Answer:
Part 1) The length of DC is [tex]13\ units[/tex]
Part 2) The measures of the angles in the isosceles triangle are
The base angles are 67.4° and the vertex angle is 45.2°
Step-by-step explanation:
step 1
In the right triangle BDC Find the length of DC
Applying the Pythagoras Theorem
[tex]DC^{2}=BC^{2} +BD^{2}[/tex]
we have
[tex]BC=AB=10/2=5\ units[/tex]
[tex]BD=12\ units[/tex]
substitute
[tex]DC^{2}=5^{2} +12^{2}[/tex]
[tex]DC^{2}=169[/tex]
[tex]DC=13\ units[/tex]
step 2
Find the measures of internal angles in the isosceles triangle ABC
we know that
∠DAC=∠DCA ------> base angles
∠ADC ------> vertex angle
Find the measure of angle DCA
In the right triangle BDC
sin(∠DCA)=BD/DC
substitute the values
sin(∠DCA)=12/13
∠DCA=arcsin(12/13)=67.4°
so
∠DAC=∠DCA=67.4°
Find the measure of angle ∠ADC
Remember that the sum of the internal angles of a triangle must be equal to 180 degrees
so
∠DAC+∠DCA+∠ADC=180°
substitute
67.4°+67.4°+∠ADC=180°
∠ADC=180°-134.8°=45.2°
Plz help me with this
Answer options: No or yes
No and the graph has a greater minimum.
Answer: YES, Graph
Step-by-step explanation:
Graph: minima (lowest point) is (4, -4)
Equation f(x) = x² - 8x + 7
[tex]x=\dfrac{-b}{2a}=\dfrac{-(-8)}{2(1)}=\dfrac{8}{2}=4\\\\y=(4)^2-8(4)+7\\.\ =16-32+7\\.\ =-9\\[/tex]
minimima is (4, -9)
The x-values are the same
The y-value of the Graph is greater (higher)
(5,6), (9,1) slope intercept form
Answer:
y = (-5/4)x + 12.25
Step-by-step explanation:
Slope intercept form:
y = mx + b
Slope form:
m = (y₂ - y₁)/(x₂ - x₁)
Let:
(x₁ , y₁) = (9 , 1)
(x₂ , y₂) = (5 , 6)
Plug in the corresponding numbers to the corresponding variables.
m = (6 - 1)/(5 - 9)
Simplify.
m = (5)/(-4)
Your slope is -5/4
Plug in -5/4 for m in the slope-intercept form equation, and use a point to solve for b. For example, we will use (9, 1):
y = mx + b
y = (-5/4)x + b
(1) = (-5/4)(9) + b
Simplify.
1 = (-11.25) + b
Isolate the variable, b. Note the equal sign, what you do to one side, you do to the other. Add 11.25 to both sides.
1 + (11.25) = -11.25 (+11.25) + b
1 + 11.25 = b
b = 12.25
your y-intercept is 12.25
Plug in the corresponding numbers to the corresponding variables.
y = mx + b
m = -5/4
b = 12.25
y = (-5/4)x + 12.25 is your answer.
~
Divide 15x15 by 3x3.
Answer:
25
Step-by-step explanation:
15 * 15 = 225
3 * 3 = 9
225 / 9 = 25
Answer:
the answer is 25
Step-by-step explanation:
So you multiple 15x15 which equals 225 then you multiply 3x3 which is 9
the you take 225 and divide it by 9 wich would then be 25................hope i helped
Which logarithmic graph can be used approximate the value of Y in the equation 2^y=5
Absolutely down graph is true!!
because, certainly 2<y<3
and we know 2^y=5 ==> log5 with base 2 =y
so it concludes we must have a node between 2<y<3 in x=5
25 Points Attachment Below Thanks
Area of a circle = PI x r^2
r is 1/2 the diameter = 0.5 inches
Area = 3.14 x 0.5^2
Area = 0.79 in^2
It looks like it’s missing something...is it a part A ?
The slope of the line passing through the points (-2, 6) and (4, 6) is
A) 0
B) no slope
C) 2
Your answer ish c. 2
A slope is also known as the gradient of a line. The correct option is B.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the line that is passing through (-2, 6) and (4, 6) can be calculated as,
Slope = (6-6)/(-2-4) = 0/(-6)
Hence, there exists no slope between the two of the given points.
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3w - 4z = 8 what is w
Final answer:
To find w from the equation 3w - 4z = 8, add 4z to both sides, and then divide by 3 to isolate w, giving w = (4z + 8) / 3.
Explanation:
The equation 3w - 4z = 8 is a linear equation in two variables (w and z). To find w in terms of z, you need to isolate w on one side of the equation. Here is the process step by step:
Add 4z to both sides of the equation: 3w - 4z + 4z = 8 + 4z.
Simplify the equation: 3w = 4z + 8.
Divide every term by 3 to solve for w: w = (4z + 8) / 3.
So, w is equal to (4z + 8) / 3 when isolated from the given equation.
What is the cos of 2
Answer:
-0.41614683654
Step-by-step explanation:
Answer: The answer is -0.41614683654. hope I helped. :)
The sum of two numbers is 12. The first number,X, is twice the second number,y, which system of equations could be used to find the two numbers ?
To solve the problem, set up two equations: X + Y = 12 and X = 2Y. Using the substitution method, replace X with 2Y in the first equation to find Y = 4, and subsequently find X = 8.
The problem given to us involves finding two numbers, X and Y, given that the sum of these two numbers is 12 and the first number, X, is twice the second number, Y. To solve for X and Y, we can set up a system of two linear equations.
The first equation comes from the sum of the two numbers:
X + Y = 12
The second equation comes from the statement that X is twice Y:
X = 2Y
Now we have a system of equations:
X + Y = 12X = 2YOne method to find solutions for X and Y is by substitution. We can substitute 2Y in place of X in the first equation:
(2Y) + Y = 123Y = 12Y = 4Now that we know Y is 4, we can find X using the second equation:
X = 2YX = 2(4)X = 8The two numbers are X = 8 and Y = 4.
What is the area of this tile?
12 in. ²
a = bh
a = 2 x 6
a = 12 in. ²
Answer:
12 in. ^2
Step-by-step explanation:
The area of a rectangle can be found by using the formula legnth x width.
Here the legnth is 2 in. and the width is 6 in.
6 x 2 = 12
Whenever you find the area, unit of measurement is ^2, thus resulting in the answer 12 in. ^2
I hope this helps!
Shelby’s recipe says to add 3/4 cup of brown sugar and 1/8 cup of white sugar how much sugar recipe call for altogether
Answer:you need common denominatord 4*2=8 3*2=6 6/8+1/8=7/8 of sugar
Step-by-step explanation:
Tina is attempting to factor the expression 10x^2-13-3. In her first step, she rewrites the expression as 10x^2-10x-3x-3. Which of the following statements in true about Tina's work?
ANSWER
B. The two middle coefficients add to the correct number but do not multiply to the correct number.
EXPLANATION
The given quadratic trinomial that Tina tries to factor is
[tex]10 {x}^{2} - 13x - 3[/tex]
Comparing to
[tex]a{x}^{2} + bx + c[/tex]
we have a=10, b=-13 and c=-3
ac=-3×10=-30
We split the middle term so that their sum is -13.
Tina use
-10,-3
to get
-10x-3x
The sum is -13x alright but the product is not -30.
B is correct.
The equation X squared plus Y squared minus 2X plus 7Y +1 equals zero can be written as which of the following equations
For this case we must write in algebraic symbology the expression described above:
We have an equation, then:
x squared plus y squared: [tex]x ^ 2 + y ^ 2[/tex]minus 2x plus 7y plus 1: [tex]-2x + 7y + 1[/tex]equals zero: [tex]= 0[/tex]We construct the equation:
[tex]x ^ 2 + y ^ 2-2x + 7y + 1 = 0[/tex]
Answer:
[tex]x ^ 2 + y ^ 2-2x + 7y + 1 = 0[/tex]
What is the first step when solving present or loan amortizations using a formula?
Answer:
determine the periods in the problem, which is the number of periods per year
Step-by-step explanation:
Answer:
determine the periods, which is the number of periods per year
Step-by-step explanation:
n/a
Jerry drove 10 miles in half the time it took Marcy to drive 10 miles. If jerry average speed was r miles per hour what was Marcy average speed in miles per hour
Answer:
0.5r
Step-by-step explanation:
If Jerry took half the time Macy did then that means Macy took twice as long as Jerry. If Jerry’s speed was r then Macy’s speed is 0.5r or half the speed of Jerry. This will mean Macy goes half as slow and takes twice as long to get there.
The average speed of Marcy in miles per hour is 0.5r.
If Jerry took half the time Marcy did then that means Marcy took twice as long as Jerry. If Jerry’s speed was r then Macy’s speed is 0.5r or half the speed of Jerry. This will mean Marcy goes half as slow and takes twice as long to get there.
Hence, The average speed of Marcy in miles per hour is 0.5r.
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On a 120:1 scale model floor plan, the kitchen has a length of 3.5 cm and a width of 2.5 cm. What is the area of the actual kitchen in square meters?
Answer: The answer is 12.6 Meters Squared
You get that from multiplying 120 to 3.5 and 2.5 . After doing that you will get 420 cm and 300 cm. Knowing that a meter is 100 cm you will get 4.2 meters and 3 meters. To find the area of the kitchen space you will multiple 4.2 and 3 meters together and get 12.6 Meters, therefore 12.6 meters squared is the area of the kitchen floor.
Using elimination, find the ordered pair.
6x + 15y = 15
-6x +7y = -37
Answer:
x = -1 and y = 7/5Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}6x+15y=15\\-6x+7y=-37\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad22x=-22\qquad\text{divide both sides by 22}\\.\qquad\qquad x=-1\\\\\text{Put the value of x to the first equation:}\\6(-1)+15y=15\\-6+15y=15\qquad\text{add 6 to both sides}\\15y=21\qquad\text{divide both sides by 15}\\y=\dfrac{21}{15}\to y=\dfrac{7}{5}[/tex]
HELP PLEASE HELP IF YOU CAN :)
Answer:
A
Step-by-step explanation:
If you plug them in you get 2≥-1
A rectangular prism with a volume of 2 cubic units is filled with cubes with side lengths of 1/4 unit. How many 1/4 unit cubes does it take to fill the prism?
Answer:
128
Step-by-step explanation:
Method A.
The volume of the prism is 2 cubic units.
Each cube has side length of 1/4 unit.
The volume of each cube is (1/4)^3 cubic unit.
The volume of each cube is 1/64 cubic unit.
To find the number of cubes that fit in the prism, we divide the volume of the prism by the volume of one cube.
(2 cubic units)/(1/64 cubic units) =
= 2/(1/64)
= 2 * 64
= 128
Method B.
Imagine that the prism has side lengths 1 unit, 1 unit, and 2 units (which does result in a 2 cubic unit volume.) Since each cube has side length 1/4 unit, then you can fit 4 cubes by 4 cubes by 8 cubes in the prism. Then the number of cubes is: 4 * 4 * 8 = 128
He right answer is 128
Which category do both shapes belong to?
A.square
B.parallelogram
C.rectangle
D.rhombus
B. Parallelogram
Explanation: both have parallel sides
The two of the given figures are parallelogram. The correct option is B.
What is parallelogram?In parallelogram the opposite sides are equals and it is not formed 90 degree angle between two sides.
In the two of the given figures, it can be observed that the two figures have opposite sides parallel and equal. Therefore, the two of the given figures are a parallelogram.
Hence, the two of the given figures are parallelogram.
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31)
Note: Figure not drawn to scale.
The circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters, what is the measure of x?
A) 40°
B) 60°
C) 70°
D) 80°
If circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters then measure of x is 60°
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given,
Circle with centre O,
Radius of circle=18 centimeters
length of arc AB = 6π centimeters
We need to find the measure θ of x
We have a formula to find the length of arc.
Length of an Arc = θ × (π/180) × r
Apply the given values in formula
6π=θ × (π/180) × 18
π gets cancelled on both the sides
6=θ/10
θ=60°
Hence if circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters then measure of x is 60°
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An Isosceles triangle has single measures 55,55,and 70. The side across from the 70 angle is 10 inches long. How long are the other sides?
Answer:
8.717 both the sides
Step-by-step explanation:
Given:
Let ABC be the given triangle with
angle A= 55
angle B=55
angle C= 70
side across angle C, c= 10 inches
side across angle B, b =?
aide across angle A,a=?
Now using the law of sin to find a and b:
a/sinA=c/sinC
a= (c/sinC)(sinA)
Putting the values:
a= (10/sin70)(sin55)
a= 8.717
As the given triangle is isosceles so side a=b
hence a=b= 8.717 inches !
Find the point, M, that divides segment AB into a ratio of 2:3 if A is at (0, 15) and B is at (20, 0).
What is segment ab? is there a picture that is supposed to go with it?
Answer: The required co-ordinates of point M are (8, 9).
Step-by-step explanation: Given that the point M divides segment AB into a ratio of 2 : 3, where A is at (0, 15) and B is at (20, 0).
We are to find the co-ordinates of point M.
We know that
the co-ordinates of a point that divides the line segment joining the points (a, b) and (c, d) are given by
[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).[/tex]
For the given division, (a, b) = (0, 15), (c, d) = (20, 0) and m : n = 2 : 3.
Therefore, the co-ordinates of point M are given by
[tex]\left(\dfrac{2\times20+3\times0}{2+3},\dfrac{2\times0+3\times15}{2+3}\right)\\\\\\=\left(\dfrac{40}{5},\dfrac{45}{5}\right)\\\\\\=\left(8,9).[/tex]
Thus, the required co-ordinates of point M are (8, 9).
3x^2-12x+8 in vertex form
Take out the 3 , to make the vertex form easier;)
Carlos found that the length of the diagonal of his laptop monitor is squared root of 290. If the manufacturer rounds to the nearest whole inch, what size is the monitor as measured by the diagonal? 12 17 97 245
Answer:
[tex]17\ in[/tex]
Step-by-step explanation:
Let
D -----> the diagonal of the laptop monitor
we have
[tex]D=\sqrt{290}\ in[/tex]
Using a calculator
[tex]D=\sqrt{290}=17.03\ in[/tex]
Round to the nearest whole number
[tex]17.03\ in=17\ in[/tex]
Answer:
17
Step-by-step explanation:
i jus did this on edg
which is not a proportion???
The answer is C. C is not a proportion.
Hope this helps!
Answer:
C
Step-by-step explanation:
By definition a proportion should be equal to each other and can be multiplied by the same number on the numerator and the denominator to make the second fraction.
[tex]\frac{x_1}{y_1}=\frac{x_2}{y_2}[/tex]
[tex]\frac{x_1}{y_1}*\frac{z}{z}=\frac{x_2}{y_2}[/tex]
A
[tex]\frac{3}{7}*\frac{3}{3}=\frac{9}{21}[/tex]
So it is a proportion.
B
[tex]\frac{24}{56}/\frac{8}{8}=\frac{3}{7}[/tex]
So it is a proportion.
C
[tex]\frac{3}{7}*\frac{3}{4}=\frac{9}{28}[/tex]
So it is not a proportion.
D
[tex]\frac{3}{7}*\frac{4}{4}=\frac{12}{28}[/tex]
equation that represents each mixed number as a sum of a whole numbers and unit fractions 3 and 1/4 5 and 1/2 to 1 2/3 and 4 3/8 solve
Answer:
1) [tex]\frac{13}{4}[/tex]
2) [tex]\frac{11}{2}[/tex]
3) [tex]\frac{5}{3}[/tex]
4) [tex]\frac{35}{8}[/tex]
Step-by-step explanation:
we know that
A mixed number is the sum of a whole number and a fraction number
case 1) we have
[tex]3\frac{1}{4}[/tex]
so
[tex]3\frac{1}{4}=3+\frac{1}{4}=\frac{3*4+1}{4}=\frac{13}{4}[/tex]
case 2) we have
[tex]5\frac{1}{2}[/tex]
so
[tex]5\frac{1}{2}=5+\frac{1}{2}=\frac{5*2+1}{2}=\frac{11}{2}[/tex]
case 3) we have
[tex]1\frac{2}{3}[/tex]
so
[tex]1\frac{2}{3}=1+\frac{2}{3}=\frac{1*3+2}{3}=\frac{5}{3}[/tex]
case 4) we have
[tex]4\frac{3}{8}[/tex]
so
[tex]4\frac{3}{8}=4+\frac{3}{8}=\frac{4*8+3}{8}=\frac{35}{8}[/tex]
What values of b satisfy 3(2b + 3)^2 = 36?
Answer:
3(2b+3)^2=36
(2b+3)^2=12
2b+3=+2 radical3
2b+3= 2 radical 3
b=- radical 3 -3 over 2
b= radical 3- 3 over 2
b=- radical 3 - 3 over 2
Answer:
The answer is A
Step-by-step explanation:
can someone please help me with this!!! pleasee
Answer:
[tex]\large\boxed{Q6.\ \sin X\approx0.778}\\\boxed{Q7.\ x\approx5.9}[/tex]
Step-by-step explanation:
Q6.
[tex]\sin\theta=\dfrac{opposite}{hypotenuse}[/tex]
We have
[tex]opposite=14\\\\hypotenuse=18[/tex]
Substitute:
[tex]\sin X=\dfrac{14}{18}=\dfrac{14:2}{18:2}=\dfrac{7}{9}=0.777...\approx0.778[/tex]
Q7.
Use sine.
We have
[tex]opposite=x\\\\hypotenuse=8\\\\\alpha=48^o\\\\\sin48^o\approx0.7431[/tex]
Substitute:
[tex]\dfrac{x}{8}=0.7431[/tex] multiply both sides by 8
[tex]x=5.9448\to x\approx5.9[/tex]
evaluate c÷d÷[-1/6] if c=103
Answer:
-618/d
Step-by-step explanation:
103 divided by d is 103/d and that divided by -1/6 is -618/d