac{GJ}{16}[/tex] ----> equation B
m∠(FGJ)=m∠(JGH) ------> because GJ is an angle bisector of ∠G
so
equate equation A and equation B
[tex]\frac{GJ}{3x-8}=\frac{GJ}{16}\\ 3x-8=16\\3x=24 \\x=8\ units[/tex]
that means
[tex]FG=3*8-8=16\ units[/tex]
[tex]FG=GH[/tex]-------> the triangle FGH is an isosceles triangle
hence
[tex]FJ=JH\\FJ=8\ units[/tex]
[tex]JH=8\ units[/tex]
[tex]FH=FJ+JH=8+8=16\ units[/tex]
therefore
the answer is
[tex]FH=16\ units[/tex]
how many times that a one-to-one function crosses the horizontal line?
We want to see how many times a one-to-one function crosses the x-axis (this is equivalent to see how many values of x are mapped into y = 0).
We will see that it crosses the x-axis only one time.
A function is a relation that maps elements from one set, the domain, into elements from another set, the range. Such that each element in the domain can be mapped into only one element in the range.
Now we add the restriction that the function is one-to-one, this means that no two elements from the domain can be mapped into the same element from the range.
With this is easy to see that the one-to-one function crosses the horizontal line only once, as the value y = 0 can be assigned to only one value in the domain.
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Solve the equation.
3(k−6) = 15
k = ____?
In calculating the monthly payment for a five-year loan, what value should be used for n, the number of periods over which the loan is repaid, as it appears in the following formula? 2007-10-03-00-00_files/i0060000.jpg a. 5 b. 12 c. 60 d. 120
Answer:
The answer is: c. 60.
Step-by-step explanation:
To calculate the monthly payment for 5 years, the 12 months of 1 year should be multiplied by the 5 years of the duration, which is equal to 60 = 5 x 12.
The answer is: c. 60.
what is the solution?
sally has scores of 88, 92, 80, and 96. find the score she must make on the next exam to have an average of 90
△RST is mapped to △R′S′T′ using the rule (x, y)→(x, −y) followed by (x, y)→(3x, 3y) .
Which statement correctly describes the relationship between △RST and △R′S′T′ ?
△RST is congruent to △R′S′T′ because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.
△RST is congruent to △R′S′T′ because the rules represent a reflection followed by a translation, which is a sequence of rigid motions.
△RST is congruent to △R′S′T′ because the rules represent a rotation followed by a translation, which is a sequence of rigid motions.
△RST is not congruent to △R′S′T′ because the rules do not represent a sequence of rigid motions.
By the way, this question DOES NOT include a picture, so don't ask please.
Answer:
△RST is not congruent to △R′S′T′ because the rules do not represent a sequence of rigid motions.
Step-by-step explanation:
Redo of telephone math ..
On average, a sample of n = 16 scores from a population with s = 10 will provide a better estimate of the population mean than you would get with a sample of n = 16 scores from a population with s = 5.
a. True
b. False
-4x<-12 choose the correct soultion
-4x < -12
divide both sides by -4
x > -12/-4
x > 3
note: when multiplying or dividing a negative inequality you flip the direction of it